Subgroups — C₂×#20245866 #26374654

Order 12032.

2750 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245866	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15689030	C₂	1	2	yes	maximal
3	C₂×#15689022	C₂	1	2	yes	maximal
4	C₂×#15689009	C₂	1	4	yes	maximal
5	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₄⋊Dic₄₇	C₂	1	2	yes	maximal
7	C₂×#15688969	C₂	1	2	yes	maximal
8	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
11	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
13	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
16	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
17	#15689030	C₂²	1	16	yes	—
18	#15689022	C₂²	1	16	yes	—
19	#15689009	C₂²	1	32	yes	—
20	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	—
21	C₄×C₄⋊Dic₄₇	C₂²	1	16	yes	—
22	#15688969	C₂²	1	16	yes	—
23	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
24	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
25	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
26	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
27	C₄²×Dic₄₇	C₂²	1	8	yes	—
28	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₄₇	C₄	1	16	yes	complemented
30	C₂×C₄×Q₈×C₄₇	C₂²	1	8	yes	—
31	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
35	C₂³×Dic₄₇	C₂³	1	4	yes	—
36	C₂³×Dic₄₇	C₂³	1	2	yes	—
37	C₂³×Dic₄₇	C₂³	1	2	yes	—
38	C₂×C₄⋊Dic₄₇	—	2	8	no	—
39	C₂×C₄⋊Dic₄₇	—	2	16	no	—
40	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	—
41	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
42	C₂×C₄×Dic₄₇	—	2	8	no	—
43	C₂×C₄×Dic₄₇	—	2	4	no	—
44	C₂×C₄×Dic₄₇	—	2	8	no	—
45	C₂×C₄×Dic₄₇	—	2	8	no	—
46	C₂×C₄×Dic₄₇	Q₈	1	8	yes	complemented
47	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
48	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
49	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
50	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
51	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
52	C₄₇⋊#95	C₂³	1	16	yes	—
53	C₄₇⋊#95	C₂³	1	16	yes	—
54	C₄₇⋊#95	C₂³	1	8	yes	—
55	C₄₇⋊#95	C₂³	1	16	yes	—
56	C₂²×Q₈×C₄₇	—	2	8	no	—
57	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	—
58	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
60	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₄₇	C₂×C₄	1	64	yes	complemented
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	16	yes	—
70	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
73	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
74	C₂×Q₈×C₄₇	—	2	32	no	—
75	C₂×Q₈×C₄₇	—	2	16	no	—
76	C₂×Q₈×C₄₇	C₂²×C₄	1	16	yes	—
77	C₂²×C₄×C₄₇	—	2	8	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	8	no	—
80	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
86	C₂²×C₄×C₄₇	#41	1	8	yes	—
87	C₂²×C₄×C₄₇	#41	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
93	C₂²×Dic₄₇	—	2	4	no	—
94	C₂²×Dic₄₇	—	2	4	no	—
95	C₂²×Dic₄₇	—	2	4	no	—
96	C₂²×Dic₄₇	—	2	4	no	—
97	C₂²×Dic₄₇	—	2	8	no	—
98	C₂²×Dic₄₇	—	2	8	no	—
99	C₂²×Dic₄₇	—	2	8	no	—
100	C₂²×Dic₄₇	C₂×Q₈	1	8	yes	—
101	C₂²×Dic₄₇	#41	1	8	yes	—
102	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
103	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
104	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
105	C₄⋊C₄×C₄₇	C₂²×C₄	1	32	yes	—
106	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
107	C₄²×C₄₇	C₂²×C₄	1	32	yes	—
108	C₄²×C₄₇	C₂²×C₄	1	16	yes	—
109	C₄⋊Dic₄₇	—	2	16	no	—
110	C₄⋊Dic₄₇	—	2	32	no	—
111	C₄×Dic₄₇	—	2	16	no	—
112	C₄×Dic₄₇	—	2	8	no	—
113	C₄×Dic₄₇	—	2	16	no	—
114	C₄×Dic₄₇	—	2	16	no	—
115	C₄×Dic₄₇	C₂×Q₈	1	16	yes	complemented
116	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
117	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
118	C₂³×C₄₇	C₂×#41	1	4	yes	—
119	C₂³×C₄₇	C₂×#41	1	4	yes	—
120	C₂³×C₄₇	C₂×#41	1	2	yes	—
121	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
122	Q₈×C₄₇	—	2	32	no	—
123	C₂×C₄×C₄₇	—	2	16	no	—
124	C₂×C₄×C₄₇	—	2	8	no	—
125	C₂×C₄×C₄₇	—	2	16	no	—
126	C₂×C₄×C₄₇	—	2	4	no	—
127	C₂×C₄×C₄₇	—	2	8	no	—
128	C₂×C₄×C₄₇	—	2	8	no	—
129	C₂×C₄×C₄₇	#117	1	16	yes	—
130	C₂×C₄×C₄₇	C₄×Q₈	1	16	yes	—
131	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
132	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
133	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
134	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
135	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
136	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
137	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
138	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
139	C₂×Dic₄₇	—	2	16	no	—
140	C₂×Dic₄₇	—	2	16	no	—
141	C₂×Dic₄₇	—	2	4	no	—
142	C₂×Dic₄₇	—	2	4	no	—
143	C₂×Dic₄₇	—	2	4	no	—
144	C₂×Dic₄₇	—	2	4	no	—
145	C₂×Dic₄₇	—	2	8	no	—
146	C₂×Dic₄₇	—	2	8	no	—
147	C₂×Dic₄₇	—	2	8	no	—
148	C₂×Dic₄₇	—	4	16	no	—
149	C₂×Dic₄₇	C₂²×Q₈	1	8	yes	—
150	C₂×Dic₄₇	C₂×#41	1	8	yes	—
151	C₂×#2295	—	47	1	no	maximal, Sylow
152	C₂²×C₄₇	C₂×#117	1	4	yes	—
153	C₂²×C₄₇	C₂×C₄×Q₈	1	4	yes	—
154	C₂²×C₄₇	C₄×#41	1	4	yes	—
155	C₂²×C₄₇	#529	1	8	yes	—
156	C₂²×C₄₇	#533	1	8	yes	—
157	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
158	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
159	C₂²×C₄₇	C₂²×#41	1	2	yes	—
160	C₂²×C₄₇	C₂²×#41	1	2	yes	—
161	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
162	C₄×C₄₇	—	2	8	no	—
163	C₄×C₄₇	—	2	4	no	—
164	C₄×C₄₇	—	2	8	no	—
165	C₄×C₄₇	C₂×#117	1	8	yes	—
166	C₄×C₄₇	C₂×C₄×Q₈	1	8	yes	—
167	Dic₄₇	—	2	8	no	—
168	Dic₄₇	—	2	8	no	—
169	Dic₄₇	—	4	8	no	—
170	C₂²×C₄×Q₈	D₄₇	1	1	yes	characteristic
171	#2295	—	47	16	no	—
172	C₂×#391	—	47	2	no	—
173	C₂×#389	—	47	2	no	—
174	C₂×#387	—	47	4	no	—
175	C₂×C₄×C₄⋊C₄	—	47	2	no	—
176	C₂×C₄×C₄⋊C₄	—	47	1	no	—
177	C₂×#376	—	47	2	no	—
178	C₂×C₄³	—	47	1	no	—
179	C₂×C₄₇	#2295	1	8	yes	complemented
180	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
181	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
182	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
183	C₂×C₄₇	C₂×#529	1	2	yes	—
184	C₂×C₄₇	C₂×#533	1	2	yes	—
185	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
186	C₂×C₄×Q₈	Dic₄₇	1	16	yes	complemented
187	C₂×C₄×Q₈	C₂×D₄₇	1	8	yes	—
188	C₂²×C₄⋊C₄	—	47	4	no	—
189	C₂²×C₄⋊C₄	—	47	2	no	—
190	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
191	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
192	C₂²×C₄²	—	47	1	no	—
193	C₂²×C₄²	—	47	2	no	—
194	C₂²×C₄²	—	47	2	no	—
195	C₂²×C₄²	—	47	1	no	—
196	C₂²×C₄²	—	47	2	no	—
197	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
198	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
199	#391	—	47	16	no	—
200	#389	—	47	16	no	—
201	#387	—	47	32	no	—
202	C₄×C₄⋊C₄	—	47	8	no	—
203	C₄×C₄⋊C₄	—	47	16	no	—
204	#376	—	47	16	no	—
205	C₂×#95	—	47	4	no	—
206	C₂×#95	—	47	4	no	—
207	C₂×#95	—	47	2	no	—
208	C₂×#95	—	47	4	no	—
209	C₄³	—	47	8	no	—
210	C₄₇	C₂×#2295	1	1	yes	characteristic, complemented, Sylow
211	C₂²×Q₈	—	2	8	no	—
212	C₂²×Q₈	C₂×Dic₄₇	1	8	yes	—
213	C₂²×Q₈	C₂²×D₄₇	1	4	yes	—
214	C₂³×C₄	—	47	2	no	—
215	C₂³×C₄	—	47	2	no	—
216	C₂³×C₄	—	47	4	no	—
217	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
218	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
219	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
220	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
222	C₄×Q₈	C₂×Dic₄₇	1	64	yes	complemented
223	C₂×C₄⋊C₄	—	47	16	no	—
224	C₂×C₄⋊C₄	—	47	8	no	—
225	C₂×C₄⋊C₄	—	94	16	no	—
226	C₂×C₄⋊C₄	—	94	8	no	—
227	C₂×C₄⋊C₄	C₂×Dic₄₇	1	16	yes	—
228	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
229	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
230	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
231	C₂×C₄²	—	47	8	no	—
232	C₂×C₄²	—	47	4	no	—
233	C₂×C₄²	—	47	4	no	—
234	C₂×C₄²	—	47	8	no	—
235	C₂×C₄²	—	47	8	no	—
236	C₂×C₄²	—	47	8	no	—
237	C₂×C₄²	—	94	8	no	—
238	C₂×C₄²	—	94	8	no	—
239	C₂×C₄²	—	94	4	no	—
240	C₂×C₄²	—	94	8	no	—
241	C₂×C₄²	C₂×Dic₄₇	1	16	yes	—
242	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
243	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
244	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
245	#95	—	47	16	no	—
246	#95	—	47	16	no	—
247	#95	—	47	8	no	—
248	#95	—	47	16	no	—
249	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
250	C₂×Q₈	—	2	32	no	—
251	C₂×Q₈	—	2	16	no	—
252	C₂×Q₈	C₂²×Dic₄₇	1	16	yes	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	47	8	no	—
257	C₂²×C₄	—	47	8	no	—
258	C₂²×C₄	—	47	4	no	—
259	C₂²×C₄	—	47	4	no	—
260	C₂²×C₄	—	47	8	no	—
261	C₂²×C₄	—	94	4	no	—
262	C₂²×C₄	—	94	4	no	—
263	C₂²×C₄	—	94	4	no	—
264	C₂²×C₄	—	94	4	no	—
265	C₂²×C₄	—	94	8	no	—
266	C₂²×C₄	—	94	8	no	—
267	C₂²×C₄	—	94	8	no	—
268	C₂²×C₄	#10625350	1	8	yes	—
269	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
270	C₂²×C₄	#10625354	1	4	yes	—
271	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
272	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
273	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
274	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
275	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
276	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
277	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
278	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
279	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
280	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
281	C₄⋊C₄	—	94	32	no	—
282	C₄⋊C₄	—	94	16	no	—
283	C₄⋊C₄	C₂²×Dic₄₇	1	32	yes	—
284	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	—
285	C₄²	—	47	16	no	—
286	C₄²	—	94	16	no	—
287	C₄²	—	94	16	no	—
288	C₄²	—	94	8	no	—
289	C₄²	—	94	16	no	—
290	C₄²	C₂²×Dic₄₇	1	32	yes	—
291	C₄²	C₂²×Dic₄₇	1	16	yes	—
292	C₂³	C₂³×Dic₄₇	1	2	yes	—
293	C₂³	C₂×Q₈×D₄₇	1	2	yes	—
294	C₂³	#41×D₄₇	1	4	yes	—
295	C₂³	C₂×#10625350	1	4	yes	—
296	C₂³	C₂×#10625354	1	2	yes	—
297	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
298	Q₈	—	2	32	no	—
299	C₂×C₄	—	2	16	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	16	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	47	8	no	—
306	C₂×C₄	—	47	8	no	—
307	C₂×C₄	—	94	16	no	—
308	C₂×C₄	—	94	16	no	—
309	C₂×C₄	—	94	4	no	—
310	C₂×C₄	—	94	4	no	—
311	C₂×C₄	—	94	4	no	—
312	C₂×C₄	—	94	4	no	—
313	C₂×C₄	—	94	8	no	—
314	C₂×C₄	—	94	8	no	—
315	C₂×C₄	—	94	8	no	—
316	C₂×C₄	—	188	16	no	—
317	C₂×C₄	#13093983	1	16	yes	—
318	C₂×C₄	Q₈×Dic₄₇	1	16	yes	—
319	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
320	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
321	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
322	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
323	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
324	C₂×C₄	C₂×Q₈×D₄₇	1	4	yes	—
325	C₂×C₄	C₂×#10625350	1	8	yes	—
326	C₂×C₄	C₂×#10625354	1	4	yes	—
327	C₂²	C₂×#13093983	1	4	yes	—
328	C₂²	C₂×Q₈×Dic₄₇	1	4	yes	—
329	C₂²	#41×Dic₄₇	1	4	yes	—
330	C₂²	#15689660	1	8	yes	—
331	C₂²	#15689677	1	8	yes	—
332	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
333	C₂²	C₂²×Q₈×D₄₇	1	1	yes	characteristic
334	C₂²	C₂×#41×D₄₇	1	2	yes	—
335	C₂²	C₂²×#10625350	1	2	yes	—
336	C₂²	C₂²×#10625354	1	1	yes	characteristic
337	C₄	—	2	8	no	—
338	C₄	—	2	4	no	—
339	C₄	—	2	8	no	—
340	C₄	—	94	8	no	—
341	C₄	—	94	8	no	—
342	C₄	—	188	8	no	—
343	C₄	C₂×#13093983	1	8	yes	—
344	C₄	C₂×Q₈×Dic₄₇	1	8	yes	—
345	C₂	#20245866	1	8	yes	direct product factor
346	C₂	C₂²×#13093983	1	1	yes	characteristic
347	C₂	C₂²×Q₈×Dic₄₇	1	1	yes	characteristic
348	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
349	C₂	C₂×#15689660	1	2	yes	—
350	C₂	C₂×#15689677	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂²×C₄×Q₈×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂⁴
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×C₄×Q₈	D₄₇
hypocenter	C₄₇	C₂×#2295
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #20245866	C₂	direct (N × H)
29. C₂×C₄×Q₈×C₄₇	C₄	semidirect
46. C₂×C₄×Dic₄₇	Q₈	semidirect
64. C₄×Q₈×C₄₇	C₂×C₄	semidirect
115. C₄×Dic₄₇	C₂×Q₈	semidirect
179. C₂×C₄₇	#2295	semidirect
186. C₂×C₄×Q₈	Dic₄₇	semidirect
210. C₄₇	C₂×#2295	semidirect
222. C₄×Q₈	C₂×Dic₄₇	semidirect
345. C₂	#20245866	direct (N × H)

Maximal subgroups

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

subgroup	index
#20245866	2
C₂×#15689030	2
C₂×#15689022	2
C₂×#15689009	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×#15688969	2
C₂×C₄²×Dic₄₇	2
C₂²×C₄×Q₈×C₄₇	2
C₂×#2295	47

Subgroups — C2×#20245866 #26374654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245866 #26374654