Subgroups — #72262804

Order 2048.

At least 9627 conjugacy classes of subgroups; only the 614 normal subgroups are shown.

The subgroup lattice has 407 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262803	C₂	1	2	yes	maximal, complemented
2	#72262802	C₂	1	2	yes	maximal, complemented
3	#72262801	C₂	1	1	yes	maximal, characteristic, complemented
4	#72262779	C₂	1	2	yes	maximal, complemented
5	#72262776	C₂	1	2	yes	maximal, complemented
6	#72262775	C₂	1	2	yes	maximal, complemented
7	#72262774	C₂	1	2	yes	maximal, complemented
8	#72262465	C₂	1	1	yes	maximal, characteristic, complemented
9	#72237028	C₂	1	1	yes	maximal, characteristic, complemented
10	#72235717	C₂	1	2	yes	maximal, complemented
11	#72235675	C₂	1	2	yes	maximal, complemented
12	#72235671	C₂	1	2	yes	maximal, complemented
13	#72234757	C₂	1	2	yes	maximal, complemented
14	#72234687	C₂	1	1	yes	maximal, characteristic, complemented
15	#72234607	C₂	1	1	yes	maximal, characteristic, complemented
16	#72233792	C₂	1	2	yes	maximal, complemented
17	#72233388	C₂	1	2	yes	maximal, complemented
18	#72232937	C₂	1	1	yes	maximal, characteristic, complemented
19	#72232735	C₂	1	1	yes	maximal, characteristic, complemented
20	#10586472	C₂²	1	1	yes	characteristic, complemented
21	#6499870	C₂²	1	2	yes	complemented
22	#6346728	C₂²	1	2	yes	—
23	#6346698	C₂²	1	2	yes	complemented
24	#5522188	C₂²	1	1	yes	characteristic, complemented
25	#5228710	C₂²	1	1	yes	characteristic, complemented
26	#5082787	C₂²	1	1	yes	characteristic, complemented
27	#5024691	C₂²	1	1	yes	characteristic, complemented
28	#5022312	C₂²	1	1	yes	characteristic, complemented
29	#4976042	C₂²	1	1	yes	characteristic, complemented
30	#4466055	C₂²	1	1	yes	characteristic, complemented
31	#4420586	C₂²	1	1	yes	characteristic
32	#4122222	C₂²	1	1	yes	characteristic, complemented
33	#4035827	C₂²	1	1	yes	characteristic, complemented
34	#3067944	C₂²	1	1	yes	characteristic, complemented
35	#2109240	C₂²	1	1	yes	characteristic, complemented
36	#2050373	C₂²	1	1	yes	characteristic, complemented
37	#686207	C₂²	1	1	yes	characteristic
38	#649038	C₂²	1	1	yes	characteristic
39	#485385	C₂²	1	4	yes	complemented
40	#485039	C₂²	1	4	yes	complemented
41	#347052	C₂²	1	2	yes	complemented
42	#347052	C₂²	1	2	yes	complemented
43	#347043	C₂²	1	2	yes	—
44	#347043	C₂²	1	2	yes	complemented
45	#346459	C₂²	1	2	yes	complemented
46	#346456	C₂²	1	2	yes	complemented
47	#346449	C₂²	1	2	yes	—
48	#346449	C₂²	1	2	yes	—
49	#346449	C₂²	1	2	yes	complemented
50	#346446	C₂²	1	2	yes	—
51	#346446	C₂²	1	2	yes	complemented
52	#346446	C₂²	1	2	yes	complemented
53	#188087	C₂²	1	1	yes	characteristic, complemented
54	#188087	C₂²	1	1	yes	characteristic, complemented
55	#188035	C₂²	1	1	yes	characteristic, complemented
56	#187949	C₂²	1	2	yes	complemented
57	#185282	C₂²	1	2	yes	complemented
58	#185270	C₂²	1	2	yes	complemented
59	#144621	C₂²	1	4	yes	complemented
60	#144616	C₂²	1	4	yes	complemented
61	#142982	C₂²	1	4	yes	complemented
62	#142969	C₂²	1	4	yes	complemented
63	#142568	C₂²	1	4	yes	complemented
64	#142537	C₂²	1	4	yes	complemented
65	#142537	C₂²	1	4	yes	complemented
66	#142536	C₂²	1	4	yes	complemented
67	#140051	C₂²	1	4	yes	complemented
68	#140032	C₂²	1	4	yes	complemented
69	#140032	C₂²	1	4	yes	complemented
70	#140024	C₂²	1	4	yes	complemented
71	#139908	C₂²	1	2	yes	complemented
72	#139908	C₂²	1	2	yes	complemented
73	#139906	C₂²	1	2	yes	complemented
74	#139906	C₂²	1	2	yes	complemented
75	#139645	C₂²	1	4	yes	complemented
76	#139624	C₂²	1	4	yes	complemented
77	#139504	C₂²	1	2	yes	complemented
78	#139504	C₂²	1	2	yes	complemented
79	#139504	C₂²	1	2	yes	complemented
80	#139486	C₂²	1	2	yes	complemented
81	#139472	C₂²	1	2	yes	complemented
82	#139472	C₂²	1	2	yes	complemented
83	#139472	C₂²	1	2	yes	complemented
84	#139434	C₂²	1	2	yes	complemented
85	#135573	C₂²	1	2	yes	complemented
86	#135485	C₂²	1	2	yes	complemented
87	#135479	C₂²	1	2	yes	complemented
88	#134036	C₂²	1	2	yes	complemented
89	#133121	C₂²	1	2	yes	complemented
90	#133093	C₂²	1	2	yes	complemented
91	#62818	C₂³	1	2	yes	—
92	#62818	C₂³	1	2	yes	—
93	#62817	C₂³	1	2	yes	—
94	C₂²×D₄²	C₂³	1	1	yes	characteristic
95	C₂²×#535	D₄	1	1	yes	characteristic, complemented
96	C₂³×#127	D₄	1	1	yes	characteristic, complemented
97	C₂×#2760	C₂³	1	1	yes	characteristic, complemented
98	C₂×#2433	C₂³	1	1	yes	characteristic
99	C₂×#2408	D₄	1	1	yes	characteristic, complemented
100	C₂×#2403	D₄	1	1	yes	characteristic
101	C₂×#2403	D₄	1	1	yes	characteristic
102	C₂×#2403	C₂³	1	1	yes	characteristic, complemented
103	C₂×#2615	C₂³	1	1	yes	characteristic
104	C₂×#2613	C₂³	1	1	yes	characteristic
105	C₂×#2388	D₄	1	1	yes	characteristic, complemented
106	#23985	C₂³	1	4	yes	—
107	#23984	C₂³	1	4	yes	—
108	#21746	C₂³	1	2	yes	—
109	#18163	C₂³	1	4	yes	—
110	#18162	C₂³	1	4	yes	—
111	#18162	C₂³	1	4	yes	—
112	#18162	C₂³	1	4	yes	—
113	#17396	C₂³	1	2	yes	—
114	#17396	C₂³	1	2	yes	—
115	#17105	C₂³	1	1	yes	characteristic, complemented
116	#17102	C₂³	1	1	yes	characteristic, complemented
117	#16245	C₂³	1	1	yes	characteristic, complemented
118	#16208	C₂³	1	1	yes	characteristic, complemented
119	#15984	C₂³	1	1	yes	characteristic
120	#15984	C₂³	1	1	yes	characteristic
121	#15948	D₄	1	1	yes	characteristic
122	#15947	D₄	1	1	yes	characteristic
123	#15673	D₄	1	1	yes	characteristic, complemented
124	#15673	C₂³	1	1	yes	characteristic
125	#15561	C₂³	1	1	yes	characteristic, complemented
126	#15561	C₂³	1	1	yes	characteristic, complemented
127	#15467	C₂³	1	1	yes	characteristic, complemented
128	#15310	D₄	1	1	yes	characteristic, complemented
129	#15310	D₄	1	1	yes	characteristic, complemented
130	#15310	D₄	1	1	yes	characteristic, complemented
131	#15310	C₂³	1	1	yes	characteristic
132	#15310	C₂³	1	1	yes	characteristic
133	#15310	C₂³	1	1	yes	characteristic
134	#15267	C₂³	1	1	yes	characteristic, complemented
135	#15261	D₄	1	1	yes	characteristic
136	#15259	D₄	1	1	yes	characteristic, complemented
137	#15259	C₂³	1	1	yes	characteristic
138	#15258	D₄	1	1	yes	characteristic
139	#15258	D₄	1	1	yes	characteristic, complemented
140	#15258	D₄	1	1	yes	characteristic, complemented
141	#15258	D₄	1	1	yes	characteristic, complemented
142	#15258	C₂³	1	1	yes	characteristic
143	#15258	C₂³	1	1	yes	characteristic
144	#15258	C₂³	1	1	yes	characteristic
145	#15257	C₂³	1	1	yes	characteristic
146	#15257	C₂³	1	1	yes	characteristic
147	#14698	C₂³	1	1	yes	characteristic
148	#14657	C₂³	1	1	yes	characteristic
149	#14649	C₂³	1	1	yes	characteristic, complemented
150	#14533	C₂³	1	1	yes	characteristic, complemented
151	#14533	C₂³	1	1	yes	characteristic, complemented
152	#14507	C₂³	1	1	yes	characteristic, complemented
153	#14335	D₄	1	1	yes	characteristic
154	#14335	D₄	1	1	yes	characteristic
155	#14207	C₂³	1	1	yes	characteristic, complemented
156	#14136	C₂³	1	1	yes	characteristic
157	#13902	D₄	1	1	yes	characteristic, complemented
158	#13902	D₄	1	1	yes	characteristic, complemented
159	#13871	D₄	1	1	yes	characteristic, complemented
160	#13827	C₂³	1	1	yes	characteristic, complemented
161	C₄×#386	D₄	1	1	yes	characteristic, complemented
162	#11808	C₂³	1	4	yes	complemented
163	#11796	C₂³	1	4	yes	complemented
164	#11796	C₂³	1	4	yes	complemented
165	#11796	C₂³	1	4	yes	complemented
166	#11500	C₂³	1	4	yes	complemented
167	#11499	C₂³	1	4	yes	complemented
168	#8549	C₂³	1	2	yes	—
169	#8549	C₂³	1	2	yes	—
170	#8547	C₂³	1	2	yes	—
171	#8547	C₂³	1	2	yes	—
172	#8542	C₂³	1	2	yes	—
173	#8542	C₂³	1	2	yes	—
174	#8535	C₂³	1	4	yes	—
175	#8535	C₂³	1	4	yes	—
176	#8346	C₂³	1	4	yes	—
177	#8346	C₂³	1	4	yes	—
178	#8346	C₂³	1	4	yes	—
179	#8346	C₂³	1	4	yes	—
180	#7324	C₂³	1	4	yes	complemented
181	#7324	C₂³	1	4	yes	complemented
182	#7213	C₂³	1	4	yes	complemented
183	#7213	C₂³	1	4	yes	complemented
184	#7213	C₂³	1	4	yes	complemented
185	#7213	C₂³	1	4	yes	complemented
186	C₂³×#41	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
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	#3490	C₂⁴	1	4	yes	—
194	C₂²×#127	C₂×D₄	1	1	yes	characteristic
195	C₂²×#127	C₂×D₄	1	1	yes	characteristic
196	C₂²×#127	C₂×D₄	1	1	yes	characteristic
197	C₂²×#127	C₂×D₄	1	1	yes	characteristic
198	C₂²×#127	C₂×D₄	1	1	yes	characteristic
199	C₂²×#127	C₂×D₄	1	1	yes	characteristic
200	C₂²×#127	C₂×D₄	1	1	yes	characteristic
201	C₂²×#124	C₂×D₄	1	1	yes	characteristic
202	C₂²×#124	C₂×D₄	1	1	yes	characteristic
203	C₂²×#123	C₂×D₄	1	1	yes	characteristic
204	C₂²×#121	C₂×D₄	1	1	yes	characteristic
205	C₂²×#121	C₂×D₄	1	1	yes	characteristic
206	C₂²×#121	C₂⁴	1	1	yes	characteristic
207	C₂²×#121	C₂⁴	1	1	yes	characteristic
208	C₂²×#120	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
219	C₂²×#117	C₂×D₄	1	1	yes	characteristic
220	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
221	C₂×#395	C₂×D₄	1	1	yes	characteristic
222	C₂×#394	C₂×D₄	1	1	yes	characteristic
223	C₂×#394	C₂×D₄	1	1	yes	characteristic
224	C₂×#394	C₂×D₄	1	1	yes	characteristic
225	C₂×#393	C₂×D₄	1	1	yes	characteristic
226	C₂×#393	C₂×D₄	1	1	yes	characteristic
227	C₂×#393	C₂⁴	1	1	yes	characteristic
228	C₂×#392	C₂×D₄	1	1	yes	characteristic
229	C₂×#392	C₂×D₄	1	1	yes	characteristic
230	C₂×#392	C₂×D₄	1	1	yes	characteristic
231	C₂×#392	C₂×D₄	1	1	yes	characteristic
232	C₂×#392	C₂×D₄	1	1	yes	characteristic
233	C₂×#392	C₂×D₄	1	1	yes	characteristic
234	C₂×#392	C₂⁴	1	1	yes	characteristic
235	C₂×#392	C₂⁴	1	1	yes	characteristic
236	C₂×#392	C₂⁴	1	1	yes	characteristic
237	C₂×#386	C₂×D₄	1	1	yes	characteristic
238	C₂×#386	C₂×D₄	1	1	yes	characteristic
239	C₂×#386	C₂×D₄	1	1	yes	characteristic
240	C₂×#386	C₂×D₄	1	1	yes	characteristic
241	C₂×#381	C₂⁴	1	1	yes	characteristic
242	C₂×#380	C₂×D₄	1	1	yes	characteristic
243	C₂×#380	C₂×D₄	1	1	yes	characteristic
244	C₂×#379	C₂×D₄	1	1	yes	characteristic
245	C₂×#379	C₂×D₄	1	1	yes	characteristic
246	C₂×#379	C₂×D₄	1	1	yes	characteristic
247	C₂×#379	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
249	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
250	#1819	C₂⁴	1	4	yes	—
251	#1462	C₂⁴	1	4	yes	—
252	#1462	C₂⁴	1	4	yes	—
253	#1440	C₂⁴	1	1	yes	characteristic
254	#1440	C₂⁴	1	1	yes	characteristic
255	#1438	C₂×D₄	1	1	yes	characteristic
256	#1438	C₂×D₄	1	1	yes	characteristic
257	#1438	C₂×D₄	1	1	yes	characteristic
258	#1438	C₂×D₄	1	1	yes	characteristic
259	#1438	C₂×D₄	1	1	yes	characteristic
260	#1438	C₂×D₄	1	1	yes	characteristic
261	#1438	C₂×D₄	1	1	yes	characteristic
262	#1438	C₂×D₄	1	1	yes	characteristic
263	#1438	C₂×D₄	1	1	yes	characteristic
264	#1438	C₂×D₄	1	1	yes	characteristic
265	#1438	C₂×D₄	1	1	yes	characteristic
266	#1438	C₂×D₄	1	1	yes	characteristic
267	#1438	C₂×D₄	1	1	yes	characteristic
268	#1438	C₂×D₄	1	1	yes	characteristic
269	#1438	C₂×D₄	1	1	yes	characteristic
270	#1438	C₂×D₄	1	1	yes	characteristic
271	#1438	C₂×D₄	1	1	yes	characteristic
272	#1438	C₂×D₄	1	1	yes	characteristic
273	#1437	C₂×D₄	1	1	yes	characteristic
274	#1437	C₂×D₄	1	1	yes	characteristic
275	#1437	C₂×D₄	1	1	yes	characteristic
276	#1437	C₂×D₄	1	1	yes	characteristic
277	#1437	C₂×D₄	1	1	yes	characteristic
278	#1437	C₂×D₄	1	1	yes	characteristic
279	#1437	C₂×D₄	1	1	yes	characteristic
280	#1437	C₂×D₄	1	1	yes	characteristic
281	#1437	C₂⁴	1	1	yes	characteristic
282	#1437	C₂⁴	1	1	yes	characteristic
283	#1437	C₂⁴	1	1	yes	characteristic
284	#1437	C₂⁴	1	1	yes	characteristic
285	#1436	C₂×D₄	1	1	yes	characteristic
286	#1436	C₂×D₄	1	1	yes	characteristic
287	#1436	C₂×D₄	1	1	yes	characteristic
288	#1436	C₂×D₄	1	1	yes	characteristic
289	C₂⁶	#120	1	1	yes	characteristic
290	C₂⁶	#120	1	1	yes	characteristic
291	C₂⁶	#120	1	1	yes	characteristic
292	C₂⁶	C₂²×D₄	1	1	yes	characteristic
293	C₂⁶	C₂²×D₄	1	1	yes	characteristic
294	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
295	C₂³×D₄	#120	1	1	yes	characteristic
296	C₂³×D₄	#120	1	1	yes	characteristic
297	C₂³×D₄	#120	1	1	yes	characteristic
298	C₂³×D₄	#120	1	1	yes	characteristic
299	C₂³×D₄	#120	1	1	yes	characteristic
300	C₂³×D₄	#120	1	1	yes	characteristic
301	C₂³×D₄	#120	1	1	yes	characteristic
302	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
303	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
304	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
305	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
306	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
307	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
308	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
309	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
310	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
311	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
312	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
313	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
314	C₂⁴×C₄	#120	1	1	yes	characteristic
315	C₂⁴×C₄	#120	1	1	yes	characteristic
316	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
317	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
318	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
319	#543	H(5,𝔽₂)	1	4	yes	—
320	#534	H(5,𝔽₂)	1	4	yes	—
321	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
325	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	C₂⁵	1	1	yes	characteristic
337	C₂²×C₄²	#120	1	1	yes	characteristic
338	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
340	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
342	C₂×#95	C₂²×D₄	1	1	yes	characteristic
343	C₂×#95	C₂²×D₄	1	1	yes	characteristic
344	C₂×#95	C₂²×D₄	1	1	yes	characteristic
345	C₂×#95	C₂²×D₄	1	1	yes	characteristic
346	C₂×#95	C₂²×D₄	1	1	yes	characteristic
347	C₂×#95	C₂²×D₄	1	1	yes	characteristic
348	C₂×#95	C₂²×D₄	1	1	yes	characteristic
349	C₂×#95	C₂²×D₄	1	1	yes	characteristic
350	C₂⁵	C₂×#120	1	1	yes	characteristic
351	C₂⁵	C₂×#120	1	1	yes	characteristic
352	C₂⁵	C₂×#120	1	1	yes	characteristic
353	C₂⁵	C₂×#120	1	1	yes	characteristic
354	C₂⁵	C₂×#120	1	1	yes	characteristic
355	C₂⁵	C₂×#120	1	1	yes	characteristic
356	C₂⁵	C₂×#120	1	1	yes	characteristic
357	C₂⁵	C₂³×D₄	1	1	yes	characteristic
358	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
359	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
360	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
361	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
362	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
363	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
364	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
365	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
366	C₂³×C₄	C₂×#120	1	1	yes	characteristic
367	C₂³×C₄	C₂×#120	1	1	yes	characteristic
368	C₂³×C₄	C₂×#120	1	1	yes	characteristic
369	C₂³×C₄	C₂×#120	1	1	yes	characteristic
370	C₂³×C₄	C₂×#120	1	1	yes	characteristic
371	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
372	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	4	yes	—
374	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
375	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
376	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
377	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
378	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
379	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
380	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
381	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
382	C₂⁴	C₂²×#120	1	1	yes	characteristic
383	C₂⁴	#3484	1	2	yes	—
384	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
385	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
386	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
387	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
388	C₂²×C₄	#3484	1	2	yes	—
389	C₂²×C₄	#3484	1	2	yes	—
390	C₂³	#33551	1	2	yes	—
391	C₂³	#35346	1	1	yes	characteristic
392	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
393	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
394	C₂×C₄	#33551	1	2	yes	—
395	C₂×C₄	#33557	1	2	yes	—
396	C₂²	#6499855	1	1	yes	characteristic
397	C₂²	#6499861	1	1	yes	characteristic
398	C₂²	#6499867	1	1	yes	characteristic
399	C₂²	C₂×#33551	1	1	yes	characteristic
400	C₂²	C₂×#33551	1	1	yes	characteristic
401	C₂²	C₂×#33557	1	1	yes	characteristic
402	C₂²	#7622875	1	1	yes	characteristic
403	C₂	#72233417	1	1	yes	characteristic
404	C₂	#72233427	1	1	yes	characteristic
405	C₂	#72238471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6499867
commutator, Frattini, cosocle	C₂²×C₂²⋊C₄	C₂⁵
LCS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262803	C₂	semidirect
2. #72262802	C₂	semidirect
3. #72262801	C₂	semidirect
4. #72262779	C₂	semidirect
5. #72262776	C₂	semidirect
6. #72262775	C₂	semidirect
7. #72262774	C₂	semidirect
8. #72262465	C₂	semidirect
9. #72237028	C₂	semidirect
10. #72235717	C₂	semidirect
11. #72235675	C₂	semidirect
12. #72235671	C₂	semidirect
13. #72234757	C₂	semidirect
14. #72234687	C₂	semidirect
15. #72234607	C₂	semidirect
16. #72233792	C₂	semidirect
17. #72233388	C₂	semidirect
18. #72232937	C₂	semidirect
19. #72232735	C₂	semidirect
20. #10586472	C₂²	semidirect
21. #6499870	C₂²	semidirect
23. #6346698	C₂²	semidirect
24. #5522188	C₂²	semidirect
25. #5228710	C₂²	semidirect
26. #5082787	C₂²	semidirect
27. #5024691	C₂²	semidirect
28. #5022312	C₂²	semidirect
29. #4976042	C₂²	semidirect
30. #4466055	C₂²	semidirect
32. #4122222	C₂²	semidirect
33. #4035827	C₂²	semidirect
34. #3067944	C₂²	semidirect
35. #2109240	C₂²	semidirect
36. #2050373	C₂²	semidirect
39. #485385	C₂²	semidirect
40. #485039	C₂²	semidirect
41. #347052	C₂²	semidirect
42. #347052	C₂²	semidirect
44. #347043	C₂²	semidirect
45. #346459	C₂²	semidirect
46. #346456	C₂²	semidirect
49. #346449	C₂²	semidirect
51. #346446	C₂²	semidirect
52. #346446	C₂²	semidirect
53. #188087	C₂²	semidirect
54. #188087	C₂²	semidirect
55. #188035	C₂²	semidirect
56. #187949	C₂²	semidirect
57. #185282	C₂²	semidirect
58. #185270	C₂²	semidirect
59. #144621	C₂²	semidirect
60. #144616	C₂²	semidirect
61. #142982	C₂²	semidirect
62. #142969	C₂²	semidirect
63. #142568	C₂²	semidirect
64. #142537	C₂²	semidirect
65. #142537	C₂²	semidirect
66. #142536	C₂²	semidirect
67. #140051	C₂²	semidirect
68. #140032	C₂²	semidirect
69. #140032	C₂²	semidirect
70. #140024	C₂²	semidirect
71. #139908	C₂²	semidirect
72. #139908	C₂²	semidirect
73. #139906	C₂²	semidirect
74. #139906	C₂²	semidirect
75. #139645	C₂²	semidirect
76. #139624	C₂²	semidirect
77. #139504	C₂²	semidirect
78. #139504	C₂²	semidirect
79. #139504	C₂²	semidirect
80. #139486	C₂²	semidirect
81. #139472	C₂²	semidirect
82. #139472	C₂²	semidirect
83. #139472	C₂²	semidirect
84. #139434	C₂²	semidirect
85. #135573	C₂²	semidirect
86. #135485	C₂²	semidirect
87. #135479	C₂²	semidirect
88. #134036	C₂²	semidirect
89. #133121	C₂²	semidirect
90. #133093	C₂²	semidirect
95. C₂²×#535	D₄	semidirect
96. C₂³×#127	D₄	semidirect
97. C₂×#2760	C₂³	semidirect
99. C₂×#2408	D₄	semidirect
102. C₂×#2403	C₂³	semidirect
105. C₂×#2388	D₄	semidirect
115. #17105	C₂³	semidirect
116. #17102	C₂³	semidirect
117. #16245	C₂³	semidirect
118. #16208	C₂³	semidirect
123. #15673	D₄	semidirect
125. #15561	C₂³	semidirect
126. #15561	C₂³	semidirect
127. #15467	C₂³	semidirect
128. #15310	D₄	semidirect
129. #15310	D₄	semidirect
130. #15310	D₄	semidirect
134. #15267	C₂³	semidirect
136. #15259	D₄	semidirect
139. #15258	D₄	semidirect
140. #15258	D₄	semidirect
141. #15258	D₄	semidirect
149. #14649	C₂³	semidirect
150. #14533	C₂³	semidirect
151. #14533	C₂³	semidirect
152. #14507	C₂³	semidirect
155. #14207	C₂³	semidirect
157. #13902	D₄	semidirect
158. #13902	D₄	semidirect
159. #13871	D₄	semidirect
160. #13827	C₂³	semidirect
161. C₄×#386	D₄	semidirect
162. #11808	C₂³	semidirect
163. #11796	C₂³	semidirect
164. #11796	C₂³	semidirect
165. #11796	C₂³	semidirect
166. #11500	C₂³	semidirect
167. #11499	C₂³	semidirect
180. #7324	C₂³	semidirect
181. #7324	C₂³	semidirect
182. #7213	C₂³	semidirect
183. #7213	C₂³	semidirect
184. #7213	C₂³	semidirect
185. #7213	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72262803	2
#72262802	2
#72262801	2
#72262779	2
#72262776	2
#72262775	2
#72262774	2
#72262465	2
#72237028	2
#72235717	2
#72235675	2
#72235671	2
#72234757	2
#72234687	2
#72234607	2
#72233792	2
#72233388	2
#72232937	2
#72232735	2