Subgroups — #72338871

Order 2048.

At least 6928 conjugacy classes of subgroups; only the 990 normal subgroups are shown.

The subgroup lattice has 440 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338865	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338861	C₂	1	1	yes	maximal, characteristic, complemented
3	#72338834	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338817	C₂	1	2	yes	maximal, complemented
5	#72338756	C₂	1	1	yes	maximal, characteristic, complemented
6	#72338732	C₂	1	2	yes	maximal, complemented
7	#72338711	C₂	1	2	yes	maximal, complemented
8	#72338705	C₂	1	2	yes	maximal, complemented
9	#72338682	C₂	1	4	yes	maximal, complemented
10	#72338680	C₂	1	4	yes	maximal, complemented
11	#72338666	C₂	1	1	yes	maximal, characteristic, complemented
12	#72316705	C₂	1	2	yes	maximal, complemented
13	#72316013	C₂	1	2	yes	maximal, complemented
14	#72282389	C₂	1	1	yes	maximal, characteristic, complemented
15	#72236189	C₂	1	1	yes	maximal, characteristic, complemented
16	#72231273	C₂	1	2	yes	maximal, complemented
17	#72231271	C₂	1	2	yes	maximal, complemented
18	#10581778	C₂²	1	1	yes	characteristic, complemented
19	#8698894	C₂²	1	4	yes	—
20	#8195808	C₂²	1	2	yes	—
21	#7985294	C₂²	1	2	yes	—
22	#7737411	C₂²	1	2	yes	—
23	D₄³	C₂²	1	2	yes	—
24	#7672751	C₂²	1	1	yes	characteristic
25	#7667013	C₂²	1	1	yes	characteristic
26	#7667013	C₂²	1	1	yes	characteristic
27	#6491480	C₂²	1	2	yes	complemented
28	#6453831	C₂²	1	1	yes	characteristic, complemented
29	#6347158	C₂²	1	1	yes	characteristic, complemented
30	#6346505	C₂²	1	2	yes	complemented
31	#512008	C₂²	1	2	yes	complemented
32	#511908	C₂²	1	2	yes	complemented
33	#508249	C₂²	1	2	yes	complemented
34	#508193	C₂²	1	2	yes	complemented
35	#496520	C₂²	1	2	yes	complemented
36	#493707	C₂²	1	1	yes	characteristic, complemented
37	#486613	C₂²	1	2	yes	complemented
38	#486593	C₂²	1	4	yes	complemented
39	#486533	C₂²	1	2	yes	complemented
40	#486513	C₂²	1	4	yes	complemented
41	#486464	C₂²	1	1	yes	characteristic, complemented
42	#486416	C₂²	1	1	yes	characteristic, complemented
43	#486367	C₂²	1	1	yes	characteristic, complemented
44	#486347	C₂²	1	4	yes	complemented
45	#486263	C₂²	1	1	yes	characteristic, complemented
46	#486243	C₂²	1	4	yes	complemented
47	#482633	C₂²	1	2	yes	complemented
48	#482258	C₂²	1	2	yes	complemented
49	#482051	C₂²	1	2	yes	complemented
50	#480583	C₂²	1	2	yes	complemented
51	#480104	C₂²	1	1	yes	characteristic, complemented
52	#248507	C₂²	1	4	yes	complemented
53	#248506	C₂²	1	4	yes	complemented
54	#248456	C₂²	1	4	yes	complemented
55	#248455	C₂²	1	4	yes	complemented
56	#248000	C₂²	1	2	yes	complemented
57	#247999	C₂²	1	2	yes	complemented
58	#247880	C₂²	1	2	yes	complemented
59	#247879	C₂²	1	2	yes	complemented
60	#201391	C₂²	1	2	yes	complemented
61	#200593	C₂²	1	1	yes	characteristic, complemented
62	#193890	C₂²	1	2	yes	complemented
63	#193836	C₂²	1	1	yes	characteristic, complemented
64	#185785	C₂²	1	1	yes	characteristic, complemented
65	#185628	C₂²	1	2	yes	complemented
66	#130982	C₂²	1	4	yes	complemented
67	#130982	C₂²	1	4	yes	complemented
68	#130773	C₂²	1	4	yes	complemented
69	#130768	C₂²	1	2	yes	complemented
70	#130768	C₂²	1	2	yes	complemented
71	#130740	C₂²	1	4	yes	complemented
72	#130740	C₂²	1	4	yes	complemented
73	#130403	C₂²	1	4	yes	complemented
74	#130355	C₂²	1	4	yes	complemented
75	#130355	C₂²	1	4	yes	complemented
76	#130313	C₂²	1	2	yes	complemented
77	#130260	C₂²	1	4	yes	complemented
78	#130260	C₂²	1	4	yes	complemented
79	#130226	C₂²	1	2	yes	complemented
80	#129645	C₂²	1	4	yes	complemented
81	#129607	C₂²	1	2	yes	complemented
82	#129607	C₂²	1	2	yes	complemented
83	C₂×#3498	D₄	1	1	yes	characteristic, complemented
84	C₂×#3498	C₂³	1	1	yes	characteristic
85	#62781	C₂³	1	1	yes	characteristic, complemented
86	C₂²×D₄²	D₄	1	2	yes	complemented
87	#61560	C₂³	1	2	yes	complemented
88	#61559	C₂³	1	2	yes	complemented
89	#60282	C₂³	1	1	yes	characteristic, complemented
90	#60045	D₄	1	2	yes	—
91	#60045	D₄	1	2	yes	complemented
92	#59945	D₄	1	2	yes	—
93	#59945	C₂³	1	2	yes	—
94	#59864	D₄	1	1	yes	characteristic
95	#59864	C₂³	1	1	yes	characteristic
96	#59816	D₄	1	1	yes	characteristic
97	#59816	C₂³	1	1	yes	characteristic
98	#59220	D₄	1	2	yes	complemented
99	#59041	D₄	1	2	yes	—
100	#58997	C₂³	1	4	yes	—
101	#56384	D₄	1	8	yes	complemented
102	#52988	D₄	1	4	yes	complemented
103	#52301	D₄	1	2	yes	complemented
104	#52301	C₂³	1	2	yes	—
105	#45599	C₂³	1	4	yes	—
106	#45355	D₄	1	4	yes	complemented
107	#39361	D₄	1	2	yes	complemented
108	#39361	C₂³	1	2	yes	—
109	#38904	D₄	1	4	yes	complemented
110	#38904	C₂³	1	4	yes	—
111	C₂×#2867	D₄	1	1	yes	characteristic, complemented
112	#36128	D₄	1	2	yes	complemented
113	D₄×#127	C₂³	1	2	yes	—
114	D₄×#120	D₄	1	4	yes	complemented
115	D₄×#120	C₂³	1	4	yes	—
116	#35272	D₄	1	1	yes	characteristic, complemented
117	#35272	C₂³	1	1	yes	characteristic
118	#35237	D₄	1	2	yes	complemented
119	#35237	D₄	1	2	yes	complemented
120	#34963	C₂³	1	2	yes	—
121	#34963	C₂³	1	2	yes	—
122	#34943	D₄	1	2	yes	complemented
123	#34364	D₄	1	2	yes	complemented
124	C₄×D₄²	C₂³	1	2	yes	—
125	C₄×#532	D₄	1	1	yes	characteristic, complemented
126	C₄×#532	C₂³	1	1	yes	characteristic
127	#24350	C₂³	1	4	yes	complemented
128	#24314	C₂³	1	1	yes	characteristic, complemented
129	#24312	C₂³	1	1	yes	characteristic
130	#24260	C₂³	1	4	yes	complemented
131	#24224	C₂³	1	1	yes	characteristic, complemented
132	#24222	C₂³	1	1	yes	characteristic
133	#20728	C₂³	1	1	yes	characteristic, complemented
134	#20632	C₂³	1	2	yes	complemented
135	#18389	C₂³	1	2	yes	complemented
136	#18387	C₂³	1	2	yes	complemented
137	#18205	C₂³	1	2	yes	complemented
138	#18203	C₂³	1	2	yes	complemented
139	#18196	C₂³	1	2	yes	—
140	#18194	C₂³	1	2	yes	—
141	#17366	C₂³	1	1	yes	characteristic, complemented
142	#17349	C₂³	1	2	yes	complemented
143	#12798	C₂³	1	2	yes	complemented
144	#12797	C₂³	1	2	yes	—
145	#12793	C₂³	1	4	yes	complemented
146	#12793	C₂³	1	4	yes	complemented
147	#11903	C₂³	1	2	yes	complemented
148	#11903	C₂³	1	2	yes	complemented
149	#11899	C₂³	1	4	yes	complemented
150	#11880	C₂³	1	2	yes	—
151	#11880	C₂³	1	2	yes	—
152	#11877	C₂³	1	4	yes	complemented
153	#11877	C₂³	1	4	yes	complemented
154	#11873	C₂³	1	4	yes	—
155	#11477	C₂³	1	2	yes	complemented
156	#11475	C₂³	1	1	yes	characteristic
157	#11475	C₂³	1	1	yes	characteristic
158	#11471	C₂³	1	4	yes	complemented
159	#11471	C₂³	1	4	yes	complemented
160	#9469	C₂³	1	4	yes	complemented
161	#9468	C₂³	1	4	yes	—
162	#9397	C₂³	1	2	yes	complemented
163	#9397	C₂³	1	2	yes	complemented
164	#8965	C₂³	1	4	yes	complemented
165	#8965	C₂³	1	4	yes	complemented
166	#8959	C₂³	1	2	yes	—
167	#8957	C₂³	1	2	yes	complemented
168	#8383	C₂³	1	2	yes	complemented
169	#8383	C₂³	1	2	yes	complemented
170	#8375	C₂³	1	4	yes	complemented
171	#8375	C₂³	1	4	yes	complemented
172	C₂⁴×D₄	C₂×D₄	1	4	yes	—
173	#3501	C₂⁴	1	1	yes	characteristic
174	#3496	C₂⁴	1	1	yes	characteristic
175	C₂×#550	C₂×D₄	1	2	yes	—
176	C₂×#550	C₂×D₄	1	2	yes	—
177	C₂×D₄²	C₂×D₄	1	2	yes	—
178	C₂×D₄²	C₂×D₄	1	4	yes	—
179	C₂×D₄²	C₂×D₄	1	2	yes	—
180	C₂×D₄²	C₂⁴	1	2	yes	—
181	C₂×#532	C₂×D₄	1	1	yes	characteristic
182	C₂×#532	C₂×D₄	1	2	yes	—
183	C₂×#532	C₂×D₄	1	1	yes	characteristic
184	C₂²×#127	C₂×D₄	1	2	yes	—
185	C₂²×#127	C₂×D₄	1	1	yes	characteristic
186	C₂²×#127	C₂×D₄	1	1	yes	characteristic
187	C₂²×#121	C₂×D₄	1	4	yes	—
188	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
189	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
191	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
192	#2972	C₂⁴	1	2	yes	—
193	#2867	C₂×D₄	1	2	yes	—
194	#2867	C₂×D₄	1	2	yes	—
195	#2847	C₂×D₄	1	4	yes	—
196	#2847	C₂×D₄	1	4	yes	—
197	#2826	C₂×D₄	1	8	yes	—
198	#2804	C₂×D₄	1	2	yes	—
199	#2804	C₂×D₄	1	2	yes	—
200	#2782	C₂×D₄	1	4	yes	—
201	#2684	C₂×D₄	1	4	yes	—
202	#2679	C₂×D₄	1	2	yes	—
203	#2679	C₂×D₄	1	2	yes	—
204	#2675	C₂×D₄	1	8	yes	—
205	#2668	C₂×D₄	1	8	yes	—
206	#2619	C₂×D₄	1	4	yes	—
207	#2598	C₂×D₄	1	4	yes	—
208	#2598	C₂×D₄	1	4	yes	—
209	#2572	C₂×D₄	1	4	yes	—
210	#2571	C₂×D₄	1	2	yes	—
211	#2548	C₂×D₄	1	2	yes	—
212	#2548	C₂×D₄	1	2	yes	—
213	#2541	C₂×D₄	1	2	yes	—
214	#2541	C₂⁴	1	2	yes	—
215	#2537	C₂×D₄	1	2	yes	—
216	#2504	C₂×D₄	1	4	yes	—
217	#2487	C₂×D₄	1	2	yes	—
218	#2487	C₂×D₄	1	2	yes	—
219	#2487	C₂×D₄	1	2	yes	—
220	#2487	C₂⁴	1	2	yes	—
221	#2482	C₂×D₄	1	4	yes	—
222	#2433	C₂×D₄	1	4	yes	—
223	#2408	C₂×D₄	1	4	yes	—
224	#2408	C₂×D₄	1	2	yes	—
225	#2408	C₂×D₄	1	2	yes	—
226	#2408	C₂×D₄	1	2	yes	—
227	#2408	C₂⁴	1	2	yes	—
228	#2404	C₂×D₄	1	4	yes	—
229	#2403	C₂×D₄	1	8	yes	—
230	#2398	C₂×D₄	1	4	yes	—
231	#2397	C₂×D₄	1	4	yes	—
232	#2366	C₂×D₄	1	2	yes	—
233	#2358	C₂×D₄	1	4	yes	—
234	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
235	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
236	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
237	C₄×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
238	C₄×#127	C₂×D₄	1	1	yes	characteristic
239	C₄×#127	C₂⁴	1	1	yes	characteristic
240	C₄×#124	C₂×D₄	1	1	yes	characteristic
241	C₄×#124	C₂×D₄	1	1	yes	characteristic
242	C₄×#124	C₂×D₄	1	1	yes	characteristic
243	C₄×#124	C₂⁴	1	1	yes	characteristic
244	C₄×#120	C₂×D₄	1	4	yes	—
245	C₄×#120	C₂⁴	1	4	yes	—
246	#2297	C₂×D₄	1	1	yes	characteristic
247	#2297	C₂×D₄	1	1	yes	characteristic
248	#2293	C₂×D₄	1	2	yes	—
249	#2285	C₂×D₄	1	1	yes	characteristic
250	#2285	C₂×D₄	1	1	yes	characteristic
251	#2283	C₂×D₄	1	2	yes	—
252	#2283	C₂×D₄	1	2	yes	—
253	C₄²×D₄	C₂×D₄	1	2	yes	—
254	C₂×C₄³	C₂×D₄	1	1	yes	characteristic
255	#1800	C₂⁴	1	1	yes	characteristic
256	#1800	C₂⁴	1	1	yes	characteristic
257	#1799	C₂⁴	1	4	yes	—
258	#1460	C₂⁴	1	2	yes	—
259	#1459	C₂⁴	1	2	yes	—
260	#1459	C₂⁴	1	2	yes	—
261	C₂²×#41	#120	1	1	yes	characteristic
262	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
263	C₂³×D₄	#120	1	2	yes	—
264	C₂³×D₄	#120	1	2	yes	—
265	C₂³×D₄	#120	1	2	yes	—
266	C₂³×D₄	C₂²×D₄	1	4	yes	—
267	C₂³×D₄	C₂²×D₄	1	2	yes	—
268	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
269	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
270	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
271	C₂×#127	#120	1	4	yes	—
272	C₂×#127	#120	1	2	yes	—
273	C₂×#127	#120	1	2	yes	—
274	C₂×#127	#120	1	1	yes	characteristic
275	C₂×#127	C₂²×D₄	1	1	yes	characteristic
276	C₂×#127	C₂²×D₄	1	2	yes	—
277	C₂×#127	C₂²×D₄	1	2	yes	—
278	C₂×#124	#120	1	1	yes	characteristic
279	C₂×#124	C₂²×D₄	1	1	yes	characteristic
280	C₂×#121	#120	1	2	yes	—
281	C₂×#121	C₂²×D₄	1	4	yes	—
282	C₂×#120	#120	1	4	yes	—
283	C₂×#120	C₂²×D₄	1	4	yes	—
284	C₂×C₄×Q₈	#120	1	1	yes	characteristic
285	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×D₄	#120	1	1	yes	characteristic
289	C₂×C₄×D₄	#120	1	4	yes	—
290	C₂×C₄×D₄	#120	1	4	yes	—
291	C₂×C₄×D₄	#120	1	4	yes	—
292	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
294	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
295	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
296	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
298	C₂×#117	#120	1	1	yes	characteristic
299	C₂×#117	C₂²×D₄	1	1	yes	characteristic
300	C₂×#117	C₂²×D₄	1	2	yes	—
301	C₂²×C₄⋊C₄	#120	1	2	yes	—
302	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
303	C₂²×C₂²⋊C₄	#120	1	4	yes	—
304	C₂²×C₄²	#120	1	1	yes	characteristic
305	C₂²×C₄²	#120	1	1	yes	characteristic
306	C₂²×C₄²	C₂²×D₄	1	2	yes	—
307	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
308	#400	#120	1	4	yes	—
309	#400	C₂²×D₄	1	4	yes	—
310	#399	#120	1	4	yes	—
311	#399	C₂²×D₄	1	4	yes	—
312	#394	#120	1	8	yes	—
313	#394	#120	1	4	yes	—
314	#394	C₂²×D₄	1	4	yes	—
315	#392	#120	1	4	yes	—
316	#392	C₂²×D₄	1	8	yes	—
317	#392	C₂²×D₄	1	4	yes	—
318	#391	#120	1	1	yes	characteristic
319	#391	#120	1	1	yes	characteristic
320	#391	#120	1	1	yes	characteristic
321	#391	C₂²×D₄	1	1	yes	characteristic
322	#390	#120	1	1	yes	characteristic
323	#390	C₂²×D₄	1	1	yes	characteristic
324	#390	C₂²×D₄	1	1	yes	characteristic
325	#390	C₂²×D₄	1	1	yes	characteristic
326	#386	#120	1	4	yes	—
327	#386	C₂²×D₄	1	4	yes	—
328	#385	#120	1	4	yes	—
329	#385	C₂²×D₄	1	4	yes	—
330	#384	#120	1	1	yes	characteristic
331	#384	C₂²×D₄	1	1	yes	characteristic
332	#383	#120	1	4	yes	—
333	#382	#120	1	1	yes	characteristic
334	#382	#120	1	2	yes	—
335	#382	C₂²×D₄	1	1	yes	characteristic
336	#381	#120	1	4	yes	—
337	#380	#120	1	2	yes	—
338	#380	#120	1	2	yes	—
339	#380	#120	1	2	yes	—
340	#380	C₂²×D₄	1	2	yes	—
341	#380	C₂²×D₄	1	2	yes	—
342	#379	#120	1	4	yes	—
343	#379	C₂²×D₄	1	4	yes	—
344	C₄×C₄⋊C₄	C₂²×D₄	1	2	yes	—
345	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
346	#376	#120	1	4	yes	—
347	C₄³	#120	1	1	yes	characteristic
348	C₄³	#120	1	1	yes	characteristic
349	C₄³	C₂²×D₄	1	1	yes	characteristic
350	C₄³	C₂²×D₄	1	1	yes	characteristic
351	C₂⁵	C₂×#120	1	4	yes	—
352	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
353	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
354	C₂²×D₄	C₂×#120	1	2	yes	—
355	C₂²×D₄	C₂×#120	1	4	yes	—
356	C₂²×D₄	C₂×#120	1	1	yes	characteristic
357	C₂²×D₄	C₂×#120	1	2	yes	—
358	C₂²×D₄	C₂×#120	1	4	yes	—
359	C₂²×D₄	C₂×#120	1	4	yes	—
360	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
361	C₂³×C₄	C₂×#120	1	2	yes	—
362	C₂³×C₄	C₂×#120	1	1	yes	characteristic
363	C₂³×C₄	C₂×#120	1	2	yes	—
364	C₂³×C₄	C₂×#120	1	1	yes	characteristic
365	C₂³×C₄	C₂×#120	1	1	yes	characteristic
366	C₂³×C₄	C₂×#120	1	4	yes	—
367	C₂³×C₄	C₂³×D₄	1	2	yes	—
368	#127	B(4,𝔽₂)	1	2	yes	—
369	#127	B(4,𝔽₂)	1	2	yes	—
370	#127	#576	1	2	yes	—
371	#127	#577	1	2	yes	—
372	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
373	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
374	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
378	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
383	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
385	C₂×C₄²	C₂×#120	1	1	yes	characteristic
386	C₂×C₄²	C₂×#120	1	1	yes	characteristic
387	C₂×C₄²	C₂×#120	1	2	yes	—
388	C₂×C₄²	C₂×#120	1	2	yes	—
389	C₂×C₄²	C₂×#120	1	2	yes	—
390	C₂×C₄²	C₂×#120	1	1	yes	characteristic
391	C₂×C₄²	C₂×#120	1	1	yes	characteristic
392	C₂×C₄²	C₂×#120	1	1	yes	characteristic
393	C₂×C₄²	C₂×#120	1	1	yes	characteristic
394	C₂×C₄²	C₂×#120	1	1	yes	characteristic
395	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
396	#95	C₂×#120	1	4	yes	—
397	#95	C₂×#120	1	4	yes	—
398	#95	C₂×#120	1	4	yes	—
399	C₂⁴	#2846	1	1	yes	characteristic
400	C₂⁴	C₂²×#120	1	2	yes	—
401	C₂×D₄	#3012	1	2	yes	—
402	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
403	C₂×D₄	C₂×#576	1	1	yes	characteristic
404	C₂×D₄	C₂×#577	1	1	yes	characteristic
405	C₂×D₄	#3585	1	2	yes	—
406	C₂²×C₄	#2846	1	2	yes	—
407	C₂²×C₄	#2846	1	1	yes	characteristic
408	C₂²×C₄	#2846	1	1	yes	characteristic
409	C₂²×C₄	#2846	1	2	yes	—
410	C₂²×C₄	#2846	1	1	yes	characteristic
411	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
412	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
413	C₂²×C₄	C₂²×#120	1	2	yes	—
414	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
415	C₄²	#3012	1	2	yes	—
416	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
417	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
418	C₄²	#3026	1	1	yes	characteristic
419	C₄²	#3026	1	1	yes	characteristic
420	C₂³	C₂×#2846	1	1	yes	characteristic
421	C₂³	#60372	1	2	yes	—
422	C₂³	#60373	1	2	yes	—
423	C₂×C₄	#32898	1	1	yes	characteristic
424	C₂×C₄	#32898	1	1	yes	characteristic
425	C₂×C₄	#32898	1	1	yes	characteristic
426	C₂×C₄	#32898	1	1	yes	characteristic
427	C₂×C₄	C₂×#3012	1	1	yes	characteristic
428	C₂×C₄	#60367	1	1	yes	characteristic
429	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
430	C₂×C₄	C₂×#3026	1	1	yes	characteristic
431	C₂²	#6628857	1	1	yes	characteristic
432	C₂²	#6628883	1	1	yes	characteristic
433	C₂²	C₂×#32898	1	1	yes	characteristic
434	C₄	#511819	1	2	yes	—
435	C₄	#7622880	1	2	yes	—
436	C₂	C₂×#511819	1	1	yes	characteristic
437	C₂	#72238193	1	1	yes	characteristic
438	C₂	#72251988	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×#3498 ◁ 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. #72338865	C₂	semidirect
2. #72338861	C₂	semidirect
3. #72338834	C₂	semidirect
4. #72338817	C₂	semidirect
5. #72338756	C₂	semidirect
6. #72338732	C₂	semidirect
7. #72338711	C₂	semidirect
8. #72338705	C₂	semidirect
9. #72338682	C₂	semidirect
10. #72338680	C₂	semidirect
11. #72338666	C₂	semidirect
12. #72316705	C₂	semidirect
13. #72316013	C₂	semidirect
14. #72282389	C₂	semidirect
15. #72236189	C₂	semidirect
16. #72231273	C₂	semidirect
17. #72231271	C₂	semidirect
18. #10581778	C₂²	semidirect
27. #6491480	C₂²	semidirect
28. #6453831	C₂²	semidirect
29. #6347158	C₂²	semidirect
30. #6346505	C₂²	semidirect
31. #512008	C₂²	semidirect
32. #511908	C₂²	semidirect
33. #508249	C₂²	semidirect
34. #508193	C₂²	semidirect
35. #496520	C₂²	semidirect
36. #493707	C₂²	semidirect
37. #486613	C₂²	semidirect
38. #486593	C₂²	semidirect
39. #486533	C₂²	semidirect
40. #486513	C₂²	semidirect
41. #486464	C₂²	semidirect
42. #486416	C₂²	semidirect
43. #486367	C₂²	semidirect
44. #486347	C₂²	semidirect
45. #486263	C₂²	semidirect
46. #486243	C₂²	semidirect
47. #482633	C₂²	semidirect
48. #482258	C₂²	semidirect
49. #482051	C₂²	semidirect
50. #480583	C₂²	semidirect
51. #480104	C₂²	semidirect
52. #248507	C₂²	semidirect
53. #248506	C₂²	semidirect
54. #248456	C₂²	semidirect
55. #248455	C₂²	semidirect
56. #248000	C₂²	semidirect
57. #247999	C₂²	semidirect
58. #247880	C₂²	semidirect
59. #247879	C₂²	semidirect
60. #201391	C₂²	semidirect
61. #200593	C₂²	semidirect
62. #193890	C₂²	semidirect
63. #193836	C₂²	semidirect
64. #185785	C₂²	semidirect
65. #185628	C₂²	semidirect
66. #130982	C₂²	semidirect
67. #130982	C₂²	semidirect
68. #130773	C₂²	semidirect
69. #130768	C₂²	semidirect
70. #130768	C₂²	semidirect
71. #130740	C₂²	semidirect
72. #130740	C₂²	semidirect
73. #130403	C₂²	semidirect
74. #130355	C₂²	semidirect
75. #130355	C₂²	semidirect
76. #130313	C₂²	semidirect
77. #130260	C₂²	semidirect
78. #130260	C₂²	semidirect
79. #130226	C₂²	semidirect
80. #129645	C₂²	semidirect
81. #129607	C₂²	semidirect
82. #129607	C₂²	semidirect
83. C₂×#3498	D₄	semidirect
85. #62781	C₂³	semidirect
86. C₂²×D₄²	D₄	semidirect
87. #61560	C₂³	semidirect
88. #61559	C₂³	semidirect
89. #60282	C₂³	semidirect
91. #60045	D₄	semidirect
98. #59220	D₄	semidirect
101. #56384	D₄	semidirect
102. #52988	D₄	semidirect
103. #52301	D₄	semidirect
106. #45355	D₄	semidirect
107. #39361	D₄	semidirect
109. #38904	D₄	semidirect
111. C₂×#2867	D₄	semidirect
112. #36128	D₄	semidirect
114. D₄×#120	D₄	semidirect
116. #35272	D₄	semidirect
118. #35237	D₄	semidirect
119. #35237	D₄	semidirect
122. #34943	D₄	semidirect
123. #34364	D₄	semidirect
125. C₄×#532	D₄	semidirect
127. #24350	C₂³	semidirect
128. #24314	C₂³	semidirect
130. #24260	C₂³	semidirect
131. #24224	C₂³	semidirect
133. #20728	C₂³	semidirect
134. #20632	C₂³	semidirect
135. #18389	C₂³	semidirect
136. #18387	C₂³	semidirect
137. #18205	C₂³	semidirect
138. #18203	C₂³	semidirect
141. #17366	C₂³	semidirect
142. #17349	C₂³	semidirect
143. #12798	C₂³	semidirect
145. #12793	C₂³	semidirect
146. #12793	C₂³	semidirect
147. #11903	C₂³	semidirect
148. #11903	C₂³	semidirect
149. #11899	C₂³	semidirect
152. #11877	C₂³	semidirect
153. #11877	C₂³	semidirect
155. #11477	C₂³	semidirect
158. #11471	C₂³	semidirect
159. #11471	C₂³	semidirect
160. #9469	C₂³	semidirect
162. #9397	C₂³	semidirect
163. #9397	C₂³	semidirect
164. #8965	C₂³	semidirect
165. #8965	C₂³	semidirect
167. #8957	C₂³	semidirect
168. #8383	C₂³	semidirect
169. #8383	C₂³	semidirect
170. #8375	C₂³	semidirect
171. #8375	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72338865	2
#72338861	2
#72338834	2
#72338817	2
#72338756	2
#72338732	2
#72338711	2
#72338705	2
#72338682	2
#72338680	2
#72338666	2
#72316705	2
#72316013	2
#72282389	2
#72236189	2
#72231273	2
#72231271	2