Subgroups — C₂×#20257039 #27124445

Order 12032.

11254 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094072	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257039	C₂	1	32	yes	maximal, direct product factor
3	C₂×Q₈×C₂²⋊D₄₇	C₂	1	8	yes	maximal, complemented
4	C₂×#15689784	C₂	1	8	yes	maximal, complemented
5	C₂×#15689697	C₂	1	6	yes	maximal, complemented
6	C₂×#15689634	C₂	1	6	yes	maximal, complemented
7	C₂×#15689601	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13094072	—	2	16	no	—
10	C₂×#13094072	C₂²	1	16	yes	complemented
11	C₂²×#10625354	C₂²	1	4	yes	complemented
12	C₂²×#10625350	C₂²	1	6	yes	—
13	C₂²×Q₈×D₄₇	C₂²	1	4	yes	complemented
14	Q₈×C₂²⋊D₄₇	C₂²	1	128	yes	complemented
15	#15689784	C₂²	1	128	yes	complemented
16	#15689697	C₂²	1	96	yes	complemented
17	C₂×#13094022	C₂²	1	12	yes	complemented
18	C₂×#13094013	C₂²	1	12	yes	complemented
19	#15689634	C₂²	1	96	yes	complemented
20	C₂×#13094007	C₂²	1	12	yes	—
21	C₂×#13094003	C₂²	1	12	yes	—
22	C₂×#13094000	C₂²	1	24	yes	complemented
23	C₂×#13093998	C₂²	1	12	yes	—
24	C₂×#13093993	C₂²	1	4	yes	—
25	#15689601	C₂²	1	16	yes	complemented
26	C₂×Q₈×Dic₄₇	C₂²	1	8	yes	complemented
27	C₂×C₄×C₂²⋊D₄₇	C₂²	1	24	yes	—
28	C₂×#13093983	C₂²	1	6	yes	—
29	C₂³×Q₈×C₄₇	—	2	16	no	—
30	C₂³×Q₈×C₄₇	C₂²	1	8	yes	—
31	C₂³×Q₈×C₄₇	C₂²	1	3	yes	—
32	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂³×Q₈×C₄₇	C₂²	1	16	yes	complemented
34	C₂⁴×C₄×C₄₇	C₂²	1	3	yes	—
35	#13094072	—	2	128	no	—
36	C₂×#10625354	—	2	32	no	—
37	C₂×#10625354	C₂³	1	32	yes	complemented
38	C₂×#10625350	—	2	48	no	—
39	C₂×#10625350	C₂³	1	48	yes	—
40	C₂²×Dic₉₄	C₂³	1	6	yes	—
41	C₂×Q₈×D₄₇	—	2	32	no	—
42	C₂×Q₈×D₄₇	C₂³	1	32	yes	complemented
43	C₂²×D₁₈₈	C₂³	1	6	yes	—
44	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
45	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
46	C₂²×C₄×D₄₇	C₂³	1	12	yes	—
47	#13094022	C₂³	1	96	yes	complemented
48	#13094013	C₂³	1	96	yes	complemented
49	#13094007	C₂³	1	96	yes	—
50	#13094003	C₂³	1	96	yes	—
51	#13094000	C₂³	1	192	yes	complemented
52	#13093998	C₂³	1	96	yes	—
53	#13093993	C₂³	1	32	yes	—
54	Q₈×Dic₄₇	C₂³	1	64	yes	complemented
55	C₄×C₂²⋊D₄₇	C₂³	1	192	yes	—
56	#13093983	C₂³	1	48	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
58	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
59	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
60	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
61	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	12	yes	—
63	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₄₇	—	2	64	no	—
65	C₂²×Q₈×C₄₇	—	2	128	no	—
66	C₂²×Q₈×C₄₇	—	2	24	no	—
67	C₂²×Q₈×C₄₇	D₄	1	16	yes	complemented
68	C₂²×Q₈×C₄₇	C₂³	1	64	yes	—
69	C₂²×Q₈×C₄₇	C₂³	1	12	yes	—
70	C₂²×Q₈×C₄₇	C₂³	1	24	yes	—
71	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
72	C₂²×Q₈×C₄₇	C₂³	1	8	yes	—
73	C₂³×C₄×C₄₇	—	2	24	no	—
74	C₂³×C₄×C₄₇	C₂³	1	12	yes	—
75	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
76	C₂³×C₄×C₄₇	C₂³	1	24	yes	—
77	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
78	C₂⁴×C₄₇	—	2	4	no	—
79	C₂⁴×C₄₇	—	2	8	no	—
80	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
81	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
82	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
83	C₂³×D₄₇	C₂⁴	1	4	yes	—
84	C₂×Q₈×C₄₇	—	2	256	no	—
85	C₂×Q₈×C₄₇	—	2	48	no	—
86	C₂×Q₈×C₄₇	—	2	96	no	—
87	C₂×Q₈×C₄₇	C₂×D₄	1	32	yes	—
88	C₂×Q₈×C₄₇	C₂×D₄	1	64	yes	complemented
89	C₂×Q₈×C₄₇	C₂⁴	1	48	yes	—
90	C₂×Q₈×C₄₇	C₂⁴	1	16	yes	—
91	C₂²×C₄×C₄₇	—	2	12	no	—
92	C₂²×C₄×C₄₇	—	2	48	no	—
93	C₂²×C₄×C₄₇	—	2	96	no	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	24	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	48	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
98	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
99	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
100	C₂×C₂²⋊D₄₇	—	2	16	no	—
101	C₂×C₂²⋊D₄₇	—	2	32	no	—
102	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
103	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
104	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
105	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
106	#10625354	—	2	128	no	—
107	Q₈×D₄₇	—	2	128	no	—
108	#10625350	—	2	192	no	—
109	C₂×D₁₈₈	—	2	24	no	—
110	C₂×D₁₈₈	C₂⁴	1	24	yes	—
111	C₂×C₄×D₄₇	—	2	48	no	—
112	C₂×C₄×D₄₇	C₂⁴	1	48	yes	—
113	C₂×Dic₉₄	—	2	24	no	—
114	C₂×Dic₉₄	C₂⁴	1	24	yes	—
115	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
116	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
117	(C₂×D₄₇)⋊C₄	C₂⁴	1	96	yes	—
118	C₄⋊Dic₄₇	C₂⁴	1	48	yes	—
119	Dic₄₇⋊C₄	C₂⁴	1	96	yes	—
120	C₄×Dic₄₇	C₂⁴	1	48	yes	—
121	C₂³×C₄₇	—	2	32	no	—
122	C₂³×C₄₇	—	2	8	no	—
123	C₂³×C₄₇	—	2	4	no	—
124	C₂³×C₄₇	—	2	4	no	—
125	C₂³×C₄₇	—	2	4	no	—
126	C₂³×C₄₇	—	2	16	no	—
127	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
128	C₂³×C₄₇	2₋¹⁺⁴	1	8	yes	complemented
129	C₂³×C₄₇	C₂⁵	1	2	yes	—
130	C₂³×C₄₇	C₂⁵	1	4	yes	—
131	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
132	C₂²×D₄₇	—	2	8	no	—
133	C₂²×D₄₇	—	2	16	no	—
134	C₂²×D₄₇	C₂⁵	1	8	yes	—
135	Q₈×C₄₇	—	2	96	no	—
136	Q₈×C₄₇	C₂²×D₄	1	64	yes	—
137	C₂×C₄×C₄₇	—	2	24	no	—
138	C₂×C₄×C₄₇	—	2	12	no	—
139	C₂×C₄×C₄₇	—	2	96	no	—
140	C₂×C₄×C₄₇	C₂²×D₄	1	24	yes	—
141	C₂×C₄×C₄₇	C₂²×D₄	1	48	yes	—
142	C₂×C₄×C₄₇	C₂⁵	1	12	yes	—
143	C₂×C₄×C₄₇	C₂⁵	1	12	yes	—
144	C₂²⋊D₄₇	—	2	32	no	—
145	C₂²⋊D₄₇	—	2	64	no	—
146	C₂×Dic₄₇	—	2	8	no	—
147	C₂×Dic₄₇	—	2	16	no	—
148	C₂×Dic₄₇	C₂⁵	1	16	yes	—
149	C₂×Dic₄₇	C₂⁵	1	8	yes	—
150	D₁₈₈	—	2	48	no	—
151	C₄×D₄₇	—	2	96	no	—
152	Dic₉₄	—	2	48	no	—
153	C₂×#3486	—	47	1	no	maximal, Sylow
154	C₂²×C₄₇	—	2	32	no	—
155	C₂²×C₄₇	—	2	4	no	—
156	C₂²×C₄₇	—	2	4	no	—
157	C₂²×C₄₇	—	2	4	no	—
158	C₂²×C₄₇	—	2	8	no	—
159	C₂²×C₄₇	—	2	16	no	—
160	C₂²×C₄₇	C₂³×D₄	1	4	yes	—
161	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
162	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	4	yes	—
163	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	8	yes	complemented
164	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
165	C₂×D₄₇	—	2	8	no	—
166	C₂×D₄₇	—	2	16	no	—
167	C₂×D₄₇	—	4	16	no	—
168	C₄×C₄₇	—	2	12	no	—
169	C₄×C₄₇	C₂³×D₄	1	24	yes	—
170	Dic₄₇	—	2	8	no	—
171	Dic₄₇	—	2	16	no	—
172	C₂²×2₋¹⁺⁴	—	47	1	no	—
173	C₂⁴×Q₈	D₄₇	1	1	yes	characteristic, complemented
174	#3486	—	47	32	no	—
175	C₂×D₄×Q₈	—	47	8	no	—
176	C₂×#548	—	47	8	no	—
177	C₂×#536	—	47	6	no	—
178	C₂×#525	—	47	6	no	—
179	C₂×#519	—	47	1	no	—
180	C₂×C₄₇	—	2	4	no	—
181	C₂×C₄₇	—	2	8	no	—
182	C₂×C₄₇	#3486	1	4	yes	complemented
183	C₂×C₄₇	C₂⁴×D₄	1	1	yes	characteristic
184	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	2	yes	—
185	D₄₇	—	4	8	no	—
186	C₂×2₋¹⁺⁴	—	47	16	no	—
187	C₂×2₋¹⁺⁴	—	94	16	no	—
188	C₂²×#41	—	47	4	no	—
189	C₂²×#41	—	47	6	no	—
190	C₂³×Q₈	—	2	16	no	—
191	C₂³×Q₈	—	47	4	no	—
192	C₂³×Q₈	C₂×D₄₇	1	3	yes	—
193	C₂³×Q₈	C₂×D₄₇	1	8	yes	—
194	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
195	C₂³×Q₈	C₂×D₄₇	1	16	yes	complemented
196	C₂⁴×C₄	C₂×D₄₇	1	3	yes	—
197	D₄×Q₈	—	47	128	no	—
198	#548	—	47	128	no	—
199	#536	—	47	96	no	—
200	C₂×C₄⋊Q₈	—	47	12	no	—
201	C₂×#124	—	47	12	no	—
202	#525	—	47	96	no	—
203	C₂×#123	—	47	12	no	—
204	C₂×C₂²⋊Q₈	—	47	24	no	—
205	C₂×C₂²⋊Q₈	—	47	12	no	—
206	C₂×#121	—	47	12	no	—
207	C₂×#120	—	47	4	no	—
208	#519	—	47	16	no	—
209	C₂×C₄×Q₈	—	47	8	no	—
210	C₂×C₄×D₄	—	47	24	no	—
211	C₂×#117	—	47	6	no	—
212	C₄₇	C₂×#3486	1	1	yes	characteristic, complemented, Sylow
213	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
214	2₋¹⁺⁴	—	94	128	no	—
215	C₂×#41	—	47	32	no	—
216	C₂×#41	—	47	48	no	—
217	C₂×#41	—	94	32	no	—
218	C₂×#41	—	94	48	no	—
219	C₂²×Q₈	—	2	64	no	—
220	C₂²×Q₈	—	2	128	no	—
221	C₂²×Q₈	—	2	24	no	—
222	C₂²×Q₈	—	47	32	no	—
223	C₂²×Q₈	—	47	6	no	—
224	C₂²×Q₈	—	94	32	no	—
225	C₂²×Q₈	C₂²⋊D₄₇	1	16	yes	complemented
226	C₂²×Q₈	C₂²×D₄₇	1	12	yes	—
227	C₂²×Q₈	C₂²×D₄₇	1	24	yes	—
228	C₂²×Q₈	C₂²×D₄₇	1	64	yes	—
229	C₂²×Q₈	C₂²×D₄₇	1	4	yes	—
230	C₂²×Q₈	C₂²×D₄₇	1	8	yes	—
231	C₂²×D₄	—	47	8	no	—
232	C₂²×D₄	—	47	4	no	—
233	C₂²×D₄	—	47	6	no	—
234	C₂³×C₄	—	2	24	no	—
235	C₂³×C₄	—	47	12	no	—
236	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
237	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
238	C₂³×C₄	C₂²×D₄₇	1	24	yes	—
239	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
240	C₄⋊Q₈	—	47	96	no	—
241	#124	—	47	96	no	—
242	#123	—	47	96	no	—
243	C₂²⋊Q₈	—	47	192	no	—
244	C₂²⋊Q₈	—	47	96	no	—
245	#121	—	47	96	no	—
246	#120	—	47	32	no	—
247	C₄×Q₈	—	47	64	no	—
248	C₄×D₄	—	47	192	no	—
249	#117	—	47	48	no	—
250	C₂×C₄⋊C₄	—	47	12	no	—
251	C₂×C₄⋊C₄	—	47	24	no	—
252	C₂×C₂²⋊C₄	—	47	4	no	—
253	C₂×C₂²⋊C₄	—	47	8	no	—
254	C₂×C₂²⋊C₄	—	47	24	no	—
255	C₂×C₄²	—	47	12	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	8	no	—
258	C₂⁴	—	47	4	no	—
259	C₂⁴	C₂³×D₄₇	1	4	yes	—
260	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
261	C₂⁴	C₂³×D₄₇	1	2	yes	—
262	#41	—	94	128	no	—
263	#41	—	94	192	no	—
264	C₂×Q₈	—	2	256	no	—
265	C₂×Q₈	—	2	48	no	—
266	C₂×Q₈	—	2	96	no	—
267	C₂×Q₈	—	47	24	no	—
268	C₂×Q₈	—	94	128	no	—
269	C₂×Q₈	—	94	24	no	—
270	C₂×Q₈	C₂×C₂²⋊D₄₇	1	32	yes	—
271	C₂×Q₈	C₂×C₂²⋊D₄₇	1	64	yes	complemented
272	C₂×Q₈	C₂³×D₄₇	1	48	yes	—
273	C₂×Q₈	C₂³×D₄₇	1	16	yes	—
274	C₂×D₄	—	47	32	no	—
275	C₂×D₄	—	47	16	no	—
276	C₂×D₄	—	47	24	no	—
277	C₂×D₄	—	94	16	no	—
278	C₂×D₄	—	94	32	no	—
279	C₂×D₄	—	94	24	no	—
280	C₂²×C₄	—	2	12	no	—
281	C₂²×C₄	—	2	48	no	—
282	C₂²×C₄	—	2	96	no	—
283	C₂²×C₄	—	47	8	no	—
284	C₂²×C₄	—	47	4	no	—
285	C₂²×C₄	—	47	48	no	—
286	C₂²×C₄	—	94	48	no	—
287	C₂²×C₄	C₂×C₂²⋊D₄₇	1	24	yes	—
288	C₂²×C₄	C₂³×D₄₇	1	48	yes	—
289	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
290	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
291	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
292	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
293	C₄⋊C₄	—	47	96	no	—
294	C₄⋊C₄	—	47	48	no	—
295	C₂²⋊C₄	—	47	16	no	—
296	C₂²⋊C₄	—	47	32	no	—
297	C₂²⋊C₄	—	47	96	no	—
298	C₄²	—	47	48	no	—
299	C₂³	—	2	32	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	47	8	no	—
306	C₂³	—	94	8	no	—
307	C₂³	—	94	16	no	—
308	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
309	C₂³	#13094072	1	8	yes	complemented
310	C₂³	C₂⁴×D₄₇	1	2	yes	—
311	C₂³	C₂⁴×D₄₇	1	4	yes	—
312	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
313	Q₈	—	2	96	no	—
314	Q₈	—	94	48	no	—
315	Q₈	C₂²×C₂²⋊D₄₇	1	64	yes	—
316	D₄	—	94	32	no	—
317	D₄	—	94	64	no	—
318	D₄	—	94	48	no	—
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	96	no	—
322	C₂×C₄	—	47	16	no	—
323	C₂×C₄	—	47	8	no	—
324	C₂×C₄	—	94	8	no	—
325	C₂×C₄	—	94	16	no	—
326	C₂×C₄	—	94	96	no	—
327	C₂×C₄	C₂²×C₂²⋊D₄₇	1	24	yes	—
328	C₂×C₄	C₂²×C₂²⋊D₄₇	1	48	yes	—
329	C₂×C₄	C₂⁴×D₄₇	1	12	yes	—
330	C₂×C₄	C₂⁴×D₄₇	1	12	yes	—
331	C₂²	—	2	32	no	—
332	C₂²	—	2	8	no	—
333	C₂²	—	2	16	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	94	8	no	—
338	C₂²	—	94	16	no	—
339	C₂²	—	188	16	no	—
340	C₂²	C₂³×C₂²⋊D₄₇	1	4	yes	—
341	C₂²	C₂³×C₂²⋊D₄₇	1	2	yes	—
342	C₂²	C₂×#13094072	1	4	yes	—
343	C₂²	C₂×#13094072	1	8	yes	complemented
344	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
345	C₄	—	2	12	no	—
346	C₄	—	94	8	no	—
347	C₄	—	94	16	no	—
348	C₄	C₂³×C₂²⋊D₄₇	1	24	yes	—
349	C₂	—	2	4	no	—
350	C₂	—	2	8	no	—
351	C₂	—	188	8	no	—
352	C₂	#20257039	1	4	yes	direct product factor
353	C₂	C₂⁴×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂	C₂²×#13094072	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂⁴×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂⁴×Q₈	D₄₇
hypocenter	C₄₇	C₂×#3486
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#13094072	C₂	semidirect
2. #20257039	C₂	direct (N × H)
3. C₂×Q₈×C₂²⋊D₄₇	C₂	semidirect
4. C₂×#15689784	C₂	semidirect
5. C₂×#15689697	C₂	semidirect
6. C₂×#15689634	C₂	semidirect
7. C₂×#15689601	C₂	semidirect
8. C₂⁴×Q₈×C₄₇	C₂	semidirect
10. C₂×#13094072	C₂²	semidirect
11. C₂²×#10625354	C₂²	semidirect
13. C₂²×Q₈×D₄₇	C₂²	semidirect
14. Q₈×C₂²⋊D₄₇	C₂²	semidirect
15. #15689784	C₂²	semidirect
16. #15689697	C₂²	semidirect
17. C₂×#13094022	C₂²	semidirect
18. C₂×#13094013	C₂²	semidirect
19. #15689634	C₂²	semidirect
22. C₂×#13094000	C₂²	semidirect
25. #15689601	C₂²	semidirect
26. C₂×Q₈×Dic₄₇	C₂²	semidirect
33. C₂³×Q₈×C₄₇	C₂²	semidirect
37. C₂×#10625354	C₂³	semidirect
42. C₂×Q₈×D₄₇	C₂³	semidirect
47. #13094022	C₂³	semidirect
48. #13094013	C₂³	semidirect
51. #13094000	C₂³	semidirect
54. Q₈×Dic₄₇	C₂³	semidirect
67. C₂²×Q₈×C₄₇	D₄	semidirect
88. C₂×Q₈×C₄₇	C₂×D₄	semidirect
128. C₂³×C₄₇	2₋¹⁺⁴	semidirect
163. C₂²×C₄₇	C₂×2₋¹⁺⁴	semidirect
173. C₂⁴×Q₈	D₄₇	semidirect
182. C₂×C₄₇	#3486	semidirect
195. C₂³×Q₈	C₂×D₄₇	semidirect
212. C₄₇	C₂×#3486	semidirect
225. C₂²×Q₈	C₂²⋊D₄₇	semidirect
271. C₂×Q₈	C₂×C₂²⋊D₄₇	semidirect
309. C₂³	#13094072	semidirect
343. C₂²	C₂×#13094072	semidirect
352. C₂	#20257039	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×#13094072	2
#20257039	2
C₂×Q₈×C₂²⋊D₄₇	2
C₂×#15689784	2
C₂×#15689697	2
C₂×#15689634	2
C₂×#15689601	2
C₂⁴×Q₈×C₄₇	2
C₂×#3486	47

Subgroups — C2×#20257039 #27124445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257039 #27124445