Subgroups — #72262808

Order 2048.

At least 8872 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	#72262806	C₂	1	2	yes	maximal, complemented
2	#72262805	C₂	1	1	yes	maximal, characteristic, complemented
3	#72262802	C₂	1	2	yes	maximal, complemented
4	#72262782	C₂	1	2	yes	maximal, complemented
5	#72262780	C₂	1	2	yes	maximal, complemented
6	#72262777	C₂	1	2	yes	maximal, complemented
7	#72262773	C₂	1	2	yes	maximal, complemented
8	#72262566	C₂	1	1	yes	maximal, characteristic, complemented
9	#72262562	C₂	1	1	yes	maximal, characteristic, complemented
10	#72262465	C₂	1	1	yes	maximal, characteristic, complemented
11	#72237028	C₂	1	1	yes	maximal, characteristic, complemented
12	#72235719	C₂	1	2	yes	maximal, complemented
13	#72235715	C₂	1	2	yes	maximal, complemented
14	#72235698	C₂	1	2	yes	maximal, complemented
15	#72235685	C₂	1	2	yes	maximal, complemented
16	#72235677	C₂	1	2	yes	maximal, complemented
17	#72234757	C₂	1	2	yes	maximal, complemented
18	#72234687	C₂	1	1	yes	maximal, characteristic, complemented
19	#72234607	C₂	1	1	yes	maximal, characteristic, complemented
20	#10586472	C₂²	1	1	yes	characteristic
21	#6499870	C₂²	1	2	yes	—
22	#6346729	C₂²	1	2	yes	—
23	#6346698	C₂²	1	2	yes	—
24	#5522188	C₂²	1	1	yes	characteristic, complemented
25	#5474149	C₂²	1	1	yes	characteristic, complemented
26	#5228463	C₂²	1	1	yes	characteristic, complemented
27	#5037287	C₂²	1	1	yes	characteristic, complemented
28	#4650470	C₂²	1	1	yes	characteristic, complemented
29	#4466055	C₂²	1	1	yes	characteristic, complemented
30	#4430405	C₂²	1	1	yes	characteristic, complemented
31	#4420586	C₂²	1	1	yes	characteristic
32	#4047168	C₂²	1	1	yes	characteristic, complemented
33	#2228038	C₂²	1	1	yes	characteristic, complemented
34	#2040406	C₂²	1	1	yes	characteristic, complemented
35	#1484729	C₂²	1	1	yes	characteristic, complemented
36	#686207	C₂²	1	1	yes	characteristic
37	#654056	C₂²	1	1	yes	characteristic, complemented
38	#649042	C₂²	1	1	yes	characteristic
39	#485385	C₂²	1	4	yes	complemented
40	#485081	C₂²	1	4	yes	complemented
41	#347052	C₂²	1	2	yes	—
42	#347052	C₂²	1	2	yes	—
43	#347043	C₂²	1	2	yes	—
44	#347043	C₂²	1	2	yes	—
45	#346459	C₂²	1	2	yes	—
46	#346459	C₂²	1	2	yes	—
47	#346459	C₂²	1	2	yes	—
48	#346456	C₂²	1	2	yes	—
49	#346456	C₂²	1	2	yes	—
50	#346456	C₂²	1	2	yes	—
51	#346449	C₂²	1	2	yes	—
52	#346446	C₂²	1	2	yes	—
53	#188087	C₂²	1	1	yes	characteristic
54	#188087	C₂²	1	1	yes	characteristic
55	#188035	C₂²	1	1	yes	characteristic
56	#187949	C₂²	1	2	yes	—
57	#185282	C₂²	1	2	yes	—
58	#185270	C₂²	1	2	yes	—
59	#144617	C₂²	1	4	yes	complemented
60	#144616	C₂²	1	4	yes	complemented
61	#142999	C₂²	1	4	yes	complemented
62	#142982	C₂²	1	4	yes	complemented
63	#142569	C₂²	1	4	yes	complemented
64	#142569	C₂²	1	4	yes	complemented
65	#142568	C₂²	1	4	yes	complemented
66	#142536	C₂²	1	4	yes	complemented
67	#140058	C₂²	1	4	yes	complemented
68	#140058	C₂²	1	4	yes	complemented
69	#140051	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	#139622	C₂²	1	4	yes	complemented
77	#139504	C₂²	1	2	yes	complemented
78	#139486	C₂²	1	2	yes	complemented
79	#139486	C₂²	1	2	yes	complemented
80	#139486	C₂²	1	2	yes	complemented
81	#139472	C₂²	1	2	yes	complemented
82	#139434	C₂²	1	2	yes	complemented
83	#139434	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	#133222	C₂²	1	2	yes	complemented
90	#133121	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×#124	D₄	1	1	yes	characteristic, complemented
97	C₂×#2760	C₂³	1	1	yes	characteristic, complemented
98	C₂×#2840	C₂³	1	1	yes	characteristic, complemented
99	C₂×#2436	C₂³	1	1	yes	characteristic
100	C₂×#2409	D₄	1	1	yes	characteristic, complemented
101	C₂×#2403	D₄	1	1	yes	characteristic
102	C₂×#2403	D₄	1	1	yes	characteristic
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	#18163	C₂³	1	4	yes	—
111	#18163	C₂³	1	4	yes	—
112	#18162	C₂³	1	4	yes	—
113	#17396	C₂³	1	2	yes	—
114	#17396	C₂³	1	2	yes	—
115	#17198	C₂³	1	1	yes	characteristic, complemented
116	#17105	C₂³	1	1	yes	characteristic, complemented
117	#16208	C₂³	1	1	yes	characteristic, complemented
118	#15984	C₂³	1	1	yes	characteristic
119	#15984	C₂³	1	1	yes	characteristic
120	#15948	D₄	1	1	yes	characteristic
121	#15947	D₄	1	1	yes	characteristic
122	#15930	C₂³	1	1	yes	characteristic, complemented
123	#15930	C₂³	1	1	yes	characteristic, complemented
124	#15673	D₄	1	1	yes	characteristic, complemented
125	#15673	D₄	1	1	yes	characteristic, complemented
126	#15673	D₄	1	1	yes	characteristic, complemented
127	#15673	C₂³	1	1	yes	characteristic
128	#15673	C₂³	1	1	yes	characteristic
129	#15673	C₂³	1	1	yes	characteristic
130	#15616	C₂³	1	1	yes	characteristic, complemented
131	#15467	C₂³	1	1	yes	characteristic, complemented
132	#15310	D₄	1	1	yes	characteristic, complemented
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	D₄	1	1	yes	characteristic, complemented
138	#15259	D₄	1	1	yes	characteristic, complemented
139	#15259	C₂³	1	1	yes	characteristic
140	#15259	C₂³	1	1	yes	characteristic
141	#15259	C₂³	1	1	yes	characteristic
142	#15258	D₄	1	1	yes	characteristic
143	#15258	D₄	1	1	yes	characteristic, complemented
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	#14609	C₂³	1	1	yes	characteristic, complemented
151	#14609	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	C₂²⋊C₄²	C₂³	1	1	yes	characteristic, complemented
161	C₄×#386	D₄	1	1	yes	characteristic, complemented
162	#11808	C₂³	1	4	yes	complemented
163	#11808	C₂³	1	4	yes	complemented
164	#11808	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×Q₈	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×#124	C₂×D₄	1	1	yes	characteristic
198	C₂²×#124	C₂×D₄	1	1	yes	characteristic
199	C₂²×#124	C₂×D₄	1	1	yes	characteristic
200	C₂²×#124	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×#395	C₂×D₄	1	1	yes	characteristic
223	C₂×#395	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	C₂×D₄	1	1	yes	characteristic
228	C₂×#393	C₂×D₄	1	1	yes	characteristic
229	C₂×#393	C₂×D₄	1	1	yes	characteristic
230	C₂×#393	C₂×D₄	1	1	yes	characteristic
231	C₂×#393	C₂⁴	1	1	yes	characteristic
232	C₂×#393	C₂⁴	1	1	yes	characteristic
233	C₂×#393	C₂⁴	1	1	yes	characteristic
234	C₂×#392	C₂×D₄	1	1	yes	characteristic
235	C₂×#392	C₂×D₄	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×Q₈	C₂²×D₄	1	1	yes	characteristic
296	C₂³×Q₈	C₂²×D₄	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	#120	1	1	yes	characteristic
303	C₂³×D₄	#120	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	#33558	1	2	yes	—
396	C₂²	#6499856	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×#33558	1	1	yes	characteristic
402	C₂²	#7622875	1	1	yes	characteristic
403	C₂	#72238456	1	1	yes	characteristic
404	C₂	#72238483	1	1	yes	characteristic
405	C₂	#72256333	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. #72262806	C₂	semidirect
2. #72262805	C₂	semidirect
3. #72262802	C₂	semidirect
4. #72262782	C₂	semidirect
5. #72262780	C₂	semidirect
6. #72262777	C₂	semidirect
7. #72262773	C₂	semidirect
8. #72262566	C₂	semidirect
9. #72262562	C₂	semidirect
10. #72262465	C₂	semidirect
11. #72237028	C₂	semidirect
12. #72235719	C₂	semidirect
13. #72235715	C₂	semidirect
14. #72235698	C₂	semidirect
15. #72235685	C₂	semidirect
16. #72235677	C₂	semidirect
17. #72234757	C₂	semidirect
18. #72234687	C₂	semidirect
19. #72234607	C₂	semidirect
24. #5522188	C₂²	semidirect
25. #5474149	C₂²	semidirect
26. #5228463	C₂²	semidirect
27. #5037287	C₂²	semidirect
28. #4650470	C₂²	semidirect
29. #4466055	C₂²	semidirect
30. #4430405	C₂²	semidirect
32. #4047168	C₂²	semidirect
33. #2228038	C₂²	semidirect
34. #2040406	C₂²	semidirect
35. #1484729	C₂²	semidirect
37. #654056	C₂²	semidirect
39. #485385	C₂²	semidirect
40. #485081	C₂²	semidirect
59. #144617	C₂²	semidirect
60. #144616	C₂²	semidirect
61. #142999	C₂²	semidirect
62. #142982	C₂²	semidirect
63. #142569	C₂²	semidirect
64. #142569	C₂²	semidirect
65. #142568	C₂²	semidirect
66. #142536	C₂²	semidirect
67. #140058	C₂²	semidirect
68. #140058	C₂²	semidirect
69. #140051	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. #139622	C₂²	semidirect
77. #139504	C₂²	semidirect
78. #139486	C₂²	semidirect
79. #139486	C₂²	semidirect
80. #139486	C₂²	semidirect
81. #139472	C₂²	semidirect
82. #139434	C₂²	semidirect
83. #139434	C₂²	semidirect
84. #139434	C₂²	semidirect
85. #135573	C₂²	semidirect
86. #135485	C₂²	semidirect
87. #135479	C₂²	semidirect
88. #134036	C₂²	semidirect
89. #133222	C₂²	semidirect
90. #133121	C₂²	semidirect
95. C₂²×#535	D₄	semidirect
96. C₂³×#124	D₄	semidirect
97. C₂×#2760	C₂³	semidirect
98. C₂×#2840	C₂³	semidirect
100. C₂×#2409	D₄	semidirect
105. C₂×#2388	D₄	semidirect
115. #17198	C₂³	semidirect
116. #17105	C₂³	semidirect
117. #16208	C₂³	semidirect
122. #15930	C₂³	semidirect
123. #15930	C₂³	semidirect
124. #15673	D₄	semidirect
125. #15673	D₄	semidirect
126. #15673	D₄	semidirect
130. #15616	C₂³	semidirect
131. #15467	C₂³	semidirect
132. #15310	D₄	semidirect
134. #15267	C₂³	semidirect
136. #15259	D₄	semidirect
137. #15259	D₄	semidirect
138. #15259	D₄	semidirect
143. #15258	D₄	semidirect
149. #14649	C₂³	semidirect
150. #14609	C₂³	semidirect
151. #14609	C₂³	semidirect
152. #14507	C₂³	semidirect
155. #14207	C₂³	semidirect
157. #13902	D₄	semidirect
158. #13902	D₄	semidirect
159. #13871	D₄	semidirect
160. C₂²⋊C₄²	C₂³	semidirect
161. C₄×#386	D₄	semidirect
162. #11808	C₂³	semidirect
163. #11808	C₂³	semidirect
164. #11808	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
#72262806	2
#72262805	2
#72262802	2
#72262782	2
#72262780	2
#72262777	2
#72262773	2
#72262566	2
#72262562	2
#72262465	2
#72237028	2
#72235719	2
#72235715	2
#72235698	2
#72235685	2
#72235677	2
#72234757	2
#72234687	2
#72234607	2