Subgroups — C₂×#20256717 #27123115

Order 12032.

11662 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256717	C₂	1	32	yes	maximal, direct product factor
3	C₂×#15689701	C₂	1	4	yes	maximal, complemented
4	C₂×#15689697	C₂	1	2	yes	maximal, complemented
5	C₂×#15689694	C₂	1	2	yes	maximal, complemented
6	C₂×#15689690	C₂	1	2	yes	maximal, complemented
7	C₂×#15689687	C₂	1	2	yes	maximal, complemented
8	C₂×#15689682	C₂	1	4	yes	maximal, complemented
9	C₂×#15689669	C₂	1	4	yes	maximal, complemented
10	C₂×#15689634	C₂	1	4	yes	maximal, complemented
11	C₂×#15689630	C₂	1	4	yes	maximal, complemented
12	C₂²×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#10625350	—	2	16	no	—
15	C₂²×#10625350	C₂²	1	2	yes	—
16	C₂²×#10625350	C₂²	1	2	yes	—
17	C₂²×#10625350	C₂²	1	2	yes	complemented
18	C₂²×#10625350	C₂²	1	2	yes	complemented
19	C₂²×#10625350	C₂²	1	16	yes	complemented
20	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₂²⋊D₄₇	C₂²	1	2	yes	—
23	C₂³×C₄×D₄₇	C₂²	1	2	yes	complemented
24	#15689701	C₂²	1	64	yes	complemented
25	#15689697	C₂²	1	32	yes	complemented
26	#15689694	C₂²	1	32	yes	complemented
27	#15689690	C₂²	1	32	yes	complemented
28	#15689687	C₂²	1	32	yes	complemented
29	#15689682	C₂²	1	64	yes	complemented
30	#15689669	C₂²	1	64	yes	complemented
31	C₂×#13094022	C₂²	1	4	yes	complemented
32	C₂×#13094020	C₂²	1	4	yes	complemented
33	C₂×#13094013	C₂²	1	4	yes	complemented
34	C₂×#13094011	C₂²	1	4	yes	complemented
35	#15689634	C₂²	1	64	yes	complemented
36	#15689630	C₂²	1	64	yes	complemented
37	C₂×#13094007	C₂²	1	8	yes	complemented
38	C₂×#13094005	C₂²	1	8	yes	complemented
39	C₂×#13094003	C₂²	1	8	yes	complemented
40	C₂×#13094000	C₂²	1	8	yes	complemented
41	C₂×#13093998	C₂²	1	8	yes	complemented
42	C₂×#13093996	C₂²	1	16	yes	complemented
43	C₂×#13093995	C₂²	1	8	yes	complemented
44	C₂×#13093993	C₂²	1	8	yes	complemented
45	C₂×#13093992	C₂²	1	8	yes	complemented
46	C₂×C₄×C₂²⋊D₄₇	C₂²	1	16	yes	complemented
47	C₂×#13093983	C₂²	1	2	yes	complemented
48	C₂×#13093983	C₂²	1	2	yes	complemented
49	C₂×#13093983	C₂²	1	2	yes	complemented
50	C₂×#13093983	C₂²	1	2	yes	complemented
51	C₂×#13093983	C₂²	1	16	yes	complemented
52	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
53	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
54	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	complemented
55	C₂²×#41×C₄₇	—	2	16	no	—
56	C₂²×#41×C₄₇	C₂²	1	2	yes	—
57	C₂²×#41×C₄₇	C₂²	1	2	yes	—
58	C₂²×#41×C₄₇	C₂²	1	2	yes	complemented
59	C₂²×#41×C₄₇	C₂²	1	2	yes	complemented
60	C₂²×#41×C₄₇	C₂²	1	16	yes	complemented
61	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
62	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
63	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
64	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
65	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	complemented
66	C₂⁴×D₄₇	C₂³	1	2	yes	—
67	C₂×#10625350	—	2	16	no	—
68	C₂×#10625350	—	2	16	no	—
69	C₂×#10625350	—	2	16	no	—
70	C₂×#10625350	—	2	16	no	—
71	C₂×#10625350	—	2	128	no	—
72	C₂×#10625350	C₂³	1	16	yes	—
73	C₂×#10625350	C₂³	1	16	yes	—
74	C₂×#10625350	C₂³	1	16	yes	complemented
75	C₂×#10625350	C₂³	1	16	yes	complemented
76	C₂²×Dic₉₄	—	2	8	no	—
77	C₂²×Dic₉₄	C₂³	1	2	yes	—
78	C₂²×Dic₉₄	C₂³	1	2	yes	—
79	C₂²×Dic₉₄	C₂³	1	8	yes	complemented
80	C₂²×D₁₈₈	—	2	8	no	—
81	C₂²×D₁₈₈	C₂³	1	2	yes	—
82	C₂²×D₁₈₈	C₂³	1	2	yes	—
83	C₂²×D₁₈₈	C₂³	1	8	yes	complemented
84	C₂²×C₂²⋊D₄₇	—	2	16	no	—
85	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
86	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
87	C₂²×C₂²⋊D₄₇	C₂³	1	16	yes	—
88	C₂²×C₂²⋊D₄₇	C₂³	1	16	yes	—
89	C₂³×Dic₄₇	C₂³	1	2	yes	—
90	C₂³×Dic₄₇	C₂³	1	4	yes	—
91	C₂²×C₄×D₄₇	—	2	16	no	—
92	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
93	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
94	C₂²×C₄×D₄₇	C₂³	1	16	yes	complemented
95	#13094022	C₂³	1	32	yes	complemented
96	#13094020	C₂³	1	32	yes	complemented
97	#13094013	C₂³	1	32	yes	complemented
98	#13094011	C₂³	1	32	yes	complemented
99	#13094007	C₂³	1	64	yes	complemented
100	#13094005	C₂³	1	64	yes	complemented
101	#13094003	C₂³	1	64	yes	complemented
102	#13094000	C₂³	1	64	yes	complemented
103	#13093998	C₂³	1	64	yes	complemented
104	#13093996	C₂³	1	128	yes	complemented
105	#13093995	C₂³	1	64	yes	complemented
106	#13093993	C₂³	1	64	yes	complemented
107	#13093992	C₂³	1	64	yes	complemented
108	C₄×C₂²⋊D₄₇	C₂³	1	128	yes	complemented
109	#13093983	C₂³	1	16	yes	complemented
110	#13093983	C₂³	1	16	yes	complemented
111	#13093983	C₂³	1	16	yes	complemented
112	#13093983	C₂³	1	16	yes	complemented
113	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
114	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
115	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
116	C₂×Dic₄₇⋊C₄	C₂³	1	16	yes	—
117	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
118	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
119	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
120	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
121	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	—
122	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
123	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
124	C₂×C₄×Dic₄₇	C₂³	1	16	yes	complemented
125	C₂⁵×C₄₇	C₂³	1	2	yes	—
126	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×#41×C₄₇	—	2	16	no	—
128	C₂×#41×C₄₇	—	2	16	no	—
129	C₂×#41×C₄₇	—	2	16	no	—
130	C₂×#41×C₄₇	—	2	16	no	—
131	C₂×#41×C₄₇	—	2	128	no	—
132	C₂×#41×C₄₇	C₂³	1	16	yes	—
133	C₂×#41×C₄₇	C₂³	1	16	yes	—
134	C₂×#41×C₄₇	C₂³	1	16	yes	complemented
135	C₂×#41×C₄₇	C₂³	1	16	yes	complemented
136	C₂²×Q₈×C₄₇	—	2	8	no	—
137	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
138	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
139	C₂²×Q₈×C₄₇	C₂³	1	8	yes	complemented
140	C₂²×D₄×C₄₇	—	2	16	no	—
141	C₂²×D₄×C₄₇	—	2	8	no	—
142	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
143	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
144	C₂²×D₄×C₄₇	C₂³	1	16	yes	—
145	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
146	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
147	C₂²×D₄×C₄₇	C₂³	1	8	yes	complemented
148	C₂³×C₄×C₄₇	—	2	16	no	—
149	C₂³×C₄×C₄₇	D₄	1	16	yes	complemented
150	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
151	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
152	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
153	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
160	C₂³×C₄×C₄₇	C₂³	1	16	yes	complemented
161	C₂⁴×C₄₇	—	2	8	no	—
162	C₂⁴×C₄₇	—	4	4	no	—
163	C₂⁴×C₄₇	—	4	8	no	—
164	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
165	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
166	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
170	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
171	C₂³×D₄₇	—	2	8	no	—
172	C₂³×D₄₇	—	4	8	no	—
173	C₂³×D₄₇	C₂⁴	1	4	yes	—
174	C₂³×D₄₇	C₂⁴	1	8	yes	—
175	#41×C₄₇	—	2	64	no	—
176	#41×C₄₇	—	2	64	no	—
177	#41×C₄₇	—	2	64	no	—
178	#41×C₄₇	—	2	64	no	—
179	C₂×Q₈×C₄₇	—	2	8	no	—
180	C₂×Q₈×C₄₇	—	2	8	no	—
181	C₂×Q₈×C₄₇	—	2	32	no	—
182	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
183	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
184	C₂×D₄×C₄₇	—	2	16	no	—
185	C₂×D₄×C₄₇	—	2	16	no	—
186	C₂×D₄×C₄₇	—	2	64	no	—
187	C₂×D₄×C₄₇	—	2	8	no	—
188	C₂×D₄×C₄₇	—	2	8	no	—
189	C₂×D₄×C₄₇	—	2	32	no	—
190	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
191	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
192	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
193	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
194	C₂²×C₄×C₄₇	—	2	8	no	—
195	C₂²×C₄×C₄₇	—	2	16	no	—
196	C₂²×C₄×C₄₇	—	2	16	no	—
197	C₂²×C₄×C₄₇	—	2	64	no	—
198	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
199	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
200	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
201	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
202	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
203	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
204	C₂²×C₄×C₄₇	C₂×D₄	1	64	yes	complemented
205	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
207	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
208	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
209	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
219	C₂×C₂²⋊D₄₇	—	2	16	no	—
220	C₂×C₂²⋊D₄₇	—	2	16	no	—
221	C₂×C₂²⋊D₄₇	—	2	64	no	—
222	C₂×C₂²⋊D₄₇	—	4	32	no	—
223	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
224	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
225	C₂×C₂²⋊D₄₇	C₂⁴	1	64	yes	—
226	C₂²×Dic₄₇	—	2	8	no	—
227	C₂²×Dic₄₇	—	4	8	no	—
228	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
229	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
230	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
231	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
232	#10625350	—	2	64	no	—
233	#10625350	—	2	64	no	—
234	#10625350	—	2	64	no	—
235	#10625350	—	2	64	no	—
236	C₂×D₁₈₈	—	2	8	no	—
237	C₂×D₁₈₈	—	2	8	no	—
238	C₂×D₁₈₈	—	2	32	no	—
239	C₂×D₁₈₈	C₂⁴	1	8	yes	—
240	C₂×D₁₈₈	C₂⁴	1	8	yes	—
241	C₂×C₄×D₄₇	—	2	16	no	—
242	C₂×C₄×D₄₇	—	2	16	no	—
243	C₂×C₄×D₄₇	—	2	64	no	—
244	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
245	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
246	C₂×Dic₉₄	—	2	8	no	—
247	C₂×Dic₉₄	—	2	8	no	—
248	C₂×Dic₉₄	—	2	32	no	—
249	C₂×Dic₉₄	C₂⁴	1	8	yes	—
250	C₂×Dic₉₄	C₂⁴	1	8	yes	—
251	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
252	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
253	C₂²⋊Dic₄₇	C₂⁴	1	64	yes	—
254	(C₂×D₄₇)⋊C₄	C₂⁴	1	64	yes	—
255	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
256	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
257	Dic₄₇⋊C₄	C₂⁴	1	64	yes	—
258	C₄×Dic₄₇	C₂⁴	1	16	yes	—
259	C₄×Dic₄₇	C₂⁴	1	16	yes	—
260	C₂³×C₄₇	—	2	4	no	—
261	C₂³×C₄₇	—	2	4	no	—
262	C₂³×C₄₇	—	2	4	no	—
263	C₂³×C₄₇	—	2	16	no	—
264	C₂³×C₄₇	—	2	8	no	—
265	C₂³×C₄₇	—	2	16	no	—
266	C₂³×C₄₇	—	4	16	no	—
267	C₂³×C₄₇	—	4	8	no	—
268	C₂³×C₄₇	—	4	16	no	—
269	C₂³×C₄₇	—	4	32	no	—
270	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
271	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
272	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
273	C₂³×C₄₇	C₂²×D₄	1	16	yes	—
274	C₂³×C₄₇	C₂⁵	1	8	yes	—
275	C₂³×C₄₇	C₂⁵	1	2	yes	—
276	C₂³×C₄₇	C₂⁵	1	2	yes	—
277	C₂³×C₄₇	C₂⁵	1	2	yes	—
278	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
279	C₂²×D₄₇	—	2	16	no	—
280	C₂²×D₄₇	—	2	8	no	—
281	C₂²×D₄₇	—	2	16	no	—
282	C₂²×D₄₇	—	4	16	no	—
283	C₂²×D₄₇	—	4	32	no	—
284	C₂²×D₄₇	C₂⁵	1	8	yes	—
285	Q₈×C₄₇	—	2	16	no	—
286	Q₈×C₄₇	—	2	16	no	—
287	D₄×C₄₇	—	2	32	no	—
288	D₄×C₄₇	—	2	32	no	—
289	D₄×C₄₇	—	2	16	no	—
290	D₄×C₄₇	—	2	16	no	—
291	C₂×C₄×C₄₇	—	2	16	no	—
292	C₂×C₄×C₄₇	—	2	8	no	—
293	C₂×C₄×C₄₇	—	2	32	no	—
294	C₂×C₄×C₄₇	—	2	32	no	—
295	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	—
298	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
299	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
300	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	—
301	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	—
302	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	—
303	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	—
304	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	—
305	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
306	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
307	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
308	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
309	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
310	C₂²⋊D₄₇	—	2	32	no	—
311	C₂²⋊D₄₇	—	2	32	no	—
312	C₂²⋊D₄₇	—	4	64	no	—
313	C₂×Dic₄₇	—	2	16	no	—
314	C₂×Dic₄₇	—	2	8	no	—
315	C₂×Dic₄₇	—	2	16	no	—
316	C₂×Dic₄₇	—	4	16	no	—
317	C₂×Dic₄₇	C₂⁵	1	16	yes	—
318	C₂×Dic₄₇	C₂⁵	1	8	yes	—
319	D₁₈₈	—	2	16	no	—
320	D₁₈₈	—	2	16	no	—
321	C₄×D₄₇	—	2	32	no	—
322	C₄×D₄₇	—	2	32	no	—
323	Dic₉₄	—	2	16	no	—
324	Dic₉₄	—	2	16	no	—
325	C₂×#3449	—	47	1	no	maximal, Sylow
326	C₂²×C₄₇	—	2	4	no	—
327	C₂²×C₄₇	—	2	4	no	—
328	C₂²×C₄₇	—	2	4	no	—
329	C₂²×C₄₇	—	2	8	no	—
330	C₂²×C₄₇	—	2	8	no	—
331	C₂²×C₄₇	—	2	8	no	—
332	C₂²×C₄₇	—	2	8	no	—
333	C₂²×C₄₇	—	2	16	no	—
334	C₂²×C₄₇	—	4	16	no	—
335	C₂²×C₄₇	—	4	32	no	—
336	C₂²×C₄₇	—	4	16	no	—
337	C₂²×C₄₇	C₂³×D₄	1	4	yes	—
338	C₂²×C₄₇	C₂³×D₄	1	4	yes	—
339	C₂²×C₄₇	C₂³×D₄	1	4	yes	—
340	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
341	C₂²×C₄₇	#585	1	4	yes	—
342	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
343	C₂×D₄₇	—	2	8	no	—
344	C₂×D₄₇	—	2	16	no	—
345	C₂×D₄₇	—	4	32	no	—
346	C₂×D₄₇	—	4	16	no	—
347	C₄×C₄₇	—	2	8	no	—
348	C₄×C₄₇	C₂³×D₄	1	4	yes	—
349	C₄×C₄₇	C₂³×D₄	1	4	yes	—
350	C₄×C₄₇	C₂³×D₄	1	4	yes	—
351	C₄×C₄₇	C₂³×D₄	1	4	yes	—
352	Dic₄₇	—	2	8	no	—
353	Dic₄₇	—	2	16	no	—
354	C₂³×#41	—	47	1	no	—
355	C₂³×#41	D₄₇	1	1	yes	characteristic, complemented
356	#3449	—	47	32	no	—
357	C₂×#537	—	47	4	no	—
358	C₂×#536	—	47	2	no	—
359	C₂×#536	—	47	2	no	—
360	C₂×#535	—	47	2	no	—
361	C₂×#535	—	47	2	no	—
362	C₂×#534	—	47	4	no	—
363	C₂×#532	—	47	4	no	—
364	C₂×#525	—	47	4	no	—
365	C₂×#525	—	47	4	no	—
366	C₂²×#117	—	47	1	no	—
367	C₂×C₄₇	—	2	4	no	—
368	C₂×C₄₇	—	2	4	no	—
369	C₂×C₄₇	—	2	4	no	—
370	C₂×C₄₇	—	4	8	no	—
371	C₂×C₄₇	#3449	1	4	yes	complemented
372	C₂×C₄₇	C₂⁴×D₄	1	1	yes	characteristic
373	C₂×C₄₇	C₂×#585	1	2	yes	—
374	D₄₇	—	4	8	no	—
375	C₂²×#41	—	2	16	no	—
376	C₂²×#41	—	47	2	no	—
377	C₂²×#41	—	47	2	no	—
378	C₂²×#41	—	47	2	no	—
379	C₂²×#41	—	47	2	no	—
380	C₂²×#41	—	47	16	no	—
381	C₂²×#41	—	94	16	no	—
382	C₂²×#41	C₂×D₄₇	1	2	yes	—
383	C₂²×#41	C₂×D₄₇	1	2	yes	—
384	C₂²×#41	C₂×D₄₇	1	2	yes	complemented
385	C₂²×#41	C₂×D₄₇	1	2	yes	complemented
386	C₂²×#41	C₂×D₄₇	1	16	yes	complemented
387	C₂³×Q₈	—	47	1	no	—
388	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
389	C₂³×D₄	—	47	2	no	—
390	C₂³×D₄	—	47	1	no	—
391	C₂³×D₄	C₂×D₄₇	1	2	yes	—
392	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
393	C₂⁴×C₄	—	47	2	no	—
394	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
395	C₂⁴×C₄	C₂×D₄₇	1	2	yes	complemented
396	#537	—	47	64	no	—
397	#536	—	47	32	no	—
398	#536	—	47	32	no	—
399	#535	—	47	32	no	—
400	#535	—	47	32	no	—
401	#534	—	47	64	no	—
402	#532	—	47	64	no	—
403	C₂×C₄⋊Q₈	—	47	4	no	—
404	C₂×#127	—	47	4	no	—
405	C₂×#124	—	47	4	no	—
406	C₂×#124	—	47	4	no	—
407	#525	—	47	64	no	—
408	#525	—	47	64	no	—
409	C₂×#123	—	47	8	no	—
410	C₂×#123	—	47	8	no	—
411	C₂×C₂²⋊Q₈	—	47	8	no	—
412	C₂×C₂²⋊Q₈	—	47	8	no	—
413	C₂×#121	—	47	8	no	—
414	C₂×#121	—	47	16	no	—
415	C₂×#121	—	47	8	no	—
416	C₂×#120	—	47	8	no	—
417	C₂×#120	—	47	8	no	—
418	C₂×C₄×D₄	—	47	16	no	—
419	C₂×#117	—	47	2	no	—
420	C₂×#117	—	47	2	no	—
421	C₂×#117	—	47	2	no	—
422	C₂×#117	—	47	2	no	—
423	C₂×#117	—	47	16	no	—
424	C₂²×C₄⋊C₄	—	47	2	no	—
425	C₂²×C₂²⋊C₄	—	47	2	no	—
426	C₂²×C₄²	—	47	2	no	—
427	C₄₇	C₂×#3449	1	1	yes	characteristic, complemented, Sylow
428	C₂⁵	—	47	2	no	—
429	C₂⁵	C₂²×D₄₇	1	2	yes	—
430	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
431	C₂×#41	—	2	16	no	—
432	C₂×#41	—	2	16	no	—
433	C₂×#41	—	2	16	no	—
434	C₂×#41	—	2	16	no	—
435	C₂×#41	—	2	128	no	—
436	C₂×#41	—	47	16	no	—
437	C₂×#41	—	47	16	no	—
438	C₂×#41	—	47	16	no	—
439	C₂×#41	—	47	16	no	—
440	C₂×#41	—	94	16	no	—
441	C₂×#41	—	94	16	no	—
442	C₂×#41	—	94	16	no	—
443	C₂×#41	—	94	16	no	—
444	C₂×#41	—	94	128	no	—
445	C₂×#41	C₂²×D₄₇	1	16	yes	—
446	C₂×#41	C₂²×D₄₇	1	16	yes	—
447	C₂×#41	C₂²×D₄₇	1	16	yes	complemented
448	C₂×#41	C₂²×D₄₇	1	16	yes	complemented
449	C₂²×Q₈	—	2	8	no	—
450	C₂²×Q₈	—	47	2	no	—
451	C₂²×Q₈	—	47	2	no	—
452	C₂²×Q₈	—	47	8	no	—
453	C₂²×Q₈	—	94	8	no	—
454	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
455	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
456	C₂²×Q₈	C₂²×D₄₇	1	8	yes	complemented
457	C₂²×D₄	—	2	16	no	—
458	C₂²×D₄	—	2	8	no	—
459	C₂²×D₄	—	47	4	no	—
460	C₂²×D₄	—	47	4	no	—
461	C₂²×D₄	—	47	16	no	—
462	C₂²×D₄	—	47	16	no	—
463	C₂²×D₄	—	47	2	no	—
464	C₂²×D₄	—	47	2	no	—
465	C₂²×D₄	—	47	8	no	—
466	C₂²×D₄	—	94	16	no	—
467	C₂²×D₄	—	94	8	no	—
468	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
469	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
470	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
471	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
472	C₂²×D₄	C₂²×D₄₇	1	16	yes	—
473	C₂²×D₄	C₂²×D₄₇	1	8	yes	complemented
474	C₂³×C₄	—	2	16	no	—
475	C₂³×C₄	—	47	2	no	—
476	C₂³×C₄	—	47	4	no	—
477	C₂³×C₄	—	47	4	no	—
478	C₂³×C₄	—	47	16	no	—
479	C₂³×C₄	—	47	4	no	—
480	C₂³×C₄	—	94	16	no	—
481	C₂³×C₄	C₂²⋊D₄₇	1	16	yes	complemented
482	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
483	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
484	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
485	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
486	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
487	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
488	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
489	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
490	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
491	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
492	C₂³×C₄	C₂²×D₄₇	1	16	yes	complemented
493	C₄⋊Q₈	—	47	32	no	—
494	#127	—	47	32	no	—
495	#124	—	47	32	no	—
496	#124	—	47	32	no	—
497	#123	—	47	64	no	—
498	#123	—	47	64	no	—
499	C₂²⋊Q₈	—	47	64	no	—
500	C₂²⋊Q₈	—	47	64	no	—
501	#121	—	47	64	no	—
502	#121	—	47	128	no	—
503	#121	—	47	64	no	—
504	#120	—	47	64	no	—
505	#120	—	47	64	no	—
506	C₄×D₄	—	47	128	no	—
507	#117	—	47	16	no	—
508	#117	—	47	16	no	—
509	#117	—	47	16	no	—
510	#117	—	47	16	no	—
511	C₂×C₄⋊C₄	—	47	4	no	—
512	C₂×C₄⋊C₄	—	47	4	no	—
513	C₂×C₄⋊C₄	—	47	16	no	—
514	C₂×C₄⋊C₄	—	47	16	no	—
515	C₂×C₂²⋊C₄	—	47	4	no	—
516	C₂×C₂²⋊C₄	—	47	4	no	—
517	C₂×C₂²⋊C₄	—	47	16	no	—
518	C₂×C₂²⋊C₄	—	47	16	no	—
519	C₂×C₂²⋊C₄	—	47	16	no	—
520	C₂×C₄²	—	47	4	no	—
521	C₂×C₄²	—	47	16	no	—
522	C₂×C₄²	—	47	4	no	—
523	C₂⁴	—	2	8	no	—
524	C₂⁴	—	4	4	no	—
525	C₂⁴	—	4	8	no	—
526	C₂⁴	—	47	4	no	—
527	C₂⁴	—	47	8	no	—
528	C₂⁴	—	94	8	no	—
529	C₂⁴	—	188	8	no	—
530	C₂⁴	C₂×C₂²⋊D₄₇	1	8	yes	—
531	C₂⁴	C₂³×D₄₇	1	4	yes	—
532	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
533	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
534	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
535	C₂⁴	C₂³×D₄₇	1	8	yes	—
536	C₂⁴	C₂³×D₄₇	1	4	yes	—
537	#41	—	2	64	no	—
538	#41	—	2	64	no	—
539	#41	—	2	64	no	—
540	#41	—	2	64	no	—
541	#41	—	94	64	no	—
542	#41	—	94	64	no	—
543	#41	—	94	64	no	—
544	#41	—	94	64	no	—
545	C₂×Q₈	—	2	8	no	—
546	C₂×Q₈	—	2	8	no	—
547	C₂×Q₈	—	2	32	no	—
548	C₂×Q₈	—	47	8	no	—
549	C₂×Q₈	—	47	8	no	—
550	C₂×Q₈	—	94	8	no	—
551	C₂×Q₈	—	94	8	no	—
552	C₂×Q₈	—	94	32	no	—
553	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
554	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
555	C₂×D₄	—	2	16	no	—
556	C₂×D₄	—	2	16	no	—
557	C₂×D₄	—	2	64	no	—
558	C₂×D₄	—	2	8	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	2	32	no	—
561	C₂×D₄	—	47	16	no	—
562	C₂×D₄	—	47	16	no	—
563	C₂×D₄	—	47	64	no	—
564	C₂×D₄	—	47	8	no	—
565	C₂×D₄	—	47	8	no	—
566	C₂×D₄	—	94	16	no	—
567	C₂×D₄	—	94	16	no	—
568	C₂×D₄	—	94	64	no	—
569	C₂×D₄	—	94	8	no	—
570	C₂×D₄	—	94	8	no	—
571	C₂×D₄	—	94	32	no	—
572	C₂×D₄	—	188	32	no	—
573	C₂×D₄	C₂³×D₄₇	1	16	yes	—
574	C₂×D₄	C₂³×D₄₇	1	16	yes	—
575	C₂×D₄	C₂³×D₄₇	1	8	yes	—
576	C₂×D₄	C₂³×D₄₇	1	8	yes	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	16	no	—
579	C₂²×C₄	—	2	16	no	—
580	C₂²×C₄	—	2	64	no	—
581	C₂²×C₄	—	47	8	no	—
582	C₂²×C₄	—	47	4	no	—
583	C₂²×C₄	—	47	8	no	—
584	C₂²×C₄	—	47	16	no	—
585	C₂²×C₄	—	47	16	no	—
586	C₂²×C₄	—	47	16	no	—
587	C₂²×C₄	—	94	8	no	—
588	C₂²×C₄	—	94	16	no	—
589	C₂²×C₄	—	94	16	no	—
590	C₂²×C₄	—	94	64	no	—
591	C₂²×C₄	—	188	8	no	—
592	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
593	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
594	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
595	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
596	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
597	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
598	C₂²×C₄	C₂×C₂²⋊D₄₇	1	64	yes	complemented
599	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
600	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
601	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
602	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
603	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
604	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
605	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
606	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
607	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
608	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
609	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
610	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
611	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
612	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
613	C₄⋊C₄	—	47	64	no	—
614	C₄⋊C₄	—	47	16	no	—
615	C₄⋊C₄	—	47	16	no	—
616	C₂²⋊C₄	—	47	16	no	—
617	C₂²⋊C₄	—	47	16	no	—
618	C₂²⋊C₄	—	47	64	no	—
619	C₂²⋊C₄	—	47	64	no	—
620	C₄²	—	47	16	no	—
621	C₄²	—	47	16	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	16	no	—
626	C₂³	—	2	8	no	—
627	C₂³	—	2	16	no	—
628	C₂³	—	4	16	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	16	no	—
631	C₂³	—	4	32	no	—
632	C₂³	—	47	8	no	—
633	C₂³	—	94	16	no	—
634	C₂³	—	94	8	no	—
635	C₂³	—	94	16	no	—
636	C₂³	—	188	16	no	—
637	C₂³	—	188	32	no	—
638	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
639	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
640	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
641	C₂³	C₂²×C₂²⋊D₄₇	1	16	yes	—
642	C₂³	C₂⁴×D₄₇	1	8	yes	—
643	C₂³	C₂⁴×D₄₇	1	2	yes	—
644	C₂³	C₂⁴×D₄₇	1	2	yes	—
645	C₂³	C₂⁴×D₄₇	1	2	yes	—
646	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
647	Q₈	—	2	16	no	—
648	Q₈	—	2	16	no	—
649	Q₈	—	94	16	no	—
650	Q₈	—	94	16	no	—
651	D₄	—	2	32	no	—
652	D₄	—	2	32	no	—
653	D₄	—	2	16	no	—
654	D₄	—	2	16	no	—
655	D₄	—	94	32	no	—
656	D₄	—	94	32	no	—
657	D₄	—	94	16	no	—
658	D₄	—	94	16	no	—
659	D₄	—	188	64	no	—
660	C₂×C₄	—	2	16	no	—
661	C₂×C₄	—	2	8	no	—
662	C₂×C₄	—	2	32	no	—
663	C₂×C₄	—	2	32	no	—
664	C₂×C₄	—	47	16	no	—
665	C₂×C₄	—	47	8	no	—
666	C₂×C₄	—	94	16	no	—
667	C₂×C₄	—	94	8	no	—
668	C₂×C₄	—	94	16	no	—
669	C₂×C₄	—	94	32	no	—
670	C₂×C₄	—	94	32	no	—
671	C₂×C₄	—	188	16	no	—
672	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
673	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
674	C₂×C₄	C₂²×C₂²⋊D₄₇	1	16	yes	—
675	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
676	C₂×C₄	C₂²×C₂²⋊D₄₇	1	16	yes	—
677	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
678	C₂×C₄	C₂²×C₂²⋊D₄₇	1	16	yes	—
679	C₂×C₄	C₂²×C₂²⋊D₄₇	1	16	yes	—
680	C₂×C₄	C₂²×C₂²⋊D₄₇	1	16	yes	—
681	C₂×C₄	C₂²×C₂²⋊D₄₇	1	16	yes	—
682	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
683	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
684	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
685	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
686	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	8	no	—
691	C₂²	—	2	8	no	—
692	C₂²	—	2	8	no	—
693	C₂²	—	2	8	no	—
694	C₂²	—	2	16	no	—
695	C₂²	—	4	16	no	—
696	C₂²	—	4	32	no	—
697	C₂²	—	4	16	no	—
698	C₂²	—	94	8	no	—
699	C₂²	—	94	16	no	—
700	C₂²	—	188	32	no	—
701	C₂²	—	188	16	no	—
702	C₂²	C₂³×C₂²⋊D₄₇	1	4	yes	—
703	C₂²	C₂³×C₂²⋊D₄₇	1	4	yes	—
704	C₂²	C₂³×C₂²⋊D₄₇	1	4	yes	—
705	C₂²	C₂³×C₂²⋊D₄₇	1	2	yes	—
706	C₂²	#15689959	1	4	yes	—
707	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
708	C₄	—	2	8	no	—
709	C₄	—	94	8	no	—
710	C₄	—	94	16	no	—
711	C₄	C₂³×C₂²⋊D₄₇	1	4	yes	—
712	C₄	C₂³×C₂²⋊D₄₇	1	4	yes	—
713	C₄	C₂³×C₂²⋊D₄₇	1	4	yes	—
714	C₄	C₂³×C₂²⋊D₄₇	1	4	yes	—
715	C₂	—	2	4	no	—
716	C₂	—	2	4	no	—
717	C₂	—	2	4	no	—
718	C₂	—	4	8	no	—
719	C₂	—	188	8	no	—
720	C₂	#20256717	1	4	yes	direct product factor
721	C₂	C₂⁴×C₂²⋊D₄₇	1	1	yes	characteristic
722	C₂	C₂×#15689959	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂³×#41×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂³×#41	D₄₇
hypocenter	C₄₇	C₂×#3449
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂³×#10625350	C₂	semidirect
2. #20256717	C₂	direct (N × H)
3. C₂×#15689701	C₂	semidirect
4. C₂×#15689697	C₂	semidirect
5. C₂×#15689694	C₂	semidirect
6. C₂×#15689690	C₂	semidirect
7. C₂×#15689687	C₂	semidirect
8. C₂×#15689682	C₂	semidirect
9. C₂×#15689669	C₂	semidirect
10. C₂×#15689634	C₂	semidirect
11. C₂×#15689630	C₂	semidirect
12. C₂²×#13093983	C₂	semidirect
13. C₂³×#41×C₄₇	C₂	semidirect
17. C₂²×#10625350	C₂²	semidirect
18. C₂²×#10625350	C₂²	semidirect
19. C₂²×#10625350	C₂²	semidirect
20. C₂³×Dic₉₄	C₂²	semidirect
21. C₂³×D₁₈₈	C₂²	semidirect
23. C₂³×C₄×D₄₇	C₂²	semidirect
24. #15689701	C₂²	semidirect
25. #15689697	C₂²	semidirect
26. #15689694	C₂²	semidirect
27. #15689690	C₂²	semidirect
28. #15689687	C₂²	semidirect
29. #15689682	C₂²	semidirect
30. #15689669	C₂²	semidirect
31. C₂×#13094022	C₂²	semidirect
32. C₂×#13094020	C₂²	semidirect
33. C₂×#13094013	C₂²	semidirect
34. C₂×#13094011	C₂²	semidirect
35. #15689634	C₂²	semidirect
36. #15689630	C₂²	semidirect
37. C₂×#13094007	C₂²	semidirect
38. C₂×#13094005	C₂²	semidirect
39. C₂×#13094003	C₂²	semidirect
40. C₂×#13094000	C₂²	semidirect
41. C₂×#13093998	C₂²	semidirect
42. C₂×#13093996	C₂²	semidirect
43. C₂×#13093995	C₂²	semidirect
44. C₂×#13093993	C₂²	semidirect
45. C₂×#13093992	C₂²	semidirect
46. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
47. C₂×#13093983	C₂²	semidirect
48. C₂×#13093983	C₂²	semidirect
49. C₂×#13093983	C₂²	semidirect
50. C₂×#13093983	C₂²	semidirect
51. C₂×#13093983	C₂²	semidirect
52. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
54. C₂²×C₄×Dic₄₇	C₂²	semidirect
58. C₂²×#41×C₄₇	C₂²	semidirect
59. C₂²×#41×C₄₇	C₂²	semidirect
60. C₂²×#41×C₄₇	C₂²	semidirect
61. C₂³×Q₈×C₄₇	C₂²	semidirect
63. C₂³×D₄×C₄₇	C₂²	semidirect
65. C₂⁴×C₄×C₄₇	C₂²	semidirect
74. C₂×#10625350	C₂³	semidirect
75. C₂×#10625350	C₂³	semidirect
79. C₂²×Dic₉₄	C₂³	semidirect
83. C₂²×D₁₈₈	C₂³	semidirect
94. C₂²×C₄×D₄₇	C₂³	semidirect
95. #13094022	C₂³	semidirect
96. #13094020	C₂³	semidirect
97. #13094013	C₂³	semidirect
98. #13094011	C₂³	semidirect
99. #13094007	C₂³	semidirect
100. #13094005	C₂³	semidirect
101. #13094003	C₂³	semidirect
102. #13094000	C₂³	semidirect
103. #13093998	C₂³	semidirect
104. #13093996	C₂³	semidirect
105. #13093995	C₂³	semidirect
106. #13093993	C₂³	semidirect
107. #13093992	C₂³	semidirect
108. C₄×C₂²⋊D₄₇	C₂³	semidirect
109. #13093983	C₂³	semidirect
110. #13093983	C₂³	semidirect
111. #13093983	C₂³	semidirect
112. #13093983	C₂³	semidirect
115. C₂×C₄⋊Dic₄₇	C₂³	semidirect
124. C₂×C₄×Dic₄₇	C₂³	semidirect
134. C₂×#41×C₄₇	C₂³	semidirect
135. C₂×#41×C₄₇	C₂³	semidirect
139. C₂²×Q₈×C₄₇	C₂³	semidirect
147. C₂²×D₄×C₄₇	C₂³	semidirect
149. C₂³×C₄×C₄₇	D₄	semidirect
160. C₂³×C₄×C₄₇	C₂³	semidirect
204. C₂²×C₄×C₄₇	C₂×D₄	semidirect
355. C₂³×#41	D₄₇	semidirect
371. C₂×C₄₇	#3449	semidirect
384. C₂²×#41	C₂×D₄₇	semidirect
385. C₂²×#41	C₂×D₄₇	semidirect
386. C₂²×#41	C₂×D₄₇	semidirect
388. C₂³×Q₈	C₂×D₄₇	semidirect
392. C₂³×D₄	C₂×D₄₇	semidirect
395. C₂⁴×C₄	C₂×D₄₇	semidirect
427. C₄₇	C₂×#3449	semidirect
447. C₂×#41	C₂²×D₄₇	semidirect
448. C₂×#41	C₂²×D₄₇	semidirect
456. C₂²×Q₈	C₂²×D₄₇	semidirect
473. C₂²×D₄	C₂²×D₄₇	semidirect
481. C₂³×C₄	C₂²⋊D₄₇	semidirect
492. C₂³×C₄	C₂²×D₄₇	semidirect
598. C₂²×C₄	C₂×C₂²⋊D₄₇	semidirect
720. C₂	#20256717	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10625350	2
#20256717	2
C₂×#15689701	2
C₂×#15689697	2
C₂×#15689694	2
C₂×#15689690	2
C₂×#15689687	2
C₂×#15689682	2
C₂×#15689669	2
C₂×#15689634	2
C₂×#15689630	2
C₂²×#13093983	2
C₂³×#41×C₄₇	2
C₂×#3449	47

Subgroups — C2×#20256717 #27123115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20256717 #27123115