Subgroups — C₂×#20244107 #26219544

Order 12032.

1246 conjugacy classes of subgroups.

The subgroup lattice has 348 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	2	yes	maximal
2	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#20244107	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688878	C₂	1	2	yes	maximal
6	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
8	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	8	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
14	C₂×C₄×C₄₇⋊C₈	—	2	4	no	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
16	#15688878	C₂²	1	8	yes	—
17	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
19	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₇	C₄	1	4	yes	—
22	C₄×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
23	C₂×#95×C₄₇	C₄	1	2	yes	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	4	no	—
29	C₂²×C₄₇⋊C₈	—	2	4	no	—
30	C₂²×C₄₇⋊C₈	—	2	4	no	—
31	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
32	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	—
33	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
34	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
35	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
36	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
37	C₄⋊(C₄₇⋊C₈)	—	2	16	no	—
38	C₄×C₄₇⋊C₈	—	2	8	no	—
39	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₇	C₈	1	8	yes	complemented
46	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₄₇	—	2	4	no	—
49	C₂×C₄²×C₄₇	—	2	4	no	—
50	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₇	D₄	1	4	yes	—
53	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
54	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
55	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
56	#95×C₄₇	C₂×C₄	1	8	yes	—
57	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	—	2	4	no	—
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	—	2	4	no	—
62	C₂²×C₄×C₄₇	—	2	4	no	—
63	C₂²×C₄×C₄₇	—	2	4	no	—
64	C₂²×C₄×C₄₇	—	2	4	no	—
65	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
66	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
67	C₂²×C₄×C₄₇	C₂×C₈	1	8	yes	—
68	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
69	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
70	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
71	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
73	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
78	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
79	C₂²×C₄×C₄₇	#41	1	2	yes	—
80	C₂²×C₄×C₄₇	#41	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
82	C₄⋊C₄×C₄₇	—	2	8	no	—
83	C₄⋊C₄×C₄₇	C₂×C₈	1	16	yes	complemented
84	C₄²×C₄₇	—	2	8	no	—
85	C₄²×C₄₇	—	2	4	no	—
86	C₄²×C₄₇	—	2	4	no	—
87	C₄²×C₄₇	C₄⋊C₄	1	8	yes	—
88	C₄²×C₄₇	C₂×D₄	1	4	yes	—
89	C₄²×C₄₇	C₂×Q₈	1	4	yes	—
90	C₂×C₄₇⋊C₈	—	2	8	no	—
91	C₂×C₄₇⋊C₈	—	2	8	no	—
92	C₂×C₄₇⋊C₈	—	2	2	no	—
93	C₂×C₄₇⋊C₈	—	2	2	no	—
94	C₂×C₄₇⋊C₈	—	2	2	no	—
95	C₂×C₄₇⋊C₈	—	2	2	no	—
96	C₂×C₄₇⋊C₈	—	2	4	no	—
97	C₂×C₄₇⋊C₈	—	2	4	no	—
98	C₂×C₄₇⋊C₈	—	2	4	no	—
99	C₂×C₄₇⋊C₈	—	4	8	no	—
100	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
101	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
102	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
103	C₂³×C₄₇	C₄×D₄	1	2	yes	—
104	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
105	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
106	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
107	C₂³×C₄₇	#131	1	2	yes	—
108	C₂³×C₄₇	#131	1	2	yes	—
109	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
110	C₂×C₄×C₄₇	—	2	4	no	—
111	C₂×C₄×C₄₇	—	2	2	no	—
112	C₂×C₄×C₄₇	—	2	2	no	—
113	C₂×C₄×C₄₇	—	2	4	no	—
114	C₂×C₄×C₄₇	—	2	8	no	—
115	C₂×C₄×C₄₇	—	2	16	no	—
116	C₂×C₄×C₄₇	—	2	4	no	—
117	C₂×C₄×C₄₇	—	2	4	no	—
118	C₂×C₄×C₄₇	—	2	4	no	—
119	C₂×C₄×C₄₇	—	4	8	no	—
120	C₂×C₄×C₄₇	C₄⋊C₈	1	16	yes	complemented
121	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
122	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
123	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
124	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
125	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
126	C₂×C₄×C₄₇	#121	1	4	yes	—
127	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
128	C₂×C₄×C₄₇	#125	1	4	yes	—
129	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
130	C₂×C₄×C₄₇	C₂²×C₈	1	8	yes	—
131	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
132	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
133	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
139	C₄₇⋊C₈	—	2	4	no	—
140	C₄₇⋊C₈	—	2	4	no	—
141	C₄₇⋊C₈	—	4	4	no	—
142	C₂×#1939	—	47	1	no	maximal, Sylow
143	C₂²×C₄₇	#389	1	4	yes	—
144	C₂²×C₄₇	C₂×C₄⋊C₈	1	4	yes	—
145	C₂²×C₄₇	#424	1	4	yes	—
146	C₂²×C₄₇	C₈×D₄	1	4	yes	—
147	C₂²×C₄₇	#436	1	4	yes	—
148	C₂²×C₄₇	C₈×Q₈	1	4	yes	—
149	C₂²×C₄₇	#446	1	4	yes	—
150	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
152	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
153	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
154	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
155	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
156	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
157	C₄×C₄₇	—	2	4	no	—
158	C₄×C₄₇	—	2	8	no	—
159	C₄×C₄₇	—	4	4	no	—
160	C₄×C₄₇	#389	1	4	yes	—
161	C₄×C₄₇	C₂×C₄⋊C₈	1	8	yes	complemented
162	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
163	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
164	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
165	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
166	C₂²×C₄⋊C₈	—	47	2	no	—
167	C₂²×C₄⋊C₈	—	47	1	no	—
168	C₂²×C₄×C₈	—	47	1	no	—
169	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
170	#1939	—	47	8	no	—
171	C₂×#336	—	47	2	no	—
172	C₂×C₄₇	#1939	1	8	yes	complemented
173	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
174	C₂×C₄₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
175	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
176	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
177	C₂×C₄₇	C₂×#436	1	1	yes	characteristic
178	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
179	C₂×C₄₇	C₂×#446	1	1	yes	characteristic
180	C₂³×C₈	—	47	1	no	—
181	C₂³×C₈	—	47	1	no	—
182	C₂³×C₈	—	47	2	no	—
183	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
185	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
186	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
187	C₂×C₄⋊C₈	—	47	8	no	—
188	C₂×C₄⋊C₈	—	47	4	no	—
189	C₂×C₄⋊C₈	—	94	8	no	—
190	C₂×C₄⋊C₈	—	94	4	no	—
191	C₂×C₄×C₈	—	47	4	no	—
192	C₂×C₄×C₈	—	94	4	no	—
193	C₄×C₄⋊C₄	Dic₄₇	1	4	yes	—
194	C₄×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
195	C₂×#95	Dic₄₇	1	2	yes	—
196	#336	—	47	8	no	—
197	C₄₇	C₂×#1939	1	1	yes	characteristic, complemented, Sylow
198	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
199	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
200	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
201	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
202	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
203	C₂²×C₈	—	47	4	no	—
204	C₂²×C₈	—	47	4	no	—
205	C₂²×C₈	—	47	2	no	—
206	C₂²×C₈	—	47	2	no	—
207	C₂²×C₈	—	47	4	no	—
208	C₂²×C₈	—	94	2	no	—
209	C₂²×C₈	—	94	2	no	—
210	C₂²×C₈	—	94	2	no	—
211	C₂²×C₈	—	94	2	no	—
212	C₂²×C₈	—	94	4	no	—
213	C₂²×C₈	—	94	4	no	—
214	C₂²×C₈	—	94	4	no	—
215	C₂×C₄⋊C₄	—	2	4	no	—
216	C₂×C₄⋊C₄	C₄₇⋊C₈	1	8	yes	complemented
217	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
218	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
219	C₂×C₄²	—	2	4	no	—
220	C₂×C₄²	—	2	4	no	—
221	C₂×C₄²	Dic₉₄	1	4	yes	—
222	C₂×C₄²	D₁₈₈	1	4	yes	—
223	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
224	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
225	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
226	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
227	C₄⋊C₈	—	94	16	no	—
228	C₄⋊C₈	—	94	8	no	—
229	C₄×C₈	—	94	8	no	—
230	#95	C₂×Dic₄₇	1	8	yes	—
231	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	C₂×C₄₇⋊C₈	1	8	yes	—
240	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
241	C₂²×C₄	#10625329	1	4	yes	—
242	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
243	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
244	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
245	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
246	C₂²×C₄	D₄×D₄₇	1	2	yes	—
247	C₂²×C₄	#10625352	1	2	yes	—
248	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
249	C₂²×C₄	#10625354	1	2	yes	—
250	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
251	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
252	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
253	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
254	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
255	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
256	C₂×C₈	—	47	4	no	—
257	C₂×C₈	—	47	4	no	—
258	C₂×C₈	—	94	8	no	—
259	C₂×C₈	—	94	8	no	—
260	C₂×C₈	—	94	2	no	—
261	C₂×C₈	—	94	2	no	—
262	C₂×C₈	—	94	2	no	—
263	C₂×C₈	—	94	2	no	—
264	C₂×C₈	—	94	4	no	—
265	C₂×C₈	—	94	4	no	—
266	C₂×C₈	—	94	4	no	—
267	C₂×C₈	—	188	8	no	—
268	C₄⋊C₄	—	2	8	no	—
269	C₄⋊C₄	C₂×C₄₇⋊C₈	1	16	yes	complemented
270	C₄²	—	2	8	no	—
271	C₄²	—	2	4	no	—
272	C₄²	—	2	4	no	—
273	C₄²	C₄⋊Dic₄₇	1	8	yes	—
274	C₄²	C₂×Dic₉₄	1	4	yes	—
275	C₄²	C₂×D₁₈₈	1	4	yes	—
276	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
277	C₂³	D₄×Dic₄₇	1	2	yes	—
278	C₂³	Q₈×Dic₄₇	1	2	yes	—
279	C₂³	C₂²×C₄₇⋊C₈	1	2	yes	—
280	C₂³	C₂×#10625329	1	2	yes	—
281	C₂³	#13094031	1	2	yes	—
282	C₂³	#13094031	1	2	yes	—
283	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	8	no	—
289	C₂×C₄	—	2	16	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	4	8	no	—
294	C₂×C₄	C₄⋊(C₄₇⋊C₈)	1	16	yes	complemented
295	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
296	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
297	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
298	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
299	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
300	C₂×C₄	#13093999	1	4	yes	—
301	C₂×C₄	#13094004	1	4	yes	—
302	C₂×C₄	#13094015	1	4	yes	—
303	C₂×C₄	#13094023	1	4	yes	—
304	C₂×C₄	C₂²×C₄₇⋊C₈	1	8	yes	—
305	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
306	C₂×C₄	C₂×#10625329	1	4	yes	—
307	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
308	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
309	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
310	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
311	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
312	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
313	C₈	—	94	4	no	—
314	C₈	—	94	4	no	—
315	C₈	—	188	4	no	—
316	C₂²	#15689022	1	4	yes	—
317	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	4	yes	—
318	C₂²	#15689150	1	4	yes	—
319	C₂²	D₄×C₄₇⋊C₈	1	4	yes	—
320	C₂²	#15689201	1	4	yes	—
321	C₂²	Q₈×C₄₇⋊C₈	1	4	yes	—
322	C₂²	#15689254	1	4	yes	—
323	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
324	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
325	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
326	C₂²	C₂³×C₄₇⋊C₈	1	1	yes	characteristic
327	C₂²	C₂²×#10625329	1	1	yes	characteristic
328	C₂²	C₂×#13094031	1	1	yes	characteristic
329	C₂²	C₂×#13094031	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	8	no	—
332	C₄	—	4	4	no	—
333	C₄	#15689022	1	4	yes	—
334	C₄	C₂×C₄⋊(C₄₇⋊C₈)	1	8	yes	complemented
335	C₄	C₂×#13093999	1	1	yes	characteristic
336	C₄	C₂×#13094004	1	1	yes	characteristic
337	C₄	C₂×#13094015	1	1	yes	characteristic
338	C₄	C₂×#13094023	1	1	yes	characteristic
339	C₂	#20244107	1	8	yes	direct product factor
340	C₂	C₂×#15689022	1	1	yes	characteristic
341	C₂	C₂²×C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
342	C₂	C₂×#15689150	1	1	yes	characteristic
343	C₂	C₂×D₄×C₄₇⋊C₈	1	1	yes	characteristic
344	C₂	C₂×#15689201	1	1	yes	characteristic
345	C₂	C₂×Q₈×C₄₇⋊C₈	1	1	yes	characteristic
346	C₂	C₂×#15689254	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₂×#1939
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #20244107	C₂	direct (N × H)
45. C₂×C₄⋊C₄×C₄₇	C₈	semidirect
83. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
120. C₂×C₄×C₄₇	C₄⋊C₈	semidirect
161. C₄×C₄₇	C₂×C₄⋊C₈	semidirect
172. C₂×C₄₇	#1939	semidirect
197. C₄₇	C₂×#1939	semidirect
216. C₂×C₄⋊C₄	C₄₇⋊C₈	semidirect
269. C₄⋊C₄	C₂×C₄₇⋊C₈	semidirect
294. C₂×C₄	C₄⋊(C₄₇⋊C₈)	semidirect
334. C₄	C₂×C₄⋊(C₄₇⋊C₈)	semidirect
339. C₂	#20244107	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
C₂²×C₄×C₄₇⋊C₈	2
#20244107	2
C₂×#15688878	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₂×#1939	47

Subgroups — C2×#20244107 #26219544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244107 #26219544