Subgroups — C₂²×#15689354 #27083364

Order 12032.

3350 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625336	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13093998	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689354	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#13093955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13093944	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₂³×C₂²⋊D₄₇	—	2	1	no	—
11	C₂²×#10625336	—	2	8	no	—
12	C₂²×#10625336	C₂²	1	12	yes	complemented
13	C₂³×C₄₇⋊C₈	—	2	8	no	—
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂³×C₄₇⋊C₈	C₂²	1	12	yes	complemented
17	C₂×#13093998	—	2	6	no	—
18	C₂×#13093998	C₂²	1	12	yes	—
19	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂²×(C₂×D₄₇)⋊C₄	—	2	1	no	—
21	#15689354	C₂²	1	64	yes	direct product factor
22	C₂×#13093955	C₂²	1	12	yes	complemented
23	C₂×#13093948	C₂²	1	12	yes	complemented
24	C₂×#13093944	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	complemented
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	C₂⁴×D₄₇	—	2	1	no	—
33	C₂²×D₁₈₈	—	2	4	no	—
34	C₂²×D₁₈₈	—	2	4	no	—
35	C₂²×D₁₈₈	—	2	3	no	—
36	C₂²×D₁₈₈	C₂³	1	6	yes	—
37	C₂²×C₂²⋊D₄₇	—	2	12	no	—
38	C₂²×C₂²⋊D₄₇	—	4	8	no	—
39	C₂³×Dic₄₇	—	2	1	no	—
40	C₂×#10625336	—	2	48	no	—
41	C₂×#10625336	C₂³	1	16	yes	complemented
42	C₂²×C₄₇⋊C₈	—	2	4	no	—
43	C₂²×C₄₇⋊C₈	—	2	48	no	—
44	C₂²×C₄₇⋊C₈	D₄	1	8	yes	complemented
45	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	16	yes	complemented
48	#13093998	—	2	24	no	—
49	#13093998	C₂³	1	16	yes	—
50	C₂×C₄⋊Dic₄₇	—	2	3	no	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
52	C₂×(C₂×D₄₇)⋊C₄	—	2	12	no	—
53	#13093955	C₂³	1	16	yes	complemented
54	#13093948	C₂³	1	16	yes	complemented
55	#13093944	C₂³	1	16	yes	complemented
56	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₄₇	—	2	3	no	—
58	C₂²×Q₈×C₄₇	—	2	4	no	—
59	C₂²×Q₈×C₄₇	—	2	4	no	—
60	C₂²×Q₈×C₄₇	C₂³	1	6	yes	—
61	C₂³×C₄×C₄₇	—	2	4	no	—
62	C₂³×C₄×C₄₇	—	2	4	no	—
63	C₂³×C₄×C₄₇	—	2	1	no	—
64	C₂³×C₄×C₄₇	—	2	1	no	—
65	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	D₄	1	6	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
68	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂²⋊Q₈×C₄₇	—	2	24	no	—
70	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
71	C₂×C₄⋊C₄×C₄₇	—	2	12	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	3	no	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	12	no	—
75	C₂⁴×C₄₇	—	2	4	no	—
76	C₂⁴×C₄₇	—	2	4	no	—
77	C₂⁴×C₄₇	SD₁₆	1	8	yes	complemented
78	C₂⁴×C₄₇	C₂×D₄	1	6	yes	—
79	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂³×D₄₇	—	2	6	no	—
81	C₂³×D₄₇	—	4	4	no	—
82	C₂³×D₄₇	—	4	4	no	—
83	C₂³×D₄₇	—	4	4	no	—
84	C₂×Q₈×C₄₇	—	2	6	no	—
85	C₂×Q₈×C₄₇	—	2	12	no	—
86	C₂×Q₈×C₄₇	—	2	12	no	—
87	C₂×Q₈×C₄₇	—	4	12	no	—
88	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	24	no	—
91	C₂²×C₄×C₄₇	—	2	12	no	—
92	C₂²×C₄×C₄₇	—	2	12	no	—
93	C₂²×C₄×C₄₇	—	2	6	no	—
94	C₂²×C₄×C₄₇	—	2	6	no	—
95	C₂²×C₄×C₄₇	—	4	4	no	—
96	C₂²×C₄×C₄₇	—	4	4	no	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	12	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₄₇	#41	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
104	C₂×C₂²⋊D₄₇	—	2	16	no	—
105	C₂×C₂²⋊D₄₇	—	4	48	no	—
106	C₂²×Dic₄₇	—	2	6	no	—
107	C₂²×Dic₄₇	—	4	4	no	—
108	C₂×D₁₈₈	—	2	12	no	—
109	C₂×D₁₈₈	—	2	12	no	—
110	C₂×D₁₈₈	—	2	6	no	—
111	C₂×D₁₈₈	—	4	12	no	—
112	C₂×D₁₈₈	C₂⁴	1	4	yes	—
113	C₄⋊C₄×C₄₇	—	2	16	no	—
114	C₄⋊C₄×C₄₇	—	2	6	no	—
115	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
116	C₂²⋊C₄×C₄₇	—	2	16	no	—
117	#10625336	—	2	32	no	—
118	(C₂×D₄₇)⋊C₄	—	2	16	no	—
119	C₄⋊Dic₄₇	—	2	6	no	—
120	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
121	C₂×C₄₇⋊C₈	—	2	12	no	—
122	C₂×C₄₇⋊C₈	—	2	32	no	—
123	C₂×C₄₇⋊C₈	C₂×D₄	1	24	yes	complemented
124	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
125	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
126	C₂³×C₄₇	—	2	12	no	—
127	C₂³×C₄₇	—	2	12	no	—
128	C₂³×C₄₇	—	2	32	no	—
129	C₂³×C₄₇	#121	1	4	yes	—
130	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
131	C₂³×C₄₇	C₂×SD₁₆	1	24	yes	complemented
132	C₂³×C₄₇	#135	1	4	yes	—
133	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
134	C₂³×C₄₇	C₂²×D₄	1	3	yes	—
135	C₂²×D₄₇	—	2	4	no	—
136	C₂²×D₄₇	—	4	12	no	—
137	C₂²×D₄₇	—	4	12	no	—
138	C₂²×D₄₇	—	4	12	no	—
139	C₂²×D₄₇	—	8	16	no	—
140	Q₈×C₄₇	—	2	4	no	—
141	Q₈×C₄₇	—	2	4	no	—
142	Q₈×C₄₇	—	4	12	no	—
143	C₂×C₄×C₄₇	—	2	12	no	—
144	C₂×C₄×C₄₇	—	2	24	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	4	12	no	—
150	C₂×C₄×C₄₇	—	4	12	no	—
151	C₂×C₄×C₄₇	#121	1	12	yes	—
152	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
153	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
155	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
156	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
157	C₂²⋊D₄₇	—	4	32	no	—
158	C₂×Dic₄₇	—	2	4	no	—
159	C₂×Dic₄₇	—	4	12	no	—
160	D₁₈₈	—	2	4	no	—
161	D₁₈₈	—	2	4	no	—
162	D₁₈₈	—	4	12	no	—
163	C₄₇⋊C₈	—	2	4	no	—
164	C₄₇⋊C₈	C₂²×D₄	1	8	yes	complemented
165	C₂²×#465	—	47	1	no	maximal, Sylow
166	C₂²×C₄₇	—	2	4	no	—
167	C₂²×C₄₇	—	2	48	no	—
168	C₂²×C₄₇	—	2	4	no	—
169	C₂²×C₄₇	#465	1	16	yes	complemented
170	C₂²×C₄₇	C₂×#121	1	6	yes	—
171	C₂²×C₄₇	C₂²×SD₁₆	1	6	yes	—
172	C₂²×C₄₇	C₂²×SD₁₆	1	8	yes	complemented
173	C₂²×C₄₇	C₂×#135	1	6	yes	—
174	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
175	C₂×D₄₇	—	4	4	no	—
176	C₂×D₄₇	—	4	4	no	—
177	C₂×D₄₇	—	4	4	no	—
178	C₂×D₄₇	—	8	24	no	—
179	C₄×C₄₇	—	2	4	no	—
180	C₄×C₄₇	—	4	4	no	—
181	C₄×C₄₇	—	4	4	no	—
182	C₄×C₄₇	C₂×#121	1	6	yes	—
183	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
184	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
185	Dic₄₇	—	4	4	no	—
186	C₂³×SD₁₆	—	47	1	no	—
187	C₂⁴×C₈	—	47	1	no	—
188	C₂²×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
189	C₂²×#121	—	47	1	no	—
190	C₂×#465	—	47	24	no	—
191	C₂²×#106	—	47	1	no	—
192	C₂²×#103	—	47	1	no	—
193	C₂²×#102	—	47	1	no	—
194	C₂×C₄₇	—	2	8	no	—
195	C₂×C₄₇	C₂×#465	1	12	yes	complemented
196	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
197	C₂×C₄₇	C₂³×SD₁₆	1	1	yes	characteristic
198	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
199	D₄₇	—	8	4	no	—
200	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
201	C₂³×D₄	—	47	1	no	—
202	C₂³×D₄	—	94	1	no	—
203	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
204	C₂²×SD₁₆	—	47	12	no	—
205	C₂²×SD₁₆	—	94	8	no	—
206	C₂³×C₈	—	47	1	no	—
207	C₂³×C₈	—	47	1	no	—
208	C₂³×C₈	—	47	12	no	—
209	C₂³×C₈	—	94	8	no	—
210	C₂×C₂²⋊Q₈	—	2	6	no	—
211	C₂×C₂²⋊Q₈	C₂×D₄₇	1	12	yes	complemented
212	C₂×#121	—	47	12	no	—
213	C₂×#121	—	94	6	no	—
214	C₂²×C₄⋊C₄	—	2	1	no	—
215	C₂²×C₄⋊C₄	—	47	1	no	—
216	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
217	C₂²×C₂²⋊C₄	—	2	1	no	—
218	C₂²×C₂²⋊C₄	—	94	1	no	—
219	#465	—	47	64	no	—
220	C₂×#106	—	47	12	no	—
221	C₂×#103	—	47	12	no	—
222	C₂×#102	—	47	12	no	—
223	C₄₇	C₂²×#465	1	1	yes	characteristic, complemented, Sylow
224	C₂⁵	—	94	1	no	—
225	C₂⁵	C₂²⋊D₄₇	1	1	yes	characteristic
226	C₂²×Q₈	—	2	3	no	—
227	C₂²×Q₈	—	2	4	no	—
228	C₂²×Q₈	—	2	4	no	—
229	C₂²×Q₈	C₂²×D₄₇	1	6	yes	—
230	C₂²×D₄	—	47	6	no	—
231	C₂²×D₄	—	94	12	no	—
232	C₂²×D₄	—	94	4	no	—
233	C₂²×D₄	—	94	4	no	—
234	C₂²×D₄	—	94	3	no	—
235	C₂²×D₄	—	188	8	no	—
236	C₂³×C₄	—	2	4	no	—
237	C₂³×C₄	—	2	4	no	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	—	94	1	no	—
241	C₂³×C₄	C₂²⋊D₄₇	1	6	yes	—
242	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
243	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
244	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
245	C₂×SD₁₆	—	47	16	no	—
246	C₂×SD₁₆	—	94	48	no	—
247	C₂²×C₈	—	47	8	no	—
248	C₂²×C₈	—	47	6	no	—
249	C₂²×C₈	—	47	6	no	—
250	C₂²×C₈	—	47	16	no	—
251	C₂²×C₈	—	94	48	no	—
252	C₂²×C₈	—	94	4	no	—
253	C₂²⋊Q₈	—	2	24	no	—
254	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
255	#121	—	47	16	no	—
256	#121	—	94	24	no	—
257	C₂×C₄⋊C₄	—	2	12	no	—
258	C₂×C₄⋊C₄	—	2	3	no	—
259	C₂×C₄⋊C₄	—	47	6	no	—
260	C₂×C₄⋊C₄	—	94	3	no	—
261	C₂×C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
262	C₂×C₂²⋊C₄	—	2	12	no	—
263	C₂×C₂²⋊C₄	—	94	12	no	—
264	#106	—	47	16	no	—
265	#103	—	47	16	no	—
266	#102	—	47	16	no	—
267	C₂⁴	—	2	4	no	—
268	C₂⁴	—	2	4	no	—
269	C₂⁴	—	94	6	no	—
270	C₂⁴	—	188	4	no	—
271	C₂⁴	—	188	4	no	—
272	C₂⁴	—	188	4	no	—
273	C₂⁴	#10625336	1	8	yes	complemented
274	C₂⁴	C₂×C₂²⋊D₄₇	1	6	yes	—
275	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
276	C₂×Q₈	—	2	6	no	—
277	C₂×Q₈	—	2	12	no	—
278	C₂×Q₈	—	2	12	no	—
279	C₂×Q₈	—	4	12	no	—
280	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
281	C₂×D₄	—	47	4	no	—
282	C₂×D₄	—	94	16	no	—
283	C₂×D₄	—	94	12	no	—
284	C₂×D₄	—	94	6	no	—
285	C₂×D₄	—	94	12	no	—
286	C₂×D₄	—	188	48	no	—
287	C₂×D₄	—	188	12	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	24	no	—
290	C₂²×C₄	—	2	12	no	—
291	C₂²×C₄	—	2	12	no	—
292	C₂²×C₄	—	2	6	no	—
293	C₂²×C₄	—	2	6	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	4	4	no	—
296	C₂²×C₄	—	94	6	no	—
297	C₂²×C₄	—	188	4	no	—
298	C₂²×C₄	D₄×D₄₇	1	4	yes	—
299	C₂²×C₄	#10625352	1	4	yes	—
300	C₂²×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
301	C₂²×C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
302	C₂²×C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
303	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
304	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
305	SD₁₆	—	94	32	no	—
306	C₂×C₈	—	47	24	no	—
307	C₂×C₈	—	47	4	no	—
308	C₂×C₈	—	47	4	no	—
309	C₂×C₈	—	94	32	no	—
310	C₂×C₈	—	94	12	no	—
311	C₄⋊C₄	—	2	16	no	—
312	C₄⋊C₄	—	2	6	no	—
313	C₄⋊C₄	—	47	4	no	—
314	C₄⋊C₄	—	94	6	no	—
315	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
316	C₂²⋊C₄	—	2	16	no	—
317	C₂²⋊C₄	—	94	16	no	—
318	C₂³	—	2	32	no	—
319	C₂³	—	2	12	no	—
320	C₂³	—	2	12	no	—
321	C₂³	—	94	4	no	—
322	C₂³	—	376	16	no	—
323	C₂³	—	188	12	no	—
324	C₂³	—	188	12	no	—
325	C₂³	—	188	12	no	—
326	C₂³	#13093996	1	4	yes	—
327	C₂³	C₂×#10625336	1	4	yes	—
328	C₂³	C₂×#10625336	1	24	yes	complemented
329	C₂³	#13094044	1	4	yes	—
330	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
331	C₂³	C₂²×C₂²⋊D₄₇	1	3	yes	—
332	Q₈	—	2	4	no	—
333	Q₈	—	2	4	no	—
334	Q₈	—	4	12	no	—
335	D₄	—	94	4	no	—
336	D₄	—	94	4	no	—
337	D₄	—	188	32	no	—
338	D₄	—	188	12	no	—
339	C₂×C₄	—	2	12	no	—
340	C₂×C₄	—	2	24	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	12	no	—
346	C₂×C₄	—	4	12	no	—
347	C₂×C₄	—	94	4	no	—
348	C₂×C₄	—	188	12	no	—
349	C₂×C₄	#13093996	1	12	yes	—
350	C₂×C₄	C₂×D₄×D₄₇	1	6	yes	—
351	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
352	C₂×C₄	C₂²×C₂²⋊D₄₇	1	3	yes	—
353	C₂×C₄	C₂×#10625352	1	6	yes	—
354	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
355	C₈	—	47	8	no	—
356	C₈	—	94	4	no	—
357	C₂²	—	2	48	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	376	24	no	—
361	C₂²	—	188	4	no	—
362	C₂²	—	188	4	no	—
363	C₂²	—	188	4	no	—
364	C₂²	#15689354	1	16	yes	direct product factor
365	C₂²	C₂×#13093996	1	6	yes	—
366	C₂²	C₂²×#10625336	1	6	yes	—
367	C₂²	C₂²×#10625336	1	8	yes	complemented
368	C₂²	C₂×#13094044	1	6	yes	—
369	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
370	C₄	—	2	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	4	no	—
373	C₄	—	188	4	no	—
374	C₄	C₂×#13093996	1	6	yes	—
375	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
376	C₄	C₂²×#10625352	1	1	yes	characteristic
377	C₂	—	2	8	no	—
378	C₂	—	376	4	no	—
379	C₂	C₂×#15689354	1	12	yes	direct product factor
380	C₂	C₂²×#13093996	1	1	yes	characteristic
381	C₂	C₂³×#10625336	1	1	yes	characteristic
382	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	C₂²×#13093998	C₂
hypercenter	C₂²×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	C₂²×#465
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×#10625336	C₂	semidirect
2. C₂⁴×C₄₇⋊C₈	C₂	semidirect
4. C₂×#15689354	C₂	direct (N × H)
5. C₂²×#13093955	C₂	semidirect
6. C₂²×#13093948	C₂	semidirect
7. C₂²×#13093944	C₂	semidirect
8. C₂²×C₂²⋊Q₈×C₄₇	C₂	semidirect
12. C₂²×#10625336	C₂²	semidirect
16. C₂³×C₄₇⋊C₈	C₂²	semidirect
21. #15689354	C₂²	direct (N × H)
22. C₂×#13093955	C₂²	semidirect
23. C₂×#13093948	C₂²	semidirect
24. C₂×#13093944	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
41. C₂×#10625336	C₂³	semidirect
44. C₂²×C₄₇⋊C₈	D₄	semidirect
47. C₂²×C₄₇⋊C₈	C₂³	semidirect
53. #13093955	C₂³	semidirect
54. #13093948	C₂³	semidirect
55. #13093944	C₂³	semidirect
70. C₂²⋊Q₈×C₄₇	C₂³	semidirect
77. C₂⁴×C₄₇	SD₁₆	semidirect
123. C₂×C₄₇⋊C₈	C₂×D₄	semidirect
131. C₂³×C₄₇	C₂×SD₁₆	semidirect
164. C₄₇⋊C₈	C₂²×D₄	semidirect
169. C₂²×C₄₇	#465	semidirect
172. C₂²×C₄₇	C₂²×SD₁₆	semidirect
188. C₂²×C₂²⋊Q₈	D₄₇	semidirect
195. C₂×C₄₇	C₂×#465	semidirect
211. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
223. C₄₇	C₂²×#465	semidirect
254. C₂²⋊Q₈	C₂²×D₄₇	semidirect
273. C₂⁴	#10625336	semidirect
328. C₂³	C₂×#10625336	semidirect
364. C₂²	#15689354	direct (N × H)
367. C₂²	C₂²×#10625336	semidirect
379. C₂	C₂×#15689354	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×#10625336	2
C₂⁴×C₄₇⋊C₈	2
C₂²×#13093998	2
C₂×#15689354	2
C₂²×#13093955	2
C₂²×#13093948	2
C₂²×#13093944	2
C₂²×C₂²⋊Q₈×C₄₇	2
C₂²×#465	47

Subgroups — C22×#15689354 #27083364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689354 #27083364