Subgroups — #72261300

Order 2048.

At least 13933 conjugacy classes of subgroups; only the 988 normal subgroups are shown.

The subgroup lattice has 548 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261283	C₂	1	2	yes	maximal, complemented
2	#72261277	C₂	1	4	yes	maximal, complemented
3	#72261270	C₂	1	2	yes	maximal, complemented
4	#72261263	C₂	1	2	yes	maximal, complemented
5	#72261257	C₂	1	4	yes	maximal, complemented
6	#72261249	C₂	1	2	yes	maximal, complemented
7	#72261184	C₂	1	1	yes	maximal, characteristic, complemented
8	#72261064	C₂	1	1	yes	maximal, characteristic, complemented
9	#72238583	C₂	1	1	yes	maximal, characteristic, complemented
10	#72234197	C₂	1	1	yes	maximal, characteristic, complemented
11	#72234193	C₂	1	1	yes	maximal, characteristic, complemented
12	#72234146	C₂	1	1	yes	maximal, characteristic, complemented
13	#72233417	C₂	1	2	yes	maximal, complemented
14	#72233051	C₂	1	2	yes	maximal, complemented
15	#72232835	C₂	1	2	yes	maximal, complemented
16	#72232771	C₂	1	2	yes	maximal, complemented
17	#72219653	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#60399	C₂²	1	1	yes	characteristic, complemented
19	C₂×#60388	C₂²	1	1	yes	characteristic, complemented
20	#8943482	C₂²	1	2	yes	complemented
21	#8898169	C₂²	1	2	yes	—
22	#8797683	C₂²	1	2	yes	complemented
23	#8196400	C₂²	1	1	yes	characteristic, complemented
24	#8195113	C₂²	1	1	yes	characteristic, complemented
25	#8110542	C₂²	1	1	yes	characteristic, complemented
26	#7819605	C₂²	1	2	yes	—
27	#7739388	C₂²	1	1	yes	characteristic
28	#7737411	C₂²	1	1	yes	characteristic
29	#7671946	C₂²	1	1	yes	characteristic
30	#7670609	C₂²	1	1	yes	characteristic, complemented
31	#6628896	C₂²	1	2	yes	complemented
32	#6628876	C₂²	1	2	yes	complemented
33	#6628872	C₂²	1	1	yes	characteristic, complemented
34	#499877	C₂²	1	2	yes	complemented
35	#499875	C₂²	1	2	yes	complemented
36	#499861	C₂²	1	4	yes	complemented
37	#499844	C₂²	1	2	yes	complemented
38	#499844	C₂²	1	2	yes	complemented
39	#499831	C₂²	1	4	yes	complemented
40	#499811	C₂²	1	4	yes	complemented
41	#499803	C₂²	1	4	yes	complemented
42	#499799	C₂²	1	4	yes	complemented
43	#499791	C₂²	1	4	yes	complemented
44	#494738	C₂²	1	2	yes	complemented
45	#494721	C₂²	1	2	yes	complemented
46	#494700	C₂²	1	2	yes	complemented
47	#494682	C₂²	1	2	yes	complemented
48	#493441	C₂²	1	1	yes	characteristic, complemented
49	#493430	C₂²	1	1	yes	characteristic, complemented
50	#493424	C₂²	1	2	yes	complemented
51	#449496	C₂²	1	2	yes	complemented
52	#417841	C₂²	1	2	yes	complemented
53	#417562	C₂²	1	2	yes	complemented
54	#417540	C₂²	1	2	yes	complemented
55	#374034	C₂²	1	1	yes	characteristic, complemented
56	#359601	C₂²	1	1	yes	characteristic, complemented
57	#359593	C₂²	1	1	yes	characteristic, complemented
58	#254516	C₂²	1	4	yes	complemented
59	#254474	C₂²	1	4	yes	complemented
60	#246345	C₂²	1	4	yes	complemented
61	#246319	C₂²	1	4	yes	complemented
62	#214619	C₂²	1	2	yes	complemented
63	#214616	C₂²	1	2	yes	complemented
64	#213906	C₂²	1	2	yes	complemented
65	#134030	C₂²	1	2	yes	complemented
66	#133918	C₂²	1	2	yes	complemented
67	#133902	C₂²	1	2	yes	complemented
68	#133843	C₂²	1	2	yes	complemented
69	#133474	C₂²	1	4	yes	complemented
70	#133470	C₂²	1	4	yes	complemented
71	#133418	C₂²	1	4	yes	complemented
72	#133414	C₂²	1	4	yes	complemented
73	#133403	C₂²	1	4	yes	complemented
74	#133399	C₂²	1	4	yes	complemented
75	#133386	C₂²	1	4	yes	complemented
76	#133382	C₂²	1	4	yes	complemented
77	#133365	C₂²	1	4	yes	complemented
78	#133350	C₂²	1	4	yes	complemented
79	#133343	C₂²	1	2	yes	complemented
80	#133342	C₂²	1	2	yes	complemented
81	#133326	C₂²	1	2	yes	complemented
82	#133326	C₂²	1	2	yes	complemented
83	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
84	C₂×#3498	C₂³	1	1	yes	characteristic
85	C₂×#3484	D₄	1	1	yes	characteristic, complemented
86	C₂×#3484	C₂³	1	1	yes	characteristic
87	C₂×#3532	D₄	1	2	yes	complemented
88	C₂×#3483	D₄	1	1	yes	characteristic, complemented
89	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
90	C₂³×#127	D₄	1	1	yes	characteristic, complemented
91	C₂×#3027	C₂³	1	2	yes	complemented
92	C₂×#3025	C₂³	1	2	yes	complemented
93	C₂×#3021	C₂³	1	2	yes	—
94	C₂×#3018	C₂³	1	2	yes	—
95	#60369	C₂³	1	2	yes	complemented
96	C₂×#2888	C₂³	1	1	yes	characteristic
97	C₂×#2883	C₂³	1	1	yes	characteristic
98	#59179	C₂³	1	2	yes	—
99	#59126	D₄	1	1	yes	characteristic, complemented
100	#59126	D₄	1	1	yes	characteristic, complemented
101	#59084	D₄	1	1	yes	characteristic, complemented
102	#59084	C₂³	1	1	yes	characteristic
103	#59056	D₄	1	1	yes	characteristic, complemented
104	#59056	C₂³	1	1	yes	characteristic
105	#59041	C₂³	1	1	yes	characteristic
106	#59041	C₂³	1	1	yes	characteristic
107	#58990	D₄	1	2	yes	complemented
108	C₂×#2679	D₄	1	2	yes	complemented
109	#52004	D₄	1	2	yes	complemented
110	#52004	C₂³	1	2	yes	—
111	#51896	D₄	1	2	yes	complemented
112	#51896	C₂³	1	2	yes	—
113	#50856	D₄	1	2	yes	complemented
114	#50646	D₄	1	2	yes	complemented
115	#49562	C₂³	1	2	yes	—
116	#49545	C₂³	1	2	yes	—
117	#46454	D₄	1	2	yes	complemented
118	#46452	D₄	1	2	yes	complemented
119	#46425	D₄	1	2	yes	complemented
120	#46424	C₂³	1	2	yes	—
121	#46355	C₂³	1	2	yes	—
122	#46354	D₄	1	2	yes	complemented
123	#45452	C₂³	1	2	yes	—
124	#45439	D₄	1	2	yes	complemented
125	#37273	D₄	1	2	yes	complemented
126	#36818	C₂³	1	2	yes	—
127	#36812	D₄	1	2	yes	complemented
128	#36703	D₄	1	2	yes	complemented
129	#36702	D₄	1	2	yes	complemented
130	#36702	D₄	1	2	yes	complemented
131	#36624	C₂³	1	1	yes	characteristic
132	#35528	D₄	1	1	yes	characteristic, complemented
133	#35528	C₂³	1	1	yes	characteristic
134	#35527	D₄	1	1	yes	characteristic, complemented
135	#35527	C₂³	1	1	yes	characteristic
136	#35513	C₂³	1	2	yes	—
137	#35439	C₂³	1	2	yes	—
138	#35438	D₄	1	2	yes	complemented
139	#35390	D₄	1	2	yes	complemented
140	#35346	C₂³	1	2	yes	—
141	#35274	C₂³	1	1	yes	characteristic
142	#35272	D₄	1	1	yes	characteristic, complemented
143	#35222	D₄	1	1	yes	characteristic, complemented
144	#35222	C₂³	1	1	yes	characteristic
145	#34408	D₄	1	2	yes	complemented
146	#34368	D₄	1	1	yes	characteristic, complemented
147	#34364	D₄	1	1	yes	characteristic, complemented
148	#34210	D₄	1	1	yes	characteristic, complemented
149	C₄×#525	D₄	1	1	yes	characteristic, complemented
150	#32899	C₂³	1	4	yes	—
151	#32899	C₂³	1	4	yes	—
152	#32893	C₂³	1	4	yes	complemented
153	#32890	C₂³	1	4	yes	complemented
154	#20606	C₂³	1	2	yes	complemented
155	#20592	C₂³	1	2	yes	—
156	#20592	C₂³	1	1	yes	characteristic
157	#20585	C₂³	1	2	yes	—
158	#13095	C₂³	1	4	yes	complemented
159	#13093	C₂³	1	4	yes	complemented
160	#13091	C₂³	1	4	yes	complemented
161	#13089	C₂³	1	4	yes	complemented
162	#13087	C₂³	1	4	yes	—
163	#13087	C₂³	1	4	yes	—
164	#13083	C₂³	1	4	yes	—
165	#13083	C₂³	1	4	yes	—
166	#12703	C₂³	1	2	yes	—
167	#12701	C₂³	1	2	yes	—
168	#12697	C₂³	1	2	yes	—
169	#12695	C₂³	1	2	yes	—
170	#12691	C₂³	1	4	yes	complemented
171	#12689	C₂³	1	4	yes	complemented
172	#11148	C₂³	1	2	yes	complemented
173	#10993	C₂³	1	2	yes	complemented
174	#10987	C₂³	1	2	yes	—
175	#10984	C₂³	1	2	yes	complemented
176	#10979	C₂³	1	2	yes	—
177	#10973	C₂³	1	2	yes	complemented
178	#9511	C₂³	1	4	yes	—
179	#9511	C₂³	1	4	yes	—
180	#9445	C₂³	1	4	yes	complemented
181	#9443	C₂³	1	4	yes	complemented
182	#8739	C₂³	1	4	yes	complemented
183	#8516	C₂³	1	4	yes	complemented
184	C₂×#585	C₂⁴	1	2	yes	—
185	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
186	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
187	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
189	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
190	C₂×#560	C₂×D₄	1	2	yes	complemented
191	C₂×Q₈²	C₂×D₄	1	1	yes	characteristic, complemented
192	C₂×#555	C₂×D₄	1	1	yes	characteristic, complemented
193	C₂×#555	C₂×D₄	1	2	yes	complemented
194	C₂×#551	C₂×D₄	1	2	yes	complemented
195	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
196	C₂×D₄²	C₂×D₄	1	2	yes	complemented
197	C₂×D₄²	C₂×D₄	1	2	yes	complemented
198	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
199	C₂×#538	C₂×D₄	1	2	yes	complemented
200	C₂×#537	C₂×D₄	1	2	yes	—
201	C₂×#535	C₂×D₄	1	2	yes	—
202	C₂×#535	C₂×D₄	1	1	yes	characteristic
203	C₂×#535	C₂×D₄	1	1	yes	characteristic
204	C₂×#535	C₂×D₄	1	1	yes	characteristic
205	C₂×#535	C₂×D₄	1	1	yes	characteristic
206	C₂×#535	C₂×D₄	1	1	yes	characteristic
207	C₂×#535	C₂×D₄	1	1	yes	characteristic
208	C₂×#535	C₂×D₄	1	1	yes	characteristic
209	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂×#535	C₂⁴	1	1	yes	characteristic
212	C₂×#535	C₂⁴	1	1	yes	characteristic
213	C₂×#535	C₂⁴	1	1	yes	characteristic
214	C₂×#534	C₂×D₄	1	2	yes	—
215	C₂×#534	C₂×D₄	1	2	yes	—
216	C₂×#534	C₂×D₄	1	2	yes	complemented
217	C₂×#532	C₂×D₄	1	1	yes	characteristic
218	C₂×#532	C₂×D₄	1	2	yes	—
219	C₂×#532	C₂×D₄	1	1	yes	characteristic
220	C₂×#532	C₂⁴	1	1	yes	characteristic
221	C₂²×#127	C₂×D₄	1	1	yes	characteristic
222	C₂²×#127	C₂×D₄	1	1	yes	characteristic
223	C₂²×#127	C₂×D₄	1	1	yes	characteristic
224	C₂²×#127	C₂×D₄	1	1	yes	characteristic
225	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
227	C₂×#525	C₂×D₄	1	1	yes	characteristic
228	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
229	C₂×#525	C₂⁴	1	1	yes	characteristic
230	C₂²×#120	C₂×D₄	1	2	yes	—
231	C₂²×#120	C₂×D₄	1	2	yes	—
232	C₂²×#120	C₂×D₄	1	2	yes	—
233	C₂²×#120	C₂×D₄	1	2	yes	—
234	C₂²×#120	C₂×D₄	1	2	yes	—
235	C₂×#518	C₂×D₄	1	1	yes	characteristic
236	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
237	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
238	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
239	C₂×#413	C₂⁴	1	2	yes	—
240	C₂×#410	C₂⁴	1	2	yes	—
241	#2879	C₂⁴	1	2	yes	—
242	#2816	C₂×D₄	1	2	yes	complemented
243	#2815	C₂×D₄	1	2	yes	complemented
244	#2733	C₂×D₄	1	2	yes	complemented
245	#2733	C₂×D₄	1	2	yes	complemented
246	#2731	C₂×D₄	1	2	yes	complemented
247	#2731	C₂×D₄	1	2	yes	complemented
248	#2684	C₂×D₄	1	2	yes	complemented
249	#2684	C₂×D₄	1	2	yes	complemented
250	#2684	C₂×D₄	1	2	yes	complemented
251	#2684	C₂×D₄	1	2	yes	complemented
252	#2679	C₂×D₄	1	2	yes	complemented
253	#2679	C₂×D₄	1	2	yes	complemented
254	#2679	C₂×D₄	1	2	yes	complemented
255	#2679	C₂×D₄	1	2	yes	complemented
256	#2669	C₂×D₄	1	2	yes	complemented
257	#2669	C₂×D₄	1	2	yes	complemented
258	#2669	C₂×D₄	1	2	yes	complemented
259	#2669	C₂×D₄	1	2	yes	complemented
260	#2608	C₂×D₄	1	2	yes	complemented
261	#2607	C₂×D₄	1	2	yes	complemented
262	#2561	C₂×D₄	1	2	yes	complemented
263	#2539	C₂×D₄	1	2	yes	complemented
264	#2539	C₂×D₄	1	2	yes	complemented
265	#2539	C₂×D₄	1	2	yes	complemented
266	#2435	C₂×D₄	1	2	yes	—
267	#2435	C₂×D₄	1	2	yes	—
268	#2433	C₂×D₄	1	2	yes	—
269	#2433	C₂×D₄	1	2	yes	—
270	#2433	C₂×D₄	1	2	yes	—
271	#2433	C₂×D₄	1	2	yes	—
272	#2432	C₂×D₄	1	2	yes	—
273	#2432	C₂⁴	1	2	yes	—
274	#2431	C₂×D₄	1	2	yes	—
275	#2431	C₂×D₄	1	2	yes	—
276	#2431	C₂×D₄	1	2	yes	—
277	#2431	C₂⁴	1	2	yes	—
278	#2404	C₂×D₄	1	2	yes	—
279	#2404	C₂×D₄	1	2	yes	—
280	#2404	C₂⁴	1	2	yes	—
281	#2404	C₂⁴	1	2	yes	—
282	#2403	C₂×D₄	1	2	yes	—
283	#2403	C₂×D₄	1	2	yes	—
284	#2403	C₂×D₄	1	2	yes	—
285	#2403	C₂×D₄	1	2	yes	—
286	#2380	C₂×D₄	1	2	yes	complemented
287	#2379	C₂×D₄	1	2	yes	complemented
288	#2376	C₂×D₄	1	2	yes	complemented
289	#2375	C₂×D₄	1	2	yes	complemented
290	#2374	C₂×D₄	1	2	yes	complemented
291	#2369	C₂×D₄	1	1	yes	characteristic, complemented
292	#2369	C₂×D₄	1	1	yes	characteristic, complemented
293	#2366	C₂×D₄	1	1	yes	characteristic, complemented
294	#2366	C₂×D₄	1	1	yes	characteristic, complemented
295	#2358	C₂×D₄	1	2	yes	complemented
296	#2333	C₂×D₄	1	2	yes	complemented
297	#2333	C₂×D₄	1	2	yes	complemented
298	#2333	C₂×D₄	1	2	yes	complemented
299	#2332	C₂×D₄	1	2	yes	complemented
300	#2312	C₂×D₄	1	2	yes	complemented
301	#2311	C₂×D₄	1	2	yes	—
302	#2309	C₂×D₄	1	1	yes	characteristic
303	#2309	C₂×D₄	1	1	yes	characteristic, complemented
304	#2309	C₂×D₄	1	1	yes	characteristic, complemented
305	#2309	C₂×D₄	1	1	yes	characteristic, complemented
306	#2308	C₂×D₄	1	2	yes	—
307	#2308	C₂×D₄	1	2	yes	—
308	#2308	C₂×D₄	1	2	yes	—
309	#2297	C₂×D₄	1	2	yes	—
310	#2297	C₂×D₄	1	1	yes	characteristic
311	#2297	C₂×D₄	1	1	yes	characteristic, complemented
312	#2297	C₂⁴	1	1	yes	characteristic
313	#2296	C₂×D₄	1	1	yes	characteristic, complemented
314	C₂×#390	C₂×D₄	1	2	yes	—
315	#2285	C₂×D₄	1	1	yes	characteristic, complemented
316	#2280	C₂×D₄	1	1	yes	characteristic, complemented
317	#2273	C₂×D₄	1	2	yes	complemented
318	C₄×#117	C₂×D₄	1	1	yes	characteristic, complemented
319	#1785	C₂⁴	1	4	yes	—
320	#1782	C₂⁴	1	4	yes	—
321	C₂⁶	#120	1	2	yes	—
322	C₂⁶	#120	1	2	yes	—
323	C₂²×#41	#120	1	1	yes	characteristic
324	C₂²×#41	#120	1	1	yes	characteristic
325	C₂²×#41	#120	1	2	yes	—
326	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
327	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
328	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
329	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
330	C₂²×#41	C₂²×D₄	1	2	yes	—
331	C₂²×#41	C₂⁵	1	1	yes	characteristic
332	C₂³×D₄	#120	1	2	yes	—
333	C₂³×D₄	#120	1	1	yes	characteristic
334	C₂³×D₄	#120	1	2	yes	—
335	C₂³×D₄	#120	1	2	yes	—
336	C₂³×D₄	#120	1	1	yes	characteristic
337	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
338	C₂³×D₄	C₂²×D₄	1	2	yes	—
339	C₂³×D₄	C₂²×D₄	1	2	yes	—
340	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
341	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
342	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
343	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
345	C₂³×D₄	C₂²×D₄	1	2	yes	—
346	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
349	C₂×#127	#120	1	1	yes	characteristic
350	C₂×#127	#120	1	1	yes	characteristic
351	C₂×#127	#120	1	1	yes	characteristic
352	C₂×#127	#120	1	1	yes	characteristic
353	C₂×#127	#120	1	1	yes	characteristic
354	C₂×#127	#120	1	1	yes	characteristic
355	C₂×#127	#120	1	2	yes	—
356	C₂×#127	#120	1	2	yes	—
357	C₂×#127	#120	1	2	yes	—
358	C₂×#127	#120	1	2	yes	—
359	C₂×#127	#120	1	2	yes	—
360	C₂×#127	C₂²×D₄	1	1	yes	characteristic
361	C₂×#127	C₂²×D₄	1	1	yes	characteristic
362	C₂×#127	C₂²×D₄	1	1	yes	characteristic
363	C₂×#127	C₂²×D₄	1	2	yes	—
364	C₂×#124	#120	1	1	yes	characteristic
365	C₂×#124	#120	1	1	yes	characteristic
366	C₂×#124	#120	1	2	yes	—
367	C₂×#124	#120	1	2	yes	—
368	C₂×#124	#120	1	2	yes	—
369	C₂×#124	C₂²×D₄	1	1	yes	characteristic
370	C₂×#124	C₂²×D₄	1	1	yes	characteristic
371	C₂×#124	C₂²×D₄	1	1	yes	characteristic
372	C₂×#124	C₂²×D₄	1	2	yes	—
373	C₂×#124	C₂²×D₄	1	1	yes	characteristic
374	C₂×#124	C₂²×D₄	1	2	yes	—
375	C₂×#123	#120	1	1	yes	characteristic
376	C₂×#123	#120	1	1	yes	characteristic
377	C₂×#123	C₂²×D₄	1	2	yes	—
378	C₂×C₂²⋊Q₈	#120	1	2	yes	—
379	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
380	C₂×#121	#120	1	2	yes	—
381	C₂×#121	C₂²×D₄	1	2	yes	—
382	C₂×#121	C₂²×D₄	1	2	yes	—
383	C₂×#121	C₂²×D₄	1	2	yes	—
384	C₂×#120	#120	1	2	yes	—
385	C₂×#120	#120	1	1	yes	characteristic
386	C₂×#120	#120	1	1	yes	characteristic
387	C₂×#120	#120	1	2	yes	—
388	C₂×#120	#120	1	2	yes	—
389	C₂×#120	#120	1	2	yes	—
390	C₂×#120	#120	1	2	yes	—
391	C₂×#120	#120	1	2	yes	—
392	C₂×#120	C₂²×D₄	1	2	yes	—
393	C₂×#120	C₂²×D₄	1	2	yes	—
394	C₂×#120	C₂²×D₄	1	2	yes	—
395	C₂×#120	C₂²×D₄	1	2	yes	—
396	C₂×#120	C₂²×D₄	1	2	yes	—
397	C₂×#120	C₂²×D₄	1	2	yes	—
398	C₂×#120	C₂²×D₄	1	2	yes	—
399	C₂×#117	#120	1	2	yes	—
400	C₂×#117	#120	1	1	yes	characteristic
401	C₂×#117	#120	1	1	yes	characteristic
402	C₂×#117	C₂²×D₄	1	1	yes	characteristic
403	C₂×#117	C₂²×D₄	1	1	yes	characteristic
404	C₂×#117	C₂²×D₄	1	1	yes	characteristic
405	C₂×#117	C₂²×D₄	1	1	yes	characteristic
406	C₂×#117	C₂²×D₄	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	#120	1	2	yes	—
408	C₂²×C₂²⋊C₄	#120	1	2	yes	—
409	C₂²×C₂²⋊C₄	#120	1	2	yes	—
410	C₂²×C₂²⋊C₄	#120	1	2	yes	—
411	C₂²×C₂²⋊C₄	#120	1	2	yes	—
412	C₂²×C₂²⋊C₄	#120	1	2	yes	—
413	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
414	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
415	C₂²×C₄²	#120	1	1	yes	characteristic
416	C₂²×C₄²	#120	1	1	yes	characteristic
417	C₂²×C₄²	#120	1	2	yes	—
418	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
419	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
420	#391	#120	1	1	yes	characteristic
421	#391	#120	1	1	yes	characteristic
422	#391	C₂²×D₄	1	2	yes	—
423	#391	C₂²×D₄	1	2	yes	—
424	#390	#120	1	1	yes	characteristic
425	#390	#120	1	2	yes	—
426	#390	#120	1	2	yes	—
427	#390	#120	1	2	yes	—
428	#390	#120	1	2	yes	—
429	#390	#120	1	2	yes	—
430	#390	#120	1	2	yes	—
431	#390	#120	1	1	yes	characteristic
432	#390	C₂²×D₄	1	2	yes	—
433	#390	C₂²×D₄	1	2	yes	—
434	#386	#120	1	2	yes	—
435	#386	#120	1	2	yes	—
436	#386	#120	1	2	yes	—
437	#386	#120	1	2	yes	—
438	#386	C₂²×D₄	1	2	yes	—
439	#386	C₂²×D₄	1	2	yes	—
440	#386	C₂²×D₄	1	2	yes	—
441	#386	C₂²×D₄	1	2	yes	—
442	#381	C₂²×D₄	1	2	yes	—
443	#381	C₂²×D₄	1	2	yes	—
444	#379	#120	1	2	yes	—
445	#379	#120	1	2	yes	—
446	C₄×C₂²⋊C₄	#120	1	2	yes	—
447	C₄×C₂²⋊C₄	#120	1	2	yes	—
448	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
449	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
452	C₂⁵	C₂×#120	1	2	yes	—
453	C₂⁵	C₂×#120	1	2	yes	—
454	C₂⁵	C₂×#120	1	1	yes	characteristic
455	C₂⁵	C₂×#120	1	2	yes	—
456	C₂⁵	C₂×#120	1	2	yes	—
457	C₂⁵	C₂×#120	1	2	yes	—
458	C₂⁵	C₂×#120	1	2	yes	—
459	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
460	C₂²×Q₈	C₂×#120	1	2	yes	—
461	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
463	C₂²×D₄	C₂×#120	1	1	yes	characteristic
464	C₂²×D₄	C₂×#120	1	2	yes	—
465	C₂²×D₄	C₂×#120	1	2	yes	—
466	C₂²×D₄	C₂×#120	1	1	yes	characteristic
467	C₂²×D₄	C₂×#120	1	1	yes	characteristic
468	C₂²×D₄	C₂×#120	1	1	yes	characteristic
469	C₂²×D₄	C₂×#120	1	1	yes	characteristic
470	C₂²×D₄	C₂×#120	1	2	yes	—
471	C₂²×D₄	C₂×#120	1	2	yes	—
472	C₂²×D₄	C₂×#120	1	1	yes	characteristic
473	C₂²×D₄	C₂×#120	1	2	yes	—
474	C₂²×D₄	C₂×#120	1	1	yes	characteristic
475	C₂²×D₄	C₂×#120	1	1	yes	characteristic
476	C₂²×D₄	C₂×#120	1	2	yes	—
477	C₂²×D₄	C₂×#120	1	2	yes	—
478	C₂²×D₄	C₂³×D₄	1	2	yes	—
479	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
480	C₂³×C₄	C₂×#120	1	2	yes	—
481	C₂³×C₄	C₂×#120	1	1	yes	characteristic
482	C₂³×C₄	C₂×#120	1	1	yes	characteristic
483	C₂³×C₄	C₂×#120	1	1	yes	characteristic
484	C₂³×C₄	C₂×#120	1	2	yes	—
485	C₂³×C₄	C₂×#120	1	2	yes	—
486	C₂³×C₄	C₂×#120	1	2	yes	—
487	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
488	C₂³×C₄	C₂³×D₄	1	2	yes	—
489	#127	B(4,𝔽₂)	1	4	yes	—
490	#123	B(4,𝔽₂)	1	4	yes	—
491	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
494	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
502	C₂×C₄²	C₂×#120	1	1	yes	characteristic
503	C₂×C₄²	C₂×#120	1	1	yes	characteristic
504	C₂×C₄²	C₂×#120	1	1	yes	characteristic
505	C₂×C₄²	C₂×#120	1	1	yes	characteristic
506	C₂×C₄²	C₂×#120	1	2	yes	—
507	C₂×C₄²	C₂×#120	1	2	yes	—
508	C₂×C₄²	C₂×#120	1	2	yes	—
509	C₂×C₄²	C₂×#120	1	2	yes	—
510	C₂×C₄²	C₂×#120	1	2	yes	—
511	C₂×C₄²	C₂×#120	1	1	yes	characteristic
512	C₂×C₄²	C₂×#120	1	1	yes	characteristic
513	C₂⁴	#2846	1	2	yes	—
514	C₂⁴	#2846	1	1	yes	characteristic
515	C₂⁴	#2846	1	1	yes	characteristic
516	C₂⁴	#2846	1	2	yes	—
517	C₂⁴	C₂²×#120	1	2	yes	—
518	C₂⁴	C₂²×#120	1	1	yes	characteristic
519	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
520	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
521	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
522	C₂×D₄	#3026	1	2	yes	—
523	C₂×D₄	#3026	1	2	yes	—
524	C₂²×C₄	#2846	1	1	yes	characteristic
525	C₂²×C₄	#2846	1	1	yes	characteristic
526	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
527	C₂²×C₄	C₂²×#120	1	2	yes	—
528	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
529	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
530	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
531	C₄²	C₂×B(4,𝔽₂)	1	2	yes	—
532	C₂³	#32898	1	2	yes	—
533	C₂³	#32898	1	4	yes	—
534	C₂³	C₂×#2846	1	1	yes	characteristic
535	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
536	C₂³	C₂×#3026	1	1	yes	characteristic
537	C₂×C₄	#32898	1	2	yes	—
538	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
539	C₂×C₄	C₂×#3026	1	1	yes	characteristic
540	C₂×C₄	#60399	1	2	yes	—
541	C₂²	C₂×#32898	1	1	yes	characteristic
542	C₂²	C₂×#32898	1	1	yes	characteristic
543	C₂²	#6628896	1	1	yes	characteristic
544	C₂	#72216323	1	1	yes	characteristic
545	C₂	#72234102	1	1	yes	characteristic
546	C₂	#72260545	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6628896
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
LCS	G ▷ C₂²×#41 ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #35527 ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261283	C₂	semidirect
2. #72261277	C₂	semidirect
3. #72261270	C₂	semidirect
4. #72261263	C₂	semidirect
5. #72261257	C₂	semidirect
6. #72261249	C₂	semidirect
7. #72261184	C₂	semidirect
8. #72261064	C₂	semidirect
9. #72238583	C₂	semidirect
10. #72234197	C₂	semidirect
11. #72234193	C₂	semidirect
12. #72234146	C₂	semidirect
13. #72233417	C₂	semidirect
14. #72233051	C₂	semidirect
15. #72232835	C₂	semidirect
16. #72232771	C₂	semidirect
17. #72219653	C₂	semidirect
18. C₂×#60399	C₂²	semidirect
19. C₂×#60388	C₂²	semidirect
20. #8943482	C₂²	semidirect
22. #8797683	C₂²	semidirect
23. #8196400	C₂²	semidirect
24. #8195113	C₂²	semidirect
25. #8110542	C₂²	semidirect
30. #7670609	C₂²	semidirect
31. #6628896	C₂²	semidirect
32. #6628876	C₂²	semidirect
33. #6628872	C₂²	semidirect
34. #499877	C₂²	semidirect
35. #499875	C₂²	semidirect
36. #499861	C₂²	semidirect
37. #499844	C₂²	semidirect
38. #499844	C₂²	semidirect
39. #499831	C₂²	semidirect
40. #499811	C₂²	semidirect
41. #499803	C₂²	semidirect
42. #499799	C₂²	semidirect
43. #499791	C₂²	semidirect
44. #494738	C₂²	semidirect
45. #494721	C₂²	semidirect
46. #494700	C₂²	semidirect
47. #494682	C₂²	semidirect
48. #493441	C₂²	semidirect
49. #493430	C₂²	semidirect
50. #493424	C₂²	semidirect
51. #449496	C₂²	semidirect
52. #417841	C₂²	semidirect
53. #417562	C₂²	semidirect
54. #417540	C₂²	semidirect
55. #374034	C₂²	semidirect
56. #359601	C₂²	semidirect
57. #359593	C₂²	semidirect
58. #254516	C₂²	semidirect
59. #254474	C₂²	semidirect
60. #246345	C₂²	semidirect
61. #246319	C₂²	semidirect
62. #214619	C₂²	semidirect
63. #214616	C₂²	semidirect
64. #213906	C₂²	semidirect
65. #134030	C₂²	semidirect
66. #133918	C₂²	semidirect
67. #133902	C₂²	semidirect
68. #133843	C₂²	semidirect
69. #133474	C₂²	semidirect
70. #133470	C₂²	semidirect
71. #133418	C₂²	semidirect
72. #133414	C₂²	semidirect
73. #133403	C₂²	semidirect
74. #133399	C₂²	semidirect
75. #133386	C₂²	semidirect
76. #133382	C₂²	semidirect
77. #133365	C₂²	semidirect
78. #133350	C₂²	semidirect
79. #133343	C₂²	semidirect
80. #133342	C₂²	semidirect
81. #133326	C₂²	semidirect
82. #133326	C₂²	semidirect
85. C₂×#3484	D₄	semidirect
87. C₂×#3532	D₄	semidirect
88. C₂×#3483	D₄	semidirect
89. C₂²×D₄²	D₄	semidirect
90. C₂³×#127	D₄	semidirect
91. C₂×#3027	C₂³	semidirect
92. C₂×#3025	C₂³	semidirect
95. #60369	C₂³	semidirect
99. #59126	D₄	semidirect
100. #59126	D₄	semidirect
101. #59084	D₄	semidirect
103. #59056	D₄	semidirect
107. #58990	D₄	semidirect
108. C₂×#2679	D₄	semidirect
109. #52004	D₄	semidirect
111. #51896	D₄	semidirect
113. #50856	D₄	semidirect
114. #50646	D₄	semidirect
117. #46454	D₄	semidirect
118. #46452	D₄	semidirect
119. #46425	D₄	semidirect
122. #46354	D₄	semidirect
124. #45439	D₄	semidirect
125. #37273	D₄	semidirect
127. #36812	D₄	semidirect
128. #36703	D₄	semidirect
129. #36702	D₄	semidirect
130. #36702	D₄	semidirect
132. #35528	D₄	semidirect
134. #35527	D₄	semidirect
138. #35438	D₄	semidirect
139. #35390	D₄	semidirect
142. #35272	D₄	semidirect
143. #35222	D₄	semidirect
145. #34408	D₄	semidirect
146. #34368	D₄	semidirect
147. #34364	D₄	semidirect
148. #34210	D₄	semidirect
149. C₄×#525	D₄	semidirect
152. #32893	C₂³	semidirect
153. #32890	C₂³	semidirect
154. #20606	C₂³	semidirect
158. #13095	C₂³	semidirect
159. #13093	C₂³	semidirect
160. #13091	C₂³	semidirect
161. #13089	C₂³	semidirect
170. #12691	C₂³	semidirect
171. #12689	C₂³	semidirect
172. #11148	C₂³	semidirect
173. #10993	C₂³	semidirect
175. #10984	C₂³	semidirect
177. #10973	C₂³	semidirect
180. #9445	C₂³	semidirect
181. #9443	C₂³	semidirect
182. #8739	C₂³	semidirect
183. #8516	C₂³	semidirect
188. C₂⁴×D₄	C₂×D₄	semidirect
189. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
190. C₂×#560	C₂×D₄	semidirect
191. C₂×Q₈²	C₂×D₄	semidirect
192. C₂×#555	C₂×D₄	semidirect
193. C₂×#555	C₂×D₄	semidirect
194. C₂×#551	C₂×D₄	semidirect
195. C₂×D₄²	C₂×D₄	semidirect
196. C₂×D₄²	C₂×D₄	semidirect
197. C₂×D₄²	C₂×D₄	semidirect
198. C₂×D₄²	C₂×D₄	semidirect
199. C₂×#538	C₂×D₄	semidirect
209. C₂×#535	C₂×D₄	semidirect
210. C₂×#535	C₂×D₄	semidirect
216. C₂×#534	C₂×D₄	semidirect
225. C₂²×#127	C₂×D₄	semidirect
226. C₂²×#127	C₂×D₄	semidirect
228. C₂×#525	C₂×D₄	semidirect
236. C₂×#518	C₂×D₄	semidirect
238. C₂³×C₄²	C₂×D₄	semidirect
242. #2816	C₂×D₄	semidirect
243. #2815	C₂×D₄	semidirect
244. #2733	C₂×D₄	semidirect
245. #2733	C₂×D₄	semidirect
246. #2731	C₂×D₄	semidirect
247. #2731	C₂×D₄	semidirect
248. #2684	C₂×D₄	semidirect
249. #2684	C₂×D₄	semidirect
250. #2684	C₂×D₄	semidirect
251. #2684	C₂×D₄	semidirect
252. #2679	C₂×D₄	semidirect
253. #2679	C₂×D₄	semidirect
254. #2679	C₂×D₄	semidirect
255. #2679	C₂×D₄	semidirect
256. #2669	C₂×D₄	semidirect
257. #2669	C₂×D₄	semidirect
258. #2669	C₂×D₄	semidirect
259. #2669	C₂×D₄	semidirect
260. #2608	C₂×D₄	semidirect
261. #2607	C₂×D₄	semidirect
262. #2561	C₂×D₄	semidirect
263. #2539	C₂×D₄	semidirect
264. #2539	C₂×D₄	semidirect
265. #2539	C₂×D₄	semidirect
286. #2380	C₂×D₄	semidirect
287. #2379	C₂×D₄	semidirect
288. #2376	C₂×D₄	semidirect
289. #2375	C₂×D₄	semidirect
290. #2374	C₂×D₄	semidirect
291. #2369	C₂×D₄	semidirect
292. #2369	C₂×D₄	semidirect
293. #2366	C₂×D₄	semidirect
294. #2366	C₂×D₄	semidirect
295. #2358	C₂×D₄	semidirect
296. #2333	C₂×D₄	semidirect
297. #2333	C₂×D₄	semidirect
298. #2333	C₂×D₄	semidirect
299. #2332	C₂×D₄	semidirect
300. #2312	C₂×D₄	semidirect
303. #2309	C₂×D₄	semidirect
304. #2309	C₂×D₄	semidirect
305. #2309	C₂×D₄	semidirect
311. #2297	C₂×D₄	semidirect
313. #2296	C₂×D₄	semidirect
315. #2285	C₂×D₄	semidirect
316. #2280	C₂×D₄	semidirect
317. #2273	C₂×D₄	semidirect
318. C₄×#117	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72261283	2
#72261277	2
#72261270	2
#72261263	2
#72261257	2
#72261249	2
#72261184	2
#72261064	2
#72238583	2
#72234197	2
#72234193	2
#72234146	2
#72233417	2
#72233051	2
#72232835	2
#72232771	2
#72219653	2