Subgroups — C₂×C₄×#13093948 #26214022

Order 12032.

1726 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093948	C₂	1	2	yes	maximal
2	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄×#13093948	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688885	C₂	1	2	yes	maximal
6	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₄₇	—	2	1	no	—
10	C₂×#13093948	C₄	1	16	yes	direct product factor
11	C₂×#13093948	C₂²	1	8	yes	—
12	C₂×C₄×C₄₇⋊C₈	—	2	4	no	—
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
14	C₄×C₄⋊Dic₄₇	—	2	2	no	—
15	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	—
16	C₂×C₄₇⋊#95	—	2	1	no	—
17	#15688885	C₂²	1	8	yes	—
18	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
20	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
21	C₂×C₄×Q₈×C₄₇	C₄	1	8	yes	complemented
22	C₂×C₄×Q₈×C₄₇	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₄₇	—	2	1	no	—
26	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×Dic₄₇	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	4	no	—
29	C₂²×C₄₇⋊C₈	—	2	4	no	—
30	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
31	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	4	no	—
34	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
35	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
36	C₂×C₄×Dic₄₇	—	2	4	no	—
37	C₂×C₄×Dic₄₇	—	4	4	no	—
38	#13093948	C₂×C₄	1	32	yes	direct product factor
39	C₄×C₄₇⋊C₈	—	2	8	no	—
40	C₄₇⋊#95	—	2	4	no	—
41	C₂²×Q₈×C₄₇	—	2	2	no	—
42	C₂²×Q₈×C₄₇	—	2	1	no	—
43	C₂²×Q₈×C₄₇	—	2	4	no	—
44	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	—
45	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
46	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₇	—	2	1	no	—
48	C₂³×C₄×C₄₇	—	2	1	no	—
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₄₇	—	2	16	no	—
53	C₄×Q₈×C₄₇	—	2	8	no	—
54	C₄×Q₈×C₄₇	C₂×C₄	1	16	yes	complemented
55	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
61	C₂×C₄²×C₄₇	—	2	8	no	—
62	C₂×C₄²×C₄₇	—	2	4	no	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	D₄	1	2	yes	—
65	C₂×C₄²×C₄₇	D₄	1	4	yes	—
66	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
67	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂×Q₈×C₄₇	—	2	4	no	—
69	C₂×Q₈×C₄₇	—	2	8	no	—
70	C₂×Q₈×C₄₇	—	2	8	no	—
71	C₂×Q₈×C₄₇	—	2	16	no	—
72	C₂×Q₈×C₄₇	—	2	2	no	—
73	C₂×Q₈×C₄₇	—	2	4	no	—
74	C₂×Q₈×C₄₇	C₄²	1	16	yes	complemented
75	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
76	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	8	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	4	4	no	—
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
87	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₇	#41	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₇	—	2	8	no	—
97	C₂²×Dic₄₇	—	2	4	no	—
98	C₂²×Dic₄₇	—	4	4	no	—
99	C₂²×Dic₄₇	—	4	4	no	—
100	C₄⋊C₄×C₄₇	—	2	16	no	—
101	C₄⋊C₄×C₄₇	—	2	4	no	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
104	C₄²×C₄₇	—	2	16	no	—
105	C₄²×C₄₇	C₂²⋊C₄	1	8	yes	—
106	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
107	C₄²×C₄₇	C₂×D₄	1	4	yes	—
108	C₄⋊Dic₄₇	—	2	8	no	—
109	C₄⋊Dic₄₇	—	2	4	no	—
110	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
111	C₄×Dic₄₇	—	4	8	no	—
112	C₂×C₄₇⋊C₈	—	2	16	no	—
113	C₂×C₄₇⋊C₈	—	2	4	no	—
114	C₂×C₄₇⋊C₈	—	2	4	no	—
115	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
116	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂³×C₄₇	C₄×D₄	1	4	yes	—
118	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
119	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
120	C₂³×C₄₇	#135	1	4	yes	—
121	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
122	Q₈×C₄₇	—	2	4	no	—
123	Q₈×C₄₇	—	2	8	no	—
124	Q₈×C₄₇	—	2	16	no	—
125	Q₈×C₄₇	C₂×C₄²	1	8	yes	complemented
126	C₂×C₄×C₄₇	—	2	4	no	—
127	C₂×C₄×C₄₇	—	2	8	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	16	no	—
130	C₂×C₄×C₄₇	—	2	8	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	4	4	no	—
133	C₂×C₄×C₄₇	—	4	8	no	—
134	C₂×C₄×C₄₇	#103	1	16	yes	complemented
135	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
136	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
137	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
139	C₂×C₄×C₄₇	#117	1	4	yes	—
140	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
141	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
142	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
143	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
148	C₂×Dic₄₇	—	2	8	no	—
149	C₂×Dic₄₇	—	4	4	no	—
150	C₂×Dic₄₇	—	4	4	no	—
151	C₂×Dic₄₇	—	4	16	no	—
152	C₄₇⋊C₈	—	2	8	no	—
153	C₂×C₄×#103	—	47	1	no	maximal, Sylow
154	C₂²×C₄₇	C₄×C₂²⋊C₄	1	4	yes	—
155	C₂²×C₄₇	C₂×#103	1	4	yes	—
156	C₂²×C₄₇	#416	1	4	yes	—
157	C₂²×C₄₇	C₄×SD₁₆	1	8	yes	—
158	C₂²×C₄₇	C₄×Q₁₆	1	8	yes	—
159	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
161	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
162	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
163	C₂²×C₄₇	C₂×#135	1	2	yes	—
164	C₄×C₄₇	—	2	4	no	—
165	C₄×C₄₇	—	2	8	no	—
166	C₄×C₄₇	—	4	4	no	—
167	C₄×C₄₇	C₄×C₂²⋊C₄	1	4	yes	—
168	C₄×C₄₇	C₂×#103	1	8	yes	complemented
169	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
170	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
171	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
172	Dic₄₇	—	4	8	no	—
173	C₂²×C₄×Q₈	D₄₇	1	1	yes	characteristic
174	C₂²×#103	—	47	2	no	—
175	C₂²×C₄×C₈	—	47	1	no	—
176	C₂×C₄×C₄⋊C₄	—	47	1	no	—
177	C₄×#103	—	47	8	no	—
178	C₂×#340	—	47	2	no	—
179	C₂×C₄₇	C₄×#103	1	8	yes	complemented
180	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
182	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
183	C₂×C₄₇	C₂×C₄×SD₁₆	1	2	yes	—
184	C₂×C₄₇	C₂×C₄×Q₁₆	1	2	yes	—
185	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
186	C₂³×C₈	—	47	2	no	—
187	C₂×C₄×Q₈	—	2	4	no	—
188	C₂×C₄×Q₈	—	2	2	no	—
189	C₂×C₄×Q₈	Dic₄₇	1	8	yes	complemented
190	C₂×C₄×Q₈	C₂×D₄₇	1	4	yes	—
191	C₂²×C₄⋊C₄	—	2	1	no	—
192	C₂²×C₄⋊C₄	—	47	2	no	—
193	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
194	C₂²×C₄²	—	2	1	no	—
195	C₂²×C₄²	—	94	1	no	—
196	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
197	C₂×#103	—	47	16	no	—
198	C₂×#103	—	47	8	no	—
199	C₂×C₄×C₈	—	47	4	no	—
200	C₂×C₄×C₈	—	94	4	no	—
201	C₄×C₄⋊C₄	—	47	4	no	—
202	C₄×C₄⋊C₄	—	94	2	no	—
203	C₂×#95	—	94	1	no	—
204	#340	—	47	8	no	—
205	C₄₇	C₂×C₄×#103	1	1	yes	characteristic, complemented, Sylow
206	C₂²×Q₈	—	2	4	no	—
207	C₂²×Q₈	—	2	2	no	—
208	C₂²×Q₈	—	2	1	no	—
209	C₂²×Q₈	C₄×D₄₇	1	8	yes	—
210	C₂²×Q₈	C₂×Dic₄₇	1	4	yes	—
211	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
212	C₂³×C₄	—	2	1	no	—
213	C₂³×C₄	—	2	1	no	—
214	C₂³×C₄	—	94	2	no	—
215	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
216	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
218	C₂²×C₈	—	47	8	no	—
219	C₂²×C₈	—	47	4	no	—
220	C₂²×C₈	—	94	4	no	—
221	C₂²×C₈	—	94	4	no	—
222	C₄×Q₈	—	2	16	no	—
223	C₄×Q₈	—	2	8	no	—
224	C₄×Q₈	C₂×Dic₄₇	1	16	yes	complemented
225	C₂×C₄⋊C₄	—	2	8	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	47	8	no	—
230	C₂×C₄⋊C₄	—	47	4	no	—
231	C₂×C₄⋊C₄	—	94	4	no	—
232	C₂×C₄⋊C₄	—	94	2	no	—
233	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
234	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
235	C₂×C₄²	—	2	8	no	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	—	94	4	no	—
238	C₂×C₄²	—	188	4	no	—
239	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
240	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
241	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
242	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
243	#103	—	47	32	no	—
244	C₄×C₈	—	94	8	no	—
245	#95	—	94	4	no	—
246	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
247	C₂×Q₈	—	2	4	no	—
248	C₂×Q₈	—	2	8	no	—
249	C₂×Q₈	—	2	16	no	—
250	C₂×Q₈	—	2	8	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	2	4	no	—
253	C₂×Q₈	C₄×Dic₄₇	1	16	yes	complemented
254	C₂×Q₈	C₂×C₄×D₄₇	1	8	yes	—
255	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	—	94	8	no	—
264	C₂²×C₄	—	94	4	no	—
265	C₂²×C₄	—	188	4	no	—
266	C₂²×C₄	—	188	4	no	—
267	C₂²×C₄	#10625336	1	4	yes	—
268	C₂²×C₄	#10625337	1	4	yes	—
269	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
270	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
271	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
272	C₂²×C₄	#10625350	1	4	yes	—
273	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
274	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
275	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
277	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
278	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
279	C₂×C₈	—	47	8	no	—
280	C₂×C₈	—	94	16	no	—
281	C₂×C₈	—	94	4	no	—
282	C₂×C₈	—	94	4	no	—
283	C₄⋊C₄	—	2	16	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	47	8	no	—
287	C₄⋊C₄	—	94	8	no	—
288	C₄⋊C₄	—	94	4	no	—
289	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
290	C₄²	—	2	16	no	—
291	C₄²	—	188	8	no	—
292	C₄²	C₂²⋊Dic₄₇	1	8	yes	—
293	C₄²	C₂²×Dic₄₇	1	4	yes	—
294	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
295	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
296	C₂³	C₄×C₂²⋊D₄₇	1	4	yes	—
297	C₂³	C₂×#10625336	1	2	yes	—
298	C₂³	C₂×#10625337	1	2	yes	—
299	C₂³	#13094044	1	4	yes	—
300	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
301	Q₈	—	2	16	no	—
302	Q₈	—	2	4	no	—
303	Q₈	—	2	8	no	—
304	Q₈	C₂×C₄×Dic₄₇	1	8	yes	complemented
305	C₂×C₄	—	2	16	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	8	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	94	8	no	—
314	C₂×C₄	—	188	4	no	—
315	C₂×C₄	—	188	4	no	—
316	C₂×C₄	—	188	16	no	—
317	C₂×C₄	#13093948	1	16	yes	direct product factor
318	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
319	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
320	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
321	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
322	C₂×C₄	#13093983	1	4	yes	—
323	C₂×C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
324	C₂×C₄	C₄×C₂²⋊D₄₇	1	8	yes	—
325	C₂×C₄	C₂×#10625336	1	4	yes	—
326	C₂×C₄	C₂×#10625337	1	4	yes	—
327	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
328	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
330	C₂×C₄	C₂×#10625350	1	2	yes	—
331	C₈	—	94	8	no	—
332	C₂²	C₄×C₂²⋊Dic₄₇	1	4	yes	—
333	C₂²	C₂×#13093948	1	4	yes	—
334	C₂²	#15689119	1	4	yes	—
335	C₂²	C₄×#10625336	1	8	yes	—
336	C₂²	C₄×#10625337	1	8	yes	—
337	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
338	C₂²	C₂×C₄×C₂²⋊D₄₇	1	2	yes	—
339	C₂²	C₂²×#10625336	1	1	yes	characteristic
340	C₂²	C₂²×#10625337	1	1	yes	characteristic
341	C₂²	C₂×#13094044	1	2	yes	—
342	C₄	—	2	8	no	—
343	C₄	—	2	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	188	8	no	—
346	C₄	C₄×C₂²⋊Dic₄₇	1	4	yes	—
347	C₄	C₂×#13093948	1	8	yes	direct product factor
348	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
349	C₄	C₂×#13093983	1	1	yes	characteristic
350	C₄	C₂×C₄×C₂²⋊D₄₇	1	2	yes	—
351	C₂	C₄×#13093948	1	8	yes	direct product factor
352	C₂	C₂×C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
353	C₂	C₂²×#13093948	1	1	yes	characteristic
354	C₂	C₂×#15689119	1	1	yes	characteristic
355	C₂	C₂×C₄×#10625336	1	2	yes	—
356	C₂	C₂×C₄×#10625337	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×C₄×Q₈×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×C₄×Q₈	D₄₇
hypocenter	C₄₇	C₂×C₄×#103
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
4. C₄×#13093948	C₂	direct (N × H)
10. C₂×#13093948	C₄	direct (N × H)
21. C₂×C₄×Q₈×C₄₇	C₄	semidirect
38. #13093948	C₂×C₄	direct (N × H)
54. C₄×Q₈×C₄₇	C₂×C₄	semidirect
74. C₂×Q₈×C₄₇	C₄²	semidirect
125. Q₈×C₄₇	C₂×C₄²	semidirect
134. C₂×C₄×C₄₇	#103	semidirect
168. C₄×C₄₇	C₂×#103	semidirect
179. C₂×C₄₇	C₄×#103	semidirect
189. C₂×C₄×Q₈	Dic₄₇	semidirect
205. C₄₇	C₂×C₄×#103	semidirect
224. C₄×Q₈	C₂×Dic₄₇	semidirect
253. C₂×Q₈	C₄×Dic₄₇	semidirect
304. Q₈	C₂×C₄×Dic₄₇	semidirect
317. C₂×C₄	#13093948	direct (N × H)
347. C₄	C₂×#13093948	direct (N × H)
351. C₂	C₄×#13093948	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×#13093948	2
C₂²×C₄×C₄₇⋊C₈	2
C₂×C₄×C₄⋊Dic₄₇	2
C₄×#13093948	2
C₂×#15688885	2
C₂²×C₄×Q₈×C₄₇	2
C₂×C₄×#103	47

Subgroups — C2×C4×#13093948 #26214022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#13093948 #26214022