Subgroups — #6345414

Order 512.

1585 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60536	C₂	1	1	yes	maximal, characteristic
2	#60287	C₂	1	1	yes	maximal, characteristic, complemented
3	#60283	C₂	1	1	yes	maximal, characteristic, complemented
4	#18045	C₂	1	1	yes	maximal, characteristic, complemented
5	#18043	C₂	1	1	yes	maximal, characteristic, complemented
6	#18041	C₂	1	1	yes	maximal, characteristic, complemented
7	#18041	C₂	1	1	yes	maximal, characteristic, complemented
8	#18039	C₂	1	1	yes	maximal, characteristic, complemented
9	#18037	C₂	1	1	yes	maximal, characteristic, complemented
10	#18037	C₂	1	1	yes	maximal, characteristic, complemented
11	#18035	C₂	1	1	yes	maximal, characteristic, complemented
12	#18032	C₂	1	2	yes	maximal, complemented
13	#18030	C₂	1	2	yes	maximal, complemented
14	#18028	C₂	1	2	yes	maximal, complemented
15	#18026	C₂	1	2	yes	maximal, complemented
16	#17955	C₂	1	2	yes	maximal, complemented
17	#17954	C₂	1	2	yes	maximal, complemented
18	#17927	C₂	1	2	yes	maximal, complemented
19	#17926	C₂	1	2	yes	maximal, complemented
20	#17816	C₂	1	1	yes	maximal, characteristic, complemented
21	#17494	C₂	1	1	yes	maximal, characteristic, complemented
22	#17450	C₂	1	1	yes	maximal, characteristic, complemented
23	#17324	C₂	1	1	yes	maximal, characteristic, complemented
24	#3444	C₂²	1	1	yes	characteristic
25	C₂×C₄×#41	C₂²	1	1	yes	characteristic
26	#3108	C₄	1	1	yes	characteristic
27	#3108	C₄	1	1	yes	characteristic
28	#3107	C₄	1	1	yes	characteristic
29	#3107	C₄	1	1	yes	characteristic
30	#3106	C₄	1	1	yes	characteristic
31	#3106	C₄	1	1	yes	characteristic
32	#3105	C₄	1	1	yes	characteristic
33	#3105	C₄	1	1	yes	characteristic
34	#3104	C₂²	1	1	yes	characteristic
35	#3103	C₂²	1	1	yes	characteristic
36	#3102	C₂²	1	1	yes	characteristic
37	#3102	C₂²	1	1	yes	characteristic
38	#3102	C₂²	1	1	yes	characteristic
39	#3102	C₂²	1	1	yes	characteristic
40	#3101	C₂²	1	1	yes	characteristic
41	#3100	C₂²	1	1	yes	characteristic
42	#3091	C₄	1	1	yes	characteristic
43	#3091	C₄	1	1	yes	characteristic
44	#3076	C₄	1	1	yes	characteristic
45	#3076	C₄	1	1	yes	characteristic
46	#3035	C₄	1	1	yes	characteristic
47	#3035	C₄	1	1	yes	characteristic
48	#3002	C₄	1	1	yes	characteristic
49	#3002	C₄	1	1	yes	characteristic
50	#2993	—	2	2	no	—
51	#2993	C₂²	1	2	yes	complemented
52	#2993	C₂²	1	2	yes	complemented
53	#2989	—	2	2	no	—
54	#2989	C₂²	1	2	yes	—
55	#2988	C₂²	1	2	yes	—
56	#2986	C₂²	1	2	yes	—
57	#2984	C₂²	1	2	yes	—
58	#2979	C₂²	1	2	yes	—
59	#2978	—	2	2	no	—
60	#2974	—	2	2	no	—
61	#2974	C₂²	1	2	yes	—
62	#2971	—	2	1	no	—
63	#2971	C₂²	1	1	yes	characteristic
64	#2971	C₂²	1	1	yes	characteristic
65	#2971	C₂²	1	1	yes	characteristic, complemented
66	#2971	C₂²	1	1	yes	characteristic, complemented
67	#2970	—	2	1	no	—
68	#2970	—	2	1	no	—
69	#2970	—	2	1	no	—
70	#2970	C₂²	1	1	yes	characteristic
71	#2970	C₂²	1	1	yes	characteristic
72	#2970	C₂²	1	1	yes	characteristic, complemented
73	#2970	C₂²	1	1	yes	characteristic, complemented
74	C₄×#135	C₂²	1	1	yes	characteristic
75	C₄×#135	C₂²	1	1	yes	characteristic
76	C₄×#135	C₂²	1	1	yes	characteristic
77	C₄×#135	C₂²	1	1	yes	characteristic
78	#2923	—	2	1	no	—
79	#2923	—	2	1	no	—
80	#2920	—	2	1	no	—
81	#2920	C₂²	1	1	yes	characteristic
82	#2920	C₂²	1	1	yes	characteristic
83	#2920	C₂²	1	1	yes	characteristic
84	C₂×#432	—	2	1	no	—
85	C₂×#432	C₂²	1	1	yes	characteristic
86	C₂×#431	C₂²	1	1	yes	characteristic
87	#1594	C₂²	1	2	yes	complemented
88	#1593	C₂²	1	2	yes	complemented
89	#1592	C₂²	1	2	yes	complemented
90	#1592	C₂²	1	2	yes	complemented
91	#1591	C₂²	1	2	yes	complemented
92	#1590	C₂²	1	2	yes	complemented
93	#1590	C₂²	1	2	yes	complemented
94	#1589	C₂²	1	2	yes	complemented
95	#1588	C₂²	1	2	yes	complemented
96	#1588	C₂²	1	2	yes	complemented
97	#1587	C₂²	1	2	yes	complemented
98	#1587	C₂²	1	2	yes	complemented
99	#1586	C₂²	1	2	yes	complemented
100	#1586	C₂²	1	2	yes	complemented
101	#1585	C₂²	1	2	yes	complemented
102	#1585	C₂²	1	2	yes	complemented
103	#1584	C₂²	1	2	yes	complemented
104	#1584	C₂²	1	2	yes	complemented
105	#1583	C₂²	1	2	yes	complemented
106	#1583	C₂²	1	2	yes	complemented
107	#1582	C₂²	1	2	yes	complemented
108	#1582	C₂²	1	2	yes	complemented
109	#1581	C₂²	1	2	yes	complemented
110	#1581	C₂²	1	2	yes	complemented
111	#1580	C₂²	1	2	yes	complemented
112	#1579	C₂²	1	2	yes	complemented
113	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
114	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
115	C₈×Q₁₆	C₂²	1	2	yes	complemented
116	C₈×SD₁₆	C₂²	1	2	yes	complemented
117	C₈×SD₁₆	C₂²	1	2	yes	complemented
118	C₈×D₈	C₂²	1	2	yes	complemented
119	#1572	C₂²	1	2	yes	—
120	#1572	C₂²	1	2	yes	—
121	#1571	C₂²	1	2	yes	complemented
122	#1570	C₂²	1	2	yes	complemented
123	#1568	C₂²	1	1	yes	characteristic, complemented
124	#1568	C₂²	1	1	yes	characteristic, complemented
125	#1568	C₂²	1	1	yes	characteristic, complemented
126	#1568	C₂²	1	1	yes	characteristic, complemented
127	#1497	C₂²	1	2	yes	—
128	#1496	C₂²	1	2	yes	—
129	#1489	C₂²	1	2	yes	—
130	#1489	C₂²	1	2	yes	—
131	#1488	C₂²	1	1	yes	characteristic
132	#1488	C₂²	1	1	yes	characteristic
133	#1488	C₂²	1	1	yes	characteristic
134	#1488	C₂²	1	1	yes	characteristic
135	#1488	C₂²	1	1	yes	characteristic, complemented
136	#1488	C₂²	1	1	yes	characteristic, complemented
137	#1488	C₂²	1	1	yes	characteristic, complemented
138	#1488	C₂²	1	1	yes	characteristic, complemented
139	#1483	C₂²	1	2	yes	complemented
140	#1483	C₂²	1	2	yes	complemented
141	#1479	C₂²	1	2	yes	—
142	#1478	C₂²	1	2	yes	—
143	#1454	C₂²	1	2	yes	—
144	#1454	C₂²	1	2	yes	—
145	#1453	C₂²	1	2	yes	complemented
146	#1453	C₂²	1	2	yes	complemented
147	#1451	C₂²	1	1	yes	characteristic, complemented
148	#1451	C₂²	1	1	yes	characteristic, complemented
149	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
150	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
151	C₂²×#41	C₂×C₄	1	1	yes	characteristic
152	C₂×#135	C₂×C₄	1	1	yes	characteristic
153	C₂×#135	C₂×C₄	1	1	yes	characteristic
154	C₂×#135	C₂×C₄	1	1	yes	characteristic
155	C₂×#135	C₂×C₄	1	1	yes	characteristic
156	#533	C₂×C₄	1	1	yes	characteristic
157	#533	C₂×C₄	1	1	yes	characteristic
158	#533	C₂³	1	1	yes	characteristic
159	#532	C₂×C₄	1	1	yes	characteristic
160	#532	C₂×C₄	1	1	yes	characteristic
161	#532	C₂³	1	1	yes	characteristic
162	#529	—	2	1	no	—
163	#529	—	2	1	no	—
164	#529	—	2	1	no	—
165	#529	—	2	1	no	—
166	#529	C₂×C₄	1	1	yes	characteristic
167	#529	C₂×C₄	1	1	yes	characteristic
168	#529	C₂³	1	1	yes	characteristic
169	#529	C₂³	1	1	yes	characteristic
170	#525	—	2	1	no	—
171	#525	—	2	1	no	—
172	#525	C₂×C₄	1	1	yes	characteristic
173	#525	C₂×C₄	1	1	yes	characteristic
174	C₄×#41	—	2	1	no	—
175	C₄×#41	—	2	1	no	—
176	C₄×#41	—	2	1	no	—
177	C₄×#41	—	2	1	no	—
178	C₄×#41	—	2	1	no	—
179	C₄×#41	—	2	1	no	—
180	C₄×#41	C₂×C₄	1	1	yes	characteristic
181	C₄×#41	C₂×C₄	1	1	yes	characteristic
182	C₄×#41	C₂×C₄	1	1	yes	characteristic
183	C₄×#41	C₂×C₄	1	1	yes	characteristic
184	C₄×#41	C₂³	1	1	yes	characteristic
185	C₄×#41	C₂³	1	1	yes	characteristic
186	C₄×#41	C₂³	1	1	yes	characteristic
187	C₄×#41	C₂³	1	1	yes	characteristic
188	C₄×#41	C₂³	1	1	yes	characteristic
189	C₄×#41	C₂³	1	1	yes	characteristic
190	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
191	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
192	C₂×C₄×D₄	—	2	1	no	—
193	C₂×C₄×D₄	—	2	1	no	—
194	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
196	C₂×#117	—	2	1	no	—
197	C₂×#117	C₂×C₄	1	1	yes	characteristic
198	C₂²×C₄²	—	2	1	no	—
199	C₂²×C₄²	C₂³	1	1	yes	characteristic
200	#485	C₂×C₄	1	1	yes	characteristic
201	#485	C₂×C₄	1	1	yes	characteristic
202	#485	C₂×C₄	1	1	yes	characteristic
203	#485	C₂×C₄	1	1	yes	characteristic
204	#484	C₂×C₄	1	1	yes	characteristic
205	#484	C₂×C₄	1	1	yes	characteristic
206	#483	C₂×C₄	1	1	yes	characteristic
207	#483	C₂×C₄	1	1	yes	characteristic
208	#482	C₂×C₄	1	1	yes	characteristic
209	#482	C₂×C₄	1	1	yes	characteristic
210	#482	C₂×C₄	1	1	yes	characteristic
211	#482	C₂×C₄	1	1	yes	characteristic
212	#481	C₂×C₄	1	1	yes	characteristic
213	#481	C₂×C₄	1	1	yes	characteristic
214	#480	C₂×C₄	1	1	yes	characteristic
215	#480	C₂×C₄	1	1	yes	characteristic
216	#479	C₂×C₄	1	1	yes	characteristic
217	#479	C₂×C₄	1	1	yes	characteristic
218	#479	C₂×C₄	1	1	yes	characteristic
219	#479	C₂×C₄	1	1	yes	characteristic
220	#478	C₂×C₄	1	1	yes	characteristic
221	#478	C₂×C₄	1	1	yes	characteristic
222	#478	C₂×C₄	1	1	yes	characteristic
223	#478	C₂×C₄	1	1	yes	characteristic
224	#477	C₂×C₄	1	1	yes	characteristic
225	#477	C₂×C₄	1	1	yes	characteristic
226	#476	C₂×C₄	1	1	yes	characteristic
227	#476	C₂×C₄	1	1	yes	characteristic
228	#475	C₂×C₄	1	1	yes	characteristic
229	#475	C₂×C₄	1	1	yes	characteristic
230	#474	C₂×C₄	1	1	yes	characteristic
231	#474	C₂×C₄	1	1	yes	characteristic
232	#464	C₂×C₄	1	1	yes	characteristic
233	#464	C₂×C₄	1	1	yes	characteristic
234	#464	C₂×C₄	1	1	yes	characteristic
235	#464	C₂×C₄	1	1	yes	characteristic
236	#463	C₂×C₄	1	1	yes	characteristic
237	#463	C₂×C₄	1	1	yes	characteristic
238	#463	C₂×C₄	1	1	yes	characteristic
239	#463	C₂×C₄	1	1	yes	characteristic
240	#462	C₂×C₄	1	1	yes	characteristic
241	#462	C₂×C₄	1	1	yes	characteristic
242	#461	C₂×C₄	1	1	yes	characteristic
243	#461	C₂×C₄	1	1	yes	characteristic
244	#460	C₂×C₄	1	1	yes	characteristic
245	#460	C₂×C₄	1	1	yes	characteristic
246	#459	C₂×C₄	1	1	yes	characteristic
247	#459	C₂×C₄	1	1	yes	characteristic
248	#452	C₂×C₄	1	1	yes	characteristic
249	#452	C₂×C₄	1	1	yes	characteristic
250	#452	C₂×C₄	1	1	yes	characteristic
251	#452	C₂×C₄	1	1	yes	characteristic
252	#451	C₂×C₄	1	1	yes	characteristic
253	#451	C₂×C₄	1	1	yes	characteristic
254	#450	C₂×C₄	1	1	yes	characteristic
255	#450	C₂×C₄	1	1	yes	characteristic
256	#449	C₂×C₄	1	1	yes	characteristic
257	#449	C₂×C₄	1	1	yes	characteristic
258	#449	C₂×C₄	1	1	yes	characteristic
259	#449	C₂×C₄	1	1	yes	characteristic
260	#448	C₂×C₄	1	1	yes	characteristic
261	#448	C₂×C₄	1	1	yes	characteristic
262	#447	C₂×C₄	1	1	yes	characteristic
263	#447	C₂×C₄	1	1	yes	characteristic
264	#446	—	2	2	no	—
265	#446	—	2	2	no	—
266	#446	—	2	2	no	—
267	#446	C₂³	1	2	yes	—
268	#446	C₂³	1	2	yes	—
269	#446	C₂³	1	2	yes	—
270	#446	C₂³	1	2	yes	—
271	C₈×Q₈	—	2	2	no	—
272	C₈×Q₈	C₂³	1	2	yes	—
273	C₈×Q₈	C₂³	1	2	yes	—
274	C₈×Q₈	C₂³	1	2	yes	—
275	C₈×Q₈	C₂³	1	2	yes	—
276	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
277	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
278	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
279	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
280	C₄×Q₁₆	C₂³	1	1	yes	characteristic
281	C₄×Q₁₆	C₂³	1	1	yes	characteristic
282	C₄×Q₁₆	C₂³	1	1	yes	characteristic
283	C₄×Q₁₆	C₂³	1	1	yes	characteristic
284	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
285	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
286	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
287	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
288	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
289	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
290	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
291	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
292	C₄×SD₁₆	C₂³	1	1	yes	characteristic
293	C₄×SD₁₆	C₂³	1	1	yes	characteristic
294	C₄×SD₁₆	C₂³	1	1	yes	characteristic
295	C₄×SD₁₆	C₂³	1	1	yes	characteristic
296	C₄×SD₁₆	C₂³	1	1	yes	characteristic
297	C₄×SD₁₆	C₂³	1	1	yes	characteristic
298	C₄×SD₁₆	C₂³	1	1	yes	characteristic
299	C₄×SD₁₆	C₂³	1	1	yes	characteristic
300	C₄×D₈	C₂×C₄	1	1	yes	characteristic
301	C₄×D₈	C₂×C₄	1	1	yes	characteristic
302	C₄×D₈	C₂×C₄	1	1	yes	characteristic
303	C₄×D₈	C₂×C₄	1	1	yes	characteristic
304	C₄×D₈	C₂³	1	1	yes	characteristic
305	C₄×D₈	C₂³	1	1	yes	characteristic
306	C₄×D₈	C₂³	1	1	yes	characteristic
307	C₄×D₈	C₂³	1	1	yes	characteristic
308	#436	—	2	2	no	—
309	#436	—	2	2	no	—
310	#436	—	2	2	no	—
311	#436	—	2	2	no	—
312	#436	—	2	2	no	—
313	#436	—	2	2	no	—
314	#436	—	2	2	no	—
315	#436	C₂³	1	2	yes	—
316	#436	C₂³	1	2	yes	—
317	#436	C₂³	1	2	yes	—
318	#436	C₂³	1	2	yes	—
319	#435	—	2	2	no	—
320	#435	—	2	2	no	—
321	#435	—	2	2	no	—
322	#435	—	2	2	no	—
323	#435	—	2	2	no	—
324	#435	—	2	2	no	—
325	#435	—	2	2	no	—
326	#435	—	2	2	no	—
327	#435	—	2	2	no	—
328	#435	—	2	2	no	—
329	C₈×D₄	—	2	2	no	—
330	C₈×D₄	—	2	2	no	—
331	C₈×D₄	—	2	2	no	—
332	C₈×D₄	C₂³	1	2	yes	—
333	C₈×D₄	C₂³	1	2	yes	—
334	C₈×D₄	C₂³	1	2	yes	—
335	C₈×D₄	C₂³	1	2	yes	—
336	#433	—	2	2	no	—
337	#433	—	2	2	no	—
338	#433	—	2	2	no	—
339	#433	—	2	2	no	—
340	#432	—	2	1	no	—
341	#432	—	2	1	no	—
342	#432	—	2	1	no	—
343	#432	—	2	1	no	—
344	#432	—	2	1	no	—
345	#432	—	2	2	no	—
346	#432	—	2	2	no	—
347	#432	—	2	1	no	—
348	#432	—	2	1	no	—
349	#432	—	2	1	no	—
350	#432	—	2	1	no	—
351	#432	—	2	1	no	—
352	#432	—	2	1	no	—
353	#432	—	2	1	no	—
354	#432	—	2	1	no	—
355	#432	D₄	1	1	yes	characteristic
356	#432	D₄	1	1	yes	characteristic
357	#432	D₄	1	1	yes	characteristic
358	#432	D₄	1	1	yes	characteristic
359	#432	C₂³	1	1	yes	characteristic
360	#432	C₂³	1	1	yes	characteristic
361	#432	C₂³	1	1	yes	characteristic
362	#432	C₂³	1	1	yes	characteristic
363	#432	C₂³	1	2	yes	—
364	#431	—	2	1	no	—
365	#431	—	2	2	no	—
366	#431	—	2	2	no	—
367	#431	C₂×C₄	1	1	yes	characteristic
368	#431	C₂×C₄	1	1	yes	characteristic
369	#431	C₂×C₄	1	1	yes	characteristic
370	#431	C₂×C₄	1	1	yes	characteristic
371	#431	C₂³	1	2	yes	—
372	#431	C₂³	1	1	yes	characteristic
373	#431	C₂³	1	1	yes	characteristic
374	#431	C₂³	1	2	yes	—
375	#431	C₂³	1	1	yes	characteristic
376	#431	C₂³	1	1	yes	characteristic
377	#431	C₂³	1	1	yes	characteristic
378	#431	C₂³	1	1	yes	characteristic
379	#431	C₂³	1	2	yes	—
380	#431	C₂³	1	2	yes	—
381	#427	C₂×C₄	1	1	yes	characteristic
382	#427	C₂×C₄	1	1	yes	characteristic
383	#427	C₂×C₄	1	1	yes	characteristic
384	#427	C₂×C₄	1	1	yes	characteristic
385	#424	—	2	2	no	—
386	#424	—	2	2	no	—
387	#423	—	2	1	no	—
388	#423	—	2	2	no	—
389	#423	D₄	1	2	yes	—
390	#423	C₂³	1	2	yes	—
391	C₂×C₄⋊C₈	—	2	2	no	—
392	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
393	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
394	C₂×C₄⋊C₈	C₂³	1	2	yes	—
395	#416	C₂×C₄	1	1	yes	characteristic
396	#416	C₂×C₄	1	1	yes	characteristic
397	#416	C₂×C₄	1	1	yes	characteristic
398	#416	C₂×C₄	1	1	yes	characteristic
399	#416	C₂×C₄	1	1	yes	characteristic
400	#416	C₂×C₄	1	1	yes	characteristic
401	#416	C₂×C₄	1	1	yes	characteristic
402	#416	C₂×C₄	1	1	yes	characteristic
403	#408	—	2	2	no	—
404	#408	—	2	2	no	—
405	#407	—	2	1	no	—
406	#407	—	2	1	no	—
407	#407	—	2	2	no	—
408	#407	D₄	1	2	yes	—
409	C₂×C₂²⋊C₈	—	2	1	no	—
410	C₂×C₂²⋊C₈	—	2	2	no	—
411	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
412	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
413	C₄×M₁₆	—	2	1	no	—
414	C₄×M₁₆	—	2	1	no	—
415	C₄×M₁₆	—	2	1	no	—
416	C₄×M₁₆	—	2	1	no	—
417	C₄×M₁₆	—	2	1	no	—
418	C₄×M₁₆	C₂³	1	2	yes	—
419	C₄×M₁₆	C₂³	1	1	yes	characteristic
420	C₄×M₁₆	C₂³	1	1	yes	characteristic
421	C₂×#97	—	2	1	no	—
422	C₂×#97	—	2	1	no	—
423	C₂×#97	—	2	1	no	—
424	C₂×#97	—	2	1	no	—
425	C₂×#97	—	2	1	no	—
426	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
427	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
428	#335	C₂³	1	2	yes	—
429	#335	C₂³	1	2	yes	—
430	#335	C₂³	1	2	yes	—
431	#335	C₂³	1	2	yes	—
432	#334	C₂³	1	2	yes	—
433	#334	C₂³	1	2	yes	—
434	#334	C₂³	1	2	yes	—
435	#334	C₂³	1	2	yes	—
436	Q₈⋊C₈	C₂³	1	2	yes	—
437	Q₈⋊C₈	C₂³	1	2	yes	—
438	Q₈⋊C₈	C₂³	1	2	yes	—
439	Q₈⋊C₈	C₂³	1	2	yes	—
440	Q₈⋊C₈	C₂³	1	2	yes	—
441	Q₈⋊C₈	C₂³	1	2	yes	—
442	Q₈⋊C₈	C₂³	1	2	yes	—
443	Q₈⋊C₈	C₂³	1	2	yes	—
444	D₄⋊C₈	C₂³	1	2	yes	—
445	D₄⋊C₈	C₂³	1	2	yes	—
446	D₄⋊C₈	C₂³	1	2	yes	—
447	D₄⋊C₈	C₂³	1	2	yes	—
448	D₄⋊C₈	C₂³	1	2	yes	—
449	D₄⋊C₈	C₂³	1	2	yes	—
450	D₄⋊C₈	C₂³	1	2	yes	—
451	D₄⋊C₈	C₂³	1	2	yes	—
452	#322	C₂³	1	2	yes	—
453	#322	C₂³	1	2	yes	—
454	#322	C₂³	1	2	yes	—
455	#322	C₂³	1	2	yes	—
456	#322	C₂³	1	2	yes	—
457	#322	C₂³	1	2	yes	—
458	C₈²	C₂³	1	2	yes	—
459	C₈²	C₂³	1	2	yes	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	—	4	2	no	—
465	C₂×#41	—	4	2	no	—
466	C₂×#41	C₂²×C₄	1	1	yes	characteristic
467	C₂×#41	C₂²×C₄	1	1	yes	characteristic
468	C₂×#41	C₂²×C₄	1	1	yes	characteristic
469	C₂×#41	C₂²×C₄	1	1	yes	characteristic
470	C₂×#41	C₂²×C₄	1	1	yes	characteristic
471	C₂×#41	C₂²×C₄	1	1	yes	characteristic
472	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
479	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
480	C₂³×C₄	#41	1	1	yes	characteristic
481	#135	—	4	2	no	—
482	#135	—	4	2	no	—
483	#135	—	4	2	no	—
484	#135	—	4	2	no	—
485	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
486	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
487	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
488	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
489	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
490	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
491	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
492	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
493	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
494	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
495	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
496	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
497	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
498	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
499	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
500	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
501	C₂×M₁₆	—	2	2	no	—
502	C₂×M₁₆	—	2	2	no	—
503	C₂×M₁₆	—	2	2	no	—
504	C₂×M₁₆	—	2	2	no	—
505	C₂×M₁₆	—	2	2	no	—
506	C₂×M₁₆	—	2	2	no	—
507	C₂×M₁₆	C₂×D₄	1	2	yes	—
508	C₂×M₁₆	C₂×D₄	1	2	yes	—
509	C₂²×C₈	—	2	2	no	—
510	C₂²×C₈	—	2	2	no	—
511	C₂²×C₈	—	2	2	no	—
512	C₂²×C₈	—	2	2	no	—
513	C₂²×C₈	—	2	2	no	—
514	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
515	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
516	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
517	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
518	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
519	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
520	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
521	#127	C₂²×C₄	1	1	yes	characteristic
522	#126	—	2	1	no	—
523	#126	—	2	1	no	—
524	#126	—	2	1	no	—
525	#126	—	2	1	no	—
526	#125	—	2	1	no	—
527	#125	—	2	1	no	—
528	#125	C₂²×C₄	1	1	yes	characteristic
529	#125	C₂²×C₄	1	1	yes	characteristic
530	#124	—	2	1	no	—
531	#124	—	2	1	no	—
532	#124	C₂²×C₄	1	1	yes	characteristic
533	#124	C₂²×C₄	1	1	yes	characteristic
534	#123	—	2	1	no	—
535	#123	—	2	1	no	—
536	#123	—	2	1	no	—
537	#123	—	2	1	no	—
538	#123	—	2	1	no	—
539	#123	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
545	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
546	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
547	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
548	#121	—	2	1	no	—
549	#121	—	2	1	no	—
550	#121	—	2	1	no	—
551	#121	—	2	1	no	—
552	#121	C₂²×C₄	1	1	yes	characteristic
553	#121	C₂²×C₄	1	1	yes	characteristic
554	#121	C₂²×C₄	1	1	yes	characteristic
555	#121	C₂²×C₄	1	1	yes	characteristic
556	#120	—	2	1	no	—
557	#120	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	—	2	1	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
567	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
568	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
569	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
570	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
571	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
572	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
573	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
574	C₄×Q₈	C₂⁴	1	1	yes	characteristic
575	C₄×Q₈	C₂⁴	1	1	yes	characteristic
576	C₄×Q₈	C₂⁴	1	1	yes	characteristic
577	C₄×Q₈	C₂⁴	1	1	yes	characteristic
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
615	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
616	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
617	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
618	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
619	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
620	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
621	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
622	C₄×D₄	C₂⁴	1	1	yes	characteristic
623	C₄×D₄	C₂⁴	1	1	yes	characteristic
624	C₄×D₄	C₂⁴	1	1	yes	characteristic
625	C₄×D₄	C₂⁴	1	1	yes	characteristic
626	#117	—	2	1	no	—
627	#117	—	2	1	no	—
628	#117	—	2	1	no	—
629	#117	—	2	1	no	—
630	#117	—	2	1	no	—
631	#117	—	2	1	no	—
632	#117	—	2	1	no	—
633	#117	—	2	1	no	—
634	#117	—	2	1	no	—
635	#117	—	2	1	no	—
636	#117	—	2	1	no	—
637	#117	—	2	1	no	—
638	#117	—	2	1	no	—
639	#117	—	2	1	no	—
640	#117	—	2	1	no	—
641	#117	—	2	1	no	—
642	#117	—	2	1	no	—
643	#117	—	2	1	no	—
644	#117	C₂²×C₄	1	1	yes	characteristic
645	#117	C₂²×C₄	1	1	yes	characteristic
646	#117	C₂²×C₄	1	1	yes	characteristic
647	#117	C₂²×C₄	1	1	yes	characteristic
648	#117	C₂²×C₄	1	1	yes	characteristic
649	#117	C₂²×C₄	1	1	yes	characteristic
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
671	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
672	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
673	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
676	C₂×C₄²	#41	1	1	yes	characteristic
677	C₂×C₄²	#41	1	1	yes	characteristic
678	C₂×C₄²	#41	1	1	yes	characteristic
679	C₂×C₄²	C₂⁴	1	1	yes	characteristic
680	C₂×C₄²	C₂⁴	1	1	yes	characteristic
681	C₂×C₄²	C₂⁴	1	1	yes	characteristic
682	#107	C₂²×C₄	1	1	yes	characteristic
683	#107	C₂²×C₄	1	1	yes	characteristic
684	#107	C₂²×C₄	1	1	yes	characteristic
685	#107	C₂²×C₄	1	1	yes	characteristic
686	#107	C₂²×C₄	1	1	yes	characteristic
687	#107	C₂²×C₄	1	1	yes	characteristic
688	#107	C₂²×C₄	1	1	yes	characteristic
689	#107	C₂²×C₄	1	1	yes	characteristic
690	#106	C₂²×C₄	1	1	yes	characteristic
691	#106	C₂²×C₄	1	1	yes	characteristic
692	#106	C₂²×C₄	1	1	yes	characteristic
693	#106	C₂²×C₄	1	1	yes	characteristic
694	#106	C₂²×C₄	1	1	yes	characteristic
695	#106	C₂²×C₄	1	1	yes	characteristic
696	#106	C₂²×C₄	1	1	yes	characteristic
697	#106	C₂²×C₄	1	1	yes	characteristic
698	C₄⋊C₈	—	2	2	no	—
699	C₄⋊C₈	—	2	2	no	—
700	C₄⋊C₈	—	2	2	no	—
701	C₄⋊C₈	—	2	2	no	—
702	C₄⋊C₈	—	2	2	no	—
703	C₄⋊C₈	—	2	2	no	—
704	C₄⋊C₈	—	2	2	no	—
705	C₄⋊C₈	—	2	2	no	—
706	C₄⋊C₈	—	2	2	no	—
707	C₄⋊C₈	—	2	2	no	—
708	C₄⋊C₈	—	2	1	no	—
709	C₄⋊C₈	—	2	1	no	—
710	C₄⋊C₈	—	2	2	no	—
711	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
712	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
713	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
714	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
715	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
716	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
717	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
718	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
719	C₄⋊C₈	C₂×D₄	1	2	yes	—
720	C₄⋊C₈	C₂×D₄	1	2	yes	—
721	C₄⋊C₈	C₂×D₄	1	2	yes	—
722	C₄⋊C₈	C₂×D₄	1	2	yes	—
723	C₄⋊C₈	C₂⁴	1	2	yes	—
724	C₄⋊C₈	C₂⁴	1	2	yes	—
725	C₄⋊C₈	C₂⁴	1	2	yes	—
726	C₄⋊C₈	C₂⁴	1	2	yes	—
727	#103	C₂²×C₄	1	1	yes	characteristic
728	#103	C₂²×C₄	1	1	yes	characteristic
729	#103	C₂²×C₄	1	1	yes	characteristic
730	#103	C₂²×C₄	1	1	yes	characteristic
731	#103	C₂²×C₄	1	1	yes	characteristic
732	#103	C₂²×C₄	1	1	yes	characteristic
733	#103	C₂²×C₄	1	1	yes	characteristic
734	#103	C₂²×C₄	1	1	yes	characteristic
735	#103	C₂²×C₄	1	1	yes	characteristic
736	#103	C₂²×C₄	1	1	yes	characteristic
737	#103	C₂²×C₄	1	1	yes	characteristic
738	#103	C₂²×C₄	1	1	yes	characteristic
739	#103	C₂²×C₄	1	1	yes	characteristic
740	#103	C₂²×C₄	1	1	yes	characteristic
741	#103	C₂²×C₄	1	1	yes	characteristic
742	#103	C₂²×C₄	1	1	yes	characteristic
743	#102	C₂²×C₄	1	1	yes	characteristic
744	#102	C₂²×C₄	1	1	yes	characteristic
745	#102	C₂²×C₄	1	1	yes	characteristic
746	#102	C₂²×C₄	1	1	yes	characteristic
747	#102	C₂²×C₄	1	1	yes	characteristic
748	#102	C₂²×C₄	1	1	yes	characteristic
749	#102	C₂²×C₄	1	1	yes	characteristic
750	#102	C₂²×C₄	1	1	yes	characteristic
751	#102	C₂²×C₄	1	1	yes	characteristic
752	#102	C₂²×C₄	1	1	yes	characteristic
753	#102	C₂²×C₄	1	1	yes	characteristic
754	#102	C₂²×C₄	1	1	yes	characteristic
755	#102	C₂²×C₄	1	1	yes	characteristic
756	#102	C₂²×C₄	1	1	yes	characteristic
757	#102	C₂²×C₄	1	1	yes	characteristic
758	#102	C₂²×C₄	1	1	yes	characteristic
759	C₂²⋊C₈	—	2	2	no	—
760	C₂²⋊C₈	—	2	1	no	—
761	C₂²⋊C₈	—	2	1	no	—
762	C₂²⋊C₈	—	2	2	no	—
763	C₂²⋊C₈	—	2	1	no	—
764	C₂²⋊C₈	—	2	1	no	—
765	C₂²⋊C₈	—	2	2	no	—
766	C₂²⋊C₈	—	2	1	no	—
767	C₂²⋊C₈	—	2	1	no	—
768	C₂²⋊C₈	—	2	2	no	—
769	C₂²⋊C₈	—	2	2	no	—
770	C₂²⋊C₈	—	2	2	no	—
771	C₂²⋊C₈	—	2	2	no	—
772	C₂²⋊C₈	—	2	2	no	—
773	C₂²⋊C₈	—	2	2	no	—
774	C₂²⋊C₈	—	2	2	no	—
775	C₂²⋊C₈	—	2	2	no	—
776	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
777	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
778	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
779	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
780	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
781	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
782	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
783	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
784	C₂²⋊C₈	C₂×D₄	1	2	yes	—
785	C₂²⋊C₈	C₂×D₄	1	2	yes	—
786	C₂²⋊C₈	C₂×D₄	1	2	yes	—
787	C₂²⋊C₈	C₂×D₄	1	2	yes	—
788	#97	—	2	2	no	—
789	#97	—	2	2	no	—
790	#97	—	2	2	no	—
791	#97	—	2	2	no	—
792	#97	—	2	1	no	—
793	#97	—	2	1	no	—
794	#97	—	2	1	no	—
795	#97	—	2	2	no	—
796	#97	—	2	1	no	—
797	#97	—	2	2	no	—
798	#97	C₂×D₄	1	1	yes	characteristic
799	#97	C₂×D₄	1	1	yes	characteristic
800	#97	C₂×D₄	1	1	yes	characteristic
801	#97	C₂×D₄	1	1	yes	characteristic
802	C₄×C₈	—	2	2	no	—
803	C₄×C₈	—	2	2	no	—
804	C₄×C₈	—	2	2	no	—
805	C₄×C₈	—	2	2	no	—
806	C₄×C₈	—	2	2	no	—
807	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
808	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
809	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
810	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
811	C₄×C₈	C₂⁴	1	2	yes	—
812	C₄×C₈	C₂⁴	1	2	yes	—
813	C₄×C₈	C₂⁴	1	1	yes	characteristic
814	C₄×C₈	C₂⁴	1	1	yes	characteristic
815	C₄×C₈	C₂⁴	1	1	yes	characteristic
816	C₄×C₈	C₂⁴	1	1	yes	characteristic
817	C₄×C₈	C₂⁴	1	2	yes	—
818	C₄×C₈	C₂⁴	1	2	yes	—
819	C₂⁴	—	2	1	no	—
820	C₂⁴	C₄×D₄	1	1	yes	characteristic
821	#41	—	2	2	no	—
822	#41	—	2	2	no	—
823	#41	—	2	2	no	—
824	#41	—	2	2	no	—
825	#41	—	4	1	no	—
826	#41	—	4	1	no	—
827	#41	—	4	1	no	—
828	#41	—	4	1	no	—
829	#41	—	4	4	no	—
830	#41	—	4	1	no	—
831	#41	—	4	1	no	—
832	#41	—	4	1	no	—
833	#41	—	4	1	no	—
834	#41	—	4	4	no	—
835	#41	—	8	2	no	—
836	#41	—	8	2	no	—
837	C₂×Q₈	—	2	1	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	2	no	—
841	C₂×Q₈	—	4	1	no	—
842	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
843	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
844	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
845	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	1	no	—
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	—	2	1	no	—
855	C₂×D₄	—	2	1	no	—
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	2	1	no	—
858	C₂×D₄	—	2	1	no	—
859	C₂×D₄	—	2	1	no	—
860	C₂×D₄	—	4	1	no	—
861	C₂×D₄	—	4	4	no	—
862	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
863	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
864	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
865	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	1	no	—
887	C₂²×C₄	—	4	1	no	—
888	C₂²×C₄	—	4	1	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	—	4	4	no	—
891	C₂²×C₄	—	8	2	no	—
892	C₂²×C₄	—	8	1	no	—
893	C₂²×C₄	—	8	2	no	—
894	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
896	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
898	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
899	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
900	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
901	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
902	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
903	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
904	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
905	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
906	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
907	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
908	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
909	C₂²×C₄	C₂×#41	1	1	yes	characteristic
910	C₂²×C₄	C₂×#41	1	1	yes	characteristic
911	C₂²×C₄	C₂×#41	1	1	yes	characteristic
912	Q₁₆	—	2	2	no	—
913	Q₁₆	—	2	2	no	—
914	Q₁₆	—	4	1	no	—
915	Q₁₆	—	4	1	no	—
916	SD₁₆	—	2	2	no	—
917	SD₁₆	—	2	2	no	—
918	SD₁₆	—	2	2	no	—
919	SD₁₆	—	2	2	no	—
920	SD₁₆	—	4	1	no	—
921	SD₁₆	—	4	1	no	—
922	SD₁₆	—	4	1	no	—
923	SD₁₆	—	4	1	no	—
924	D₈	—	2	2	no	—
925	D₈	—	2	2	no	—
926	D₈	—	4	1	no	—
927	D₈	—	4	1	no	—
928	M₁₆	—	4	2	no	—
929	M₁₆	—	4	2	no	—
930	M₁₆	—	8	2	no	—
931	M₁₆	—	8	2	no	—
932	M₁₆	—	8	2	no	—
933	M₁₆	—	8	2	no	—
934	M₁₆	—	8	2	no	—
935	M₁₆	—	8	2	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	2	2	no	—
938	C₂×C₈	—	2	2	no	—
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	2	2	no	—
941	C₂×C₈	—	2	2	no	—
942	C₂×C₈	—	4	1	no	—
943	C₂×C₈	—	4	1	no	—
944	C₂×C₈	—	4	1	no	—
945	C₂×C₈	—	4	1	no	—
946	C₂×C₈	—	8	2	no	—
947	C₂×C₈	—	8	2	no	—
948	C₂×C₈	—	8	2	no	—
949	C₂×C₈	—	8	2	no	—
950	C₂×C₈	—	8	2	no	—
951	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
952	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
953	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
954	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
955	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
956	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
957	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
958	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
959	C₂×C₈	C₂²×D₄	1	2	yes	—
960	C₂×C₈	C₂²×D₄	1	2	yes	—
961	C₂×C₈	C₂²×D₄	1	2	yes	—
962	C₂×C₈	C₂²×D₄	1	2	yes	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
990	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
991	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
992	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
993	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
995	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
996	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	C₄×D₄	1	1	yes	characteristic
1046	C₄²	C₄×D₄	1	1	yes	characteristic
1047	C₄²	C₄×D₄	1	1	yes	characteristic
1048	C₄²	C₄×D₄	1	1	yes	characteristic
1049	C₄²	C₄×D₄	1	1	yes	characteristic
1050	C₄²	C₄×D₄	1	1	yes	characteristic
1051	C₄²	C₂³×C₄	1	1	yes	characteristic
1052	C₄²	C₂³×C₄	1	1	yes	characteristic
1053	C₄²	C₂³×C₄	1	1	yes	characteristic
1054	C₄²	C₂²×D₄	1	1	yes	characteristic
1055	C₄²	C₂²×D₄	1	1	yes	characteristic
1056	C₄²	C₂²×D₄	1	1	yes	characteristic
1057	C₄²	C₂×#41	1	1	yes	characteristic
1058	C₄²	C₂×#41	1	1	yes	characteristic
1059	C₄²	C₂×#41	1	1	yes	characteristic
1060	C₄²	C₂⁵	1	1	yes	characteristic
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	4	1	no	—
1066	C₂³	—	4	1	no	—
1067	C₂³	—	4	1	no	—
1068	C₂³	—	4	2	no	—
1069	C₂³	—	4	2	no	—
1070	C₂³	—	8	1	no	—
1071	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1072	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1073	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1074	Q₈	—	2	1	no	—
1075	Q₈	—	2	1	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	2	1	no	—
1080	Q₈	—	2	1	no	—
1081	Q₈	—	4	2	no	—
1082	Q₈	—	4	2	no	—
1083	Q₈	—	8	1	no	—
1084	Q₈	#568	1	2	yes	—
1085	D₄	—	2	4	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	1	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	8	1	no	—
1099	D₄	—	8	1	no	—
1100	D₄	—	8	1	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	1	no	—
1104	D₄	—	8	1	no	—
1105	D₄	#568	1	2	yes	—
1106	C₂×C₄	—	2	4	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	4	2	no	—
1144	C₂×C₄	—	4	2	no	—
1145	C₂×C₄	—	4	2	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	4	2	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	8	1	no	—
1150	C₂×C₄	—	8	1	no	—
1151	C₂×C₄	—	8	1	no	—
1152	C₂×C₄	—	8	1	no	—
1153	C₂×C₄	—	8	1	no	—
1154	C₂×C₄	—	8	1	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	—	8	1	no	—
1160	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1161	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1162	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1163	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1164	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1165	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1166	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1167	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1168	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1169	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1170	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1171	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1172	C₈	—	2	2	no	—
1173	C₈	—	2	2	no	—
1174	C₈	—	2	2	no	—
1175	C₈	—	2	2	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	1	no	—
1178	C₈	—	2	1	no	—
1179	C₈	—	2	1	no	—
1180	C₈	—	2	1	no	—
1181	C₈	—	2	1	no	—
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	4	2	no	—
1185	C₈	—	4	2	no	—
1186	C₈	—	4	2	no	—
1187	C₈	—	4	2	no	—
1188	C₈	—	4	2	no	—
1189	C₈	—	4	2	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	1	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	8	2	no	—
1212	C₂²	—	8	4	no	—
1213	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1214	C₄	—	2	1	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	2	1	no	—
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	2	2	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	C₂×#568	1	1	yes	characteristic
1237	C₄	C₂×#568	1	1	yes	characteristic
1238	C₄	#3584	1	2	yes	—
1239	C₂	—	4	1	no	—
1240	C₂	—	4	1	no	—
1241	C₂	—	4	1	no	—
1242	C₂	—	4	2	no	—
1243	C₂	—	8	1	no	—
1244	C₂	—	8	1	no	—
1245	C₂	—	8	1	no	—
1246	C₂	#60141	1	1	yes	characteristic
1247	C₂	#60167	1	1	yes	characteristic
1248	C₂	#60182	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₄²	C₂⁵
socle	C₂²	C₂²×C₄×D₄
prime radical	#60536	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #2920 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #60287	C₂	semidirect
3. #60283	C₂	semidirect
4. #18045	C₂	semidirect
5. #18043	C₂	semidirect
6. #18041	C₂	semidirect
7. #18041	C₂	semidirect
8. #18039	C₂	semidirect
9. #18037	C₂	semidirect
10. #18037	C₂	semidirect
11. #18035	C₂	semidirect
12. #18032	C₂	semidirect
13. #18030	C₂	semidirect
14. #18028	C₂	semidirect
15. #18026	C₂	semidirect
16. #17955	C₂	semidirect
17. #17954	C₂	semidirect
18. #17927	C₂	semidirect
19. #17926	C₂	semidirect
20. #17816	C₂	semidirect
21. #17494	C₂	semidirect
22. #17450	C₂	semidirect
23. #17324	C₂	semidirect
51. #2993	C₂²	semidirect
52. #2993	C₂²	semidirect
65. #2971	C₂²	semidirect
66. #2971	C₂²	semidirect
72. #2970	C₂²	semidirect
73. #2970	C₂²	semidirect
87. #1594	C₂²	semidirect
88. #1593	C₂²	semidirect
89. #1592	C₂²	semidirect
90. #1592	C₂²	semidirect
91. #1591	C₂²	semidirect
92. #1590	C₂²	semidirect
93. #1590	C₂²	semidirect
94. #1589	C₂²	semidirect
95. #1588	C₂²	semidirect
96. #1588	C₂²	semidirect
97. #1587	C₂²	semidirect
98. #1587	C₂²	semidirect
99. #1586	C₂²	semidirect
100. #1586	C₂²	semidirect
101. #1585	C₂²	semidirect
102. #1585	C₂²	semidirect
103. #1584	C₂²	semidirect
104. #1584	C₂²	semidirect
105. #1583	C₂²	semidirect
106. #1583	C₂²	semidirect
107. #1582	C₂²	semidirect
108. #1582	C₂²	semidirect
109. #1581	C₂²	semidirect
110. #1581	C₂²	semidirect
111. #1580	C₂²	semidirect
112. #1579	C₂²	semidirect
113. SD₁₆⋊C₈	C₂²	semidirect
114. SD₁₆⋊C₈	C₂²	semidirect
115. C₈×Q₁₆	C₂²	semidirect
116. C₈×SD₁₆	C₂²	semidirect
117. C₈×SD₁₆	C₂²	semidirect
118. C₈×D₈	C₂²	semidirect
121. #1571	C₂²	semidirect
122. #1570	C₂²	semidirect
123. #1568	C₂²	semidirect
124. #1568	C₂²	semidirect
125. #1568	C₂²	semidirect
126. #1568	C₂²	semidirect
135. #1488	C₂²	semidirect
136. #1488	C₂²	semidirect
137. #1488	C₂²	semidirect
138. #1488	C₂²	semidirect
139. #1483	C₂²	semidirect
140. #1483	C₂²	semidirect
145. #1453	C₂²	semidirect
146. #1453	C₂²	semidirect
147. #1451	C₂²	semidirect
148. #1451	C₂²	semidirect
149. C₈×M₁₆	C₂²	semidirect
150. C₈×M₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#60536	2
#60287	2
#60283	2
#18045	2
#18043	2
#18041	2
#18039	2
#18037	2
#18035	2
#18032	2
#18030	2
#18028	2
#18026	2
#17955	2
#17954	2
#17927	2
#17926	2
#17816	2
#17494	2
#17450	2
#17324	2