Subgroups — #72262604

Order 2048.

At least 10944 conjugacy classes of subgroups; only the 770 normal subgroups are shown.

The subgroup lattice has 464 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262602	C₂	1	2	yes	maximal, complemented
2	#72262601	C₂	1	1	yes	maximal, characteristic, complemented
3	#72262600	C₂	1	2	yes	maximal, complemented
4	#72262599	C₂	1	2	yes	maximal, complemented
5	#72262597	C₂	1	2	yes	maximal, complemented
6	#72262595	C₂	1	2	yes	maximal, complemented
7	#72262560	C₂	1	2	yes	maximal, complemented
8	#72262506	C₂	1	2	yes	maximal, complemented
9	#72262458	C₂	1	2	yes	maximal, complemented
10	#72238496	C₂	1	2	yes	maximal, complemented
11	#72237362	C₂	1	2	yes	maximal, complemented
12	#72235808	C₂	1	2	yes	maximal, complemented
13	#72235800	C₂	1	1	yes	maximal, characteristic, complemented
14	#72235794	C₂	1	1	yes	maximal, characteristic, complemented
15	#72235768	C₂	1	1	yes	maximal, characteristic, complemented
16	#72235727	C₂	1	1	yes	maximal, characteristic, complemented
17	#72235723	C₂	1	1	yes	maximal, characteristic, complemented
18	#72235690	C₂	1	2	yes	maximal, complemented
19	#72234732	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#62818	C₂²	1	1	yes	characteristic
21	C₂×#47031	C₂²	1	1	yes	characteristic, complemented
22	C₂×#35250	C₂²	1	1	yes	characteristic
23	#6451874	C₂²	1	2	yes	complemented
24	#6346729	C₂²	1	2	yes	—
25	#6346728	C₂²	1	2	yes	—
26	#6346698	C₂²	1	2	yes	—
27	#6346698	C₂²	1	2	yes	—
28	#6346594	C₂²	1	2	yes	—
29	#6346594	C₂²	1	2	yes	—
30	#6346594	C₂²	1	2	yes	complemented
31	C₂×#17396	C₂²	1	1	yes	characteristic
32	#5474087	C₂²	1	1	yes	characteristic, complemented
33	#5085422	C₂²	1	1	yes	characteristic, complemented
34	#5036788	C₂²	1	1	yes	characteristic, complemented
35	#4866548	C₂²	1	1	yes	characteristic, complemented
36	#4335643	C₂²	1	1	yes	characteristic, complemented
37	#4123560	C₂²	1	1	yes	characteristic, complemented
38	#4037131	C₂²	1	1	yes	characteristic, complemented
39	#4035358	C₂²	1	1	yes	characteristic, complemented
40	#2203033	C₂²	1	1	yes	characteristic, complemented
41	#2081109	C₂²	1	1	yes	characteristic, complemented
42	#618316	C₂²	1	1	yes	characteristic
43	#617709	C₂²	1	1	yes	characteristic
44	#587352	C₂²	1	1	yes	characteristic, complemented
45	#485388	C₂²	1	4	yes	complemented
46	#485388	C₂²	1	4	yes	complemented
47	#485078	C₂²	1	4	yes	complemented
48	#485044	C₂²	1	4	yes	complemented
49	#482549	C₂²	1	2	yes	complemented
50	#482549	C₂²	1	2	yes	complemented
51	#482549	C₂²	1	2	yes	complemented
52	#480250	C₂²	1	2	yes	complemented
53	#347052	C₂²	1	2	yes	—
54	#347052	C₂²	1	2	yes	complemented
55	#347043	C₂²	1	2	yes	—
56	#347043	C₂²	1	2	yes	complemented
57	#346459	C₂²	1	2	yes	—
58	#346459	C₂²	1	2	yes	complemented
59	#346449	C₂²	1	2	yes	—
60	#346449	C₂²	1	2	yes	complemented
61	C₂×#8549	C₂²	1	1	yes	characteristic
62	C₂×#8542	C₂²	1	1	yes	characteristic
63	#187945	C₂²	1	2	yes	complemented
64	#185255	C₂²	1	2	yes	complemented
65	#142999	C₂²	1	4	yes	complemented
66	#142982	C₂²	1	4	yes	complemented
67	#142982	C₂²	1	4	yes	complemented
68	#142969	C₂²	1	4	yes	complemented
69	#142569	C₂²	1	4	yes	complemented
70	#142568	C₂²	1	4	yes	complemented
71	#142537	C₂²	1	4	yes	complemented
72	#142536	C₂²	1	4	yes	complemented
73	#140056	C₂²	1	4	yes	complemented
74	#140049	C₂²	1	4	yes	complemented
75	#140034	C₂²	1	4	yes	complemented
76	#140026	C₂²	1	4	yes	complemented
77	#139908	C₂²	1	2	yes	complemented
78	#139908	C₂²	1	2	yes	complemented
79	#139906	C₂²	1	2	yes	complemented
80	#139906	C₂²	1	2	yes	complemented
81	#139472	C₂²	1	2	yes	complemented
82	#139472	C₂²	1	2	yes	complemented
83	#139434	C₂²	1	2	yes	complemented
84	#139434	C₂²	1	2	yes	complemented
85	#133222	C₂²	1	2	yes	complemented
86	#133121	C₂²	1	2	yes	complemented
87	#133121	C₂²	1	2	yes	complemented
88	#133093	C₂²	1	2	yes	complemented
89	#128157	C₂²	1	2	yes	complemented
90	#127215	C₂²	1	2	yes	complemented
91	C₂⁴×#41	D₄	1	1	yes	characteristic, complemented
92	#62818	C₂³	1	2	yes	—
93	#62818	C₂³	1	2	yes	—
94	C₂×#3490	C₂³	1	2	yes	—
95	C₂²×#535	D₄	1	1	yes	characteristic, complemented
96	C₂³×#121	C₂³	1	1	yes	characteristic
97	C₂×#2670	C₂³	1	1	yes	characteristic, complemented
98	C₂×#2670	C₂³	1	1	yes	characteristic, complemented
99	C₂×#2815	C₂³	1	1	yes	characteristic, complemented
100	C₂×#2607	C₂³	1	1	yes	characteristic, complemented
101	C₂×#2406	D₄	1	1	yes	characteristic, complemented
102	C₂×#2404	D₄	1	1	yes	characteristic, complemented
103	C₂×#2404	D₄	1	1	yes	characteristic, complemented
104	C₂×#2404	C₂³	1	1	yes	characteristic
105	C₂×#2404	C₂³	1	1	yes	characteristic
106	C₂×#2404	C₂³	1	1	yes	characteristic
107	C₂×#2436	D₄	1	1	yes	characteristic, complemented
108	C₂×#2436	C₂³	1	1	yes	characteristic
109	C₂×#2433	D₄	1	1	yes	characteristic, complemented
110	C₂×#2433	C₂³	1	1	yes	characteristic
111	C₂×#2403	D₄	1	1	yes	characteristic
112	C₂×#2403	D₄	1	1	yes	characteristic
113	C₂×#2615	D₄	1	1	yes	characteristic, complemented
114	C₂×#2615	D₄	1	1	yes	characteristic, complemented
115	C₂×#2615	C₂³	1	1	yes	characteristic
116	C₂×#2615	C₂³	1	1	yes	characteristic
117	C₂×#2308	C₂³	1	1	yes	characteristic
118	C₂×#2280	D₄	1	1	yes	characteristic, complemented
119	#23985	C₂³	1	4	yes	—
120	#23984	C₂³	1	4	yes	—
121	C₂×#1819	C₂³	1	2	yes	—
122	#18192	D₄	1	8	yes	complemented
123	#18163	C₂³	1	4	yes	—
124	#18163	C₂³	1	4	yes	—
125	#18163	C₂³	1	4	yes	—
126	#18162	C₂³	1	4	yes	—
127	#18162	C₂³	1	4	yes	—
128	#18162	C₂³	1	4	yes	—
129	#18133	D₄	1	4	yes	complemented
130	#18132	D₄	1	4	yes	complemented
131	#17396	C₂³	1	2	yes	—
132	#17396	C₂³	1	2	yes	—
133	C₂×#1462	C₂³	1	2	yes	—
134	C₂×#1462	C₂³	1	2	yes	—
135	#17198	C₂³	1	1	yes	characteristic, complemented
136	#17105	C₂³	1	1	yes	characteristic, complemented
137	#17105	C₂³	1	1	yes	characteristic, complemented
138	#17102	C₂³	1	1	yes	characteristic, complemented
139	#15984	D₄	1	1	yes	characteristic
140	#15984	D₄	1	1	yes	characteristic
141	#15984	C₂³	1	1	yes	characteristic
142	#15984	C₂³	1	1	yes	characteristic
143	#15930	C₂³	1	1	yes	characteristic, complemented
144	#15673	D₄	1	1	yes	characteristic, complemented
145	#15673	D₄	1	1	yes	characteristic, complemented
146	#15673	C₂³	1	1	yes	characteristic
147	#15673	C₂³	1	1	yes	characteristic
148	#15561	C₂³	1	1	yes	characteristic, complemented
149	#15467	C₂³	1	1	yes	characteristic, complemented
150	#15310	D₄	1	1	yes	characteristic, complemented
151	#15310	D₄	1	1	yes	characteristic, complemented
152	#15310	C₂³	1	1	yes	characteristic
153	#15310	C₂³	1	1	yes	characteristic
154	#15267	C₂³	1	1	yes	characteristic, complemented
155	#15257	D₄	1	1	yes	characteristic
156	#15257	D₄	1	1	yes	characteristic
157	#15257	C₂³	1	1	yes	characteristic
158	#15257	C₂³	1	1	yes	characteristic
159	#14651	C₂³	1	1	yes	characteristic, complemented
160	#14567	C₂³	1	1	yes	characteristic, complemented
161	#14537	C₂³	1	1	yes	characteristic, complemented
162	#14341	C₂³	1	1	yes	characteristic
163	#14335	D₄	1	1	yes	characteristic, complemented
164	#14232	C₂³	1	1	yes	characteristic, complemented
165	#13870	D₄	1	1	yes	characteristic, complemented
166	#13868	C₂³	1	1	yes	characteristic
167	#13867	D₄	1	1	yes	characteristic
168	#13867	D₄	1	1	yes	characteristic
169	#11808	C₂³	1	4	yes	complemented
170	#11808	C₂³	1	4	yes	complemented
171	#11808	C₂³	1	4	yes	complemented
172	#11796	C₂³	1	4	yes	complemented
173	#11796	C₂³	1	4	yes	complemented
174	#11796	C₂³	1	4	yes	complemented
175	#11500	C₂³	1	4	yes	complemented
176	#11499	C₂³	1	4	yes	complemented
177	#8549	C₂³	1	2	yes	—
178	#8549	C₂³	1	2	yes	—
179	#8542	C₂³	1	2	yes	—
180	#8542	C₂³	1	2	yes	—
181	#8535	C₂³	1	4	yes	—
182	#8535	C₂³	1	4	yes	—
183	#8346	C₂³	1	4	yes	—
184	#8346	C₂³	1	4	yes	—
185	#7324	C₂³	1	4	yes	complemented
186	#7324	C₂³	1	4	yes	complemented
187	#7213	C₂³	1	4	yes	complemented
188	#7213	C₂³	1	4	yes	complemented
189	C₂³×#41	C₂×D₄	1	1	yes	characteristic
190	C₂³×#41	C₂×D₄	1	1	yes	characteristic
191	C₂³×#41	C₂×D₄	1	1	yes	characteristic
192	C₂³×#41	C₂×D₄	1	1	yes	characteristic
193	C₂³×#41	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
196	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
199	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
200	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
201	#3490	C₂×D₄	1	4	yes	—
202	#3490	C₂⁴	1	4	yes	—
203	C₂×#543	C₂×D₄	1	2	yes	—
204	C₂×#534	C₂×D₄	1	2	yes	—
205	C₂²×#127	C₂×D₄	1	1	yes	characteristic
206	C₂²×#127	C₂×D₄	1	1	yes	characteristic
207	C₂²×#124	C₂×D₄	1	1	yes	characteristic
208	C₂²×#124	C₂×D₄	1	1	yes	characteristic
209	C₂²×#121	C₂×D₄	1	1	yes	characteristic
210	C₂²×#121	C₂×D₄	1	1	yes	characteristic
211	C₂²×#121	C₂×D₄	1	1	yes	characteristic
212	C₂²×#121	C₂×D₄	1	1	yes	characteristic
213	C₂²×#121	C₂×D₄	1	1	yes	characteristic
214	C₂²×#121	C₂×D₄	1	1	yes	characteristic
215	C₂²×#121	C₂⁴	1	1	yes	characteristic
216	C₂²×#121	C₂⁴	1	1	yes	characteristic
217	C₂²×#120	C₂×D₄	1	1	yes	characteristic
218	C₂²×#120	C₂×D₄	1	1	yes	characteristic
219	C₂²×#120	C₂×D₄	1	1	yes	characteristic
220	C₂²×#120	C₂×D₄	1	1	yes	characteristic
221	C₂²×#117	C₂×D₄	1	1	yes	characteristic
222	C₂³×C₄⋊C₄	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	C₂⁴	1	1	yes	characteristic
226	#2404	C₂×D₄	1	4	yes	—
227	#2404	C₂×D₄	1	4	yes	—
228	C₂×#395	C₂×D₄	1	1	yes	characteristic
229	C₂×#395	C₂×D₄	1	1	yes	characteristic
230	C₂×#394	C₂×D₄	1	1	yes	characteristic
231	C₂×#394	C₂×D₄	1	1	yes	characteristic
232	C₂×#393	C₂×D₄	1	1	yes	characteristic
233	C₂×#393	C₂×D₄	1	1	yes	characteristic
234	C₂×#393	C₂×D₄	1	1	yes	characteristic
235	C₂×#393	C₂×D₄	1	1	yes	characteristic
236	C₂×#393	C₂×D₄	1	1	yes	characteristic
237	C₂×#393	C₂×D₄	1	1	yes	characteristic
238	C₂×#393	C₂×D₄	1	1	yes	characteristic
239	C₂×#393	C₂⁴	1	1	yes	characteristic
240	C₂×#393	C₂⁴	1	1	yes	characteristic
241	C₂×#393	C₂⁴	1	1	yes	characteristic
242	C₂×#392	C₂×D₄	1	1	yes	characteristic
243	C₂×#392	C₂×D₄	1	1	yes	characteristic
244	C₂×#392	C₂×D₄	1	1	yes	characteristic
245	C₂×#392	C₂×D₄	1	1	yes	characteristic
246	C₂×#392	C₂×D₄	1	1	yes	characteristic
247	C₂×#392	C₂×D₄	1	1	yes	characteristic
248	C₂×#392	C₂×D₄	1	1	yes	characteristic
249	C₂×#392	C₂⁴	1	1	yes	characteristic
250	C₂×#392	C₂⁴	1	1	yes	characteristic
251	C₂×#392	C₂⁴	1	1	yes	characteristic
252	C₂×#386	C₂×D₄	1	1	yes	characteristic
253	C₂×#386	C₂×D₄	1	1	yes	characteristic
254	C₂×#386	C₂×D₄	1	1	yes	characteristic
255	C₂×#386	C₂×D₄	1	1	yes	characteristic
256	C₂×#381	C₂×D₄	1	1	yes	characteristic
257	C₂×#381	C₂×D₄	1	1	yes	characteristic
258	C₂×#381	C₂×D₄	1	1	yes	characteristic
259	C₂×#381	C₂×D₄	1	1	yes	characteristic
260	C₂×#381	C₂×D₄	1	1	yes	characteristic
261	C₂×#381	C₂⁴	1	1	yes	characteristic
262	C₂×#380	C₂×D₄	1	1	yes	characteristic
263	C₂×#380	C₂×D₄	1	1	yes	characteristic
264	C₂×#379	C₂×D₄	1	1	yes	characteristic
265	C₂×#379	C₂×D₄	1	1	yes	characteristic
266	C₂×#379	C₂×D₄	1	1	yes	characteristic
267	C₂×#379	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
269	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
270	#1819	C₂⁴	1	4	yes	—
271	#1602	C₂×D₄	1	8	yes	—
272	#1601	C₂×D₄	1	8	yes	—
273	#1596	C₂×D₄	1	8	yes	—
274	#1595	C₂×D₄	1	8	yes	—
275	#1462	C₂×D₄	1	4	yes	—
276	#1462	C₂⁴	1	4	yes	—
277	#1462	C₂⁴	1	4	yes	—
278	C₂×#323	C₂×D₄	1	4	yes	—
279	#1440	C₂×D₄	1	1	yes	characteristic
280	#1440	C₂×D₄	1	1	yes	characteristic
281	#1440	C₂⁴	1	1	yes	characteristic
282	#1440	C₂⁴	1	1	yes	characteristic
283	#1438	C₂×D₄	1	1	yes	characteristic
284	#1438	C₂×D₄	1	1	yes	characteristic
285	#1438	C₂×D₄	1	1	yes	characteristic
286	#1438	C₂×D₄	1	1	yes	characteristic
287	#1438	C₂×D₄	1	1	yes	characteristic
288	#1438	C₂×D₄	1	1	yes	characteristic
289	#1438	C₂×D₄	1	1	yes	characteristic
290	#1438	C₂×D₄	1	1	yes	characteristic
291	#1438	C₂×D₄	1	1	yes	characteristic
292	#1438	C₂×D₄	1	1	yes	characteristic
293	#1438	C₂×D₄	1	1	yes	characteristic
294	#1438	C₂×D₄	1	1	yes	characteristic
295	#1437	C₂×D₄	1	1	yes	characteristic
296	#1437	C₂×D₄	1	1	yes	characteristic
297	#1437	C₂⁴	1	1	yes	characteristic
298	#1437	C₂⁴	1	1	yes	characteristic
299	#1436	C₂×D₄	1	1	yes	characteristic
300	#1436	C₂×D₄	1	1	yes	characteristic
301	#1436	C₂×D₄	1	1	yes	characteristic
302	#1436	C₂×D₄	1	1	yes	characteristic
303	C₂⁶	#120	1	1	yes	characteristic
304	C₂⁶	#120	1	1	yes	characteristic
305	C₂⁶	C₂²×D₄	1	1	yes	characteristic
306	C₂⁶	C₂²×D₄	1	1	yes	characteristic
307	C₂²×#41	#120	1	2	yes	—
308	C₂²×#41	#120	1	2	yes	—
309	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
310	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
311	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
312	C₂³×D₄	#120	1	1	yes	characteristic
313	C₂³×D₄	#120	1	1	yes	characteristic
314	C₂³×D₄	#120	1	1	yes	characteristic
315	C₂³×D₄	#120	1	1	yes	characteristic
316	C₂³×D₄	#120	1	1	yes	characteristic
317	C₂³×D₄	#120	1	1	yes	characteristic
318	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
319	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
320	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
321	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
322	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
323	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
324	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
325	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
326	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
327	C₂⁴×C₄	#120	1	1	yes	characteristic
328	C₂⁴×C₄	#120	1	1	yes	characteristic
329	C₂⁴×C₄	#120	1	1	yes	characteristic
330	C₂⁴×C₄	#120	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
336	#543	C₂²×D₄	1	4	yes	—
337	#534	C₂²×D₄	1	4	yes	—
338	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
340	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
342	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
343	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
350	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
351	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
354	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
358	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
359	C₂²×C₂²⋊C₄	C₂⁵	1	1	yes	characteristic
360	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
361	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
362	#393	#120	1	4	yes	—
363	#393	C₂²×D₄	1	4	yes	—
364	#392	#120	1	4	yes	—
365	#392	C₂²×D₄	1	4	yes	—
366	#381	#120	1	2	yes	—
367	#381	#120	1	2	yes	—
368	C₂×#95	C₂²×D₄	1	1	yes	characteristic
369	C₂×#95	C₂²×D₄	1	1	yes	characteristic
370	C₂×#95	C₂²×D₄	1	1	yes	characteristic
371	C₂×#95	C₂²×D₄	1	1	yes	characteristic
372	C₂×#95	C₂²×D₄	1	1	yes	characteristic
373	C₂×#95	C₂²×D₄	1	1	yes	characteristic
374	C₂×#95	C₂²×D₄	1	1	yes	characteristic
375	C₂×#95	C₂²×D₄	1	1	yes	characteristic
376	#323	C₂²×D₄	1	8	yes	—
377	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
378	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
379	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
380	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
381	C₂⁵	C₂×#120	1	1	yes	characteristic
382	C₂⁵	C₂×#120	1	1	yes	characteristic
383	C₂⁵	C₂×#120	1	1	yes	characteristic
384	C₂⁵	C₂×#120	1	1	yes	characteristic
385	C₂⁵	C₂×#120	1	1	yes	characteristic
386	C₂⁵	C₂×#120	1	1	yes	characteristic
387	C₂⁵	D₄²	1	2	yes	—
388	C₂⁵	D₄²	1	2	yes	—
389	C₂⁵	C₂³×D₄	1	1	yes	characteristic
390	C₂²×Q₈	C₂×#120	1	2	yes	—
391	C₂²×D₄	C₂×#120	1	2	yes	—
392	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
393	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
394	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
395	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
396	C₂³×C₄	C₂×#120	1	1	yes	characteristic
397	C₂³×C₄	C₂×#120	1	1	yes	characteristic
398	C₂³×C₄	C₂×#120	1	1	yes	characteristic
399	C₂³×C₄	C₂×#120	1	1	yes	characteristic
400	C₂³×C₄	C₂×#120	1	1	yes	characteristic
401	C₂³×C₄	C₂×#120	1	1	yes	characteristic
402	C₂³×C₄	C₂×#120	1	1	yes	characteristic
403	C₂³×C₄	C₂×#120	1	1	yes	characteristic
404	C₂³×C₄	#534	1	1	yes	characteristic
405	C₂³×C₄	#534	1	1	yes	characteristic
406	C₂³×C₄	D₄²	1	2	yes	—
407	C₂³×C₄	D₄²	1	2	yes	—
408	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
409	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
411	C₂×C₂²⋊C₄	#534	1	2	yes	—
412	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
413	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
414	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
415	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	2	yes	—
418	#95	C₂×#120	1	2	yes	—
419	#95	C₂×#120	1	2	yes	—
420	C₂⁴	#2403	1	2	yes	—
421	C₂⁴	#2403	1	1	yes	characteristic
422	C₂⁴	#2403	1	1	yes	characteristic
423	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
424	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
425	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
426	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
427	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
428	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
429	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
430	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
431	C₂⁴	C₂²×#120	1	1	yes	characteristic
432	C₂⁴	C₂×D₄²	1	2	yes	—
433	C₂²×C₄	#2403	1	2	yes	—
434	C₂²×C₄	#2403	1	1	yes	characteristic
435	C₂²×C₄	#2403	1	1	yes	characteristic
436	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
437	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
438	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
441	C₂²×C₄	C₂×#534	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄²	1	2	yes	—
443	C₂³	#23900	1	1	yes	characteristic
444	C₂³	#23900	1	1	yes	characteristic
445	C₂³	#23900	1	1	yes	characteristic
446	C₂³	#23900	1	1	yes	characteristic
447	C₂³	#33551	1	2	yes	—
448	C₂³	C₂×#2403	1	1	yes	characteristic
449	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
450	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
451	C₂×C₄	#33551	1	2	yes	—
452	C₂×C₄	#33551	1	2	yes	—
453	C₂²	#6437575	1	1	yes	characteristic
454	C₂²	#6437587	1	1	yes	characteristic
455	C₂²	C₂×#23900	1	1	yes	characteristic
456	C₂²	C₂×#33551	1	1	yes	characteristic
457	C₂²	C₂×#33551	1	1	yes	characteristic
458	C₂²	C₂×#33551	1	1	yes	characteristic
459	C₂²	#7622875	1	1	yes	characteristic
460	C₂	#72218077	1	1	yes	characteristic
461	C₂	#72235210	1	1	yes	characteristic
462	C₂	#72235270	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂²×C₂²⋊C₄	C₂⁵
LCS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#121 ◁ 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. #72262602	C₂	semidirect
2. #72262601	C₂	semidirect
3. #72262600	C₂	semidirect
4. #72262599	C₂	semidirect
5. #72262597	C₂	semidirect
6. #72262595	C₂	semidirect
7. #72262560	C₂	semidirect
8. #72262506	C₂	semidirect
9. #72262458	C₂	semidirect
10. #72238496	C₂	semidirect
11. #72237362	C₂	semidirect
12. #72235808	C₂	semidirect
13. #72235800	C₂	semidirect
14. #72235794	C₂	semidirect
15. #72235768	C₂	semidirect
16. #72235727	C₂	semidirect
17. #72235723	C₂	semidirect
18. #72235690	C₂	semidirect
19. #72234732	C₂	semidirect
21. C₂×#47031	C₂²	semidirect
23. #6451874	C₂²	semidirect
30. #6346594	C₂²	semidirect
32. #5474087	C₂²	semidirect
33. #5085422	C₂²	semidirect
34. #5036788	C₂²	semidirect
35. #4866548	C₂²	semidirect
36. #4335643	C₂²	semidirect
37. #4123560	C₂²	semidirect
38. #4037131	C₂²	semidirect
39. #4035358	C₂²	semidirect
40. #2203033	C₂²	semidirect
41. #2081109	C₂²	semidirect
44. #587352	C₂²	semidirect
45. #485388	C₂²	semidirect
46. #485388	C₂²	semidirect
47. #485078	C₂²	semidirect
48. #485044	C₂²	semidirect
49. #482549	C₂²	semidirect
50. #482549	C₂²	semidirect
51. #482549	C₂²	semidirect
52. #480250	C₂²	semidirect
54. #347052	C₂²	semidirect
56. #347043	C₂²	semidirect
58. #346459	C₂²	semidirect
60. #346449	C₂²	semidirect
63. #187945	C₂²	semidirect
64. #185255	C₂²	semidirect
65. #142999	C₂²	semidirect
66. #142982	C₂²	semidirect
67. #142982	C₂²	semidirect
68. #142969	C₂²	semidirect
69. #142569	C₂²	semidirect
70. #142568	C₂²	semidirect
71. #142537	C₂²	semidirect
72. #142536	C₂²	semidirect
73. #140056	C₂²	semidirect
74. #140049	C₂²	semidirect
75. #140034	C₂²	semidirect
76. #140026	C₂²	semidirect
77. #139908	C₂²	semidirect
78. #139908	C₂²	semidirect
79. #139906	C₂²	semidirect
80. #139906	C₂²	semidirect
81. #139472	C₂²	semidirect
82. #139472	C₂²	semidirect
83. #139434	C₂²	semidirect
84. #139434	C₂²	semidirect
85. #133222	C₂²	semidirect
86. #133121	C₂²	semidirect
87. #133121	C₂²	semidirect
88. #133093	C₂²	semidirect
89. #128157	C₂²	semidirect
90. #127215	C₂²	semidirect
91. C₂⁴×#41	D₄	semidirect
95. C₂²×#535	D₄	semidirect
97. C₂×#2670	C₂³	semidirect
98. C₂×#2670	C₂³	semidirect
99. C₂×#2815	C₂³	semidirect
100. C₂×#2607	C₂³	semidirect
101. C₂×#2406	D₄	semidirect
102. C₂×#2404	D₄	semidirect
103. C₂×#2404	D₄	semidirect
107. C₂×#2436	D₄	semidirect
109. C₂×#2433	D₄	semidirect
113. C₂×#2615	D₄	semidirect
114. C₂×#2615	D₄	semidirect
118. C₂×#2280	D₄	semidirect
122. #18192	D₄	semidirect
129. #18133	D₄	semidirect
130. #18132	D₄	semidirect
135. #17198	C₂³	semidirect
136. #17105	C₂³	semidirect
137. #17105	C₂³	semidirect
138. #17102	C₂³	semidirect
143. #15930	C₂³	semidirect
144. #15673	D₄	semidirect
145. #15673	D₄	semidirect
148. #15561	C₂³	semidirect
149. #15467	C₂³	semidirect
150. #15310	D₄	semidirect
151. #15310	D₄	semidirect
154. #15267	C₂³	semidirect
159. #14651	C₂³	semidirect
160. #14567	C₂³	semidirect
161. #14537	C₂³	semidirect
163. #14335	D₄	semidirect
164. #14232	C₂³	semidirect
165. #13870	D₄	semidirect
169. #11808	C₂³	semidirect
170. #11808	C₂³	semidirect
171. #11808	C₂³	semidirect
172. #11796	C₂³	semidirect
173. #11796	C₂³	semidirect
174. #11796	C₂³	semidirect
175. #11500	C₂³	semidirect
176. #11499	C₂³	semidirect
185. #7324	C₂³	semidirect
186. #7324	C₂³	semidirect
187. #7213	C₂³	semidirect
188. #7213	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72262602	2
#72262601	2
#72262600	2
#72262599	2
#72262597	2
#72262595	2
#72262560	2
#72262506	2
#72262458	2
#72238496	2
#72237362	2
#72235808	2
#72235800	2
#72235794	2
#72235768	2
#72235727	2
#72235723	2
#72235690	2
#72234732	2