Subgroups — C₂×#20244255 #26220095

Order 12032.

2046 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093945	C₂	1	2	yes	maximal, complemented
3	C₂²×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689026	C₂	1	2	yes	maximal, complemented
5	#20244255	C₂	1	8	yes	maximal, direct product factor
6	C₂³×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂²×C₂²⋊Dic₄₇	—	2	4	no	—
10	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂×#13093958	—	2	4	no	—
12	C₂×#13093958	C₂²	1	4	yes	complemented
13	C₂×#13093945	—	2	8	no	—
14	C₂×#13093945	C₂²	1	8	yes	complemented
15	C₂×C₈×Dic₄₇	—	2	4	no	—
16	C₂×C₈×Dic₄₇	C₂²	1	4	yes	complemented
17	#15689026	—	2	4	no	—
18	#15689026	C₂²	1	8	yes	complemented
19	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
20	C₂²×D₈×C₄₇	—	2	4	no	—
21	C₂²×D₈×C₄₇	—	2	4	no	—
22	C₂²×D₈×C₄₇	C₄	1	8	yes	complemented
23	C₂²×D₈×C₄₇	C₂²	1	4	yes	—
24	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂³×Dic₄₇	—	2	2	no	—
26	C₂³×Dic₄₇	D₄	1	2	yes	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
30	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
31	C₂×C₄⋊Dic₄₇	—	2	4	no	—
32	C₂×C₄⋊Dic₄₇	—	2	4	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
35	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
36	C₂×C₂²⋊Dic₄₇	—	4	16	no	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	—	2	2	no	—
39	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
40	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
41	#13093958	—	2	8	no	—
42	#13093945	—	2	16	no	—
43	C₈×Dic₄₇	—	2	8	no	—
44	C₂⁵×C₄₇	—	2	2	no	—
45	C₂²×D₄×C₄₇	—	2	4	no	—
46	C₂²×D₄×C₄₇	—	2	4	no	—
47	C₂²×D₄×C₄₇	—	2	4	no	—
48	C₂²×D₄×C₄₇	—	2	2	no	—
49	C₂²×D₄×C₄₇	—	2	4	no	—
50	C₂²×D₄×C₄₇	—	2	4	no	—
51	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
52	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂×D₈×C₄₇	—	2	32	no	—
55	C₂×D₈×C₄₇	—	2	8	no	—
56	C₂×D₈×C₄₇	—	2	8	no	—
57	C₂×D₈×C₄₇	C₂×C₄	1	16	yes	complemented
58	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
59	C₂²×C₈×C₄₇	D₄	1	4	yes	—
60	C₂²×C₈×C₄₇	D₄	1	4	yes	—
61	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
62	C₂⁴×C₄₇	—	2	8	no	—
63	C₂⁴×C₄₇	—	2	4	no	—
64	C₂⁴×C₄₇	—	4	4	no	—
65	C₂⁴×C₄₇	—	4	4	no	—
66	C₂⁴×C₄₇	—	4	8	no	—
67	C₂⁴×C₄₇	—	4	8	no	—
68	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₄₇	—	2	16	no	—
70	C₂×D₄×C₄₇	—	2	16	no	—
71	C₂×D₄×C₄₇	—	2	8	no	—
72	C₂×D₄×C₄₇	—	2	4	no	—
73	C₂×D₄×C₄₇	—	2	4	no	—
74	C₂×D₄×C₄₇	—	2	4	no	—
75	C₂×D₄×C₄₇	—	2	4	no	—
76	C₂×D₄×C₄₇	—	2	4	no	—
77	C₂×D₄×C₄₇	—	4	8	no	—
78	C₂×D₄×C₄₇	—	4	4	no	—
79	C₂×D₄×C₄₇	—	4	8	no	—
80	C₂×D₄×C₄₇	—	4	4	no	—
81	C₂×D₄×C₄₇	C₂²×C₄	1	8	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	2	yes	—
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×C₄×C₄₇	#41	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₇	—	2	4	no	—
91	C₂²×Dic₄₇	—	2	4	no	—
92	C₂²×Dic₄₇	—	2	4	no	—
93	C₂²×Dic₄₇	—	4	4	no	—
94	C₂²×Dic₄₇	—	4	8	no	—
95	C₂²×Dic₄₇	D₈	1	8	yes	complemented
96	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
97	D₈×C₄₇	—	2	32	no	—
98	C₂×C₈×C₄₇	C₂²⋊C₄	1	16	yes	complemented
99	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
101	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
102	C₂²⋊Dic₄₇	—	4	32	no	—
103	C₄⋊Dic₄₇	—	2	4	no	—
104	C₄⋊Dic₄₇	—	2	4	no	—
105	C₄⋊Dic₄₇	—	4	4	no	—
106	C₄×Dic₄₇	—	2	4	no	—
107	C₄×Dic₄₇	—	2	2	no	—
108	C₄×Dic₄₇	—	2	2	no	—
109	C₂×C₄₇⋊C₈	—	2	8	no	—
110	C₂×C₄₇⋊C₈	—	2	2	no	—
111	C₂×C₄₇⋊C₈	—	2	2	no	—
112	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
113	C₂³×C₄₇	—	2	8	no	—
114	C₂³×C₄₇	—	4	4	no	—
115	C₂³×C₄₇	—	4	4	no	—
116	C₂³×C₄₇	—	4	8	no	—
117	C₂³×C₄₇	—	4	8	no	—
118	C₂³×C₄₇	—	4	16	no	—
119	C₂³×C₄₇	—	4	32	no	—
120	C₂³×C₄₇	—	8	16	no	—
121	C₂³×C₄₇	—	8	8	no	—
122	C₂³×C₄₇	—	8	8	no	—
123	C₂³×C₄₇	C₄×D₄	1	2	yes	—
124	C₂³×C₄₇	#121	1	2	yes	—
125	C₂³×C₄₇	#127	1	2	yes	—
126	C₂³×C₄₇	C₂×D₈	1	4	yes	—
127	C₂³×C₄₇	#135	1	4	yes	—
128	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
129	D₄×C₄₇	—	2	8	no	—
130	D₄×C₄₇	—	2	8	no	—
131	D₄×C₄₇	—	4	4	no	—
132	D₄×C₄₇	—	4	4	no	—
133	D₄×C₄₇	—	4	16	no	—
134	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
136	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₄₇	#121	1	4	yes	—
138	C₂×C₄×C₄₇	#121	1	2	yes	—
139	C₂×C₄×C₄₇	#124	1	4	yes	—
140	C₂×C₄×C₄₇	#127	1	2	yes	—
141	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
147	C₂×Dic₄₇	—	2	4	no	—
148	C₂×Dic₄₇	—	2	4	no	—
149	C₂×Dic₄₇	—	2	16	no	—
150	C₂×Dic₄₇	—	4	4	no	—
151	C₂×Dic₄₇	—	4	8	no	—
152	C₂×Dic₄₇	—	8	8	no	—
153	C₂×Dic₄₇	C₂×D₈	1	8	yes	complemented
154	C₈×C₄₇	C₂×C₂²⋊C₄	1	8	yes	complemented
155	C₄₇⋊C₈	—	2	4	no	—
156	C₂×#1970	—	47	1	no	maximal, Sylow
157	C₂²×C₄₇	—	4	16	no	—
158	C₂²×C₄₇	—	4	8	no	—
159	C₂²×C₄₇	—	8	4	no	—
160	C₂²×C₄₇	—	8	4	no	—
161	C₂²×C₄₇	—	8	32	no	—
162	C₂²×C₄₇	—	8	8	no	—
163	C₂²×C₄₇	#390	1	4	yes	—
164	C₂²×C₄₇	C₄×D₈	1	8	yes	—
165	C₂²×C₄₇	#466	1	8	yes	—
166	C₂²×C₄₇	#493	1	4	yes	—
167	C₂²×C₄₇	#495	1	4	yes	—
168	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
169	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
171	C₂²×C₄₇	C₂²×D₈	1	2	yes	—
172	C₂²×C₄₇	C₂×#135	1	2	yes	—
173	C₄×C₄₇	#390	1	4	yes	—
174	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
175	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
176	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
177	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
178	Dic₄₇	—	2	8	no	—
179	Dic₄₇	—	8	4	no	—
180	C₂³×D₈	D₄₇	1	1	yes	characteristic
181	C₂²×#107	—	47	1	no	—
182	C₂²×#102	—	47	2	no	—
183	C₂²×C₄×C₈	—	47	1	no	—
184	C₂×#390	—	47	2	no	—
185	#1970	—	47	8	no	—
186	C₂×C₄₇	—	8	8	no	—
187	C₂×C₄₇	#1970	1	8	yes	complemented
188	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
189	C₂×C₄₇	C₂×C₄×D₈	1	2	yes	—
190	C₂×C₄₇	C₂×#466	1	2	yes	—
191	C₂×C₄₇	C₂×#493	1	1	yes	characteristic
192	C₂×C₄₇	C₂×#495	1	1	yes	characteristic
193	C₂³×D₄	C₂×D₄₇	1	2	yes	—
194	C₂²×D₈	—	2	4	no	—
195	C₂²×D₈	—	2	4	no	—
196	C₂²×D₈	Dic₄₇	1	8	yes	complemented
197	C₂²×D₈	C₂×D₄₇	1	4	yes	—
198	C₂³×C₈	—	47	1	no	—
199	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
200	C₂²×C₄⋊C₄	—	47	2	no	—
201	C₂²×C₂²⋊C₄	—	94	4	no	—
202	C₂²×C₄²	—	47	1	no	—
203	C₂×#107	—	47	4	no	—
204	C₂×#107	—	94	4	no	—
205	C₂×#102	—	47	8	no	—
206	C₂×#102	—	94	8	no	—
207	C₂×C₄×C₈	—	47	4	no	—
208	C₂×C₄×C₈	—	94	4	no	—
209	#390	—	47	8	no	—
210	#390	—	94	4	no	—
211	C₄₇	C₂×#1970	1	1	yes	characteristic, complemented, Sylow
212	C₂⁵	—	2	2	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	2	2	no	—
215	C₂²×D₄	—	2	4	no	—
216	C₂²×D₄	—	2	4	no	—
217	C₂²×D₄	—	2	4	no	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
220	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
221	C₂³×C₄	—	47	2	no	—
222	C₂³×C₄	—	94	2	no	—
223	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
224	C₂×D₈	—	2	32	no	—
225	C₂×D₈	—	2	8	no	—
226	C₂×D₈	—	2	8	no	—
227	C₂×D₈	C₂×Dic₄₇	1	16	yes	complemented
228	C₂²×C₈	—	47	4	no	—
229	C₂²×C₈	—	47	2	no	—
230	C₂²×C₈	—	94	2	no	—
231	C₂²×C₈	—	94	2	no	—
232	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
233	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
234	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
235	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
236	C₂×C₄⋊C₄	—	47	4	no	—
237	C₂×C₄⋊C₄	—	94	4	no	—
238	C₂×C₄⋊C₄	—	94	4	no	—
239	C₂×C₄⋊C₄	—	94	2	no	—
240	C₂×C₂²⋊C₄	—	94	16	no	—
241	C₂×C₂²⋊C₄	—	188	16	no	—
242	C₂×C₄²	—	47	2	no	—
243	C₂×C₄²	—	47	2	no	—
244	C₂×C₄²	—	94	2	no	—
245	C₂×C₄²	—	94	2	no	—
246	#107	—	94	8	no	—
247	#102	—	94	16	no	—
248	C₄×C₈	—	94	8	no	—
249	C₂⁴	—	2	8	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	4	4	no	—
252	C₂⁴	—	4	4	no	—
253	C₂⁴	—	4	8	no	—
254	C₂⁴	—	4	8	no	—
255	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
256	C₂×D₄	—	2	16	no	—
257	C₂×D₄	—	2	16	no	—
258	C₂×D₄	—	2	8	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	4	4	no	—
265	C₂×D₄	—	4	8	no	—
266	C₂×D₄	—	4	8	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
269	C₂²×C₄	—	47	8	no	—
270	C₂²×C₄	—	47	4	no	—
271	C₂²×C₄	—	94	4	no	—
272	C₂²×C₄	—	94	4	no	—
273	C₂²×C₄	—	94	4	no	—
274	C₂²×C₄	—	188	4	no	—
275	C₂²×C₄	—	188	8	no	—
276	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
277	C₂²×C₄	D₄×D₄₇	1	2	yes	—
278	C₂²×C₄	#10625352	1	2	yes	—
279	C₂²×C₄	#10625352	1	2	yes	—
280	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
281	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
282	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
283	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
284	D₈	—	2	32	no	—
285	C₂×C₈	—	47	4	no	—
286	C₂×C₈	—	94	8	no	—
287	C₂×C₈	—	94	2	no	—
288	C₂×C₈	—	94	2	no	—
289	C₂×C₈	C₂²⋊Dic₄₇	1	16	yes	complemented
290	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
291	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
292	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
293	C₄⋊C₄	—	94	4	no	—
294	C₄⋊C₄	—	94	4	no	—
295	C₄⋊C₄	—	188	4	no	—
296	C₂²⋊C₄	—	188	32	no	—
297	C₄²	—	94	4	no	—
298	C₄²	—	94	2	no	—
299	C₄²	—	94	2	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	4	16	no	—
302	C₂³	—	4	4	no	—
303	C₂³	—	4	8	no	—
304	C₂³	—	4	8	no	—
305	C₂³	—	4	4	no	—
306	C₂³	—	4	32	no	—
307	C₂³	—	8	8	no	—
308	C₂³	—	8	8	no	—
309	C₂³	—	8	16	no	—
310	C₂³	D₄×Dic₄₇	1	2	yes	—
311	C₂³	#13093995	1	2	yes	—
312	C₂³	#13094020	1	2	yes	—
313	C₂³	D₈×D₄₇	1	4	yes	—
314	C₂³	#13094043	1	4	yes	—
315	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
316	D₄	—	2	8	no	—
317	D₄	—	2	8	no	—
318	D₄	—	4	16	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	4	no	—
321	C₂×C₄	—	47	8	no	—
322	C₂×C₄	—	94	16	no	—
323	C₂×C₄	—	94	4	no	—
324	C₂×C₄	—	94	4	no	—
325	C₂×C₄	—	376	8	no	—
326	C₂×C₄	—	188	8	no	—
327	C₂×C₄	—	188	4	no	—
328	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
329	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
330	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
331	C₂×C₄	#13093995	1	2	yes	—
332	C₂×C₄	#13093995	1	4	yes	—
333	C₂×C₄	#13094011	1	4	yes	—
334	C₂×C₄	#13094020	1	2	yes	—
335	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
336	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
339	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
340	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
341	C₈	—	94	4	no	—
342	C₈	C₂×C₂²⋊Dic₄₇	1	8	yes	complemented
343	C₂²	—	4	8	no	—
344	C₂²	—	4	16	no	—
345	C₂²	—	8	8	no	—
346	C₂²	—	8	32	no	—
347	C₂²	—	8	4	no	—
348	C₂²	—	8	4	no	—
349	C₂²	#15689026	1	4	yes	—
350	C₂²	D₈×Dic₄₇	1	8	yes	—
351	C₂²	#15689356	1	8	yes	—
352	C₂²	#15689498	1	4	yes	—
353	C₂²	#15689506	1	4	yes	—
354	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
355	C₂²	C₂×#13093995	1	1	yes	characteristic
356	C₂²	C₂×#13094020	1	1	yes	characteristic
357	C₂²	C₂×D₈×D₄₇	1	2	yes	—
358	C₂²	C₂×#13094043	1	2	yes	—
359	C₄	—	94	8	no	—
360	C₄	—	376	4	no	—
361	C₄	#15689026	1	4	yes	—
362	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
363	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
364	C₄	C₂×#13093995	1	1	yes	characteristic
365	C₄	C₂×#13094011	1	1	yes	characteristic
366	C₂	—	8	8	no	—
367	C₂	#20244255	1	8	yes	direct product factor
368	C₂	C₂×#15689026	1	1	yes	characteristic
369	C₂	C₂×D₈×Dic₄₇	1	2	yes	—
370	C₂	C₂×#15689356	1	2	yes	—
371	C₂	C₂×#15689498	1	1	yes	characteristic
372	C₂	C₂×#15689506	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂³×D₈×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂³×D₈	D₄₇
hypocenter	C₄₇	C₂×#1970
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093958	C₂	semidirect
2. C₂²×#13093945	C₂	semidirect
3. C₂²×C₈×Dic₄₇	C₂	semidirect
4. C₂×#15689026	C₂	semidirect
5. #20244255	C₂	direct (N × H)
12. C₂×#13093958	C₂²	semidirect
14. C₂×#13093945	C₂²	semidirect
16. C₂×C₈×Dic₄₇	C₂²	semidirect
18. #15689026	C₂²	semidirect
22. C₂²×D₈×C₄₇	C₄	semidirect
57. C₂×D₈×C₄₇	C₂×C₄	semidirect
95. C₂²×Dic₄₇	D₈	semidirect
98. C₂×C₈×C₄₇	C₂²⋊C₄	semidirect
153. C₂×Dic₄₇	C₂×D₈	semidirect
154. C₈×C₄₇	C₂×C₂²⋊C₄	semidirect
187. C₂×C₄₇	#1970	semidirect
196. C₂²×D₈	Dic₄₇	semidirect
211. C₄₇	C₂×#1970	semidirect
227. C₂×D₈	C₂×Dic₄₇	semidirect
289. C₂×C₈	C₂²⋊Dic₄₇	semidirect
342. C₈	C₂×C₂²⋊Dic₄₇	semidirect
367. C₂	#20244255	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×#13093958	2
C₂²×#13093945	2
C₂²×C₈×Dic₄₇	2
C₂×#15689026	2
#20244255	2
C₂³×D₈×C₄₇	2
C₂×#1970	47

Subgroups — C2×#20244255 #26220095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244255 #26220095