Subgroups — C₄×Q₈×Dic₉₄ #26376282

Order 12032.

2324 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic
2	#20246477	C₂	1	3	yes	maximal
3	#20246475	C₂	1	6	yes	maximal
4	Q₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×Dic₉₄	C₂	1	3	yes	maximal
6	Q₈×Dic₄₇⋊C₄	C₂	1	2	yes	maximal
7	C₄×#13094024	C₂	1	3	yes	maximal
8	C₄×#13094023	C₂	1	6	yes	maximal
9	C₄×Q₈×Dic₄₇	C₂	1	2	yes	maximal
10	C₄²×Dic₉₄	C₂	1	3	yes	maximal
11	C₄²×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	Q₈×Dic₉₄	C₄	1	16	yes	direct product factor
13	C₂×#13094024	C₂²	1	3	yes	—
14	C₂×#13094023	C₂²	1	6	yes	—
15	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
16	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
17	C₂×C₄×Dic₉₄	C₂²	1	3	yes	—
18	C₂×C₄×Dic₉₄	C₂²	1	6	yes	—
19	C₂×C₄×Dic₉₄	C₂²	1	3	yes	—
20	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
21	#15689029	C₂²	1	6	yes	—
22	#15689027	C₂²	1	12	yes	—
23	#15689022	C₂²	1	6	yes	—
24	#15689021	C₂²	1	6	yes	—
25	#15689021	C₂²	1	6	yes	—
26	#15689020	C₂²	1	12	yes	—
27	#15689019	C₂²	1	6	yes	—
28	#15688993	C₂²	1	3	yes	—
29	#15688992	C₂²	1	6	yes	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	6	yes	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	6	yes	—
32	C₄×Dic₄₇⋊C₄	C₂²	1	6	yes	—
33	C₄×Dic₄₇⋊C₄	C₂²	1	6	yes	—
34	C₄×Dic₄₇⋊C₄	C₂²	1	6	yes	—
35	C₄×C₄⋊Dic₄₇	C₂²	1	3	yes	—
36	C₄×C₄⋊Dic₄₇	C₂²	1	6	yes	—
37	C₄×C₄⋊Dic₄₇	C₂²	1	3	yes	—
38	C₄×C₄⋊Dic₄₇	C₂²	1	3	yes	—
39	C₄²×Dic₄₇	C₂²	1	6	yes	—
40	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
44	C₄×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
45	C₄×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
46	C₄³×C₄₇	C₂²	1	3	yes	—
47	C₂²×Dic₉₄	C₂³	1	6	yes	—
48	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
49	#13094024	C₂×C₄	1	24	yes	—
50	#13094023	C₂×C₄	1	48	yes	—
51	Q₈×Dic₄₇	—	2	8	no	—
52	Q₈×Dic₄₇	C₂×C₄	1	16	yes	—
53	C₄×Dic₉₄	—	2	12	no	—
54	C₄×Dic₉₄	—	4	12	no	—
55	C₄×Dic₉₄	C₂×C₄	1	24	yes	—
56	C₄×Dic₉₄	Q₈	1	8	yes	direct product factor
57	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
62	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
63	C₂×Dic₄₇⋊C₄	C₂³	1	6	yes	—
64	C₂×Dic₄₇⋊C₄	C₂³	1	12	yes	—
65	C₂×Dic₄₇⋊C₄	C₂³	1	6	yes	—
66	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
67	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
68	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
69	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
70	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
71	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
72	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
73	C₄₇⋊#95	C₂³	1	6	yes	—
74	C₄₇⋊#95	C₂³	1	6	yes	—
75	C₄₇⋊#95	C₂³	1	6	yes	—
76	C₄₇⋊#95	C₂³	1	12	yes	—
77	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₄₇	—	2	4	no	—
79	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
80	C₄×Q₈×C₄₇	Q₈	1	8	yes	complemented
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
85	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
88	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	#95×C₄₇	C₂³	1	6	yes	—
92	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂×Q₈×C₄₇	C₂×Q₈	1	4	yes	—
94	C₂×Q₈×C₄₇	#41	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
103	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
104	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
105	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
106	C₂×Dic₉₄	—	4	6	no	—
107	C₂×Dic₉₄	—	4	6	no	—
108	C₂×Dic₉₄	C₂²×C₄	1	24	yes	—
109	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
110	C₂×Dic₉₄	C₂×Q₈	1	4	yes	—
111	C₂×Dic₉₄	#41	1	4	yes	—
112	C₄⋊C₄×C₄₇	—	2	6	no	—
113	C₄⋊C₄×C₄₇	C₂²×C₄	1	12	yes	—
114	C₄⋊C₄×C₄₇	C₂×Q₈	1	12	yes	—
115	C₄²×C₄₇	—	2	6	no	—
116	C₄²×C₄₇	—	2	6	no	—
117	C₄²×C₄₇	—	2	6	no	—
118	C₄²×C₄₇	—	4	3	no	—
119	C₄²×C₄₇	C₂²×C₄	1	12	yes	—
120	C₄²×C₄₇	C₂×Q₈	1	12	yes	—
121	C₄²×C₄₇	C₂×Q₈	1	4	yes	—
122	C₄⋊Dic₄₇	—	2	6	no	—
123	C₄⋊Dic₄₇	—	2	12	no	—
124	C₄⋊Dic₄₇	—	4	6	no	—
125	C₄⋊Dic₄₇	C₂²×C₄	1	12	yes	—
126	C₄⋊Dic₄₇	C₂²×C₄	1	24	yes	—
127	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
128	Dic₄₇⋊C₄	—	2	12	no	—
129	Dic₄₇⋊C₄	—	4	12	no	—
130	Dic₄₇⋊C₄	C₂²×C₄	1	24	yes	—
131	Dic₄₇⋊C₄	C₂×Q₈	1	8	yes	—
132	C₄×Dic₄₇	—	2	12	no	—
133	C₄×Dic₄₇	—	2	12	no	—
134	C₄×Dic₄₇	—	2	12	no	—
135	C₄×Dic₄₇	—	4	6	no	—
136	C₄×Dic₄₇	C₂²×C₄	1	24	yes	—
137	C₄×Dic₄₇	C₂×Q₈	1	8	yes	—
138	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
139	Q₈×C₄₇	C₄×Q₈	1	16	yes	complemented
140	C₂×C₄×C₄₇	—	2	3	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	3	no	—
143	C₂×C₄×C₄₇	—	2	3	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	3	no	—
146	C₂×C₄×C₄₇	—	2	3	no	—
147	C₂×C₄×C₄₇	—	2	3	no	—
148	C₂×C₄×C₄₇	—	2	3	no	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	C₂²×Q₈	1	6	yes	—
156	C₂×C₄×C₄₇	C₂²×Q₈	1	6	yes	—
157	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
160	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	6	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	6	no	—
165	C₂×Dic₄₇	—	2	6	no	—
166	C₂×Dic₄₇	—	2	6	no	—
167	C₂×Dic₄₇	—	2	6	no	—
168	C₂×Dic₄₇	C₂³×C₄	1	12	yes	—
169	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
170	C₂×Dic₄₇	C₂²×Q₈	1	4	yes	—
171	C₂×Dic₄₇	C₂²×Q₈	1	4	yes	—
172	C₂×Dic₄₇	C₂×#41	1	4	yes	—
173	Dic₉₄	—	4	24	no	—
174	Dic₉₄	C₄×Q₈	1	16	yes	direct product factor
175	C₄×Q₈²	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
177	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
178	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
179	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
180	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
181	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
182	C₂²×C₄₇	#585	1	1	yes	characteristic
183	C₄×C₄₇	—	2	6	no	—
184	C₄×C₄₇	—	2	6	no	—
185	C₄×C₄₇	—	2	2	no	—
186	C₄×C₄₇	—	4	3	no	—
187	C₄×C₄₇	C₂×C₄×Q₈	1	4	yes	—
188	C₄×C₄₇	C₂×C₄×Q₈	1	12	yes	—
189	C₄×C₄₇	Q₈²	1	4	yes	complemented
190	Dic₄₇	—	2	12	no	—
191	Dic₄₇	—	2	4	no	—
192	Dic₄₇	—	4	6	no	—
193	Dic₄₇	C₂×C₄×Q₈	1	8	yes	—
194	C₂×Q₈²	—	47	1	no	—
195	#2369	—	47	6	no	—
196	#2369	—	47	3	no	—
197	Q₈×C₄⋊C₄	—	47	3	no	—
198	Q₈×C₄⋊C₄	—	47	2	no	—
199	Q₈×C₄⋊C₄	—	47	1	no	—
200	C₄×C₄⋊Q₈	—	47	6	no	—
201	C₄×C₄⋊Q₈	—	47	3	no	—
202	C₄²×Q₈	—	47	3	no	—
203	C₄²×Q₈	—	47	2	no	—
204	C₄²×Q₈	D₄₇	1	1	yes	characteristic
205	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
206	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
207	C₂×C₄₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄₇	C₂×Q₈²	1	1	yes	characteristic
209	C₂×C₄₇	Q₈×#41	1	1	yes	characteristic
210	C₂×C₄₇	Q₈×#41	1	1	yes	characteristic
211	C₂×C₄₇	#3483	1	1	yes	characteristic
212	Q₈²	—	47	16	no	—
213	C₂×C₄⋊Q₈	—	47	6	no	—
214	C₂×C₄⋊Q₈	—	47	3	no	—
215	C₂×C₄×Q₈	—	47	2	no	—
216	C₂×C₄×Q₈	—	47	2	no	—
217	C₂×C₄×Q₈	—	47	3	no	—
218	C₂×C₄×Q₈	—	47	1	no	—
219	C₂×C₄×Q₈	—	47	3	no	—
220	C₂×C₄×Q₈	—	47	6	no	—
221	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
224	#391	—	47	6	no	—
225	#391	—	47	12	no	—
226	#389	—	47	6	no	—
227	#389	—	47	6	no	—
228	#389	—	47	6	no	—
229	#389	—	47	6	no	—
230	#389	—	47	12	no	—
231	#384	—	47	6	no	—
232	#384	—	47	3	no	—
233	C₄×C₄⋊C₄	—	47	6	no	—
234	C₄×C₄⋊C₄	—	47	6	no	—
235	C₄×C₄⋊C₄	—	47	6	no	—
236	C₄×C₄⋊C₄	—	47	3	no	—
237	C₄×C₄⋊C₄	—	47	6	no	—
238	C₄×C₄⋊C₄	—	47	3	no	—
239	C₄×C₄⋊C₄	—	47	3	no	—
240	C₄×C₄⋊C₄	—	47	6	no	—
241	C₄×C₄⋊C₄	—	47	6	no	—
242	C₄×C₄⋊C₄	C₂×D₄₇	1	3	yes	—
243	C₄×C₄⋊C₄	C₂×D₄₇	1	3	yes	—
244	C₄×C₄⋊C₄	C₂×D₄₇	1	3	yes	—
245	C₄³	—	47	6	no	—
246	C₄³	C₂×D₄₇	1	3	yes	—
247	C₄₇	C₄×Q₈²	1	1	yes	characteristic, complemented, Sylow
248	C₂²×Q₈	—	47	1	no	—
249	C₂²×Q₈	—	47	6	no	—
250	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
251	C₄⋊Q₈	—	47	48	no	—
252	C₄⋊Q₈	—	47	24	no	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×Q₈	—	47	16	no	—
255	C₄×Q₈	—	47	24	no	—
256	C₄×Q₈	—	47	8	no	—
257	C₄×Q₈	—	94	12	no	—
258	C₄×Q₈	—	94	8	no	—
259	C₄×Q₈	—	188	12	no	—
260	C₄×Q₈	Dic₉₄	1	8	yes	direct product factor
261	C₄×Q₈	C₄×D₄₇	1	8	yes	—
262	C₂×C₄⋊C₄	—	47	6	no	—
263	C₂×C₄⋊C₄	—	47	3	no	—
264	C₂×C₄⋊C₄	—	47	6	no	—
265	C₂×C₄⋊C₄	—	47	2	no	—
266	C₂×C₄⋊C₄	—	47	1	no	—
267	C₂×C₄⋊C₄	—	47	6	no	—
268	C₂×C₄⋊C₄	—	47	3	no	—
269	C₂×C₄⋊C₄	—	47	6	no	—
270	C₂×C₄⋊C₄	—	47	12	no	—
271	C₂×C₄⋊C₄	—	47	6	no	—
272	C₂×C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
273	C₂×C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
274	C₂×C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
275	C₂×C₄²	—	47	6	no	—
276	C₂×C₄²	—	47	2	no	—
277	C₂×C₄²	—	47	6	no	—
278	C₂×C₄²	—	47	6	no	—
279	C₂×C₄²	—	47	6	no	—
280	C₂×C₄²	—	47	6	no	—
281	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
282	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
283	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
284	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
285	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
286	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
287	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
288	#95	—	47	6	no	—
289	#95	—	47	6	no	—
290	#95	—	47	6	no	—
291	#95	—	47	12	no	—
292	#95	C₂²×D₄₇	1	6	yes	—
293	C₂×Q₈	—	47	4	no	—
294	C₂×Q₈	—	47	24	no	—
295	C₂×Q₈	—	47	4	no	—
296	C₂×Q₈	—	47	4	no	—
297	C₂×Q₈	—	188	6	no	—
298	C₂×Q₈	—	188	6	no	—
299	C₂×Q₈	C₂×Dic₉₄	1	4	yes	—
300	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
301	C₂×Q₈	#10625350	1	4	yes	—
302	C₂²×C₄	—	47	2	no	—
303	C₂²×C₄	—	47	2	no	—
304	C₂²×C₄	—	47	6	no	—
305	C₂²×C₄	—	47	6	no	—
306	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
307	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
308	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
310	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
312	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
313	C₄⋊C₄	—	2	6	no	—
314	C₄⋊C₄	—	47	24	no	—
315	C₄⋊C₄	—	47	12	no	—
316	C₄⋊C₄	—	47	24	no	—
317	C₄⋊C₄	—	47	8	no	—
318	C₄⋊C₄	—	47	4	no	—
319	C₄⋊C₄	—	94	12	no	—
320	C₄⋊C₄	—	94	6	no	—
321	C₄⋊C₄	—	94	12	no	—
322	C₄⋊C₄	—	188	12	no	—
323	C₄⋊C₄	—	188	6	no	—
324	C₄⋊C₄	C₂×Dic₉₄	1	12	yes	—
325	C₄⋊C₄	C₂×C₄×D₄₇	1	12	yes	—
326	C₄²	—	2	6	no	—
327	C₄²	—	2	6	no	—
328	C₄²	—	2	6	no	—
329	C₄²	—	4	3	no	—
330	C₄²	—	47	24	no	—
331	C₄²	—	47	8	no	—
332	C₄²	—	94	12	no	—
333	C₄²	—	94	12	no	—
334	C₄²	—	94	12	no	—
335	C₄²	—	188	6	no	—
336	C₄²	C₂×Dic₉₄	1	12	yes	—
337	C₄²	C₂×C₄×D₄₇	1	12	yes	—
338	C₄²	Q₈×D₄₇	1	4	yes	—
339	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
340	Q₈	—	47	16	no	—
341	Q₈	—	188	24	no	—
342	Q₈	C₄×Dic₉₄	1	16	yes	direct product factor
343	C₂×C₄	—	2	3	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	3	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	3	no	—
348	C₂×C₄	—	2	3	no	—
349	C₂×C₄	—	2	3	no	—
350	C₂×C₄	—	2	3	no	—
351	C₂×C₄	—	2	3	no	—
352	C₂×C₄	—	47	4	no	—
353	C₂×C₄	—	47	4	no	—
354	C₂×C₄	—	47	4	no	—
355	C₂×C₄	—	47	12	no	—
356	C₂×C₄	—	47	4	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	6	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	6	no	—
361	C₂×C₄	—	94	6	no	—
362	C₂×C₄	—	94	6	no	—
363	C₂×C₄	—	94	6	no	—
364	C₂×C₄	C₂²×C₄×D₄₇	1	6	yes	—
365	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
366	C₂×C₄	C₂²×C₄×D₄₇	1	6	yes	—
367	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
368	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
369	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
370	C₂×C₄	C₂²×Dic₉₄	1	6	yes	—
371	C₂×C₄	C₂²×Dic₉₄	1	6	yes	—
372	C₂×C₄	C₂²×Dic₉₄	1	2	yes	—
373	C₂×C₄	#41×D₄₇	1	2	yes	—
374	C₂×C₄	C₂×#10625350	1	6	yes	—
375	C₂×C₄	#13094070	1	2	yes	—
376	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
377	C₂²	C₂²×Q₈×D₄₇	1	1	yes	characteristic
378	C₂²	C₂³×Dic₉₄	1	1	yes	characteristic
379	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
380	C₂²	C₂²×#10625350	1	1	yes	characteristic
381	C₂²	C₂×#13094070	1	1	yes	characteristic
382	C₂²	#15689959	1	1	yes	characteristic
383	C₄	—	2	6	no	—
384	C₄	—	2	6	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	3	no	—
387	C₄	—	47	8	no	—
388	C₄	—	94	12	no	—
389	C₄	—	94	4	no	—
390	C₄	—	188	6	no	—
391	C₄	C₄×Q₈×D₄₇	1	4	yes	—
392	C₄	C₂×C₄×Dic₉₄	1	12	yes	—
393	C₄	Q₈×Dic₉₄	1	4	yes	direct product factor
394	C₂	C₂×C₄×Q₈×D₄₇	1	1	yes	characteristic
395	C₂	C₂²×C₄×Dic₉₄	1	1	yes	characteristic
396	C₂	C₄×#13094070	1	1	yes	characteristic
397	C₂	C₂×Q₈×Dic₉₄	1	1	yes	characteristic
398	C₂	#41×Dic₉₄	1	1	yes	characteristic
399	C₂	Q₈×#10625350	1	1	yes	characteristic
400	C₂	#20257014	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₄²×Q₈×C₄₇	C₂
socle, prime radical, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₄²×Q₈	D₄₇
hypocenter	C₄₇	C₄×Q₈²
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
12. Q₈×Dic₉₄	C₄	direct (N × H)
56. C₄×Dic₉₄	Q₈	direct (N × H)
80. C₄×Q₈×C₄₇	Q₈	semidirect
139. Q₈×C₄₇	C₄×Q₈	semidirect
174. Dic₉₄	C₄×Q₈	direct (N × H)
189. C₄×C₄₇	Q₈²	semidirect
247. C₄₇	C₄×Q₈²	semidirect
260. C₄×Q₈	Dic₉₄	direct (N × H)
342. Q₈	C₄×Dic₉₄	direct (N × H)
393. C₄	Q₈×Dic₉₄	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Q₈×Dic₉₄	2
#20246477	2
#20246475	2
Q₈×C₄⋊Dic₄₇	2
C₄⋊C₄×Dic₉₄	2
Q₈×Dic₄₇⋊C₄	2
C₄×#13094024	2
C₄×#13094023	2
C₄×Q₈×Dic₄₇	2
C₄²×Dic₉₄	2
C₄²×Q₈×C₄₇	2
C₄×Q₈²	47

Subgroups — C4×Q8×Dic94 #26376282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×Dic₉₄ #26376282