Subgroups — #72262309

Order 2048.

At least 14927 conjugacy classes of subgroups; only the 978 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	#72262307	C₂	1	4	yes	maximal, complemented
2	#72262305	C₂	1	2	yes	maximal, complemented
3	#72262302	C₂	1	2	yes	maximal, complemented
4	#72262281	C₂	1	2	yes	maximal, complemented
5	#72262280	C₂	1	2	yes	maximal, complemented
6	#72261438	C₂	1	2	yes	maximal, complemented
7	#72249538	C₂	1	1	yes	maximal, characteristic, complemented
8	#72238594	C₂	1	1	yes	maximal, characteristic, complemented
9	#72238471	C₂	1	2	yes	maximal, complemented
10	#72238456	C₂	1	2	yes	maximal, complemented
11	#72236896	C₂	1	1	yes	maximal, characteristic, complemented
12	#72236837	C₂	1	1	yes	maximal, characteristic, complemented
13	#72233383	C₂	1	4	yes	maximal, complemented
14	#72233358	C₂	1	2	yes	maximal, complemented
15	#72233065	C₂	1	1	yes	maximal, characteristic, complemented
16	#72231810	C₂	1	1	yes	maximal, characteristic, complemented
17	#72225994	C₂	1	1	yes	maximal, characteristic, complemented
18	#8126631	C₂²	1	2	yes	—
19	#8125493	C₂²	1	2	yes	—
20	#8108077	C₂²	1	2	yes	complemented
21	#8108057	C₂²	1	2	yes	complemented
22	#8093660	C₂²	1	1	yes	characteristic, complemented
23	#8093623	C₂²	1	1	yes	characteristic, complemented
24	#7681968	C₂²	1	1	yes	characteristic, complemented
25	#7681927	C₂²	1	1	yes	characteristic, complemented
26	#7642273	C₂²	1	1	yes	characteristic
27	#7642244	C₂²	1	1	yes	characteristic
28	C₂×#35346	C₂²	1	1	yes	characteristic, complemented
29	C₂×#34980	C₂²	1	1	yes	characteristic
30	#6628892	C₂²	1	2	yes	complemented
31	C₂×#32898	C₂²	1	1	yes	characteristic, complemented
32	C₂×#32898	C₂²	1	1	yes	characteristic, complemented
33	#6628867	C₂²	1	2	yes	complemented
34	#500071	C₂²	1	4	yes	complemented
35	#500067	C₂²	1	4	yes	complemented
36	#500053	C₂²	1	4	yes	complemented
37	#500049	C₂²	1	4	yes	complemented
38	#499797	C₂²	1	4	yes	complemented
39	#499795	C₂²	1	4	yes	complemented
40	#499789	C₂²	1	4	yes	complemented
41	#499787	C₂²	1	4	yes	complemented
42	#496231	C₂²	1	2	yes	complemented
43	#496231	C₂²	1	2	yes	complemented
44	#496225	C₂²	1	2	yes	complemented
45	#496225	C₂²	1	2	yes	complemented
46	#496194	C₂²	1	2	yes	complemented
47	#496194	C₂²	1	2	yes	complemented
48	#449501	C₂²	1	2	yes	complemented
49	#449475	C₂²	1	2	yes	complemented
50	#417508	C₂²	1	2	yes	—
51	#417508	C₂²	1	2	yes	complemented
52	#382422	C₂²	1	1	yes	characteristic, complemented
53	#379754	C₂²	1	1	yes	characteristic, complemented
54	#379754	C₂²	1	1	yes	characteristic, complemented
55	#249355	C₂²	1	4	yes	complemented
56	#249331	C₂²	1	2	yes	complemented
57	#249319	C₂²	1	2	yes	complemented
58	#245246	C₂²	1	4	yes	complemented
59	#245226	C₂²	1	2	yes	complemented
60	#245225	C₂²	1	2	yes	complemented
61	#201687	C₂²	1	2	yes	complemented
62	#201322	C₂²	1	2	yes	complemented
63	C₂×#8547	C₂²	1	1	yes	characteristic, complemented
64	C₂×#8541	C₂²	1	1	yes	characteristic, complemented
65	#133925	C₂²	1	2	yes	complemented
66	#133893	C₂²	1	2	yes	complemented
67	#133893	C₂²	1	2	yes	complemented
68	#133822	C₂²	1	2	yes	complemented
69	#133533	C₂²	1	4	yes	complemented
70	#133531	C₂²	1	4	yes	complemented
71	#133529	C₂²	1	4	yes	complemented
72	#133527	C₂²	1	4	yes	complemented
73	#133396	C₂²	1	4	yes	complemented
74	#133394	C₂²	1	4	yes	complemented
75	#133392	C₂²	1	4	yes	complemented
76	#133390	C₂²	1	4	yes	complemented
77	#133293	C₂²	1	4	yes	complemented
78	#133291	C₂²	1	2	yes	complemented
79	#133290	C₂²	1	2	yes	complemented
80	#133281	C₂²	1	4	yes	complemented
81	#133279	C₂²	1	2	yes	complemented
82	#133278	C₂²	1	2	yes	complemented
83	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
84	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
85	C₂×#3490	D₄	1	1	yes	characteristic, complemented
86	C₂×#3484	D₄	1	1	yes	characteristic, complemented
87	C₂³×#120	C₂³	1	1	yes	characteristic
88	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
89	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
90	#59193	C₂³	1	2	yes	—
91	#59006	C₂³	1	2	yes	—
92	#58992	C₂³	1	2	yes	—
93	#58990	C₂³	1	2	yes	—
94	#52012	D₄	1	2	yes	complemented
95	#52004	D₄	1	2	yes	complemented
96	#51993	D₄	1	2	yes	complemented
97	#51945	D₄	1	2	yes	complemented
98	#51940	D₄	1	2	yes	complemented
99	#51940	D₄	1	2	yes	complemented
100	#51902	D₄	1	2	yes	complemented
101	#51895	D₄	1	2	yes	complemented
102	#50856	D₄	1	2	yes	complemented
103	#50646	D₄	1	2	yes	complemented
104	#48922	D₄	1	2	yes	complemented
105	#48143	D₄	1	2	yes	complemented
106	#48113	D₄	1	2	yes	complemented
107	#48088	D₄	1	2	yes	complemented
108	#47848	D₄	1	2	yes	complemented
109	#47827	D₄	1	2	yes	complemented
110	#45568	C₂³	1	2	yes	—
111	#45537	C₂³	1	2	yes	—
112	#45439	C₂³	1	2	yes	—
113	#45438	C₂³	1	2	yes	—
114	#36714	D₄	1	2	yes	complemented
115	#36714	C₂³	1	2	yes	—
116	#36703	D₄	1	2	yes	complemented
117	#36703	C₂³	1	2	yes	—
118	C₂×#2849	D₄	1	1	yes	characteristic, complemented
119	C₂×#2849	C₂³	1	1	yes	characteristic
120	C₂×#2846	D₄	1	1	yes	characteristic, complemented
121	C₂×#2846	C₂³	1	1	yes	characteristic
122	#35390	D₄	1	1	yes	characteristic, complemented
123	#35390	C₂³	1	1	yes	characteristic
124	#35367	D₄	1	1	yes	characteristic, complemented
125	#35367	C₂³	1	1	yes	characteristic
126	#35350	D₄	1	1	yes	characteristic, complemented
127	#35350	C₂³	1	1	yes	characteristic
128	#35346	D₄	1	1	yes	characteristic, complemented
129	#35346	C₂³	1	1	yes	characteristic
130	#35346	C₂³	1	2	yes	—
131	#35346	C₂³	1	2	yes	—
132	#35222	C₂³	1	2	yes	—
133	#35050	D₄	1	2	yes	complemented
134	#34980	D₄	1	2	yes	complemented
135	#34980	C₂³	1	2	yes	—
136	C₂×#2405	D₄	1	1	yes	characteristic, complemented
137	C₂×#2405	D₄	1	1	yes	characteristic, complemented
138	C₂×#2410	D₄	1	1	yes	characteristic, complemented
139	C₂×#2410	D₄	1	1	yes	characteristic, complemented
140	C₂×#2410	C₂³	1	1	yes	characteristic
141	C₂×#2410	C₂³	1	1	yes	characteristic
142	C₂×#2403	C₂³	1	1	yes	characteristic
143	C₂×#2403	C₂³	1	1	yes	characteristic
144	#34176	D₄	1	1	yes	characteristic, complemented
145	#34171	D₄	1	1	yes	characteristic, complemented
146	C₂×#2308	C₂³	1	1	yes	characteristic
147	C₂²×#379	D₄	1	1	yes	characteristic, complemented
148	#32900	C₂³	1	4	yes	—
149	#32898	C₂³	1	4	yes	—
150	#32891	C₂³	1	4	yes	—
151	#32888	C₂³	1	4	yes	—
152	C₂×#1790	C₂³	1	2	yes	—
153	C₂×#1790	C₂³	1	2	yes	—
154	C₂×#1783	C₂³	1	2	yes	—
155	C₂×#1781	C₂³	1	2	yes	—
156	C₂×#1781	C₂³	1	1	yes	characteristic
157	C₂×#1781	C₂³	1	1	yes	characteristic
158	#13090	C₂³	1	4	yes	—
159	#13090	C₂³	1	4	yes	—
160	#13088	C₂³	1	4	yes	—
161	#13088	C₂³	1	4	yes	—
162	#13086	C₂³	1	4	yes	—
163	#13086	C₂³	1	4	yes	—
164	#13084	C₂³	1	4	yes	—
165	#13084	C₂³	1	4	yes	—
166	#12852	C₂³	1	4	yes	—
167	#12852	C₂³	1	4	yes	—
168	#12687	C₂³	1	4	yes	—
169	#12687	C₂³	1	4	yes	—
170	#11174	C₂³	1	2	yes	—
171	#11174	C₂³	1	2	yes	—
172	#10991	C₂³	1	2	yes	—
173	#10991	C₂³	1	2	yes	—
174	#10965	C₂³	1	2	yes	—
175	#10965	C₂³	1	2	yes	—
176	#9499	C₂³	1	4	yes	—
177	#9495	C₂³	1	4	yes	—
178	#9463	C₂³	1	4	yes	—
179	#9459	C₂³	1	4	yes	—
180	#8547	C₂³	1	2	yes	—
181	#8547	C₂³	1	2	yes	—
182	#8541	C₂³	1	2	yes	—
183	#8541	C₂³	1	2	yes	—
184	C₂⁷	C₂×D₄	1	1	yes	characteristic
185	C₂⁷	C₂×D₄	1	1	yes	characteristic
186	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
187	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
188	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
195	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
196	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
197	C₂×#560	C₂×D₄	1	2	yes	complemented
198	C₂×#551	C₂×D₄	1	2	yes	complemented
199	C₂×D₄²	C₂×D₄	1	2	yes	complemented
200	C₂×#543	C₂×D₄	1	1	yes	characteristic
201	C₂×#538	C₂×D₄	1	2	yes	—
202	C₂×#535	C₂×D₄	1	2	yes	—
203	C₂×#535	C₂×D₄	1	2	yes	—
204	C₂×#534	C₂×D₄	1	2	yes	—
205	C₂×#534	C₂×D₄	1	2	yes	—
206	C₂×#534	C₂×D₄	1	2	yes	—
207	C₂×#534	C₂×D₄	1	1	yes	characteristic
208	C₂×#525	C₂×D₄	1	2	yes	—
209	C₂²×#120	C₂×D₄	1	1	yes	characteristic
210	C₂²×#120	C₂×D₄	1	1	yes	characteristic
211	C₂²×#120	C₂×D₄	1	1	yes	characteristic
212	C₂²×#120	C₂×D₄	1	1	yes	characteristic
213	C₂²×#120	C₂×D₄	1	1	yes	characteristic
214	C₂²×#120	C₂×D₄	1	1	yes	characteristic
215	C₂²×#120	C₂×D₄	1	1	yes	characteristic
216	C₂²×#120	C₂×D₄	1	1	yes	characteristic
217	C₂²×#120	C₂×D₄	1	2	yes	—
218	C₂²×#120	C₂⁴	1	1	yes	characteristic
219	C₂²×#120	C₂⁴	1	1	yes	characteristic
220	C₂²×#120	C₂⁴	1	1	yes	characteristic
221	C₂²×#120	C₂⁴	1	1	yes	characteristic
222	C₂×#518	C₂×D₄	1	1	yes	characteristic
223	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₂²×#99	C₂⁴	1	2	yes	—
229	C₂²×#99	C₂⁴	1	2	yes	—
230	#2804	C₂×D₄	1	2	yes	complemented
231	#2748	C₂×D₄	1	2	yes	complemented
232	#2748	C₂×D₄	1	2	yes	complemented
233	#2717	C₂×D₄	1	2	yes	complemented
234	#2709	C₂×D₄	1	2	yes	complemented
235	#2697	C₂×D₄	1	2	yes	complemented
236	#2697	C₂×D₄	1	2	yes	complemented
237	#2684	C₂×D₄	1	2	yes	complemented
238	#2684	C₂×D₄	1	2	yes	complemented
239	#2684	C₂×D₄	1	2	yes	complemented
240	#2683	C₂×D₄	1	2	yes	complemented
241	#2679	C₂×D₄	1	2	yes	complemented
242	#2679	C₂×D₄	1	2	yes	complemented
243	#2669	C₂×D₄	1	2	yes	complemented
244	#2669	C₂×D₄	1	2	yes	complemented
245	#2669	C₂×D₄	1	2	yes	complemented
246	#2561	C₂×D₄	1	2	yes	—
247	#2561	C₂×D₄	1	2	yes	—
248	#2539	C₂×D₄	1	2	yes	—
249	#2539	C₂×D₄	1	2	yes	—
250	#2435	C₂×D₄	1	2	yes	—
251	#2435	C₂×D₄	1	2	yes	—
252	#2435	C₂×D₄	1	2	yes	—
253	#2435	C₂⁴	1	2	yes	—
254	#2433	C₂×D₄	1	2	yes	—
255	#2433	C₂×D₄	1	2	yes	—
256	#2433	C₂×D₄	1	2	yes	—
257	#2433	C₂⁴	1	2	yes	—
258	#2405	C₂×D₄	1	2	yes	—
259	#2405	C₂×D₄	1	2	yes	—
260	#2405	C₂×D₄	1	2	yes	—
261	#2405	C₂×D₄	1	2	yes	—
262	#2405	C₂×D₄	1	2	yes	—
263	#2405	C₂⁴	1	2	yes	—
264	#2403	C₂×D₄	1	2	yes	—
265	#2403	C₂×D₄	1	2	yes	—
266	#2403	C₂×D₄	1	2	yes	—
267	#2403	C₂×D₄	1	2	yes	—
268	#2403	C₂×D₄	1	2	yes	—
269	#2403	C₂×D₄	1	2	yes	—
270	#2403	C₂×D₄	1	2	yes	—
271	#2403	C₂×D₄	1	2	yes	—
272	#2403	C₂×D₄	1	2	yes	—
273	#2403	C₂×D₄	1	2	yes	—
274	#2403	C₂×D₄	1	2	yes	—
275	#2403	C₂×D₄	1	2	yes	—
276	#2403	C₂×D₄	1	2	yes	—
277	#2403	C₂⁴	1	2	yes	—
278	#2380	C₂×D₄	1	2	yes	complemented
279	#2379	C₂×D₄	1	2	yes	complemented
280	#2376	C₂×D₄	1	2	yes	complemented
281	#2375	C₂×D₄	1	2	yes	complemented
282	#2375	C₂×D₄	1	2	yes	complemented
283	#2375	C₂×D₄	1	2	yes	complemented
284	#2374	C₂×D₄	1	2	yes	complemented
285	#2372	C₂×D₄	1	2	yes	complemented
286	#2366	C₂×D₄	1	2	yes	complemented
287	#2358	C₂×D₄	1	2	yes	complemented
288	#2358	C₂×D₄	1	2	yes	complemented
289	#2358	C₂×D₄	1	2	yes	complemented
290	#2312	C₂×D₄	1	2	yes	—
291	#2309	C₂×D₄	1	2	yes	—
292	#2309	C₂×D₄	1	2	yes	—
293	#2309	C₂×D₄	1	2	yes	—
294	#2308	C₂×D₄	1	1	yes	characteristic
295	#2308	C₂×D₄	1	1	yes	characteristic
296	#2308	C₂×D₄	1	2	yes	—
297	#2308	C₂×D₄	1	2	yes	—
298	#2308	C₂⁴	1	2	yes	—
299	C₂×#386	C₂×D₄	1	1	yes	characteristic
300	C₂×#386	C₂×D₄	1	1	yes	characteristic
301	C₂×#386	C₂⁴	1	1	yes	characteristic
302	C₂×#386	C₂⁴	1	1	yes	characteristic
303	C₂×#385	C₂×D₄	1	1	yes	characteristic
304	C₂×#385	C₂×D₄	1	1	yes	characteristic
305	C₂×#385	C₂×D₄	1	1	yes	characteristic
306	C₂×#385	C₂×D₄	1	1	yes	characteristic
307	#2280	C₂×D₄	1	2	yes	—
308	C₂×#379	C₂×D₄	1	2	yes	—
309	C₂×#379	C₂×D₄	1	1	yes	characteristic
310	C₂×#379	C₂×D₄	1	1	yes	characteristic
311	C₂×#379	C₂×D₄	1	1	yes	characteristic
312	C₂×#379	C₂×D₄	1	1	yes	characteristic
313	C₂×#379	C₂×D₄	1	1	yes	characteristic
314	C₂×#379	C₂×D₄	1	1	yes	characteristic
315	C₂×#379	C₂×D₄	1	1	yes	characteristic
316	C₂×#379	C₂×D₄	1	1	yes	characteristic
317	#2273	C₂×D₄	1	1	yes	characteristic
318	#2273	C₂×D₄	1	1	yes	characteristic
319	#1783	C₂⁴	1	4	yes	—
320	#1781	C₂⁴	1	4	yes	—
321	C₂⁶	#120	1	1	yes	characteristic
322	C₂⁶	#120	1	1	yes	characteristic
323	C₂⁶	#120	1	1	yes	characteristic
324	C₂⁶	#120	1	1	yes	characteristic
325	C₂⁶	C₂²×D₄	1	1	yes	characteristic
326	C₂⁶	C₂²×D₄	1	1	yes	characteristic
327	C₂⁶	C₂²×D₄	1	1	yes	characteristic
328	C₂⁶	C₂²×D₄	1	1	yes	characteristic
329	C₂⁶	C₂²×D₄	1	1	yes	characteristic
330	C₂⁶	C₂²×D₄	1	1	yes	characteristic
331	C₂²×#41	#120	1	2	yes	complemented
332	C₂³×D₄	#120	1	1	yes	characteristic
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	2	yes	—
337	C₂³×D₄	#120	1	2	yes	—
338	C₂³×D₄	#120	1	1	yes	characteristic
339	C₂³×D₄	#120	1	1	yes	characteristic
340	C₂³×D₄	#120	1	2	yes	complemented
341	C₂³×D₄	#120	1	2	yes	complemented
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	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
347	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
348	C₂³×D₄	C₂²×D₄	1	2	yes	—
349	C₂³×D₄	C₂²×D₄	1	2	yes	—
350	C₂³×D₄	C₂²×D₄	1	2	yes	—
351	C₂³×D₄	C₂²×D₄	1	2	yes	—
352	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
353	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
354	C₂³×D₄	C₂⁵	1	1	yes	characteristic
355	C₂⁴×C₄	#120	1	1	yes	characteristic
356	C₂⁴×C₄	#120	1	1	yes	characteristic
357	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
358	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
359	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
360	C₂×#127	#120	1	2	yes	complemented
361	C₂×#127	#120	1	2	yes	complemented
362	C₂×#127	C₂²×D₄	1	2	yes	—
363	C₂×#127	C₂²×D₄	1	2	yes	—
364	C₂×#124	#120	1	2	yes	complemented
365	C₂×#124	#120	1	2	yes	complemented
366	C₂×#124	C₂²×D₄	1	2	yes	—
367	C₂×#124	C₂²×D₄	1	2	yes	—
368	C₂×#123	#120	1	2	yes	complemented
369	C₂×#123	#120	1	2	yes	complemented
370	C₂×#123	C₂²×D₄	1	2	yes	—
371	C₂×#123	C₂²×D₄	1	2	yes	—
372	C₂×C₂²⋊Q₈	#120	1	2	yes	complemented
373	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
374	C₂×#121	#120	1	2	yes	complemented
375	C₂×#121	C₂²×D₄	1	2	yes	—
376	C₂×#120	#120	1	2	yes	—
377	C₂×#120	#120	1	2	yes	—
378	C₂×#120	#120	1	2	yes	—
379	C₂×#120	#120	1	2	yes	—
380	C₂×#120	#120	1	2	yes	complemented
381	C₂×#120	#120	1	2	yes	complemented
382	C₂×#120	C₂²×D₄	1	2	yes	—
383	C₂×#120	C₂²×D₄	1	2	yes	—
384	C₂×#120	C₂²×D₄	1	2	yes	—
385	C₂×#120	C₂²×D₄	1	2	yes	—
386	C₂×#120	C₂²×D₄	1	2	yes	—
387	C₂×#120	C₂²×D₄	1	2	yes	—
388	C₂×#117	#120	1	2	yes	complemented
389	C₂×#117	#120	1	2	yes	complemented
390	C₂×#117	#120	1	2	yes	complemented
391	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
396	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
397	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
398	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
399	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
400	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
401	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
405	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
406	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
412	#390	#120	1	2	yes	complemented
413	#390	#120	1	2	yes	complemented
414	#390	#120	1	2	yes	complemented
415	#390	#120	1	2	yes	complemented
416	#390	C₂²×D₄	1	2	yes	—
417	#390	C₂²×D₄	1	2	yes	—
418	#390	C₂²×D₄	1	2	yes	—
419	#390	C₂²×D₄	1	2	yes	—
420	#386	#120	1	2	yes	—
421	#386	#120	1	2	yes	—
422	#386	#120	1	2	yes	—
423	#386	#120	1	2	yes	—
424	#386	#120	1	2	yes	complemented
425	#386	#120	1	2	yes	complemented
426	#386	#120	1	2	yes	complemented
427	#386	#120	1	2	yes	complemented
428	#386	C₂²×D₄	1	2	yes	—
429	#386	C₂²×D₄	1	2	yes	—
430	#386	C₂²×D₄	1	2	yes	—
431	#386	C₂²×D₄	1	2	yes	—
432	#386	C₂²×D₄	1	2	yes	—
433	#386	C₂²×D₄	1	2	yes	—
434	#386	C₂²×D₄	1	2	yes	—
435	#386	C₂²×D₄	1	2	yes	—
436	#379	#120	1	1	yes	characteristic
437	#379	#120	1	1	yes	characteristic
438	#379	#120	1	1	yes	characteristic
439	#379	#120	1	1	yes	characteristic
440	#379	#120	1	1	yes	characteristic
441	#379	#120	1	1	yes	characteristic
442	#379	#120	1	1	yes	characteristic
443	#379	#120	1	1	yes	characteristic
444	#379	#120	1	2	yes	complemented
445	#379	#120	1	2	yes	complemented
446	#379	C₂²×D₄	1	2	yes	—
447	#379	C₂²×D₄	1	2	yes	—
448	C₄×C₂²⋊C₄	#120	1	2	yes	complemented
449	C₄×C₂²⋊C₄	#120	1	2	yes	complemented
450	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
452	C₂⁵	B(4,𝔽₂)	1	2	yes	—
453	C₂⁵	B(4,𝔽₂)	1	2	yes	—
454	C₂⁵	C₂×#120	1	1	yes	characteristic
455	C₂⁵	C₂×#120	1	1	yes	characteristic
456	C₂⁵	C₂×#120	1	1	yes	characteristic
457	C₂⁵	C₂×#120	1	1	yes	characteristic
458	C₂⁵	C₂×#120	1	1	yes	characteristic
459	C₂⁵	C₂×#120	1	1	yes	characteristic
460	C₂⁵	C₂×#120	1	2	yes	—
461	C₂⁵	C₂×#120	1	1	yes	characteristic
462	C₂⁵	C₂×#120	1	2	yes	—
463	C₂⁵	C₂×#120	1	1	yes	characteristic
464	C₂⁵	C₂×#120	1	1	yes	characteristic
465	C₂⁵	C₂×#120	1	1	yes	characteristic
466	C₂⁵	C₂×#120	1	2	yes	—
467	C₂⁵	C₂×#120	1	2	yes	—
468	C₂⁵	C₂×#120	1	2	yes	—
469	C₂⁵	C₂×#120	1	1	yes	characteristic
470	C₂⁵	C₂³×D₄	1	1	yes	characteristic
471	C₂⁵	C₂³×D₄	1	1	yes	characteristic
472	C₂²×Q₈	C₂×#120	1	2	yes	—
473	C₂²×D₄	C₂×#120	1	2	yes	—
474	C₂²×D₄	C₂×#120	1	2	yes	—
475	C₂²×D₄	C₂×#120	1	2	yes	—
476	C₂²×D₄	C₂×#120	1	2	yes	—
477	C₂²×D₄	C₂×#120	1	2	yes	—
478	C₂²×D₄	C₂×#120	1	2	yes	—
479	C₂²×D₄	C₂×#120	1	2	yes	—
480	C₂²×D₄	C₂³×D₄	1	2	yes	—
481	C₂²×D₄	C₂³×D₄	1	2	yes	—
482	C₂³×C₄	C₂×#120	1	1	yes	characteristic
483	C₂³×C₄	C₂×#120	1	1	yes	characteristic
484	C₂³×C₄	C₂×#120	1	1	yes	characteristic
485	C₂³×C₄	C₂×#120	1	1	yes	characteristic
486	C₂³×C₄	C₂×#120	1	1	yes	characteristic
487	C₂³×C₄	C₂×#120	1	2	yes	—
488	C₂³×C₄	C₂×#120	1	2	yes	—
489	C₂³×C₄	C₂×#120	1	2	yes	—
490	C₂³×C₄	C₂×#120	1	2	yes	—
491	C₂³×C₄	C₂×#120	1	2	yes	—
492	C₂³×C₄	C₂×#120	1	2	yes	—
493	C₂³×C₄	C₂×#120	1	2	yes	—
494	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
496	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
508	C₂×C₂²⋊C₄	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	2	yes	—
512	C₂×C₄²	C₂×#120	1	2	yes	—
513	C₂⁴	#2846	1	1	yes	characteristic
514	C₂⁴	#2846	1	1	yes	characteristic
515	C₂⁴	#2846	1	2	yes	—
516	C₂⁴	#2846	1	1	yes	characteristic
517	C₂⁴	#2846	1	1	yes	characteristic
518	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
519	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
520	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
521	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
522	C₂⁴	#3026	1	1	yes	characteristic
523	C₂⁴	#3026	1	1	yes	characteristic
524	C₂⁴	C₂²×#120	1	1	yes	characteristic
525	C₂⁴	C₂²×#120	1	2	yes	—
526	C₂⁴	C₂²×#120	1	1	yes	characteristic
527	C₂⁴	C₂²×#120	1	1	yes	characteristic
528	C₂²×C₄	#2846	1	2	yes	—
529	C₂²×C₄	C₂²×#120	1	2	yes	—
530	C₂³	#32898	1	1	yes	characteristic
531	C₂³	#32898	1	1	yes	characteristic
532	C₂³	#32898	1	1	yes	characteristic
533	C₂³	#32898	1	1	yes	characteristic
534	C₂³	#33551	1	4	yes	—
535	C₂³	C₂×#2846	1	1	yes	characteristic
536	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
537	C₂³	C₂×#3026	1	1	yes	characteristic
538	C₂³	#60399	1	2	yes	—
539	C₂³	#60399	1	2	yes	—
540	C₂²	C₂×#32898	1	1	yes	characteristic
541	C₂²	#6628896	1	1	yes	characteristic
542	C₂²	#6628896	1	1	yes	characteristic
543	C₂²	C₂×#33551	1	2	yes	—
544	C₂	#72219040	1	1	yes	characteristic
545	C₂	#72225712	1	1	yes	characteristic
546	C₂	#72235130	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262307	C₂	semidirect
2. #72262305	C₂	semidirect
3. #72262302	C₂	semidirect
4. #72262281	C₂	semidirect
5. #72262280	C₂	semidirect
6. #72261438	C₂	semidirect
7. #72249538	C₂	semidirect
8. #72238594	C₂	semidirect
9. #72238471	C₂	semidirect
10. #72238456	C₂	semidirect
11. #72236896	C₂	semidirect
12. #72236837	C₂	semidirect
13. #72233383	C₂	semidirect
14. #72233358	C₂	semidirect
15. #72233065	C₂	semidirect
16. #72231810	C₂	semidirect
17. #72225994	C₂	semidirect
20. #8108077	C₂²	semidirect
21. #8108057	C₂²	semidirect
22. #8093660	C₂²	semidirect
23. #8093623	C₂²	semidirect
24. #7681968	C₂²	semidirect
25. #7681927	C₂²	semidirect
28. C₂×#35346	C₂²	semidirect
30. #6628892	C₂²	semidirect
31. C₂×#32898	C₂²	semidirect
32. C₂×#32898	C₂²	semidirect
33. #6628867	C₂²	semidirect
34. #500071	C₂²	semidirect
35. #500067	C₂²	semidirect
36. #500053	C₂²	semidirect
37. #500049	C₂²	semidirect
38. #499797	C₂²	semidirect
39. #499795	C₂²	semidirect
40. #499789	C₂²	semidirect
41. #499787	C₂²	semidirect
42. #496231	C₂²	semidirect
43. #496231	C₂²	semidirect
44. #496225	C₂²	semidirect
45. #496225	C₂²	semidirect
46. #496194	C₂²	semidirect
47. #496194	C₂²	semidirect
48. #449501	C₂²	semidirect
49. #449475	C₂²	semidirect
51. #417508	C₂²	semidirect
52. #382422	C₂²	semidirect
53. #379754	C₂²	semidirect
54. #379754	C₂²	semidirect
55. #249355	C₂²	semidirect
56. #249331	C₂²	semidirect
57. #249319	C₂²	semidirect
58. #245246	C₂²	semidirect
59. #245226	C₂²	semidirect
60. #245225	C₂²	semidirect
61. #201687	C₂²	semidirect
62. #201322	C₂²	semidirect
63. C₂×#8547	C₂²	semidirect
64. C₂×#8541	C₂²	semidirect
65. #133925	C₂²	semidirect
66. #133893	C₂²	semidirect
67. #133893	C₂²	semidirect
68. #133822	C₂²	semidirect
69. #133533	C₂²	semidirect
70. #133531	C₂²	semidirect
71. #133529	C₂²	semidirect
72. #133527	C₂²	semidirect
73. #133396	C₂²	semidirect
74. #133394	C₂²	semidirect
75. #133392	C₂²	semidirect
76. #133390	C₂²	semidirect
77. #133293	C₂²	semidirect
78. #133291	C₂²	semidirect
79. #133290	C₂²	semidirect
80. #133281	C₂²	semidirect
81. #133279	C₂²	semidirect
82. #133278	C₂²	semidirect
84. C₂⁵×D₄	D₄	semidirect
85. C₂×#3490	D₄	semidirect
86. C₂×#3484	D₄	semidirect
94. #52012	D₄	semidirect
95. #52004	D₄	semidirect
96. #51993	D₄	semidirect
97. #51945	D₄	semidirect
98. #51940	D₄	semidirect
99. #51940	D₄	semidirect
100. #51902	D₄	semidirect
101. #51895	D₄	semidirect
102. #50856	D₄	semidirect
103. #50646	D₄	semidirect
104. #48922	D₄	semidirect
105. #48143	D₄	semidirect
106. #48113	D₄	semidirect
107. #48088	D₄	semidirect
108. #47848	D₄	semidirect
109. #47827	D₄	semidirect
114. #36714	D₄	semidirect
116. #36703	D₄	semidirect
118. C₂×#2849	D₄	semidirect
120. C₂×#2846	D₄	semidirect
122. #35390	D₄	semidirect
124. #35367	D₄	semidirect
126. #35350	D₄	semidirect
128. #35346	D₄	semidirect
133. #35050	D₄	semidirect
134. #34980	D₄	semidirect
136. C₂×#2405	D₄	semidirect
137. C₂×#2405	D₄	semidirect
138. C₂×#2410	D₄	semidirect
139. C₂×#2410	D₄	semidirect
144. #34176	D₄	semidirect
145. #34171	D₄	semidirect
147. C₂²×#379	D₄	semidirect
196. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
197. C₂×#560	C₂×D₄	semidirect
198. C₂×#551	C₂×D₄	semidirect
199. C₂×D₄²	C₂×D₄	semidirect
230. #2804	C₂×D₄	semidirect
231. #2748	C₂×D₄	semidirect
232. #2748	C₂×D₄	semidirect
233. #2717	C₂×D₄	semidirect
234. #2709	C₂×D₄	semidirect
235. #2697	C₂×D₄	semidirect
236. #2697	C₂×D₄	semidirect
237. #2684	C₂×D₄	semidirect
238. #2684	C₂×D₄	semidirect
239. #2684	C₂×D₄	semidirect
240. #2683	C₂×D₄	semidirect
241. #2679	C₂×D₄	semidirect
242. #2679	C₂×D₄	semidirect
243. #2669	C₂×D₄	semidirect
244. #2669	C₂×D₄	semidirect
245. #2669	C₂×D₄	semidirect
278. #2380	C₂×D₄	semidirect
279. #2379	C₂×D₄	semidirect
280. #2376	C₂×D₄	semidirect
281. #2375	C₂×D₄	semidirect
282. #2375	C₂×D₄	semidirect
283. #2375	C₂×D₄	semidirect
284. #2374	C₂×D₄	semidirect
285. #2372	C₂×D₄	semidirect
286. #2366	C₂×D₄	semidirect
287. #2358	C₂×D₄	semidirect
288. #2358	C₂×D₄	semidirect
289. #2358	C₂×D₄	semidirect
331. C₂²×#41	#120	semidirect
340. C₂³×D₄	#120	semidirect
341. C₂³×D₄	#120	semidirect
360. C₂×#127	#120	semidirect
361. C₂×#127	#120	semidirect
364. C₂×#124	#120	semidirect
365. C₂×#124	#120	semidirect
368. C₂×#123	#120	semidirect
369. C₂×#123	#120	semidirect
372. C₂×C₂²⋊Q₈	#120	semidirect
374. C₂×#121	#120	semidirect
380. C₂×#120	#120	semidirect
381. C₂×#120	#120	semidirect
388. C₂×#117	#120	semidirect
389. C₂×#117	#120	semidirect
390. C₂×#117	#120	semidirect
397. C₂²×C₂²⋊C₄	#120	semidirect
398. C₂²×C₂²⋊C₄	#120	semidirect
399. C₂²×C₂²⋊C₄	#120	semidirect
400. C₂²×C₂²⋊C₄	#120	semidirect
412. #390	#120	semidirect
413. #390	#120	semidirect
414. #390	#120	semidirect
415. #390	#120	semidirect
424. #386	#120	semidirect
425. #386	#120	semidirect
426. #386	#120	semidirect
427. #386	#120	semidirect
444. #379	#120	semidirect
445. #379	#120	semidirect
448. C₄×C₂²⋊C₄	#120	semidirect
449. C₄×C₂²⋊C₄	#120	semidirect

Maximal subgroups

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

subgroup	index
#72262307	2
#72262305	2
#72262302	2
#72262281	2
#72262280	2
#72261438	2
#72249538	2
#72238594	2
#72238471	2
#72238456	2
#72236896	2
#72236837	2
#72233383	2
#72233358	2
#72233065	2
#72231810	2
#72225994	2