Subgroups — #72339572

Order 1024.

At least 8049 conjugacy classes of subgroups; only the 975 normal subgroups are shown.

The subgroup lattice has 574 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10586478	C₂	1	1	yes	maximal, characteristic, complemented
2	#6491100	C₂	1	1	yes	maximal, characteristic, complemented
3	#6437543	C₂	1	1	yes	maximal, characteristic, complemented
4	#6437541	C₂	1	1	yes	maximal, characteristic, complemented
5	#6437518	C₂	1	1	yes	maximal, characteristic, complemented
6	#6346767	C₂	1	1	yes	maximal, characteristic, complemented
7	#6346765	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#18198	C₂	1	1	yes	maximal, characteristic, complemented
9	#346552	C₂	1	4	yes	maximal, complemented
10	#346550	C₂	1	4	yes	maximal, complemented
11	#346520	C₂	1	4	yes	maximal, complemented
12	#346519	C₂	1	4	yes	maximal, complemented
13	#185679	C₂	1	1	yes	maximal, characteristic, complemented
14	#185675	C₂	1	1	yes	maximal, characteristic, complemented
15	#185623	C₂	1	1	yes	maximal, characteristic, complemented
16	#185357	C₂	1	1	yes	maximal, characteristic, complemented
17	#185355	C₂	1	1	yes	maximal, characteristic, complemented
18	#185343	C₂	1	1	yes	maximal, characteristic, complemented
19	#184923	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
21	#62984	C₂²	1	2	yes	complemented
22	#62983	C₂²	1	2	yes	complemented
23	#62893	C₂²	1	2	yes	complemented
24	#62892	C₂²	1	2	yes	complemented
25	#62819	C₂²	1	1	yes	characteristic
26	#62818	C₂²	1	1	yes	characteristic
27	C₂×#3489	C₂²	1	1	yes	characteristic
28	C₂×#3488	C₂²	1	1	yes	characteristic
29	#62773	C₂²	1	1	yes	characteristic
30	C₂×#3505	C₂²	1	1	yes	characteristic
31	C₂×D₄×#41	C₂²	1	1	yes	characteristic
32	C₂×#3003	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#450	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#447	C₂²	1	1	yes	characteristic, complemented
35	#35222	C₂²	1	1	yes	characteristic, complemented
36	#35222	C₂²	1	1	yes	characteristic, complemented
37	C₂×#2408	C₂²	1	1	yes	characteristic, complemented
38	#32926	C₂²	1	4	yes	complemented
39	#29684	C₂²	1	4	yes	complemented
40	#23858	C₂²	1	2	yes	complemented
41	#23858	C₂²	1	4	yes	complemented
42	#23855	C₂²	1	2	yes	complemented
43	#23855	C₂²	1	4	yes	complemented
44	#23851	C₂²	1	2	yes	complemented
45	#23851	C₂²	1	4	yes	complemented
46	#23848	C₂²	1	2	yes	complemented
47	#23848	C₂²	1	4	yes	complemented
48	#21874	C₂²	1	1	yes	characteristic, complemented
49	#21874	C₂²	1	1	yes	characteristic, complemented
50	#20973	C₂²	1	1	yes	characteristic, complemented
51	#20972	C₂²	1	1	yes	characteristic, complemented
52	#20971	C₂²	1	1	yes	characteristic, complemented
53	#20898	C₂²	1	1	yes	characteristic, complemented
54	#20897	C₂²	1	1	yes	characteristic, complemented
55	#20897	C₂²	1	1	yes	characteristic, complemented
56	#20722	C₂²	1	1	yes	characteristic, complemented
57	#20601	C₂²	1	1	yes	characteristic, complemented
58	#20597	C₂²	1	1	yes	characteristic, complemented
59	#20597	C₂²	1	1	yes	characteristic, complemented
60	#18198	C₂²	1	4	yes	complemented
61	#18198	C₂²	1	4	yes	complemented
62	#18198	C₂²	1	4	yes	complemented
63	#18198	C₂²	1	4	yes	complemented
64	#18196	C₂²	1	4	yes	complemented
65	#18194	C₂²	1	4	yes	complemented
66	#17578	C₂²	1	1	yes	characteristic, complemented
67	#17577	C₂²	1	1	yes	characteristic, complemented
68	#17572	C₂²	1	1	yes	characteristic, complemented
69	#17572	C₂²	1	1	yes	characteristic, complemented
70	C₂×#1520	C₂²	1	1	yes	characteristic, complemented
71	C₂×#1519	C₂²	1	1	yes	characteristic, complemented
72	#17381	C₂²	1	1	yes	characteristic, complemented
73	#17381	C₂²	1	1	yes	characteristic, complemented
74	C₂×#1459	C₂²	1	1	yes	characteristic, complemented
75	#8381	C₂²	1	2	yes	complemented
76	#8381	C₂²	1	4	yes	complemented
77	#8379	C₂²	1	2	yes	complemented
78	#8379	C₂²	1	4	yes	complemented
79	#8377	C₂²	1	2	yes	complemented
80	#8377	C₂²	1	4	yes	complemented
81	#8375	C₂²	1	2	yes	complemented
82	#8375	C₂²	1	4	yes	complemented
83	#8352	C₂²	1	4	yes	complemented
84	#8352	C₂²	1	4	yes	complemented
85	#8352	C₂²	1	4	yes	complemented
86	#8352	C₂²	1	4	yes	complemented
87	#8351	C₂²	1	4	yes	complemented
88	#8350	C₂²	1	4	yes	complemented
89	#8317	C₂²	1	4	yes	complemented
90	#8316	C₂²	1	4	yes	complemented
91	C₂²×2₋¹⁺⁴	D₄	1	1	yes	characteristic, complemented
92	C₂²×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
93	C₂³×#41	D₄	1	1	yes	characteristic, complemented
94	C₂³×#41	C₂³	1	1	yes	characteristic
95	C₂⁴×D₄	C₂³	1	1	yes	characteristic
96	C₂³×SD₁₆	C₂³	1	2	yes	—
97	C₂³×D₈	C₂³	1	2	yes	—
98	C₂³×M₁₆	C₂³	1	1	yes	characteristic
99	#3538	D₄	1	2	yes	complemented
100	#3537	D₄	1	2	yes	complemented
101	#3536	D₄	1	2	yes	complemented
102	#3536	D₄	1	2	yes	complemented
103	#3535	D₄	1	4	yes	complemented
104	#3534	D₄	1	4	yes	complemented
105	#3505	D₄	1	1	yes	characteristic
106	#3505	D₄	1	1	yes	characteristic
107	#3505	D₄	1	2	yes	complemented
108	#3505	D₄	1	2	yes	complemented
109	#3505	C₂³	1	2	yes	—
110	#3505	C₂³	1	2	yes	—
111	#3505	C₂³	1	2	yes	—
112	#3505	C₂³	1	2	yes	—
113	#3501	D₄	1	1	yes	characteristic
114	#3501	C₂³	1	2	yes	—
115	#3496	D₄	1	1	yes	characteristic
116	#3496	C₂³	1	2	yes	—
117	#3490	D₄	1	2	yes	—
118	#3484	D₄	1	2	yes	—
119	C₂×#550	D₄	1	1	yes	characteristic, complemented
120	C₂×#550	D₄	1	2	yes	complemented
121	C₂×D₄×Q₈	C₂³	1	1	yes	characteristic
122	C₂×D₄×Q₈	C₂³	1	2	yes	—
123	C₂×#548	D₄	1	1	yes	characteristic, complemented
124	C₂×#548	D₄	1	2	yes	complemented
125	C₂×#548	C₂³	1	1	yes	characteristic
126	C₂×#548	C₂³	1	2	yes	—
127	C₂×#547	D₄	1	1	yes	characteristic, complemented
128	C₂×#547	D₄	1	2	yes	complemented
129	C₂×#546	D₄	1	1	yes	characteristic, complemented
130	C₂×#546	D₄	1	2	yes	complemented
131	C₂×#546	C₂³	1	1	yes	characteristic
132	C₂×#546	C₂³	1	2	yes	—
133	C₂×D₄²	C₂³	1	1	yes	characteristic
134	C₂×D₄²	C₂³	1	2	yes	—
135	#3459	C₂³	1	2	yes	—
136	C₂×#539	D₄	1	2	yes	complemented
137	C₂×#538	D₄	1	2	yes	complemented
138	C₂×#537	D₄	1	1	yes	characteristic, complemented
139	C₂×#537	D₄	1	1	yes	characteristic, complemented
140	C₂×#536	D₄	1	1	yes	characteristic, complemented
141	C₂×#535	D₄	1	1	yes	characteristic, complemented
142	C₂×#532	D₄	1	1	yes	characteristic, complemented
143	C₂×#525	D₄	1	1	yes	characteristic, complemented
144	C₂×#525	C₂³	1	1	yes	characteristic
145	C₂×#525	C₂³	1	1	yes	characteristic
146	C₂×#525	C₂³	1	1	yes	characteristic
147	C₂²×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
148	C₂²×#121	C₂³	1	1	yes	characteristic
149	C₄×H(5,𝔽₂)	C₂³	1	2	yes	—
150	C₂×#520	D₄	1	1	yes	characteristic, complemented
151	C₂×#520	D₄	1	1	yes	characteristic, complemented
152	C₂×C₄×#41	D₄	1	1	yes	characteristic, complemented
153	C₂²×C₄×D₄	C₂³	1	1	yes	characteristic
154	C₂×#450	C₂³	1	2	yes	—
155	C₂×#450	C₂³	1	4	yes	—
156	C₂×#447	C₂³	1	2	yes	—
157	C₂×#447	C₂³	1	4	yes	—
158	C₂×#407	C₂³	1	1	yes	characteristic
159	C₂²×C₂²⋊C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₂²⋊C₈	C₂³	1	1	yes	characteristic
161	#2408	C₂³	1	4	yes	—
162	#2408	C₂³	1	4	yes	—
163	#2408	C₂³	1	2	yes	—
164	#2408	C₂³	1	2	yes	—
165	#2280	C₂³	1	1	yes	characteristic
166	#2280	C₂³	1	1	yes	characteristic
167	C₂×#380	C₂³	1	1	yes	characteristic
168	#1893	C₂³	1	2	yes	—
169	#1893	C₂³	1	4	yes	—
170	#1892	C₂³	1	2	yes	—
171	#1892	C₂³	1	4	yes	—
172	#1869	C₂³	1	2	yes	—
173	#1869	C₂³	1	4	yes	—
174	#1869	C₂³	1	4	yes	—
175	#1869	C₂³	1	2	yes	—
176	#1799	C₂³	1	4	yes	—
177	#1799	C₂³	1	4	yes	—
178	#1799	C₂³	1	2	yes	—
179	#1799	C₂³	1	2	yes	—
180	#1787	C₂³	1	2	yes	—
181	#1787	C₂³	1	2	yes	—
182	#1787	C₂³	1	2	yes	—
183	#1786	C₂³	1	2	yes	—
184	#1786	C₂³	1	2	yes	—
185	#1786	C₂³	1	2	yes	—
186	#1520	C₂³	1	2	yes	—
187	#1520	C₂³	1	4	yes	—
188	#1520	C₂³	1	4	yes	—
189	#1520	C₂³	1	2	yes	—
190	#1519	C₂³	1	2	yes	—
191	#1519	C₂³	1	4	yes	—
192	#1519	C₂³	1	4	yes	—
193	#1519	C₂³	1	2	yes	—
194	#1459	C₂³	1	4	yes	—
195	#1459	C₂³	1	4	yes	—
196	#1459	C₂³	1	2	yes	—
197	#1459	C₂³	1	2	yes	—
198	C₂×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
199	C₂²×#41	C₂×D₄	1	1	yes	characteristic
200	C₂²×#41	C₂×D₄	1	1	yes	characteristic
201	C₂²×#41	C₂×D₄	1	1	yes	characteristic
202	C₂²×#41	C₂×D₄	1	1	yes	characteristic
203	C₂²×#41	C₂×D₄	1	1	yes	characteristic
204	C₂²×#41	C₂×D₄	1	1	yes	characteristic
205	C₂²×#41	C₂×D₄	1	1	yes	characteristic
206	C₂²×#41	C₂×D₄	1	1	yes	characteristic
207	C₂²×#41	C₂×D₄	1	1	yes	characteristic
208	C₂²×#41	C₂×D₄	1	1	yes	characteristic
209	C₂²×#41	C₂×D₄	1	1	yes	characteristic
210	C₂²×#41	C₂×D₄	1	1	yes	characteristic
211	C₂²×#41	C₂×D₄	1	1	yes	characteristic
212	C₂²×#41	C₂×D₄	1	1	yes	characteristic
213	C₂²×#41	C₂×D₄	1	1	yes	characteristic
214	C₂²×#41	C₂×D₄	1	1	yes	characteristic
215	C₂²×#41	C₂×D₄	1	1	yes	characteristic
216	C₂²×#41	C₂×D₄	1	2	yes	complemented
217	C₂²×#41	C₂×D₄	1	2	yes	complemented
218	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic
219	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic
220	C₂³×Q₈	C₂×D₄	1	2	yes	complemented
221	C₂³×Q₈	C₂⁴	1	1	yes	characteristic
222	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
223	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
224	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
225	C₂³×D₄	C₂×D₄	1	2	yes	complemented
226	C₂³×D₄	C₂⁴	1	2	yes	—
227	C₂³×D₄	C₂⁴	1	1	yes	characteristic
228	C₂⁴×C₄	C₂×D₄	1	1	yes	characteristic
229	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
230	C₂³×C₈	C₂⁴	1	2	yes	—
231	#544	C₂×D₄	1	4	yes	complemented
232	#543	C₂×D₄	1	2	yes	—
233	#543	C₂×D₄	1	4	yes	complemented
234	#539	C₂×D₄	1	4	yes	—
235	#539	C₂×D₄	1	4	yes	—
236	#539	C₂×D₄	1	4	yes	complemented
237	#539	C₂×D₄	1	4	yes	complemented
238	#538	C₂×D₄	1	4	yes	—
239	#538	C₂×D₄	1	4	yes	—
240	#538	C₂×D₄	1	4	yes	complemented
241	#538	C₂×D₄	1	4	yes	complemented
242	#537	C₂×D₄	1	4	yes	complemented
243	#534	C₂×D₄	1	2	yes	—
244	#534	C₂×D₄	1	2	yes	—
245	#534	C₂×D₄	1	2	yes	—
246	#534	C₂×D₄	1	4	yes	complemented
247	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
248	C₂×C₄⋊Q₈	C₂×D₄	1	2	yes	complemented
249	C₂×#127	C₂×D₄	1	1	yes	characteristic
250	C₂×#127	C₂×D₄	1	2	yes	complemented
251	C₂×#124	C₂×D₄	1	1	yes	characteristic
252	C₂×#124	C₂×D₄	1	1	yes	characteristic
253	C₂×#124	C₂×D₄	1	2	yes	complemented
254	C₂×#124	C₂×D₄	1	2	yes	complemented
255	#525	C₂×D₄	1	2	yes	—
256	#525	C₂×D₄	1	2	yes	—
257	#525	C₂×D₄	1	2	yes	—
258	#525	C₂×D₄	1	2	yes	—
259	C₂×#123	C₂×D₄	1	2	yes	—
260	C₂×#123	C₂×D₄	1	2	yes	—
261	C₂×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
262	C₂×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
263	C₂×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
264	C₂×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
265	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
266	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
267	C₂×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
268	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
269	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
270	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
271	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
272	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
273	C₂×C₂²⋊Q₈	C₂×D₄	1	2	yes	complemented
274	C₂×C₂²⋊Q₈	C₂×D₄	1	2	yes	complemented
275	C₂×C₂²⋊Q₈	C₂⁴	1	2	yes	—
276	C₂×C₂²⋊Q₈	C₂⁴	1	1	yes	characteristic
277	C₂×#121	C₂×D₄	1	2	yes	—
278	C₂×#121	C₂×D₄	1	2	yes	—
279	C₂×#121	C₂×D₄	1	2	yes	—
280	C₂×#121	C₂×D₄	1	2	yes	—
281	C₂×#121	C₂×D₄	1	1	yes	characteristic
282	C₂×#121	C₂×D₄	1	1	yes	characteristic
283	C₂×#121	C₂×D₄	1	2	yes	—
284	C₂×#121	C₂×D₄	1	1	yes	characteristic
285	C₂×#121	C₂×D₄	1	1	yes	characteristic
286	C₂×#121	C₂×D₄	1	1	yes	characteristic
287	C₂×#121	C₂×D₄	1	1	yes	characteristic
288	C₂×#121	C₂×D₄	1	1	yes	characteristic
289	C₂×#121	C₂×D₄	1	2	yes	complemented
290	C₂×#121	C₂×D₄	1	2	yes	complemented
291	C₂×#121	C₂⁴	1	2	yes	—
292	C₂×#121	C₂⁴	1	1	yes	characteristic
293	C₂×#120	C₂×D₄	1	2	yes	—
294	C₂×#120	C₂×D₄	1	2	yes	—
295	#518	C₂×D₄	1	2	yes	—
296	#518	C₂×D₄	1	2	yes	—
297	#518	C₂×D₄	1	2	yes	—
298	C₂×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
300	C₂×C₄×Q₈	C₂×D₄	1	2	yes	complemented
301	C₂×C₄×Q₈	C₂×D₄	1	2	yes	complemented
302	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
304	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
307	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
310	C₂×C₄×D₄	C₂×D₄	1	2	yes	—
311	C₂×C₄×D₄	C₂×D₄	1	2	yes	—
312	C₂×C₄×D₄	C₂×D₄	1	2	yes	complemented
313	C₂×C₄×D₄	C₂×D₄	1	2	yes	complemented
314	C₂×C₄×D₄	C₂⁴	1	1	yes	characteristic
315	C₂×C₄×D₄	C₂⁴	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂⁴	1	2	yes	—
317	C₂×C₄×D₄	C₂⁴	1	2	yes	—
318	C₂×#117	C₂×D₄	1	1	yes	characteristic
319	C₂×#117	C₂×D₄	1	1	yes	characteristic
320	C₂×#117	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄²	C₂×D₄	1	1	yes	characteristic
327	C₂×C₂²⋊C₈	C₂⁴	1	2	yes	—
328	C₂×C₂²⋊C₈	C₂⁴	1	2	yes	—
329	C₂×C₂²⋊C₈	C₂⁴	1	2	yes	—
330	#380	C₂⁴	1	2	yes	—
331	#380	C₂⁴	1	2	yes	—
332	#380	C₂⁴	1	2	yes	—
333	C₂⁵	#120	1	1	yes	characteristic
334	C₂⁵	C₂²×D₄	1	1	yes	characteristic
335	C₂×#41	#120	1	1	yes	characteristic
336	C₂×#41	#120	1	1	yes	characteristic
337	C₂×#41	#120	1	1	yes	characteristic
338	C₂×#41	#120	1	1	yes	characteristic
339	C₂×#41	#120	1	1	yes	characteristic
340	C₂×#41	#120	1	1	yes	characteristic
341	C₂×#41	#120	1	1	yes	characteristic
342	C₂×#41	#120	1	1	yes	characteristic
343	C₂×#41	#120	1	1	yes	characteristic
344	C₂×#41	#120	1	1	yes	characteristic
345	C₂×#41	#120	1	1	yes	characteristic
346	C₂×#41	#120	1	1	yes	characteristic
347	C₂×#41	#120	1	2	yes	—
348	C₂×#41	#120	1	2	yes	—
349	C₂×#41	#120	1	1	yes	characteristic
350	C₂×#41	#120	1	1	yes	characteristic
351	C₂×#41	#120	1	1	yes	characteristic
352	C₂×#41	#120	1	1	yes	characteristic
353	C₂²×Q₈	#120	1	2	yes	—
354	C₂²×Q₈	#120	1	2	yes	—
355	C₂²×Q₈	#120	1	1	yes	characteristic
356	C₂²×Q₈	#120	1	1	yes	characteristic
357	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
358	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
359	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
360	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
361	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
362	C₂²×Q₈	C₂²×D₄	1	2	yes	—
363	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
364	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
365	C₂²×D₄	#120	1	1	yes	characteristic
366	C₂²×D₄	#120	1	1	yes	characteristic
367	C₂²×D₄	#120	1	2	yes	—
368	C₂²×D₄	#120	1	2	yes	—
369	C₂²×D₄	#120	1	1	yes	characteristic
370	C₂²×D₄	#120	1	1	yes	characteristic
371	C₂²×D₄	#120	1	2	yes	—
372	C₂²×D₄	#120	1	2	yes	—
373	C₂²×D₄	#120	1	2	yes	—
374	C₂²×D₄	#120	1	2	yes	—
375	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
376	C₂²×D₄	C₂²×D₄	1	2	yes	—
377	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
378	C₂²×D₄	C₂²×D₄	1	2	yes	—
379	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
380	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
381	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
382	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
383	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
384	C₂²×D₄	C₂²×D₄	1	2	yes	—
385	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
386	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
387	C₂³×C₄	#120	1	1	yes	characteristic
388	C₂³×C₄	#120	1	1	yes	characteristic
389	C₂³×C₄	#120	1	1	yes	characteristic
390	C₂³×C₄	#120	1	1	yes	characteristic
391	C₂³×C₄	#120	1	1	yes	characteristic
392	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
393	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
394	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
395	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
396	C₂³×C₄	C₂²×D₄	1	2	yes	—
397	C₂³×C₄	C₂²×D₄	1	2	yes	—
398	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
399	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
400	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
401	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
402	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
403	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
404	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
405	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
406	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
407	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
408	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
409	C₂³×C₄	C₂⁵	1	1	yes	characteristic
410	C₂²⋊Q₈	#120	1	4	yes	—
411	C₂²⋊Q₈	#120	1	4	yes	—
412	C₂²⋊Q₈	#120	1	2	yes	—
413	C₂²⋊Q₈	#120	1	2	yes	—
414	C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
415	C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
416	C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
417	C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
418	#121	#120	1	4	yes	—
419	#121	#120	1	4	yes	—
420	#121	#120	1	2	yes	—
421	#121	#120	1	2	yes	—
422	#121	C₂²×D₄	1	4	yes	—
423	#121	C₂²×D₄	1	4	yes	—
424	#121	C₂²×D₄	1	2	yes	—
425	#121	C₂²×D₄	1	2	yes	—
426	#117	#120	1	2	yes	—
427	#117	#120	1	2	yes	—
428	C₂×C₄⋊C₄	#120	1	1	yes	characteristic
429	C₂×C₄⋊C₄	#120	1	1	yes	characteristic
430	C₂×C₄⋊C₄	#120	1	1	yes	characteristic
431	C₂×C₄⋊C₄	#120	1	2	yes	—
432	C₂×C₄⋊C₄	#120	1	1	yes	characteristic
433	C₂×C₄⋊C₄	#120	1	1	yes	characteristic
434	C₂×C₄⋊C₄	#120	1	1	yes	characteristic
435	C₂×C₄⋊C₄	#120	1	2	yes	—
436	C₂×C₄⋊C₄	#120	1	2	yes	—
437	C₂×C₄⋊C₄	#120	1	2	yes	—
438	C₂×C₄⋊C₄	#120	1	2	yes	—
439	C₂×C₄⋊C₄	#120	1	2	yes	—
440	C₂×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂²×D₄	1	2	yes	—
443	C₂×C₄⋊C₄	C₂²×D₄	1	2	yes	—
444	C₂×C₄⋊C₄	C₂²×D₄	1	2	yes	—
445	C₂×C₄⋊C₄	C₂²×D₄	1	2	yes	—
446	C₂×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	#120	1	2	yes	—
450	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	#120	1	2	yes	—
454	C₂×C₂²⋊C₄	#120	1	2	yes	—
455	C₂×C₂²⋊C₄	#120	1	2	yes	—
456	C₂×C₂²⋊C₄	#120	1	2	yes	—
457	C₂×C₂²⋊C₄	#120	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
466	C₂×C₄²	#120	1	1	yes	characteristic
467	C₂×C₄²	#120	1	1	yes	characteristic
468	C₂×C₄²	C₂²×D₄	1	2	yes	—
469	C₂×C₄²	C₂²×D₄	1	2	yes	—
470	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
472	C₂⁴	C₂×#120	1	1	yes	characteristic
473	C₂⁴	C₂×#120	1	1	yes	characteristic
474	C₂⁴	C₂×#120	1	1	yes	characteristic
475	C₂⁴	C₂×#120	1	2	yes	—
476	C₂⁴	C₂×#120	1	1	yes	characteristic
477	C₂⁴	C₂×#120	1	2	yes	—
478	C₂⁴	C₂×#120	1	1	yes	characteristic
479	C₂⁴	C₂×#120	1	1	yes	characteristic
480	C₂⁴	C₂×#120	1	1	yes	characteristic
481	C₂⁴	C₂×#120	1	1	yes	characteristic
482	C₂⁴	C₂³×D₄	1	1	yes	characteristic
483	#41	B(4,𝔽₂)	1	4	yes	complemented
484	C₂×Q₈	C₂×#120	1	1	yes	characteristic
485	C₂×Q₈	C₂×#120	1	1	yes	characteristic
486	C₂×Q₈	C₂×#120	1	1	yes	characteristic
487	C₂×Q₈	C₂×#120	1	1	yes	characteristic
488	C₂×Q₈	C₂×#120	1	4	yes	—
489	C₂×Q₈	C₂×#120	1	2	yes	—
490	C₂×D₄	C₂×#120	1	1	yes	characteristic
491	C₂×D₄	C₂×#120	1	1	yes	characteristic
492	C₂×D₄	C₂×#120	1	1	yes	characteristic
493	C₂×D₄	C₂×#120	1	1	yes	characteristic
494	C₂×D₄	C₂×#120	1	2	yes	—
495	C₂×D₄	C₂×#120	1	4	yes	—
496	C₂²×C₄	C₂×#120	1	1	yes	characteristic
497	C₂²×C₄	C₂×#120	1	2	yes	—
498	C₂²×C₄	C₂×#120	1	1	yes	characteristic
499	C₂²×C₄	C₂×#120	1	2	yes	—
500	C₂²×C₄	C₂×#120	1	1	yes	characteristic
501	C₂²×C₄	C₂×#120	1	1	yes	characteristic
502	C₂²×C₄	C₂×#120	1	1	yes	characteristic
503	C₂²×C₄	C₂×#120	1	1	yes	characteristic
504	C₂²×C₄	C₂×#120	1	1	yes	characteristic
505	C₂²×C₄	C₂×#120	1	1	yes	characteristic
506	C₂²×C₄	C₂×#120	1	1	yes	characteristic
507	C₂²×C₄	C₂×#120	1	1	yes	characteristic
508	C₂²×C₄	C₂×#120	1	1	yes	characteristic
509	C₂²×C₄	C₂×#120	1	1	yes	characteristic
510	C₂²×C₄	C₂×#120	1	1	yes	characteristic
511	C₂²×C₄	C₂×#120	1	1	yes	characteristic
512	C₂²×C₄	C₂×#120	1	1	yes	characteristic
513	C₂²×C₄	C₂×#120	1	2	yes	—
514	C₂²×C₄	C₂×#120	1	1	yes	characteristic
515	C₂²×C₄	C₂×#120	1	2	yes	—
516	C₂²×C₄	C₂×#120	1	1	yes	characteristic
517	C₂²×C₄	C₂×#120	1	2	yes	—
518	C₂²×C₄	C₂×#120	1	1	yes	characteristic
519	C₂²×C₄	C₂×#120	1	2	yes	—
520	C₂²×C₄	C₂×#120	1	1	yes	characteristic
521	C₂²×C₄	C₂×#120	1	1	yes	characteristic
522	C₂²×C₄	C₂×#120	1	1	yes	characteristic
523	C₂²×C₄	C₂×#120	1	1	yes	characteristic
524	C₂²×C₄	C₂×#120	1	1	yes	characteristic
525	C₂²×C₄	C₂×#120	1	1	yes	characteristic
526	C₂²×C₄	C₂×#120	1	1	yes	characteristic
527	C₂²×C₄	C₂×#120	1	1	yes	characteristic
528	C₂²×C₄	C₂×#120	1	1	yes	characteristic
529	C₂²×C₄	C₂×#120	1	1	yes	characteristic
530	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
531	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
532	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
533	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
534	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
535	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
536	C₄⋊C₄	C₂×#120	1	4	yes	—
537	C₄⋊C₄	C₂×#120	1	4	yes	—
538	C₄⋊C₄	C₂×#120	1	2	yes	—
539	C₄⋊C₄	C₂×#120	1	2	yes	—
540	C₂³	#2846	1	1	yes	characteristic
541	C₂³	#2846	1	1	yes	characteristic
542	C₂³	#2846	1	1	yes	characteristic
543	C₂³	#2846	1	1	yes	characteristic
544	C₂³	C₂²×#120	1	1	yes	characteristic
545	C₂³	C₂²×#120	1	1	yes	characteristic
546	C₂³	C₂²×#120	1	1	yes	characteristic
547	C₂³	#3584	1	2	yes	—
548	C₂³	#3585	1	2	yes	—
549	Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
550	D₄	C₂×B(4,𝔽₂)	1	2	yes	—
551	C₂×C₄	#2846	1	1	yes	characteristic
552	C₂×C₄	#2846	1	1	yes	characteristic
553	C₂×C₄	#2846	1	1	yes	characteristic
554	C₂×C₄	#2846	1	1	yes	characteristic
555	C₂×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
556	C₂×C₄	#3026	1	2	yes	—
557	C₂×C₄	C₂²×#120	1	1	yes	characteristic
558	C₂×C₄	C₂²×#120	1	1	yes	characteristic
559	C₂×C₄	C₂²×#120	1	1	yes	characteristic
560	C₂×C₄	C₂²×#120	1	1	yes	characteristic
561	C₂²	#32898	1	2	yes	—
562	C₂²	C₂×#2846	1	1	yes	characteristic
563	C₂²	#60366	1	1	yes	characteristic
564	C₂²	#60369	1	1	yes	characteristic
565	C₂²	#60376	1	2	yes	—
566	C₂²	#60376	1	2	yes	—
567	C₄	#32898	1	2	yes	—
568	C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
569	C₄	C₂×#3026	1	1	yes	characteristic
570	C₂	#6628855	1	1	yes	characteristic
571	C₂	#6628885	1	1	yes	characteristic
572	C₂	C₂×#32898	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#2846
commutator, Frattini, cosocle	C₂³×C₄	C₂⁵
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #10586478	C₂	semidirect
2. #6491100	C₂	semidirect
3. #6437543	C₂	semidirect
4. #6437541	C₂	semidirect
5. #6437518	C₂	semidirect
6. #6346767	C₂	semidirect
7. #6346765	C₂	semidirect
8. C₂×#18198	C₂	semidirect
9. #346552	C₂	semidirect
10. #346550	C₂	semidirect
11. #346520	C₂	semidirect
12. #346519	C₂	semidirect
13. #185679	C₂	semidirect
14. #185675	C₂	semidirect
15. #185623	C₂	semidirect
16. #185357	C₂	semidirect
17. #185355	C₂	semidirect
18. #185343	C₂	semidirect
19. #184923	C₂	semidirect
20. C₂³×AGL(1,ℤ/8)	C₂²	semidirect
21. #62984	C₂²	semidirect
22. #62983	C₂²	semidirect
23. #62893	C₂²	semidirect
24. #62892	C₂²	semidirect
32. C₂×#3003	C₂²	semidirect
33. C₂²×#450	C₂²	semidirect
34. C₂²×#447	C₂²	semidirect
35. #35222	C₂²	semidirect
36. #35222	C₂²	semidirect
37. C₂×#2408	C₂²	semidirect
38. #32926	C₂²	semidirect
39. #29684	C₂²	semidirect
40. #23858	C₂²	semidirect
41. #23858	C₂²	semidirect
42. #23855	C₂²	semidirect
43. #23855	C₂²	semidirect
44. #23851	C₂²	semidirect
45. #23851	C₂²	semidirect
46. #23848	C₂²	semidirect
47. #23848	C₂²	semidirect
48. #21874	C₂²	semidirect
49. #21874	C₂²	semidirect
50. #20973	C₂²	semidirect
51. #20972	C₂²	semidirect
52. #20971	C₂²	semidirect
53. #20898	C₂²	semidirect
54. #20897	C₂²	semidirect
55. #20897	C₂²	semidirect
56. #20722	C₂²	semidirect
57. #20601	C₂²	semidirect
58. #20597	C₂²	semidirect
59. #20597	C₂²	semidirect
60. #18198	C₂²	semidirect
61. #18198	C₂²	semidirect
62. #18198	C₂²	semidirect
63. #18198	C₂²	semidirect
64. #18196	C₂²	semidirect
65. #18194	C₂²	semidirect
66. #17578	C₂²	semidirect
67. #17577	C₂²	semidirect
68. #17572	C₂²	semidirect
69. #17572	C₂²	semidirect
70. C₂×#1520	C₂²	semidirect
71. C₂×#1519	C₂²	semidirect
72. #17381	C₂²	semidirect
73. #17381	C₂²	semidirect
74. C₂×#1459	C₂²	semidirect
75. #8381	C₂²	semidirect
76. #8381	C₂²	semidirect
77. #8379	C₂²	semidirect
78. #8379	C₂²	semidirect
79. #8377	C₂²	semidirect
80. #8377	C₂²	semidirect
81. #8375	C₂²	semidirect
82. #8375	C₂²	semidirect
83. #8352	C₂²	semidirect
84. #8352	C₂²	semidirect
85. #8352	C₂²	semidirect
86. #8352	C₂²	semidirect
87. #8351	C₂²	semidirect
88. #8350	C₂²	semidirect
89. #8317	C₂²	semidirect
90. #8316	C₂²	semidirect
91. C₂²×2₋¹⁺⁴	D₄	semidirect
92. C₂²×H(5,𝔽₂)	D₄	semidirect
93. C₂³×#41	D₄	semidirect
99. #3538	D₄	semidirect
100. #3537	D₄	semidirect
101. #3536	D₄	semidirect
102. #3536	D₄	semidirect
103. #3535	D₄	semidirect
104. #3534	D₄	semidirect
107. #3505	D₄	semidirect
108. #3505	D₄	semidirect
119. C₂×#550	D₄	semidirect
120. C₂×#550	D₄	semidirect
123. C₂×#548	D₄	semidirect
124. C₂×#548	D₄	semidirect
127. C₂×#547	D₄	semidirect
128. C₂×#547	D₄	semidirect
129. C₂×#546	D₄	semidirect
130. C₂×#546	D₄	semidirect
136. C₂×#539	D₄	semidirect
137. C₂×#538	D₄	semidirect
138. C₂×#537	D₄	semidirect
139. C₂×#537	D₄	semidirect
140. C₂×#536	D₄	semidirect
141. C₂×#535	D₄	semidirect
142. C₂×#532	D₄	semidirect
143. C₂×#525	D₄	semidirect
150. C₂×#520	D₄	semidirect
151. C₂×#520	D₄	semidirect
152. C₂×C₄×#41	D₄	semidirect
216. C₂²×#41	C₂×D₄	semidirect
217. C₂²×#41	C₂×D₄	semidirect
220. C₂³×Q₈	C₂×D₄	semidirect
225. C₂³×D₄	C₂×D₄	semidirect
231. #544	C₂×D₄	semidirect
233. #543	C₂×D₄	semidirect
236. #539	C₂×D₄	semidirect
237. #539	C₂×D₄	semidirect
240. #538	C₂×D₄	semidirect
241. #538	C₂×D₄	semidirect
242. #537	C₂×D₄	semidirect
246. #534	C₂×D₄	semidirect
248. C₂×C₄⋊Q₈	C₂×D₄	semidirect
250. C₂×#127	C₂×D₄	semidirect
253. C₂×#124	C₂×D₄	semidirect
254. C₂×#124	C₂×D₄	semidirect
273. C₂×C₂²⋊Q₈	C₂×D₄	semidirect
274. C₂×C₂²⋊Q₈	C₂×D₄	semidirect
289. C₂×#121	C₂×D₄	semidirect
290. C₂×#121	C₂×D₄	semidirect
300. C₂×C₄×Q₈	C₂×D₄	semidirect
301. C₂×C₄×Q₈	C₂×D₄	semidirect
312. C₂×C₄×D₄	C₂×D₄	semidirect
313. C₂×C₄×D₄	C₂×D₄	semidirect
483. #41	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#10586478	2
#6491100	2
#6437543	2
#6437541	2
#6437518	2
#6346767	2
#6346765	2
C₂×#18198	2
#346552	2
#346550	2
#346520	2
#346519	2
#185679	2
#185675	2
#185623	2
#185357	2
#185355	2
#185343	2
#184923	2