Subgroups — C₂×#20241272 #26106362

Order 12032.

878 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688993	C₂	1	1	yes	maximal, characteristic
3	#20241272	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₇⋊C₈	—	2	1	no	—
6	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
7	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
8	C₂²×C₄⋊Dic₄₇	C₄	1	2	yes	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	4	yes	complemented
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	#15688993	—	2	1	no	—
14	#15688993	—	2	1	no	—
15	#15688993	C₄	1	2	yes	—
16	#15688993	C₂²	1	2	yes	—
17	C₂³×C₈×C₄₇	—	2	1	no	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
20	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
21	C₂×C₄⋊C₈×C₄₇	C₄	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂³×Dic₄₇	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	4	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	4	2	no	—
27	C₂²×C₄₇⋊C₈	—	4	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	4	2	no	—
34	C₂×C₄⋊Dic₄₇	—	4	2	no	—
35	C₂×C₄⋊Dic₄₇	—	4	2	no	—
36	C₂×C₄⋊Dic₄₇	—	4	2	no	—
37	C₂×C₄⋊Dic₄₇	—	4	4	no	—
38	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
39	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
40	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
41	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
42	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₄₇	—	2	4	no	—
46	C₂²×C₈×C₄₇	—	2	2	no	—
47	C₂²×C₈×C₄₇	—	4	2	no	—
48	C₂²×C₈×C₄₇	—	4	2	no	—
49	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	D₄	1	2	yes	—
55	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
56	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₄₇	—	2	4	no	—
58	C₄⋊C₈×C₄₇	—	2	2	no	—
59	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
60	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
64	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	D₈	1	2	yes	—
73	C₂²×C₄×C₄₇	D₈	1	2	yes	—
74	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
76	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
79	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×Dic₄₇	—	2	4	no	—
84	C₂²×Dic₄₇	—	4	4	no	—
85	C₂²×Dic₄₇	—	4	4	no	—
86	C₂²×Dic₄₇	—	4	4	no	—
87	C₂×C₈×C₄₇	—	2	4	no	—
88	C₂×C₈×C₄₇	—	4	8	no	—
89	C₂×C₈×C₄₇	—	4	2	no	—
90	C₂×C₈×C₄₇	—	4	2	no	—
91	C₄²×C₄₇	C₄²	1	2	yes	—
92	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
93	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
97	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
101	C₄⋊Dic₄₇	—	4	4	no	—
102	C₄⋊Dic₄₇	—	4	4	no	—
103	C₄⋊Dic₄₇	—	4	4	no	—
104	C₄⋊Dic₄₇	—	4	2	no	—
105	C₄⋊Dic₄₇	—	4	2	no	—
106	C₄⋊Dic₄₇	—	4	2	no	—
107	C₄⋊Dic₄₇	—	4	2	no	—
108	C₄⋊Dic₄₇	—	4	4	no	—
109	C₂×C₄₇⋊C₈	—	2	4	no	—
110	C₂×C₄₇⋊C₈	—	4	8	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	2	no	—
113	C₂³×C₄₇	#95	1	2	yes	—
114	C₂³×C₄₇	#100	1	2	yes	—
115	C₂³×C₄₇	#101	1	2	yes	—
116	C₂³×C₄₇	#102	1	2	yes	—
117	C₂³×C₄₇	#102	1	2	yes	—
118	C₂³×C₄₇	#103	1	2	yes	—
119	C₂³×C₄₇	#103	1	2	yes	—
120	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₄₇	—	2	4	no	—
122	C₂×C₄×C₄₇	—	2	4	no	—
123	C₂×C₄×C₄₇	—	2	1	no	—
124	C₂×C₄×C₄₇	—	2	1	no	—
125	C₂×C₄×C₄₇	—	2	1	no	—
126	C₂×C₄×C₄₇	—	2	1	no	—
127	C₂×C₄×C₄₇	#95	1	2	yes	—
128	C₂×C₄×C₄₇	#95	1	2	yes	—
129	C₂×C₄×C₄₇	#95	1	2	yes	—
130	C₂×C₄×C₄₇	#102	1	2	yes	—
131	C₂×C₄×C₄₇	#102	1	4	yes	—
132	C₂×C₄×C₄₇	#102	1	2	yes	—
133	C₂×C₄×C₄₇	#102	1	4	yes	—
134	C₂×C₄×C₄₇	#103	1	2	yes	—
135	C₂×C₄×C₄₇	#103	1	4	yes	—
136	C₂×C₄×C₄₇	#103	1	2	yes	—
137	C₂×C₄×C₄₇	#103	1	4	yes	—
138	C₂×C₄×C₄₇	#106	1	4	yes	—
139	C₂×C₄×C₄₇	#106	1	4	yes	—
140	C₂×C₄×C₄₇	#107	1	4	yes	—
141	C₂×C₄×C₄₇	#107	1	4	yes	—
142	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
156	C₂×Dic₄₇	—	4	4	no	—
157	C₂×Dic₄₇	—	4	4	no	—
158	C₂×Dic₄₇	—	4	4	no	—
159	C₂×Dic₄₇	—	8	8	no	—
160	C₈×C₄₇	—	4	4	no	—
161	C₄₇⋊C₈	—	4	4	no	—
162	C₂×#1296	—	47	1	no	maximal, Sylow
163	C₂²×C₄₇	#331	1	4	yes	—
164	C₂²×C₄₇	#332	1	4	yes	—
165	C₂²×C₄₇	#332	1	4	yes	—
166	C₂²×C₄₇	#333	1	4	yes	—
167	C₂²×C₄₇	#340	1	4	yes	—
168	C₂²×C₄₇	#340	1	4	yes	—
169	C₂²×C₄₇	#343	1	4	yes	—
170	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	—	2	1	no	—
180	C₄×C₄₇	#340	1	4	yes	—
181	C₄×C₄₇	#340	1	4	yes	—
182	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
183	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
184	C₄×C₄₇	C₂×#103	1	1	yes	characteristic
185	C₄×C₄₇	C₂×#103	1	1	yes	characteristic
186	C₄×C₄₇	C₂×#106	1	1	yes	characteristic
187	C₄×C₄₇	C₂×#106	1	1	yes	characteristic
188	C₄×C₄₇	C₂×#107	1	1	yes	characteristic
189	C₄×C₄₇	C₂×#107	1	1	yes	characteristic
190	Dic₄₇	—	8	4	no	—
191	C₂²×C₄⋊C₈	—	47	1	no	—
192	C₂²×C₄⋊C₈	D₄₇	1	1	yes	characteristic
193	C₂×#384	—	47	1	no	—
194	#1296	—	47	4	no	—
195	C₂×C₄₇	#1296	1	8	yes	complemented
196	C₂×C₄₇	C₂×#331	1	1	yes	characteristic
197	C₂×C₄₇	C₂×#332	1	1	yes	characteristic
198	C₂×C₄₇	C₂×#332	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#333	1	1	yes	characteristic
200	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
201	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
202	C₂×C₄₇	C₂×#343	1	1	yes	characteristic
203	C₂³×C₈	—	2	1	no	—
204	C₂³×C₈	—	94	1	no	—
205	C₂²×C₄⋊C₄	—	47	2	no	—
206	C₂²×C₄⋊C₄	—	94	1	no	—
207	C₂²×C₄⋊C₄	—	94	1	no	—
208	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
209	C₂×C₄⋊C₈	—	2	1	no	—
210	C₂×C₄⋊C₈	—	2	2	no	—
211	C₂×C₄⋊C₈	—	47	4	no	—
212	C₂×C₄⋊C₈	—	47	2	no	—
213	C₂×C₄⋊C₈	—	94	1	no	—
214	C₂×C₄⋊C₈	—	94	2	no	—
215	C₂×C₄⋊C₈	Dic₄₇	1	4	yes	complemented
216	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
217	#384	—	47	2	no	—
218	#384	—	47	2	no	—
219	#384	—	94	1	no	—
220	#384	—	94	1	no	—
221	C₄₇	C₂×#1296	1	1	yes	characteristic, complemented, Sylow
222	C₂³×C₄	—	94	2	no	—
223	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
224	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	4	2	no	—
229	C₂²×C₈	—	4	2	no	—
230	C₂²×C₈	—	94	4	no	—
231	C₂²×C₈	—	94	2	no	—
232	C₂²×C₈	—	188	2	no	—
233	C₂²×C₈	—	188	2	no	—
234	C₂×C₄⋊C₄	—	47	4	no	—
235	C₂×C₄⋊C₄	—	94	2	no	—
236	C₂×C₄⋊C₄	—	94	2	no	—
237	C₂×C₄⋊C₄	—	94	2	no	—
238	C₂×C₄⋊C₄	—	94	2	no	—
239	C₂×C₄⋊C₄	—	94	2	no	—
240	C₂×C₄⋊C₄	—	188	4	no	—
241	C₂×C₄⋊C₄	—	188	2	no	—
242	C₂×C₄⋊C₄	—	188	2	no	—
243	C₂×C₄⋊C₄	—	188	2	no	—
244	C₂×C₄⋊C₄	—	188	2	no	—
245	C₂×C₄²	Dic₉₄	1	2	yes	—
246	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
247	C₂×C₄²	C₄×D₄₇	1	2	yes	—
248	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
249	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
250	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
252	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	47	4	no	—
256	C₄⋊C₈	—	94	4	no	—
257	C₄⋊C₈	—	94	2	no	—
258	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
259	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	94	4	no	—
263	C₂²×C₄	—	188	4	no	—
264	C₂²×C₄	—	188	4	no	—
265	C₂²×C₄	—	188	4	no	—
266	C₂²×C₄	#10625325	1	2	yes	—
267	C₂²×C₄	#10625325	1	2	yes	—
268	C₂²×C₄	D₃₇₆	1	2	yes	—
269	C₂²×C₄	Dic₁₈₈	1	2	yes	—
270	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
271	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
272	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
273	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
274	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
278	C₂²×C₄	#10625334	1	2	yes	—
279	C₂²×C₄	#10625335	1	2	yes	—
280	C₂²×C₄	#10625336	1	2	yes	—
281	C₂²×C₄	#10625337	1	2	yes	—
282	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
283	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	4	8	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	94	4	no	—
291	C₂×C₈	—	188	8	no	—
292	C₂×C₈	—	188	2	no	—
293	C₂×C₈	—	188	2	no	—
294	C₄⋊C₄	—	188	4	no	—
295	C₄⋊C₄	—	188	4	no	—
296	C₄⋊C₄	—	188	4	no	—
297	C₄⋊C₄	—	188	4	no	—
298	C₄⋊C₄	—	188	2	no	—
299	C₄⋊C₄	—	188	2	no	—
300	C₄⋊C₄	—	188	2	no	—
301	C₄⋊C₄	—	188	2	no	—
302	C₄²	C₄×Dic₄₇	1	2	yes	—
303	C₄²	Dic₄₇⋊C₄	1	2	yes	—
304	C₄²	Dic₄₇⋊C₄	1	2	yes	—
305	C₄²	C₄⋊Dic₄₇	1	2	yes	—
306	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
307	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
308	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
309	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
310	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
311	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
312	C₂³	C₄₇⋊#95	1	2	yes	—
313	C₂³	#13093940	1	2	yes	—
314	C₂³	#13093942	1	2	yes	—
315	C₂³	#13093944	1	2	yes	—
316	C₂³	#13093946	1	2	yes	—
317	C₂³	#13093947	1	2	yes	—
318	C₂³	#13093949	1	2	yes	—
319	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	376	8	no	—
327	C₂×C₄	—	188	4	no	—
328	C₂×C₄	—	188	4	no	—
329	C₂×C₄	—	188	4	no	—
330	C₂×C₄	C₄₇⋊#95	1	2	yes	—
331	C₂×C₄	C₄₇⋊#95	1	2	yes	—
332	C₂×C₄	C₄₇⋊#95	1	2	yes	—
333	C₂×C₄	#13093944	1	2	yes	—
334	C₂×C₄	#13093945	1	4	yes	—
335	C₂×C₄	#13093946	1	4	yes	—
336	C₂×C₄	#13093946	1	2	yes	—
337	C₂×C₄	#13093947	1	2	yes	—
338	C₂×C₄	#13093948	1	4	yes	—
339	C₂×C₄	#13093949	1	4	yes	—
340	C₂×C₄	#13093949	1	2	yes	—
341	C₂×C₄	#13093955	1	4	yes	—
342	C₂×C₄	#13093956	1	4	yes	—
343	C₂×C₄	#13093957	1	4	yes	—
344	C₂×C₄	#13093958	1	4	yes	—
345	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
346	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
348	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
351	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
352	C₂×C₄	C₂×D₃₇₆	1	1	yes	characteristic
353	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
354	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
355	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
356	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
357	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
358	C₂×C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
359	C₈	—	4	4	no	—
360	C₈	—	188	4	no	—
361	C₂²	#15688866	1	4	yes	—
362	C₂²	#15688868	1	4	yes	—
363	C₂²	#15688870	1	4	yes	—
364	C₂²	#15688871	1	4	yes	—
365	C₂²	#15688885	1	4	yes	—
366	C₂²	#15688886	1	4	yes	—
367	C₂²	#15688891	1	4	yes	—
368	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
369	C₂²	C₂×#13093940	1	1	yes	characteristic
370	C₂²	C₂×#13093942	1	1	yes	characteristic
371	C₂²	C₂×#13093944	1	1	yes	characteristic
372	C₂²	C₂×#13093946	1	1	yes	characteristic
373	C₂²	C₂×#13093947	1	1	yes	characteristic
374	C₂²	C₂×#13093949	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	376	4	no	—
379	C₄	#15688885	1	4	yes	—
380	C₄	#15688886	1	4	yes	—
381	C₄	C₂×#13093945	1	1	yes	characteristic
382	C₄	C₂×#13093946	1	1	yes	characteristic
383	C₄	C₂×#13093948	1	1	yes	characteristic
384	C₄	C₂×#13093949	1	1	yes	characteristic
385	C₄	C₂×#13093955	1	1	yes	characteristic
386	C₄	C₂×#13093956	1	1	yes	characteristic
387	C₄	C₂×#13093957	1	1	yes	characteristic
388	C₄	C₂×#13093958	1	1	yes	characteristic
389	C₂	#20241272	1	8	yes	direct product factor
390	C₂	C₂×#15688866	1	1	yes	characteristic
391	C₂	C₂×#15688868	1	1	yes	characteristic
392	C₂	C₂×#15688870	1	1	yes	characteristic
393	C₂	C₂×#15688871	1	1	yes	characteristic
394	C₂	C₂×#15688885	1	1	yes	characteristic
395	C₂	C₂×#15688886	1	1	yes	characteristic
396	C₂	C₂×#15688891	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂²×C₄⋊C₈×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂²×C₄⋊C₈	D₄₇
hypocenter	C₄₇	C₂×#1296
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #20241272	C₂	direct (N × H)
11. C₂×C₄⋊(C₄₇⋊C₈)	C₄	semidirect
21. C₂×C₄⋊C₈×C₄₇	C₄	semidirect
41. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
59. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
195. C₂×C₄₇	#1296	semidirect
215. C₂×C₄⋊C₈	Dic₄₇	semidirect
221. C₄₇	C₂×#1296	semidirect
258. C₄⋊C₈	C₂×Dic₄₇	semidirect
389. C₂	#20241272	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×C₄⋊(C₄₇⋊C₈)	2
C₂×#15688993	2
#20241272	2
C₂²×C₄⋊C₈×C₄₇	2
C₂×#1296	47

Subgroups — C2×#20241272 #26106362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241272 #26106362