Subgroups — C₂×#20246448 #26375872

Order 12032.

3158 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×Dic₄₇	C₂	1	2	yes	maximal
2	#20246448	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689030	C₂	1	2	yes	maximal
4	C₂×#15689022	C₂	1	2	yes	maximal
5	C₂×#15689009	C₂	1	4	yes	maximal
6	C₂×C₄⋊C₄×Dic₄₇	C₂	1	2	yes	maximal
7	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂×Q₈×Dic₄₇	—	2	16	no	—
11	C₂×Q₈×Dic₄₇	C₂²	1	16	yes	—
12	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
13	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
18	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
19	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
20	#15689030	C₂²	1	16	yes	—
21	#15689022	C₂²	1	16	yes	—
22	#15689009	C₂²	1	32	yes	—
23	C₄⋊C₄×Dic₄₇	C₂²	1	16	yes	—
24	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	—
25	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	—
26	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
27	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
28	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
29	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
30	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
31	C₂×C₄⋊Q₈×C₄₇	C₄	1	16	yes	complemented
32	C₂×C₄⋊Q₈×C₄₇	C₂²	1	8	yes	—
33	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
36	C₂³×Dic₄₇	C₂³	1	2	yes	—
37	C₂³×Dic₄₇	C₂³	1	2	yes	—
38	C₂³×Dic₄₇	C₂³	1	2	yes	—
39	C₂³×Dic₄₇	C₂³	1	2	yes	—
40	Q₈×Dic₄₇	—	2	64	no	—
41	C₂×C₄⋊Dic₄₇	—	2	4	no	—
42	C₂×C₄⋊Dic₄₇	—	2	4	no	—
43	C₂×C₄⋊Dic₄₇	—	2	16	no	—
44	C₂×C₄⋊Dic₄₇	D₄	1	8	yes	—
45	C₂×C₄⋊Dic₄₇	Q₈	1	8	yes	complemented
46	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
51	C₂×C₄×Dic₄₇	—	2	8	no	—
52	C₂×C₄×Dic₄₇	—	2	8	no	—
53	C₂×C₄×Dic₄₇	—	2	16	no	—
54	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
56	C₂×C₄×Dic₄₇	C₂³	1	16	yes	—
57	C₄₇⋊#95	C₂³	1	8	yes	—
58	C₄₇⋊#95	C₂³	1	8	yes	—
59	C₄₇⋊#95	C₂³	1	16	yes	—
60	C₄₇⋊#95	C₂³	1	16	yes	—
61	C₂²×Q₈×C₄₇	—	2	8	no	—
62	C₂²×Q₈×C₄₇	—	2	8	no	—
63	C₂²×Q₈×C₄₇	C₂×C₄	1	16	yes	—
64	C₂²×Q₈×C₄₇	C₂³	1	8	yes	—
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₄₇	C₂×C₄	1	64	yes	complemented
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
74	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
76	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
77	C₂×Q₈×C₄₇	—	2	64	no	—
78	C₂×Q₈×C₄₇	—	2	16	no	—
79	C₂×Q₈×C₄₇	—	2	16	no	—
80	C₂×Q₈×C₄₇	C₂²×C₄	1	32	yes	—
81	C₂²×C₄×C₄₇	—	2	8	no	—
82	C₂²×C₄×C₄₇	—	2	8	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₄₇	#41	1	4	yes	—
92	C₂²×C₄×C₄₇	#41	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
97	C₂²×Dic₄₇	—	2	4	no	—
98	C₂²×Dic₄₇	—	2	4	no	—
99	C₂²×Dic₄₇	—	2	4	no	—
100	C₂²×Dic₄₇	—	2	4	no	—
101	C₂²×Dic₄₇	—	2	4	no	—
102	C₂²×Dic₄₇	—	2	4	no	—
103	C₂²×Dic₄₇	—	2	4	no	—
104	C₂²×Dic₄₇	—	2	4	no	—
105	C₂²×Dic₄₇	—	2	4	no	—
106	C₂²×Dic₄₇	—	2	4	no	—
107	C₂²×Dic₄₇	C₂×D₄	1	8	yes	—
108	C₂²×Dic₄₇	C₂×Q₈	1	8	yes	—
109	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
110	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
111	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
112	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
113	C₄⋊C₄×C₄₇	C₂²×C₄	1	32	yes	—
114	C₄⋊C₄×C₄₇	C₂²×C₄	1	32	yes	—
115	C₄²×C₄₇	C₂²×C₄	1	16	yes	—
116	C₄⋊Dic₄₇	—	2	8	no	—
117	C₄⋊Dic₄₇	—	2	8	no	—
118	C₄⋊Dic₄₇	—	2	32	no	—
119	C₄⋊Dic₄₇	C₂×D₄	1	16	yes	—
120	C₄⋊Dic₄₇	C₂×Q₈	1	16	yes	complemented
121	C₄×Dic₄₇	—	2	16	no	—
122	C₄×Dic₄₇	—	2	16	no	—
123	C₄×Dic₄₇	—	2	32	no	—
124	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
125	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
126	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
127	C₂³×C₄₇	C₂×#41	1	2	yes	—
128	C₂³×C₄₇	C₂×#41	1	2	yes	—
129	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
130	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
131	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
132	Q₈×C₄₇	—	2	64	no	—
133	C₂×C₄×C₄₇	—	2	32	no	—
134	C₂×C₄×C₄₇	—	2	8	no	—
135	C₂×C₄×C₄₇	—	2	8	no	—
136	C₂×C₄×C₄₇	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	C₄×D₄	1	16	yes	—
140	C₂×C₄×C₄₇	C₄×Q₈	1	16	yes	complemented
141	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
142	C₂×C₄×C₄₇	C₂³×C₄	1	16	yes	—
143	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
145	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
146	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
147	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
148	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
149	C₂×Dic₄₇	—	2	16	no	—
150	C₂×Dic₄₇	—	2	16	no	—
151	C₂×Dic₄₇	—	2	4	no	—
152	C₂×Dic₄₇	—	2	4	no	—
153	C₂×Dic₄₇	—	2	4	no	—
154	C₂×Dic₄₇	—	2	4	no	—
155	C₂×Dic₄₇	—	2	4	no	—
156	C₂×Dic₄₇	—	2	4	no	—
157	C₂×Dic₄₇	—	2	4	no	—
158	C₂×Dic₄₇	—	2	4	no	—
159	C₂×Dic₄₇	—	2	4	no	—
160	C₂×Dic₄₇	—	2	4	no	—
161	C₂×Dic₄₇	—	4	8	no	—
162	C₂×Dic₄₇	—	4	8	no	—
163	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
164	C₂×Dic₄₇	C₂²×Q₈	1	8	yes	—
165	C₂×#2365	—	47	1	no	maximal, Sylow
166	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
167	C₂²×C₄₇	C₂×C₄×Q₈	1	4	yes	—
168	C₂²×C₄₇	#519	1	4	yes	—
169	C₂²×C₄₇	#547	1	4	yes	—
170	C₂²×C₄₇	D₄×Q₈	1	4	yes	—
171	C₂²×C₄₇	#556	1	4	yes	—
172	C₂²×C₄₇	#557	1	4	yes	—
173	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
174	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
175	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
176	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
177	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
180	C₄×C₄₇	—	2	16	no	—
181	C₄×C₄₇	—	2	4	no	—
182	C₄×C₄₇	C₂×C₄×D₄	1	8	yes	—
183	C₄×C₄₇	C₂×C₄×Q₈	1	8	yes	complemented
184	Dic₄₇	—	2	8	no	—
185	Dic₄₇	—	2	8	no	—
186	Dic₄₇	—	4	4	no	—
187	Dic₄₇	—	4	4	no	—
188	C₂²×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
189	C₂²×C₄×Q₈	—	47	2	no	—
190	#2365	—	47	16	no	—
191	C₂×#391	—	47	2	no	—
192	C₂×#389	—	47	2	no	—
193	C₂×#387	—	47	4	no	—
194	C₂×C₄×C₄⋊C₄	—	47	1	no	—
195	C₂×C₄×C₄⋊C₄	—	47	1	no	—
196	C₂×C₄×C₄⋊C₄	—	47	2	no	—
197	C₂×C₄₇	#2365	1	8	yes	complemented
198	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
199	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
200	C₂×C₄₇	C₂×#519	1	1	yes	characteristic
201	C₂×C₄₇	C₂×#547	1	1	yes	characteristic
202	C₂×C₄₇	C₂×D₄×Q₈	1	1	yes	characteristic
203	C₂×C₄₇	C₂×#556	1	1	yes	characteristic
204	C₂×C₄₇	C₂×#557	1	1	yes	characteristic
205	C₂³×Q₈	C₂×D₄₇	1	2	yes	—
206	C₂×C₄⋊Q₈	Dic₄₇	1	16	yes	complemented
207	C₂×C₄⋊Q₈	C₂×D₄₇	1	8	yes	—
208	C₂×C₄×Q₈	—	47	16	no	—
209	C₂×C₄×Q₈	—	94	16	no	—
210	C₂²×C₄⋊C₄	—	47	1	no	—
211	C₂²×C₄⋊C₄	—	47	1	no	—
212	C₂²×C₄⋊C₄	—	47	4	no	—
213	C₂²×C₄⋊C₄	—	47	1	no	—
214	C₂²×C₄⋊C₄	—	47	1	no	—
215	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
217	C₂²×C₄²	—	47	4	no	—
218	C₂²×C₄²	—	47	2	no	—
219	C₂²×C₄²	—	47	2	no	—
220	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
221	#391	—	47	16	no	—
222	#389	—	47	16	no	—
223	#387	—	47	32	no	—
224	C₄×C₄⋊C₄	—	47	16	no	—
225	C₄×C₄⋊C₄	—	47	8	no	—
226	C₄×C₄⋊C₄	—	47	8	no	—
227	C₂×#95	—	47	2	no	—
228	C₂×#95	—	47	2	no	—
229	C₂×#95	—	47	4	no	—
230	C₂×#95	—	47	4	no	—
231	C₄₇	C₂×#2365	1	1	yes	characteristic, complemented, Sylow
232	C₂²×Q₈	—	2	8	no	—
233	C₂²×Q₈	—	2	8	no	—
234	C₂²×Q₈	C₂×Dic₄₇	1	16	yes	—
235	C₂²×Q₈	C₂²×D₄₇	1	8	yes	—
236	C₂³×C₄	—	47	2	no	—
237	C₂³×C₄	—	47	2	no	—
238	C₂³×C₄	—	47	2	no	—
239	C₂³×C₄	—	47	2	no	—
240	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
241	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
242	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
243	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
244	C₄⋊Q₈	C₂×Dic₄₇	1	64	yes	complemented
245	C₄×Q₈	—	94	64	no	—
246	C₂×C₄⋊C₄	—	47	8	no	—
247	C₂×C₄⋊C₄	—	47	8	no	—
248	C₂×C₄⋊C₄	—	47	4	no	—
249	C₂×C₄⋊C₄	—	47	4	no	—
250	C₂×C₄⋊C₄	—	47	16	no	—
251	C₂×C₄⋊C₄	—	47	4	no	—
252	C₂×C₄⋊C₄	—	47	4	no	—
253	C₂×C₄⋊C₄	—	94	16	no	—
254	C₂×C₄⋊C₄	—	94	4	no	—
255	C₂×C₄⋊C₄	—	94	4	no	—
256	C₂×C₄⋊C₄	C₂×Dic₄₇	1	16	yes	—
257	C₂×C₄⋊C₄	C₂×Dic₄₇	1	16	yes	—
258	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
259	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
260	C₂×C₄²	—	47	16	no	—
261	C₂×C₄²	—	47	8	no	—
262	C₂×C₄²	—	47	8	no	—
263	C₂×C₄²	—	94	16	no	—
264	C₂×C₄²	—	94	8	no	—
265	C₂×C₄²	—	94	8	no	—
266	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
267	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
268	#95	—	47	8	no	—
269	#95	—	47	8	no	—
270	#95	—	47	16	no	—
271	#95	—	47	16	no	—
272	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
273	C₂×Q₈	—	2	64	no	—
274	C₂×Q₈	—	2	16	no	—
275	C₂×Q₈	—	2	16	no	—
276	C₂×Q₈	C₂²×Dic₄₇	1	32	yes	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	47	8	no	—
282	C₂²×C₄	—	47	8	no	—
283	C₂²×C₄	—	47	4	no	—
284	C₂²×C₄	—	47	4	no	—
285	C₂²×C₄	—	47	4	no	—
286	C₂²×C₄	—	47	4	no	—
287	C₂²×C₄	—	94	4	no	—
288	C₂²×C₄	—	94	4	no	—
289	C₂²×C₄	—	94	4	no	—
290	C₂²×C₄	—	94	4	no	—
291	C₂²×C₄	—	94	4	no	—
292	C₂²×C₄	—	94	4	no	—
293	C₂²×C₄	—	94	4	no	—
294	C₂²×C₄	—	94	4	no	—
295	C₂²×C₄	—	94	4	no	—
296	C₂²×C₄	—	94	4	no	—
297	C₂²×C₄	D₄×D₄₇	1	4	yes	—
298	C₂²×C₄	#10625352	1	4	yes	—
299	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
300	C₂²×C₄	#10625354	1	4	yes	—
301	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
302	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
303	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
304	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
305	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
306	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
307	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
308	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
309	C₄⋊C₄	—	47	16	no	—
310	C₄⋊C₄	—	47	16	no	—
311	C₄⋊C₄	—	94	32	no	—
312	C₄⋊C₄	—	94	8	no	—
313	C₄⋊C₄	—	94	8	no	—
314	C₄⋊C₄	C₂²×Dic₄₇	1	32	yes	—
315	C₄⋊C₄	C₂²×Dic₄₇	1	32	yes	—
316	C₄²	—	94	32	no	—
317	C₄²	—	94	16	no	—
318	C₄²	—	94	16	no	—
319	C₄²	C₂²×Dic₄₇	1	16	yes	—
320	C₂³	C₂³×Dic₄₇	1	2	yes	—
321	C₂³	C₂×D₄×D₄₇	1	2	yes	—
322	C₂³	C₂×Q₈×D₄₇	1	2	yes	—
323	C₂³	C₂×#10625352	1	2	yes	—
324	C₂³	C₂×#10625354	1	2	yes	—
325	C₂³	#13094072	1	2	yes	—
326	C₂³	#13094072	1	2	yes	—
327	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
328	Q₈	—	2	64	no	—
329	C₂×C₄	—	2	32	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	47	8	no	—
336	C₂×C₄	—	47	8	no	—
337	C₂×C₄	—	94	16	no	—
338	C₂×C₄	—	94	16	no	—
339	C₂×C₄	—	94	4	no	—
340	C₂×C₄	—	94	4	no	—
341	C₂×C₄	—	94	4	no	—
342	C₂×C₄	—	94	4	no	—
343	C₂×C₄	—	94	4	no	—
344	C₂×C₄	—	94	4	no	—
345	C₂×C₄	—	94	4	no	—
346	C₂×C₄	—	94	4	no	—
347	C₂×C₄	—	94	4	no	—
348	C₂×C₄	—	94	4	no	—
349	C₂×C₄	—	188	8	no	—
350	C₂×C₄	—	188	8	no	—
351	C₂×C₄	D₄×Dic₄₇	1	16	yes	—
352	C₂×C₄	Q₈×Dic₄₇	1	16	yes	complemented
353	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
354	C₂×C₄	C₂³×Dic₄₇	1	16	yes	—
355	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
356	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
357	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
358	C₂×C₄	C₂×Q₈×D₄₇	1	4	yes	—
359	C₂×C₄	C₂×#10625352	1	4	yes	—
360	C₂×C₄	C₂×#10625354	1	4	yes	—
361	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
362	C₂²	C₂×Q₈×Dic₄₇	1	4	yes	—
363	C₂²	#15689601	1	4	yes	—
364	C₂²	#15689776	1	4	yes	—
365	C₂²	#15689788	1	4	yes	—
366	C₂²	#15689847	1	4	yes	—
367	C₂²	#15689848	1	4	yes	—
368	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
369	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
370	C₂²	C₂²×Q₈×D₄₇	1	1	yes	characteristic
371	C₂²	C₂²×#10625352	1	1	yes	characteristic
372	C₂²	C₂²×#10625354	1	1	yes	characteristic
373	C₂²	C₂×#13094072	1	1	yes	characteristic
374	C₂²	C₂×#13094072	1	1	yes	characteristic
375	C₄	—	2	16	no	—
376	C₄	—	2	4	no	—
377	C₄	—	94	8	no	—
378	C₄	—	94	8	no	—
379	C₄	—	188	4	no	—
380	C₄	—	188	4	no	—
381	C₄	C₂×D₄×Dic₄₇	1	8	yes	—
382	C₄	C₂×Q₈×Dic₄₇	1	8	yes	complemented
383	C₂	#20246448	1	8	yes	direct product factor
384	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
385	C₂	C₂²×Q₈×Dic₄₇	1	1	yes	characteristic
386	C₂	C₂×#15689601	1	1	yes	characteristic
387	C₂	C₂×#15689776	1	1	yes	characteristic
388	C₂	C₂×#15689788	1	1	yes	characteristic
389	C₂	C₂×#15689847	1	1	yes	characteristic
390	C₂	C₂×#15689848	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂²×C₄⋊Q₈×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂⁴
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	C₂×#2365
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #20246448	C₂	direct (N × H)
31. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
45. C₂×C₄⋊Dic₄₇	Q₈	semidirect
69. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
120. C₄⋊Dic₄₇	C₂×Q₈	semidirect
140. C₂×C₄×C₄₇	C₄×Q₈	semidirect
183. C₄×C₄₇	C₂×C₄×Q₈	semidirect
197. C₂×C₄₇	#2365	semidirect
206. C₂×C₄⋊Q₈	Dic₄₇	semidirect
231. C₄₇	C₂×#2365	semidirect
244. C₄⋊Q₈	C₂×Dic₄₇	semidirect
352. C₂×C₄	Q₈×Dic₄₇	semidirect
382. C₄	C₂×Q₈×Dic₄₇	semidirect
383. C₂	#20246448	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×Q₈×Dic₄₇	2
#20246448	2
C₂×#15689030	2
C₂×#15689022	2
C₂×#15689009	2
C₂×C₄⋊C₄×Dic₄₇	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂²×C₄⋊Q₈×C₄₇	2
C₂×#2365	47

Subgroups — C2×#20246448 #26375872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20246448 #26375872