Subgroups — #72282776

Order 2048.

At least 17174 conjugacy classes of subgroups; only the 1044 normal subgroups are shown.

The subgroup lattice has 907 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72282764	C₂	1	1	yes	maximal, characteristic, complemented
2	#72282742	C₂	1	1	yes	maximal, characteristic, complemented
3	#72282718	C₂	1	1	yes	maximal, characteristic, complemented
4	#72282706	C₂	1	1	yes	maximal, characteristic, complemented
5	#72282694	C₂	1	1	yes	maximal, characteristic, complemented
6	#72282677	C₂	1	1	yes	maximal, characteristic, complemented
7	#72282650	C₂	1	1	yes	maximal, characteristic, complemented
8	#72282633	C₂	1	1	yes	maximal, characteristic, complemented
9	#72282617	C₂	1	1	yes	maximal, characteristic, complemented
10	#72282607	C₂	1	1	yes	maximal, characteristic, complemented
11	#72282594	C₂	1	1	yes	maximal, characteristic, complemented
12	#72282577	C₂	1	1	yes	maximal, characteristic, complemented
13	#72282562	C₂	1	1	yes	maximal, characteristic, complemented
14	#72282538	C₂	1	1	yes	maximal, characteristic, complemented
15	#72282522	C₂	1	1	yes	maximal, characteristic, complemented
16	#72282516	C₂	1	1	yes	maximal, characteristic, complemented
17	#72282502	C₂	1	1	yes	maximal, characteristic, complemented
18	#72282488	C₂	1	1	yes	maximal, characteristic, complemented
19	#72282483	C₂	1	1	yes	maximal, characteristic, complemented
20	#72282469	C₂	1	1	yes	maximal, characteristic, complemented
21	#72282408	C₂	1	1	yes	maximal, characteristic, complemented
22	#72282398	C₂	1	1	yes	maximal, characteristic, complemented
23	#72282369	C₂	1	1	yes	maximal, characteristic, complemented
24	#72282351	C₂	1	1	yes	maximal, characteristic, complemented
25	#72281939	C₂	1	1	yes	maximal, characteristic, complemented
26	#72281868	C₂	1	1	yes	maximal, characteristic, complemented
27	#72281825	C₂	1	1	yes	maximal, characteristic, complemented
28	#72281775	C₂	1	1	yes	maximal, characteristic, complemented
29	#72281283	C₂	1	1	yes	maximal, characteristic, complemented
30	#72257443	C₂	1	1	yes	maximal, characteristic, complemented
31	#72249888	C₂	1	1	yes	maximal, characteristic, complemented
32	#10580309	C₂²	1	1	yes	characteristic, complemented
33	#8064148	C₂²	1	1	yes	characteristic
34	#8064118	C₂²	1	1	yes	characteristic
35	#8063888	C₂²	1	1	yes	characteristic
36	#8063858	C₂²	1	1	yes	characteristic
37	#8063148	C₂²	1	1	yes	characteristic
38	#8062966	C₂²	1	1	yes	characteristic
39	#8062936	C₂²	1	1	yes	characteristic
40	#8062881	C₂²	1	1	yes	characteristic
41	#7702254	C₂²	1	1	yes	characteristic
42	#7666983	C₂²	1	1	yes	characteristic
43	#7665869	C₂²	1	1	yes	characteristic
44	#7636738	C₂²	1	1	yes	characteristic
45	#7636737	C₂²	1	1	yes	characteristic
46	D₄×#525	C₂²	1	1	yes	characteristic
47	C₄×#3529	C₂²	1	1	yes	characteristic
48	#6454043	C₂²	1	1	yes	characteristic, complemented
49	#6454043	C₂²	1	1	yes	characteristic, complemented
50	#6453831	C₂²	1	1	yes	characteristic, complemented
51	#6347334	C₂²	1	1	yes	characteristic, complemented
52	#6346643	C₂²	1	1	yes	characteristic, complemented
53	#6346643	C₂²	1	1	yes	characteristic, complemented
54	#512013	C₂²	1	1	yes	characteristic, complemented
55	#512012	C₂²	1	1	yes	characteristic, complemented
56	#512012	C₂²	1	1	yes	characteristic, complemented
57	#512011	C₂²	1	1	yes	characteristic, complemented
58	#511913	C₂²	1	1	yes	characteristic, complemented
59	#511912	C₂²	1	1	yes	characteristic, complemented
60	#511912	C₂²	1	1	yes	characteristic, complemented
61	#511911	C₂²	1	1	yes	characteristic, complemented
62	#493997	C₂²	1	1	yes	characteristic, complemented
63	#493997	C₂²	1	1	yes	characteristic, complemented
64	#493957	C₂²	1	1	yes	characteristic, complemented
65	#486369	C₂²	1	1	yes	characteristic, complemented
66	#486369	C₂²	1	1	yes	characteristic, complemented
67	#486368	C₂²	1	1	yes	characteristic, complemented
68	#486367	C₂²	1	1	yes	characteristic, complemented
69	#486356	C₂²	1	1	yes	characteristic, complemented
70	#486355	C₂²	1	1	yes	characteristic, complemented
71	#486354	C₂²	1	1	yes	characteristic, complemented
72	#486353	C₂²	1	1	yes	characteristic, complemented
73	#486350	C₂²	1	1	yes	characteristic, complemented
74	#486349	C₂²	1	1	yes	characteristic, complemented
75	#486348	C₂²	1	1	yes	characteristic, complemented
76	#486347	C₂²	1	1	yes	characteristic, complemented
77	#486265	C₂²	1	1	yes	characteristic, complemented
78	#486265	C₂²	1	1	yes	characteristic, complemented
79	#486264	C₂²	1	1	yes	characteristic, complemented
80	#486263	C₂²	1	1	yes	characteristic, complemented
81	#486252	C₂²	1	1	yes	characteristic, complemented
82	#486251	C₂²	1	1	yes	characteristic, complemented
83	#486250	C₂²	1	1	yes	characteristic, complemented
84	#486249	C₂²	1	1	yes	characteristic, complemented
85	#486246	C₂²	1	1	yes	characteristic, complemented
86	#486245	C₂²	1	1	yes	characteristic, complemented
87	#486244	C₂²	1	1	yes	characteristic, complemented
88	#486243	C₂²	1	1	yes	characteristic, complemented
89	#482381	C₂²	1	1	yes	characteristic, complemented
90	#482381	C₂²	1	1	yes	characteristic, complemented
91	#482368	C₂²	1	1	yes	characteristic, complemented
92	#482368	C₂²	1	1	yes	characteristic, complemented
93	#482361	C₂²	1	1	yes	characteristic, complemented
94	#482361	C₂²	1	1	yes	characteristic, complemented
95	#480392	C₂²	1	1	yes	characteristic, complemented
96	#480378	C₂²	1	1	yes	characteristic, complemented
97	#480378	C₂²	1	1	yes	characteristic, complemented
98	#248540	C₂²	1	1	yes	characteristic, complemented
99	#248539	C₂²	1	1	yes	characteristic, complemented
100	#248528	C₂²	1	1	yes	characteristic, complemented
101	#248527	C₂²	1	1	yes	characteristic, complemented
102	#248516	C₂²	1	1	yes	characteristic, complemented
103	#248515	C₂²	1	1	yes	characteristic, complemented
104	#248504	C₂²	1	1	yes	characteristic, complemented
105	#248503	C₂²	1	1	yes	characteristic, complemented
106	#248492	C₂²	1	1	yes	characteristic
107	#248491	C₂²	1	1	yes	characteristic
108	#248480	C₂²	1	1	yes	characteristic, complemented
109	#248479	C₂²	1	1	yes	characteristic, complemented
110	#248468	C₂²	1	1	yes	characteristic, complemented
111	#248467	C₂²	1	1	yes	characteristic, complemented
112	#248456	C₂²	1	1	yes	characteristic, complemented
113	#248455	C₂²	1	1	yes	characteristic, complemented
114	#248060	C₂²	1	1	yes	characteristic, complemented
115	#248059	C₂²	1	1	yes	characteristic, complemented
116	#248036	C₂²	1	1	yes	characteristic, complemented
117	#248035	C₂²	1	1	yes	characteristic, complemented
118	#248000	C₂²	1	1	yes	characteristic, complemented
119	#247999	C₂²	1	1	yes	characteristic, complemented
120	#247976	C₂²	1	1	yes	characteristic, complemented
121	#247975	C₂²	1	1	yes	characteristic, complemented
122	#201393	C₂²	1	1	yes	characteristic, complemented
123	#201393	C₂²	1	1	yes	characteristic, complemented
124	#200531	C₂²	1	1	yes	characteristic, complemented
125	#193894	C₂²	1	1	yes	characteristic, complemented
126	#193894	C₂²	1	1	yes	characteristic, complemented
127	#193836	C₂²	1	1	yes	characteristic, complemented
128	#185759	C₂²	1	1	yes	characteristic, complemented
129	#185645	C₂²	1	1	yes	characteristic, complemented
130	#185645	C₂²	1	1	yes	characteristic, complemented
131	#130775	C₂²	1	1	yes	characteristic, complemented
132	#130775	C₂²	1	1	yes	characteristic, complemented
133	#130774	C₂²	1	1	yes	characteristic, complemented
134	#130774	C₂²	1	1	yes	characteristic, complemented
135	#130773	C₂²	1	1	yes	characteristic, complemented
136	#130773	C₂²	1	1	yes	characteristic, complemented
137	#130772	C₂²	1	1	yes	characteristic, complemented
138	#130772	C₂²	1	1	yes	characteristic, complemented
139	#130747	C₂²	1	1	yes	characteristic, complemented
140	#130747	C₂²	1	1	yes	characteristic, complemented
141	#130746	C₂²	1	1	yes	characteristic, complemented
142	#130746	C₂²	1	1	yes	characteristic, complemented
143	#130745	C₂²	1	1	yes	characteristic, complemented
144	#130745	C₂²	1	1	yes	characteristic, complemented
145	#130744	C₂²	1	1	yes	characteristic, complemented
146	#130744	C₂²	1	1	yes	characteristic, complemented
147	#130743	C₂²	1	1	yes	characteristic, complemented
148	#130743	C₂²	1	1	yes	characteristic, complemented
149	#130742	C₂²	1	1	yes	characteristic, complemented
150	#130742	C₂²	1	1	yes	characteristic, complemented
151	#130741	C₂²	1	1	yes	characteristic
152	#130741	C₂²	1	1	yes	characteristic
153	#130740	C₂²	1	1	yes	characteristic, complemented
154	#130740	C₂²	1	1	yes	characteristic, complemented
155	#130267	C₂²	1	1	yes	characteristic, complemented
156	#130267	C₂²	1	1	yes	characteristic, complemented
157	#130266	C₂²	1	1	yes	characteristic, complemented
158	#130266	C₂²	1	1	yes	characteristic, complemented
159	#130265	C₂²	1	1	yes	characteristic, complemented
160	#130265	C₂²	1	1	yes	characteristic, complemented
161	#130264	C₂²	1	1	yes	characteristic, complemented
162	#130264	C₂²	1	1	yes	characteristic, complemented
163	#130263	C₂²	1	1	yes	characteristic, complemented
164	#130263	C₂²	1	1	yes	characteristic, complemented
165	#130262	C₂²	1	1	yes	characteristic, complemented
166	#130262	C₂²	1	1	yes	characteristic, complemented
167	#130261	C₂²	1	1	yes	characteristic, complemented
168	#130261	C₂²	1	1	yes	characteristic, complemented
169	#130260	C₂²	1	1	yes	characteristic, complemented
170	#130260	C₂²	1	1	yes	characteristic, complemented
171	#130228	C₂²	1	1	yes	characteristic, complemented
172	#130228	C₂²	1	1	yes	characteristic, complemented
173	#130228	C₂²	1	1	yes	characteristic, complemented
174	#130228	C₂²	1	1	yes	characteristic, complemented
175	#130227	C₂²	1	1	yes	characteristic, complemented
176	#130227	C₂²	1	1	yes	characteristic, complemented
177	#130226	C₂²	1	1	yes	characteristic, complemented
178	#130226	C₂²	1	1	yes	characteristic, complemented
179	#129612	C₂²	1	1	yes	characteristic, complemented
180	#129612	C₂²	1	1	yes	characteristic, complemented
181	#129611	C₂²	1	1	yes	characteristic, complemented
182	#129611	C₂²	1	1	yes	characteristic, complemented
183	#129610	C₂²	1	1	yes	characteristic, complemented
184	#129610	C₂²	1	1	yes	characteristic, complemented
185	#129610	C₂²	1	1	yes	characteristic, complemented
186	#129610	C₂²	1	1	yes	characteristic, complemented
187	#62781	C₂³	1	1	yes	characteristic
188	C₂×D₄×#41	D₄	1	1	yes	characteristic, complemented
189	C₂×D₄×#41	C₂³	1	1	yes	characteristic
190	C₂×#3529	D₄	1	1	yes	characteristic
191	C₂²×#532	D₄	1	1	yes	characteristic, complemented
192	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
193	#61695	C₂³	1	1	yes	characteristic
194	#61694	C₂³	1	1	yes	characteristic
195	#61560	C₂³	1	1	yes	characteristic
196	#61559	C₂³	1	1	yes	characteristic
197	#60282	C₂³	1	1	yes	characteristic
198	#59847	D₄	1	2	yes	complemented
199	#59843	C₂³	1	1	yes	characteristic
200	#59843	C₂³	1	1	yes	characteristic
201	#59836	D₄	1	2	yes	complemented
202	#59827	C₂³	1	1	yes	characteristic
203	#59816	C₂³	1	1	yes	characteristic
204	#59803	D₄	1	2	yes	complemented
205	#59660	D₄	1	2	yes	complemented
206	#59628	C₂³	1	1	yes	characteristic
207	#59375	C₂³	1	1	yes	characteristic
208	#59198	C₂³	1	1	yes	characteristic
209	#58997	C₂³	1	1	yes	characteristic
210	#52168	D₄	1	2	yes	complemented
211	#52168	D₄	1	2	yes	complemented
212	#52163	D₄	1	2	yes	complemented
213	#45489	D₄	1	2	yes	complemented
214	#45488	C₂³	1	1	yes	characteristic
215	#45487	C₂³	1	1	yes	characteristic
216	#45479	C₂³	1	1	yes	characteristic
217	#45478	C₂³	1	1	yes	characteristic
218	#45476	D₄	1	2	yes	complemented
219	#39363	D₄	1	1	yes	characteristic, complemented
220	#39363	D₄	1	1	yes	characteristic, complemented
221	#39362	C₂³	1	1	yes	characteristic
222	#39362	C₂³	1	1	yes	characteristic
223	#39361	D₄	1	1	yes	characteristic, complemented
224	#39361	C₂³	1	1	yes	characteristic
225	#39360	D₄	1	1	yes	characteristic, complemented
226	#39360	C₂³	1	1	yes	characteristic
227	#39339	D₄	1	1	yes	characteristic, complemented
228	#39339	C₂³	1	1	yes	characteristic
229	#39338	D₄	1	1	yes	characteristic, complemented
230	#39338	C₂³	1	1	yes	characteristic
231	#39337	D₄	1	1	yes	characteristic, complemented
232	#39337	C₂³	1	1	yes	characteristic
233	#39336	D₄	1	1	yes	characteristic, complemented
234	#39336	C₂³	1	1	yes	characteristic
235	#36652	D₄	1	2	yes	complemented
236	#36644	D₄	1	1	yes	characteristic, complemented
237	#36624	D₄	1	1	yes	characteristic, complemented
238	#36624	D₄	1	1	yes	characteristic, complemented
239	#36103	D₄	1	1	yes	characteristic, complemented
240	#36103	C₂³	1	1	yes	characteristic
241	#36102	D₄	1	1	yes	characteristic, complemented
242	#36102	C₂³	1	1	yes	characteristic
243	D₄×#123	D₄	1	1	yes	characteristic, complemented
244	D₄×#123	C₂³	1	1	yes	characteristic
245	D₄×#120	D₄	1	1	yes	characteristic, complemented
246	D₄×#120	C₂³	1	1	yes	characteristic
247	#34976	D₄	1	2	yes	complemented
248	#34956	D₄	1	2	yes	complemented
249	#34937	D₄	1	1	yes	characteristic, complemented
250	#34937	C₂³	1	1	yes	characteristic
251	#34936	D₄	1	1	yes	characteristic, complemented
252	#34936	D₄	1	1	yes	characteristic, complemented
253	#34935	C₂³	1	1	yes	characteristic
254	#34935	C₂³	1	1	yes	characteristic
255	C₄×#563	D₄	1	1	yes	characteristic
256	C₄×#563	C₂³	1	1	yes	characteristic
257	C₄×H(3,𝔽₄)	D₄	1	1	yes	characteristic
258	C₄×H(3,𝔽₄)	C₂³	1	1	yes	characteristic
259	C₄×#560	D₄	1	1	yes	characteristic
260	C₄×#560	D₄	1	1	yes	characteristic
261	C₄×#560	C₂³	1	1	yes	characteristic
262	C₄×#560	C₂³	1	1	yes	characteristic
263	#34346	D₄	1	1	yes	characteristic
264	#34342	D₄	1	1	yes	characteristic
265	#34342	D₄	1	1	yes	characteristic
266	D₄×#117	D₄	1	1	yes	characteristic, complemented
267	D₄×#117	D₄	1	1	yes	characteristic, complemented
268	C₄×#532	C₂³	1	1	yes	characteristic
269	C₄×#525	C₂³	1	1	yes	characteristic
270	C₄×#525	C₂³	1	1	yes	characteristic
271	C₂×#2293	D₄	1	1	yes	characteristic, complemented
272	#24351	C₂³	1	1	yes	characteristic
273	#24351	C₂³	1	1	yes	characteristic
274	#24350	C₂³	1	1	yes	characteristic
275	#24350	C₂³	1	1	yes	characteristic
276	#24314	C₂³	1	1	yes	characteristic
277	#24312	C₂³	1	1	yes	characteristic
278	#24261	C₂³	1	1	yes	characteristic
279	#24261	C₂³	1	1	yes	characteristic
280	#24260	C₂³	1	1	yes	characteristic
281	#24260	C₂³	1	1	yes	characteristic
282	#24224	C₂³	1	1	yes	characteristic
283	#24222	C₂³	1	1	yes	characteristic
284	#20728	C₂³	1	1	yes	characteristic
285	#20723	C₂³	1	1	yes	characteristic
286	#20723	C₂³	1	1	yes	characteristic
287	#18396	C₂³	1	1	yes	characteristic
288	#18394	C₂³	1	1	yes	characteristic
289	#18389	C₂³	1	1	yes	characteristic
290	#18387	C₂³	1	1	yes	characteristic
291	#18204	C₂³	1	1	yes	characteristic
292	#18204	C₂³	1	1	yes	characteristic
293	#18202	C₂³	1	1	yes	characteristic
294	#18202	C₂³	1	1	yes	characteristic
295	#18196	C₂³	1	1	yes	characteristic
296	#18196	C₂³	1	1	yes	characteristic
297	#18194	C₂³	1	1	yes	characteristic
298	#18194	C₂³	1	1	yes	characteristic
299	#17366	C₂³	1	1	yes	characteristic
300	#17363	C₂³	1	1	yes	characteristic
301	#17363	C₂³	1	1	yes	characteristic
302	#12798	C₂³	1	1	yes	characteristic
303	#12798	C₂³	1	1	yes	characteristic
304	#12797	C₂³	1	1	yes	characteristic
305	#12797	C₂³	1	1	yes	characteristic
306	#12794	C₂³	1	1	yes	characteristic
307	#12794	C₂³	1	1	yes	characteristic
308	#12794	C₂³	1	1	yes	characteristic
309	#12794	C₂³	1	1	yes	characteristic
310	#12793	C₂³	1	1	yes	characteristic
311	#12793	C₂³	1	1	yes	characteristic
312	#12793	C₂³	1	1	yes	characteristic
313	#12793	C₂³	1	1	yes	characteristic
314	#11881	C₂³	1	1	yes	characteristic
315	#11881	C₂³	1	1	yes	characteristic
316	#11881	C₂³	1	1	yes	characteristic
317	#11881	C₂³	1	1	yes	characteristic
318	#11880	C₂³	1	1	yes	characteristic
319	#11880	C₂³	1	1	yes	characteristic
320	#11880	C₂³	1	1	yes	characteristic
321	#11880	C₂³	1	1	yes	characteristic
322	#11878	C₂³	1	1	yes	characteristic
323	#11878	C₂³	1	1	yes	characteristic
324	#11878	C₂³	1	1	yes	characteristic
325	#11878	C₂³	1	1	yes	characteristic
326	#11877	C₂³	1	1	yes	characteristic
327	#11877	C₂³	1	1	yes	characteristic
328	#11877	C₂³	1	1	yes	characteristic
329	#11877	C₂³	1	1	yes	characteristic
330	#11874	C₂³	1	1	yes	characteristic
331	#11874	C₂³	1	1	yes	characteristic
332	#11874	C₂³	1	1	yes	characteristic
333	#11874	C₂³	1	1	yes	characteristic
334	#11873	C₂³	1	1	yes	characteristic
335	#11873	C₂³	1	1	yes	characteristic
336	#11873	C₂³	1	1	yes	characteristic
337	#11873	C₂³	1	1	yes	characteristic
338	#11477	C₂³	1	1	yes	characteristic
339	#11477	C₂³	1	1	yes	characteristic
340	#11475	C₂³	1	1	yes	characteristic
341	#11475	C₂³	1	1	yes	characteristic
342	#11472	C₂³	1	1	yes	characteristic
343	#11472	C₂³	1	1	yes	characteristic
344	#11472	C₂³	1	1	yes	characteristic
345	#11472	C₂³	1	1	yes	characteristic
346	#11471	C₂³	1	1	yes	characteristic
347	#11471	C₂³	1	1	yes	characteristic
348	#11471	C₂³	1	1	yes	characteristic
349	#11471	C₂³	1	1	yes	characteristic
350	#9470	C₂³	1	1	yes	characteristic
351	#9470	C₂³	1	1	yes	characteristic
352	#9470	C₂³	1	1	yes	characteristic
353	#9470	C₂³	1	1	yes	characteristic
354	#9468	C₂³	1	1	yes	characteristic
355	#9468	C₂³	1	1	yes	characteristic
356	#9468	C₂³	1	1	yes	characteristic
357	#9468	C₂³	1	1	yes	characteristic
358	#9397	C₂³	1	1	yes	characteristic
359	#9397	C₂³	1	1	yes	characteristic
360	#9393	C₂³	1	1	yes	characteristic
361	#9393	C₂³	1	1	yes	characteristic
362	#8966	C₂³	1	1	yes	characteristic
363	#8966	C₂³	1	1	yes	characteristic
364	#8966	C₂³	1	1	yes	characteristic
365	#8966	C₂³	1	1	yes	characteristic
366	#8965	C₂³	1	1	yes	characteristic
367	#8965	C₂³	1	1	yes	characteristic
368	#8965	C₂³	1	1	yes	characteristic
369	#8965	C₂³	1	1	yes	characteristic
370	#8959	C₂³	1	1	yes	characteristic
371	#8959	C₂³	1	1	yes	characteristic
372	#8957	C₂³	1	1	yes	characteristic
373	#8957	C₂³	1	1	yes	characteristic
374	#8387	C₂³	1	1	yes	characteristic
375	#8387	C₂³	1	1	yes	characteristic
376	#8383	C₂³	1	1	yes	characteristic
377	#8383	C₂³	1	1	yes	characteristic
378	#8376	C₂³	1	1	yes	characteristic
379	#8376	C₂³	1	1	yes	characteristic
380	#8376	C₂³	1	1	yes	characteristic
381	#8376	C₂³	1	1	yes	characteristic
382	#8375	C₂³	1	1	yes	characteristic
383	#8375	C₂³	1	1	yes	characteristic
384	#8375	C₂³	1	1	yes	characteristic
385	#8375	C₂³	1	1	yes	characteristic
386	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
387	C₂×#563	C₂×D₄	1	1	yes	characteristic
388	C₂×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
389	C₂×#560	C₂×D₄	1	1	yes	characteristic
390	C₂×#560	C₂×D₄	1	1	yes	characteristic
391	#3501	C₂⁴	1	1	yes	characteristic
392	#3496	C₂⁴	1	1	yes	characteristic
393	C₂×#550	C₂×D₄	1	1	yes	characteristic
394	C₂×#550	C₂×D₄	1	1	yes	characteristic
395	C₂×D₄×Q₈	C₂×D₄	1	1	yes	characteristic
396	C₂×D₄×Q₈	C₂×D₄	1	1	yes	characteristic
397	C₂×#547	C₂×D₄	1	1	yes	characteristic
398	C₂×#547	C₂×D₄	1	1	yes	characteristic
399	C₂×#547	C₂×D₄	1	1	yes	characteristic
400	C₂×#547	C₂⁴	1	1	yes	characteristic
401	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
402	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
403	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
404	C₂×D₄²	C₂⁴	1	1	yes	characteristic
405	C₂×#532	C₂×D₄	1	1	yes	characteristic
406	C₂×#532	C₂×D₄	1	1	yes	characteristic
407	C₂×#532	C₂×D₄	1	1	yes	characteristic
408	C₂×#532	C₂×D₄	1	1	yes	characteristic
409	C₂×#532	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
411	C₂²×#127	C₂×D₄	1	1	yes	characteristic
412	C₂×#525	C₂×D₄	1	1	yes	characteristic
413	C₂×#525	C₂×D₄	1	1	yes	characteristic
414	C₂²×#121	C₂×D₄	1	1	yes	characteristic
415	C₂²×#121	C₂×D₄	1	1	yes	characteristic
416	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
417	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
419	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
420	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
422	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
423	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
424	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
425	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
426	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
427	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
428	#2972	C₂⁴	1	1	yes	characteristic
429	#2972	C₂⁴	1	1	yes	characteristic
430	#2868	C₂×D₄	1	1	yes	characteristic
431	#2867	C₂×D₄	1	1	yes	characteristic
432	#2858	C₂×D₄	1	1	yes	characteristic
433	#2858	C₂×D₄	1	1	yes	characteristic
434	#2854	C₂×D₄	1	1	yes	characteristic
435	#2854	C₂×D₄	1	1	yes	characteristic
436	#2854	C₂×D₄	1	1	yes	characteristic
437	#2854	C₂×D₄	1	1	yes	characteristic
438	#2847	C₂×D₄	1	1	yes	characteristic
439	#2847	C₂×D₄	1	1	yes	characteristic
440	#2847	C₂×D₄	1	1	yes	characteristic
441	#2847	C₂×D₄	1	1	yes	characteristic
442	#2817	C₂×D₄	1	2	yes	—
443	#2815	C₂×D₄	1	2	yes	—
444	#2812	C₂×D₄	1	2	yes	—
445	#2812	C₂×D₄	1	2	yes	—
446	#2728	C₂×D₄	1	2	yes	—
447	#2728	C₂×D₄	1	2	yes	—
448	#2724	C₂×D₄	1	2	yes	—
449	#2722	C₂×D₄	1	2	yes	—
450	#2722	C₂×D₄	1	2	yes	—
451	#2712	C₂×D₄	1	2	yes	—
452	#2712	C₂×D₄	1	2	yes	—
453	#2693	C₂×D₄	1	2	yes	—
454	#2693	C₂×D₄	1	2	yes	—
455	#2679	C₂×D₄	1	2	yes	—
456	#2675	C₂×D₄	1	2	yes	—
457	#2675	C₂×D₄	1	2	yes	—
458	#2609	C₂×D₄	1	2	yes	—
459	#2609	C₂×D₄	1	2	yes	—
460	#2600	C₂×D₄	1	2	yes	—
461	#2600	C₂×D₄	1	2	yes	—
462	#2582	C₂×D₄	1	2	yes	—
463	#2548	C₂×D₄	1	1	yes	characteristic
464	#2548	C₂×D₄	1	1	yes	characteristic
465	#2547	C₂×D₄	1	1	yes	characteristic
466	#2547	C₂⁴	1	1	yes	characteristic
467	#2546	C₂×D₄	1	1	yes	characteristic
468	#2546	C₂×D₄	1	1	yes	characteristic
469	#2543	C₂×D₄	1	2	yes	—
470	#2543	C₂×D₄	1	2	yes	—
471	#2541	C₂×D₄	1	1	yes	characteristic
472	#2541	C₂⁴	1	1	yes	characteristic
473	#2537	C₂×D₄	1	2	yes	—
474	#2536	C₂×D₄	1	2	yes	—
475	#2536	C₂×D₄	1	2	yes	—
476	#2535	C₂×D₄	1	2	yes	—
477	#2535	C₂×D₄	1	2	yes	—
478	#2501	C₂×D₄	1	1	yes	characteristic
479	#2501	C₂×D₄	1	1	yes	characteristic
480	#2501	C₂×D₄	1	1	yes	characteristic
481	#2501	C₂×D₄	1	1	yes	characteristic
482	#2486	C₂×D₄	1	1	yes	characteristic
483	#2486	C₂×D₄	1	1	yes	characteristic
484	#2486	C₂⁴	1	1	yes	characteristic
485	#2486	C₂⁴	1	1	yes	characteristic
486	#2483	C₂×D₄	1	2	yes	—
487	#2433	C₂×D₄	1	1	yes	characteristic
488	#2433	C₂×D₄	1	1	yes	characteristic
489	#2433	C₂×D₄	1	1	yes	characteristic
490	#2433	C₂×D₄	1	1	yes	characteristic
491	#2408	C₂×D₄	1	1	yes	characteristic
492	#2408	C₂×D₄	1	1	yes	characteristic
493	#2408	C₂⁴	1	1	yes	characteristic
494	#2408	C₂⁴	1	1	yes	characteristic
495	#2403	C₂×D₄	1	2	yes	—
496	#2392	C₂×D₄	1	2	yes	—
497	#2392	C₂×D₄	1	2	yes	—
498	#2392	C₂×D₄	1	2	yes	—
499	#2392	C₂×D₄	1	2	yes	—
500	#2392	C₂×D₄	1	2	yes	—
501	#2392	C₂×D₄	1	2	yes	—
502	#2380	C₂×D₄	1	1	yes	characteristic
503	#2380	C₂×D₄	1	1	yes	characteristic
504	#2379	C₂×D₄	1	1	yes	characteristic
505	#2379	C₂×D₄	1	1	yes	characteristic
506	#2376	C₂×D₄	1	1	yes	characteristic
507	#2376	C₂×D₄	1	1	yes	characteristic
508	#2376	C₂×D₄	1	1	yes	characteristic
509	#2376	C₂×D₄	1	1	yes	characteristic
510	#2375	C₂×D₄	1	1	yes	characteristic
511	#2375	C₂×D₄	1	1	yes	characteristic
512	#2375	C₂×D₄	1	1	yes	characteristic
513	#2375	C₂×D₄	1	1	yes	characteristic
514	#2344	C₂×D₄	1	1	yes	characteristic
515	#2344	C₂×D₄	1	1	yes	characteristic
516	#2344	C₂×D₄	1	1	yes	characteristic
517	#2344	C₂×D₄	1	1	yes	characteristic
518	D₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
519	D₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
520	D₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
521	D₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
522	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
523	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
524	C₄×#127	C₂×D₄	1	1	yes	characteristic
525	C₄×#127	C₂⁴	1	1	yes	characteristic
526	C₄×#124	C₂×D₄	1	1	yes	characteristic
527	C₄×#124	C₂×D₄	1	1	yes	characteristic
528	C₄×#124	C₂×D₄	1	1	yes	characteristic
529	C₄×#124	C₂⁴	1	1	yes	characteristic
530	C₄×#123	C₂×D₄	1	1	yes	characteristic
531	C₄×#123	C₂×D₄	1	1	yes	characteristic
532	C₄×#123	C₂×D₄	1	1	yes	characteristic
533	C₄×#123	C₂×D₄	1	1	yes	characteristic
534	C₄×#123	C₂×D₄	1	1	yes	characteristic
535	C₄×#123	C₂×D₄	1	1	yes	characteristic
536	C₄×#123	C₂⁴	1	1	yes	characteristic
537	C₄×#123	C₂⁴	1	1	yes	characteristic
538	C₄×#120	C₂×D₄	1	1	yes	characteristic
539	C₄×#120	C₂×D₄	1	1	yes	characteristic
540	C₄×#120	C₂×D₄	1	1	yes	characteristic
541	C₄×#120	C₂×D₄	1	1	yes	characteristic
542	C₄×#120	C₂×D₄	1	1	yes	characteristic
543	C₄×#120	C₂×D₄	1	1	yes	characteristic
544	C₄×#120	C₂⁴	1	1	yes	characteristic
545	C₄×#120	C₂⁴	1	1	yes	characteristic
546	#2297	C₂×D₄	1	1	yes	characteristic
547	#2297	C₂×D₄	1	1	yes	characteristic
548	#2297	C₂×D₄	1	1	yes	characteristic
549	#2297	C₂×D₄	1	1	yes	characteristic
550	#2296	C₂×D₄	1	1	yes	characteristic
551	#2296	C₂×D₄	1	1	yes	characteristic
552	#2293	C₂×D₄	1	1	yes	characteristic
553	#2293	C₂×D₄	1	1	yes	characteristic
554	#2293	C₂×D₄	1	1	yes	characteristic
555	#2293	C₂×D₄	1	1	yes	characteristic
556	#2285	C₂×D₄	1	1	yes	characteristic
557	#2285	C₂×D₄	1	1	yes	characteristic
558	#2285	C₂×D₄	1	1	yes	characteristic
559	#2280	C₂×D₄	1	1	yes	characteristic
560	#2280	C₂×D₄	1	1	yes	characteristic
561	C₄×#117	C₂×D₄	1	1	yes	characteristic
562	C₄×#117	C₂×D₄	1	1	yes	characteristic
563	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
564	C₂×C₄³	C₂×D₄	1	1	yes	characteristic
565	#1800	C₂⁴	1	1	yes	characteristic
566	#1800	C₂⁴	1	1	yes	characteristic
567	#1799	C₂⁴	1	1	yes	characteristic
568	#1799	C₂⁴	1	1	yes	characteristic
569	#1799	C₂⁴	1	1	yes	characteristic
570	#1799	C₂⁴	1	1	yes	characteristic
571	#1460	C₂⁴	1	1	yes	characteristic
572	#1460	C₂⁴	1	1	yes	characteristic
573	#1459	C₂⁴	1	1	yes	characteristic
574	#1459	C₂⁴	1	1	yes	characteristic
575	#1459	C₂⁴	1	1	yes	characteristic
576	#1459	C₂⁴	1	1	yes	characteristic
577	C₂²×#41	#120	1	1	yes	characteristic
578	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
579	C₂³×D₄	#120	1	1	yes	characteristic
580	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
581	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
582	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
583	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
584	C₂⁴×C₄	#120	1	1	yes	characteristic
585	C₂⁴×C₄	#120	1	1	yes	characteristic
586	C₂⁴×C₄	#120	1	1	yes	characteristic
587	C₂⁴×C₄	#120	1	1	yes	characteristic
588	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
589	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
590	#563	AGL(1,ℤ/8)	1	4	yes	complemented
591	H(3,𝔽₄)	AGL(1,ℤ/8)	1	4	yes	complemented
592	#560	AGL(1,ℤ/8)	1	4	yes	complemented
593	#560	AGL(1,ℤ/8)	1	4	yes	complemented
594	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
595	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
596	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
597	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
598	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
599	C₂×#127	#120	1	1	yes	characteristic
600	C₂×#127	#120	1	1	yes	characteristic
601	C₂×#127	C₂²×D₄	1	1	yes	characteristic
602	C₂×#127	C₂²×D₄	1	1	yes	characteristic
603	C₂×#127	C₂²×D₄	1	1	yes	characteristic
604	C₂×#124	#120	1	1	yes	characteristic
605	C₂×#124	C₂²×D₄	1	1	yes	characteristic
606	C₂×#123	#120	1	1	yes	characteristic
607	C₂×#123	#120	1	1	yes	characteristic
608	C₂×#123	C₂²×D₄	1	1	yes	characteristic
609	C₂×#123	C₂²×D₄	1	1	yes	characteristic
610	C₂×#121	#120	1	1	yes	characteristic
611	C₂×#121	#120	1	1	yes	characteristic
612	C₂×#121	#120	1	2	yes	—
613	C₂×#121	C₂²×D₄	1	1	yes	characteristic
614	C₂×#121	C₂²×D₄	1	1	yes	characteristic
615	C₂×#121	C₂²×D₄	1	1	yes	characteristic
616	C₂×#121	C₂²×D₄	1	1	yes	characteristic
617	C₂×#120	#120	1	1	yes	characteristic
618	C₂×#120	#120	1	1	yes	characteristic
619	C₂×#120	C₂²×D₄	1	1	yes	characteristic
620	C₂×#120	C₂²×D₄	1	1	yes	characteristic
621	C₂×C₄×Q₈	#120	1	1	yes	characteristic
622	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
623	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
624	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
625	C₂×C₄×D₄	#120	1	1	yes	characteristic
626	C₂×C₄×D₄	#120	1	1	yes	characteristic
627	C₂×C₄×D₄	#120	1	1	yes	characteristic
628	C₂×C₄×D₄	#120	1	1	yes	characteristic
629	C₂×C₄×D₄	#120	1	2	yes	—
630	C₂×C₄×D₄	#120	1	1	yes	characteristic
631	C₂×C₄×D₄	#120	1	2	yes	—
632	C₂×C₄×D₄	#120	1	2	yes	—
633	C₂×C₄×D₄	#120	1	2	yes	—
634	C₂×C₄×D₄	#120	1	2	yes	—
635	C₂×C₄×D₄	#120	1	1	yes	characteristic
636	C₂×C₄×D₄	#120	1	1	yes	characteristic
637	C₂×C₄×D₄	#120	1	1	yes	characteristic
638	C₂×C₄×D₄	#120	1	1	yes	characteristic
639	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
640	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
641	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
642	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
643	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
648	C₂×#117	#120	1	1	yes	characteristic
649	C₂×#117	#120	1	1	yes	characteristic
650	C₂×#117	#120	1	1	yes	characteristic
651	C₂×#117	#120	1	1	yes	characteristic
652	C₂×#117	#120	1	1	yes	characteristic
653	C₂×#117	C₂²×D₄	1	1	yes	characteristic
654	C₂×#117	C₂²×D₄	1	1	yes	characteristic
655	C₂×#117	C₂²×D₄	1	1	yes	characteristic
656	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
657	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
658	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
659	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
660	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
661	C₂²×C₄²	#120	1	1	yes	characteristic
662	C₂²×C₄²	#120	1	1	yes	characteristic
663	C₂²×C₄²	#120	1	1	yes	characteristic
664	C₂²×C₄²	#120	1	1	yes	characteristic
665	C₂²×C₄²	#120	1	1	yes	characteristic
666	C₂²×C₄²	#120	1	1	yes	characteristic
667	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
668	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
669	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
670	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
671	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
672	#398	#120	1	2	yes	—
673	#398	#120	1	2	yes	—
674	#398	#120	1	2	yes	—
675	#398	#120	1	2	yes	—
676	#398	C₂²×D₄	1	2	yes	—
677	#398	C₂²×D₄	1	2	yes	—
678	#397	#120	1	2	yes	—
679	#397	#120	1	2	yes	—
680	#397	C₂²×D₄	1	2	yes	—
681	#397	C₂²×D₄	1	2	yes	—
682	#397	C₂²×D₄	1	2	yes	—
683	#397	C₂²×D₄	1	2	yes	—
684	#394	#120	1	2	yes	—
685	#394	#120	1	2	yes	—
686	#394	#120	1	2	yes	—
687	#394	#120	1	2	yes	—
688	#394	C₂²×D₄	1	2	yes	—
689	#394	C₂²×D₄	1	2	yes	—
690	#392	#120	1	2	yes	—
691	#392	#120	1	2	yes	—
692	#392	C₂²×D₄	1	2	yes	—
693	#392	C₂²×D₄	1	2	yes	—
694	#392	C₂²×D₄	1	2	yes	—
695	#392	C₂²×D₄	1	2	yes	—
696	#391	#120	1	1	yes	characteristic
697	#391	#120	1	1	yes	characteristic
698	#391	#120	1	1	yes	characteristic
699	#391	C₂²×D₄	1	1	yes	characteristic
700	#390	#120	1	1	yes	characteristic
701	#390	C₂²×D₄	1	1	yes	characteristic
702	#390	C₂²×D₄	1	1	yes	characteristic
703	#390	C₂²×D₄	1	1	yes	characteristic
704	#386	#120	1	1	yes	characteristic
705	#386	#120	1	1	yes	characteristic
706	#386	#120	1	1	yes	characteristic
707	#386	#120	1	1	yes	characteristic
708	#386	C₂²×D₄	1	1	yes	characteristic
709	#386	C₂²×D₄	1	1	yes	characteristic
710	#386	C₂²×D₄	1	1	yes	characteristic
711	#386	C₂²×D₄	1	1	yes	characteristic
712	#385	#120	1	1	yes	characteristic
713	#385	#120	1	1	yes	characteristic
714	#385	#120	1	1	yes	characteristic
715	#385	#120	1	1	yes	characteristic
716	#385	C₂²×D₄	1	1	yes	characteristic
717	#385	C₂²×D₄	1	1	yes	characteristic
718	#385	C₂²×D₄	1	1	yes	characteristic
719	#385	C₂²×D₄	1	1	yes	characteristic
720	#384	#120	1	1	yes	characteristic
721	#384	C₂²×D₄	1	1	yes	characteristic
722	#382	#120	1	1	yes	characteristic
723	#382	#120	1	2	yes	—
724	#382	#120	1	2	yes	—
725	#382	C₂²×D₄	1	1	yes	characteristic
726	#381	#120	1	1	yes	characteristic
727	#381	#120	1	1	yes	characteristic
728	#381	C₂²×D₄	1	1	yes	characteristic
729	#381	C₂²×D₄	1	1	yes	characteristic
730	#380	C₂²×D₄	1	1	yes	characteristic
731	#380	C₂²×D₄	1	1	yes	characteristic
732	#380	C₂²×D₄	1	1	yes	characteristic
733	#380	C₂²×D₄	1	1	yes	characteristic
734	#379	#120	1	1	yes	characteristic
735	#379	#120	1	1	yes	characteristic
736	#379	C₂²×D₄	1	1	yes	characteristic
737	#379	C₂²×D₄	1	1	yes	characteristic
738	C₄×C₄⋊C₄	#120	1	2	yes	—
739	C₄×C₄⋊C₄	#120	1	2	yes	—
740	C₄×C₄⋊C₄	#120	1	2	yes	—
741	C₄×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
742	C₄×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
743	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
744	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
745	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
746	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
747	C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
748	C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
749	C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
750	C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
751	C₂×#95	#120	1	2	yes	—
752	C₄³	#120	1	1	yes	characteristic
753	C₄³	#120	1	1	yes	characteristic
754	C₄³	C₂²×D₄	1	1	yes	characteristic
755	C₄³	C₂²×D₄	1	1	yes	characteristic
756	C₂⁵	C₂×#120	1	1	yes	characteristic
757	C₂⁵	C₂×#120	1	1	yes	characteristic
758	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
759	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
760	C₂²×D₄	C₂×#120	1	1	yes	characteristic
761	C₂²×D₄	C₂×#120	1	1	yes	characteristic
762	C₂²×D₄	C₂×#120	1	1	yes	characteristic
763	C₂²×D₄	C₂×#120	1	1	yes	characteristic
764	C₂²×D₄	C₂×#120	1	1	yes	characteristic
765	C₂²×D₄	C₂×#120	1	1	yes	characteristic
766	C₂²×D₄	C₂×#120	1	1	yes	characteristic
767	C₂²×D₄	C₂×#120	1	2	yes	—
768	C₂²×D₄	C₂×#120	1	2	yes	—
769	C₂²×D₄	C₂×#120	1	2	yes	—
770	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
771	C₂³×C₄	C₂×#120	1	1	yes	characteristic
772	C₂³×C₄	C₂×#120	1	1	yes	characteristic
773	C₂³×C₄	C₂×#120	1	1	yes	characteristic
774	C₂³×C₄	C₂×#120	1	1	yes	characteristic
775	C₂³×C₄	C₂×#120	1	1	yes	characteristic
776	C₂³×C₄	C₂×#120	1	1	yes	characteristic
777	C₂³×C₄	C₂×#120	1	1	yes	characteristic
778	C₂³×C₄	C₂×#120	1	1	yes	characteristic
779	C₂³×C₄	C₂×#120	1	1	yes	characteristic
780	C₂³×C₄	C₂×#120	1	1	yes	characteristic
781	C₂³×C₄	C₂×#120	1	1	yes	characteristic
782	C₂³×C₄	C₂×#120	1	1	yes	characteristic
783	C₂³×C₄	C₂×#120	1	1	yes	characteristic
784	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
785	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
786	#127	C₂×AGL(1,ℤ/8)	1	2	yes	—
787	#127	C₂×AGL(1,ℤ/8)	1	2	yes	—
788	#124	C₂×AGL(1,ℤ/8)	1	2	yes	—
789	#124	C₂×AGL(1,ℤ/8)	1	2	yes	—
790	#123	C₂×AGL(1,ℤ/8)	1	2	yes	—
791	#123	C₂×AGL(1,ℤ/8)	1	2	yes	—
792	#123	C₂×AGL(1,ℤ/8)	1	2	yes	—
793	#123	C₂×AGL(1,ℤ/8)	1	2	yes	—
794	#120	C₂×AGL(1,ℤ/8)	1	2	yes	—
795	#120	C₂×AGL(1,ℤ/8)	1	2	yes	—
796	#120	C₂×AGL(1,ℤ/8)	1	2	yes	—
797	#120	C₂×AGL(1,ℤ/8)	1	2	yes	—
798	C₄×D₄	B(4,𝔽₂)	1	2	yes	—
799	C₄×D₄	B(4,𝔽₂)	1	2	yes	—
800	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
803	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
804	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
805	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
806	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
807	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
808	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
809	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
810	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
811	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
812	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
813	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
815	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
819	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
820	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
821	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
822	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
823	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
824	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
825	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
826	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
827	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
828	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
829	C₂×C₄²	C₂×#120	1	1	yes	characteristic
830	C₂×C₄²	C₂×#120	1	1	yes	characteristic
831	C₂×C₄²	C₂×#120	1	1	yes	characteristic
832	C₂×C₄²	C₂×#120	1	1	yes	characteristic
833	C₂×C₄²	C₂×#120	1	1	yes	characteristic
834	C₂×C₄²	C₂×#120	1	1	yes	characteristic
835	C₂×C₄²	C₂×#120	1	1	yes	characteristic
836	C₂×C₄²	C₂×#120	1	1	yes	characteristic
837	C₂×C₄²	C₂×#120	1	1	yes	characteristic
838	C₂×C₄²	C₂×#120	1	1	yes	characteristic
839	C₂×C₄²	C₂×#120	1	1	yes	characteristic
840	C₂×C₄²	C₂×#120	1	1	yes	characteristic
841	C₂×C₄²	C₂×#120	1	1	yes	characteristic
842	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
843	#95	C₂×#120	1	2	yes	—
844	#95	C₂×#120	1	2	yes	—
845	#95	C₂×#120	1	2	yes	—
846	#95	C₂×#120	1	2	yes	—
847	#95	C₂×#120	1	2	yes	—
848	#95	C₂×#120	1	2	yes	—
849	C₂⁴	#2846	1	1	yes	characteristic
850	C₂⁴	#3003	1	2	yes	—
851	C₂⁴	#3003	1	2	yes	—
852	C₂⁴	C₂²×#120	1	1	yes	characteristic
853	C₂⁴	C₂²×#120	1	1	yes	characteristic
854	C₂×Q₈	#3003	1	2	yes	—
855	C₂×D₄	#3003	1	2	yes	—
856	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
857	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
858	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
859	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
860	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
861	C₂²×C₄	#2846	1	1	yes	characteristic
862	C₂²×C₄	#2846	1	1	yes	characteristic
863	C₂²×C₄	#2846	1	1	yes	characteristic
864	C₂²×C₄	#2846	1	1	yes	characteristic
865	C₂²×C₄	#2846	1	1	yes	characteristic
866	C₂²×C₄	#2846	1	1	yes	characteristic
867	C₂²×C₄	#2846	1	1	yes	characteristic
868	C₂²×C₄	#3003	1	2	yes	—
869	C₂²×C₄	#3003	1	2	yes	—
870	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
871	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
872	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
873	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
874	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
875	C₄⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
876	C₂²⋊C₄	#3003	1	2	yes	—
877	C₂²⋊C₄	#3003	1	2	yes	—
878	C₂²⋊C₄	#3003	1	2	yes	—
879	C₂²⋊C₄	#3003	1	2	yes	—
880	C₄²	#3003	1	2	yes	—
881	C₄²	#3003	1	2	yes	—
882	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
883	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
884	C₄²	#3026	1	1	yes	characteristic
885	C₄²	#3026	1	1	yes	characteristic
886	C₂³	C₂×#2846	1	1	yes	characteristic
887	C₂³	C₂×#3003	1	1	yes	characteristic
888	C₂³	C₂×#3003	1	1	yes	characteristic
889	C₂³	C₂×#3003	1	1	yes	characteristic
890	C₂³	C₂×#3003	1	1	yes	characteristic
891	C₂×C₄	#32898	1	1	yes	characteristic
892	C₂×C₄	#32898	1	1	yes	characteristic
893	C₂×C₄	#32898	1	1	yes	characteristic
894	C₂×C₄	#32898	1	1	yes	characteristic
895	C₂×C₄	C₂×#3003	1	1	yes	characteristic
896	C₂×C₄	C₂×#3003	1	1	yes	characteristic
897	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
898	C₂×C₄	C₂×#3026	1	1	yes	characteristic
899	C₂²	#6628842	1	1	yes	characteristic
900	C₂²	#6628883	1	1	yes	characteristic
901	C₂²	C₂×#32898	1	1	yes	characteristic
902	C₄	#7622868	1	2	yes	—
903	C₂	#72226680	1	1	yes	characteristic
904	C₂	#72260417	1	1	yes	characteristic
905	C₂	#72281572	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂×C₄×D₄	C₂⁵
LCS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×D₄×#41 ◁ G
LECS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #72282764	C₂	semidirect
2. #72282742	C₂	semidirect
3. #72282718	C₂	semidirect
4. #72282706	C₂	semidirect
5. #72282694	C₂	semidirect
6. #72282677	C₂	semidirect
7. #72282650	C₂	semidirect
8. #72282633	C₂	semidirect
9. #72282617	C₂	semidirect
10. #72282607	C₂	semidirect
11. #72282594	C₂	semidirect
12. #72282577	C₂	semidirect
13. #72282562	C₂	semidirect
14. #72282538	C₂	semidirect
15. #72282522	C₂	semidirect
16. #72282516	C₂	semidirect
17. #72282502	C₂	semidirect
18. #72282488	C₂	semidirect
19. #72282483	C₂	semidirect
20. #72282469	C₂	semidirect
21. #72282408	C₂	semidirect
22. #72282398	C₂	semidirect
23. #72282369	C₂	semidirect
24. #72282351	C₂	semidirect
25. #72281939	C₂	semidirect
26. #72281868	C₂	semidirect
27. #72281825	C₂	semidirect
28. #72281775	C₂	semidirect
29. #72281283	C₂	semidirect
30. #72257443	C₂	semidirect
31. #72249888	C₂	semidirect
32. #10580309	C₂²	semidirect
48. #6454043	C₂²	semidirect
49. #6454043	C₂²	semidirect
50. #6453831	C₂²	semidirect
51. #6347334	C₂²	semidirect
52. #6346643	C₂²	semidirect
53. #6346643	C₂²	semidirect
54. #512013	C₂²	semidirect
55. #512012	C₂²	semidirect
56. #512012	C₂²	semidirect
57. #512011	C₂²	semidirect
58. #511913	C₂²	semidirect
59. #511912	C₂²	semidirect
60. #511912	C₂²	semidirect
61. #511911	C₂²	semidirect
62. #493997	C₂²	semidirect
63. #493997	C₂²	semidirect
64. #493957	C₂²	semidirect
65. #486369	C₂²	semidirect
66. #486369	C₂²	semidirect
67. #486368	C₂²	semidirect
68. #486367	C₂²	semidirect
69. #486356	C₂²	semidirect
70. #486355	C₂²	semidirect
71. #486354	C₂²	semidirect
72. #486353	C₂²	semidirect
73. #486350	C₂²	semidirect
74. #486349	C₂²	semidirect
75. #486348	C₂²	semidirect
76. #486347	C₂²	semidirect
77. #486265	C₂²	semidirect
78. #486265	C₂²	semidirect
79. #486264	C₂²	semidirect
80. #486263	C₂²	semidirect
81. #486252	C₂²	semidirect
82. #486251	C₂²	semidirect
83. #486250	C₂²	semidirect
84. #486249	C₂²	semidirect
85. #486246	C₂²	semidirect
86. #486245	C₂²	semidirect
87. #486244	C₂²	semidirect
88. #486243	C₂²	semidirect
89. #482381	C₂²	semidirect
90. #482381	C₂²	semidirect
91. #482368	C₂²	semidirect
92. #482368	C₂²	semidirect
93. #482361	C₂²	semidirect
94. #482361	C₂²	semidirect
95. #480392	C₂²	semidirect
96. #480378	C₂²	semidirect
97. #480378	C₂²	semidirect
98. #248540	C₂²	semidirect
99. #248539	C₂²	semidirect
100. #248528	C₂²	semidirect
101. #248527	C₂²	semidirect
102. #248516	C₂²	semidirect
103. #248515	C₂²	semidirect
104. #248504	C₂²	semidirect
105. #248503	C₂²	semidirect
108. #248480	C₂²	semidirect
109. #248479	C₂²	semidirect
110. #248468	C₂²	semidirect
111. #248467	C₂²	semidirect
112. #248456	C₂²	semidirect
113. #248455	C₂²	semidirect
114. #248060	C₂²	semidirect
115. #248059	C₂²	semidirect
116. #248036	C₂²	semidirect
117. #248035	C₂²	semidirect
118. #248000	C₂²	semidirect
119. #247999	C₂²	semidirect
120. #247976	C₂²	semidirect
121. #247975	C₂²	semidirect
122. #201393	C₂²	semidirect
123. #201393	C₂²	semidirect
124. #200531	C₂²	semidirect
125. #193894	C₂²	semidirect
126. #193894	C₂²	semidirect
127. #193836	C₂²	semidirect
128. #185759	C₂²	semidirect
129. #185645	C₂²	semidirect
130. #185645	C₂²	semidirect
131. #130775	C₂²	semidirect
132. #130775	C₂²	semidirect
133. #130774	C₂²	semidirect
134. #130774	C₂²	semidirect
135. #130773	C₂²	semidirect
136. #130773	C₂²	semidirect
137. #130772	C₂²	semidirect
138. #130772	C₂²	semidirect
139. #130747	C₂²	semidirect
140. #130747	C₂²	semidirect
141. #130746	C₂²	semidirect
142. #130746	C₂²	semidirect
143. #130745	C₂²	semidirect
144. #130745	C₂²	semidirect
145. #130744	C₂²	semidirect
146. #130744	C₂²	semidirect
147. #130743	C₂²	semidirect
148. #130743	C₂²	semidirect
149. #130742	C₂²	semidirect
150. #130742	C₂²	semidirect
153. #130740	C₂²	semidirect
154. #130740	C₂²	semidirect
155. #130267	C₂²	semidirect
156. #130267	C₂²	semidirect
157. #130266	C₂²	semidirect
158. #130266	C₂²	semidirect
159. #130265	C₂²	semidirect
160. #130265	C₂²	semidirect
161. #130264	C₂²	semidirect
162. #130264	C₂²	semidirect
163. #130263	C₂²	semidirect
164. #130263	C₂²	semidirect
165. #130262	C₂²	semidirect
166. #130262	C₂²	semidirect
167. #130261	C₂²	semidirect
168. #130261	C₂²	semidirect
169. #130260	C₂²	semidirect
170. #130260	C₂²	semidirect
171. #130228	C₂²	semidirect
172. #130228	C₂²	semidirect
173. #130228	C₂²	semidirect
174. #130228	C₂²	semidirect
175. #130227	C₂²	semidirect
176. #130227	C₂²	semidirect
177. #130226	C₂²	semidirect
178. #130226	C₂²	semidirect
179. #129612	C₂²	semidirect
180. #129612	C₂²	semidirect
181. #129611	C₂²	semidirect
182. #129611	C₂²	semidirect
183. #129610	C₂²	semidirect
184. #129610	C₂²	semidirect
185. #129610	C₂²	semidirect
186. #129610	C₂²	semidirect
188. C₂×D₄×#41	D₄	semidirect
191. C₂²×#532	D₄	semidirect
192. C₂³×C₄×D₄	D₄	semidirect
198. #59847	D₄	semidirect
201. #59836	D₄	semidirect
204. #59803	D₄	semidirect
205. #59660	D₄	semidirect
210. #52168	D₄	semidirect
211. #52168	D₄	semidirect
212. #52163	D₄	semidirect
213. #45489	D₄	semidirect
218. #45476	D₄	semidirect
219. #39363	D₄	semidirect
220. #39363	D₄	semidirect
223. #39361	D₄	semidirect
225. #39360	D₄	semidirect
227. #39339	D₄	semidirect
229. #39338	D₄	semidirect
231. #39337	D₄	semidirect
233. #39336	D₄	semidirect
235. #36652	D₄	semidirect
236. #36644	D₄	semidirect
237. #36624	D₄	semidirect
238. #36624	D₄	semidirect
239. #36103	D₄	semidirect
241. #36102	D₄	semidirect
243. D₄×#123	D₄	semidirect
245. D₄×#120	D₄	semidirect
247. #34976	D₄	semidirect
248. #34956	D₄	semidirect
249. #34937	D₄	semidirect
251. #34936	D₄	semidirect
252. #34936	D₄	semidirect
266. D₄×#117	D₄	semidirect
267. D₄×#117	D₄	semidirect
271. C₂×#2293	D₄	semidirect
590. #563	AGL(1,ℤ/8)	semidirect
591. H(3,𝔽₄)	AGL(1,ℤ/8)	semidirect
592. #560	AGL(1,ℤ/8)	semidirect
593. #560	AGL(1,ℤ/8)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#72282764	2
#72282742	2
#72282718	2
#72282706	2
#72282694	2
#72282677	2
#72282650	2
#72282633	2
#72282617	2
#72282607	2
#72282594	2
#72282577	2
#72282562	2
#72282538	2
#72282522	2
#72282516	2
#72282502	2
#72282488	2
#72282483	2
#72282469	2
#72282408	2
#72282398	2
#72282369	2
#72282351	2
#72281939	2
#72281868	2
#72281825	2
#72281775	2
#72281283	2
#72257443	2
#72249888	2