Subgroups — C₂×#20243411 #26215833

Order 12032.

1790 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093955	C₂	1	2	yes	maximal, complemented
3	C₂×#15688983	C₂	1	1	yes	maximal, characteristic
4	#20243411	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688885	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₇⋊C₈	—	2	8	no	—
8	C₂³×C₄₇⋊C₈	C₄	1	8	yes	complemented
9	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	4	yes	—
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
13	C₂²×C₂²⋊Dic₄₇	—	2	1	no	—
14	C₂×#13093955	—	2	8	no	—
15	C₂×#13093955	C₂²	1	8	yes	complemented
16	#15688983	—	2	2	no	—
17	#15688983	C₂²	1	4	yes	—
18	C₂×C₄₇⋊#95	—	2	1	no	—
19	#15688885	C₂²	1	8	yes	complemented
20	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
23	C₄₇×#380	—	2	2	no	—
24	C₄₇×#380	C₂²	1	4	yes	—
25	C₂×#95×C₄₇	—	2	1	no	—
26	C₂³×Dic₄₇	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	—	2	4	no	—
28	C₂²×C₄₇⋊C₈	—	2	32	no	—
29	C₂²×C₄₇⋊C₈	—	2	16	no	—
30	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
31	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
32	C₂²×C₄₇⋊C₈	C₂×C₄	1	16	yes	complemented
33	C₂²×C₄₇⋊C₈	D₄	1	8	yes	—
34	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
35	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
36	C₂×C₄⋊Dic₄₇	—	2	4	no	—
37	C₂×C₄⋊Dic₄₇	—	2	4	no	—
38	C₂×C₄⋊Dic₄₇	—	2	2	no	—
39	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
40	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
41	C₂×C₂²⋊Dic₄₇	—	4	4	no	—
42	#13093955	—	2	16	no	—
43	C₄₇⋊#95	—	2	4	no	—
44	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	—	2	4	no	—
46	C₂³×C₄×C₄₇	—	2	4	no	—
47	C₂³×C₄×C₄₇	—	2	2	no	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	2	yes	—
51	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
52	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
60	#95×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	—	2	4	no	—
62	C₂⁴×C₄₇	—	2	4	no	—
63	C₂⁴×C₄₇	C₄⋊C₄	1	4	yes	—
64	C₂⁴×C₄₇	SD₁₆	1	4	yes	—
65	C₂⁴×C₄₇	SD₁₆	1	4	yes	—
66	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
67	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	—	2	4	no	—
69	C₂²×C₄×C₄₇	—	2	8	no	—
70	C₂²×C₄×C₄₇	—	2	8	no	—
71	C₂²×C₄×C₄₇	—	2	8	no	—
72	C₂²×C₄×C₄₇	—	2	16	no	—
73	C₂²×C₄×C₄₇	—	2	4	no	—
74	C₂²×C₄×C₄₇	—	2	4	no	—
75	C₂²×C₄×C₄₇	—	2	4	no	—
76	C₂²×C₄×C₄₇	—	4	4	no	—
77	C₂²×C₄×C₄₇	—	4	4	no	—
78	C₂²×C₄×C₄₇	—	4	4	no	—
79	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	8	yes	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₄₇	#41	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₇	—	2	4	no	—
91	C₂²×Dic₄₇	—	4	4	no	—
92	C₂²×Dic₄₇	—	4	4	no	—
93	C₂²×Dic₄₇	—	4	4	no	—
94	C₄⋊C₄×C₄₇	—	2	4	no	—
95	C₄⋊C₄×C₄₇	—	2	4	no	—
96	C₄⋊C₄×C₄₇	—	4	4	no	—
97	C₂²⋊C₄×C₄₇	—	4	8	no	—
98	C₂²⋊Dic₄₇	—	4	8	no	—
99	C₄⋊Dic₄₇	—	2	4	no	—
100	C₄⋊Dic₄₇	—	2	4	no	—
101	C₄⋊Dic₄₇	—	4	4	no	—
102	C₂×C₄₇⋊C₈	—	2	8	no	—
103	C₂×C₄₇⋊C₈	—	2	4	no	—
104	C₂×C₄₇⋊C₈	—	2	32	no	—
105	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	16	yes	complemented
106	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
107	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
108	C₂×C₄₇⋊C₈	C₂×D₄	1	8	yes	—
109	C₂³×C₄₇	—	2	4	no	—
110	C₂³×C₄₇	—	2	4	no	—
111	C₂³×C₄₇	—	2	8	no	—
112	C₂³×C₄₇	—	2	8	no	—
113	C₂³×C₄₇	—	2	16	no	—
114	C₂³×C₄₇	—	2	16	no	—
115	C₂³×C₄₇	#106	1	16	yes	complemented
116	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
117	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
118	C₂³×C₄₇	#121	1	4	yes	—
119	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
120	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
121	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
122	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
123	C₂³×C₄₇	#135	1	4	yes	—
124	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	2	8	no	—
127	C₂×C₄×C₄₇	—	2	4	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	8	no	—
130	C₂×C₄×C₄₇	—	2	16	no	—
131	C₂×C₄×C₄₇	—	4	4	no	—
132	C₂×C₄×C₄₇	—	4	4	no	—
133	C₂×C₄×C₄₇	—	4	4	no	—
134	C₂×C₄×C₄₇	—	8	8	no	—
135	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
136	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₄₇	#117	1	4	yes	—
139	C₂×C₄×C₄₇	#121	1	4	yes	—
140	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
141	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
145	C₂×Dic₄₇	—	4	4	no	—
146	C₂×Dic₄₇	—	4	4	no	—
147	C₂×Dic₄₇	—	4	4	no	—
148	C₂×Dic₄₇	—	8	8	no	—
149	C₄₇⋊C₈	—	2	4	no	—
150	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	8	yes	complemented
151	C₂×#1807	—	47	1	no	maximal, Sylow
152	C₂²×C₄₇	—	2	32	no	—
153	C₂²×C₄₇	—	2	4	no	—
154	C₂²×C₄₇	—	2	4	no	—
155	C₂²×C₄₇	—	2	8	no	—
156	C₂²×C₄₇	—	2	8	no	—
157	C₂²×C₄₇	#380	1	4	yes	—
158	C₂²×C₄₇	C₂×#106	1	4	yes	—
159	C₂²×C₄₇	C₂×#106	1	8	yes	complemented
160	C₂²×C₄₇	#427	1	4	yes	—
161	C₂²×C₄₇	#465	1	8	yes	—
162	C₂²×C₄₇	#465	1	8	yes	—
163	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×C₄₇	C₂×#121	1	2	yes	—
165	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
166	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×#135	1	2	yes	—
168	C₄×C₄₇	—	2	4	no	—
169	C₄×C₄₇	—	8	4	no	—
170	C₄×C₄₇	#380	1	4	yes	—
171	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
173	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
174	Dic₄₇	—	8	4	no	—
175	C₂⁴×C₈	—	47	1	no	—
176	C₂²×#106	—	47	2	no	—
177	C₂×#380	—	47	1	no	—
178	C₂×#380	D₄₇	1	1	yes	characteristic
179	#1807	—	47	8	no	—
180	C₂×#340	—	47	2	no	—
181	C₂×C₄₇	—	2	8	no	—
182	C₂×C₄₇	#1807	1	8	yes	complemented
183	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
184	C₂×C₄₇	C₂²×#106	1	1	yes	characteristic
185	C₂×C₄₇	C₂×#427	1	1	yes	characteristic
186	C₂×C₄₇	C₂×#465	1	2	yes	—
187	C₂×C₄₇	C₂×#465	1	2	yes	—
188	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
189	C₂³×C₈	—	47	1	no	—
190	C₂³×C₈	—	47	8	no	—
191	C₂³×C₈	—	47	4	no	—
192	C₂³×C₈	—	47	1	no	—
193	C₂³×C₈	—	94	8	no	—
194	C₂²×C₄⋊C₄	—	47	2	no	—
195	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
196	C₂²×C₂²⋊C₄	—	2	1	no	—
197	C₂²×C₂²⋊C₄	—	94	1	no	—
198	C₂×#106	—	47	8	no	—
199	C₂×#106	—	94	8	no	—
200	#380	—	2	2	no	—
201	#380	—	47	4	no	—
202	#380	—	94	2	no	—
203	#380	C₂×D₄₇	1	4	yes	—
204	C₂×#95	—	2	1	no	—
205	C₂×#95	—	94	1	no	—
206	#340	—	47	8	no	—
207	C₄₇	C₂×#1807	1	1	yes	characteristic, complemented, Sylow
208	C₂⁵	C₂²⋊D₄₇	1	1	yes	characteristic
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	—	2	4	no	—
211	C₂³×C₄	—	2	2	no	—
212	C₂³×C₄	—	94	2	no	—
213	C₂³×C₄	Dic₉₄	1	4	yes	—
214	C₂³×C₄	C₄×D₄₇	1	4	yes	—
215	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
216	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
218	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
219	C₂²×C₈	—	47	4	no	—
220	C₂²×C₈	—	47	8	no	—
221	C₂²×C₈	—	47	2	no	—
222	C₂²×C₈	—	47	4	no	—
223	C₂²×C₈	—	47	16	no	—
224	C₂²×C₈	—	47	2	no	—
225	C₂²×C₈	—	94	32	no	—
226	C₂²×C₈	—	94	16	no	—
227	C₂²×C₈	—	94	4	no	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	47	4	no	—
232	C₂×C₄⋊C₄	—	94	4	no	—
233	C₂×C₄⋊C₄	—	94	4	no	—
234	C₂×C₄⋊C₄	—	94	2	no	—
235	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
236	C₂×C₂²⋊C₄	—	2	4	no	—
237	C₂×C₂²⋊C₄	—	4	4	no	—
238	C₂×C₂²⋊C₄	—	94	4	no	—
239	C₂×C₂²⋊C₄	—	188	4	no	—
240	#106	—	94	16	no	—
241	#95	—	2	4	no	—
242	#95	—	94	4	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	Dic₄₇⋊C₄	1	4	yes	—
246	C₂⁴	#10625335	1	4	yes	—
247	C₂⁴	#10625336	1	4	yes	—
248	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
249	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	16	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	—	4	4	no	—
261	C₂²×C₄	—	94	4	no	—
262	C₂²×C₄	—	188	4	no	—
263	C₂²×C₄	—	188	4	no	—
264	C₂²×C₄	—	188	4	no	—
265	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
266	C₂²×C₄	Dic₄₇⋊C₄	1	8	yes	—
267	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
268	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
269	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
270	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
271	C₂²×C₄	D₄×D₄₇	1	4	yes	—
272	C₂²×C₄	#10625352	1	4	yes	—
273	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
274	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
275	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
276	C₂×C₈	—	47	16	no	—
277	C₂×C₈	—	47	4	no	—
278	C₂×C₈	—	47	8	no	—
279	C₂×C₈	—	47	4	no	—
280	C₂×C₈	—	94	32	no	—
281	C₂×C₈	—	94	8	no	—
282	C₂×C₈	—	94	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	4	4	no	—
286	C₄⋊C₄	—	94	4	no	—
287	C₄⋊C₄	—	94	4	no	—
288	C₄⋊C₄	—	188	4	no	—
289	C₂²⋊C₄	—	4	8	no	—
290	C₂²⋊C₄	—	188	8	no	—
291	C₂³	—	2	8	no	—
292	C₂³	—	2	16	no	—
293	C₂³	—	2	16	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	2	8	no	—
297	C₂³	#13093955	1	16	yes	complemented
298	C₂³	C₂×Dic₄₇⋊C₄	1	4	yes	—
299	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
300	C₂³	#13093996	1	4	yes	—
301	C₂³	C₂×#10625336	1	4	yes	—
302	C₂³	C₂×#10625336	1	2	yes	—
303	C₂³	C₂×#10625335	1	4	yes	—
304	C₂³	C₂×#10625335	1	2	yes	—
305	C₂³	#13094044	1	4	yes	—
306	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	16	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	8	8	no	—
317	C₂×C₄	—	376	8	no	—
318	C₂×C₄	—	188	4	no	—
319	C₂×C₄	—	188	4	no	—
320	C₂×C₄	—	188	4	no	—
321	C₂×C₄	C₂²⋊C₄×D₄₇	1	4	yes	—
322	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
323	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
324	C₂×C₄	#13093980	1	4	yes	—
325	C₂×C₄	#13093996	1	4	yes	—
326	C₂×C₄	#13094001	1	8	yes	—
327	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
328	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
329	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
330	C₂×C₄	C₂×#10625352	1	2	yes	—
331	C₈	—	47	8	no	—
332	C₈	—	94	4	no	—
333	C₂²	—	2	8	no	—
334	C₂²	—	2	8	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	32	no	—
337	C₂²	—	2	4	no	—
338	C₂²	#15688981	1	4	yes	—
339	C₂²	C₂×#13093955	1	4	yes	—
340	C₂²	C₂×#13093955	1	8	yes	complemented
341	C₂²	#15689159	1	4	yes	—
342	C₂²	#15689350	1	8	yes	—
343	C₂²	#15689354	1	8	yes	—
344	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
345	C₂²	C₂×#13093996	1	2	yes	—
346	C₂²	C₂²×#10625336	1	1	yes	characteristic
347	C₂²	C₂²×#10625335	1	1	yes	characteristic
348	C₂²	C₂×#13094044	1	2	yes	—
349	C₄	—	2	4	no	—
350	C₄	—	8	4	no	—
351	C₄	—	376	4	no	—
352	C₄	#15688981	1	4	yes	—
353	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
354	C₄	C₂×#13093980	1	1	yes	characteristic
355	C₄	C₂×#13094001	1	2	yes	—
356	C₂	—	2	8	no	—
357	C₂	#20243411	1	8	yes	direct product factor
358	C₂	C₂×#15688981	1	1	yes	characteristic
359	C₂	C₂²×#13093955	1	1	yes	characteristic
360	C₂	C₂×#15689159	1	1	yes	characteristic
361	C₂	C₂×#15689350	1	2	yes	—
362	C₂	C₂×#15689354	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#380	C₂
socle	C₂⁴×C₄₇	C₂×D₄
prime radical	C₂⁵×C₄₇	D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#380	D₄₇
hypocenter	C₄₇	C₂×#1807
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂×#380

Complements

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

N	H ≅ G/N	type
2. C₂²×#13093955	C₂	semidirect
4. #20243411	C₂	direct (N × H)
5. C₂×#15688885	C₂	semidirect
8. C₂³×C₄₇⋊C₈	C₄	semidirect
15. C₂×#13093955	C₂²	semidirect
19. #15688885	C₂²	semidirect
32. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
105. C₂×C₄₇⋊C₈	C₂²⋊C₄	semidirect
115. C₂³×C₄₇	#106	semidirect
150. C₄₇⋊C₈	C₂×C₂²⋊C₄	semidirect
159. C₂²×C₄₇	C₂×#106	semidirect
182. C₂×C₄₇	#1807	semidirect
207. C₄₇	C₂×#1807	semidirect
297. C₂³	#13093955	semidirect
340. C₂²	C₂×#13093955	semidirect
357. C₂	#20243411	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄₇⋊C₈	2
C₂²×#13093955	2
C₂×#15688983	2
#20243411	2
C₂×#15688885	2
C₂×C₄₇×#380	2
C₂×#1807	47

Subgroups — C2×#20243411 #26215833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243411 #26215833