Subgroups — C₂²×#15689362 #27083374

Order 12032.

3006 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625337	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13094003	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689362	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#13093957	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13093947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic
10	C₂²×#10625337	—	2	8	no	—
11	C₂²×#10625337	C₂²	1	12	yes	complemented
12	C₂³×C₄₇⋊C₈	—	2	8	no	—
13	C₂³×C₄₇⋊C₈	C₂²	1	12	yes	—
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×#13094003	—	2	6	no	—
17	C₂×#13094003	C₂²	1	12	yes	—
18	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
19	C₂²×Dic₄₇⋊C₄	—	2	1	no	—
20	C₂²×C₂²⋊Dic₄₇	—	2	1	no	—
21	#15689362	C₂²	1	64	yes	direct product factor
22	C₂×#13093957	C₂²	1	12	yes	complemented
23	C₂×#13093948	C₂²	1	12	yes	complemented
24	C₂×#13093947	C₂²	1	12	yes	complemented
25	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₄₇	—	2	6	no	—
28	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	12	yes	—
29	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
30	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
32	C₂²×Dic₉₄	—	2	4	no	—
33	C₂²×Dic₉₄	—	2	4	no	—
34	C₂²×Dic₉₄	—	2	3	no	—
35	C₂²×Dic₉₄	C₂³	1	6	yes	—
36	C₂³×Dic₄₇	—	2	1	no	—
37	C₂³×Dic₄₇	—	2	1	no	—
38	C₂×#10625337	—	2	48	no	—
39	C₂×#10625337	C₂³	1	16	yes	complemented
40	C₂²×C₄₇⋊C₈	—	2	4	no	—
41	C₂²×C₄₇⋊C₈	—	2	48	no	—
42	C₂²×C₄₇⋊C₈	D₄	1	8	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	16	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
46	#13094003	—	2	24	no	—
47	#13094003	C₂³	1	16	yes	—
48	C₂×C₄⋊Dic₄₇	—	2	3	no	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
50	C₂×Dic₄₇⋊C₄	—	2	12	no	—
51	C₂×C₂²⋊Dic₄₇	—	2	12	no	—
52	#13093957	C₂³	1	16	yes	complemented
53	#13093948	C₂³	1	16	yes	complemented
54	#13093947	C₂³	1	16	yes	complemented
55	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₄₇	—	2	3	no	—
57	C₂²×Q₈×C₄₇	—	2	4	no	—
58	C₂²×Q₈×C₄₇	—	2	4	no	—
59	C₂²×Q₈×C₄₇	C₂³	1	6	yes	—
60	C₂³×C₄×C₄₇	—	2	4	no	—
61	C₂³×C₄×C₄₇	—	2	4	no	—
62	C₂³×C₄×C₄₇	—	2	1	no	—
63	C₂³×C₄×C₄₇	—	2	1	no	—
64	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	D₄	1	6	yes	—
66	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂²⋊Q₈×C₄₇	—	2	24	no	—
69	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
70	C₂×C₄⋊C₄×C₄₇	—	2	12	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	3	no	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	12	no	—
74	C₂⁴×C₄₇	—	2	4	no	—
75	C₂⁴×C₄₇	—	2	4	no	—
76	C₂⁴×C₄₇	Q₁₆	1	8	yes	complemented
77	C₂⁴×C₄₇	C₂×D₄	1	6	yes	—
78	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₄₇	—	2	6	no	—
80	C₂×Q₈×C₄₇	—	2	12	no	—
81	C₂×Q₈×C₄₇	—	2	12	no	—
82	C₂×Q₈×C₄₇	—	4	12	no	—
83	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	24	no	—
86	C₂²×C₄×C₄₇	—	2	12	no	—
87	C₂²×C₄×C₄₇	—	2	12	no	—
88	C₂²×C₄×C₄₇	—	2	6	no	—
89	C₂²×C₄×C₄₇	—	2	6	no	—
90	C₂²×C₄×C₄₇	—	4	4	no	—
91	C₂²×C₄×C₄₇	—	4	4	no	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	12	yes	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₄₇	#41	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
99	C₂²×Dic₄₇	—	2	6	no	—
100	C₂²×Dic₄₇	—	2	6	no	—
101	C₂²×Dic₄₇	—	4	4	no	—
102	C₂²×Dic₄₇	—	4	4	no	—
103	C₂×Dic₉₄	—	2	12	no	—
104	C₂×Dic₉₄	—	2	12	no	—
105	C₂×Dic₉₄	—	2	6	no	—
106	C₂×Dic₉₄	—	4	12	no	—
107	C₂×Dic₉₄	C₂⁴	1	4	yes	—
108	C₄⋊C₄×C₄₇	—	2	16	no	—
109	C₄⋊C₄×C₄₇	—	2	6	no	—
110	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
111	C₂²⋊C₄×C₄₇	—	2	16	no	—
112	C₂²⋊Dic₄₇	—	2	16	no	—
113	#10625337	—	2	32	no	—
114	C₄⋊Dic₄₇	—	2	6	no	—
115	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
116	Dic₄₇⋊C₄	—	2	16	no	—
117	C₂×C₄₇⋊C₈	—	2	12	no	—
118	C₂×C₄₇⋊C₈	—	2	32	no	—
119	C₂×C₄₇⋊C₈	C₂×D₄	1	24	yes	—
120	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
121	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
122	C₂³×C₄₇	—	2	12	no	—
123	C₂³×C₄₇	—	2	12	no	—
124	C₂³×C₄₇	—	2	32	no	—
125	C₂³×C₄₇	#121	1	4	yes	—
126	C₂³×C₄₇	C₂×Q₁₆	1	4	yes	—
127	C₂³×C₄₇	C₂×Q₁₆	1	24	yes	complemented
128	C₂³×C₄₇	#135	1	4	yes	—
129	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
130	C₂³×C₄₇	C₂²×D₄	1	3	yes	—
131	Q₈×C₄₇	—	2	4	no	—
132	Q₈×C₄₇	—	2	4	no	—
133	Q₈×C₄₇	—	4	12	no	—
134	C₂×C₄×C₄₇	—	2	12	no	—
135	C₂×C₄×C₄₇	—	2	24	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	4	12	no	—
141	C₂×C₄×C₄₇	—	4	12	no	—
142	C₂×C₄×C₄₇	#121	1	12	yes	—
143	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
144	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
145	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
146	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
147	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
148	C₂×Dic₄₇	—	2	4	no	—
149	C₂×Dic₄₇	—	2	4	no	—
150	C₂×Dic₄₇	—	4	12	no	—
151	C₂×Dic₄₇	—	4	12	no	—
152	Dic₉₄	—	2	4	no	—
153	Dic₉₄	—	2	4	no	—
154	Dic₉₄	—	4	12	no	—
155	C₄₇⋊C₈	—	2	4	no	—
156	C₄₇⋊C₈	C₂²×D₄	1	8	yes	—
157	C₂²×#467	—	47	1	no	maximal, Sylow
158	C₂²×C₄₇	—	2	4	no	—
159	C₂²×C₄₇	—	2	48	no	—
160	C₂²×C₄₇	—	2	4	no	—
161	C₂²×C₄₇	#467	1	16	yes	complemented
162	C₂²×C₄₇	C₂×#121	1	6	yes	—
163	C₂²×C₄₇	C₂²×Q₁₆	1	6	yes	—
164	C₂²×C₄₇	C₂²×Q₁₆	1	8	yes	complemented
165	C₂²×C₄₇	C₂×#135	1	6	yes	—
166	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
167	C₄×C₄₇	—	2	4	no	—
168	C₄×C₄₇	—	4	4	no	—
169	C₄×C₄₇	—	4	4	no	—
170	C₄×C₄₇	C₂×#121	1	6	yes	—
171	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
172	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
173	Dic₄₇	—	4	4	no	—
174	Dic₄₇	—	4	4	no	—
175	C₂³×Q₁₆	—	47	1	no	—
176	C₂⁴×C₈	—	47	1	no	—
177	C₂²×C₂²⋊Q₈	—	47	1	no	—
178	C₂²×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
179	C₂×#467	—	47	24	no	—
180	C₂²×#107	—	47	1	no	—
181	C₂²×#103	—	47	1	no	—
182	C₂²×#103	—	47	1	no	—
183	C₂×C₄₇	—	2	8	no	—
184	C₂×C₄₇	C₂×#467	1	12	yes	complemented
185	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
186	C₂×C₄₇	C₂³×Q₁₆	1	1	yes	characteristic
187	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
188	C₂³×Q₈	—	47	1	no	—
189	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
190	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
191	C₂²×Q₁₆	—	47	12	no	—
192	C₂²×Q₁₆	—	94	8	no	—
193	C₂³×C₈	—	47	1	no	—
194	C₂³×C₈	—	47	1	no	—
195	C₂³×C₈	—	47	12	no	—
196	C₂³×C₈	—	94	8	no	—
197	C₂×C₂²⋊Q₈	—	2	6	no	—
198	C₂×C₂²⋊Q₈	—	47	12	no	—
199	C₂×C₂²⋊Q₈	—	94	6	no	—
200	C₂×C₂²⋊Q₈	C₂×D₄₇	1	12	yes	—
201	C₂²×C₄⋊C₄	—	2	1	no	—
202	C₂²×C₄⋊C₄	—	47	1	no	—
203	C₂²×C₄⋊C₄	—	94	1	no	—
204	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
205	C₂²×C₂²⋊C₄	—	2	1	no	—
206	C₂²×C₂²⋊C₄	—	94	1	no	—
207	#467	—	47	64	no	—
208	C₂×#107	—	47	12	no	—
209	C₂×#103	—	47	12	no	—
210	C₂×#103	—	47	12	no	—
211	C₄₇	C₂²×#467	1	1	yes	characteristic, complemented, Sylow
212	C₂⁵	C₂²⋊D₄₇	1	1	yes	characteristic
213	C₂²×Q₈	—	2	3	no	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	4	no	—
216	C₂²×Q₈	—	47	6	no	—
217	C₂²×Q₈	—	94	3	no	—
218	C₂²×Q₈	—	94	4	no	—
219	C₂²×Q₈	—	94	4	no	—
220	C₂²×Q₈	C₂²×D₄₇	1	6	yes	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	—	2	1	no	—
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	—	94	1	no	—
226	C₂³×C₄	—	94	1	no	—
227	C₂³×C₄	C₂²⋊D₄₇	1	6	yes	—
228	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
229	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
230	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
231	C₂×Q₁₆	—	47	16	no	—
232	C₂×Q₁₆	—	94	48	no	—
233	C₂²×C₈	—	47	8	no	—
234	C₂²×C₈	—	47	6	no	—
235	C₂²×C₈	—	47	6	no	—
236	C₂²×C₈	—	47	16	no	—
237	C₂²×C₈	—	94	48	no	—
238	C₂²×C₈	—	94	4	no	—
239	C₂²⋊Q₈	—	2	24	no	—
240	C₂²⋊Q₈	—	47	16	no	—
241	C₂²⋊Q₈	—	94	24	no	—
242	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	—
243	C₂×C₄⋊C₄	—	2	12	no	—
244	C₂×C₄⋊C₄	—	2	3	no	—
245	C₂×C₄⋊C₄	—	47	6	no	—
246	C₂×C₄⋊C₄	—	94	3	no	—
247	C₂×C₄⋊C₄	—	94	12	no	—
248	C₂×C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
249	C₂×C₂²⋊C₄	—	2	12	no	—
250	C₂×C₂²⋊C₄	—	94	12	no	—
251	#107	—	47	16	no	—
252	#103	—	47	16	no	—
253	#103	—	47	16	no	—
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	#10625337	1	8	yes	complemented
257	C₂⁴	C₂×C₂²⋊D₄₇	1	6	yes	—
258	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
259	C₂×Q₈	—	2	6	no	—
260	C₂×Q₈	—	2	12	no	—
261	C₂×Q₈	—	2	12	no	—
262	C₂×Q₈	—	4	12	no	—
263	C₂×Q₈	—	47	4	no	—
264	C₂×Q₈	—	94	6	no	—
265	C₂×Q₈	—	94	12	no	—
266	C₂×Q₈	—	94	12	no	—
267	C₂×Q₈	—	188	12	no	—
268	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	24	no	—
271	C₂²×C₄	—	2	12	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	6	no	—
274	C₂²×C₄	—	2	6	no	—
275	C₂²×C₄	—	4	4	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	94	6	no	—
278	C₂²×C₄	—	94	6	no	—
279	C₂²×C₄	—	188	4	no	—
280	C₂²×C₄	—	188	4	no	—
281	C₂²×C₄	D₄×D₄₇	1	4	yes	—
282	C₂²×C₄	#10625352	1	4	yes	—
283	C₂²×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
284	C₂²×C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
286	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
287	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
288	Q₁₆	—	94	32	no	—
289	C₂×C₈	—	47	24	no	—
290	C₂×C₈	—	47	4	no	—
291	C₂×C₈	—	47	4	no	—
292	C₂×C₈	—	94	32	no	—
293	C₂×C₈	—	94	12	no	—
294	C₄⋊C₄	—	2	16	no	—
295	C₄⋊C₄	—	2	6	no	—
296	C₄⋊C₄	—	47	4	no	—
297	C₄⋊C₄	—	94	16	no	—
298	C₄⋊C₄	—	94	6	no	—
299	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
300	C₂²⋊C₄	—	2	16	no	—
301	C₂²⋊C₄	—	94	16	no	—
302	C₂³	—	2	12	no	—
303	C₂³	—	2	32	no	—
304	C₂³	—	2	12	no	—
305	C₂³	#13093996	1	4	yes	—
306	C₂³	C₂×#10625337	1	4	yes	—
307	C₂³	C₂×#10625337	1	24	yes	complemented
308	C₂³	#13094044	1	4	yes	—
309	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
310	C₂³	C₂²×C₂²⋊D₄₇	1	3	yes	—
311	Q₈	—	2	4	no	—
312	Q₈	—	2	4	no	—
313	Q₈	—	4	12	no	—
314	Q₈	—	94	4	no	—
315	Q₈	—	94	4	no	—
316	Q₈	—	188	12	no	—
317	C₂×C₄	—	2	12	no	—
318	C₂×C₄	—	2	24	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	4	12	no	—
324	C₂×C₄	—	4	12	no	—
325	C₂×C₄	—	94	4	no	—
326	C₂×C₄	—	94	4	no	—
327	C₂×C₄	—	188	12	no	—
328	C₂×C₄	—	188	12	no	—
329	C₂×C₄	#13093996	1	12	yes	—
330	C₂×C₄	C₂×D₄×D₄₇	1	6	yes	—
331	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
332	C₂×C₄	C₂²×C₂²⋊D₄₇	1	3	yes	—
333	C₂×C₄	C₂×#10625352	1	6	yes	—
334	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
335	C₈	—	47	8	no	—
336	C₈	—	94	4	no	—
337	C₂²	—	2	48	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	#15689362	1	16	yes	direct product factor
341	C₂²	C₂×#13093996	1	6	yes	—
342	C₂²	C₂²×#10625337	1	6	yes	—
343	C₂²	C₂²×#10625337	1	8	yes	complemented
344	C₂²	C₂×#13094044	1	6	yes	—
345	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
346	C₄	—	2	4	no	—
347	C₄	—	4	4	no	—
348	C₄	—	4	4	no	—
349	C₄	—	188	4	no	—
350	C₄	—	188	4	no	—
351	C₄	C₂×#13093996	1	6	yes	—
352	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
353	C₄	C₂²×#10625352	1	1	yes	characteristic
354	C₂	—	2	8	no	—
355	C₂	C₂×#15689362	1	12	yes	direct product factor
356	C₂	C₂²×#13093996	1	1	yes	characteristic
357	C₂	C₂³×#10625337	1	1	yes	characteristic
358	C₂	C₂²×#13094044	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂²×C₂²⋊Q₈×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂×D₄
prime radical	C₂⁵×C₄₇	D₄
hypercenter	C₂²×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	C₂²×#467
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂²×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×#10625337	C₂	semidirect
4. C₂×#15689362	C₂	direct (N × H)
5. C₂²×#13093957	C₂	semidirect
6. C₂²×#13093948	C₂	semidirect
7. C₂²×#13093947	C₂	semidirect
11. C₂²×#10625337	C₂²	semidirect
21. #15689362	C₂²	direct (N × H)
22. C₂×#13093957	C₂²	semidirect
23. C₂×#13093948	C₂²	semidirect
24. C₂×#13093947	C₂²	semidirect
39. C₂×#10625337	C₂³	semidirect
52. #13093957	C₂³	semidirect
53. #13093948	C₂³	semidirect
54. #13093947	C₂³	semidirect
76. C₂⁴×C₄₇	Q₁₆	semidirect
127. C₂³×C₄₇	C₂×Q₁₆	semidirect
161. C₂²×C₄₇	#467	semidirect
164. C₂²×C₄₇	C₂²×Q₁₆	semidirect
184. C₂×C₄₇	C₂×#467	semidirect
211. C₄₇	C₂²×#467	semidirect
256. C₂⁴	#10625337	semidirect
307. C₂³	C₂×#10625337	semidirect
340. C₂²	#15689362	direct (N × H)
343. C₂²	C₂²×#10625337	semidirect
355. C₂	C₂×#15689362	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×#10625337	2
C₂⁴×C₄₇⋊C₈	2
C₂²×#13094003	2
C₂×#15689362	2
C₂²×#13093957	2
C₂²×#13093948	2
C₂²×#13093947	2
C₂²×C₂²⋊Q₈×C₄₇	2
C₂²×#467	47

Subgroups — C22×#15689362 #27083374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689362 #27083374