Subgroups — C₂×#20242161 #26185337

Order 12032.

770 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689174	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689145	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20242161	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688876	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625324	—	2	1	no	—
10	C₂²×C₈×D₄₇	—	2	1	no	—
11	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	#15689174	C₄	1	4	yes	—
13	#15689174	C₂²	1	4	yes	—
14	#15689145	—	2	2	no	—
15	#15689145	C₂²	1	4	yes	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₇⋊C₈	—	2	1	no	—
19	C₂×Dic₄₇⋊C₈	—	2	1	no	—
20	C₂×Dic₄₇⋊C₈	C₄	1	1	yes	characteristic
21	C₂×Dic₄₇⋊C₈	C₄	1	1	yes	characteristic
22	C₄⋊C₈×D₄₇	—	2	2	no	—
23	C₄⋊C₈×D₄₇	C₂²	1	4	yes	—
24	C₂×(C₂×D₄₇)⋊C₈	C₄	1	1	yes	characteristic
25	C₂×(C₂×D₄₇)⋊C₈	C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	#15688876	C₂²	1	4	yes	complemented
28	#15688875	C₂²	1	4	yes	complemented
29	#15688875	C₂²	1	4	yes	complemented
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#335	C₂²	1	4	yes	complemented
34	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
37	C₂×#10625324	—	2	4	no	—
38	C₂×#10625324	—	4	4	no	—
39	C₂²×C₄₇⋊C₈	—	2	1	no	—
40	C₂²×C₄₇⋊C₈	—	2	1	no	—
41	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₄₇	—	2	4	no	—
44	C₂×C₈×D₄₇	—	4	4	no	—
45	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
48	C₄²×D₄₇	C₂×C₄	1	2	yes	—
49	C₄²×D₄₇	D₄	1	2	yes	—
50	C₄²×D₄₇	Q₈	1	2	yes	—
51	C₄²×D₄₇	C₂³	1	2	yes	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	Dic₄₇⋊C₈	—	2	4	no	—
57	Dic₄₇⋊C₈	—	2	4	no	—
58	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
59	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
60	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
61	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
62	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
63	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
64	C₂²×C₈×C₄₇	—	2	1	no	—
65	C₂²×C₈×C₄₇	—	2	1	no	—
66	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₄₇	—	2	1	no	—
70	C₄⋊C₈×C₄₇	—	2	1	no	—
71	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
72	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
73	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
74	C₄×C₈×C₄₇	C₂³	1	2	yes	—
75	C₂³×D₄₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
79	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₄₇	—	2	2	no	—
83	C₂×C₄×D₄₇	—	2	2	no	—
84	C₂×C₄×D₄₇	—	4	2	no	—
85	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
86	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
87	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
88	C₂×C₄×D₄₇	D₈	1	4	yes	—
89	C₂×C₄×D₄₇	Q₁₆	1	4	yes	—
90	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
91	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
92	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
93	C₂×C₈×C₄₇	—	2	2	no	—
94	C₂×C₈×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	—	2	2	no	—
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	4	2	no	—
98	C₂×C₈×C₄₇	—	4	2	no	—
99	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
101	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
104	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
106	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
107	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
108	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
109	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
110	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
111	C₂×C₄₇⋊C₈	—	2	2	no	—
112	C₂×C₄₇⋊C₈	—	2	2	no	—
113	C₂×C₄₇⋊C₈	—	2	2	no	—
114	C₂×C₄₇⋊C₈	—	2	2	no	—
115	C₂×C₄₇⋊C₈	—	4	2	no	—
116	C₂×C₄₇⋊C₈	—	4	2	no	—
117	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
118	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
119	#10625324	—	4	8	no	—
120	C₈×D₄₇	—	4	8	no	—
121	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂²×D₄₇	—	2	2	no	—
123	C₂²×D₄₇	—	2	2	no	—
124	C₂²×D₄₇	#107	1	4	yes	—
125	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₄₇	#131	1	2	yes	—
131	C₂×C₄×C₄₇	#131	1	2	yes	—
132	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
133	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
134	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
137	C₂×Dic₄₇	—	2	2	no	—
138	C₂×Dic₄₇	—	2	2	no	—
139	C₂×Dic₄₇	#107	1	4	yes	—
140	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
143	C₄×D₄₇	—	2	2	no	—
144	C₄×D₄₇	—	2	2	no	—
145	C₄×D₄₇	—	2	4	no	—
146	C₄×D₄₇	—	4	2	no	—
147	C₄×D₄₇	—	4	2	no	—
148	C₄×D₄₇	#107	1	8	yes	—
149	C₄×D₄₇	C₂×D₈	1	4	yes	—
150	C₄×D₄₇	C₂×Q₁₆	1	4	yes	—
151	C₈×C₄₇	—	2	2	no	—
152	C₈×C₄₇	—	2	2	no	—
153	C₈×C₄₇	—	4	2	no	—
154	C₈×C₄₇	—	4	2	no	—
155	C₄₇⋊C₈	—	2	2	no	—
156	C₄₇⋊C₈	—	2	2	no	—
157	C₄₇⋊C₈	—	4	2	no	—
158	C₄₇⋊C₈	—	4	2	no	—
159	C₂×#1571	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	#424	1	2	yes	—
161	C₂²×C₄₇	C₂×#107	1	2	yes	—
162	C₂²×C₄₇	#430	1	2	yes	—
163	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
164	C₂×D₄₇	—	2	8	no	—
165	C₂×D₄₇	—	2	2	no	—
166	C₂×D₄₇	—	2	2	no	—
167	C₂×D₄₇	C₂×#107	1	4	yes	—
168	C₄×C₄₇	—	2	1	no	—
169	C₄×C₄₇	—	2	1	no	—
170	C₄×C₄₇	#424	1	2	yes	—
171	C₄×C₄₇	C₂×#107	1	2	yes	—
172	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
173	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
174	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
175	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
176	Dic₄₇	—	2	2	no	—
177	Dic₄₇	—	2	2	no	—
178	Dic₄₇	C₂×#107	1	4	yes	—
179	C₂×#431	—	47	1	no	—
180	C₂×#423	—	47	1	no	—
181	C₂²×C₄⋊C₈	—	47	1	no	—
182	#1571	—	47	8	no	—
183	C₂×#335	—	47	1	no	—
184	C₂×#335	—	47	1	no	—
185	C₂×#335	—	47	1	no	—
186	C₂×#335	D₄₇	1	1	yes	characteristic, complemented
187	C₂×C₄₇	#1571	1	4	yes	complemented
188	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
189	C₂×C₄₇	C₂²×#107	1	1	yes	characteristic
190	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
191	D₄₇	—	2	4	no	—
192	C₂²×M₁₆	—	94	1	no	—
193	C₂³×C₈	—	94	1	no	—
194	C₂²×C₄²	—	47	1	no	—
195	#431	—	47	4	no	—
196	#431	—	47	4	no	—
197	#423	—	47	4	no	—
198	#423	—	94	2	no	—
199	C₂×C₄⋊C₈	—	47	1	no	—
200	C₂×C₄⋊C₈	—	47	1	no	—
201	C₂×C₄⋊C₈	—	47	1	no	—
202	C₂×C₄⋊C₈	—	47	1	no	—
203	C₂×C₄⋊C₈	—	47	4	no	—
204	C₂×C₄⋊C₈	—	94	2	no	—
205	C₂×C₄⋊C₈	—	94	1	no	—
206	C₂×C₄⋊C₈	—	94	1	no	—
207	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
209	C₂×C₂²⋊C₈	—	47	1	no	—
210	C₂×C₂²⋊C₈	—	47	1	no	—
211	C₂×C₄×C₈	—	47	1	no	—
212	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
213	#335	—	47	4	no	—
214	#335	—	47	4	no	—
215	#335	—	47	4	no	—
216	#335	C₂×D₄₇	1	4	yes	complemented
217	C₄₇	C₂×#1571	1	1	yes	characteristic, complemented, Sylow
218	C₂³×C₄	—	47	1	no	—
219	C₂³×C₄	—	47	1	no	—
220	C₂³×C₄	—	47	1	no	—
221	C₂×M₁₆	—	94	4	no	—
222	C₂×M₁₆	—	188	4	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	47	1	no	—
226	C₂²×C₈	—	47	1	no	—
227	C₂²×C₈	—	94	4	no	—
228	C₂²×C₈	—	94	1	no	—
229	C₂²×C₈	—	94	1	no	—
230	C₂²×C₈	—	188	4	no	—
231	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
232	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
233	C₂×C₄²	—	47	1	no	—
234	C₂×C₄²	—	47	1	no	—
235	C₂×C₄²	—	47	1	no	—
236	C₂×C₄²	—	47	2	no	—
237	C₂×C₄²	—	47	2	no	—
238	C₂×C₄²	—	47	2	no	—
239	C₂×C₄²	—	47	2	no	—
240	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	47	4	no	—
244	C₄⋊C₈	—	47	4	no	—
245	C₄⋊C₈	—	47	2	no	—
246	C₄⋊C₈	—	47	2	no	—
247	C₄⋊C₈	—	94	4	no	—
248	C₄⋊C₈	—	94	4	no	—
249	C₄⋊C₈	—	94	1	no	—
250	C₄⋊C₈	—	94	1	no	—
251	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
252	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
253	C₂²⋊C₈	—	47	4	no	—
254	C₂²⋊C₈	—	47	4	no	—
255	C₄×C₈	—	47	2	no	—
256	C₄×C₈	—	47	2	no	—
257	C₄×C₈	C₄×D₄₇	1	2	yes	—
258	C₄×C₈	C₂²×D₄₇	1	2	yes	—
259	C₂⁴	—	47	1	no	—
260	C₂²×C₄	—	47	1	no	—
261	C₂²×C₄	—	47	2	no	—
262	C₂²×C₄	—	47	4	no	—
263	C₂²×C₄	—	47	4	no	—
264	C₂²×C₄	—	47	2	no	—
265	C₂²×C₄	—	47	1	no	—
266	C₂²×C₄	—	47	1	no	—
267	C₂²×C₄	—	47	2	no	—
268	C₂²×C₄	—	47	2	no	—
269	C₂²×C₄	—	47	2	no	—
270	C₂²×C₄	—	47	2	no	—
271	C₂²×C₄	—	94	2	no	—
272	C₂²×C₄	—	94	2	no	—
273	C₂²×C₄	—	188	2	no	—
274	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
275	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
276	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
277	M₁₆	—	188	8	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	4	2	no	—
283	C₂×C₈	—	4	2	no	—
284	C₂×C₈	—	47	2	no	—
285	C₂×C₈	—	47	2	no	—
286	C₂×C₈	—	94	2	no	—
287	C₂×C₈	—	94	2	no	—
288	C₂×C₈	—	94	2	no	—
289	C₂×C₈	—	94	2	no	—
290	C₂×C₈	—	188	8	no	—
291	C₂×C₈	—	188	2	no	—
292	C₂×C₈	—	188	2	no	—
293	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
294	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
295	C₄²	—	47	2	no	—
296	C₄²	—	47	2	no	—
297	C₄²	—	47	2	no	—
298	C₄²	—	47	2	no	—
299	C₄²	—	47	2	no	—
300	C₄²	—	47	2	no	—
301	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
302	C₄²	D₄×D₄₇	1	1	yes	characteristic
303	C₄²	Q₈×D₄₇	1	1	yes	characteristic
304	C₄²	C₂³×D₄₇	1	1	yes	characteristic
305	C₂³	—	47	2	no	—
306	C₂³	—	47	4	no	—
307	C₂³	—	94	2	no	—
308	C₂³	—	94	2	no	—
309	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	47	2	no	—
312	C₂×C₄	—	47	4	no	—
313	C₂×C₄	—	47	4	no	—
314	C₂×C₄	—	47	4	no	—
315	C₂×C₄	—	47	8	no	—
316	C₂×C₄	—	47	2	no	—
317	C₂×C₄	—	47	2	no	—
318	C₂×C₄	—	94	2	no	—
319	C₂×C₄	—	94	2	no	—
320	C₂×C₄	—	94	2	no	—
321	C₂×C₄	—	94	2	no	—
322	C₂×C₄	—	94	4	no	—
323	C₂×C₄	—	188	2	no	—
324	C₂×C₄	—	188	2	no	—
325	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
326	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
327	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
328	C₂×C₄	#13094030	1	2	yes	—
329	C₂×C₄	#13094032	1	2	yes	—
330	C₂×C₄	D₈×D₄₇	1	2	yes	—
331	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
332	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
333	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
334	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
335	C₈	—	2	2	no	—
336	C₈	—	2	2	no	—
337	C₈	—	4	2	no	—
338	C₈	—	4	2	no	—
339	C₈	—	94	2	no	—
340	C₈	—	94	2	no	—
341	C₈	—	188	2	no	—
342	C₈	—	188	2	no	—
343	C₂²	—	47	4	no	—
344	C₂²	—	94	2	no	—
345	C₂²	—	94	2	no	—
346	C₂²	—	94	8	no	—
347	C₂²	#15689148	1	2	yes	—
348	C₂²	#107×D₄₇	1	2	yes	—
349	C₂²	#15689170	1	2	yes	—
350	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	47	4	no	—
354	C₄	—	94	2	no	—
355	C₄	—	94	2	no	—
356	C₄	#15689148	1	2	yes	—
357	C₄	#107×D₄₇	1	2	yes	—
358	C₄	C₂×#13094030	1	1	yes	characteristic
359	C₄	C₂×#13094032	1	1	yes	characteristic
360	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
361	C₄	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
362	C₂	—	94	4	no	—
363	C₂	#20242161	1	4	yes	direct product factor
364	C₂	C₂×#15689148	1	1	yes	characteristic
365	C₂	C₂×#107×D₄₇	1	1	yes	characteristic
366	C₂	C₂×#15689170	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#335	C₂
socle	C₂³×C₄₇	C₂×C₄⋊C₄
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#335	D₄₇
hypocenter	C₄₇	C₂×#1571
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
4. #20242161	C₂	direct (N × H)
5. C₂×#15688876	C₂	semidirect
6. C₂×#15688875	C₂	semidirect
7. C₂×#15688875	C₂	semidirect
8. C₂×C₄₇×#335	C₂	semidirect
27. #15688876	C₂²	semidirect
28. #15688875	C₂²	semidirect
29. #15688875	C₂²	semidirect
33. C₄₇×#335	C₂²	semidirect
186. C₂×#335	D₄₇	semidirect
187. C₂×C₄₇	#1571	semidirect
216. #335	C₂×D₄₇	semidirect
217. C₄₇	C₂×#1571	semidirect
363. C₂	#20242161	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×#15689174	2
C₂×#15689145	2
C₂×C₄⋊C₈×D₄₇	2
#20242161	2
C₂×#15688876	2
C₂×#15688875	2
C₂×C₄₇×#335	2
C₂×#1571	47

Subgroups — C2×#20242161 #26185337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242161 #26185337