Subgroups — #7644347

Order 512.

6242 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#42983	C₂	1	4	yes	maximal, complemented
2	#42982	C₂	1	4	yes	maximal, complemented
3	#42977	C₂	1	4	yes	maximal, complemented
4	#42976	C₂	1	8	yes	maximal, complemented
5	#42975	C₂	1	4	yes	maximal, complemented
6	#42974	C₂	1	8	yes	maximal, complemented
7	#37517	C₂	1	8	yes	maximal, complemented
8	#36725	C₂	1	8	yes	maximal, complemented
9	#35558	C₂	1	2	yes	maximal, complemented
10	#35556	C₂	1	2	yes	maximal, complemented
11	#35533	C₂	1	2	yes	maximal, complemented
12	#35531	C₂	1	2	yes	maximal, complemented
13	#35222	C₂	1	2	yes	maximal, complemented
14	#34634	C₂	1	1	yes	maximal, characteristic, complemented
15	#34633	C₂	1	1	yes	maximal, characteristic, complemented
16	#34201	C₂	1	2	yes	maximal, complemented
17	C₂×#2309	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×D₄	C₂²	1	1	yes	characteristic
19	C₂×#535	C₂²	1	2	yes	—
20	C₂×#535	C₂²	1	2	yes	—
21	C₂×#533	C₂²	1	1	yes	characteristic, complemented
22	C₂×#532	C₂²	1	1	yes	characteristic, complemented
23	C₂×#525	C₂²	1	2	yes	—
24	C₂×#520	C₂²	1	2	yes	complemented
25	C₂²×#117	C₂²	1	1	yes	characteristic
26	C₂²×#117	C₂²	1	1	yes	characteristic
27	#2846	C₂²	1	8	yes	—
28	#2830	C₂²	1	8	yes	complemented
29	#2829	C₂²	1	16	yes	complemented
30	#2828	C₂²	1	8	yes	complemented
31	#2736	C₂²	1	8	yes	complemented
32	#2735	C₂²	1	16	yes	complemented
33	#2735	C₂²	1	8	yes	complemented
34	#2697	C₂²	1	16	yes	complemented
35	#2685	C₂²	1	16	yes	complemented
36	#2685	C₂²	1	16	yes	complemented
37	#2684	C₂²	1	16	yes	complemented
38	#2678	C₂²	1	16	yes	complemented
39	#2670	C₂²	1	8	yes	complemented
40	#2668	C₂²	1	8	yes	complemented
41	#2662	C₂²	1	16	yes	complemented
42	#2661	C₂²	1	16	yes	complemented
43	#2651	C₂²	1	16	yes	complemented
44	#2648	C₂²	1	16	yes	complemented
45	#2629	C₂²	1	4	yes	complemented
46	#2628	C₂²	1	2	yes	complemented
47	#2628	C₂²	1	2	yes	complemented
48	#2627	C₂²	1	4	yes	complemented
49	#2626	C₂²	1	4	yes	—
50	#2621	C₂²	1	2	yes	complemented
51	#2620	C₂²	1	4	yes	complemented
52	#2619	C₂²	1	2	yes	complemented
53	#2618	C₂²	1	4	yes	complemented
54	#2617	C₂²	1	4	yes	—
55	#2613	C₂²	1	8	yes	—
56	#2593	C₂²	1	8	yes	complemented
57	#2592	C₂²	1	8	yes	complemented
58	#2555	C₂²	1	8	yes	complemented
59	#2554	C₂²	1	16	yes	complemented
60	#2548	C₂²	1	4	yes	complemented
61	#2548	C₂²	1	8	yes	complemented
62	#2545	C₂²	1	4	yes	complemented
63	#2544	C₂²	1	4	yes	complemented
64	#2541	C₂²	1	4	yes	complemented
65	#2513	C₂²	1	8	yes	complemented
66	#2513	C₂²	1	8	yes	complemented
67	#2512	C₂²	1	8	yes	complemented
68	#2512	C₂²	1	8	yes	complemented
69	#2504	C₂²	1	4	yes	complemented
70	#2501	C₂²	1	4	yes	complemented
71	#2500	C₂²	1	4	yes	complemented
72	#2500	C₂²	1	4	yes	complemented
73	#2491	C₂²	1	8	yes	complemented
74	#2490	C₂²	1	8	yes	complemented
75	#2480	C₂²	1	16	yes	complemented
76	#2472	C₂²	1	16	yes	complemented
77	#2448	C₂²	1	8	yes	complemented
78	#2445	C₂²	1	8	yes	complemented
79	#2435	C₂²	1	8	yes	—
80	#2433	C₂²	1	8	yes	—
81	#2424	C₂²	1	16	yes	complemented
82	#2418	C₂²	1	16	yes	complemented
83	#2416	C₂²	1	8	yes	complemented
84	#2414	C₂²	1	8	yes	complemented
85	#2408	C₂²	1	8	yes	—
86	#2408	C₂²	1	8	yes	—
87	#2396	C₂²	1	4	yes	complemented
88	#2396	C₂²	1	4	yes	complemented
89	#2392	C₂²	1	4	yes	complemented
90	#2392	C₂²	1	4	yes	complemented
91	#2363	C₂²	1	8	yes	complemented
92	#2362	C₂²	1	8	yes	complemented
93	#2354	C₂²	1	8	yes	complemented
94	#2352	C₂²	1	8	yes	complemented
95	#2321	C₂²	1	8	yes	—
96	#2317	C₂²	1	2	yes	complemented
97	#2311	C₂²	1	2	yes	complemented
98	#2309	C₂²	1	2	yes	—
99	#2309	C₂²	1	2	yes	—
100	#2309	C₂²	1	4	yes	—
101	#2309	C₂²	1	4	yes	—
102	#2309	C₂²	1	4	yes	—
103	#2309	C₂²	1	4	yes	—
104	C₄×#123	C₂²	1	8	yes	complemented
105	#2297	C₂²	1	2	yes	complemented
106	#2296	C₂²	1	2	yes	complemented
107	C₂×#390	C₂²	1	4	yes	—
108	C₂×#390	C₂²	1	2	yes	—
109	C₂×#390	C₂²	1	2	yes	—
110	#2285	C₂²	1	1	yes	characteristic, complemented
111	#2285	C₂²	1	1	yes	characteristic, complemented
112	#2280	C₂²	1	2	yes	—
113	C₂×#379	C₂²	1	4	yes	—
114	#2274	C₂²	1	2	yes	complemented
115	C₂⁶	C₂³	1	2	yes	—
116	C₂²×#41	C₂³	1	2	yes	—
117	C₂³×D₄	—	2	8	no	—
118	C₂³×D₄	—	4	4	no	—
119	C₂³×D₄	—	4	4	no	—
120	C₂³×D₄	C₂³	1	2	yes	—
121	C₂³×D₄	C₂³	1	4	yes	—
122	C₂³×D₄	C₂³	1	4	yes	—
123	C₂³×D₄	C₂³	1	2	yes	—
124	C₂⁴×C₄	C₂³	1	1	yes	characteristic
125	#535	—	4	8	no	—
126	#535	—	4	8	no	—
127	#533	—	4	4	no	—
128	#532	—	4	4	no	—
129	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
130	C₂×C₄⋊Q₈	C₂³	1	2	yes	complemented
131	C₂×#127	C₂³	1	4	yes	—
132	C₂×#127	C₂³	1	4	yes	—
133	C₂×#127	C₂³	1	1	yes	characteristic, complemented
134	C₂×#126	C₂³	1	16	yes	complemented
135	C₂×#125	C₂³	1	2	yes	complemented
136	C₂×#124	C₂³	1	4	yes	—
137	C₂×#124	C₂³	1	4	yes	—
138	C₂×#124	C₂³	1	2	yes	complemented
139	C₂×#124	C₂³	1	16	yes	complemented
140	#525	—	2	16	no	—
141	C₂×#123	C₂³	1	4	yes	—
142	C₂×#123	C₂³	1	16	yes	complemented
143	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₂×#121	C₂³	1	4	yes	—
146	C₂×#121	C₂³	1	4	yes	—
147	C₂×#121	C₂³	1	4	yes	—
148	C₂×#121	C₂³	1	8	yes	—
149	C₂×#121	C₂³	1	4	yes	—
150	C₂×#121	C₂³	1	16	yes	complemented
151	C₂×#120	C₂³	1	4	yes	—
152	C₂×#120	C₂³	1	8	yes	—
153	C₂×#120	C₂³	1	8	yes	—
154	C₂×#120	C₂³	1	16	yes	—
155	C₂×#120	C₂³	1	16	yes	—
156	#520	—	4	8	no	—
157	C₂×C₄×Q₈	C₂³	1	4	yes	complemented
158	C₂×C₄×Q₈	C₂³	1	4	yes	complemented
159	C₂×C₄×D₄	C₂³	1	8	yes	—
160	C₂×C₄×D₄	C₂³	1	8	yes	—
161	C₂×C₄×D₄	C₂³	1	4	yes	complemented
162	C₂×C₄×D₄	C₂³	1	4	yes	complemented
163	C₂×#117	—	4	4	no	—
164	C₂×#117	—	4	4	no	—
165	C₂×#117	C₂³	1	2	yes	—
166	C₂×#117	C₂³	1	2	yes	—
167	C₂×#117	C₂³	1	2	yes	—
168	C₂×#117	C₂³	1	4	yes	—
169	C₂×#117	C₂³	1	4	yes	—
170	C₂×#117	C₂³	1	2	yes	—
171	C₂×#117	C₂³	1	2	yes	—
172	C₂×#117	C₂³	1	2	yes	—
173	C₂×#117	C₂³	1	2	yes	—
174	C₂×#117	C₂³	1	4	yes	complemented
175	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂²×C₄⋊C₄	C₂³	1	4	yes	complemented
178	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
181	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
182	C₂²×C₄²	C₂³	1	1	yes	characteristic
183	C₂²×C₄²	C₂³	1	1	yes	characteristic
184	C₂²×C₄²	C₂³	1	2	yes	—
185	#400	C₂³	1	4	yes	complemented
186	#400	C₂³	1	4	yes	complemented
187	#399	C₂³	1	4	yes	—
188	#399	C₂³	1	4	yes	—
189	#399	C₂³	1	16	yes	complemented
190	#398	C₂³	1	8	yes	complemented
191	#398	C₂³	1	4	yes	complemented
192	#398	C₂³	1	4	yes	complemented
193	#398	C₂³	1	8	yes	complemented
194	#397	C₂³	1	4	yes	—
195	#397	C₂³	1	4	yes	—
196	#397	C₂³	1	16	yes	complemented
197	#397	C₂³	1	16	yes	complemented
198	#397	C₂³	1	16	yes	complemented
199	#397	C₂³	1	16	yes	complemented
200	#397	C₂³	1	16	yes	complemented
201	#396	C₂³	1	8	yes	—
202	#396	C₂³	1	8	yes	—
203	#396	C₂³	1	8	yes	complemented
204	#396	C₂³	1	16	yes	complemented
205	#396	C₂³	1	16	yes	complemented
206	#396	C₂³	1	8	yes	complemented
207	#395	C₂³	1	4	yes	complemented
208	#395	C₂³	1	4	yes	complemented
209	#394	C₂³	1	16	yes	—
210	#394	C₂³	1	16	yes	—
211	#394	C₂³	1	8	yes	—
212	#394	C₂³	1	8	yes	—
213	#394	C₂³	1	4	yes	complemented
214	#394	C₂³	1	16	yes	complemented
215	#394	C₂³	1	16	yes	complemented
216	#394	C₂³	1	16	yes	complemented
217	#394	C₂³	1	16	yes	complemented
218	#394	C₂³	1	16	yes	complemented
219	#394	C₂³	1	16	yes	complemented
220	#394	C₂³	1	4	yes	complemented
221	#393	C₂³	1	4	yes	—
222	#393	C₂³	1	4	yes	—
223	#393	C₂³	1	16	yes	complemented
224	#392	C₂³	1	16	yes	—
225	#392	C₂³	1	16	yes	—
226	#392	C₂³	1	4	yes	—
227	#392	C₂³	1	4	yes	—
228	#392	C₂³	1	16	yes	complemented
229	#391	C₂³	1	4	yes	complemented
230	#391	C₂³	1	4	yes	complemented
231	#390	C₂³	1	8	yes	—
232	#390	C₂³	1	8	yes	—
233	#390	C₂³	1	8	yes	—
234	#390	C₂³	1	8	yes	—
235	#390	C₂³	1	8	yes	—
236	#390	C₂³	1	8	yes	—
237	#390	C₂³	1	4	yes	—
238	#390	C₂³	1	4	yes	—
239	#390	C₂³	1	4	yes	—
240	#390	C₂³	1	4	yes	—
241	#390	C₂³	1	8	yes	—
242	#390	C₂³	1	8	yes	—
243	#390	C₂³	1	4	yes	—
244	#390	C₂³	1	4	yes	—
245	#390	C₂³	1	8	yes	—
246	#390	C₂³	1	16	yes	—
247	#390	C₂³	1	4	yes	complemented
248	#390	C₂³	1	4	yes	complemented
249	#390	C₂³	1	16	yes	complemented
250	#390	C₂³	1	16	yes	complemented
251	#389	C₂³	1	8	yes	complemented
252	#389	C₂³	1	4	yes	complemented
253	#389	C₂³	1	4	yes	complemented
254	#388	C₂³	1	16	yes	—
255	#388	C₂³	1	16	yes	—
256	#388	C₂³	1	16	yes	complemented
257	#388	C₂³	1	16	yes	complemented
258	#388	C₂³	1	16	yes	complemented
259	#388	C₂³	1	16	yes	complemented
260	#388	C₂³	1	16	yes	complemented
261	#388	C₂³	1	16	yes	complemented
262	#388	C₂³	1	16	yes	complemented
263	#388	C₂³	1	16	yes	complemented
264	#388	C₂³	1	16	yes	complemented
265	#387	C₂³	1	16	yes	complemented
266	#386	C₂³	1	8	yes	—
267	#386	C₂³	1	16	yes	—
268	#386	C₂³	1	8	yes	—
269	#386	C₂³	1	16	yes	complemented
270	#386	C₂³	1	16	yes	complemented
271	#385	C₂³	1	8	yes	—
272	#385	C₂³	1	8	yes	—
273	#384	C₂³	1	4	yes	complemented
274	#384	C₂³	1	2	yes	complemented
275	#384	C₂³	1	2	yes	complemented
276	#382	C₂³	1	4	yes	complemented
277	#382	C₂³	1	2	yes	complemented
278	#382	C₂³	1	1	yes	characteristic, complemented
279	#382	C₂³	1	1	yes	characteristic, complemented
280	#381	C₂³	1	4	yes	—
281	#380	C₂³	1	4	yes	—
282	#380	C₂³	1	4	yes	—
283	#380	C₂³	1	4	yes	—
284	#380	C₂³	1	4	yes	—
285	#380	C₂³	1	8	yes	complemented
286	#379	C₂³	1	8	yes	—
287	#379	C₂³	1	8	yes	—
288	#379	C₂³	1	8	yes	—
289	#379	C₂³	1	8	yes	—
290	#379	C₂³	1	8	yes	—
291	#379	C₂³	1	8	yes	—
292	#379	C₂³	1	4	yes	—
293	#379	C₂³	1	16	yes	—
294	#379	C₂³	1	16	yes	—
295	C₄×C₄⋊C₄	C₂³	1	8	yes	complemented
296	C₄×C₄⋊C₄	C₂³	1	16	yes	complemented
297	C₄×C₄⋊C₄	C₂³	1	8	yes	complemented
298	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
299	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
300	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
301	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
302	C₄×C₂²⋊C₄	C₂³	1	8	yes	—
303	C₄×C₂²⋊C₄	C₂³	1	8	yes	—
304	C₄×C₂²⋊C₄	C₂³	1	16	yes	complemented
305	C₄×C₂²⋊C₄	C₂³	1	4	yes	complemented
306	C₄×C₂²⋊C₄	C₂³	1	4	yes	complemented
307	C₂⁵	—	2	8	no	—
308	C₂⁵	—	4	4	no	—
309	C₂⁵	—	4	4	no	—
310	C₂⁵	—	8	8	no	—
311	C₂⁵	C₂⁴	1	4	yes	—
312	C₂⁵	C₂⁴	1	1	yes	characteristic
313	C₂⁵	C₂⁴	1	8	yes	—
314	C₂×#41	—	2	8	no	—
315	C₂×#41	—	2	8	no	—
316	C₂×#41	—	2	8	no	—
317	C₂²×Q₈	C₂⁴	1	2	yes	—
318	C₂²×Q₈	C₂⁴	1	4	yes	—
319	C₂²×D₄	—	2	16	no	—
320	C₂²×D₄	—	2	16	no	—
321	C₂²×D₄	—	2	8	no	—
322	C₂²×D₄	—	2	8	no	—
323	C₂²×D₄	—	2	8	no	—
324	C₂²×D₄	—	2	8	no	—
325	C₂²×D₄	—	4	8	no	—
326	C₂²×D₄	—	4	8	no	—
327	C₂²×D₄	—	4	8	no	—
328	C₂²×D₄	—	4	8	no	—
329	C₂²×D₄	—	4	4	no	—
330	C₂²×D₄	—	4	4	no	—
331	C₂²×D₄	—	4	64	no	—
332	C₂²×D₄	C₂⁴	1	4	yes	—
333	C₂²×D₄	C₂⁴	1	2	yes	—
334	C₂²×D₄	C₂⁴	1	4	yes	—
335	C₂²×D₄	C₂⁴	1	4	yes	—
336	C₂²×D₄	C₂⁴	1	8	yes	—
337	C₂²×D₄	C₂⁴	1	8	yes	—
338	C₂²×D₄	C₂⁴	1	4	yes	—
339	C₂²×D₄	C₂⁴	1	8	yes	—
340	C₂²×D₄	C₂⁴	1	16	yes	—
341	C₂²×D₄	C₂⁴	1	8	yes	—
342	C₂³×C₄	—	2	4	no	—
343	C₂³×C₄	—	2	4	no	—
344	C₂³×C₄	#41	1	8	yes	—
345	C₂³×C₄	C₂⁴	1	4	yes	—
346	C₂³×C₄	C₂⁴	1	1	yes	characteristic
347	C₂³×C₄	C₂⁴	1	2	yes	—
348	C₂³×C₄	C₂⁴	1	2	yes	—
349	C₂³×C₄	C₂⁴	1	4	yes	—
350	C₂³×C₄	C₂⁴	1	2	yes	—
351	C₂³×C₄	C₂⁴	1	2	yes	—
352	C₂³×C₄	C₂⁴	1	8	yes	—
353	C₂³×C₄	C₂⁴	1	1	yes	characteristic
354	C₄⋊Q₈	—	4	4	no	—
355	C₄⋊Q₈	—	4	2	no	—
356	#127	—	4	8	no	—
357	#127	—	4	8	no	—
358	#127	—	4	2	no	—
359	#126	—	8	16	no	—
360	#125	—	4	4	no	—
361	#124	—	4	8	no	—
362	#124	—	4	8	no	—
363	#124	—	4	4	no	—
364	#124	—	8	16	no	—
365	#123	—	2	16	no	—
366	#123	—	8	16	no	—
367	C₂²⋊Q₈	—	2	16	no	—
368	C₂²⋊Q₈	—	4	8	no	—
369	#121	—	2	16	no	—
370	#121	—	4	8	no	—
371	#121	—	4	8	no	—
372	#121	—	4	16	no	—
373	#121	—	4	8	no	—
374	#121	—	8	16	no	—
375	#120	—	2	16	no	—
376	#120	—	4	16	no	—
377	#120	—	4	16	no	—
378	#120	—	8	16	no	—
379	#120	—	8	16	no	—
380	C₄×Q₈	—	4	8	no	—
381	C₄×Q₈	—	4	8	no	—
382	C₄×D₄	—	2	32	no	—
383	C₄×D₄	—	4	8	no	—
384	C₄×D₄	—	4	8	no	—
385	C₄×D₄	—	4	16	no	—
386	#117	—	2	8	no	—
387	#117	—	2	8	no	—
388	#117	—	2	8	no	—
389	#117	—	4	4	no	—
390	#117	—	4	4	no	—
391	#117	—	4	4	no	—
392	#117	—	4	4	no	—
393	#117	—	4	8	no	—
394	#117	—	4	8	no	—
395	#117	—	4	8	no	—
396	C₂×C₄⋊C₄	—	2	8	no	—
397	C₂×C₄⋊C₄	—	4	8	no	—
398	C₂×C₄⋊C₄	—	4	4	no	—
399	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
400	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
401	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
402	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
404	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
405	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
406	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
409	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
411	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
412	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
413	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
414	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
415	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
416	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
417	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
418	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
419	C₂×C₂²⋊C₄	—	4	4	no	—
420	C₂×C₂²⋊C₄	—	4	4	no	—
421	C₂×C₂²⋊C₄	—	8	8	no	—
422	C₂×C₂²⋊C₄	—	8	8	no	—
423	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
427	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
428	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
429	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
434	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
435	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
436	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
437	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
438	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
439	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
440	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
443	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
444	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
445	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
446	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
447	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
448	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
449	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
450	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
451	C₂×C₄²	—	2	4	no	—
452	C₂×C₄²	—	2	4	no	—
453	C₂×C₄²	—	4	4	no	—
454	C₂×C₄²	C₂⁴	1	2	yes	—
455	C₂×C₄²	C₂⁴	1	2	yes	—
456	C₂×C₄²	C₂⁴	1	1	yes	characteristic
457	C₂×C₄²	C₂⁴	1	1	yes	characteristic
458	C₂×C₄²	C₂⁴	1	1	yes	characteristic
459	C₂×C₄²	C₂⁴	1	1	yes	characteristic
460	C₂×C₄²	C₂⁴	1	4	yes	—
461	C₂×C₄²	C₂⁴	1	4	yes	—
462	C₂×C₄²	C₂⁴	1	4	yes	—
463	C₂×C₄²	C₂⁴	1	8	yes	—
464	C₂×C₄²	C₂⁴	1	8	yes	—
465	C₂×C₄²	C₂⁴	1	16	yes	—
466	#95	C₂⁴	1	8	yes	—
467	#95	C₂⁴	1	8	yes	—
468	#95	C₂⁴	1	16	yes	—
469	#95	C₂⁴	1	16	yes	—
470	#95	C₂⁴	1	8	yes	—
471	#95	C₂⁴	1	8	yes	—
472	#95	C₂⁴	1	4	yes	—
473	#95	C₂⁴	1	4	yes	—
474	#95	C₂⁴	1	4	yes	—
475	#95	C₂⁴	1	4	yes	—
476	#95	C₂⁴	1	16	yes	—
477	#95	C₂⁴	1	8	yes	—
478	#95	C₂⁴	1	8	yes	—
479	C₂⁴	—	2	2	no	—
480	C₂⁴	—	2	2	no	—
481	C₂⁴	—	2	8	no	—
482	C₂⁴	—	2	16	no	—
483	C₂⁴	—	2	8	no	—
484	C₂⁴	—	2	8	no	—
485	C₂⁴	—	4	4	no	—
486	C₂⁴	—	4	8	no	—
487	C₂⁴	—	4	8	no	—
488	C₂⁴	—	4	8	no	—
489	C₂⁴	—	4	8	no	—
490	C₂⁴	—	4	16	no	—
491	C₂⁴	—	4	16	no	—
492	C₂⁴	—	4	32	no	—
493	C₂⁴	—	8	32	no	—
494	C₂⁴	—	8	32	no	—
495	C₂⁴	—	8	32	no	—
496	C₂⁴	C₂×#41	1	4	yes	—
497	C₂⁴	C₂⁵	1	8	yes	—
498	C₂⁴	C₂⁵	1	4	yes	—
499	C₂⁴	C₂⁵	1	2	yes	—
500	C₂⁴	C₂⁵	1	1	yes	characteristic
501	#41	—	4	32	no	—
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	2	4	no	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	—	4	8	no	—
507	C₂×D₄	—	2	8	no	—
508	C₂×D₄	—	2	8	no	—
509	C₂×D₄	—	2	8	no	—
510	C₂×D₄	—	2	16	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	16	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	8	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	8	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	8	no	—
520	C₂×D₄	—	2	8	no	—
521	C₂×D₄	—	4	8	no	—
522	C₂×D₄	—	4	8	no	—
523	C₂×D₄	—	4	32	no	—
524	C₂×D₄	—	4	64	no	—
525	C₂×D₄	—	4	64	no	—
526	C₂×D₄	—	4	4	no	—
527	C₂×D₄	—	4	8	no	—
528	C₂×D₄	—	4	8	no	—
529	C₂×D₄	—	4	8	no	—
530	C₂×D₄	—	4	8	no	—
531	C₂×D₄	—	4	16	no	—
532	C₂×D₄	—	4	8	no	—
533	C₂×D₄	—	4	16	no	—
534	C₂×D₄	—	4	16	no	—
535	C₂×D₄	—	4	16	no	—
536	C₂×D₄	—	4	16	no	—
537	C₂×D₄	—	4	32	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	32	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	8	no	—
548	C₂²×C₄	—	2	8	no	—
549	C₂²×C₄	—	2	8	no	—
550	C₂²×C₄	—	2	8	no	—
551	C₂²×C₄	—	4	8	no	—
552	C₂²×C₄	—	4	4	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	—	4	8	no	—
555	C₂²×C₄	—	4	16	no	—
556	C₂²×C₄	C₂×#41	1	8	yes	—
557	C₂²×C₄	C₂×#41	1	8	yes	—
558	C₂²×C₄	C₂×#41	1	4	yes	—
559	C₂²×C₄	C₂×#41	1	4	yes	—
560	C₂²×C₄	H(5,𝔽₂)	1	4	yes	—
561	C₂²×C₄	H(5,𝔽₂)	1	4	yes	—
562	C₂²×C₄	C₂⁵	1	4	yes	—
563	C₂²×C₄	C₂⁵	1	8	yes	—
564	C₂²×C₄	C₂⁵	1	8	yes	—
565	C₂²×C₄	C₂⁵	1	2	yes	—
566	C₂²×C₄	C₂⁵	1	4	yes	—
567	C₂²×C₄	C₂⁵	1	2	yes	—
568	C₂²×C₄	C₂⁵	1	8	yes	—
569	C₂²×C₄	C₂⁵	1	4	yes	—
570	C₂²×C₄	C₂⁵	1	2	yes	—
571	C₂²×C₄	C₂⁵	1	2	yes	—
572	C₂²×C₄	C₂⁵	1	2	yes	—
573	C₂²×C₄	C₂⁵	1	1	yes	characteristic
574	C₂²×C₄	C₂⁵	1	1	yes	characteristic
575	C₄⋊C₄	—	2	8	no	—
576	C₄⋊C₄	—	2	16	no	—
577	C₄⋊C₄	—	2	8	no	—
578	C₄⋊C₄	—	2	8	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	8	no	—
582	C₄⋊C₄	—	4	2	no	—
583	C₄⋊C₄	—	4	2	no	—
584	C₄⋊C₄	—	4	2	no	—
585	C₄⋊C₄	—	4	2	no	—
586	C₄⋊C₄	—	4	8	no	—
587	C₄⋊C₄	—	4	4	no	—
588	C₄⋊C₄	—	4	8	no	—
589	C₄⋊C₄	—	4	4	no	—
590	C₄⋊C₄	—	4	8	no	—
591	C₄⋊C₄	—	4	8	no	—
592	C₄⋊C₄	—	4	16	no	—
593	C₄⋊C₄	—	4	8	no	—
594	C₄⋊C₄	—	4	8	no	—
595	C₂²⋊C₄	—	2	8	no	—
596	C₂²⋊C₄	—	2	16	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	16	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	4	2	no	—
603	C₂²⋊C₄	—	4	2	no	—
604	C₂²⋊C₄	—	4	8	no	—
605	C₂²⋊C₄	—	4	16	no	—
606	C₂²⋊C₄	—	4	16	no	—
607	C₂²⋊C₄	—	4	16	no	—
608	C₂²⋊C₄	—	4	16	no	—
609	C₂²⋊C₄	—	4	8	no	—
610	C₂²⋊C₄	—	4	8	no	—
611	C₂²⋊C₄	—	4	8	no	—
612	C₂²⋊C₄	—	4	16	no	—
613	C₂²⋊C₄	—	4	8	no	—
614	C₂²⋊C₄	—	4	8	no	—
615	C₂²⋊C₄	—	4	8	no	—
616	C₂²⋊C₄	—	4	16	no	—
617	C₂²⋊C₄	—	4	16	no	—
618	C₂²⋊C₄	—	4	16	no	—
619	C₂²⋊C₄	—	4	16	no	—
620	C₂²⋊C₄	—	4	16	no	—
621	C₂²⋊C₄	—	4	8	no	—
622	C₂²⋊C₄	—	4	8	no	—
623	C₄²	—	2	8	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	—	2	2	no	—
627	C₄²	—	2	2	no	—
628	C₄²	—	2	2	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	8	no	—
631	C₄²	—	2	8	no	—
632	C₄²	—	4	8	no	—
633	C₄²	—	4	8	no	—
634	C₄²	—	4	16	no	—
635	C₂³	—	2	4	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	8	no	—
641	C₂³	—	2	4	no	—
642	C₂³	—	2	8	no	—
643	C₂³	—	2	4	no	—
644	C₂³	—	2	4	no	—
645	C₂³	—	2	8	no	—
646	C₂³	—	2	8	no	—
647	C₂³	—	2	16	no	—
648	C₂³	—	2	16	no	—
649	C₂³	—	2	8	no	—
650	C₂³	—	2	8	no	—
651	C₂³	—	4	8	no	—
652	C₂³	—	4	8	no	—
653	C₂³	—	4	8	no	—
654	C₂³	—	4	32	no	—
655	C₂³	—	4	32	no	—
656	C₂³	—	4	16	no	—
657	C₂³	—	8	16	no	—
658	C₂³	—	8	8	no	—
659	C₂³	—	8	8	no	—
660	C₂³	—	8	32	no	—
661	C₂³	—	8	16	no	—
662	C₂³	—	8	16	no	—
663	C₂³	—	8	32	no	—
664	C₂³	—	8	128	no	—
665	C₂³	C₂²×#41	1	4	yes	—
666	C₂³	C₂²×#41	1	2	yes	—
667	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
668	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
669	C₂³	C₂⁶	1	1	yes	characteristic
670	Q₈	—	4	8	no	—
671	Q₈	—	8	8	no	—
672	D₄	—	4	32	no	—
673	D₄	—	4	16	no	—
674	D₄	—	4	16	no	—
675	D₄	—	4	16	no	—
676	D₄	—	4	8	no	—
677	D₄	—	8	16	no	—
678	D₄	—	8	8	no	—
679	D₄	—	16	16	no	—
680	D₄	—	16	8	no	—
681	D₄	—	16	8	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	8	no	—
685	C₂×C₄	—	2	16	no	—
686	C₂×C₄	—	2	16	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	8	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	8	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	8	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	16	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	8	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	8	no	—
710	C₂×C₄	—	4	16	no	—
711	C₂×C₄	—	8	4	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	8	no	—
714	C₂×C₄	—	16	8	no	—
715	C₂×C₄	#538	1	16	yes	—
716	C₂×C₄	C₂²×#41	1	4	yes	—
717	C₂×C₄	C₂²×#41	1	2	yes	—
718	C₂×C₄	C₂²×#41	1	2	yes	—
719	C₂×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
720	C₂×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
721	C₂×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
722	C₂×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	8	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	4	16	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	8	no	—
733	C₂²	—	4	16	no	—
734	C₂²	—	4	8	no	—
735	C₂²	—	4	16	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	8	no	—
739	C₂²	—	4	8	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	8	no	—
742	C₂²	—	8	32	no	—
743	C₂²	—	8	64	no	—
744	C₂²	C₂×#538	1	4	yes	—
745	C₂²	C₂³×#41	1	1	yes	characteristic
746	C₂²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
747	C₂²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
748	C₂²	H(7,𝔽₂)	1	4	yes	—
749	C₄	—	2	4	no	—
750	C₄	—	4	8	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	8	no	—
756	C₄	—	4	8	no	—
757	C₄	—	4	4	no	—
758	C₄	—	4	4	no	—
759	C₄	—	4	4	no	—
760	C₄	C₂×#538	1	4	yes	—
761	C₄	C₂×#538	1	4	yes	—
762	C₂	—	2	4	no	—
763	C₂	—	4	4	no	—
764	C₂	—	8	4	no	—
765	C₂	—	8	8	no	—
766	C₂	C₂²×#538	1	1	yes	characteristic
767	C₂	#62855	1	2	yes	—
768	C₂	#62874	1	2	yes	—
769	C₂	#62876	1	2	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. #42983	C₂	semidirect
2. #42982	C₂	semidirect
3. #42977	C₂	semidirect
4. #42976	C₂	semidirect
5. #42975	C₂	semidirect
6. #42974	C₂	semidirect
7. #37517	C₂	semidirect
8. #36725	C₂	semidirect
9. #35558	C₂	semidirect
10. #35556	C₂	semidirect
11. #35533	C₂	semidirect
12. #35531	C₂	semidirect
13. #35222	C₂	semidirect
14. #34634	C₂	semidirect
15. #34633	C₂	semidirect
16. #34201	C₂	semidirect
17. C₂×#2309	C₂	semidirect
21. C₂×#533	C₂²	semidirect
22. C₂×#532	C₂²	semidirect
24. C₂×#520	C₂²	semidirect
28. #2830	C₂²	semidirect
29. #2829	C₂²	semidirect
30. #2828	C₂²	semidirect
31. #2736	C₂²	semidirect
32. #2735	C₂²	semidirect
33. #2735	C₂²	semidirect
34. #2697	C₂²	semidirect
35. #2685	C₂²	semidirect
36. #2685	C₂²	semidirect
37. #2684	C₂²	semidirect
38. #2678	C₂²	semidirect
39. #2670	C₂²	semidirect
40. #2668	C₂²	semidirect
41. #2662	C₂²	semidirect
42. #2661	C₂²	semidirect
43. #2651	C₂²	semidirect
44. #2648	C₂²	semidirect
45. #2629	C₂²	semidirect
46. #2628	C₂²	semidirect
47. #2628	C₂²	semidirect
48. #2627	C₂²	semidirect
50. #2621	C₂²	semidirect
51. #2620	C₂²	semidirect
52. #2619	C₂²	semidirect
53. #2618	C₂²	semidirect
56. #2593	C₂²	semidirect
57. #2592	C₂²	semidirect
58. #2555	C₂²	semidirect
59. #2554	C₂²	semidirect
60. #2548	C₂²	semidirect
61. #2548	C₂²	semidirect
62. #2545	C₂²	semidirect
63. #2544	C₂²	semidirect
64. #2541	C₂²	semidirect
65. #2513	C₂²	semidirect
66. #2513	C₂²	semidirect
67. #2512	C₂²	semidirect
68. #2512	C₂²	semidirect
69. #2504	C₂²	semidirect
70. #2501	C₂²	semidirect
71. #2500	C₂²	semidirect
72. #2500	C₂²	semidirect
73. #2491	C₂²	semidirect
74. #2490	C₂²	semidirect
75. #2480	C₂²	semidirect
76. #2472	C₂²	semidirect
77. #2448	C₂²	semidirect
78. #2445	C₂²	semidirect
81. #2424	C₂²	semidirect
82. #2418	C₂²	semidirect
83. #2416	C₂²	semidirect
84. #2414	C₂²	semidirect
87. #2396	C₂²	semidirect
88. #2396	C₂²	semidirect
89. #2392	C₂²	semidirect
90. #2392	C₂²	semidirect
91. #2363	C₂²	semidirect
92. #2362	C₂²	semidirect
93. #2354	C₂²	semidirect
94. #2352	C₂²	semidirect
96. #2317	C₂²	semidirect
97. #2311	C₂²	semidirect
104. C₄×#123	C₂²	semidirect
105. #2297	C₂²	semidirect
106. #2296	C₂²	semidirect
110. #2285	C₂²	semidirect
111. #2285	C₂²	semidirect
114. #2274	C₂²	semidirect
129. C₂×C₄⋊Q₈	C₂³	semidirect
130. C₂×C₄⋊Q₈	C₂³	semidirect
133. C₂×#127	C₂³	semidirect
134. C₂×#126	C₂³	semidirect
135. C₂×#125	C₂³	semidirect
138. C₂×#124	C₂³	semidirect
139. C₂×#124	C₂³	semidirect
142. C₂×#123	C₂³	semidirect
150. C₂×#121	C₂³	semidirect
157. C₂×C₄×Q₈	C₂³	semidirect
158. C₂×C₄×Q₈	C₂³	semidirect
161. C₂×C₄×D₄	C₂³	semidirect
162. C₂×C₄×D₄	C₂³	semidirect
174. C₂×#117	C₂³	semidirect
177. C₂²×C₄⋊C₄	C₂³	semidirect
185. #400	C₂³	semidirect
186. #400	C₂³	semidirect
189. #399	C₂³	semidirect
190. #398	C₂³	semidirect
191. #398	C₂³	semidirect
192. #398	C₂³	semidirect
193. #398	C₂³	semidirect
196. #397	C₂³	semidirect
197. #397	C₂³	semidirect
198. #397	C₂³	semidirect
199. #397	C₂³	semidirect
200. #397	C₂³	semidirect
203. #396	C₂³	semidirect
204. #396	C₂³	semidirect
205. #396	C₂³	semidirect
206. #396	C₂³	semidirect
207. #395	C₂³	semidirect
208. #395	C₂³	semidirect
213. #394	C₂³	semidirect
214. #394	C₂³	semidirect
215. #394	C₂³	semidirect
216. #394	C₂³	semidirect
217. #394	C₂³	semidirect
218. #394	C₂³	semidirect
219. #394	C₂³	semidirect
220. #394	C₂³	semidirect
223. #393	C₂³	semidirect
228. #392	C₂³	semidirect
229. #391	C₂³	semidirect
230. #391	C₂³	semidirect
247. #390	C₂³	semidirect
248. #390	C₂³	semidirect
249. #390	C₂³	semidirect
250. #390	C₂³	semidirect
251. #389	C₂³	semidirect
252. #389	C₂³	semidirect
253. #389	C₂³	semidirect
256. #388	C₂³	semidirect
257. #388	C₂³	semidirect
258. #388	C₂³	semidirect
259. #388	C₂³	semidirect
260. #388	C₂³	semidirect
261. #388	C₂³	semidirect
262. #388	C₂³	semidirect
263. #388	C₂³	semidirect
264. #388	C₂³	semidirect
265. #387	C₂³	semidirect
269. #386	C₂³	semidirect
270. #386	C₂³	semidirect
273. #384	C₂³	semidirect
274. #384	C₂³	semidirect
275. #384	C₂³	semidirect
276. #382	C₂³	semidirect
277. #382	C₂³	semidirect
278. #382	C₂³	semidirect
279. #382	C₂³	semidirect
285. #380	C₂³	semidirect
295. C₄×C₄⋊C₄	C₂³	semidirect
296. C₄×C₄⋊C₄	C₂³	semidirect
297. C₄×C₄⋊C₄	C₂³	semidirect
298. C₄×C₄⋊C₄	C₂³	semidirect
299. C₄×C₄⋊C₄	C₂³	semidirect
300. C₄×C₄⋊C₄	C₂³	semidirect
301. C₄×C₄⋊C₄	C₂³	semidirect
304. C₄×C₂²⋊C₄	C₂³	semidirect
305. C₄×C₂²⋊C₄	C₂³	semidirect
306. 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
#42983	2
#42982	2
#42977	2
#42976	2
#42975	2
#42974	2
#37517	2
#36725	2
#35558	2
#35556	2
#35533	2
#35531	2
#35222	2
#34634	2
#34633	2
#34201	2
C₂×#2309	2