Subgroups — #37576221

Order 24448.

608 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	C₂×#20259321	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#20259301	C₂	1	1	yes	maximal, characteristic
3	C₂×#20259299	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₉₁⋊C₄	C₂	1	1	yes	maximal, characteristic
5	#27132597	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132596	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132584	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132583	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132560	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132560	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132538	C₂	1	1	yes	maximal, characteristic
12	#27132532	C₂	1	1	yes	maximal, characteristic, complemented
13	#27132521	C₂	1	1	yes	maximal, characteristic
14	C₂²⋊C₄×Dic₁₉₁	C₂	1	1	yes	maximal, characteristic
15	#385×C₁₉₁	C₂	1	1	yes	maximal, characteristic
16	C₂²×Dic₃₈₂	C₂²	1	1	yes	characteristic
17	C₂²×Dic₃₈₂	C₂²	1	1	yes	characteristic
18	C₂³×Dic₁₉₁	C₂²	1	1	yes	characteristic
19	C₂³×Dic₁₉₁	C₂²	1	1	yes	characteristic
20	#20259321	—	2	4	no	—
21	#20259301	—	2	4	no	—
22	#20259299	—	2	4	no	—
23	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
27	C₂×Dic₁₉₁⋊C₄	—	2	4	no	—
28	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
42	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
43	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
44	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
45	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
46	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
47	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
48	C₂³×C₄×C₁₉₁	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
53	#95×C₁₉₁	C₂²	1	1	yes	characteristic
54	#95×C₁₉₁	C₂²	1	1	yes	characteristic
55	C₂×Dic₃₈₂	—	2	2	no	—
56	C₂×Dic₃₈₂	—	2	2	no	—
57	C₂×Dic₃₈₂	—	2	2	no	—
58	C₂×Dic₃₈₂	—	2	2	no	—
59	C₂×Dic₃₈₂	—	4	1	no	—
60	C₂×Dic₃₈₂	—	4	1	no	—
61	C₂²×Dic₁₉₁	—	2	2	no	—
62	C₂²×Dic₁₉₁	—	2	2	no	—
63	C₂²×Dic₁₉₁	—	2	2	no	—
64	C₂²×Dic₁₉₁	—	2	2	no	—
65	C₂²×Dic₁₉₁	—	4	1	no	—
66	C₂²×Dic₁₉₁	Q₈	1	4	yes	complemented
67	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
68	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
69	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
70	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
71	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
72	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
73	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
74	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
75	C₄⋊Dic₁₉₁	—	2	2	no	—
76	C₄⋊Dic₁₉₁	—	2	2	no	—
77	C₄⋊Dic₁₉₁	—	2	2	no	—
78	C₄⋊Dic₁₉₁	—	4	1	no	—
79	Dic₁₉₁⋊C₄	—	2	2	no	—
80	Dic₁₉₁⋊C₄	—	2	2	no	—
81	Dic₁₉₁⋊C₄	—	2	2	no	—
82	Dic₁₉₁⋊C₄	—	2	2	no	—
83	Dic₁₉₁⋊C₄	—	2	2	no	—
84	Dic₁₉₁⋊C₄	—	2	2	no	—
85	Dic₁₉₁⋊C₄	—	2	2	no	—
86	Dic₁₉₁⋊C₄	—	2	2	no	—
87	Dic₁₉₁⋊C₄	—	2	2	no	—
88	Dic₁₉₁⋊C₄	D₄	1	4	yes	—
89	C₂²⋊Dic₁₉₁	—	2	2	no	—
90	C₂²⋊Dic₁₉₁	D₄	1	4	yes	—
91	C₄×Dic₁₉₁	—	2	2	no	—
92	C₄×Dic₁₉₁	—	2	2	no	—
93	C₂⁴×C₁₉₁	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₉₁	—	2	2	no	—
95	C₂²×C₄×C₁₉₁	—	2	2	no	—
96	C₂²×C₄×C₁₉₁	—	4	1	no	—
97	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
103	C₄⋊C₄×C₁₉₁	—	2	2	no	—
104	C₄⋊C₄×C₁₉₁	—	4	1	no	—
105	C₂²⋊C₄×C₁₉₁	—	2	2	no	—
106	C₂²⋊C₄×C₁₉₁	Q₈	1	4	yes	complemented
107	Dic₃₈₂	—	4	4	no	—
108	Dic₃₈₂	—	4	4	no	—
109	C₂×Dic₁₉₁	—	2	1	no	—
110	C₂×Dic₁₉₁	—	2	1	no	—
111	C₂×Dic₁₉₁	—	2	1	no	—
112	C₂×Dic₁₉₁	—	2	1	no	—
113	C₂×Dic₁₉₁	—	2	1	no	—
114	C₂×Dic₁₉₁	—	2	1	no	—
115	C₂×Dic₁₉₁	—	2	1	no	—
116	C₂×Dic₁₉₁	—	2	1	no	—
117	C₂×Dic₁₉₁	—	2	8	no	—
118	C₂×Dic₁₉₁	—	2	1	no	—
119	C₂×Dic₁₉₁	—	2	1	no	—
120	C₂×Dic₁₉₁	—	2	1	no	—
121	C₂×Dic₁₉₁	—	2	1	no	—
122	C₂×Dic₁₉₁	—	2	1	no	—
123	C₂×Dic₁₉₁	—	2	1	no	—
124	C₂×Dic₁₉₁	—	2	1	no	—
125	C₂×Dic₁₉₁	—	2	1	no	—
126	C₂×Dic₁₉₁	—	2	1	no	—
127	C₂×Dic₁₉₁	—	4	4	no	—
128	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
129	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
130	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
131	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
132	C₂×Dic₁₉₁	C₂×Q₈	1	2	yes	—
133	C₂×Dic₁₉₁	C₂×Q₈	1	2	yes	—
134	C₂×Dic₁₉₁	#41	1	2	yes	—
135	C₂³×C₁₉₁	—	2	1	no	—
136	C₂³×C₁₉₁	—	2	1	no	—
137	C₂³×C₁₉₁	—	2	1	no	—
138	C₂³×C₁₉₁	—	2	1	no	—
139	C₂³×C₁₉₁	C₂×D₄	1	2	yes	—
140	C₂³×C₁₉₁	C₂×Q₈	1	2	yes	—
141	C₂³×C₁₉₁	C₂×Q₈	1	2	yes	—
142	C₂³×C₁₉₁	C₂⁴	1	1	yes	characteristic
143	C₂×C₄×C₁₉₁	—	2	1	no	—
144	C₂×C₄×C₁₉₁	—	2	1	no	—
145	C₂×C₄×C₁₉₁	—	2	1	no	—
146	C₂×C₄×C₁₉₁	—	2	1	no	—
147	C₂×C₄×C₁₉₁	—	2	1	no	—
148	C₂×C₄×C₁₉₁	—	2	1	no	—
149	C₂×C₄×C₁₉₁	—	2	1	no	—
150	C₂×C₄×C₁₉₁	—	2	1	no	—
151	C₂×C₄×C₁₉₁	—	2	1	no	—
152	C₂×C₄×C₁₉₁	—	2	1	no	—
153	C₂×C₄×C₁₉₁	—	2	1	no	—
154	C₂×C₄×C₁₉₁	—	2	1	no	—
155	C₂×C₄×C₁₉₁	—	2	1	no	—
156	C₂×C₄×C₁₉₁	—	2	1	no	—
157	C₂×C₄×C₁₉₁	—	2	1	no	—
158	C₂×C₄×C₁₉₁	—	4	4	no	—
159	C₂×C₄×C₁₉₁	C₂×D₄	1	2	yes	—
160	C₂×C₄×C₁₉₁	C₂×Q₈	1	2	yes	—
161	C₂×C₄×C₁₉₁	C₂×Q₈	1	2	yes	—
162	C₂²×C₁₉₁	—	2	2	no	—
163	C₂²×C₁₉₁	—	2	2	no	—
164	C₂²×C₁₉₁	—	2	2	no	—
165	C₂²×C₁₉₁	—	2	2	no	—
166	C₂²×C₁₉₁	—	2	2	no	—
167	C₂²×C₁₉₁	—	2	2	no	—
168	C₂²×C₁₉₁	C₄⋊Q₈	1	4	yes	complemented
169	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
170	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
171	C₂²×C₁₉₁	C₂²×Q₈	1	1	yes	characteristic
172	C₂²×C₁₉₁	C₂²×Q₈	1	1	yes	characteristic
173	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
174	C₂²×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²×C₁₉₁	2₋¹⁺⁴	1	1	yes	characteristic
176	C₄×C₁₉₁	—	2	2	no	—
177	C₄×C₁₉₁	—	2	2	no	—
178	C₄×C₁₉₁	—	2	2	no	—
179	C₄×C₁₉₁	—	4	1	no	—
180	C₄×C₁₉₁	—	4	1	no	—
181	C₄×C₁₉₁	—	4	1	no	—
182	Dic₁₉₁	—	2	2	no	—
183	Dic₁₉₁	—	2	2	no	—
184	Dic₁₉₁	—	2	2	no	—
185	Dic₁₉₁	—	2	2	no	—
186	Dic₁₉₁	—	4	1	no	—
187	Dic₁₉₁	—	4	1	no	—
188	Dic₁₉₁	—	4	1	no	—
189	Dic₁₉₁	C₂²⋊Q₈	1	4	yes	complemented
190	C₂×C₁₉₁	—	2	4	no	—
191	C₂×C₁₉₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₁₉₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
193	C₂×C₁₉₁	#544	1	1	yes	characteristic
194	C₂×C₁₉₁	D₄²	1	1	yes	characteristic
195	C₂×C₁₉₁	#547	1	1	yes	characteristic
196	C₂×C₁₉₁	D₄×Q₈	1	1	yes	characteristic
197	C₂×C₁₉₁	#554	1	1	yes	characteristic
198	C₁₉₁	#2440	1	1	yes	characteristic, complemented, Sylow
199	#2440	—	191	1	no	maximal, Sylow
200	C₂×C₄⋊Q₈	—	191	1	no	—
201	C₂×C₂²⋊Q₈	—	191	1	no	—
202	C₂×C₂²⋊Q₈	—	191	1	no	—
203	C₂²×C₄⋊C₄	—	191	1	no	—
204	#398	—	191	1	no	—
205	#398	—	191	1	no	—
206	#395	—	191	1	no	—
207	#395	—	191	1	no	—
208	#389	—	191	1	no	—
209	#389	—	191	1	no	—
210	#385	—	191	1	no	—
211	#385	D₁₉₁	1	1	yes	characteristic
212	#384	—	191	1	no	—
213	#380	—	191	1	no	—
214	C₄×C₂²⋊C₄	—	191	1	no	—
215	C₂²×Q₈	—	191	1	no	—
216	C₂²×Q₈	—	191	1	no	—
217	C₂³×C₄	—	191	1	no	—
218	C₂³×C₄	—	191	1	no	—
219	C₂³×C₄	C₂×D₁₉₁	1	1	yes	characteristic
220	C₄⋊Q₈	—	382	4	no	—
221	C₂²⋊Q₈	—	382	4	no	—
222	C₂²⋊Q₈	—	382	4	no	—
223	C₂×C₄⋊C₄	—	382	4	no	—
224	C₂×C₄⋊C₄	—	191	1	no	—
225	C₂×C₄⋊C₄	—	191	1	no	—
226	C₂×C₄⋊C₄	—	191	1	no	—
227	C₂×C₄⋊C₄	—	191	1	no	—
228	C₂×C₄⋊C₄	—	191	1	no	—
229	C₂×C₄⋊C₄	—	191	1	no	—
230	C₂×C₄⋊C₄	—	191	1	no	—
231	C₂×C₄⋊C₄	—	191	1	no	—
232	C₂×C₄⋊C₄	—	191	1	no	—
233	C₂×C₄⋊C₄	—	191	1	no	—
234	C₂×C₄⋊C₄	—	191	1	no	—
235	C₂×C₄⋊C₄	—	191	1	no	—
236	C₂×C₄⋊C₄	—	191	1	no	—
237	C₂×C₄⋊C₄	—	191	1	no	—
238	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	—	191	1	no	—
241	C₂×C₂²⋊C₄	—	191	1	no	—
242	C₂×C₂²⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
244	C₂×C₄²	—	191	1	no	—
245	C₂×C₄²	—	191	1	no	—
246	#95	—	191	1	no	—
247	#95	—	191	1	no	—
248	#95	—	191	1	no	—
249	#95	—	191	1	no	—
250	#95	—	191	1	no	—
251	#95	—	191	1	no	—
252	#95	C₂×D₁₉₁	1	1	yes	characteristic
253	#95	C₂×D₁₉₁	1	1	yes	characteristic
254	C₂⁴	C₂²×D₁₉₁	1	1	yes	characteristic
255	C₂×Q₈	—	382	2	no	—
256	C₂×Q₈	—	382	2	no	—
257	C₂×Q₈	—	382	2	no	—
258	C₂×Q₈	—	382	2	no	—
259	C₂×Q₈	—	764	1	no	—
260	C₂×Q₈	—	764	1	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	—	382	2	no	—
265	C₂²×C₄	—	382	2	no	—
266	C₂²×C₄	—	382	2	no	—
267	C₂²×C₄	—	382	2	no	—
268	C₂²×C₄	—	191	1	no	—
269	C₂²×C₄	—	191	1	no	—
270	C₂²×C₄	—	191	1	no	—
271	C₂²×C₄	—	191	4	no	—
272	C₂²×C₄	—	191	1	no	—
273	C₂²×C₄	—	191	1	no	—
274	C₂²×C₄	—	191	1	no	—
275	C₂²×C₄	—	191	1	no	—
276	C₂²×C₄	—	191	1	no	—
277	C₂²×C₄	—	764	1	no	—
278	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
283	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	382	2	no	—
287	C₄⋊C₄	—	382	2	no	—
288	C₄⋊C₄	—	382	2	no	—
289	C₄⋊C₄	—	382	2	no	—
290	C₄⋊C₄	—	382	2	no	—
291	C₄⋊C₄	—	382	2	no	—
292	C₄⋊C₄	—	382	2	no	—
293	C₄⋊C₄	—	382	2	no	—
294	C₄⋊C₄	—	382	2	no	—
295	C₄⋊C₄	—	382	2	no	—
296	C₄⋊C₄	—	382	2	no	—
297	C₄⋊C₄	—	382	2	no	—
298	C₄⋊C₄	—	191	4	no	—
299	C₄⋊C₄	—	764	1	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	382	2	no	—
302	C₂²⋊C₄	—	191	4	no	—
303	C₂²⋊C₄	Dic₃₈₂	1	4	yes	complemented
304	C₄²	—	382	2	no	—
305	C₄²	—	382	2	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	D₄×D₁₉₁	1	2	yes	—
311	C₂³	Q₈×D₁₉₁	1	2	yes	—
312	C₂³	C₂×Dic₃₈₂	1	2	yes	—
313	C₂³	C₂³×D₁₉₁	1	1	yes	characteristic
314	Q₈	—	764	4	no	—
315	Q₈	—	764	4	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
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	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	382	1	no	—
333	C₂×C₄	—	382	1	no	—
334	C₂×C₄	—	382	1	no	—
335	C₂×C₄	—	382	1	no	—
336	C₂×C₄	—	382	1	no	—
337	C₂×C₄	—	382	1	no	—
338	C₂×C₄	—	382	1	no	—
339	C₂×C₄	—	382	1	no	—
340	C₂×C₄	—	382	8	no	—
341	C₂×C₄	—	382	1	no	—
342	C₂×C₄	—	382	1	no	—
343	C₂×C₄	—	382	1	no	—
344	C₂×C₄	—	382	1	no	—
345	C₂×C₄	—	382	1	no	—
346	C₂×C₄	—	382	1	no	—
347	C₂×C₄	—	382	1	no	—
348	C₂×C₄	—	382	1	no	—
349	C₂×C₄	—	382	1	no	—
350	C₂×C₄	—	191	2	no	—
351	C₂×C₄	—	191	2	no	—
352	C₂×C₄	—	191	2	no	—
353	C₂×C₄	—	191	2	no	—
354	C₂×C₄	—	191	2	no	—
355	C₂×C₄	—	191	2	no	—
356	C₂×C₄	—	191	2	no	—
357	C₂×C₄	—	764	4	no	—
358	C₂×C₄	D₄×D₁₉₁	1	2	yes	—
359	C₂×C₄	C₂×Dic₃₈₂	1	2	yes	—
360	C₂×C₄	C₂×Dic₃₈₂	1	2	yes	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	#20259321	1	4	yes	complemented
368	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
369	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
370	C₂²	C₂×Q₈×D₁₉₁	1	1	yes	characteristic
371	C₂²	C₂²×Dic₃₈₂	1	1	yes	characteristic
372	C₂²	#41×D₁₉₁	1	1	yes	characteristic
373	C₂²	#20259367	1	1	yes	characteristic
374	C₂²	#20259369	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	382	2	no	—
382	C₄	—	382	2	no	—
383	C₄	—	382	2	no	—
384	C₄	—	382	2	no	—
385	C₄	—	191	4	no	—
386	C₄	—	764	1	no	—
387	C₄	—	764	1	no	—
388	C₄	—	764	1	no	—
389	C₂	—	2	4	no	—
390	C₂	C₂²⋊Q₈×D₁₉₁	1	1	yes	characteristic
391	C₂	C₂×#20259321	1	1	yes	characteristic
392	C₂	#27133292	1	1	yes	characteristic
393	C₂	#27133295	1	1	yes	characteristic
394	C₂	#27133311	1	1	yes	characteristic
395	C₂	D₄×Dic₃₈₂	1	1	yes	characteristic
396	C₂	#27133372	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉₁
commutator, socle, cosocle	C₂³×C₁₉₁	C₂⁴
Fitting	#385×C₁₉₁	C₂
prime radical	C₂⁴×C₁₉₁	C₂³
hypercenter	#385	D₁₉₁
hypocenter	C₁₉₁	#2440
LCS	G ▷ C₂³×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂³ ◁ #385

Complements

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

N	H ≅ G/N	type
1. C₂×#20259321	C₂	semidirect
5. #27132597	C₂	semidirect
6. #27132596	C₂	semidirect
7. #27132584	C₂	semidirect
8. #27132583	C₂	semidirect
9. #27132560	C₂	semidirect
10. #27132560	C₂	semidirect
12. #27132532	C₂	semidirect
66. C₂²×Dic₁₉₁	Q₈	semidirect
106. C₂²⋊C₄×C₁₉₁	Q₈	semidirect
168. C₂²×C₁₉₁	C₄⋊Q₈	semidirect
189. Dic₁₉₁	C₂²⋊Q₈	semidirect
198. C₁₉₁	#2440	semidirect
303. C₂²⋊C₄	Dic₃₈₂	semidirect
367. C₂²	#20259321	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20259321	2
C₂×#20259301	2
C₂×#20259299	2
C₂²×Dic₁₉₁⋊C₄	2
#27132597	2
#27132596	2
#27132584	2
#27132583	2
#27132560	2
#27132538	2
#27132532	2
#27132521	2
C₂²⋊C₄×Dic₁₉₁	2
#385×C₁₉₁	2
#2440	191