Subgroups — C₂²×#3545 #10586153

Order 512.

35914 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3545	C₂	1	96	yes	maximal, direct product factor
2	C₂²×#555	C₂	1	2	yes	maximal, complemented
3	C₂²×#551	C₂	1	2	yes	maximal, complemented
4	C₂²×#551	C₂	1	4	yes	maximal, complemented
5	C₂²×#546	C₂	1	4	yes	maximal, complemented
6	C₂²×#563	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#562	C₂	1	2	yes	maximal, complemented
8	C₂²×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#536	C₂	1	2	yes	maximal, complemented
10	C₂²×#542	C₂	1	4	yes	maximal, complemented
11	C₂²×#538	C₂	1	4	yes	maximal, complemented
12	C₂²×#534	C₂	1	2	yes	maximal, complemented
13	C₂²×#529	C₂	1	2	yes	maximal, complemented
14	C₂³×#124	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×#41	C₂²	1	2	yes	—
16	C₂⁴×Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×D₄	C₂²	1	1	yes	characteristic
18	C₂⁴×D₄	C₂²	1	2	yes	complemented
19	#3545	C₂²	1	1024	yes	direct product factor
20	C₂×#563	C₂²	1	48	yes	complemented
21	C₂×#562	C₂²	1	96	yes	complemented
22	C₂×H(3,𝔽₄)	C₂²	1	48	yes	complemented
23	C₂×#555	C₂²	1	96	yes	complemented
24	C₂×#551	C₂²	1	96	yes	complemented
25	C₂×#551	C₂²	1	192	yes	complemented
26	C₂×#546	C₂²	1	192	yes	complemented
27	C₂×#542	C₂²	1	192	yes	complemented
28	C₂×#538	C₂²	1	192	yes	complemented
29	C₂×#536	C₂²	1	96	yes	complemented
30	C₂×#534	C₂²	1	96	yes	complemented
31	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
33	C₂×#529	C₂²	1	96	yes	complemented
34	C₂²×#126	C₂²	1	4	yes	complemented
35	C₂²×#126	C₂²	1	4	yes	complemented
36	C₂²×#126	C₂²	1	4	yes	complemented
37	C₂²×#125	C₂²	1	2	yes	complemented
38	C₂²×#124	C₂²	1	1	yes	characteristic
39	C₂²×#124	C₂²	1	1	yes	characteristic
40	C₂²×#124	C₂²	1	4	yes	complemented
41	C₂²×#124	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#124	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#124	C₂²	1	2	yes	complemented
44	C₂²×#124	C₂²	1	2	yes	complemented
45	C₂²×#124	C₂²	1	4	yes	complemented
46	C₂²×#124	C₂²	1	4	yes	complemented
47	C₂²×#124	C₂²	1	2	yes	complemented
48	C₂²×#124	C₂²	1	48	yes	complemented
49	C₂²×#123	C₂²	1	2	yes	—
50	C₂²×#123	C₂²	1	4	yes	complemented
51	C₂²×#123	C₂²	1	2	yes	complemented
52	C₂²×#123	C₂²	1	4	yes	complemented
53	C₂²×#123	C₂²	1	4	yes	complemented
54	C₂²×#123	C₂²	1	4	yes	complemented
55	C₂²×#123	C₂²	1	4	yes	complemented
56	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	C₂²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
58	C₂²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
59	C₂²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
61	C₂²×#121	C₂²	1	2	yes	—
62	C₂²×#121	C₂²	1	4	yes	—
63	C₂²×#121	C₂²	1	4	yes	complemented
64	C₂²×#121	C₂²	1	4	yes	complemented
65	C₂²×#121	C₂²	1	4	yes	complemented
66	C₂²×#120	C₂²	1	2	yes	—
67	C₂²×#120	C₂²	1	4	yes	—
68	C₂²×#120	C₂²	1	2	yes	complemented
69	C₂²×#120	C₂²	1	4	yes	complemented
70	C₂²×C₄×Q₈	C₂²	1	2	yes	complemented
71	C₂²×C₄×D₄	C₂²	1	2	yes	complemented
72	C₂²×C₄×D₄	C₂²	1	4	yes	complemented
73	C₂²×C₄×D₄	C₂²	1	4	yes	complemented
74	C₂²×C₄×D₄	C₂²	1	4	yes	complemented
75	C₂²×#117	C₂²	1	4	yes	complemented
76	C₂²×#117	C₂²	1	4	yes	complemented
77	C₂²×#117	C₂²	1	2	yes	complemented
78	C₂³×C₂²⋊C₄	C₂²	1	4	yes	complemented
79	C₂³×C₂²⋊C₄	C₂²	1	2	yes	complemented
80	C₂³×C₂²⋊C₄	C₂²	1	4	yes	complemented
81	C₂³×C₄²	C₂²	1	1	yes	characteristic, complemented
82	C₂⁶	C₂³	1	2	yes	—
83	C₂⁶	C₂³	1	2	yes	—
84	C₂²×#41	—	4	16	no	—
85	C₂²×#41	C₂³	1	48	yes	—
86	C₂³×Q₈	—	4	8	no	—
87	C₂³×Q₈	C₂³	1	1	yes	characteristic
88	C₂³×Q₈	C₂³	1	2	yes	—
89	C₂³×Q₈	C₂³	1	1	yes	characteristic
90	C₂³×Q₈	C₂³	1	2	yes	—
91	C₂³×Q₈	C₂³	1	2	yes	—
92	C₂³×Q₈	C₂³	1	24	yes	complemented
93	C₂³×D₄	—	4	8	no	—
94	C₂³×D₄	—	4	16	no	—
95	C₂³×D₄	C₂³	1	4	yes	—
96	C₂³×D₄	C₂³	1	1	yes	characteristic
97	C₂³×D₄	C₂³	1	2	yes	—
98	C₂³×D₄	C₂³	1	1	yes	characteristic
99	C₂³×D₄	C₂³	1	24	yes	—
100	C₂³×D₄	C₂³	1	4	yes	—
101	C₂³×D₄	C₂³	1	2	yes	—
102	C₂³×D₄	C₂³	1	4	yes	—
103	C₂³×D₄	C₂³	1	4	yes	—
104	C₂³×D₄	C₂³	1	2	yes	—
105	C₂³×D₄	C₂³	1	48	yes	complemented
106	C₂⁴×C₄	C₂³	1	1	yes	characteristic
107	C₂⁴×C₄	C₂³	1	2	yes	—
108	C₂⁴×C₄	C₂³	1	2	yes	—
109	C₂⁴×C₄	C₂³	1	4	yes	—
110	C₂⁴×C₄	C₂³	1	2	yes	—
111	C₂⁴×C₄	C₂³	1	4	yes	—
112	C₂⁴×C₄	C₂³	1	4	yes	—
113	#563	C₂³	1	256	yes	complemented
114	#562	C₂³	1	512	yes	complemented
115	H(3,𝔽₄)	C₂³	1	256	yes	complemented
116	#555	C₂³	1	512	yes	complemented
117	#551	C₂³	1	512	yes	complemented
118	#551	C₂³	1	1024	yes	complemented
119	#546	C₂³	1	1024	yes	complemented
120	#542	C₂³	1	1024	yes	complemented
121	#538	C₂³	1	1024	yes	complemented
122	#536	C₂³	1	512	yes	complemented
123	#534	C₂³	1	512	yes	complemented
124	C₂×C₄⋊Q₈	C₂³	1	48	yes	complemented
125	C₂×C₄⋊Q₈	C₂³	1	48	yes	complemented
126	#529	C₂³	1	512	yes	complemented
127	C₂×#126	C₂³	1	96	yes	complemented
128	C₂×#126	C₂³	1	96	yes	complemented
129	C₂×#126	C₂³	1	96	yes	complemented
130	C₂×#125	C₂³	1	48	yes	complemented
131	C₂×#124	C₂³	1	24	yes	—
132	C₂×#124	C₂³	1	24	yes	—
133	C₂×#124	C₂³	1	96	yes	complemented
134	C₂×#124	C₂³	1	24	yes	complemented
135	C₂×#124	C₂³	1	24	yes	complemented
136	C₂×#124	C₂³	1	48	yes	complemented
137	C₂×#124	C₂³	1	48	yes	complemented
138	C₂×#124	C₂³	1	48	yes	complemented
139	C₂×#124	C₂³	1	96	yes	complemented
140	C₂×#124	C₂³	1	96	yes	complemented
141	C₂×#124	C₂³	1	256	yes	complemented
142	C₂×#123	C₂³	1	48	yes	—
143	C₂×#123	C₂³	1	96	yes	complemented
144	C₂×#123	C₂³	1	48	yes	complemented
145	C₂×#123	C₂³	1	96	yes	complemented
146	C₂×#123	C₂³	1	96	yes	complemented
147	C₂×#123	C₂³	1	96	yes	complemented
148	C₂×#123	C₂³	1	96	yes	complemented
149	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
150	C₂×C₂²⋊Q₈	C₂³	1	96	yes	complemented
151	C₂×C₂²⋊Q₈	C₂³	1	96	yes	complemented
152	C₂×C₂²⋊Q₈	C₂³	1	96	yes	complemented
153	C₂×C₂²⋊Q₈	C₂³	1	96	yes	complemented
154	C₂×#121	C₂³	1	48	yes	—
155	C₂×#121	C₂³	1	96	yes	—
156	C₂×#121	C₂³	1	96	yes	complemented
157	C₂×#121	C₂³	1	96	yes	complemented
158	C₂×#121	C₂³	1	96	yes	complemented
159	C₂×#120	C₂³	1	96	yes	—
160	C₂×#120	C₂³	1	48	yes	—
161	C₂×#120	C₂³	1	48	yes	complemented
162	C₂×#120	C₂³	1	96	yes	complemented
163	C₂×C₄×Q₈	C₂³	1	48	yes	complemented
164	C₂×C₄×D₄	C₂³	1	48	yes	complemented
165	C₂×C₄×D₄	C₂³	1	96	yes	complemented
166	C₂×C₄×D₄	C₂³	1	96	yes	complemented
167	C₂×C₄×D₄	C₂³	1	96	yes	complemented
168	C₂×#117	C₂³	1	96	yes	complemented
169	C₂×#117	C₂³	1	48	yes	complemented
170	C₂×#117	C₂³	1	96	yes	complemented
171	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
172	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
173	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
174	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
175	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
176	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
177	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
180	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
181	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
182	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
183	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
184	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
185	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
187	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
189	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
190	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
191	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
192	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
193	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
195	C₂²×C₂²⋊C₄	C₂³	1	96	yes	complemented
196	C₂²×C₂²⋊C₄	C₂³	1	48	yes	complemented
197	C₂²×C₂²⋊C₄	C₂³	1	96	yes	complemented
198	C₂²×C₄²	C₂³	1	1	yes	characteristic
199	C₂²×C₄²	C₂³	1	2	yes	—
200	C₂²×C₄²	C₂³	1	1	yes	characteristic
201	C₂²×C₄²	C₂³	1	2	yes	—
202	C₂²×C₄²	C₂³	1	4	yes	—
203	C₂²×C₄²	C₂³	1	2	yes	—
204	C₂²×C₄²	C₂³	1	24	yes	complemented
205	C₂⁵	—	2	16	no	—
206	C₂⁵	—	4	8	no	—
207	C₂⁵	—	4	16	no	—
208	C₂⁵	—	4	16	no	—
209	C₂⁵	C₂⁴	1	2	yes	—
210	C₂⁵	C₂⁴	1	4	yes	—
211	C₂⁵	C₂⁴	1	2	yes	—
212	C₂⁵	C₂⁴	1	1	yes	characteristic
213	C₂⁵	C₂⁴	1	24	yes	—
214	C₂⁵	C₂⁴	1	24	yes	—
215	C₂×#41	—	4	192	no	—
216	C₂×#41	C₂⁴	1	128	yes	—
217	C₂²×Q₈	—	4	4	no	—
218	C₂²×Q₈	—	4	8	no	—
219	C₂²×Q₈	—	4	4	no	—
220	C₂²×Q₈	—	4	96	no	—
221	C₂²×Q₈	—	4	8	no	—
222	C₂²×Q₈	—	4	8	no	—
223	C₂²×Q₈	C₂⁴	1	24	yes	—
224	C₂²×Q₈	C₂⁴	1	12	yes	—
225	C₂²×Q₈	C₂⁴	1	24	yes	—
226	C₂²×Q₈	C₂⁴	1	24	yes	—
227	C₂²×Q₈	C₂⁴	1	12	yes	—
228	C₂²×Q₈	C₂⁴	1	64	yes	complemented
229	C₂²×D₄	—	2	32	no	—
230	C₂²×D₄	—	4	4	no	—
231	C₂²×D₄	—	4	8	no	—
232	C₂²×D₄	—	4	4	no	—
233	C₂²×D₄	—	4	96	no	—
234	C₂²×D₄	—	4	16	no	—
235	C₂²×D₄	—	4	16	no	—
236	C₂²×D₄	—	4	16	no	—
237	C₂²×D₄	—	4	8	no	—
238	C₂²×D₄	—	4	8	no	—
239	C₂²×D₄	—	4	192	no	—
240	C₂²×D₄	C₂⁴	1	48	yes	—
241	C₂²×D₄	C₂⁴	1	48	yes	—
242	C₂²×D₄	C₂⁴	1	48	yes	—
243	C₂²×D₄	C₂⁴	1	24	yes	—
244	C₂²×D₄	C₂⁴	1	12	yes	—
245	C₂²×D₄	C₂⁴	1	24	yes	—
246	C₂²×D₄	C₂⁴	1	24	yes	—
247	C₂²×D₄	C₂⁴	1	48	yes	—
248	C₂²×D₄	C₂⁴	1	12	yes	—
249	C₂²×D₄	C₂⁴	1	64	yes	—
250	C₂²×D₄	C₂⁴	1	128	yes	complemented
251	C₂³×C₄	—	2	8	no	—
252	C₂³×C₄	—	2	16	no	—
253	C₂³×C₄	—	4	16	no	—
254	C₂³×C₄	—	4	8	no	—
255	C₂³×C₄	—	4	16	no	—
256	C₂³×C₄	—	4	8	no	—
257	C₂³×C₄	—	4	16	no	—
258	C₂³×C₄	C₂⁴	1	24	yes	—
259	C₂³×C₄	C₂⁴	1	12	yes	—
260	C₂³×C₄	C₂⁴	1	2	yes	—
261	C₂³×C₄	C₂⁴	1	4	yes	—
262	C₂³×C₄	C₂⁴	1	2	yes	—
263	C₂³×C₄	C₂⁴	1	2	yes	—
264	C₂³×C₄	C₂⁴	1	2	yes	—
265	C₂³×C₄	C₂⁴	1	4	yes	—
266	C₂³×C₄	C₂⁴	1	1	yes	characteristic
267	C₂³×C₄	C₂⁴	1	1	yes	characteristic
268	C₂³×C₄	C₂⁴	1	4	yes	—
269	C₂³×C₄	C₂⁴	1	24	yes	—
270	C₂³×C₄	C₂⁴	1	48	yes	—
271	C₂³×C₄	C₂⁴	1	48	yes	—
272	C₂³×C₄	C₂⁴	1	48	yes	—
273	C₂³×C₄	C₂⁴	1	24	yes	—
274	C₄⋊Q₈	C₂⁴	1	128	yes	complemented
275	C₄⋊Q₈	C₂⁴	1	128	yes	complemented
276	#126	C₂⁴	1	256	yes	complemented
277	#126	C₂⁴	1	256	yes	complemented
278	#126	C₂⁴	1	256	yes	complemented
279	#125	C₂⁴	1	128	yes	complemented
280	#124	C₂⁴	1	64	yes	—
281	#124	C₂⁴	1	64	yes	—
282	#124	C₂⁴	1	256	yes	complemented
283	#124	C₂⁴	1	64	yes	complemented
284	#124	C₂⁴	1	64	yes	complemented
285	#124	C₂⁴	1	128	yes	complemented
286	#124	C₂⁴	1	128	yes	complemented
287	#124	C₂⁴	1	128	yes	complemented
288	#124	C₂⁴	1	256	yes	complemented
289	#124	C₂⁴	1	256	yes	complemented
290	#123	C₂⁴	1	128	yes	—
291	#123	C₂⁴	1	256	yes	complemented
292	#123	C₂⁴	1	128	yes	complemented
293	#123	C₂⁴	1	256	yes	complemented
294	#123	C₂⁴	1	256	yes	complemented
295	#123	C₂⁴	1	256	yes	complemented
296	#123	C₂⁴	1	256	yes	complemented
297	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
298	C₂²⋊Q₈	C₂⁴	1	256	yes	complemented
299	C₂²⋊Q₈	C₂⁴	1	256	yes	complemented
300	C₂²⋊Q₈	C₂⁴	1	256	yes	complemented
301	C₂²⋊Q₈	C₂⁴	1	256	yes	complemented
302	#121	C₂⁴	1	128	yes	—
303	#121	C₂⁴	1	256	yes	—
304	#121	C₂⁴	1	256	yes	complemented
305	#121	C₂⁴	1	256	yes	complemented
306	#121	C₂⁴	1	256	yes	complemented
307	#120	C₂⁴	1	256	yes	—
308	#120	C₂⁴	1	128	yes	—
309	#120	C₂⁴	1	128	yes	complemented
310	#120	C₂⁴	1	256	yes	complemented
311	C₄×Q₈	C₂⁴	1	128	yes	complemented
312	C₄×D₄	C₂⁴	1	128	yes	complemented
313	C₄×D₄	C₂⁴	1	256	yes	complemented
314	C₄×D₄	C₂⁴	1	256	yes	complemented
315	C₄×D₄	C₂⁴	1	256	yes	complemented
316	#117	C₂⁴	1	256	yes	complemented
317	#117	C₂⁴	1	128	yes	complemented
318	#117	C₂⁴	1	256	yes	complemented
319	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
320	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
321	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
322	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
323	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
324	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
325	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
326	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
327	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
328	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
329	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
330	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
331	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
332	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
333	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
334	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
335	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
336	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
337	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
338	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
339	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
340	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
341	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
342	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
343	C₂×C₂²⋊C₄	C₂⁴	1	256	yes	complemented
344	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	complemented
345	C₂×C₂²⋊C₄	C₂⁴	1	256	yes	complemented
346	C₂×C₄²	C₂⁴	1	12	yes	—
347	C₂×C₄²	C₂⁴	1	24	yes	—
348	C₂×C₄²	C₂⁴	1	48	yes	—
349	C₂×C₄²	C₂⁴	1	24	yes	—
350	C₂×C₄²	C₂⁴	1	24	yes	—
351	C₂×C₄²	C₂⁴	1	12	yes	—
352	C₂×C₄²	C₂⁴	1	64	yes	complemented
353	C₂⁴	—	2	8	no	—
354	C₂⁴	—	2	16	no	—
355	C₂⁴	—	2	8	no	—
356	C₂⁴	—	2	8	no	—
357	C₂⁴	—	2	16	no	—
358	C₂⁴	—	2	16	no	—
359	C₂⁴	—	2	16	no	—
360	C₂⁴	—	2	16	no	—
361	C₂⁴	—	2	96	no	—
362	C₂⁴	—	4	48	no	—
363	C₂⁴	—	4	96	no	—
364	C₂⁴	—	4	96	no	—
365	C₂⁴	—	8	64	no	—
366	C₂⁴	—	8	64	no	—
367	C₂⁴	H(5,𝔽₂)	1	8	yes	—
368	C₂⁴	C₂⁵	1	12	yes	—
369	C₂⁴	C₂⁵	1	24	yes	—
370	C₂⁴	C₂⁵	1	12	yes	—
371	C₂⁴	C₂⁵	1	6	yes	—
372	C₂⁴	C₂⁵	1	32	yes	—
373	C₂⁴	C₂⁵	1	32	yes	—
374	C₂⁴	C₂⁵	1	1	yes	characteristic
375	#41	—	4	256	no	—
376	C₂×Q₈	—	4	24	no	—
377	C₂×Q₈	—	4	48	no	—
378	C₂×Q₈	—	4	24	no	—
379	C₂×Q₈	—	4	128	no	—
380	C₂×Q₈	—	4	48	no	—
381	C₂×Q₈	—	4	48	no	—
382	C₂×Q₈	C₂⁵	1	32	yes	—
383	C₂×Q₈	C₂⁵	1	16	yes	—
384	C₂×Q₈	C₂⁵	1	32	yes	—
385	C₂×Q₈	C₂⁵	1	32	yes	—
386	C₂×Q₈	C₂⁵	1	16	yes	—
387	C₂×D₄	—	2	192	no	—
388	C₂×D₄	—	4	24	no	—
389	C₂×D₄	—	4	48	no	—
390	C₂×D₄	—	4	24	no	—
391	C₂×D₄	—	4	128	no	—
392	C₂×D₄	—	4	96	no	—
393	C₂×D₄	—	4	96	no	—
394	C₂×D₄	—	4	96	no	—
395	C₂×D₄	—	4	48	no	—
396	C₂×D₄	—	4	48	no	—
397	C₂×D₄	—	4	256	no	—
398	C₂×D₄	C₂⁵	1	64	yes	—
399	C₂×D₄	C₂⁵	1	64	yes	—
400	C₂×D₄	C₂⁵	1	64	yes	—
401	C₂×D₄	C₂⁵	1	32	yes	—
402	C₂×D₄	C₂⁵	1	16	yes	—
403	C₂×D₄	C₂⁵	1	32	yes	—
404	C₂×D₄	C₂⁵	1	32	yes	—
405	C₂×D₄	C₂⁵	1	64	yes	—
406	C₂×D₄	C₂⁵	1	16	yes	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	2	48	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	2	96	no	—
413	C₂²×C₄	—	2	16	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	16	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	2	16	no	—
418	C₂²×C₄	—	4	96	no	—
419	C₂²×C₄	—	4	48	no	—
420	C₂²×C₄	—	4	96	no	—
421	C₂²×C₄	—	4	48	no	—
422	C₂²×C₄	—	4	96	no	—
423	C₂²×C₄	C₂⁵	1	12	yes	—
424	C₂²×C₄	C₂⁵	1	24	yes	—
425	C₂²×C₄	C₂⁵	1	12	yes	—
426	C₂²×C₄	C₂⁵	1	12	yes	—
427	C₂²×C₄	C₂⁵	1	6	yes	—
428	C₂²×C₄	C₂⁵	1	6	yes	—
429	C₂²×C₄	C₂⁵	1	24	yes	—
430	C₂²×C₄	C₂⁵	1	24	yes	—
431	C₂²×C₄	C₂⁵	1	16	yes	—
432	C₂²×C₄	C₂⁵	1	12	yes	—
433	C₂²×C₄	C₂⁵	1	32	yes	—
434	C₂²×C₄	C₂⁵	1	32	yes	—
435	C₂²×C₄	C₂⁵	1	64	yes	—
436	C₂²×C₄	C₂⁵	1	64	yes	—
437	C₂²×C₄	C₂⁵	1	64	yes	—
438	C₂²×C₄	C₂⁵	1	32	yes	—
439	C₄⋊C₄	C₂⁵	1	64	yes	—
440	C₄⋊C₄	C₂⁵	1	64	yes	—
441	C₄⋊C₄	C₂⁵	1	64	yes	—
442	C₄⋊C₄	C₂⁵	1	64	yes	—
443	C₄⋊C₄	C₂⁵	1	64	yes	—
444	C₄⋊C₄	C₂⁵	1	64	yes	—
445	C₄⋊C₄	C₂⁵	1	32	yes	—
446	C₄⋊C₄	C₂⁵	1	32	yes	—
447	C₄⋊C₄	C₂⁵	1	64	yes	—
448	C₂²⋊C₄	C₂⁵	1	64	yes	—
449	C₂²⋊C₄	C₂⁵	1	64	yes	—
450	C₂²⋊C₄	C₂⁵	1	64	yes	—
451	C₂²⋊C₄	C₂⁵	1	64	yes	—
452	C₂²⋊C₄	C₂⁵	1	64	yes	—
453	C₂²⋊C₄	C₂⁵	1	32	yes	—
454	C₂²⋊C₄	C₂⁵	1	64	yes	—
455	C₂²⋊C₄	C₂⁵	1	32	yes	—
456	C₂²⋊C₄	C₂⁵	1	64	yes	—
457	C₂²⋊C₄	C₂⁵	1	64	yes	—
458	C₂²⋊C₄	C₂⁵	1	64	yes	—
459	C₂²⋊C₄	C₂⁵	1	64	yes	—
460	C₂²⋊C₄	C₂⁵	1	64	yes	—
461	C₂²⋊C₄	C₂⁵	1	64	yes	—
462	C₂²⋊C₄	C₂⁵	1	64	yes	—
463	C₄²	C₂⁵	1	16	yes	—
464	C₄²	C₂⁵	1	32	yes	—
465	C₄²	C₂⁵	1	16	yes	—
466	C₄²	C₂⁵	1	32	yes	—
467	C₄²	C₂⁵	1	64	yes	—
468	C₄²	C₂⁵	1	32	yes	—
469	C₂³	—	2	24	no	—
470	C₂³	—	2	32	no	—
471	C₂³	—	2	48	no	—
472	C₂³	—	2	24	no	—
473	C₂³	—	2	24	no	—
474	C₂³	—	2	48	no	—
475	C₂³	—	2	48	no	—
476	C₂³	—	2	48	no	—
477	C₂³	—	2	48	no	—
478	C₂³	—	2	64	no	—
479	C₂³	—	4	32	no	—
480	C₂³	—	4	64	no	—
481	C₂³	—	4	64	no	—
482	C₂³	—	4	64	no	—
483	C₂³	—	4	32	no	—
484	C₂³	—	4	32	no	—
485	C₂³	—	8	192	no	—
486	C₂³	—	8	192	no	—
487	C₂³	C₂×H(5,𝔽₂)	1	24	yes	—
488	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
489	C₂³	#585	1	8	yes	—
490	C₂³	C₂⁶	1	8	yes	—
491	C₂³	C₂⁶	1	16	yes	—
492	C₂³	C₂⁶	1	8	yes	—
493	C₂³	C₂⁶	1	4	yes	—
494	C₂³	C₂⁶	1	3	yes	—
495	Q₈	—	4	16	no	—
496	Q₈	—	4	32	no	—
497	Q₈	—	4	16	no	—
498	Q₈	—	4	32	no	—
499	Q₈	—	4	32	no	—
500	D₄	—	2	128	no	—
501	D₄	—	4	16	no	—
502	D₄	—	4	32	no	—
503	D₄	—	4	16	no	—
504	D₄	—	4	64	no	—
505	D₄	—	4	64	no	—
506	D₄	—	4	64	no	—
507	D₄	—	4	32	no	—
508	D₄	—	4	32	no	—
509	C₂×C₄	—	2	24	no	—
510	C₂×C₄	—	2	32	no	—
511	C₂×C₄	—	2	12	no	—
512	C₂×C₄	—	2	12	no	—
513	C₂×C₄	—	2	24	no	—
514	C₂×C₄	—	2	64	no	—
515	C₂×C₄	—	2	48	no	—
516	C₂×C₄	—	2	24	no	—
517	C₂×C₄	—	2	48	no	—
518	C₂×C₄	—	2	24	no	—
519	C₂×C₄	—	2	48	no	—
520	C₂×C₄	—	4	64	no	—
521	C₂×C₄	—	4	32	no	—
522	C₂×C₄	—	4	64	no	—
523	C₂×C₄	—	4	32	no	—
524	C₂×C₄	—	4	64	no	—
525	C₂×C₄	C₂⁶	1	8	yes	—
526	C₂×C₄	C₂⁶	1	8	yes	—
527	C₂×C₄	C₂⁶	1	16	yes	—
528	C₂×C₄	C₂⁶	1	8	yes	—
529	C₂×C₄	C₂⁶	1	4	yes	—
530	C₂×C₄	C₂⁶	1	4	yes	—
531	C₂×C₄	C₂⁶	1	16	yes	—
532	C₂×C₄	C₂⁶	1	16	yes	—
533	C₂×C₄	C₂⁶	1	8	yes	—
534	C₂²	—	2	48	no	—
535	C₂²	—	2	8	no	—
536	C₂²	—	2	16	no	—
537	C₂²	—	2	8	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	16	no	—
540	C₂²	—	2	16	no	—
541	C₂²	—	2	16	no	—
542	C₂²	—	2	16	no	—
543	C₂²	—	4	96	no	—
544	C₂²	—	4	48	no	—
545	C₂²	—	4	48	no	—
546	C₂²	—	8	64	no	—
547	C₂²	—	8	64	no	—
548	C₂²	#3545	1	16	yes	direct product factor
549	C₂²	C₂²×H(5,𝔽₂)	1	8	yes	—
550	C₂²	C₂²×H(5,𝔽₂)	1	6	yes	—
551	C₂²	C₂×#585	1	12	yes	—
552	C₂²	C₂⁷	1	1	yes	characteristic
553	C₄	—	2	8	no	—
554	C₄	—	2	4	no	—
555	C₄	—	2	4	no	—
556	C₄	—	2	8	no	—
557	C₄	—	2	16	no	—
558	C₄	—	2	8	no	—
559	C₄	—	2	16	no	—
560	C₄	—	2	8	no	—
561	C₄	—	2	16	no	—
562	C₂	—	2	8	no	—
563	C₂	—	4	16	no	—
564	C₂	—	4	8	no	—
565	C₂	—	4	8	no	—
566	C₂	C₂×#3545	1	12	yes	direct product factor
567	C₂	C₂³×H(5,𝔽₂)	1	1	yes	characteristic
568	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×#3545	C₂	direct (N × H)
2. C₂²×#555	C₂	semidirect
3. C₂²×#551	C₂	semidirect
4. C₂²×#551	C₂	semidirect
5. C₂²×#546	C₂	semidirect
6. C₂²×#563	C₂	semidirect
7. C₂²×#562	C₂	semidirect
8. C₂²×H(3,𝔽₄)	C₂	semidirect
9. C₂²×#536	C₂	semidirect
10. C₂²×#542	C₂	semidirect
11. C₂²×#538	C₂	semidirect
12. C₂²×#534	C₂	semidirect
13. C₂²×#529	C₂	semidirect
14. C₂³×#124	C₂	semidirect
16. C₂⁴×Q₈	C₂²	semidirect
18. C₂⁴×D₄	C₂²	semidirect
19. #3545	C₂²	direct (N × H)
20. C₂×#563	C₂²	semidirect
21. C₂×#562	C₂²	semidirect
22. C₂×H(3,𝔽₄)	C₂²	semidirect
23. C₂×#555	C₂²	semidirect
24. C₂×#551	C₂²	semidirect
25. C₂×#551	C₂²	semidirect
26. C₂×#546	C₂²	semidirect
27. C₂×#542	C₂²	semidirect
28. C₂×#538	C₂²	semidirect
29. C₂×#536	C₂²	semidirect
30. C₂×#534	C₂²	semidirect
31. C₂²×C₄⋊Q₈	C₂²	semidirect
32. C₂²×C₄⋊Q₈	C₂²	semidirect
33. C₂×#529	C₂²	semidirect
34. C₂²×#126	C₂²	semidirect
35. C₂²×#126	C₂²	semidirect
36. C₂²×#126	C₂²	semidirect
37. C₂²×#125	C₂²	semidirect
40. C₂²×#124	C₂²	semidirect
41. C₂²×#124	C₂²	semidirect
42. C₂²×#124	C₂²	semidirect
43. C₂²×#124	C₂²	semidirect
44. C₂²×#124	C₂²	semidirect
45. C₂²×#124	C₂²	semidirect
46. C₂²×#124	C₂²	semidirect
47. C₂²×#124	C₂²	semidirect
48. C₂²×#124	C₂²	semidirect
50. C₂²×#123	C₂²	semidirect
51. C₂²×#123	C₂²	semidirect
52. C₂²×#123	C₂²	semidirect
53. C₂²×#123	C₂²	semidirect
54. C₂²×#123	C₂²	semidirect
55. C₂²×#123	C₂²	semidirect
56. C₂²×C₂²⋊Q₈	C₂²	semidirect
57. C₂²×C₂²⋊Q₈	C₂²	semidirect
58. C₂²×C₂²⋊Q₈	C₂²	semidirect
59. C₂²×C₂²⋊Q₈	C₂²	semidirect
60. C₂²×C₂²⋊Q₈	C₂²	semidirect
63. C₂²×#121	C₂²	semidirect
64. C₂²×#121	C₂²	semidirect
65. C₂²×#121	C₂²	semidirect
68. C₂²×#120	C₂²	semidirect
69. C₂²×#120	C₂²	semidirect
70. C₂²×C₄×Q₈	C₂²	semidirect
71. C₂²×C₄×D₄	C₂²	semidirect
72. C₂²×C₄×D₄	C₂²	semidirect
73. C₂²×C₄×D₄	C₂²	semidirect
74. C₂²×C₄×D₄	C₂²	semidirect
75. C₂²×#117	C₂²	semidirect
76. C₂²×#117	C₂²	semidirect
77. C₂²×#117	C₂²	semidirect
78. C₂³×C₂²⋊C₄	C₂²	semidirect
79. C₂³×C₂²⋊C₄	C₂²	semidirect
80. C₂³×C₂²⋊C₄	C₂²	semidirect
81. C₂³×C₄²	C₂²	semidirect
92. C₂³×Q₈	C₂³	semidirect
105. C₂³×D₄	C₂³	semidirect
113. #563	C₂³	semidirect
114. #562	C₂³	semidirect
115. H(3,𝔽₄)	C₂³	semidirect
116. #555	C₂³	semidirect
117. #551	C₂³	semidirect
118. #551	C₂³	semidirect
119. #546	C₂³	semidirect
120. #542	C₂³	semidirect
121. #538	C₂³	semidirect
122. #536	C₂³	semidirect
123. #534	C₂³	semidirect
124. C₂×C₄⋊Q₈	C₂³	semidirect
125. C₂×C₄⋊Q₈	C₂³	semidirect
126. #529	C₂³	semidirect
127. C₂×#126	C₂³	semidirect
128. C₂×#126	C₂³	semidirect
129. C₂×#126	C₂³	semidirect
130. C₂×#125	C₂³	semidirect
133. C₂×#124	C₂³	semidirect
134. C₂×#124	C₂³	semidirect
135. C₂×#124	C₂³	semidirect
136. C₂×#124	C₂³	semidirect
137. C₂×#124	C₂³	semidirect
138. C₂×#124	C₂³	semidirect
139. C₂×#124	C₂³	semidirect
140. C₂×#124	C₂³	semidirect
141. C₂×#124	C₂³	semidirect
143. C₂×#123	C₂³	semidirect
144. C₂×#123	C₂³	semidirect
145. C₂×#123	C₂³	semidirect
146. C₂×#123	C₂³	semidirect
147. C₂×#123	C₂³	semidirect
148. C₂×#123	C₂³	semidirect
149. C₂×C₂²⋊Q₈	C₂³	semidirect
150. C₂×C₂²⋊Q₈	C₂³	semidirect
151. C₂×C₂²⋊Q₈	C₂³	semidirect
152. C₂×C₂²⋊Q₈	C₂³	semidirect
153. C₂×C₂²⋊Q₈	C₂³	semidirect
156. C₂×#121	C₂³	semidirect
157. C₂×#121	C₂³	semidirect
158. C₂×#121	C₂³	semidirect
161. C₂×#120	C₂³	semidirect
162. C₂×#120	C₂³	semidirect
163. C₂×C₄×Q₈	C₂³	semidirect
164. C₂×C₄×D₄	C₂³	semidirect
165. C₂×C₄×D₄	C₂³	semidirect
166. C₂×C₄×D₄	C₂³	semidirect
167. C₂×C₄×D₄	C₂³	semidirect
168. C₂×#117	C₂³	semidirect
169. C₂×#117	C₂³	semidirect
170. C₂×#117	C₂³	semidirect
195. C₂²×C₂²⋊C₄	C₂³	semidirect
196. C₂²×C₂²⋊C₄	C₂³	semidirect
197. C₂²×C₂²⋊C₄	C₂³	semidirect
204. C₂²×C₄²	C₂³	semidirect
228. C₂²×Q₈	C₂⁴	semidirect
250. C₂²×D₄	C₂⁴	semidirect
274. C₄⋊Q₈	C₂⁴	semidirect
275. C₄⋊Q₈	C₂⁴	semidirect
276. #126	C₂⁴	semidirect
277. #126	C₂⁴	semidirect
278. #126	C₂⁴	semidirect
279. #125	C₂⁴	semidirect
282. #124	C₂⁴	semidirect
283. #124	C₂⁴	semidirect
284. #124	C₂⁴	semidirect
285. #124	C₂⁴	semidirect
286. #124	C₂⁴	semidirect
287. #124	C₂⁴	semidirect
288. #124	C₂⁴	semidirect
289. #124	C₂⁴	semidirect
291. #123	C₂⁴	semidirect
292. #123	C₂⁴	semidirect
293. #123	C₂⁴	semidirect
294. #123	C₂⁴	semidirect
295. #123	C₂⁴	semidirect
296. #123	C₂⁴	semidirect
297. C₂²⋊Q₈	C₂⁴	semidirect
298. C₂²⋊Q₈	C₂⁴	semidirect
299. C₂²⋊Q₈	C₂⁴	semidirect
300. C₂²⋊Q₈	C₂⁴	semidirect
301. C₂²⋊Q₈	C₂⁴	semidirect
304. #121	C₂⁴	semidirect
305. #121	C₂⁴	semidirect
306. #121	C₂⁴	semidirect
309. #120	C₂⁴	semidirect
310. #120	C₂⁴	semidirect
311. C₄×Q₈	C₂⁴	semidirect
312. C₄×D₄	C₂⁴	semidirect
313. C₄×D₄	C₂⁴	semidirect
314. C₄×D₄	C₂⁴	semidirect
315. C₄×D₄	C₂⁴	semidirect
316. #117	C₂⁴	semidirect
317. #117	C₂⁴	semidirect
318. #117	C₂⁴	semidirect
343. C₂×C₂²⋊C₄	C₂⁴	semidirect
344. C₂×C₂²⋊C₄	C₂⁴	semidirect
345. C₂×C₂²⋊C₄	C₂⁴	semidirect
352. C₂×C₄²	C₂⁴	semidirect
548. C₂²	#3545	direct (N × H)
566. C₂	C₂×#3545	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×#3545	2
C₂²×#555	2
C₂²×#551	2
C₂²×#546	2
C₂²×#563	2
C₂²×#562	2
C₂²×H(3,𝔽₄)	2
C₂²×#536	2
C₂²×#542	2
C₂²×#538	2
C₂²×#534	2
C₂²×#529	2
C₂³×#124	2

Subgroups — C22×#3545 #10586153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#3545 #10586153