Subgroups — C₂³×#3506 #72301671

Order 1024.

515549 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3506	C₂	1	224	yes	maximal, direct product factor
2	C₂³×#559	C₂	1	4	yes	maximal, complemented
3	C₂³×#555	C₂	1	2	yes	maximal, complemented
4	C₂³×#556	C₂	1	2	yes	maximal, complemented
5	C₂³×#553	C₂	1	4	yes	maximal, complemented
6	C₂³×#550	C₂	1	2	yes	maximal, complemented
7	C₂³×#547	C₂	1	2	yes	maximal, complemented
8	C₂³×#535	C₂	1	2	yes	maximal, complemented
9	C₂³×#538	C₂	1	4	yes	maximal, complemented
10	C₂³×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×#532	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×#525	C₂	1	4	yes	maximal, complemented
13	C₂³×#520	C₂	1	2	yes	maximal, complemented
14	C₂⁴×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁴×#41	C₂²	1	2	yes	—
16	C₂⁴×#41	C₂²	1	4	yes	complemented
17	C₂⁵×D₄	C₂²	1	1	yes	characteristic
18	C₂⁶×C₄	C₂²	1	2	yes	—
19	C₂×#3506	C₂²	1	7168	yes	direct product factor
20	C₂²×#559	C₂²	1	448	yes	complemented
21	C₂²×#555	C₂²	1	224	yes	complemented
22	C₂²×#556	C₂²	1	224	yes	complemented
23	C₂²×#553	C₂²	1	448	yes	complemented
24	C₂²×#550	C₂²	1	224	yes	complemented
25	C₂²×#547	C₂²	1	224	yes	complemented
26	C₂²×#535	C₂²	1	224	yes	complemented
27	C₂²×#538	C₂²	1	448	yes	complemented
28	C₂²×#533	C₂²	1	112	yes	complemented
29	C₂²×#532	C₂²	1	112	yes	complemented
30	C₂³×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂³×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂³×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂³×#127	C₂²	1	4	yes	—
34	C₂³×#127	C₂²	1	1	yes	characteristic, complemented
35	C₂³×#126	C₂²	1	8	yes	complemented
36	C₂³×#125	C₂²	1	2	yes	complemented
37	C₂³×#124	C₂²	1	4	yes	—
38	C₂³×#124	C₂²	1	2	yes	complemented
39	C₂³×#124	C₂²	1	8	yes	complemented
40	C₂²×#525	C₂²	1	448	yes	complemented
41	C₂³×#123	C₂²	1	8	yes	complemented
42	C₂³×#123	C₂²	1	8	yes	complemented
43	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₂³×#121	C₂²	1	2	yes	—
47	C₂³×#121	C₂²	1	2	yes	—
48	C₂³×#121	C₂²	1	4	yes	—
49	C₂³×#121	C₂²	1	4	yes	—
50	C₂³×#121	C₂²	1	4	yes	complemented
51	C₂³×#121	C₂²	1	8	yes	complemented
52	C₂³×#120	C₂²	1	8	yes	—
53	C₂²×#520	C₂²	1	224	yes	complemented
54	C₂³×C₄×Q₈	C₂²	1	4	yes	complemented
55	C₂³×C₄×Q₈	C₂²	1	2	yes	complemented
56	C₂³×C₄×Q₈	C₂²	1	2	yes	complemented
57	C₂³×C₄×D₄	C₂²	1	2	yes	—
58	C₂³×C₄×D₄	C₂²	1	2	yes	—
59	C₂³×C₄×D₄	C₂²	1	2	yes	—
60	C₂³×C₄×D₄	C₂²	1	2	yes	—
61	C₂³×C₄×D₄	C₂²	1	8	yes	—
62	C₂³×C₄×D₄	C₂²	1	112	yes	complemented
63	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
64	C₂³×C₄×D₄	C₂²	1	8	yes	complemented
65	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
66	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
67	C₂³×#117	C₂²	1	2	yes	—
68	C₂³×#117	C₂²	1	4	yes	complemented
69	C₂³×#117	C₂²	1	4	yes	complemented
70	C₂⁴×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₂⁴×C₄⋊C₄	C₂²	1	4	yes	complemented
72	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₂⁴×C₄²	C₂²	1	1	yes	characteristic
74	C₂⁷	C₂³	1	2	yes	—
75	C₂³×#41	—	2	64	no	—
76	C₂³×#41	—	4	64	no	—
77	C₂³×#41	C₂³	1	112	yes	—
78	C₂³×#41	C₂³	1	224	yes	complemented
79	C₂⁴×Q₈	C₂³	1	2	yes	—
80	C₂⁴×Q₈	C₂³	1	2	yes	—
81	C₂⁴×Q₈	C₂³	1	2	yes	—
82	C₂⁴×D₄	—	2	32	no	—
83	C₂⁴×D₄	C₂³	1	2	yes	—
84	C₂⁴×D₄	C₂³	1	2	yes	—
85	C₂⁴×D₄	C₂³	1	56	yes	—
86	C₂⁴×D₄	C₂³	1	4	yes	—
87	C₂⁴×D₄	C₂³	1	2	yes	—
88	C₂⁴×D₄	C₂³	1	2	yes	—
89	C₂⁴×D₄	C₂³	1	8	yes	—
90	C₂⁴×D₄	C₂³	1	8	yes	—
91	C₂⁴×D₄	C₂³	1	2	yes	—
92	C₂⁵×C₄	—	4	32	no	—
93	C₂⁵×C₄	C₂³	1	1	yes	characteristic
94	C₂⁵×C₄	C₂³	1	4	yes	—
95	C₂⁵×C₄	C₂³	1	4	yes	—
96	C₂⁵×C₄	C₂³	1	2	yes	—
97	C₂⁵×C₄	C₂³	1	4	yes	—
98	C₂⁵×C₄	C₂³	1	112	yes	—
99	C₂⁵×C₄	C₂³	1	8	yes	—
100	C₂⁵×C₄	C₂³	1	1	yes	characteristic
101	C₂⁵×C₄	C₂³	1	1	yes	characteristic
102	#3506	C₂³	1	32768	yes	direct product factor
103	C₂×#559	C₂³	1	7168	yes	complemented
104	C₂×#556	C₂³	1	3584	yes	complemented
105	C₂×#555	C₂³	1	3584	yes	complemented
106	C₂×#553	C₂³	1	7168	yes	complemented
107	C₂×#550	C₂³	1	3584	yes	complemented
108	C₂×#547	C₂³	1	3584	yes	complemented
109	C₂×#538	C₂³	1	7168	yes	complemented
110	C₂×#535	C₂³	1	3584	yes	complemented
111	C₂×#533	C₂³	1	1792	yes	complemented
112	C₂×#532	C₂³	1	1792	yes	complemented
113	C₂²×C₄⋊Q₈	C₂³	1	56	yes	complemented
114	C₂²×C₄⋊Q₈	C₂³	1	56	yes	complemented
115	C₂²×C₄⋊Q₈	C₂³	1	56	yes	complemented
116	C₂²×#127	C₂³	1	224	yes	—
117	C₂²×#127	C₂³	1	56	yes	complemented
118	C₂²×#126	C₂³	1	448	yes	complemented
119	C₂²×#125	C₂³	1	112	yes	complemented
120	C₂²×#124	C₂³	1	224	yes	—
121	C₂²×#124	C₂³	1	112	yes	complemented
122	C₂²×#124	C₂³	1	448	yes	complemented
123	C₂×#525	C₂³	1	7168	yes	complemented
124	C₂²×#123	C₂³	1	448	yes	complemented
125	C₂²×#123	C₂³	1	448	yes	complemented
126	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	—
127	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	—
128	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
129	C₂²×#121	C₂³	1	112	yes	—
130	C₂²×#121	C₂³	1	112	yes	—
131	C₂²×#121	C₂³	1	224	yes	—
132	C₂²×#121	C₂³	1	224	yes	—
133	C₂²×#121	C₂³	1	224	yes	complemented
134	C₂²×#121	C₂³	1	448	yes	complemented
135	C₂²×#120	C₂³	1	448	yes	—
136	C₂×#520	C₂³	1	3584	yes	complemented
137	C₂²×C₄×Q₈	C₂³	1	224	yes	complemented
138	C₂²×C₄×Q₈	C₂³	1	112	yes	complemented
139	C₂²×C₄×Q₈	C₂³	1	112	yes	complemented
140	C₂²×C₄×D₄	C₂³	1	112	yes	—
141	C₂²×C₄×D₄	C₂³	1	112	yes	—
142	C₂²×C₄×D₄	C₂³	1	112	yes	—
143	C₂²×C₄×D₄	C₂³	1	112	yes	—
144	C₂²×C₄×D₄	C₂³	1	448	yes	—
145	C₂²×C₄×D₄	C₂³	1	1792	yes	complemented
146	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
147	C₂²×C₄×D₄	C₂³	1	448	yes	complemented
148	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
149	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
150	C₂²×#117	C₂³	1	112	yes	—
151	C₂²×#117	C₂³	1	224	yes	complemented
152	C₂²×#117	C₂³	1	224	yes	complemented
153	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂³×C₄⋊C₄	C₂³	1	56	yes	—
156	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂³×C₄⋊C₄	C₂³	1	8	yes	—
158	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
162	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
164	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂³×C₄⋊C₄	C₂³	1	224	yes	complemented
166	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂³×C₂²⋊C₄	C₂³	1	112	yes	—
169	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂³×C₂²⋊C₄	C₂³	1	8	yes	—
171	C₂³×C₂²⋊C₄	C₂³	1	8	yes	—
172	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
173	C₂³×C₂²⋊C₄	C₂³	1	8	yes	—
174	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
175	C₂³×C₄²	C₂³	1	1	yes	characteristic
176	C₂³×C₄²	C₂³	1	1	yes	characteristic
177	C₂³×C₄²	C₂³	1	1	yes	characteristic
178	C₂³×C₄²	C₂³	1	1	yes	characteristic
179	C₂³×C₄²	C₂³	1	56	yes	—
180	C₂³×C₄²	C₂³	1	4	yes	—
181	C₂³×C₄²	C₂³	1	8	yes	—
182	C₂⁶	—	2	32	no	—
183	C₂⁶	—	4	16	no	—
184	C₂⁶	—	4	16	no	—
185	C₂⁶	C₂⁴	1	4	yes	—
186	C₂⁶	C₂⁴	1	4	yes	—
187	C₂⁶	C₂⁴	1	1	yes	characteristic
188	C₂⁶	C₂⁴	1	56	yes	—
189	C₂²×#41	—	2	1792	no	—
190	C₂²×#41	—	4	1792	no	—
191	C₂²×#41	C₂⁴	1	896	yes	—
192	C₂²×#41	C₂⁴	1	1792	yes	complemented
193	C₂³×Q₈	—	2	32	no	—
194	C₂³×Q₈	—	2	32	no	—
195	C₂³×Q₈	—	4	16	no	—
196	C₂³×Q₈	C₂⁴	1	56	yes	—
197	C₂³×Q₈	C₂⁴	1	56	yes	—
198	C₂³×Q₈	C₂⁴	1	56	yes	—
199	C₂³×D₄	—	2	64	no	—
200	C₂³×D₄	—	2	32	no	—
201	C₂³×D₄	—	2	32	no	—
202	C₂³×D₄	—	2	32	no	—
203	C₂³×D₄	—	2	896	no	—
204	C₂³×D₄	—	2	32	no	—
205	C₂³×D₄	—	4	16	no	—
206	C₂³×D₄	—	4	64	no	—
207	C₂³×D₄	—	4	64	no	—
208	C₂³×D₄	C₂⁴	1	56	yes	—
209	C₂³×D₄	C₂⁴	1	56	yes	—
210	C₂³×D₄	C₂⁴	1	448	yes	—
211	C₂³×D₄	C₂⁴	1	112	yes	—
212	C₂³×D₄	C₂⁴	1	56	yes	—
213	C₂³×D₄	C₂⁴	1	56	yes	—
214	C₂³×D₄	C₂⁴	1	224	yes	—
215	C₂³×D₄	C₂⁴	1	224	yes	—
216	C₂³×D₄	C₂⁴	1	56	yes	—
217	C₂⁴×C₄	—	2	64	no	—
218	C₂⁴×C₄	—	2	16	no	—
219	C₂⁴×C₄	—	2	64	no	—
220	C₂⁴×C₄	—	4	896	no	—
221	C₂⁴×C₄	—	4	16	no	—
222	C₂⁴×C₄	—	4	32	no	—
223	C₂⁴×C₄	—	4	8	no	—
224	C₂⁴×C₄	—	4	64	no	—
225	C₂⁴×C₄	#41	1	32	yes	complemented
226	C₂⁴×C₄	C₂⁴	1	28	yes	—
227	C₂⁴×C₄	C₂⁴	1	112	yes	—
228	C₂⁴×C₄	C₂⁴	1	112	yes	—
229	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
230	C₂⁴×C₄	C₂⁴	1	4	yes	—
231	C₂⁴×C₄	C₂⁴	1	4	yes	—
232	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₄	C₂⁴	1	4	yes	—
234	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₄	C₂⁴	1	4	yes	—
236	C₂⁴×C₄	C₂⁴	1	56	yes	—
237	C₂⁴×C₄	C₂⁴	1	112	yes	—
238	C₂⁴×C₄	C₂⁴	1	896	yes	—
239	C₂⁴×C₄	C₂⁴	1	224	yes	—
240	C₂⁴×C₄	C₂⁴	1	28	yes	—
241	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
243	C₂⁴×C₄	C₂⁴	1	28	yes	—
244	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
245	#559	C₂⁴	1	16384	yes	complemented
246	#556	C₂⁴	1	8192	yes	complemented
247	#555	C₂⁴	1	8192	yes	complemented
248	#553	C₂⁴	1	16384	yes	complemented
249	#550	C₂⁴	1	8192	yes	complemented
250	#547	C₂⁴	1	8192	yes	complemented
251	#538	C₂⁴	1	16384	yes	complemented
252	#535	C₂⁴	1	8192	yes	complemented
253	#533	C₂⁴	1	4096	yes	complemented
254	#532	C₂⁴	1	4096	yes	complemented
255	C₂×C₄⋊Q₈	C₂⁴	1	448	yes	complemented
256	C₂×C₄⋊Q₈	C₂⁴	1	448	yes	complemented
257	C₂×C₄⋊Q₈	C₂⁴	1	448	yes	complemented
258	C₂×#127	C₂⁴	1	1792	yes	—
259	C₂×#127	C₂⁴	1	448	yes	complemented
260	C₂×#126	C₂⁴	1	3584	yes	complemented
261	C₂×#125	C₂⁴	1	896	yes	complemented
262	C₂×#124	C₂⁴	1	1792	yes	—
263	C₂×#124	C₂⁴	1	896	yes	complemented
264	C₂×#124	C₂⁴	1	3584	yes	complemented
265	#525	C₂⁴	1	16384	yes	complemented
266	C₂×#123	C₂⁴	1	3584	yes	complemented
267	C₂×#123	C₂⁴	1	3584	yes	complemented
268	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	—
269	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	—
270	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
271	C₂×#121	C₂⁴	1	896	yes	—
272	C₂×#121	C₂⁴	1	896	yes	—
273	C₂×#121	C₂⁴	1	1792	yes	—
274	C₂×#121	C₂⁴	1	1792	yes	—
275	C₂×#121	C₂⁴	1	1792	yes	complemented
276	C₂×#121	C₂⁴	1	3584	yes	complemented
277	C₂×#120	C₂⁴	1	3584	yes	—
278	#520	C₂⁴	1	8192	yes	complemented
279	C₂×C₄×Q₈	C₂⁴	1	1792	yes	complemented
280	C₂×C₄×Q₈	C₂⁴	1	896	yes	complemented
281	C₂×C₄×Q₈	C₂⁴	1	896	yes	complemented
282	C₂×C₄×D₄	C₂⁴	1	896	yes	—
283	C₂×C₄×D₄	C₂⁴	1	896	yes	—
284	C₂×C₄×D₄	C₂⁴	1	896	yes	—
285	C₂×C₄×D₄	C₂⁴	1	896	yes	—
286	C₂×C₄×D₄	C₂⁴	1	3584	yes	—
287	C₂×C₄×D₄	C₂⁴	1	4096	yes	complemented
288	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
289	C₂×C₄×D₄	C₂⁴	1	3584	yes	complemented
290	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
291	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
292	C₂×#117	C₂⁴	1	896	yes	—
293	C₂×#117	C₂⁴	1	1792	yes	complemented
294	C₂×#117	C₂⁴	1	1792	yes	complemented
295	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
296	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
297	C₂²×C₄⋊C₄	C₂⁴	1	448	yes	—
298	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
299	C₂²×C₄⋊C₄	C₂⁴	1	224	yes	—
300	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
301	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
302	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
303	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
304	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
305	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
306	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
307	C₂²×C₄⋊C₄	C₂⁴	1	1792	yes	complemented
308	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
309	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
310	C₂²×C₂²⋊C₄	C₂⁴	1	896	yes	—
311	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
312	C₂²×C₂²⋊C₄	C₂⁴	1	224	yes	—
313	C₂²×C₂²⋊C₄	C₂⁴	1	224	yes	—
314	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
315	C₂²×C₂²⋊C₄	C₂⁴	1	224	yes	—
316	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
317	C₂²×C₄²	C₂⁴	1	28	yes	—
318	C₂²×C₄²	C₂⁴	1	28	yes	—
319	C₂²×C₄²	C₂⁴	1	28	yes	—
320	C₂²×C₄²	C₂⁴	1	28	yes	—
321	C₂²×C₄²	C₂⁴	1	448	yes	—
322	C₂²×C₄²	C₂⁴	1	112	yes	—
323	C₂²×C₄²	C₂⁴	1	224	yes	—
324	C₂⁵	—	2	8	no	—
325	C₂⁵	—	2	8	no	—
326	C₂⁵	—	2	32	no	—
327	C₂⁵	—	2	448	no	—
328	C₂⁵	—	2	32	no	—
329	C₂⁵	—	2	32	no	—
330	C₂⁵	—	2	32	no	—
331	C₂⁵	—	2	32	no	—
332	C₂⁵	—	2	32	no	—
333	C₂⁵	—	4	224	no	—
334	C₂⁵	—	4	224	no	—
335	C₂⁵	—	4	512	no	—
336	C₂⁵	C₂×#41	1	16	yes	—
337	C₂⁵	C₂⁵	1	56	yes	—
338	C₂⁵	C₂⁵	1	56	yes	—
339	C₂⁵	C₂⁵	1	14	yes	—
340	C₂⁵	C₂⁵	1	224	yes	—
341	C₂⁵	C₂⁵	1	1	yes	characteristic
342	C₂×#41	—	2	7168	no	—
343	C₂×#41	—	4	7168	no	—
344	C₂×#41	C₂⁵	1	1024	yes	—
345	C₂×#41	C₂⁵	1	2048	yes	complemented
346	C₂²×Q₈	—	2	448	no	—
347	C₂²×Q₈	—	2	448	no	—
348	C₂²×Q₈	—	4	224	no	—
349	C₂²×Q₈	C₂⁵	1	224	yes	—
350	C₂²×Q₈	C₂⁵	1	224	yes	—
351	C₂²×Q₈	C₂⁵	1	224	yes	—
352	C₂²×D₄	—	2	896	no	—
353	C₂²×D₄	—	2	448	no	—
354	C₂²×D₄	—	2	448	no	—
355	C₂²×D₄	—	2	448	no	—
356	C₂²×D₄	—	2	3584	no	—
357	C₂²×D₄	—	2	448	no	—
358	C₂²×D₄	—	4	224	no	—
359	C₂²×D₄	—	4	896	no	—
360	C₂²×D₄	—	4	896	no	—
361	C₂²×D₄	C₂⁵	1	448	yes	—
362	C₂²×D₄	C₂⁵	1	224	yes	—
363	C₂²×D₄	C₂⁵	1	224	yes	—
364	C₂²×D₄	C₂⁵	1	224	yes	—
365	C₂²×D₄	C₂⁵	1	512	yes	—
366	C₂²×D₄	C₂⁵	1	224	yes	—
367	C₂²×D₄	C₂⁵	1	896	yes	—
368	C₂²×D₄	C₂⁵	1	224	yes	—
369	C₂²×D₄	C₂⁵	1	896	yes	—
370	C₂³×C₄	—	2	32	no	—
371	C₂³×C₄	—	2	8	no	—
372	C₂³×C₄	—	2	32	no	—
373	C₂³×C₄	—	2	32	no	—
374	C₂³×C₄	—	2	8	no	—
375	C₂³×C₄	—	2	8	no	—
376	C₂³×C₄	—	2	32	no	—
377	C₂³×C₄	—	2	896	no	—
378	C₂³×C₄	—	2	224	no	—
379	C₂³×C₄	—	2	896	no	—
380	C₂³×C₄	—	4	3584	no	—
381	C₂³×C₄	—	4	224	no	—
382	C₂³×C₄	—	4	448	no	—
383	C₂³×C₄	—	4	112	no	—
384	C₂³×C₄	—	4	896	no	—
385	C₂³×C₄	C₂×#41	1	16	yes	—
386	C₂³×C₄	C₂×#41	1	16	yes	—
387	C₂³×C₄	C₂×#41	1	448	yes	complemented
388	C₂³×C₄	H(5,𝔽₂)	1	16	yes	—
389	C₂³×C₄	C₂⁵	1	14	yes	—
390	C₂³×C₄	C₂⁵	1	56	yes	—
391	C₂³×C₄	C₂⁵	1	56	yes	—
392	C₂³×C₄	C₂⁵	1	14	yes	—
393	C₂³×C₄	C₂⁵	1	56	yes	—
394	C₂³×C₄	C₂⁵	1	14	yes	—
395	C₂³×C₄	C₂⁵	1	56	yes	—
396	C₂³×C₄	C₂⁵	1	448	yes	—
397	C₂³×C₄	C₂⁵	1	448	yes	—
398	C₂³×C₄	C₂⁵	1	112	yes	—
399	C₂³×C₄	C₂⁵	1	112	yes	—
400	C₂³×C₄	C₂⁵	1	224	yes	—
401	C₂³×C₄	C₂⁵	1	896	yes	—
402	C₂³×C₄	C₂⁵	1	448	yes	—
403	C₂³×C₄	C₂⁵	1	1024	yes	—
404	C₂³×C₄	C₂⁵	1	14	yes	—
405	C₂³×C₄	C₂⁵	1	14	yes	—
406	C₂³×C₄	C₂⁵	1	112	yes	—
407	C₂³×C₄	C₂⁵	1	14	yes	—
408	C₄⋊Q₈	C₂⁵	1	512	yes	complemented
409	C₄⋊Q₈	C₂⁵	1	512	yes	complemented
410	C₄⋊Q₈	C₂⁵	1	512	yes	complemented
411	#127	C₂⁵	1	2048	yes	—
412	#127	C₂⁵	1	512	yes	complemented
413	#126	C₂⁵	1	4096	yes	complemented
414	#125	C₂⁵	1	1024	yes	complemented
415	#124	C₂⁵	1	2048	yes	—
416	#124	C₂⁵	1	1024	yes	complemented
417	#124	C₂⁵	1	4096	yes	complemented
418	#123	C₂⁵	1	4096	yes	complemented
419	#123	C₂⁵	1	4096	yes	complemented
420	C₂²⋊Q₈	C₂⁵	1	1024	yes	—
421	C₂²⋊Q₈	C₂⁵	1	1024	yes	—
422	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
423	#121	C₂⁵	1	1024	yes	—
424	#121	C₂⁵	1	1024	yes	—
425	#121	C₂⁵	1	2048	yes	—
426	#121	C₂⁵	1	2048	yes	—
427	#121	C₂⁵	1	2048	yes	complemented
428	#121	C₂⁵	1	4096	yes	complemented
429	#120	C₂⁵	1	4096	yes	—
430	C₄×Q₈	C₂⁵	1	2048	yes	complemented
431	C₄×Q₈	C₂⁵	1	1024	yes	complemented
432	C₄×Q₈	C₂⁵	1	1024	yes	complemented
433	C₄×D₄	C₂⁵	1	1024	yes	—
434	C₄×D₄	C₂⁵	1	1024	yes	—
435	C₄×D₄	C₂⁵	1	1024	yes	—
436	C₄×D₄	C₂⁵	1	1024	yes	—
437	C₄×D₄	C₂⁵	1	4096	yes	—
438	C₄×D₄	C₂⁵	1	2048	yes	complemented
439	C₄×D₄	C₂⁵	1	4096	yes	complemented
440	C₄×D₄	C₂⁵	1	1024	yes	complemented
441	C₄×D₄	C₂⁵	1	1024	yes	complemented
442	#117	C₂⁵	1	1024	yes	—
443	#117	C₂⁵	1	2048	yes	complemented
444	#117	C₂⁵	1	2048	yes	complemented
445	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
446	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
447	C₂×C₄⋊C₄	C₂⁵	1	512	yes	—
448	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
449	C₂×C₄⋊C₄	C₂⁵	1	896	yes	—
450	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
451	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
452	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
453	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
454	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
455	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
456	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
457	C₂×C₄⋊C₄	C₂⁵	1	2048	yes	complemented
458	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
459	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
460	C₂×C₂²⋊C₄	C₂⁵	1	1024	yes	—
461	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
462	C₂×C₂²⋊C₄	C₂⁵	1	896	yes	—
463	C₂×C₂²⋊C₄	C₂⁵	1	896	yes	—
464	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
465	C₂×C₂²⋊C₄	C₂⁵	1	896	yes	—
466	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
467	C₂×C₄²	C₂⁵	1	448	yes	—
468	C₂×C₄²	C₂⁵	1	896	yes	—
469	C₂×C₄²	C₂⁵	1	112	yes	—
470	C₂×C₄²	C₂⁵	1	112	yes	—
471	C₂×C₄²	C₂⁵	1	112	yes	—
472	C₂×C₄²	C₂⁵	1	112	yes	—
473	C₂×C₄²	C₂⁵	1	512	yes	—
474	C₂⁴	—	2	56	no	—
475	C₂⁴	—	2	56	no	—
476	C₂⁴	—	2	128	no	—
477	C₂⁴	—	2	224	no	—
478	C₂⁴	—	2	896	no	—
479	C₂⁴	—	2	224	no	—
480	C₂⁴	—	2	224	no	—
481	C₂⁴	—	2	224	no	—
482	C₂⁴	—	2	224	no	—
483	C₂⁴	—	2	224	no	—
484	C₂⁴	—	4	448	no	—
485	C₂⁴	—	4	448	no	—
486	C₂⁴	—	4	3584	no	—
487	C₂⁴	—	4	256	no	—
488	C₂⁴	—	4	256	no	—
489	C₂⁴	C₂²×#41	1	112	yes	—
490	C₂⁴	C₂²×#41	1	8	yes	—
491	C₂⁴	C₂×H(5,𝔽₂)	1	8	yes	—
492	C₂⁴	#585	1	8	yes	—
493	C₂⁴	C₂⁶	1	112	yes	—
494	C₂⁴	C₂⁶	1	112	yes	—
495	C₂⁴	C₂⁶	1	28	yes	—
496	C₂⁴	C₂⁶	1	128	yes	—
497	C₂⁴	C₂⁶	1	7	yes	—
498	#41	—	2	4096	no	—
499	#41	—	4	4096	no	—
500	C₂×Q₈	—	2	896	no	—
501	C₂×Q₈	—	2	896	no	—
502	C₂×Q₈	—	4	448	no	—
503	C₂×Q₈	C₂⁶	1	128	yes	—
504	C₂×Q₈	C₂⁶	1	128	yes	—
505	C₂×Q₈	C₂⁶	1	128	yes	—
506	C₂×D₄	—	2	1792	no	—
507	C₂×D₄	—	2	896	no	—
508	C₂×D₄	—	2	896	no	—
509	C₂×D₄	—	2	896	no	—
510	C₂×D₄	—	2	2048	no	—
511	C₂×D₄	—	2	896	no	—
512	C₂×D₄	—	4	448	no	—
513	C₂×D₄	—	4	1792	no	—
514	C₂×D₄	—	4	1792	no	—
515	C₂×D₄	C₂⁶	1	256	yes	—
516	C₂×D₄	C₂⁶	1	128	yes	—
517	C₂×D₄	C₂⁶	1	128	yes	—
518	C₂×D₄	C₂⁶	1	128	yes	—
519	C₂×D₄	C₂⁶	1	128	yes	—
520	C₂×D₄	C₂⁶	1	512	yes	—
521	C₂×D₄	C₂⁶	1	128	yes	—
522	C₂×D₄	C₂⁶	1	512	yes	—
523	C₂²×C₄	—	2	224	no	—
524	C₂²×C₄	—	2	56	no	—
525	C₂²×C₄	—	2	224	no	—
526	C₂²×C₄	—	2	224	no	—
527	C₂²×C₄	—	2	56	no	—
528	C₂²×C₄	—	2	56	no	—
529	C₂²×C₄	—	2	224	no	—
530	C₂²×C₄	—	2	1792	no	—
531	C₂²×C₄	—	2	448	no	—
532	C₂²×C₄	—	2	1792	no	—
533	C₂²×C₄	—	4	2048	no	—
534	C₂²×C₄	—	4	448	no	—
535	C₂²×C₄	—	4	896	no	—
536	C₂²×C₄	—	4	224	no	—
537	C₂²×C₄	—	4	1792	no	—
538	C₂²×C₄	C₂²×#41	1	112	yes	—
539	C₂²×C₄	C₂²×#41	1	112	yes	—
540	C₂²×C₄	C₂²×#41	1	896	yes	complemented
541	C₂²×C₄	C₂×H(5,𝔽₂)	1	112	yes	—
542	C₂²×C₄	C₂⁶	1	112	yes	—
543	C₂²×C₄	C₂⁶	1	28	yes	—
544	C₂²×C₄	C₂⁶	1	112	yes	—
545	C₂²×C₄	C₂⁶	1	28	yes	—
546	C₂²×C₄	C₂⁶	1	112	yes	—
547	C₂²×C₄	C₂⁶	1	28	yes	—
548	C₂²×C₄	C₂⁶	1	64	yes	—
549	C₂²×C₄	C₂⁶	1	112	yes	—
550	C₂²×C₄	C₂⁶	1	256	yes	—
551	C₂²×C₄	C₂⁶	1	256	yes	—
552	C₂²×C₄	C₂⁶	1	64	yes	—
553	C₂²×C₄	C₂⁶	1	128	yes	—
554	C₂²×C₄	C₂⁶	1	512	yes	—
555	C₂²×C₄	C₂⁶	1	256	yes	—
556	C₂²×C₄	C₂⁶	1	28	yes	—
557	C₂²×C₄	C₂⁶	1	28	yes	—
558	C₂²×C₄	C₂⁶	1	64	yes	—
559	C₂²×C₄	C₂⁶	1	28	yes	—
560	C₄⋊C₄	C₂⁶	1	128	yes	—
561	C₄⋊C₄	C₂⁶	1	128	yes	—
562	C₄⋊C₄	C₂⁶	1	128	yes	—
563	C₄⋊C₄	C₂⁶	1	512	yes	—
564	C₄⋊C₄	C₂⁶	1	128	yes	—
565	C₄⋊C₄	C₂⁶	1	128	yes	—
566	C₄⋊C₄	C₂⁶	1	128	yes	—
567	C₄⋊C₄	C₂⁶	1	256	yes	—
568	C₄⋊C₄	C₂⁶	1	128	yes	—
569	C₄⋊C₄	C₂⁶	1	256	yes	—
570	C₄⋊C₄	C₂⁶	1	128	yes	—
571	C₂²⋊C₄	C₂⁶	1	256	yes	—
572	C₂²⋊C₄	C₂⁶	1	256	yes	—
573	C₂²⋊C₄	C₂⁶	1	256	yes	—
574	C₂²⋊C₄	C₂⁶	1	512	yes	—
575	C₂²⋊C₄	C₂⁶	1	512	yes	—
576	C₂²⋊C₄	C₂⁶	1	256	yes	—
577	C₂²⋊C₄	C₂⁶	1	512	yes	—
578	C₂²⋊C₄	C₂⁶	1	256	yes	—
579	C₄²	C₂⁶	1	64	yes	—
580	C₄²	C₂⁶	1	64	yes	—
581	C₄²	C₂⁶	1	64	yes	—
582	C₄²	C₂⁶	1	64	yes	—
583	C₄²	C₂⁶	1	256	yes	—
584	C₄²	C₂⁶	1	512	yes	—
585	C₂³	—	2	448	no	—
586	C₂³	—	2	56	no	—
587	C₂³	—	2	56	no	—
588	C₂³	—	2	224	no	—
589	C₂³	—	2	256	no	—
590	C₂³	—	2	224	no	—
591	C₂³	—	2	224	no	—
592	C₂³	—	2	224	no	—
593	C₂³	—	2	224	no	—
594	C₂³	—	2	224	no	—
595	C₂³	—	4	128	no	—
596	C₂³	—	4	128	no	—
597	C₂³	—	4	3584	no	—
598	C₂³	—	4	896	no	—
599	C₂³	—	4	896	no	—
600	C₂³	#3506	1	64	yes	direct product factor
601	C₂³	C₂³×#41	1	112	yes	—
602	C₂³	C₂³×#41	1	28	yes	—
603	C₂³	C₂²×H(5,𝔽₂)	1	28	yes	—
604	C₂³	C₂×#585	1	28	yes	—
605	C₂³	C₂⁷	1	32	yes	—
606	C₂³	C₂⁷	1	32	yes	—
607	C₂³	C₂⁷	1	8	yes	—
608	C₂³	C₂⁷	1	7	yes	—
609	Q₈	—	2	256	no	—
610	Q₈	—	2	256	no	—
611	Q₈	—	4	128	no	—
612	D₄	—	2	512	no	—
613	D₄	—	2	256	no	—
614	D₄	—	2	256	no	—
615	D₄	—	2	256	no	—
616	D₄	—	2	256	no	—
617	D₄	—	4	128	no	—
618	D₄	—	4	512	no	—
619	D₄	—	4	512	no	—
620	C₂×C₄	—	2	224	no	—
621	C₂×C₄	—	2	56	no	—
622	C₂×C₄	—	2	224	no	—
623	C₂×C₄	—	2	224	no	—
624	C₂×C₄	—	2	56	no	—
625	C₂×C₄	—	2	56	no	—
626	C₂×C₄	—	2	224	no	—
627	C₂×C₄	—	2	512	no	—
628	C₂×C₄	—	2	128	no	—
629	C₂×C₄	—	2	512	no	—
630	C₂×C₄	—	4	128	no	—
631	C₂×C₄	—	4	256	no	—
632	C₂×C₄	—	4	64	no	—
633	C₂×C₄	—	4	512	no	—
634	C₂×C₄	C₂³×#41	1	112	yes	—
635	C₂×C₄	C₂³×#41	1	112	yes	—
636	C₂×C₄	C₂³×#41	1	256	yes	complemented
637	C₂×C₄	C₂²×H(5,𝔽₂)	1	112	yes	—
638	C₂×C₄	C₂⁷	1	32	yes	—
639	C₂×C₄	C₂⁷	1	8	yes	—
640	C₂×C₄	C₂⁷	1	32	yes	—
641	C₂×C₄	C₂⁷	1	8	yes	—
642	C₂×C₄	C₂⁷	1	8	yes	—
643	C₂×C₄	C₂⁷	1	32	yes	—
644	C₂×C₄	C₂⁷	1	32	yes	—
645	C₂×C₄	C₂⁷	1	8	yes	—
646	C₂×C₄	C₂⁷	1	8	yes	—
647	C₂×C₄	C₂⁷	1	8	yes	—
648	C₂²	—	2	224	no	—
649	C₂²	—	2	8	no	—
650	C₂²	—	2	8	no	—
651	C₂²	—	2	32	no	—
652	C₂²	—	2	32	no	—
653	C₂²	—	2	32	no	—
654	C₂²	—	2	32	no	—
655	C₂²	—	2	32	no	—
656	C₂²	—	2	32	no	—
657	C₂²	—	4	512	no	—
658	C₂²	—	4	448	no	—
659	C₂²	—	4	448	no	—
660	C₂²	C₂×#3506	1	112	yes	direct product factor
661	C₂²	C₂⁴×#41	1	16	yes	—
662	C₂²	C₂⁴×#41	1	14	yes	—
663	C₂²	C₂³×H(5,𝔽₂)	1	14	yes	—
664	C₂²	C₂²×#585	1	14	yes	—
665	C₂²	C₂⁸	1	1	yes	characteristic
666	C₄	—	2	32	no	—
667	C₄	—	2	8	no	—
668	C₄	—	2	32	no	—
669	C₄	—	2	32	no	—
670	C₄	—	2	8	no	—
671	C₄	—	2	8	no	—
672	C₄	—	2	32	no	—
673	C₄	C₂⁴×#41	1	16	yes	—
674	C₄	C₂⁴×#41	1	16	yes	—
675	C₄	C₂³×H(5,𝔽₂)	1	16	yes	—
676	C₂	—	2	16	no	—
677	C₂	—	4	32	no	—
678	C₂	—	4	32	no	—
679	C₂	C₂²×#3506	1	28	yes	direct product factor
680	C₂	C₂⁵×#41	1	1	yes	characteristic
681	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂	C₂³×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁸
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×#3506	C₂	direct (N × H)
2. C₂³×#559	C₂	semidirect
3. C₂³×#555	C₂	semidirect
4. C₂³×#556	C₂	semidirect
5. C₂³×#553	C₂	semidirect
6. C₂³×#550	C₂	semidirect
7. C₂³×#547	C₂	semidirect
8. C₂³×#535	C₂	semidirect
9. C₂³×#538	C₂	semidirect
10. C₂³×#533	C₂	semidirect
11. C₂³×#532	C₂	semidirect
12. C₂³×#525	C₂	semidirect
13. C₂³×#520	C₂	semidirect
14. C₂⁴×C₄×D₄	C₂	semidirect
16. C₂⁴×#41	C₂²	semidirect
19. C₂×#3506	C₂²	direct (N × H)
20. C₂²×#559	C₂²	semidirect
21. C₂²×#555	C₂²	semidirect
22. C₂²×#556	C₂²	semidirect
23. C₂²×#553	C₂²	semidirect
24. C₂²×#550	C₂²	semidirect
25. C₂²×#547	C₂²	semidirect
26. C₂²×#535	C₂²	semidirect
27. C₂²×#538	C₂²	semidirect
28. C₂²×#533	C₂²	semidirect
29. C₂²×#532	C₂²	semidirect
30. C₂³×C₄⋊Q₈	C₂²	semidirect
31. C₂³×C₄⋊Q₈	C₂²	semidirect
32. C₂³×C₄⋊Q₈	C₂²	semidirect
34. C₂³×#127	C₂²	semidirect
35. C₂³×#126	C₂²	semidirect
36. C₂³×#125	C₂²	semidirect
38. C₂³×#124	C₂²	semidirect
39. C₂³×#124	C₂²	semidirect
40. C₂²×#525	C₂²	semidirect
41. C₂³×#123	C₂²	semidirect
42. C₂³×#123	C₂²	semidirect
45. C₂³×C₂²⋊Q₈	C₂²	semidirect
50. C₂³×#121	C₂²	semidirect
51. C₂³×#121	C₂²	semidirect
53. C₂²×#520	C₂²	semidirect
54. C₂³×C₄×Q₈	C₂²	semidirect
55. C₂³×C₄×Q₈	C₂²	semidirect
56. C₂³×C₄×Q₈	C₂²	semidirect
62. C₂³×C₄×D₄	C₂²	semidirect
63. C₂³×C₄×D₄	C₂²	semidirect
64. C₂³×C₄×D₄	C₂²	semidirect
65. C₂³×C₄×D₄	C₂²	semidirect
66. C₂³×C₄×D₄	C₂²	semidirect
68. C₂³×#117	C₂²	semidirect
69. C₂³×#117	C₂²	semidirect
71. C₂⁴×C₄⋊C₄	C₂²	semidirect
78. C₂³×#41	C₂³	semidirect
102. #3506	C₂³	direct (N × H)
103. C₂×#559	C₂³	semidirect
104. C₂×#556	C₂³	semidirect
105. C₂×#555	C₂³	semidirect
106. C₂×#553	C₂³	semidirect
107. C₂×#550	C₂³	semidirect
108. C₂×#547	C₂³	semidirect
109. C₂×#538	C₂³	semidirect
110. C₂×#535	C₂³	semidirect
111. C₂×#533	C₂³	semidirect
112. C₂×#532	C₂³	semidirect
113. C₂²×C₄⋊Q₈	C₂³	semidirect
114. C₂²×C₄⋊Q₈	C₂³	semidirect
115. C₂²×C₄⋊Q₈	C₂³	semidirect
117. C₂²×#127	C₂³	semidirect
118. C₂²×#126	C₂³	semidirect
119. C₂²×#125	C₂³	semidirect
121. C₂²×#124	C₂³	semidirect
122. C₂²×#124	C₂³	semidirect
123. C₂×#525	C₂³	semidirect
124. C₂²×#123	C₂³	semidirect
125. C₂²×#123	C₂³	semidirect
128. C₂²×C₂²⋊Q₈	C₂³	semidirect
133. C₂²×#121	C₂³	semidirect
134. C₂²×#121	C₂³	semidirect
136. C₂×#520	C₂³	semidirect
137. C₂²×C₄×Q₈	C₂³	semidirect
138. C₂²×C₄×Q₈	C₂³	semidirect
139. C₂²×C₄×Q₈	C₂³	semidirect
145. C₂²×C₄×D₄	C₂³	semidirect
146. C₂²×C₄×D₄	C₂³	semidirect
147. C₂²×C₄×D₄	C₂³	semidirect
148. C₂²×C₄×D₄	C₂³	semidirect
149. C₂²×C₄×D₄	C₂³	semidirect
151. C₂²×#117	C₂³	semidirect
152. C₂²×#117	C₂³	semidirect
165. C₂³×C₄⋊C₄	C₂³	semidirect
192. C₂²×#41	C₂⁴	semidirect
225. C₂⁴×C₄	#41	semidirect
245. #559	C₂⁴	semidirect
246. #556	C₂⁴	semidirect
247. #555	C₂⁴	semidirect
248. #553	C₂⁴	semidirect
249. #550	C₂⁴	semidirect
250. #547	C₂⁴	semidirect
251. #538	C₂⁴	semidirect
252. #535	C₂⁴	semidirect
253. #533	C₂⁴	semidirect
254. #532	C₂⁴	semidirect
255. C₂×C₄⋊Q₈	C₂⁴	semidirect
256. C₂×C₄⋊Q₈	C₂⁴	semidirect
257. C₂×C₄⋊Q₈	C₂⁴	semidirect
259. C₂×#127	C₂⁴	semidirect
260. C₂×#126	C₂⁴	semidirect
261. C₂×#125	C₂⁴	semidirect
263. C₂×#124	C₂⁴	semidirect
264. C₂×#124	C₂⁴	semidirect
265. #525	C₂⁴	semidirect
266. C₂×#123	C₂⁴	semidirect
267. C₂×#123	C₂⁴	semidirect
270. C₂×C₂²⋊Q₈	C₂⁴	semidirect
275. C₂×#121	C₂⁴	semidirect
276. C₂×#121	C₂⁴	semidirect
278. #520	C₂⁴	semidirect
279. C₂×C₄×Q₈	C₂⁴	semidirect
280. C₂×C₄×Q₈	C₂⁴	semidirect
281. C₂×C₄×Q₈	C₂⁴	semidirect
287. C₂×C₄×D₄	C₂⁴	semidirect
288. C₂×C₄×D₄	C₂⁴	semidirect
289. C₂×C₄×D₄	C₂⁴	semidirect
290. C₂×C₄×D₄	C₂⁴	semidirect
291. C₂×C₄×D₄	C₂⁴	semidirect
293. C₂×#117	C₂⁴	semidirect
294. C₂×#117	C₂⁴	semidirect
307. C₂²×C₄⋊C₄	C₂⁴	semidirect
345. C₂×#41	C₂⁵	semidirect
387. C₂³×C₄	C₂×#41	semidirect
408. C₄⋊Q₈	C₂⁵	semidirect
409. C₄⋊Q₈	C₂⁵	semidirect
410. C₄⋊Q₈	C₂⁵	semidirect
412. #127	C₂⁵	semidirect
413. #126	C₂⁵	semidirect
414. #125	C₂⁵	semidirect
416. #124	C₂⁵	semidirect
417. #124	C₂⁵	semidirect
418. #123	C₂⁵	semidirect
419. #123	C₂⁵	semidirect
422. C₂²⋊Q₈	C₂⁵	semidirect
427. #121	C₂⁵	semidirect
428. #121	C₂⁵	semidirect
430. C₄×Q₈	C₂⁵	semidirect
431. C₄×Q₈	C₂⁵	semidirect
432. C₄×Q₈	C₂⁵	semidirect
438. C₄×D₄	C₂⁵	semidirect
439. C₄×D₄	C₂⁵	semidirect
440. C₄×D₄	C₂⁵	semidirect
441. C₄×D₄	C₂⁵	semidirect
443. #117	C₂⁵	semidirect
444. #117	C₂⁵	semidirect
457. C₂×C₄⋊C₄	C₂⁵	semidirect
540. C₂²×C₄	C₂²×#41	semidirect
600. C₂³	#3506	direct (N × H)
636. C₂×C₄	C₂³×#41	semidirect
660. C₂²	C₂×#3506	direct (N × H)
679. C₂	C₂²×#3506	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#3506	2
C₂³×#559	2
C₂³×#555	2
C₂³×#556	2
C₂³×#553	2
C₂³×#550	2
C₂³×#547	2
C₂³×#535	2
C₂³×#538	2
C₂³×#533	2
C₂³×#532	2
C₂³×#525	2
C₂³×#520	2
C₂⁴×C₄×D₄	2

Subgroups — C23×#3506 #72301671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#3506 #72301671