Subgroups — C₂²×#3551 #10586139

Order 512.

35550 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3551	C₂	1	96	yes	maximal, direct product factor
2	C₂²×#555	C₂	1	2	yes	maximal, complemented
3	C₂²×#553	C₂	1	2	yes	maximal, complemented
4	C₂²×#552	C₂	1	2	yes	maximal, complemented
5	C₂²×#551	C₂	1	2	yes	maximal, complemented
6	C₂²×#548	C₂	1	2	yes	maximal, complemented
7	C₂²×#546	C₂	1	2	yes	maximal, complemented
8	C₂²×#563	C₂	1	2	yes	maximal, complemented
9	C₂²×#560	C₂	1	2	yes	maximal, complemented
10	C₂²×#536	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#540	C₂	1	4	yes	maximal, complemented
12	C₂²×#537	C₂	1	2	yes	maximal, complemented
13	C₂²×#535	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#538	C₂	1	4	yes	maximal, complemented
15	C₂²×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#529	C₂	1	2	yes	maximal, complemented
17	C₂³×#41	C₂²	1	1	yes	characteristic
18	C₂³×#41	C₂²	1	2	yes	—
19	C₂³×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂⁴×D₄	C₂²	1	1	yes	characteristic
22	#3551	C₂²	1	1024	yes	direct product factor
23	C₂×#563	C₂²	1	96	yes	complemented
24	C₂×#560	C₂²	1	96	yes	complemented
25	C₂×#555	C₂²	1	96	yes	complemented
26	C₂×#553	C₂²	1	96	yes	complemented
27	C₂×#552	C₂²	1	96	yes	complemented
28	C₂×#551	C₂²	1	96	yes	complemented
29	C₂×#548	C₂²	1	96	yes	complemented
30	C₂×#546	C₂²	1	96	yes	complemented
31	C₂×#540	C₂²	1	192	yes	complemented
32	C₂×#538	C₂²	1	192	yes	complemented
33	C₂×#537	C₂²	1	96	yes	complemented
34	C₂×#536	C₂²	1	48	yes	complemented
35	C₂×#535	C₂²	1	48	yes	complemented
36	C₂×#532	C₂²	1	48	yes	complemented
37	C₂²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
39	C₂²×#127	C₂²	1	1	yes	characteristic
40	C₂²×#127	C₂²	1	2	yes	—
41	C₂×#529	C₂²	1	96	yes	complemented
42	C₂²×#126	C₂²	1	4	yes	—
43	C₂²×#126	C₂²	1	4	yes	complemented
44	C₂²×#126	C₂²	1	4	yes	complemented
45	C₂²×#125	C₂²	1	2	yes	complemented
46	C₂²×#125	C₂²	1	4	yes	complemented
47	C₂²×#124	C₂²	1	2	yes	—
48	C₂²×#124	C₂²	1	1	yes	characteristic
49	C₂²×#124	C₂²	1	2	yes	—
50	C₂²×#124	C₂²	1	2	yes	—
51	C₂²×#124	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#124	C₂²	1	4	yes	complemented
53	C₂²×#123	C₂²	1	4	yes	—
54	C₂²×#123	C₂²	1	4	yes	—
55	C₂²×#123	C₂²	1	2	yes	—
56	C₂²×#123	C₂²	1	4	yes	complemented
57	C₂²×#123	C₂²	1	2	yes	complemented
58	C₂²×#123	C₂²	1	4	yes	complemented
59	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	—
60	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₂²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
62	C₂²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₂²×#121	C₂²	1	2	yes	—
65	C₂²×#121	C₂²	1	2	yes	—
66	C₂²×#121	C₂²	1	2	yes	—
67	C₂²×#121	C₂²	1	2	yes	—
68	C₂²×#121	C₂²	1	4	yes	—
69	C₂²×#121	C₂²	1	2	yes	complemented
70	C₂²×#121	C₂²	1	4	yes	complemented
71	C₂²×#121	C₂²	1	4	yes	complemented
72	C₂²×#121	C₂²	1	4	yes	complemented
73	C₂²×#121	C₂²	1	4	yes	complemented
74	C₂²×#121	C₂²	1	4	yes	complemented
75	C₂²×#120	C₂²	1	2	yes	—
76	C₂²×#120	C₂²	1	4	yes	—
77	C₂²×#120	C₂²	1	2	yes	—
78	C₂²×C₄×Q₈	C₂²	1	2	yes	complemented
79	C₂²×C₄×D₄	C₂²	1	2	yes	—
80	C₂²×C₄×D₄	C₂²	1	2	yes	—
81	C₂²×C₄×D₄	C₂²	1	4	yes	complemented
82	C₂²×C₄×D₄	C₂²	1	2	yes	complemented
83	C₂²×C₄×D₄	C₂²	1	4	yes	complemented
84	C₂²×C₄×D₄	C₂²	1	4	yes	complemented
85	C₂²×#117	C₂²	1	1	yes	characteristic
86	C₂²×#117	C₂²	1	4	yes	complemented
87	C₂²×#117	C₂²	1	4	yes	complemented
88	C₂²×#117	C₂²	1	1	yes	characteristic, complemented
89	C₂³×C₄⋊C₄	C₂²	1	2	yes	complemented
90	C₂³×C₂²⋊C₄	C₂²	1	4	yes	—
91	C₂³×C₄²	C₂²	1	1	yes	characteristic, complemented
92	C₂⁶	C₂³	1	2	yes	—
93	C₂²×#41	—	4	8	no	—
94	C₂²×#41	—	4	8	no	—
95	C₂²×#41	—	4	16	no	—
96	C₂²×#41	C₂³	1	24	yes	—
97	C₂²×#41	C₂³	1	48	yes	—
98	C₂²×#41	C₂³	1	24	yes	complemented
99	C₂³×Q₈	—	4	8	no	—
100	C₂³×Q₈	C₂³	1	2	yes	—
101	C₂³×Q₈	C₂³	1	2	yes	—
102	C₂³×Q₈	C₂³	1	1	yes	characteristic
103	C₂³×Q₈	C₂³	1	1	yes	characteristic
104	C₂³×Q₈	C₂³	1	24	yes	complemented
105	C₂³×D₄	—	4	8	no	—
106	C₂³×D₄	C₂³	1	2	yes	—
107	C₂³×D₄	C₂³	1	2	yes	—
108	C₂³×D₄	C₂³	1	24	yes	—
109	C₂³×D₄	C₂³	1	1	yes	characteristic
110	C₂³×D₄	C₂³	1	1	yes	characteristic
111	C₂³×D₄	C₂³	1	4	yes	—
112	C₂³×D₄	C₂³	1	1	yes	characteristic
113	C₂³×D₄	C₂³	1	2	yes	—
114	C₂³×D₄	C₂³	1	1	yes	characteristic
115	C₂³×D₄	C₂³	1	2	yes	—
116	C₂³×D₄	C₂³	1	4	yes	—
117	C₂³×D₄	C₂³	1	4	yes	—
118	C₂³×D₄	C₂³	1	4	yes	—
119	C₂³×D₄	C₂³	1	2	yes	—
120	C₂⁴×C₄	C₂³	1	1	yes	characteristic
121	C₂⁴×C₄	C₂³	1	1	yes	characteristic
122	C₂⁴×C₄	C₂³	1	1	yes	characteristic
123	C₂⁴×C₄	C₂³	1	2	yes	—
124	C₂⁴×C₄	C₂³	1	2	yes	—
125	C₂⁴×C₄	C₂³	1	4	yes	—
126	C₂⁴×C₄	C₂³	1	2	yes	—
127	C₂⁴×C₄	C₂³	1	4	yes	—
128	C₂⁴×C₄	C₂³	1	4	yes	—
129	#563	C₂³	1	512	yes	complemented
130	#560	C₂³	1	512	yes	complemented
131	#555	C₂³	1	512	yes	complemented
132	#553	C₂³	1	512	yes	complemented
133	#552	C₂³	1	512	yes	complemented
134	#551	C₂³	1	512	yes	complemented
135	#548	C₂³	1	512	yes	complemented
136	#546	C₂³	1	512	yes	complemented
137	#540	C₂³	1	1024	yes	complemented
138	#538	C₂³	1	1024	yes	complemented
139	#537	C₂³	1	512	yes	complemented
140	#536	C₂³	1	256	yes	complemented
141	#535	C₂³	1	256	yes	complemented
142	#532	C₂³	1	256	yes	complemented
143	C₂×C₄⋊Q₈	C₂³	1	24	yes	complemented
144	C₂×C₄⋊Q₈	C₂³	1	48	yes	complemented
145	C₂×#127	C₂³	1	24	yes	—
146	C₂×#127	C₂³	1	48	yes	—
147	#529	C₂³	1	512	yes	complemented
148	C₂×#126	C₂³	1	96	yes	—
149	C₂×#126	C₂³	1	96	yes	complemented
150	C₂×#126	C₂³	1	96	yes	complemented
151	C₂×#125	C₂³	1	48	yes	complemented
152	C₂×#125	C₂³	1	96	yes	complemented
153	C₂×#124	C₂³	1	48	yes	—
154	C₂×#124	C₂³	1	24	yes	—
155	C₂×#124	C₂³	1	48	yes	—
156	C₂×#124	C₂³	1	48	yes	—
157	C₂×#124	C₂³	1	24	yes	complemented
158	C₂×#124	C₂³	1	96	yes	complemented
159	C₂×#123	C₂³	1	48	yes	—
160	C₂×#123	C₂³	1	96	yes	—
161	C₂×#123	C₂³	1	96	yes	—
162	C₂×#123	C₂³	1	96	yes	complemented
163	C₂×#123	C₂³	1	48	yes	complemented
164	C₂×#123	C₂³	1	96	yes	complemented
165	C₂×C₂²⋊Q₈	C₂³	1	48	yes	—
166	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
167	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
168	C₂×C₂²⋊Q₈	C₂³	1	96	yes	complemented
169	C₂×C₂²⋊Q₈	C₂³	1	96	yes	complemented
170	C₂×#121	C₂³	1	48	yes	—
171	C₂×#121	C₂³	1	48	yes	—
172	C₂×#121	C₂³	1	48	yes	—
173	C₂×#121	C₂³	1	48	yes	—
174	C₂×#121	C₂³	1	96	yes	—
175	C₂×#121	C₂³	1	48	yes	complemented
176	C₂×#121	C₂³	1	96	yes	complemented
177	C₂×#121	C₂³	1	96	yes	complemented
178	C₂×#121	C₂³	1	96	yes	complemented
179	C₂×#121	C₂³	1	96	yes	complemented
180	C₂×#121	C₂³	1	96	yes	complemented
181	C₂×#120	C₂³	1	48	yes	—
182	C₂×#120	C₂³	1	48	yes	—
183	C₂×#120	C₂³	1	96	yes	—
184	C₂×C₄×Q₈	C₂³	1	48	yes	complemented
185	C₂×C₄×D₄	C₂³	1	48	yes	—
186	C₂×C₄×D₄	C₂³	1	48	yes	—
187	C₂×C₄×D₄	C₂³	1	96	yes	complemented
188	C₂×C₄×D₄	C₂³	1	48	yes	complemented
189	C₂×C₄×D₄	C₂³	1	96	yes	complemented
190	C₂×C₄×D₄	C₂³	1	96	yes	complemented
191	C₂×#117	C₂³	1	24	yes	—
192	C₂×#117	C₂³	1	96	yes	complemented
193	C₂×#117	C₂³	1	24	yes	complemented
194	C₂×#117	C₂³	1	96	yes	complemented
195	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
200	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
204	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
205	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
206	C₂²×C₄⋊C₄	C₂³	1	48	yes	complemented
207	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
209	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
210	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
211	C₂²×C₂²⋊C₄	C₂³	1	96	yes	—
212	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
215	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
216	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
223	C₂²×C₄²	C₂³	1	1	yes	characteristic
224	C₂²×C₄²	C₂³	1	2	yes	—
225	C₂²×C₄²	C₂³	1	1	yes	characteristic
226	C₂²×C₄²	C₂³	1	2	yes	—
227	C₂²×C₄²	C₂³	1	4	yes	—
228	C₂²×C₄²	C₂³	1	2	yes	—
229	C₂²×C₄²	C₂³	1	24	yes	complemented
230	C₂⁵	—	4	8	no	—
231	C₂⁵	—	4	16	no	—
232	C₂⁵	C₂⁴	1	1	yes	characteristic
233	C₂⁵	C₂⁴	1	4	yes	—
234	C₂⁵	C₂⁴	1	1	yes	characteristic
235	C₂⁵	C₂⁴	1	2	yes	—
236	C₂⁵	C₂⁴	1	1	yes	characteristic
237	C₂⁵	C₂⁴	1	24	yes	—
238	C₂×#41	—	4	96	no	—
239	C₂×#41	—	4	96	no	—
240	C₂×#41	—	4	192	no	—
241	C₂×#41	C₂⁴	1	64	yes	—
242	C₂×#41	C₂⁴	1	128	yes	—
243	C₂×#41	C₂⁴	1	64	yes	complemented
244	C₂²×Q₈	—	2	16	no	—
245	C₂²×Q₈	—	4	8	no	—
246	C₂²×Q₈	—	4	4	no	—
247	C₂²×Q₈	—	4	4	no	—
248	C₂²×Q₈	—	4	96	no	—
249	C₂²×Q₈	C₂⁴	1	24	yes	—
250	C₂²×Q₈	C₂⁴	1	12	yes	—
251	C₂²×Q₈	C₂⁴	1	24	yes	—
252	C₂²×Q₈	C₂⁴	1	12	yes	—
253	C₂²×Q₈	C₂⁴	1	64	yes	complemented
254	C₂²×D₄	—	2	16	no	—
255	C₂²×D₄	—	4	96	no	—
256	C₂²×D₄	—	4	8	no	—
257	C₂²×D₄	—	4	16	no	—
258	C₂²×D₄	—	4	8	no	—
259	C₂²×D₄	—	4	16	no	—
260	C₂²×D₄	—	4	16	no	—
261	C₂²×D₄	—	4	8	no	—
262	C₂²×D₄	—	4	8	no	—
263	C₂²×D₄	—	4	4	no	—
264	C₂²×D₄	—	4	4	no	—
265	C₂²×D₄	—	4	4	no	—
266	C₂²×D₄	—	4	4	no	—
267	C₂²×D₄	—	4	16	no	—
268	C₂²×D₄	C₂⁴	1	24	yes	—
269	C₂²×D₄	C₂⁴	1	24	yes	—
270	C₂²×D₄	C₂⁴	1	48	yes	—
271	C₂²×D₄	C₂⁴	1	48	yes	—
272	C₂²×D₄	C₂⁴	1	48	yes	—
273	C₂²×D₄	C₂⁴	1	24	yes	—
274	C₂²×D₄	C₂⁴	1	12	yes	—
275	C₂²×D₄	C₂⁴	1	12	yes	—
276	C₂²×D₄	C₂⁴	1	48	yes	—
277	C₂²×D₄	C₂⁴	1	24	yes	—
278	C₂²×D₄	C₂⁴	1	24	yes	—
279	C₂²×D₄	C₂⁴	1	12	yes	—
280	C₂²×D₄	C₂⁴	1	12	yes	—
281	C₂²×D₄	C₂⁴	1	64	yes	—
282	C₂³×C₄	—	2	8	no	—
283	C₂³×C₄	—	2	8	no	—
284	C₂³×C₄	—	2	16	no	—
285	C₂³×C₄	—	2	8	no	—
286	C₂³×C₄	—	4	16	no	—
287	C₂³×C₄	—	4	8	no	—
288	C₂³×C₄	—	4	16	no	—
289	C₂³×C₄	—	4	8	no	—
290	C₂³×C₄	—	4	16	no	—
291	C₂³×C₄	C₂⁴	1	24	yes	—
292	C₂³×C₄	C₂⁴	1	12	yes	—
293	C₂³×C₄	C₂⁴	1	12	yes	—
294	C₂³×C₄	C₂⁴	1	12	yes	—
295	C₂³×C₄	C₂⁴	1	2	yes	—
296	C₂³×C₄	C₂⁴	1	1	yes	characteristic
297	C₂³×C₄	C₂⁴	1	4	yes	—
298	C₂³×C₄	C₂⁴	1	4	yes	—
299	C₂³×C₄	C₂⁴	1	2	yes	—
300	C₂³×C₄	C₂⁴	1	4	yes	—
301	C₂³×C₄	C₂⁴	1	2	yes	—
302	C₂³×C₄	C₂⁴	1	1	yes	characteristic
303	C₂³×C₄	C₂⁴	1	1	yes	characteristic
304	C₂³×C₄	C₂⁴	1	48	yes	—
305	C₂³×C₄	C₂⁴	1	48	yes	—
306	C₂³×C₄	C₂⁴	1	48	yes	—
307	C₂³×C₄	C₂⁴	1	24	yes	—
308	C₂³×C₄	C₂⁴	1	24	yes	—
309	C₂³×C₄	C₂⁴	1	1	yes	characteristic
310	C₄⋊Q₈	C₂⁴	1	64	yes	complemented
311	C₄⋊Q₈	C₂⁴	1	128	yes	complemented
312	#127	C₂⁴	1	64	yes	—
313	#127	C₂⁴	1	128	yes	—
314	#126	C₂⁴	1	256	yes	—
315	#126	C₂⁴	1	256	yes	complemented
316	#126	C₂⁴	1	256	yes	complemented
317	#125	C₂⁴	1	128	yes	complemented
318	#125	C₂⁴	1	256	yes	complemented
319	#124	C₂⁴	1	128	yes	—
320	#124	C₂⁴	1	64	yes	—
321	#124	C₂⁴	1	128	yes	—
322	#124	C₂⁴	1	128	yes	—
323	#124	C₂⁴	1	64	yes	complemented
324	#124	C₂⁴	1	256	yes	complemented
325	#123	C₂⁴	1	128	yes	—
326	#123	C₂⁴	1	256	yes	—
327	#123	C₂⁴	1	256	yes	—
328	#123	C₂⁴	1	256	yes	complemented
329	#123	C₂⁴	1	128	yes	complemented
330	#123	C₂⁴	1	256	yes	complemented
331	C₂²⋊Q₈	C₂⁴	1	128	yes	—
332	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
333	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
334	C₂²⋊Q₈	C₂⁴	1	256	yes	complemented
335	C₂²⋊Q₈	C₂⁴	1	256	yes	complemented
336	#121	C₂⁴	1	128	yes	—
337	#121	C₂⁴	1	128	yes	—
338	#121	C₂⁴	1	128	yes	—
339	#121	C₂⁴	1	128	yes	—
340	#121	C₂⁴	1	256	yes	—
341	#121	C₂⁴	1	128	yes	complemented
342	#121	C₂⁴	1	256	yes	complemented
343	#121	C₂⁴	1	256	yes	complemented
344	#121	C₂⁴	1	256	yes	complemented
345	#121	C₂⁴	1	256	yes	complemented
346	#121	C₂⁴	1	256	yes	complemented
347	#120	C₂⁴	1	128	yes	—
348	#120	C₂⁴	1	128	yes	—
349	#120	C₂⁴	1	256	yes	—
350	C₄×Q₈	C₂⁴	1	128	yes	complemented
351	C₄×D₄	C₂⁴	1	128	yes	—
352	C₄×D₄	C₂⁴	1	128	yes	—
353	C₄×D₄	C₂⁴	1	256	yes	complemented
354	C₄×D₄	C₂⁴	1	128	yes	complemented
355	C₄×D₄	C₂⁴	1	256	yes	complemented
356	C₄×D₄	C₂⁴	1	256	yes	complemented
357	#117	C₂⁴	1	64	yes	—
358	#117	C₂⁴	1	256	yes	complemented
359	#117	C₂⁴	1	64	yes	complemented
360	#117	C₂⁴	1	256	yes	complemented
361	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
362	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
363	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
364	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
365	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
366	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
367	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
368	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
369	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
370	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
371	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
372	C₂×C₄⋊C₄	C₂⁴	1	128	yes	complemented
373	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
374	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
375	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
376	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
377	C₂×C₂²⋊C₄	C₂⁴	1	256	yes	—
378	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
379	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
380	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
381	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
382	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
383	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
384	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
385	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
386	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
387	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
388	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
389	C₂×C₄²	C₂⁴	1	24	yes	—
390	C₂×C₄²	C₂⁴	1	12	yes	—
391	C₂×C₄²	C₂⁴	1	48	yes	—
392	C₂×C₄²	C₂⁴	1	24	yes	—
393	C₂×C₄²	C₂⁴	1	24	yes	—
394	C₂×C₄²	C₂⁴	1	12	yes	—
395	C₂×C₄²	C₂⁴	1	64	yes	complemented
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	8	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	16	no	—
401	C₂⁴	—	2	8	no	—
402	C₂⁴	—	2	8	no	—
403	C₂⁴	—	2	16	no	—
404	C₂⁴	—	2	8	no	—
405	C₂⁴	—	2	8	no	—
406	C₂⁴	—	2	16	no	—
407	C₂⁴	—	2	8	no	—
408	C₂⁴	—	4	48	no	—
409	C₂⁴	—	4	96	no	—
410	C₂⁴	—	8	64	no	—
411	C₂⁴	C₂⁵	1	6	yes	—
412	C₂⁴	C₂⁵	1	24	yes	—
413	C₂⁴	C₂⁵	1	6	yes	—
414	C₂⁴	C₂⁵	1	12	yes	—
415	C₂⁴	C₂⁵	1	6	yes	—
416	C₂⁴	C₂⁵	1	32	yes	—
417	C₂⁴	C₂⁵	1	1	yes	characteristic
418	#41	—	4	128	no	—
419	#41	—	4	128	no	—
420	#41	—	4	256	no	—
421	C₂×Q₈	—	2	96	no	—
422	C₂×Q₈	—	4	48	no	—
423	C₂×Q₈	—	4	24	no	—
424	C₂×Q₈	—	4	24	no	—
425	C₂×Q₈	—	4	128	no	—
426	C₂×Q₈	C₂⁵	1	32	yes	—
427	C₂×Q₈	C₂⁵	1	16	yes	—
428	C₂×Q₈	C₂⁵	1	32	yes	—
429	C₂×Q₈	C₂⁵	1	16	yes	—
430	C₂×D₄	—	2	96	no	—
431	C₂×D₄	—	4	128	no	—
432	C₂×D₄	—	4	48	no	—
433	C₂×D₄	—	4	96	no	—
434	C₂×D₄	—	4	48	no	—
435	C₂×D₄	—	4	96	no	—
436	C₂×D₄	—	4	96	no	—
437	C₂×D₄	—	4	48	no	—
438	C₂×D₄	—	4	48	no	—
439	C₂×D₄	—	4	24	no	—
440	C₂×D₄	—	4	24	no	—
441	C₂×D₄	—	4	24	no	—
442	C₂×D₄	—	4	24	no	—
443	C₂×D₄	—	4	96	no	—
444	C₂×D₄	C₂⁵	1	32	yes	—
445	C₂×D₄	C₂⁵	1	32	yes	—
446	C₂×D₄	C₂⁵	1	64	yes	—
447	C₂×D₄	C₂⁵	1	64	yes	—
448	C₂×D₄	C₂⁵	1	64	yes	—
449	C₂×D₄	C₂⁵	1	32	yes	—
450	C₂×D₄	C₂⁵	1	16	yes	—
451	C₂×D₄	C₂⁵	1	16	yes	—
452	C₂×D₄	C₂⁵	1	64	yes	—
453	C₂×D₄	C₂⁵	1	32	yes	—
454	C₂×D₄	C₂⁵	1	32	yes	—
455	C₂×D₄	C₂⁵	1	16	yes	—
456	C₂×D₄	C₂⁵	1	16	yes	—
457	C₂²×C₄	—	2	8	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	16	no	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	—	2	16	no	—
464	C₂²×C₄	—	2	8	no	—
465	C₂²×C₄	—	2	16	no	—
466	C₂²×C₄	—	2	48	no	—
467	C₂²×C₄	—	2	48	no	—
468	C₂²×C₄	—	2	96	no	—
469	C₂²×C₄	—	2	48	no	—
470	C₂²×C₄	—	4	96	no	—
471	C₂²×C₄	—	4	48	no	—
472	C₂²×C₄	—	4	96	no	—
473	C₂²×C₄	—	4	48	no	—
474	C₂²×C₄	—	4	96	no	—
475	C₂²×C₄	H(5,𝔽₂)	1	8	yes	—
476	C₂²×C₄	C₂⁵	1	12	yes	—
477	C₂²×C₄	C₂⁵	1	6	yes	—
478	C₂²×C₄	C₂⁵	1	24	yes	—
479	C₂²×C₄	C₂⁵	1	12	yes	—
480	C₂²×C₄	C₂⁵	1	6	yes	—
481	C₂²×C₄	C₂⁵	1	6	yes	—
482	C₂²×C₄	C₂⁵	1	24	yes	—
483	C₂²×C₄	C₂⁵	1	24	yes	—
484	C₂²×C₄	C₂⁵	1	16	yes	—
485	C₂²×C₄	C₂⁵	1	12	yes	—
486	C₂²×C₄	C₂⁵	1	32	yes	—
487	C₂²×C₄	C₂⁵	1	16	yes	—
488	C₂²×C₄	C₂⁵	1	16	yes	—
489	C₂²×C₄	C₂⁵	1	32	yes	—
490	C₂²×C₄	C₂⁵	1	64	yes	—
491	C₂²×C₄	C₂⁵	1	64	yes	—
492	C₂²×C₄	C₂⁵	1	64	yes	—
493	C₂²×C₄	C₂⁵	1	32	yes	—
494	C₂²×C₄	C₂⁵	1	6	yes	—
495	C₄⋊C₄	C₂⁵	1	32	yes	—
496	C₄⋊C₄	C₂⁵	1	32	yes	—
497	C₄⋊C₄	C₂⁵	1	64	yes	—
498	C₄⋊C₄	C₂⁵	1	64	yes	—
499	C₄⋊C₄	C₂⁵	1	64	yes	—
500	C₄⋊C₄	C₂⁵	1	64	yes	—
501	C₄⋊C₄	C₂⁵	1	32	yes	—
502	C₄⋊C₄	C₂⁵	1	32	yes	—
503	C₄⋊C₄	C₂⁵	1	64	yes	—
504	C₄⋊C₄	C₂⁵	1	64	yes	—
505	C₄⋊C₄	C₂⁵	1	64	yes	—
506	C₂²⋊C₄	C₂⁵	1	32	yes	—
507	C₂²⋊C₄	C₂⁵	1	64	yes	—
508	C₂²⋊C₄	C₂⁵	1	64	yes	—
509	C₂²⋊C₄	C₂⁵	1	64	yes	—
510	C₂²⋊C₄	C₂⁵	1	32	yes	—
511	C₂²⋊C₄	C₂⁵	1	32	yes	—
512	C₂²⋊C₄	C₂⁵	1	64	yes	—
513	C₂²⋊C₄	C₂⁵	1	64	yes	—
514	C₂²⋊C₄	C₂⁵	1	32	yes	—
515	C₂²⋊C₄	C₂⁵	1	64	yes	—
516	C₂²⋊C₄	C₂⁵	1	32	yes	—
517	C₂²⋊C₄	C₂⁵	1	32	yes	—
518	C₂²⋊C₄	C₂⁵	1	64	yes	—
519	C₂²⋊C₄	C₂⁵	1	64	yes	—
520	C₂²⋊C₄	C₂⁵	1	64	yes	—
521	C₄²	C₂⁵	1	16	yes	—
522	C₄²	C₂⁵	1	32	yes	—
523	C₄²	C₂⁵	1	16	yes	—
524	C₄²	C₂⁵	1	32	yes	—
525	C₄²	C₂⁵	1	64	yes	—
526	C₄²	C₂⁵	1	32	yes	—
527	C₂³	—	2	12	no	—
528	C₂³	—	2	24	no	—
529	C₂³	—	2	12	no	—
530	C₂³	—	2	12	no	—
531	C₂³	—	2	48	no	—
532	C₂³	—	2	24	no	—
533	C₂³	—	2	24	no	—
534	C₂³	—	2	48	no	—
535	C₂³	—	2	24	no	—
536	C₂³	—	2	24	no	—
537	C₂³	—	2	48	no	—
538	C₂³	—	2	24	no	—
539	C₂³	—	4	32	no	—
540	C₂³	—	4	64	no	—
541	C₂³	—	4	16	no	—
542	C₂³	—	4	32	no	—
543	C₂³	—	4	16	no	—
544	C₂³	—	4	64	no	—
545	C₂³	—	4	16	no	—
546	C₂³	—	8	192	no	—
547	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
548	C₂³	#585	1	8	yes	—
549	C₂³	C₂⁶	1	4	yes	—
550	C₂³	C₂⁶	1	16	yes	—
551	C₂³	C₂⁶	1	4	yes	—
552	C₂³	C₂⁶	1	8	yes	—
553	C₂³	C₂⁶	1	4	yes	—
554	C₂³	C₂⁶	1	3	yes	—
555	Q₈	—	2	64	no	—
556	Q₈	—	4	32	no	—
557	Q₈	—	4	16	no	—
558	Q₈	—	4	16	no	—
559	D₄	—	2	64	no	—
560	D₄	—	4	32	no	—
561	D₄	—	4	64	no	—
562	D₄	—	4	32	no	—
563	D₄	—	4	64	no	—
564	D₄	—	4	64	no	—
565	D₄	—	4	32	no	—
566	D₄	—	4	32	no	—
567	D₄	—	4	16	no	—
568	D₄	—	4	16	no	—
569	D₄	—	4	16	no	—
570	D₄	—	4	16	no	—
571	D₄	—	4	64	no	—
572	C₂×C₄	—	2	24	no	—
573	C₂×C₄	—	2	12	no	—
574	C₂×C₄	—	2	12	no	—
575	C₂×C₄	—	2	12	no	—
576	C₂×C₄	—	2	48	no	—
577	C₂×C₄	—	2	24	no	—
578	C₂×C₄	—	2	48	no	—
579	C₂×C₄	—	2	24	no	—
580	C₂×C₄	—	2	48	no	—
581	C₂×C₄	—	2	32	no	—
582	C₂×C₄	—	2	32	no	—
583	C₂×C₄	—	2	64	no	—
584	C₂×C₄	—	2	32	no	—
585	C₂×C₄	—	4	64	no	—
586	C₂×C₄	—	4	32	no	—
587	C₂×C₄	—	4	64	no	—
588	C₂×C₄	—	4	32	no	—
589	C₂×C₄	—	4	64	no	—
590	C₂×C₄	C₂×H(5,𝔽₂)	1	24	yes	—
591	C₂×C₄	C₂⁶	1	8	yes	—
592	C₂×C₄	C₂⁶	1	4	yes	—
593	C₂×C₄	C₂⁶	1	8	yes	—
594	C₂×C₄	C₂⁶	1	16	yes	—
595	C₂×C₄	C₂⁶	1	4	yes	—
596	C₂×C₄	C₂⁶	1	4	yes	—
597	C₂×C₄	C₂⁶	1	16	yes	—
598	C₂×C₄	C₂⁶	1	16	yes	—
599	C₂×C₄	C₂⁶	1	8	yes	—
600	C₂×C₄	C₂⁶	1	4	yes	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	8	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	2	16	no	—
606	C₂²	—	2	8	no	—
607	C₂²	—	2	8	no	—
608	C₂²	—	2	16	no	—
609	C₂²	—	2	8	no	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	16	no	—
612	C₂²	—	2	8	no	—
613	C₂²	—	4	24	no	—
614	C₂²	—	4	48	no	—
615	C₂²	—	4	24	no	—
616	C₂²	—	4	96	no	—
617	C₂²	—	4	24	no	—
618	C₂²	—	8	64	no	—
619	C₂²	#3551	1	16	yes	direct product factor
620	C₂²	C₂²×H(5,𝔽₂)	1	6	yes	—
621	C₂²	C₂×#585	1	12	yes	—
622	C₂²	C₂⁷	1	1	yes	characteristic
623	C₄	—	2	8	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	4	no	—
626	C₄	—	2	4	no	—
627	C₄	—	2	16	no	—
628	C₄	—	2	8	no	—
629	C₄	—	2	16	no	—
630	C₄	—	2	8	no	—
631	C₄	—	2	16	no	—
632	C₄	C₂²×H(5,𝔽₂)	1	8	yes	—
633	C₂	—	4	4	no	—
634	C₂	—	4	8	no	—
635	C₂	—	4	4	no	—
636	C₂	—	4	16	no	—
637	C₂	—	4	4	no	—
638	C₂	C₂×#3551	1	12	yes	direct product factor
639	C₂	C₂³×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂	C₂²×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁷
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#3551	C₂	direct (N × H)
2. C₂²×#555	C₂	semidirect
3. C₂²×#553	C₂	semidirect
4. C₂²×#552	C₂	semidirect
5. C₂²×#551	C₂	semidirect
6. C₂²×#548	C₂	semidirect
7. C₂²×#546	C₂	semidirect
8. C₂²×#563	C₂	semidirect
9. C₂²×#560	C₂	semidirect
10. C₂²×#536	C₂	semidirect
11. C₂²×#540	C₂	semidirect
12. C₂²×#537	C₂	semidirect
13. C₂²×#535	C₂	semidirect
14. C₂²×#538	C₂	semidirect
15. C₂²×#532	C₂	semidirect
16. C₂²×#529	C₂	semidirect
19. C₂³×#41	C₂²	semidirect
20. C₂⁴×Q₈	C₂²	semidirect
22. #3551	C₂²	direct (N × H)
23. C₂×#563	C₂²	semidirect
24. C₂×#560	C₂²	semidirect
25. C₂×#555	C₂²	semidirect
26. C₂×#553	C₂²	semidirect
27. C₂×#552	C₂²	semidirect
28. C₂×#551	C₂²	semidirect
29. C₂×#548	C₂²	semidirect
30. C₂×#546	C₂²	semidirect
31. C₂×#540	C₂²	semidirect
32. C₂×#538	C₂²	semidirect
33. C₂×#537	C₂²	semidirect
34. C₂×#536	C₂²	semidirect
35. C₂×#535	C₂²	semidirect
36. C₂×#532	C₂²	semidirect
37. C₂²×C₄⋊Q₈	C₂²	semidirect
38. C₂²×C₄⋊Q₈	C₂²	semidirect
41. C₂×#529	C₂²	semidirect
43. C₂²×#126	C₂²	semidirect
44. C₂²×#126	C₂²	semidirect
45. C₂²×#125	C₂²	semidirect
46. C₂²×#125	C₂²	semidirect
51. C₂²×#124	C₂²	semidirect
52. C₂²×#124	C₂²	semidirect
56. C₂²×#123	C₂²	semidirect
57. C₂²×#123	C₂²	semidirect
58. C₂²×#123	C₂²	semidirect
60. C₂²×C₂²⋊Q₈	C₂²	semidirect
61. C₂²×C₂²⋊Q₈	C₂²	semidirect
62. C₂²×C₂²⋊Q₈	C₂²	semidirect
63. C₂²×C₂²⋊Q₈	C₂²	semidirect
69. C₂²×#121	C₂²	semidirect
70. C₂²×#121	C₂²	semidirect
71. C₂²×#121	C₂²	semidirect
72. C₂²×#121	C₂²	semidirect
73. C₂²×#121	C₂²	semidirect
74. C₂²×#121	C₂²	semidirect
78. C₂²×C₄×Q₈	C₂²	semidirect
81. C₂²×C₄×D₄	C₂²	semidirect
82. C₂²×C₄×D₄	C₂²	semidirect
83. C₂²×C₄×D₄	C₂²	semidirect
84. C₂²×C₄×D₄	C₂²	semidirect
86. C₂²×#117	C₂²	semidirect
87. C₂²×#117	C₂²	semidirect
88. C₂²×#117	C₂²	semidirect
89. C₂³×C₄⋊C₄	C₂²	semidirect
91. C₂³×C₄²	C₂²	semidirect
98. C₂²×#41	C₂³	semidirect
104. C₂³×Q₈	C₂³	semidirect
129. #563	C₂³	semidirect
130. #560	C₂³	semidirect
131. #555	C₂³	semidirect
132. #553	C₂³	semidirect
133. #552	C₂³	semidirect
134. #551	C₂³	semidirect
135. #548	C₂³	semidirect
136. #546	C₂³	semidirect
137. #540	C₂³	semidirect
138. #538	C₂³	semidirect
139. #537	C₂³	semidirect
140. #536	C₂³	semidirect
141. #535	C₂³	semidirect
142. #532	C₂³	semidirect
143. C₂×C₄⋊Q₈	C₂³	semidirect
144. C₂×C₄⋊Q₈	C₂³	semidirect
147. #529	C₂³	semidirect
149. C₂×#126	C₂³	semidirect
150. C₂×#126	C₂³	semidirect
151. C₂×#125	C₂³	semidirect
152. C₂×#125	C₂³	semidirect
157. C₂×#124	C₂³	semidirect
158. C₂×#124	C₂³	semidirect
162. C₂×#123	C₂³	semidirect
163. C₂×#123	C₂³	semidirect
164. C₂×#123	C₂³	semidirect
166. C₂×C₂²⋊Q₈	C₂³	semidirect
167. C₂×C₂²⋊Q₈	C₂³	semidirect
168. C₂×C₂²⋊Q₈	C₂³	semidirect
169. C₂×C₂²⋊Q₈	C₂³	semidirect
175. C₂×#121	C₂³	semidirect
176. C₂×#121	C₂³	semidirect
177. C₂×#121	C₂³	semidirect
178. C₂×#121	C₂³	semidirect
179. C₂×#121	C₂³	semidirect
180. C₂×#121	C₂³	semidirect
184. C₂×C₄×Q₈	C₂³	semidirect
187. C₂×C₄×D₄	C₂³	semidirect
188. C₂×C₄×D₄	C₂³	semidirect
189. C₂×C₄×D₄	C₂³	semidirect
190. C₂×C₄×D₄	C₂³	semidirect
192. C₂×#117	C₂³	semidirect
193. C₂×#117	C₂³	semidirect
194. C₂×#117	C₂³	semidirect
206. C₂²×C₄⋊C₄	C₂³	semidirect
229. C₂²×C₄²	C₂³	semidirect
243. C₂×#41	C₂⁴	semidirect
253. C₂²×Q₈	C₂⁴	semidirect
310. C₄⋊Q₈	C₂⁴	semidirect
311. C₄⋊Q₈	C₂⁴	semidirect
315. #126	C₂⁴	semidirect
316. #126	C₂⁴	semidirect
317. #125	C₂⁴	semidirect
318. #125	C₂⁴	semidirect
323. #124	C₂⁴	semidirect
324. #124	C₂⁴	semidirect
328. #123	C₂⁴	semidirect
329. #123	C₂⁴	semidirect
330. #123	C₂⁴	semidirect
332. C₂²⋊Q₈	C₂⁴	semidirect
333. C₂²⋊Q₈	C₂⁴	semidirect
334. C₂²⋊Q₈	C₂⁴	semidirect
335. C₂²⋊Q₈	C₂⁴	semidirect
341. #121	C₂⁴	semidirect
342. #121	C₂⁴	semidirect
343. #121	C₂⁴	semidirect
344. #121	C₂⁴	semidirect
345. #121	C₂⁴	semidirect
346. #121	C₂⁴	semidirect
350. C₄×Q₈	C₂⁴	semidirect
353. C₄×D₄	C₂⁴	semidirect
354. C₄×D₄	C₂⁴	semidirect
355. C₄×D₄	C₂⁴	semidirect
356. C₄×D₄	C₂⁴	semidirect
358. #117	C₂⁴	semidirect
359. #117	C₂⁴	semidirect
360. #117	C₂⁴	semidirect
372. C₂×C₄⋊C₄	C₂⁴	semidirect
395. C₂×C₄²	C₂⁴	semidirect
619. C₂²	#3551	direct (N × H)
638. C₂	C₂×#3551	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#3551	2
C₂²×#555	2
C₂²×#553	2
C₂²×#552	2
C₂²×#551	2
C₂²×#548	2
C₂²×#546	2
C₂²×#563	2
C₂²×#560	2
C₂²×#536	2
C₂²×#540	2
C₂²×#537	2
C₂²×#535	2
C₂²×#538	2
C₂²×#532	2
C₂²×#529	2

Subgroups — C22×#3551 #10586139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#3551 #10586139