Subgroups — #8094441

Order 512.

6220 conjugacy classes of subgroups.

The subgroup lattice has 715 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#53018	C₂	1	8	yes	maximal, complemented
2	#52977	C₂	1	8	yes	maximal, complemented
3	#52339	C₂	1	8	yes	maximal, complemented
4	#45697	C₂	1	8	yes	maximal, complemented
5	#45647	C₂	1	8	yes	maximal, complemented
6	#45457	C₂	1	8	yes	maximal, complemented
7	#35677	C₂	1	2	yes	maximal, complemented
8	#35672	C₂	1	1	yes	maximal, characteristic, complemented
9	#35634	C₂	1	1	yes	maximal, characteristic, complemented
10	#35558	C₂	1	2	yes	maximal, complemented
11	#35327	C₂	1	2	yes	maximal, complemented
12	#35256	C₂	1	2	yes	maximal, complemented
13	#35222	C₂	1	2	yes	maximal, complemented
14	#34742	C₂	1	2	yes	maximal, complemented
15	C₂×#2435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×D₄	C₂²	1	1	yes	characteristic
17	C₂×#537	C₂²	1	1	yes	characteristic, complemented
18	C₂×#536	C₂²	1	2	yes	complemented
19	C₂×#535	C₂²	1	2	yes	—
20	C₂×#535	C₂²	1	2	yes	—
21	C₂²×#124	C₂²	1	2	yes	—
22	C₂×#525	C₂²	1	2	yes	—
23	C₂²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×#519	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×#41	C₂²	1	2	yes	complemented
26	#2856	C₂²	1	4	yes	complemented
27	#2850	C₂²	1	8	yes	complemented
28	#2850	C₂²	1	4	yes	complemented
29	#2846	C₂²	1	8	yes	—
30	#2842	C₂²	1	8	yes	complemented
31	#2829	C₂²	1	16	yes	complemented
32	#2829	C₂²	1	16	yes	complemented
33	#2828	C₂²	1	8	yes	complemented
34	#2826	C₂²	1	16	yes	complemented
35	#2823	C₂²	1	8	yes	complemented
36	#2812	C₂²	1	8	yes	complemented
37	#2795	C₂²	1	16	yes	complemented
38	#2795	C₂²	1	8	yes	complemented
39	#2752	C₂²	1	16	yes	complemented
40	#2735	C₂²	1	16	yes	complemented
41	#2735	C₂²	1	8	yes	complemented
42	#2714	C₂²	1	16	yes	complemented
43	#2699	C₂²	1	8	yes	complemented
44	#2697	C₂²	1	16	yes	complemented
45	#2685	C₂²	1	16	yes	complemented
46	#2685	C₂²	1	16	yes	complemented
47	#2678	C₂²	1	16	yes	complemented
48	#2668	C₂²	1	8	yes	complemented
49	#2620	C₂²	1	4	yes	complemented
50	#2620	C₂²	1	8	yes	complemented
51	#2619	C₂²	1	4	yes	complemented
52	#2613	C₂²	1	8	yes	—
53	#2548	C₂²	1	4	yes	complemented
54	#2548	C₂²	1	4	yes	complemented
55	#2545	C₂²	1	4	yes	complemented
56	#2545	C₂²	1	8	yes	complemented
57	#2545	C₂²	1	4	yes	complemented
58	#2544	C₂²	1	8	yes	complemented
59	#2542	C₂²	1	8	yes	complemented
60	#2540	C₂²	1	8	yes	complemented
61	#2539	C₂²	1	4	yes	—
62	#2534	C₂²	1	16	yes	complemented
63	#2513	C₂²	1	8	yes	complemented
64	#2513	C₂²	1	8	yes	complemented
65	#2512	C₂²	1	8	yes	complemented
66	#2512	C₂²	1	8	yes	complemented
67	#2501	C₂²	1	4	yes	complemented
68	#2484	C₂²	1	4	yes	complemented
69	#2482	C₂²	1	4	yes	—
70	#2480	C₂²	1	16	yes	complemented
71	#2435	C₂²	1	8	yes	—
72	#2435	C₂²	1	8	yes	—
73	#2435	C₂²	1	8	yes	—
74	#2433	C₂²	1	8	yes	—
75	#2428	C₂²	1	8	yes	complemented
76	#2426	C₂²	1	8	yes	complemented
77	#2426	C₂²	1	8	yes	complemented
78	#2426	C₂²	1	8	yes	complemented
79	#2424	C₂²	1	16	yes	complemented
80	#2423	C₂²	1	4	yes	complemented
81	#2423	C₂²	1	8	yes	complemented
82	#2422	C₂²	1	4	yes	complemented
83	#2421	C₂²	1	8	yes	complemented
84	#2421	C₂²	1	4	yes	complemented
85	#2420	C₂²	1	4	yes	complemented
86	#2419	C₂²	1	8	yes	complemented
87	#2418	C₂²	1	8	yes	—
88	#2411	C₂²	1	16	yes	complemented
89	#2408	C₂²	1	8	yes	—
90	#2408	C₂²	1	8	yes	—
91	#2395	C₂²	1	8	yes	complemented
92	C₂×#394	C₂²	1	4	yes	—
93	#2375	C₂²	1	16	yes	complemented
94	#2317	C₂²	1	2	yes	complemented
95	#2310	C₂²	1	1	yes	characteristic, complemented
96	#2309	C₂²	1	2	yes	—
97	#2309	C₂²	1	2	yes	—
98	C₄×#123	C₂²	1	8	yes	complemented
99	#2297	C₂²	1	2	yes	complemented
100	#2296	C₂²	1	2	yes	complemented
101	C₂×#390	C₂²	1	2	yes	—
102	#2285	C₂²	1	2	yes	complemented
103	#2280	C₂²	1	2	yes	—
104	C₂×#379	C₂²	1	4	yes	—
105	#2274	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
107	C₂⁶	C₂³	1	2	yes	—
108	C₂²×#41	C₂³	1	2	yes	—
109	C₂³×Q₈	C₂³	1	1	yes	characteristic
110	C₂³×D₄	—	4	4	no	—
111	C₂³×D₄	—	4	8	no	—
112	C₂³×D₄	C₂³	1	2	yes	—
113	C₂³×D₄	C₂³	1	2	yes	—
114	C₂³×D₄	C₂³	1	8	yes	—
115	C₂⁴×C₄	C₂³	1	1	yes	characteristic
116	#537	—	4	4	no	—
117	#536	—	4	8	no	—
118	#535	—	4	8	no	—
119	#535	—	4	8	no	—
120	C₂×C₄⋊Q₈	C₂³	1	4	yes	complemented
121	C₂×#127	C₂³	1	4	yes	—
122	C₂×#127	C₂³	1	4	yes	—
123	C₂×#126	C₂³	1	16	yes	complemented
124	C₂×#124	—	4	8	no	—
125	C₂×#124	C₂³	1	4	yes	—
126	C₂×#124	C₂³	1	4	yes	—
127	C₂×#124	C₂³	1	4	yes	—
128	C₂×#124	C₂³	1	8	yes	—
129	C₂×#124	C₂³	1	4	yes	—
130	C₂×#124	C₂³	1	4	yes	complemented
131	#525	—	4	8	no	—
132	C₂×#123	C₂³	1	4	yes	—
133	C₂×#123	C₂³	1	8	yes	—
134	C₂×#123	C₂³	1	8	yes	—
135	C₂×C₂²⋊Q₈	—	4	4	no	—
136	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
137	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₂×C₂²⋊Q₈	C₂³	1	8	yes	complemented
139	C₂×C₂²⋊Q₈	C₂³	1	4	yes	complemented
140	C₂×#121	C₂³	1	4	yes	—
141	C₂×#121	C₂³	1	8	yes	—
142	C₂×#121	C₂³	1	4	yes	—
143	C₂×#121	C₂³	1	4	yes	—
144	C₂×#121	C₂³	1	4	yes	—
145	C₂×#121	C₂³	1	4	yes	complemented
146	C₂×#121	C₂³	1	16	yes	complemented
147	C₂×#120	C₂³	1	4	yes	—
148	C₂×#120	C₂³	1	8	yes	—
149	C₂×#120	C₂³	1	8	yes	—
150	C₂×#120	C₂³	1	16	yes	—
151	C₂×#120	C₂³	1	16	yes	—
152	#519	—	4	4	no	—
153	C₄×#41	—	4	8	no	—
154	C₂×C₄×Q₈	C₂³	1	4	yes	complemented
155	C₂×C₄×Q₈	C₂³	1	4	yes	complemented
156	C₂×C₄×Q₈	C₂³	1	4	yes	complemented
157	C₂×C₄×D₄	C₂³	1	8	yes	—
158	C₂×C₄×D₄	C₂³	1	8	yes	—
159	C₂×C₄×D₄	C₂³	1	4	yes	complemented
160	C₂×#117	C₂³	1	2	yes	—
161	C₂×#117	C₂³	1	2	yes	—
162	C₂×#117	C₂³	1	2	yes	—
163	C₂×#117	C₂³	1	4	yes	—
164	C₂×#117	C₂³	1	4	yes	complemented
165	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
168	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
171	C₂²×C₄²	C₂³	1	2	yes	—
172	C₂²×C₄²	C₂³	1	4	yes	complemented
173	#400	C₂³	1	8	yes	complemented
174	#400	C₂³	1	8	yes	complemented
175	#399	C₂³	1	8	yes	—
176	#399	C₂³	1	8	yes	—
177	#399	C₂³	1	8	yes	—
178	#399	C₂³	1	16	yes	complemented
179	#398	C₂³	1	8	yes	complemented
180	#398	C₂³	1	8	yes	complemented
181	#397	C₂³	1	8	yes	—
182	#397	C₂³	1	8	yes	—
183	#397	C₂³	1	16	yes	complemented
184	#397	C₂³	1	16	yes	complemented
185	#397	C₂³	1	8	yes	complemented
186	#397	C₂³	1	8	yes	complemented
187	#397	C₂³	1	16	yes	complemented
188	#396	C₂³	1	16	yes	complemented
189	#396	C₂³	1	16	yes	complemented
190	#396	C₂³	1	16	yes	complemented
191	#396	C₂³	1	16	yes	complemented
192	#396	C₂³	1	16	yes	complemented
193	#396	C₂³	1	16	yes	complemented
194	#394	C₂³	1	8	yes	—
195	#394	C₂³	1	16	yes	—
196	#394	C₂³	1	16	yes	—
197	#394	C₂³	1	16	yes	—
198	#394	C₂³	1	8	yes	—
199	#394	C₂³	1	8	yes	—
200	#394	C₂³	1	8	yes	—
201	#394	C₂³	1	16	yes	complemented
202	#394	C₂³	1	16	yes	complemented
203	#394	C₂³	1	16	yes	complemented
204	#394	C₂³	1	16	yes	complemented
205	#394	C₂³	1	16	yes	complemented
206	#394	C₂³	1	16	yes	complemented
207	#392	C₂³	1	16	yes	—
208	#392	C₂³	1	16	yes	—
209	#392	C₂³	1	8	yes	—
210	#392	C₂³	1	16	yes	complemented
211	#391	C₂³	1	8	yes	complemented
212	#391	C₂³	1	2	yes	complemented
213	#391	C₂³	1	2	yes	complemented
214	#390	C₂³	1	8	yes	—
215	#390	C₂³	1	4	yes	—
216	#390	C₂³	1	8	yes	—
217	#390	C₂³	1	4	yes	—
218	#390	C₂³	1	8	yes	—
219	#390	C₂³	1	4	yes	—
220	#390	C₂³	1	4	yes	—
221	#390	C₂³	1	16	yes	—
222	#390	C₂³	1	8	yes	—
223	#390	C₂³	1	8	yes	complemented
224	#390	C₂³	1	16	yes	complemented
225	#390	C₂³	1	16	yes	complemented
226	#390	C₂³	1	2	yes	complemented
227	#390	C₂³	1	2	yes	complemented
228	#390	C₂³	1	16	yes	complemented
229	#389	C₂³	1	8	yes	complemented
230	#389	C₂³	1	4	yes	complemented
231	#389	C₂³	1	4	yes	complemented
232	#388	C₂³	1	8	yes	—
233	#388	C₂³	1	16	yes	—
234	#388	C₂³	1	8	yes	—
235	#388	C₂³	1	16	yes	complemented
236	#388	C₂³	1	16	yes	complemented
237	#388	C₂³	1	16	yes	complemented
238	#388	C₂³	1	16	yes	complemented
239	#388	C₂³	1	16	yes	complemented
240	#388	C₂³	1	16	yes	complemented
241	#388	C₂³	1	16	yes	complemented
242	#388	C₂³	1	16	yes	complemented
243	#387	C₂³	1	8	yes	complemented
244	#387	C₂³	1	16	yes	complemented
245	#387	C₂³	1	8	yes	complemented
246	#386	C₂³	1	8	yes	—
247	#386	C₂³	1	8	yes	—
248	#386	C₂³	1	16	yes	complemented
249	#386	C₂³	1	16	yes	complemented
250	#386	C₂³	1	16	yes	complemented
251	#385	C₂³	1	8	yes	—
252	#385	C₂³	1	8	yes	—
253	#385	C₂³	1	8	yes	complemented
254	#384	C₂³	1	8	yes	complemented
255	#384	C₂³	1	4	yes	complemented
256	#384	C₂³	1	4	yes	complemented
257	#382	C₂³	1	4	yes	complemented
258	#382	C₂³	1	4	yes	complemented
259	#381	C₂³	1	4	yes	—
260	#381	C₂³	1	4	yes	—
261	#381	C₂³	1	8	yes	complemented
262	#380	C₂³	1	4	yes	—
263	#380	C₂³	1	4	yes	—
264	#380	C₂³	1	8	yes	—
265	#379	C₂³	1	8	yes	—
266	#379	C₂³	1	8	yes	—
267	#379	C₂³	1	16	yes	—
268	#379	C₂³	1	8	yes	—
269	#379	C₂³	1	4	yes	—
270	#379	C₂³	1	16	yes	—
271	#379	C₂³	1	8	yes	—
272	#379	C₂³	1	16	yes	—
273	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
274	C₄×C₄⋊C₄	C₂³	1	8	yes	complemented
275	C₄×C₄⋊C₄	C₂³	1	8	yes	complemented
276	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
277	C₄×C₂²⋊C₄	C₂³	1	4	yes	—
278	C₄×C₂²⋊C₄	C₂³	1	8	yes	—
279	C₄×C₂²⋊C₄	C₂³	1	4	yes	—
280	C₄×C₂²⋊C₄	C₂³	1	4	yes	—
281	C₄×C₂²⋊C₄	C₂³	1	8	yes	complemented
282	C₂×#95	C₂³	1	2	yes	—
283	C₂⁵	—	4	4	no	—
284	C₂⁵	—	4	8	no	—
285	C₂⁵	—	4	8	no	—
286	C₂⁵	—	8	4	no	—
287	C₂⁵	C₂⁴	1	1	yes	characteristic
288	C₂⁵	C₂⁴	1	4	yes	—
289	C₂⁵	C₂⁴	1	8	yes	—
290	C₂×#41	—	2	8	no	—
291	C₂×#41	—	2	8	no	—
292	C₂×#41	—	2	8	no	—
293	C₂²×Q₈	—	2	4	no	—
294	C₂²×Q₈	—	2	8	no	—
295	C₂²×Q₈	C₂⁴	1	4	yes	—
296	C₂²×Q₈	C₂⁴	1	2	yes	—
297	C₂²×D₄	—	2	8	no	—
298	C₂²×D₄	—	2	8	no	—
299	C₂²×D₄	—	2	8	no	—
300	C₂²×D₄	—	4	16	no	—
301	C₂²×D₄	—	4	16	no	—
302	C₂²×D₄	—	4	16	no	—
303	C₂²×D₄	—	4	4	no	—
304	C₂²×D₄	—	4	8	no	—
305	C₂²×D₄	—	4	64	no	—
306	C₂²×D₄	C₂⁴	1	4	yes	—
307	C₂²×D₄	C₂⁴	1	2	yes	—
308	C₂²×D₄	C₂⁴	1	4	yes	—
309	C₂²×D₄	C₂⁴	1	4	yes	—
310	C₂²×D₄	C₂⁴	1	8	yes	—
311	C₂²×D₄	C₂⁴	1	8	yes	—
312	C₂²×D₄	C₂⁴	1	16	yes	—
313	C₂²×D₄	C₂⁴	1	8	yes	—
314	C₂²×D₄	C₂⁴	1	4	yes	—
315	C₂²×D₄	C₂⁴	1	8	yes	—
316	C₂³×C₄	—	2	4	no	—
317	C₂³×C₄	—	2	8	no	—
318	C₂³×C₄	C₂⁴	1	2	yes	—
319	C₂³×C₄	C₂⁴	1	1	yes	characteristic
320	C₂³×C₄	C₂⁴	1	4	yes	—
321	C₂³×C₄	C₂⁴	1	4	yes	—
322	C₂³×C₄	C₂⁴	1	2	yes	—
323	C₂³×C₄	C₂⁴	1	4	yes	—
324	C₂³×C₄	C₂⁴	1	8	yes	—
325	C₂³×C₄	C₂⁴	1	1	yes	characteristic
326	C₄⋊Q₈	—	4	8	no	—
327	#127	—	4	8	no	—
328	#127	—	4	8	no	—
329	#126	—	8	16	no	—
330	#124	—	4	8	no	—
331	#124	—	4	8	no	—
332	#124	—	4	16	no	—
333	#124	—	4	8	no	—
334	#124	—	4	8	no	—
335	#124	—	4	8	no	—
336	#123	—	4	16	no	—
337	#123	—	4	8	no	—
338	#123	—	4	16	no	—
339	C₂²⋊Q₈	—	4	16	no	—
340	C₂²⋊Q₈	—	4	8	no	—
341	C₂²⋊Q₈	—	4	16	no	—
342	C₂²⋊Q₈	—	4	8	no	—
343	#121	—	4	8	no	—
344	#121	—	4	16	no	—
345	#121	—	4	8	no	—
346	#121	—	4	8	no	—
347	#121	—	4	8	no	—
348	#121	—	4	8	no	—
349	#121	—	8	16	no	—
350	#120	—	4	32	no	—
351	#120	—	4	8	no	—
352	#120	—	4	16	no	—
353	#120	—	4	16	no	—
354	#120	—	8	16	no	—
355	C₄×Q₈	—	4	8	no	—
356	C₄×Q₈	—	4	8	no	—
357	C₄×Q₈	—	4	8	no	—
358	C₄×D₄	—	4	8	no	—
359	C₄×D₄	—	4	16	no	—
360	C₄×D₄	—	4	16	no	—
361	#117	—	2	8	no	—
362	#117	—	2	8	no	—
363	#117	—	2	8	no	—
364	#117	—	4	8	no	—
365	#117	—	4	8	no	—
366	C₂×C₄⋊C₄	—	2	4	no	—
367	C₂×C₄⋊C₄	—	4	4	no	—
368	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
369	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
370	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
371	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
372	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
373	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
374	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
375	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
376	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
377	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
378	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
379	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
380	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
381	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
382	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
383	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
384	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
385	C₂×C₂²⋊C₄	—	4	4	no	—
386	C₂×C₂²⋊C₄	—	4	4	no	—
387	C₂×C₂²⋊C₄	—	4	16	no	—
388	C₂×C₂²⋊C₄	—	8	8	no	—
389	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
394	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
395	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
397	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
398	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
399	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
402	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
403	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
404	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
405	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
406	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
407	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
408	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
409	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
410	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
411	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
412	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
413	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
414	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
415	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
416	C₂×C₄²	—	2	8	no	—
417	C₂×C₄²	—	4	8	no	—
418	C₂×C₄²	C₂⁴	1	4	yes	—
419	C₂×C₄²	C₂⁴	1	4	yes	—
420	C₂×C₄²	C₂⁴	1	4	yes	—
421	C₂×C₄²	C₂⁴	1	2	yes	—
422	C₂×C₄²	C₂⁴	1	4	yes	—
423	C₂×C₄²	C₂⁴	1	2	yes	—
424	C₂×C₄²	C₂⁴	1	8	yes	—
425	C₂×C₄²	C₂⁴	1	8	yes	—
426	C₂×C₄²	C₂⁴	1	8	yes	—
427	#95	C₂⁴	1	2	yes	—
428	#95	C₂⁴	1	4	yes	—
429	#95	C₂⁴	1	2	yes	—
430	#95	C₂⁴	1	8	yes	—
431	#95	C₂⁴	1	8	yes	—
432	#95	C₂⁴	1	8	yes	—
433	#95	C₂⁴	1	8	yes	—
434	#95	C₂⁴	1	8	yes	—
435	#95	C₂⁴	1	8	yes	—
436	#95	C₂⁴	1	8	yes	—
437	#95	C₂⁴	1	8	yes	—
438	#95	C₂⁴	1	8	yes	—
439	#95	C₂⁴	1	8	yes	—
440	#95	C₂⁴	1	8	yes	—
441	#95	C₂⁴	1	16	yes	—
442	C₂⁴	—	2	2	no	—
443	C₂⁴	—	2	4	no	—
444	C₂⁴	—	2	8	no	—
445	C₂⁴	—	2	4	no	—
446	C₂⁴	—	2	8	no	—
447	C₂⁴	—	2	8	no	—
448	C₂⁴	—	2	16	no	—
449	C₂⁴	—	4	2	no	—
450	C₂⁴	—	4	8	no	—
451	C₂⁴	—	4	8	no	—
452	C₂⁴	—	4	16	no	—
453	C₂⁴	—	4	8	no	—
454	C₂⁴	—	4	16	no	—
455	C₂⁴	—	4	8	no	—
456	C₂⁴	—	4	32	no	—
457	C₂⁴	—	8	16	no	—
458	C₂⁴	—	8	64	no	—
459	C₂⁴	—	8	16	no	—
460	C₂⁴	C₂⁵	1	8	yes	—
461	C₂⁴	C₂⁵	1	4	yes	—
462	C₂⁴	C₂⁵	1	2	yes	—
463	C₂⁴	C₂⁵	1	1	yes	characteristic
464	#41	—	4	32	no	—
465	C₂×Q₈	—	2	8	no	—
466	C₂×Q₈	—	2	4	no	—
467	C₂×Q₈	—	2	8	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×Q₈	—	2	8	no	—
470	C₂×Q₈	—	2	4	no	—
471	C₂×Q₈	—	4	16	no	—
472	C₂×D₄	—	2	8	no	—
473	C₂×D₄	—	2	8	no	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	2	16	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	8	no	—
479	C₂×D₄	—	2	8	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	8	no	—
482	C₂×D₄	—	2	8	no	—
483	C₂×D₄	—	2	8	no	—
484	C₂×D₄	—	2	8	no	—
485	C₂×D₄	—	4	16	no	—
486	C₂×D₄	—	4	8	no	—
487	C₂×D₄	—	4	8	no	—
488	C₂×D₄	—	4	8	no	—
489	C₂×D₄	—	4	8	no	—
490	C₂×D₄	—	4	8	no	—
491	C₂×D₄	—	4	16	no	—
492	C₂×D₄	—	4	16	no	—
493	C₂×D₄	—	4	16	no	—
494	C₂×D₄	—	4	16	no	—
495	C₂×D₄	—	4	16	no	—
496	C₂×D₄	—	4	4	no	—
497	C₂×D₄	—	4	8	no	—
498	C₂×D₄	—	4	32	no	—
499	C₂×D₄	—	4	128	no	—
500	C₂×D₄	—	4	32	no	—
501	C₂²×C₄	—	2	8	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	8	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	8	no	—
508	C₂²×C₄	—	2	8	no	—
509	C₂²×C₄	—	2	8	no	—
510	C₂²×C₄	—	2	8	no	—
511	C₂²×C₄	—	2	8	no	—
512	C₂²×C₄	—	2	8	no	—
513	C₂²×C₄	—	4	8	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	8	no	—
518	C₂²×C₄	—	4	8	no	—
519	C₂²×C₄	—	4	16	no	—
520	C₂²×C₄	H(5,𝔽₂)	1	8	yes	—
521	C₂²×C₄	H(5,𝔽₂)	1	4	yes	—
522	C₂²×C₄	C₂⁵	1	2	yes	—
523	C₂²×C₄	C₂⁵	1	4	yes	—
524	C₂²×C₄	C₂⁵	1	4	yes	—
525	C₂²×C₄	C₂⁵	1	8	yes	—
526	C₂²×C₄	C₂⁵	1	8	yes	—
527	C₂²×C₄	C₂⁵	1	4	yes	—
528	C₂²×C₄	C₂⁵	1	4	yes	—
529	C₂²×C₄	C₂⁵	1	4	yes	—
530	C₂²×C₄	C₂⁵	1	4	yes	—
531	C₂²×C₄	C₂⁵	1	4	yes	—
532	C₂²×C₄	C₂⁵	1	2	yes	—
533	C₄⋊C₄	—	2	8	no	—
534	C₄⋊C₄	—	2	8	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	8	no	—
538	C₄⋊C₄	—	4	8	no	—
539	C₄⋊C₄	—	4	8	no	—
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	—	4	8	no	—
543	C₄⋊C₄	—	4	4	no	—
544	C₄⋊C₄	—	4	16	no	—
545	C₄⋊C₄	—	4	16	no	—
546	C₄⋊C₄	—	4	8	no	—
547	C₄⋊C₄	—	4	8	no	—
548	C₄⋊C₄	—	4	8	no	—
549	C₄⋊C₄	—	4	8	no	—
550	C₂²⋊C₄	—	2	8	no	—
551	C₂²⋊C₄	—	2	8	no	—
552	C₂²⋊C₄	—	2	8	no	—
553	C₂²⋊C₄	—	2	8	no	—
554	C₂²⋊C₄	—	2	16	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	8	no	—
558	C₂²⋊C₄	—	4	16	no	—
559	C₂²⋊C₄	—	4	16	no	—
560	C₂²⋊C₄	—	4	16	no	—
561	C₂²⋊C₄	—	4	16	no	—
562	C₂²⋊C₄	—	4	8	no	—
563	C₂²⋊C₄	—	4	8	no	—
564	C₂²⋊C₄	—	4	8	no	—
565	C₂²⋊C₄	—	4	16	no	—
566	C₂²⋊C₄	—	4	16	no	—
567	C₂²⋊C₄	—	4	8	no	—
568	C₂²⋊C₄	—	4	8	no	—
569	C₂²⋊C₄	—	4	16	no	—
570	C₂²⋊C₄	—	4	8	no	—
571	C₂²⋊C₄	—	4	16	no	—
572	C₂²⋊C₄	—	4	16	no	—
573	C₂²⋊C₄	—	4	8	no	—
574	C₂²⋊C₄	—	4	8	no	—
575	C₂²⋊C₄	—	4	16	no	—
576	C₂²⋊C₄	—	4	8	no	—
577	C₄²	—	2	4	no	—
578	C₄²	—	2	4	no	—
579	C₄²	—	2	8	no	—
580	C₄²	—	2	8	no	—
581	C₄²	—	2	8	no	—
582	C₄²	—	2	8	no	—
583	C₄²	—	4	8	no	—
584	C₄²	—	4	8	no	—
585	C₄²	—	4	8	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	8	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	4	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	2	4	no	—
594	C₂³	—	2	4	no	—
595	C₂³	—	2	8	no	—
596	C₂³	—	2	4	no	—
597	C₂³	—	2	8	no	—
598	C₂³	—	2	8	no	—
599	C₂³	—	2	16	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	16	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	4	16	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	32	no	—
606	C₂³	—	4	4	no	—
607	C₂³	—	4	32	no	—
608	C₂³	—	4	16	no	—
609	C₂³	—	8	8	no	—
610	C₂³	—	8	8	no	—
611	C₂³	—	8	16	no	—
612	C₂³	—	8	16	no	—
613	C₂³	—	8	32	no	—
614	C₂³	—	8	16	no	—
615	C₂³	—	8	32	no	—
616	C₂³	—	8	128	no	—
617	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
618	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
619	C₂³	#585	1	4	yes	—
620	C₂³	C₂⁶	1	1	yes	characteristic
621	Q₈	—	4	16	no	—
622	Q₈	—	4	8	no	—
623	D₄	—	4	32	no	—
624	D₄	—	4	16	no	—
625	D₄	—	4	16	no	—
626	D₄	—	4	16	no	—
627	D₄	—	4	8	no	—
628	D₄	—	8	16	no	—
629	D₄	—	16	8	no	—
630	D₄	—	16	4	no	—
631	D₄	—	16	8	no	—
632	D₄	—	16	16	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	8	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	8	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	8	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	8	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	4	8	no	—
660	C₂×C₄	—	4	16	no	—
661	C₂×C₄	—	4	16	no	—
662	C₂×C₄	—	8	4	no	—
663	C₂×C₄	—	8	8	no	—
664	C₂×C₄	—	8	16	no	—
665	C₂×C₄	#560	1	16	yes	—
666	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
667	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
668	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	8	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	8	no	—
674	C₂²	—	4	16	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	4	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	4	no	—
679	C₂²	—	4	8	no	—
680	C₂²	—	4	4	no	—
681	C₂²	—	4	8	no	—
682	C₂²	—	4	8	no	—
683	C₂²	—	4	8	no	—
684	C₂²	—	4	16	no	—
685	C₂²	—	4	16	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	4	8	no	—
688	C₂²	—	8	32	no	—
689	C₂²	—	8	64	no	—
690	C₂²	C₂×#560	1	4	yes	—
691	C₂²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
692	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
693	C₂²	C₂×#585	1	2	yes	—
694	C₂²	H(7,𝔽₂)	1	2	yes	—
695	C₄	—	4	4	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	4	no	—
698	C₄	—	4	4	no	—
699	C₄	—	4	4	no	—
700	C₄	—	4	8	no	—
701	C₄	—	4	8	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	4	no	—
704	C₄	—	4	4	no	—
705	C₄	C₂×#560	1	8	yes	—
706	C₂	—	2	4	no	—
707	C₂	—	4	4	no	—
708	C₂	—	8	4	no	—
709	C₂	—	8	8	no	—
710	C₂	C₂²×#560	1	1	yes	characteristic
711	C₂	#62824	1	1	yes	characteristic
712	C₂	#62876	1	1	yes	characteristic
713	C₂	#62924	1	4	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁶
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #53018	C₂	semidirect
2. #52977	C₂	semidirect
3. #52339	C₂	semidirect
4. #45697	C₂	semidirect
5. #45647	C₂	semidirect
6. #45457	C₂	semidirect
7. #35677	C₂	semidirect
8. #35672	C₂	semidirect
9. #35634	C₂	semidirect
10. #35558	C₂	semidirect
11. #35327	C₂	semidirect
12. #35256	C₂	semidirect
13. #35222	C₂	semidirect
14. #34742	C₂	semidirect
15. C₂×#2435	C₂	semidirect
17. C₂×#537	C₂²	semidirect
18. C₂×#536	C₂²	semidirect
24. C₂×#519	C₂²	semidirect
25. C₂×C₄×#41	C₂²	semidirect
26. #2856	C₂²	semidirect
27. #2850	C₂²	semidirect
28. #2850	C₂²	semidirect
30. #2842	C₂²	semidirect
31. #2829	C₂²	semidirect
32. #2829	C₂²	semidirect
33. #2828	C₂²	semidirect
34. #2826	C₂²	semidirect
35. #2823	C₂²	semidirect
36. #2812	C₂²	semidirect
37. #2795	C₂²	semidirect
38. #2795	C₂²	semidirect
39. #2752	C₂²	semidirect
40. #2735	C₂²	semidirect
41. #2735	C₂²	semidirect
42. #2714	C₂²	semidirect
43. #2699	C₂²	semidirect
44. #2697	C₂²	semidirect
45. #2685	C₂²	semidirect
46. #2685	C₂²	semidirect
47. #2678	C₂²	semidirect
48. #2668	C₂²	semidirect
49. #2620	C₂²	semidirect
50. #2620	C₂²	semidirect
51. #2619	C₂²	semidirect
53. #2548	C₂²	semidirect
54. #2548	C₂²	semidirect
55. #2545	C₂²	semidirect
56. #2545	C₂²	semidirect
57. #2545	C₂²	semidirect
58. #2544	C₂²	semidirect
59. #2542	C₂²	semidirect
60. #2540	C₂²	semidirect
62. #2534	C₂²	semidirect
63. #2513	C₂²	semidirect
64. #2513	C₂²	semidirect
65. #2512	C₂²	semidirect
66. #2512	C₂²	semidirect
67. #2501	C₂²	semidirect
68. #2484	C₂²	semidirect
70. #2480	C₂²	semidirect
75. #2428	C₂²	semidirect
76. #2426	C₂²	semidirect
77. #2426	C₂²	semidirect
78. #2426	C₂²	semidirect
79. #2424	C₂²	semidirect
80. #2423	C₂²	semidirect
81. #2423	C₂²	semidirect
82. #2422	C₂²	semidirect
83. #2421	C₂²	semidirect
84. #2421	C₂²	semidirect
85. #2420	C₂²	semidirect
86. #2419	C₂²	semidirect
88. #2411	C₂²	semidirect
91. #2395	C₂²	semidirect
93. #2375	C₂²	semidirect
94. #2317	C₂²	semidirect
95. #2310	C₂²	semidirect
98. C₄×#123	C₂²	semidirect
99. #2297	C₂²	semidirect
100. #2296	C₂²	semidirect
102. #2285	C₂²	semidirect
105. #2274	C₂²	semidirect
120. C₂×C₄⋊Q₈	C₂³	semidirect
123. C₂×#126	C₂³	semidirect
130. C₂×#124	C₂³	semidirect
138. C₂×C₂²⋊Q₈	C₂³	semidirect
139. C₂×C₂²⋊Q₈	C₂³	semidirect
145. C₂×#121	C₂³	semidirect
146. C₂×#121	C₂³	semidirect
154. C₂×C₄×Q₈	C₂³	semidirect
155. C₂×C₄×Q₈	C₂³	semidirect
156. C₂×C₄×Q₈	C₂³	semidirect
159. C₂×C₄×D₄	C₂³	semidirect
164. C₂×#117	C₂³	semidirect
172. C₂²×C₄²	C₂³	semidirect
173. #400	C₂³	semidirect
174. #400	C₂³	semidirect
178. #399	C₂³	semidirect
179. #398	C₂³	semidirect
180. #398	C₂³	semidirect
183. #397	C₂³	semidirect
184. #397	C₂³	semidirect
185. #397	C₂³	semidirect
186. #397	C₂³	semidirect
187. #397	C₂³	semidirect
188. #396	C₂³	semidirect
189. #396	C₂³	semidirect
190. #396	C₂³	semidirect
191. #396	C₂³	semidirect
192. #396	C₂³	semidirect
193. #396	C₂³	semidirect
201. #394	C₂³	semidirect
202. #394	C₂³	semidirect
203. #394	C₂³	semidirect
204. #394	C₂³	semidirect
205. #394	C₂³	semidirect
206. #394	C₂³	semidirect
210. #392	C₂³	semidirect
211. #391	C₂³	semidirect
212. #391	C₂³	semidirect
213. #391	C₂³	semidirect
223. #390	C₂³	semidirect
224. #390	C₂³	semidirect
225. #390	C₂³	semidirect
226. #390	C₂³	semidirect
227. #390	C₂³	semidirect
228. #390	C₂³	semidirect
229. #389	C₂³	semidirect
230. #389	C₂³	semidirect
231. #389	C₂³	semidirect
235. #388	C₂³	semidirect
236. #388	C₂³	semidirect
237. #388	C₂³	semidirect
238. #388	C₂³	semidirect
239. #388	C₂³	semidirect
240. #388	C₂³	semidirect
241. #388	C₂³	semidirect
242. #388	C₂³	semidirect
243. #387	C₂³	semidirect
244. #387	C₂³	semidirect
245. #387	C₂³	semidirect
248. #386	C₂³	semidirect
249. #386	C₂³	semidirect
250. #386	C₂³	semidirect
253. #385	C₂³	semidirect
254. #384	C₂³	semidirect
255. #384	C₂³	semidirect
256. #384	C₂³	semidirect
257. #382	C₂³	semidirect
258. #382	C₂³	semidirect
261. #381	C₂³	semidirect
273. C₄×C₄⋊C₄	C₂³	semidirect
274. C₄×C₄⋊C₄	C₂³	semidirect
275. C₄×C₄⋊C₄	C₂³	semidirect
276. C₄×C₄⋊C₄	C₂³	semidirect
281. C₄×C₂²⋊C₄	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#53018	2
#52977	2
#52339	2
#45697	2
#45647	2
#45457	2
#35677	2
#35672	2
#35634	2
#35558	2
#35327	2
#35256	2
#35222	2
#34742	2
C₂×#2435	2