Subgroups — C₂²×#3510 #10585986

Order 512.

35378 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3510	C₂	1	96	yes	maximal, direct product factor
2	C₂²×#559	C₂	1	4	yes	maximal, complemented
3	C₂²×#556	C₂	1	4	yes	maximal, complemented
4	C₂²×#551	C₂	1	8	yes	maximal, complemented
5	C₂²×#536	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#542	C₂	1	4	yes	maximal, complemented
7	C₂²×#535	C₂	1	1	yes	maximal, characteristic
8	C₂²×#533	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#529	C₂	1	4	yes	maximal, complemented
10	C₂³×#124	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#519	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#518	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×#41	C₂²	1	1	yes	characteristic
15	C₂⁴×Q₈	C₂²	1	1	yes	characteristic
16	C₂⁴×D₄	C₂²	1	1	yes	characteristic
17	#3510	C₂²	1	1024	yes	direct product factor
18	C₂×#559	C₂²	1	192	yes	complemented
19	C₂×#556	C₂²	1	192	yes	complemented
20	C₂×#551	C₂²	1	384	yes	complemented
21	C₂×#542	C₂²	1	192	yes	complemented
22	C₂×#536	C₂²	1	48	yes	complemented
23	C₂×#535	C₂²	1	48	yes	—
24	C₂×#533	C₂²	1	48	yes	complemented
25	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
27	C₂²×#127	C₂²	1	2	yes	—
28	C₂×#529	C₂²	1	192	yes	complemented
29	C₂²×#126	C₂²	1	8	yes	complemented
30	C₂²×#126	C₂²	1	8	yes	complemented
31	C₂²×#125	C₂²	1	2	yes	complemented
32	C₂²×#124	C₂²	1	2	yes	—
33	C₂²×#124	C₂²	1	2	yes	—
34	C₂²×#124	C₂²	1	4	yes	—
35	C₂²×#124	C₂²	1	2	yes	—
36	C₂²×#124	C₂²	1	48	yes	complemented
37	C₂²×#124	C₂²	1	8	yes	complemented
38	C₂²×#124	C₂²	1	2	yes	complemented
39	C₂²×#123	C₂²	1	4	yes	—
40	C₂²×#123	C₂²	1	8	yes	complemented
41	C₂²×#123	C₂²	1	8	yes	complemented
42	C₂²×C₂²⋊Q₈	C₂²	1	4	yes	—
43	C₂²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
44	C₂²×C₂²⋊Q₈	C₂²	1	8	yes	complemented
45	C₂²×#121	C₂²	1	4	yes	—
46	C₂²×#120	C₂²	1	4	yes	—
47	C₂×#519	C₂²	1	48	yes	complemented
48	C₂×#518	C₂²	1	48	yes	complemented
49	C₂×C₄×#41	C₂²	1	48	yes	complemented
50	C₂²×C₄×Q₈	C₂²	1	2	yes	complemented
51	C₂²×C₄×Q₈	C₂²	1	4	yes	complemented
52	C₂²×C₄×Q₈	C₂²	1	4	yes	complemented
53	C₂²×C₄×Q₈	C₂²	1	4	yes	complemented
54	C₂²×C₄×D₄	C₂²	1	4	yes	—
55	C₂²×C₄×D₄	C₂²	1	4	yes	—
56	C₂²×C₄×D₄	C₂²	1	4	yes	—
57	C₂²×C₄×D₄	C₂²	1	2	yes	complemented
58	C₂²×C₄×D₄	C₂²	1	8	yes	complemented
59	C₂²×#117	C₂²	1	1	yes	characteristic
60	C₂²×#117	C₂²	1	1	yes	characteristic
61	C₂²×#117	C₂²	1	1	yes	characteristic
62	C₂²×#117	C₂²	1	4	yes	—
63	C₂²×#117	C₂²	1	2	yes	complemented
64	C₂²×#117	C₂²	1	8	yes	complemented
65	C₂³×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₂³×C₂²⋊C₄	C₂²	1	4	yes	—
67	C₂³×C₄²	C₂²	1	1	yes	characteristic
68	C₂³×C₄²	C₂²	1	2	yes	complemented
69	C₂⁶	C₂³	1	2	yes	—
70	C₂²×#41	—	2	16	no	—
71	C₂²×#41	C₂³	1	24	yes	—
72	C₂³×Q₈	—	2	16	no	—
73	C₂³×Q₈	C₂³	1	2	yes	—
74	C₂³×Q₈	C₂³	1	2	yes	—
75	C₂³×Q₈	C₂³	1	24	yes	—
76	C₂³×Q₈	C₂³	1	1	yes	characteristic
77	C₂³×Q₈	C₂³	1	4	yes	—
78	C₂³×D₄	—	2	16	no	—
79	C₂³×D₄	C₂³	1	2	yes	—
80	C₂³×D₄	C₂³	1	2	yes	—
81	C₂³×D₄	C₂³	1	24	yes	—
82	C₂³×D₄	C₂³	1	2	yes	—
83	C₂³×D₄	C₂³	1	1	yes	characteristic
84	C₂³×D₄	C₂³	1	8	yes	—
85	C₂⁴×C₄	C₂³	1	2	yes	—
86	C₂⁴×C₄	C₂³	1	2	yes	—
87	C₂⁴×C₄	C₂³	1	2	yes	—
88	C₂⁴×C₄	C₂³	1	4	yes	—
89	C₂⁴×C₄	C₂³	1	8	yes	—
90	C₂⁴×C₄	C₂³	1	1	yes	characteristic
91	#559	C₂³	1	1024	yes	complemented
92	#556	C₂³	1	1024	yes	complemented
93	#551	C₂³	1	2048	yes	complemented
94	#542	C₂³	1	1024	yes	complemented
95	#536	C₂³	1	256	yes	complemented
96	#535	C₂³	1	256	yes	—
97	#533	C₂³	1	256	yes	complemented
98	C₂×C₄⋊Q₈	C₂³	1	48	yes	complemented
99	C₂×C₄⋊Q₈	C₂³	1	48	yes	complemented
100	C₂×#127	C₂³	1	48	yes	—
101	#529	C₂³	1	1024	yes	complemented
102	C₂×#126	C₂³	1	192	yes	complemented
103	C₂×#126	C₂³	1	192	yes	complemented
104	C₂×#125	C₂³	1	48	yes	complemented
105	C₂×#124	C₂³	1	48	yes	—
106	C₂×#124	C₂³	1	48	yes	—
107	C₂×#124	C₂³	1	96	yes	—
108	C₂×#124	C₂³	1	48	yes	—
109	C₂×#124	C₂³	1	256	yes	complemented
110	C₂×#124	C₂³	1	48	yes	complemented
111	C₂×#124	C₂³	1	192	yes	complemented
112	C₂×#123	C₂³	1	96	yes	—
113	C₂×#123	C₂³	1	192	yes	complemented
114	C₂×#123	C₂³	1	192	yes	complemented
115	C₂×C₂²⋊Q₈	C₂³	1	96	yes	—
116	C₂×C₂²⋊Q₈	C₂³	1	96	yes	complemented
117	C₂×C₂²⋊Q₈	C₂³	1	192	yes	complemented
118	C₂×#121	C₂³	1	96	yes	—
119	C₂×#120	C₂³	1	96	yes	—
120	#519	C₂³	1	256	yes	complemented
121	#518	C₂³	1	256	yes	complemented
122	C₄×#41	C₂³	1	256	yes	complemented
123	C₂×C₄×Q₈	C₂³	1	48	yes	complemented
124	C₂×C₄×Q₈	C₂³	1	96	yes	complemented
125	C₂×C₄×Q₈	C₂³	1	96	yes	complemented
126	C₂×C₄×Q₈	C₂³	1	96	yes	complemented
127	C₂×C₄×D₄	C₂³	1	96	yes	—
128	C₂×C₄×D₄	C₂³	1	96	yes	—
129	C₂×C₄×D₄	C₂³	1	96	yes	—
130	C₂×C₄×D₄	C₂³	1	48	yes	complemented
131	C₂×C₄×D₄	C₂³	1	192	yes	complemented
132	C₂×#117	C₂³	1	24	yes	—
133	C₂×#117	C₂³	1	24	yes	—
134	C₂×#117	C₂³	1	24	yes	—
135	C₂×#117	C₂³	1	96	yes	—
136	C₂×#117	C₂³	1	48	yes	complemented
137	C₂×#117	C₂³	1	192	yes	complemented
138	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂²×C₄⋊C₄	C₂³	1	8	yes	—
142	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
143	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
144	C₂²×C₄⋊C₄	C₂³	1	8	yes	—
145	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
146	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
150	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
151	C₂²×C₂²⋊C₄	C₂³	1	96	yes	—
152	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
153	C₂²×C₂²⋊C₄	C₂³	1	96	yes	—
154	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
157	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
158	C₂²×C₄²	C₂³	1	1	yes	characteristic
159	C₂²×C₄²	C₂³	1	1	yes	characteristic
160	C₂²×C₄²	C₂³	1	2	yes	—
161	C₂²×C₄²	C₂³	1	24	yes	—
162	C₂²×C₄²	C₂³	1	2	yes	—
163	C₂²×C₄²	C₂³	1	4	yes	—
164	C₂²×C₄²	C₂³	1	8	yes	—
165	C₂²×C₄²	C₂³	1	2	yes	—
166	C₂²×C₄²	C₂³	1	2	yes	—
167	C₂²×C₄²	C₂³	1	48	yes	complemented
168	C₂⁵	—	2	16	no	—
169	C₂⁵	—	4	16	no	—
170	C₂⁵	C₂⁴	1	4	yes	—
171	C₂⁵	C₂⁴	1	2	yes	—
172	C₂⁵	C₂⁴	1	1	yes	characteristic
173	C₂⁵	C₂⁴	1	24	yes	—
174	C₂×#41	—	2	192	no	—
175	C₂×#41	C₂⁴	1	64	yes	—
176	C₂²×Q₈	—	2	16	no	—
177	C₂²×Q₈	—	2	16	no	—
178	C₂²×Q₈	—	2	192	no	—
179	C₂²×Q₈	—	2	8	no	—
180	C₂²×Q₈	—	4	16	no	—
181	C₂²×Q₈	C₂⁴	1	24	yes	—
182	C₂²×Q₈	C₂⁴	1	24	yes	—
183	C₂²×Q₈	C₂⁴	1	12	yes	—
184	C₂²×Q₈	C₂⁴	1	64	yes	—
185	C₂²×Q₈	C₂⁴	1	48	yes	—
186	C₂²×D₄	—	2	16	no	—
187	C₂²×D₄	—	2	16	no	—
188	C₂²×D₄	—	2	16	no	—
189	C₂²×D₄	—	2	192	no	—
190	C₂²×D₄	—	2	8	no	—
191	C₂²×D₄	—	4	32	no	—
192	C₂²×D₄	C₂⁴	1	24	yes	—
193	C₂²×D₄	C₂⁴	1	24	yes	—
194	C₂²×D₄	C₂⁴	1	24	yes	—
195	C₂²×D₄	C₂⁴	1	12	yes	—
196	C₂²×D₄	C₂⁴	1	64	yes	—
197	C₂²×D₄	C₂⁴	1	96	yes	—
198	C₂³×C₄	—	2	16	no	—
199	C₂³×C₄	—	2	16	no	—
200	C₂³×C₄	—	4	16	no	—
201	C₂³×C₄	—	4	32	no	—
202	C₂³×C₄	—	4	8	no	—
203	C₂³×C₄	#41	1	16	yes	—
204	C₂³×C₄	C₂⁴	1	24	yes	—
205	C₂³×C₄	C₂⁴	1	24	yes	—
206	C₂³×C₄	C₂⁴	1	4	yes	—
207	C₂³×C₄	C₂⁴	1	2	yes	—
208	C₂³×C₄	C₂⁴	1	4	yes	—
209	C₂³×C₄	C₂⁴	1	2	yes	—
210	C₂³×C₄	C₂⁴	1	4	yes	—
211	C₂³×C₄	C₂⁴	1	2	yes	—
212	C₂³×C₄	C₂⁴	1	4	yes	—
213	C₂³×C₄	C₂⁴	1	24	yes	—
214	C₂³×C₄	C₂⁴	1	96	yes	—
215	C₂³×C₄	C₂⁴	1	48	yes	—
216	C₂³×C₄	C₂⁴	1	12	yes	—
217	C₂³×C₄	C₂⁴	1	1	yes	characteristic
218	C₂³×C₄	C₂⁴	1	1	yes	characteristic
219	C₄⋊Q₈	C₂⁴	1	128	yes	complemented
220	C₄⋊Q₈	C₂⁴	1	128	yes	complemented
221	#127	C₂⁴	1	128	yes	—
222	#126	C₂⁴	1	512	yes	complemented
223	#126	C₂⁴	1	512	yes	complemented
224	#125	C₂⁴	1	128	yes	complemented
225	#124	C₂⁴	1	128	yes	—
226	#124	C₂⁴	1	128	yes	—
227	#124	C₂⁴	1	256	yes	—
228	#124	C₂⁴	1	128	yes	—
229	#124	C₂⁴	1	128	yes	complemented
230	#124	C₂⁴	1	512	yes	complemented
231	#123	C₂⁴	1	256	yes	—
232	#123	C₂⁴	1	512	yes	complemented
233	#123	C₂⁴	1	512	yes	complemented
234	C₂²⋊Q₈	C₂⁴	1	256	yes	—
235	C₂²⋊Q₈	C₂⁴	1	256	yes	complemented
236	C₂²⋊Q₈	C₂⁴	1	512	yes	complemented
237	#121	C₂⁴	1	256	yes	—
238	#120	C₂⁴	1	256	yes	—
239	C₄×Q₈	C₂⁴	1	128	yes	complemented
240	C₄×Q₈	C₂⁴	1	256	yes	complemented
241	C₄×Q₈	C₂⁴	1	256	yes	complemented
242	C₄×Q₈	C₂⁴	1	256	yes	complemented
243	C₄×D₄	C₂⁴	1	256	yes	—
244	C₄×D₄	C₂⁴	1	256	yes	—
245	C₄×D₄	C₂⁴	1	256	yes	—
246	C₄×D₄	C₂⁴	1	128	yes	complemented
247	C₄×D₄	C₂⁴	1	512	yes	complemented
248	#117	C₂⁴	1	64	yes	—
249	#117	C₂⁴	1	64	yes	—
250	#117	C₂⁴	1	64	yes	—
251	#117	C₂⁴	1	256	yes	—
252	#117	C₂⁴	1	128	yes	complemented
253	#117	C₂⁴	1	512	yes	complemented
254	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
255	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
256	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
257	C₂×C₄⋊C₄	C₂⁴	1	96	yes	—
258	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
259	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
260	C₂×C₄⋊C₄	C₂⁴	1	96	yes	—
261	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
262	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
263	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
264	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
265	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
266	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
267	C₂×C₂²⋊C₄	C₂⁴	1	256	yes	—
268	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
269	C₂×C₂²⋊C₄	C₂⁴	1	256	yes	—
270	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
271	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
272	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
273	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
274	C₂×C₄²	C₂⁴	1	24	yes	—
275	C₂×C₄²	C₂⁴	1	96	yes	—
276	C₂×C₄²	C₂⁴	1	24	yes	—
277	C₂×C₄²	C₂⁴	1	24	yes	—
278	C₂×C₄²	C₂⁴	1	48	yes	—
279	C₂×C₄²	C₂⁴	1	12	yes	—
280	C₂×C₄²	C₂⁴	1	24	yes	—
281	C₂×C₄²	C₂⁴	1	64	yes	—
282	C₂×C₄²	C₂⁴	1	12	yes	—
283	C₂×C₄²	C₂⁴	1	128	yes	complemented
284	C₂⁴	—	2	8	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	—	2	16	no	—
287	C₂⁴	—	2	16	no	—
288	C₂⁴	—	2	32	no	—
289	C₂⁴	—	2	96	no	—
290	C₂⁴	—	4	96	no	—
291	C₂⁴	—	8	64	no	—
292	C₂⁴	C₂×#41	1	8	yes	—
293	C₂⁴	C₂⁵	1	24	yes	—
294	C₂⁴	C₂⁵	1	12	yes	—
295	C₂⁴	C₂⁵	1	6	yes	—
296	C₂⁴	C₂⁵	1	32	yes	—
297	C₂⁴	C₂⁵	1	1	yes	characteristic
298	#41	—	2	256	no	—
299	C₂×Q₈	—	2	96	no	—
300	C₂×Q₈	—	2	96	no	—
301	C₂×Q₈	—	2	256	no	—
302	C₂×Q₈	—	2	48	no	—
303	C₂×Q₈	—	4	96	no	—
304	C₂×Q₈	C₂⁵	1	32	yes	—
305	C₂×Q₈	C₂⁵	1	32	yes	—
306	C₂×Q₈	C₂⁵	1	16	yes	—
307	C₂×Q₈	C₂⁵	1	64	yes	—
308	C₂×D₄	—	2	96	no	—
309	C₂×D₄	—	2	96	no	—
310	C₂×D₄	—	2	96	no	—
311	C₂×D₄	—	2	256	no	—
312	C₂×D₄	—	2	48	no	—
313	C₂×D₄	—	4	192	no	—
314	C₂×D₄	C₂⁵	1	32	yes	—
315	C₂×D₄	C₂⁵	1	32	yes	—
316	C₂×D₄	C₂⁵	1	32	yes	—
317	C₂×D₄	C₂⁵	1	16	yes	—
318	C₂×D₄	C₂⁵	1	128	yes	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	96	no	—
321	C₂²×C₄	—	2	16	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	16	no	—
324	C₂²×C₄	—	2	16	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	16	no	—
327	C₂²×C₄	—	2	96	no	—
328	C₂²×C₄	—	4	96	no	—
329	C₂²×C₄	—	4	192	no	—
330	C₂²×C₄	—	4	48	no	—
331	C₂²×C₄	C₂×#41	1	8	yes	—
332	C₂²×C₄	C₂×#41	1	8	yes	—
333	C₂²×C₄	C₂×#41	1	96	yes	—
334	C₂²×C₄	C₂⁵	1	24	yes	—
335	C₂²×C₄	C₂⁵	1	12	yes	—
336	C₂²×C₄	C₂⁵	1	24	yes	—
337	C₂²×C₄	C₂⁵	1	24	yes	—
338	C₂²×C₄	C₂⁵	1	12	yes	—
339	C₂²×C₄	C₂⁵	1	12	yes	—
340	C₂²×C₄	C₂⁵	1	24	yes	—
341	C₂²×C₄	C₂⁵	1	32	yes	—
342	C₂²×C₄	C₂⁵	1	32	yes	—
343	C₂²×C₄	C₂⁵	1	32	yes	—
344	C₂²×C₄	C₂⁵	1	64	yes	—
345	C₂²×C₄	C₂⁵	1	128	yes	—
346	C₂²×C₄	C₂⁵	1	6	yes	—
347	C₂²×C₄	C₂⁵	1	6	yes	—
348	C₂²×C₄	C₂⁵	1	16	yes	—
349	C₄⋊C₄	C₂⁵	1	32	yes	—
350	C₄⋊C₄	C₂⁵	1	32	yes	—
351	C₄⋊C₄	C₂⁵	1	32	yes	—
352	C₄⋊C₄	C₂⁵	1	128	yes	—
353	C₄⋊C₄	C₂⁵	1	64	yes	—
354	C₄⋊C₄	C₂⁵	1	64	yes	—
355	C₄⋊C₄	C₂⁵	1	128	yes	—
356	C₄⋊C₄	C₂⁵	1	64	yes	—
357	C₄⋊C₄	C₂⁵	1	64	yes	—
358	C₂²⋊C₄	C₂⁵	1	32	yes	—
359	C₂²⋊C₄	C₂⁵	1	32	yes	—
360	C₂²⋊C₄	C₂⁵	1	128	yes	—
361	C₂²⋊C₄	C₂⁵	1	128	yes	—
362	C₂²⋊C₄	C₂⁵	1	128	yes	—
363	C₂²⋊C₄	C₂⁵	1	32	yes	—
364	C₂²⋊C₄	C₂⁵	1	64	yes	—
365	C₂²⋊C₄	C₂⁵	1	128	yes	—
366	C₂²⋊C₄	C₂⁵	1	128	yes	—
367	C₄²	C₂⁵	1	16	yes	—
368	C₄²	C₂⁵	1	16	yes	—
369	C₄²	C₂⁵	1	32	yes	—
370	C₄²	C₂⁵	1	32	yes	—
371	C₄²	C₂⁵	1	64	yes	—
372	C₄²	C₂⁵	1	128	yes	—
373	C₄²	C₂⁵	1	32	yes	—
374	C₄²	C₂⁵	1	32	yes	—
375	C₂³	—	2	24	no	—
376	C₂³	—	2	32	no	—
377	C₂³	—	2	24	no	—
378	C₂³	—	2	48	no	—
379	C₂³	—	2	48	no	—
380	C₂³	—	2	96	no	—
381	C₂³	—	2	64	no	—
382	C₂³	—	4	64	no	—
383	C₂³	—	4	32	no	—
384	C₂³	—	4	64	no	—
385	C₂³	—	8	192	no	—
386	C₂³	C₂²×#41	1	24	yes	—
387	C₂³	C₂²×#41	1	4	yes	—
388	C₂³	#585	1	8	yes	—
389	C₂³	C₂⁶	1	16	yes	—
390	C₂³	C₂⁶	1	8	yes	—
391	C₂³	C₂⁶	1	4	yes	—
392	C₂³	C₂⁶	1	3	yes	—
393	Q₈	—	2	64	no	—
394	Q₈	—	2	64	no	—
395	Q₈	—	2	32	no	—
396	Q₈	—	4	64	no	—
397	D₄	—	2	64	no	—
398	D₄	—	2	64	no	—
399	D₄	—	2	64	no	—
400	D₄	—	2	32	no	—
401	D₄	—	4	128	no	—
402	C₂×C₄	—	2	24	no	—
403	C₂×C₄	—	2	64	no	—
404	C₂×C₄	—	2	48	no	—
405	C₂×C₄	—	2	24	no	—
406	C₂×C₄	—	2	48	no	—
407	C₂×C₄	—	2	48	no	—
408	C₂×C₄	—	2	24	no	—
409	C₂×C₄	—	2	48	no	—
410	C₂×C₄	—	2	64	no	—
411	C₂×C₄	—	4	64	no	—
412	C₂×C₄	—	4	128	no	—
413	C₂×C₄	—	4	32	no	—
414	C₂×C₄	C₂²×#41	1	24	yes	—
415	C₂×C₄	C₂²×#41	1	24	yes	—
416	C₂×C₄	C₂²×#41	1	64	yes	—
417	C₂×C₄	C₂⁶	1	8	yes	—
418	C₂×C₄	C₂⁶	1	16	yes	—
419	C₂×C₄	C₂⁶	1	16	yes	—
420	C₂×C₄	C₂⁶	1	16	yes	—
421	C₂×C₄	C₂⁶	1	8	yes	—
422	C₂×C₄	C₂⁶	1	8	yes	—
423	C₂×C₄	C₂⁶	1	16	yes	—
424	C₂×C₄	C₂⁶	1	4	yes	—
425	C₂×C₄	C₂⁶	1	4	yes	—
426	C₂²	—	2	48	no	—
427	C₂²	—	2	8	no	—
428	C₂²	—	2	8	no	—
429	C₂²	—	2	16	no	—
430	C₂²	—	2	16	no	—
431	C₂²	—	2	32	no	—
432	C₂²	—	4	48	no	—
433	C₂²	—	4	96	no	—
434	C₂²	—	8	64	no	—
435	C₂²	#3510	1	16	yes	direct product factor
436	C₂²	C₂³×#41	1	8	yes	—
437	C₂²	C₂³×#41	1	6	yes	—
438	C₂²	C₂×#585	1	12	yes	—
439	C₂²	C₂⁷	1	1	yes	characteristic
440	C₄	—	2	8	no	—
441	C₄	—	2	16	no	—
442	C₄	—	2	8	no	—
443	C₄	—	2	16	no	—
444	C₄	—	2	16	no	—
445	C₄	—	2	8	no	—
446	C₄	—	2	16	no	—
447	C₄	C₂³×#41	1	8	yes	—
448	C₄	C₂³×#41	1	8	yes	—
449	C₂	—	2	8	no	—
450	C₂	—	4	8	no	—
451	C₂	—	4	16	no	—
452	C₂	C₂×#3510	1	12	yes	direct product factor
453	C₂	C₂⁴×#41	1	1	yes	characteristic
454	C₂	C₂²×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁷
prime radical	C₂²×#535	C₂
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×#3510	C₂	direct (N × H)
2. C₂²×#559	C₂	semidirect
3. C₂²×#556	C₂	semidirect
4. C₂²×#551	C₂	semidirect
5. C₂²×#536	C₂	semidirect
6. C₂²×#542	C₂	semidirect
8. C₂²×#533	C₂	semidirect
9. C₂²×#529	C₂	semidirect
10. C₂³×#124	C₂	semidirect
11. C₂²×#519	C₂	semidirect
12. C₂²×#518	C₂	semidirect
13. C₂²×C₄×#41	C₂	semidirect
17. #3510	C₂²	direct (N × H)
18. C₂×#559	C₂²	semidirect
19. C₂×#556	C₂²	semidirect
20. C₂×#551	C₂²	semidirect
21. C₂×#542	C₂²	semidirect
22. C₂×#536	C₂²	semidirect
24. C₂×#533	C₂²	semidirect
25. C₂²×C₄⋊Q₈	C₂²	semidirect
26. C₂²×C₄⋊Q₈	C₂²	semidirect
28. C₂×#529	C₂²	semidirect
29. C₂²×#126	C₂²	semidirect
30. C₂²×#126	C₂²	semidirect
31. C₂²×#125	C₂²	semidirect
36. C₂²×#124	C₂²	semidirect
37. C₂²×#124	C₂²	semidirect
38. C₂²×#124	C₂²	semidirect
40. C₂²×#123	C₂²	semidirect
41. C₂²×#123	C₂²	semidirect
43. C₂²×C₂²⋊Q₈	C₂²	semidirect
44. C₂²×C₂²⋊Q₈	C₂²	semidirect
47. C₂×#519	C₂²	semidirect
48. C₂×#518	C₂²	semidirect
49. C₂×C₄×#41	C₂²	semidirect
50. C₂²×C₄×Q₈	C₂²	semidirect
51. C₂²×C₄×Q₈	C₂²	semidirect
52. C₂²×C₄×Q₈	C₂²	semidirect
53. C₂²×C₄×Q₈	C₂²	semidirect
57. C₂²×C₄×D₄	C₂²	semidirect
58. C₂²×C₄×D₄	C₂²	semidirect
63. C₂²×#117	C₂²	semidirect
64. C₂²×#117	C₂²	semidirect
68. C₂³×C₄²	C₂²	semidirect
91. #559	C₂³	semidirect
92. #556	C₂³	semidirect
93. #551	C₂³	semidirect
94. #542	C₂³	semidirect
95. #536	C₂³	semidirect
97. #533	C₂³	semidirect
98. C₂×C₄⋊Q₈	C₂³	semidirect
99. C₂×C₄⋊Q₈	C₂³	semidirect
101. #529	C₂³	semidirect
102. C₂×#126	C₂³	semidirect
103. C₂×#126	C₂³	semidirect
104. C₂×#125	C₂³	semidirect
109. C₂×#124	C₂³	semidirect
110. C₂×#124	C₂³	semidirect
111. C₂×#124	C₂³	semidirect
113. C₂×#123	C₂³	semidirect
114. C₂×#123	C₂³	semidirect
116. C₂×C₂²⋊Q₈	C₂³	semidirect
117. C₂×C₂²⋊Q₈	C₂³	semidirect
120. #519	C₂³	semidirect
121. #518	C₂³	semidirect
122. C₄×#41	C₂³	semidirect
123. C₂×C₄×Q₈	C₂³	semidirect
124. C₂×C₄×Q₈	C₂³	semidirect
125. C₂×C₄×Q₈	C₂³	semidirect
126. C₂×C₄×Q₈	C₂³	semidirect
130. C₂×C₄×D₄	C₂³	semidirect
131. C₂×C₄×D₄	C₂³	semidirect
136. C₂×#117	C₂³	semidirect
137. C₂×#117	C₂³	semidirect
167. C₂²×C₄²	C₂³	semidirect
219. C₄⋊Q₈	C₂⁴	semidirect
220. C₄⋊Q₈	C₂⁴	semidirect
222. #126	C₂⁴	semidirect
223. #126	C₂⁴	semidirect
224. #125	C₂⁴	semidirect
229. #124	C₂⁴	semidirect
230. #124	C₂⁴	semidirect
232. #123	C₂⁴	semidirect
233. #123	C₂⁴	semidirect
235. C₂²⋊Q₈	C₂⁴	semidirect
236. C₂²⋊Q₈	C₂⁴	semidirect
239. C₄×Q₈	C₂⁴	semidirect
240. C₄×Q₈	C₂⁴	semidirect
241. C₄×Q₈	C₂⁴	semidirect
242. C₄×Q₈	C₂⁴	semidirect
246. C₄×D₄	C₂⁴	semidirect
247. C₄×D₄	C₂⁴	semidirect
252. #117	C₂⁴	semidirect
253. #117	C₂⁴	semidirect
283. C₂×C₄²	C₂⁴	semidirect
435. C₂²	#3510	direct (N × H)
452. C₂	C₂×#3510	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×#3510	2
C₂²×#559	2
C₂²×#556	2
C₂²×#551	2
C₂²×#536	2
C₂²×#542	2
C₂²×#535	2
C₂²×#533	2
C₂²×#529	2
C₂³×#124	2
C₂²×#519	2
C₂²×#518	2
C₂²×C₄×#41	2

Subgroups — C22×#3510 #10585986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#3510 #10585986