Subgroups — #72262785

Order 2048.

At least 9141 conjugacy classes of subgroups; only the 666 normal subgroups are shown.

The subgroup lattice has 440 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262784	C₂	1	2	yes	maximal, complemented
2	#72262783	C₂	1	1	yes	maximal, characteristic, complemented
3	#72262782	C₂	1	2	yes	maximal, complemented
4	#72262780	C₂	1	2	yes	maximal, complemented
5	#72262779	C₂	1	2	yes	maximal, complemented
6	#72262777	C₂	1	2	yes	maximal, complemented
7	#72262776	C₂	1	2	yes	maximal, complemented
8	#72262775	C₂	1	2	yes	maximal, complemented
9	#72262774	C₂	1	2	yes	maximal, complemented
10	#72262773	C₂	1	2	yes	maximal, complemented
11	#72262592	C₂	1	1	yes	maximal, characteristic, complemented
12	#72262590	C₂	1	1	yes	maximal, characteristic, complemented
13	#72235820	C₂	1	2	yes	maximal, complemented
14	#72235800	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	#72235704	C₂	1	2	yes	maximal, complemented
19	#72235690	C₂	1	2	yes	maximal, complemented
20	C₂×#62818	C₂²	1	1	yes	characteristic
21	#6451874	C₂²	1	2	yes	—
22	#6346594	C₂²	1	2	yes	—
23	C₂×#17396	C₂²	1	1	yes	characteristic
24	#5022312	C₂²	1	1	yes	characteristic, complemented
25	#4976042	C₂²	1	1	yes	characteristic, complemented
26	#4893961	C₂²	1	1	yes	characteristic, complemented
27	#4650470	C₂²	1	1	yes	characteristic, complemented
28	#4335643	C₂²	1	1	yes	characteristic, complemented
29	#3067944	C₂²	1	1	yes	characteristic, complemented
30	#2050373	C₂²	1	1	yes	characteristic, complemented
31	#2040406	C₂²	1	1	yes	characteristic, complemented
32	#1484729	C₂²	1	1	yes	characteristic, complemented
33	#654056	C₂²	1	1	yes	characteristic, complemented
34	#618316	C₂²	1	1	yes	characteristic
35	#617709	C₂²	1	1	yes	characteristic
36	#587363	C₂²	1	1	yes	characteristic, complemented
37	#576160	C₂²	1	1	yes	characteristic, complemented
38	#516385	C₂²	1	1	yes	characteristic
39	#482549	C₂²	1	2	yes	complemented
40	#480250	C₂²	1	2	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	#346449	C₂²	1	2	yes	—
48	#346449	C₂²	1	2	yes	—
49	C₂×#8549	C₂²	1	1	yes	characteristic
50	C₂×#8542	C₂²	1	1	yes	characteristic
51	#187945	C₂²	1	2	yes	—
52	#185282	C₂²	1	2	yes	—
53	#185282	C₂²	1	2	yes	—
54	#185270	C₂²	1	2	yes	—
55	#185270	C₂²	1	2	yes	—
56	#185255	C₂²	1	2	yes	—
57	#185255	C₂²	1	2	yes	—
58	#185255	C₂²	1	2	yes	—
59	#144621	C₂²	1	4	yes	complemented
60	#144617	C₂²	1	4	yes	complemented
61	#144616	C₂²	1	4	yes	complemented
62	#144616	C₂²	1	4	yes	complemented
63	#142569	C₂²	1	4	yes	complemented
64	#142568	C₂²	1	4	yes	complemented
65	#142537	C₂²	1	4	yes	complemented
66	#142536	C₂²	1	4	yes	complemented
67	#140058	C₂²	1	4	yes	complemented
68	#140051	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	#139645	C₂²	1	4	yes	complemented
77	#139624	C₂²	1	4	yes	complemented
78	#139622	C₂²	1	4	yes	complemented
79	#139472	C₂²	1	2	yes	complemented
80	#139472	C₂²	1	2	yes	complemented
81	#139434	C₂²	1	2	yes	complemented
82	#139434	C₂²	1	2	yes	complemented
83	#135485	C₂²	1	2	yes	complemented
84	#135485	C₂²	1	2	yes	complemented
85	#135479	C₂²	1	2	yes	complemented
86	#135479	C₂²	1	2	yes	complemented
87	#128157	C₂²	1	2	yes	complemented
88	#127215	C₂²	1	2	yes	complemented
89	#127215	C₂²	1	2	yes	complemented
90	#127215	C₂²	1	2	yes	complemented
91	#62818	C₂³	1	2	yes	—
92	#62818	C₂³	1	2	yes	—
93	C₂×#3490	C₂³	1	2	yes	—
94	C₂²×#535	D₄	1	1	yes	characteristic, complemented
95	C₂³×#121	C₂³	1	1	yes	characteristic
96	C₂³×#117	D₄	1	1	yes	characteristic, complemented
97	C₂×#2406	D₄	1	1	yes	characteristic, complemented
98	C₂×#2404	C₂³	1	1	yes	characteristic
99	C₂×#2403	D₄	1	1	yes	characteristic
100	C₂×#2403	D₄	1	1	yes	characteristic
101	C₂×#2308	C₂³	1	1	yes	characteristic
102	C₂×#2280	D₄	1	1	yes	characteristic, complemented
103	#23985	C₂³	1	4	yes	—
104	#23984	C₂³	1	4	yes	—
105	C₂×#1819	C₂³	1	2	yes	—
106	#18163	C₂³	1	4	yes	—
107	#18162	C₂³	1	4	yes	—
108	#17396	C₂³	1	2	yes	—
109	#17396	C₂³	1	2	yes	—
110	C₂×#1462	C₂³	1	2	yes	—
111	C₂×#1462	C₂³	1	2	yes	—
112	#16245	C₂³	1	1	yes	characteristic, complemented
113	#16208	C₂³	1	1	yes	characteristic, complemented
114	#16208	C₂³	1	1	yes	characteristic, complemented
115	#15984	D₄	1	1	yes	characteristic
116	#15984	D₄	1	1	yes	characteristic
117	#15984	C₂³	1	1	yes	characteristic
118	#15984	C₂³	1	1	yes	characteristic
119	#15930	C₂³	1	1	yes	characteristic, complemented
120	#15673	D₄	1	1	yes	characteristic, complemented
121	#15673	D₄	1	1	yes	characteristic, complemented
122	#15673	C₂³	1	1	yes	characteristic
123	#15673	C₂³	1	1	yes	characteristic
124	#15616	C₂³	1	1	yes	characteristic, complemented
125	#15561	C₂³	1	1	yes	characteristic, complemented
126	#15467	C₂³	1	1	yes	characteristic, complemented
127	#15310	D₄	1	1	yes	characteristic, complemented
128	#15310	D₄	1	1	yes	characteristic, complemented
129	#15310	C₂³	1	1	yes	characteristic
130	#15310	C₂³	1	1	yes	characteristic
131	#15267	C₂³	1	1	yes	characteristic, complemented
132	#15257	D₄	1	1	yes	characteristic
133	#15257	D₄	1	1	yes	characteristic
134	#15257	C₂³	1	1	yes	characteristic
135	#15257	C₂³	1	1	yes	characteristic
136	#14698	D₄	1	1	yes	characteristic, complemented
137	#14698	D₄	1	1	yes	characteristic, complemented
138	#14698	C₂³	1	1	yes	characteristic
139	#14698	C₂³	1	1	yes	characteristic
140	#14649	C₂³	1	1	yes	characteristic, complemented
141	#14609	C₂³	1	1	yes	characteristic, complemented
142	#14533	C₂³	1	1	yes	characteristic, complemented
143	#14507	C₂³	1	1	yes	characteristic, complemented
144	#14507	C₂³	1	1	yes	characteristic, complemented
145	#14341	C₂³	1	1	yes	characteristic
146	#14335	D₄	1	1	yes	characteristic, complemented
147	#14207	C₂³	1	1	yes	characteristic, complemented
148	#14136	D₄	1	1	yes	characteristic, complemented
149	#14136	D₄	1	1	yes	characteristic, complemented
150	#14136	C₂³	1	1	yes	characteristic
151	#14136	C₂³	1	1	yes	characteristic
152	#13870	D₄	1	1	yes	characteristic, complemented
153	#13868	D₄	1	1	yes	characteristic, complemented
154	#13868	D₄	1	1	yes	characteristic, complemented
155	#13868	C₂³	1	1	yes	characteristic
156	#13868	C₂³	1	1	yes	characteristic
157	#13868	C₂³	1	1	yes	characteristic
158	#13867	D₄	1	1	yes	characteristic
159	#13867	D₄	1	1	yes	characteristic
160	#13827	C₂³	1	1	yes	characteristic, complemented
161	C₂²⋊C₄²	C₂³	1	1	yes	characteristic, complemented
162	#11808	C₂³	1	4	yes	complemented
163	#11796	C₂³	1	4	yes	complemented
164	#11500	C₂³	1	4	yes	complemented
165	#11499	C₂³	1	4	yes	complemented
166	#8549	C₂³	1	2	yes	—
167	#8549	C₂³	1	2	yes	—
168	#8542	C₂³	1	2	yes	—
169	#8542	C₂³	1	2	yes	—
170	#8535	C₂³	1	4	yes	—
171	#8535	C₂³	1	4	yes	—
172	#8346	C₂³	1	4	yes	—
173	#8346	C₂³	1	4	yes	—
174	#8346	C₂³	1	4	yes	—
175	#8346	C₂³	1	4	yes	—
176	#8346	C₂³	1	4	yes	—
177	#8346	C₂³	1	4	yes	—
178	#7324	C₂³	1	4	yes	complemented
179	#7324	C₂³	1	4	yes	complemented
180	#7213	C₂³	1	4	yes	complemented
181	#7213	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	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
192	#3490	#41	1	4	yes	—
193	#3490	C₂⁴	1	4	yes	—
194	C₂×#543	#41	1	2	yes	—
195	C₂×#534	#41	1	2	yes	—
196	C₂²×#127	C₂×D₄	1	1	yes	characteristic
197	C₂²×#127	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×#121	C₂×D₄	1	1	yes	characteristic
201	C₂²×#121	C₂×D₄	1	1	yes	characteristic
202	C₂²×#121	C₂×D₄	1	1	yes	characteristic
203	C₂²×#121	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×#117	C₂×D₄	1	1	yes	characteristic
213	C₂²×#117	C₂×D₄	1	1	yes	characteristic
214	C₂²×#117	C₂×D₄	1	1	yes	characteristic
215	C₂²×#117	C₂×D₄	1	1	yes	characteristic
216	C₂²×#117	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
221	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
222	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
223	C₂×#395	C₂×D₄	1	1	yes	characteristic
224	C₂×#395	C₂×D₄	1	1	yes	characteristic
225	C₂×#394	C₂×D₄	1	1	yes	characteristic
226	C₂×#394	C₂×D₄	1	1	yes	characteristic
227	C₂×#393	C₂×D₄	1	1	yes	characteristic
228	C₂×#393	C₂⁴	1	1	yes	characteristic
229	C₂×#392	C₂×D₄	1	1	yes	characteristic
230	C₂×#392	C₂⁴	1	1	yes	characteristic
231	C₂×#386	C₂×D₄	1	1	yes	characteristic
232	C₂×#386	C₂×D₄	1	1	yes	characteristic
233	C₂×#386	C₂×D₄	1	1	yes	characteristic
234	C₂×#386	C₂×D₄	1	1	yes	characteristic
235	C₂×#381	C₂×D₄	1	1	yes	characteristic
236	C₂×#381	C₂×D₄	1	1	yes	characteristic
237	C₂×#381	C₂×D₄	1	1	yes	characteristic
238	C₂×#381	C₂×D₄	1	1	yes	characteristic
239	C₂×#381	C₂×D₄	1	1	yes	characteristic
240	C₂×#381	C₂⁴	1	1	yes	characteristic
241	C₂×#380	C₂×D₄	1	1	yes	characteristic
242	C₂×#380	C₂×D₄	1	1	yes	characteristic
243	C₂×#379	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	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
248	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
249	#1819	C₂⁴	1	4	yes	—
250	#1462	C₂⁴	1	4	yes	—
251	#1462	C₂⁴	1	4	yes	—
252	#1440	C₂×D₄	1	1	yes	characteristic
253	#1440	C₂×D₄	1	1	yes	characteristic
254	#1440	C₂⁴	1	1	yes	characteristic
255	#1440	C₂⁴	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	#1437	C₂×D₄	1	1	yes	characteristic
269	#1437	C₂×D₄	1	1	yes	characteristic
270	#1437	C₂×D₄	1	1	yes	characteristic
271	#1437	C₂×D₄	1	1	yes	characteristic
272	#1437	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	C₂×D₄	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	#1437	C₂⁴	1	1	yes	characteristic
286	#1437	C₂⁴	1	1	yes	characteristic
287	#1437	C₂⁴	1	1	yes	characteristic
288	#1436	C₂×D₄	1	1	yes	characteristic
289	#1436	C₂×D₄	1	1	yes	characteristic
290	#1436	C₂×D₄	1	1	yes	characteristic
291	#1436	C₂×D₄	1	1	yes	characteristic
292	C₂⁶	#120	1	1	yes	characteristic
293	C₂⁶	#120	1	1	yes	characteristic
294	C₂⁶	C₂²×D₄	1	1	yes	characteristic
295	C₂⁶	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	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	C₂⁴×C₄	#120	1	1	yes	characteristic
311	C₂⁴×C₄	#120	1	1	yes	characteristic
312	C₂⁴×C₄	#120	1	1	yes	characteristic
313	C₂⁴×C₄	#120	1	1	yes	characteristic
314	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
315	C₂⁴×C₄	C₂²×D₄	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	C₂×#41	1	4	yes	—
320	#534	C₂×#41	1	4	yes	—
321	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
324	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
325	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	#120	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	C₂²×D₄	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂²×C₂²⋊C₄	C₂×#41	1	2	yes	—
339	C₂²×C₂²⋊C₄	C₂×#41	1	2	yes	—
340	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
341	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
342	C₂²×C₂²⋊C₄	C₂⁵	1	1	yes	characteristic
343	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
344	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
345	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
346	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
347	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
348	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
349	C₂×#95	C₂²×D₄	1	1	yes	characteristic
350	C₂×#95	C₂²×D₄	1	1	yes	characteristic
351	C₂×#95	C₂²×D₄	1	1	yes	characteristic
352	C₂×#95	C₂²×D₄	1	1	yes	characteristic
353	C₂×#95	C₂²×D₄	1	1	yes	characteristic
354	C₂×#95	C₂²×D₄	1	1	yes	characteristic
355	C₂×#95	C₂²×D₄	1	1	yes	characteristic
356	C₂×#95	C₂²×D₄	1	1	yes	characteristic
357	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
358	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
359	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
360	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
361	C₂⁵	C₂×#120	1	1	yes	characteristic
362	C₂⁵	C₂×#120	1	1	yes	characteristic
363	C₂⁵	C₂×#120	1	1	yes	characteristic
364	C₂⁵	C₂×#120	1	1	yes	characteristic
365	C₂⁵	C₂×#120	1	1	yes	characteristic
366	C₂⁵	C₂×#120	1	1	yes	characteristic
367	C₂⁵	#546	1	2	yes	—
368	C₂⁵	#546	1	2	yes	—
369	C₂⁵	C₂³×D₄	1	1	yes	characteristic
370	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
371	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
372	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
373	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
374	C₂³×C₄	C₂×#120	1	1	yes	characteristic
375	C₂³×C₄	C₂×#120	1	1	yes	characteristic
376	C₂³×C₄	C₂×#120	1	1	yes	characteristic
377	C₂³×C₄	C₂×#120	1	1	yes	characteristic
378	C₂³×C₄	C₂×#120	1	1	yes	characteristic
379	C₂³×C₄	C₂×#120	1	1	yes	characteristic
380	C₂³×C₄	#525	1	1	yes	characteristic
381	C₂³×C₄	#525	1	1	yes	characteristic
382	C₂³×C₄	#535	1	1	yes	characteristic
383	C₂³×C₄	#535	1	1	yes	characteristic
384	C₂³×C₄	#546	1	2	yes	—
385	C₂³×C₄	#546	1	2	yes	—
386	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
387	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	#525	1	2	yes	—
389	C₂×C₂²⋊C₄	#535	1	2	yes	—
390	C₂×C₂²⋊C₄	#546	1	2	yes	—
391	C₂×C₂²⋊C₄	#546	1	2	yes	—
392	C₂×C₂²⋊C₄	#546	1	2	yes	—
393	C₂×C₂²⋊C₄	#546	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂²×#41	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	2	yes	—
396	C₂⁴	#2404	1	2	yes	—
397	C₂⁴	#2404	1	1	yes	characteristic
398	C₂⁴	#2404	1	1	yes	characteristic
399	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
400	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
401	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
402	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
403	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
404	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
405	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
406	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
407	C₂⁴	C₂²×#120	1	1	yes	characteristic
408	C₂⁴	C₂×#546	1	2	yes	—
409	C₂²×C₄	#2404	1	1	yes	characteristic
410	C₂²×C₄	#2404	1	1	yes	characteristic
411	C₂²×C₄	#2404	1	2	yes	—
412	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
413	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
414	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
415	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
416	C₂²×C₄	C₂×#525	1	1	yes	characteristic
417	C₂²×C₄	C₂×#535	1	1	yes	characteristic
418	C₂²×C₄	C₂×#546	1	2	yes	—
419	C₂³	#23984	1	1	yes	characteristic
420	C₂³	#23984	1	1	yes	characteristic
421	C₂³	#23984	1	1	yes	characteristic
422	C₂³	#23984	1	1	yes	characteristic
423	C₂³	#33551	1	2	yes	—
424	C₂³	C₂×#2404	1	1	yes	characteristic
425	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
426	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
427	C₂×C₄	#33551	1	2	yes	—
428	C₂×C₄	#33552	1	2	yes	—
429	C₂²	#6451776	1	1	yes	characteristic
430	C₂²	#6451785	1	1	yes	characteristic
431	C₂²	C₂×#23984	1	1	yes	characteristic
432	C₂²	C₂×#33551	1	1	yes	characteristic
433	C₂²	C₂×#33551	1	1	yes	characteristic
434	C₂²	C₂×#33552	1	1	yes	characteristic
435	C₂²	#7622875	1	1	yes	characteristic
436	C₂	#72233180	1	1	yes	characteristic
437	C₂	#72240104	1	1	yes	characteristic
438	C₂	#72255859	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23984
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. #72262784	C₂	semidirect
2. #72262783	C₂	semidirect
3. #72262782	C₂	semidirect
4. #72262780	C₂	semidirect
5. #72262779	C₂	semidirect
6. #72262777	C₂	semidirect
7. #72262776	C₂	semidirect
8. #72262775	C₂	semidirect
9. #72262774	C₂	semidirect
10. #72262773	C₂	semidirect
11. #72262592	C₂	semidirect
12. #72262590	C₂	semidirect
13. #72235820	C₂	semidirect
14. #72235800	C₂	semidirect
15. #72235768	C₂	semidirect
16. #72235727	C₂	semidirect
17. #72235723	C₂	semidirect
18. #72235704	C₂	semidirect
19. #72235690	C₂	semidirect
24. #5022312	C₂²	semidirect
25. #4976042	C₂²	semidirect
26. #4893961	C₂²	semidirect
27. #4650470	C₂²	semidirect
28. #4335643	C₂²	semidirect
29. #3067944	C₂²	semidirect
30. #2050373	C₂²	semidirect
31. #2040406	C₂²	semidirect
32. #1484729	C₂²	semidirect
33. #654056	C₂²	semidirect
36. #587363	C₂²	semidirect
37. #576160	C₂²	semidirect
39. #482549	C₂²	semidirect
40. #480250	C₂²	semidirect
59. #144621	C₂²	semidirect
60. #144617	C₂²	semidirect
61. #144616	C₂²	semidirect
62. #144616	C₂²	semidirect
63. #142569	C₂²	semidirect
64. #142568	C₂²	semidirect
65. #142537	C₂²	semidirect
66. #142536	C₂²	semidirect
67. #140058	C₂²	semidirect
68. #140051	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. #139645	C₂²	semidirect
77. #139624	C₂²	semidirect
78. #139622	C₂²	semidirect
79. #139472	C₂²	semidirect
80. #139472	C₂²	semidirect
81. #139434	C₂²	semidirect
82. #139434	C₂²	semidirect
83. #135485	C₂²	semidirect
84. #135485	C₂²	semidirect
85. #135479	C₂²	semidirect
86. #135479	C₂²	semidirect
87. #128157	C₂²	semidirect
88. #127215	C₂²	semidirect
89. #127215	C₂²	semidirect
90. #127215	C₂²	semidirect
94. C₂²×#535	D₄	semidirect
96. C₂³×#117	D₄	semidirect
97. C₂×#2406	D₄	semidirect
102. C₂×#2280	D₄	semidirect
112. #16245	C₂³	semidirect
113. #16208	C₂³	semidirect
114. #16208	C₂³	semidirect
119. #15930	C₂³	semidirect
120. #15673	D₄	semidirect
121. #15673	D₄	semidirect
124. #15616	C₂³	semidirect
125. #15561	C₂³	semidirect
126. #15467	C₂³	semidirect
127. #15310	D₄	semidirect
128. #15310	D₄	semidirect
131. #15267	C₂³	semidirect
136. #14698	D₄	semidirect
137. #14698	D₄	semidirect
140. #14649	C₂³	semidirect
141. #14609	C₂³	semidirect
142. #14533	C₂³	semidirect
143. #14507	C₂³	semidirect
144. #14507	C₂³	semidirect
146. #14335	D₄	semidirect
147. #14207	C₂³	semidirect
148. #14136	D₄	semidirect
149. #14136	D₄	semidirect
152. #13870	D₄	semidirect
153. #13868	D₄	semidirect
154. #13868	D₄	semidirect
160. #13827	C₂³	semidirect
161. C₂²⋊C₄²	C₂³	semidirect
162. #11808	C₂³	semidirect
163. #11796	C₂³	semidirect
164. #11500	C₂³	semidirect
165. #11499	C₂³	semidirect
178. #7324	C₂³	semidirect
179. #7324	C₂³	semidirect
180. #7213	C₂³	semidirect
181. #7213	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
#72262784	2
#72262783	2
#72262782	2
#72262780	2
#72262779	2
#72262777	2
#72262776	2
#72262775	2
#72262774	2
#72262773	2
#72262592	2
#72262590	2
#72235820	2
#72235800	2
#72235768	2
#72235727	2
#72235723	2
#72235704	2
#72235690	2