Subgroups — #37575522

Order 24448.

620 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259300	C₂	1	1	yes	maximal, characteristic
2	C₂×#20259287	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄⋊C₄×D₁₉₁	C₂	1	1	yes	maximal, characteristic
4	#27132567	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132560	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132558	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132549	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132544	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132534	C₂	1	1	yes	maximal, characteristic
10	#27132534	C₂	1	1	yes	maximal, characteristic
11	C₄×Dic₁₉₁⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×(C₂×D₁₉₁)⋊C₄	C₂	1	1	yes	maximal, characteristic
13	#27132510	C₂	1	1	yes	maximal, characteristic
14	#27132510	C₂	1	1	yes	maximal, characteristic
15	#389×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Dic₃₈₂	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
20	#20259300	C₄	1	8	yes	complemented
21	#20259287	—	2	4	no	—
22	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
29	C₄⋊C₄×D₁₉₁	—	2	4	no	—
30	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
39	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
40	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
41	C₁₉₁⋊#95	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	C₂×C₄⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊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×C₄²×C₁₉₁	C₂²	1	1	yes	characteristic
52	#95×C₁₉₁	C₂²	1	1	yes	characteristic
53	#95×C₁₉₁	C₂²	1	1	yes	characteristic
54	C₂³×D₁₉₁	C₂³	1	1	yes	characteristic
55	C₂×Dic₃₈₂	—	2	2	no	—
56	C₂×Dic₃₈₂	—	2	2	no	—
57	C₂×Dic₃₈₂	C₂×C₄	1	4	yes	complemented
58	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
59	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
60	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
62	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
63	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
65	C₂×C₄×D₁₉₁	—	2	2	no	—
66	C₂×C₄×D₁₉₁	—	2	2	no	—
67	C₂×C₄×D₁₉₁	—	2	2	no	—
68	C₂×C₄×D₁₉₁	—	2	2	no	—
69	C₂×C₄×D₁₉₁	—	2	2	no	—
70	C₂×C₄×D₁₉₁	—	2	2	no	—
71	C₂×C₄×D₁₉₁	—	4	1	no	—
72	C₂×C₄×D₁₉₁	—	4	1	no	—
73	C₂×C₄×D₁₉₁	C₂×C₄	1	4	yes	—
74	C₄⋊Dic₁₉₁	—	2	2	no	—
75	Dic₁₉₁⋊C₄	—	2	2	no	—
76	Dic₁₉₁⋊C₄	—	2	2	no	—
77	Dic₁₉₁⋊C₄	—	4	1	no	—
78	Dic₁₉₁⋊C₄	C₂×C₄	1	4	yes	complemented
79	Dic₁₉₁⋊C₄	C₂×C₄	1	4	yes	complemented
80	Dic₁₉₁⋊C₄	D₄	1	4	yes	—
81	(C₂×D₁₉₁)⋊C₄	—	2	2	no	—
82	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	4	yes	—
83	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	4	yes	—
84	(C₂×D₁₉₁)⋊C₄	Q₈	1	4	yes	complemented
85	C₄×Dic₁₉₁	—	2	2	no	—
86	C₄×Dic₁₉₁	—	2	2	no	—
87	C₄×Dic₁₉₁	—	2	2	no	—
88	C₄×Dic₁₉₁	—	2	2	no	—
89	C₄×Dic₁₉₁	—	4	1	no	—
90	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₁₉₁	—	2	2	no	—
98	C₄⋊C₄×C₁₉₁	—	2	2	no	—
99	C₄⋊C₄×C₁₉₁	—	4	1	no	—
100	C₄⋊C₄×C₁₉₁	C₂×C₄	1	4	yes	complemented
101	C₄²×C₁₉₁	—	4	1	no	—
102	C₂²×D₁₉₁	—	2	1	no	—
103	C₂²×D₁₉₁	—	2	1	no	—
104	C₂²×D₁₉₁	—	2	1	no	—
105	C₂²×D₁₉₁	—	2	1	no	—
106	C₂²×D₁₉₁	C₂²×C₄	1	2	yes	—
107	C₂²×D₁₉₁	C₂×Q₈	1	2	yes	—
108	C₂²×D₁₉₁	#41	1	2	yes	—
109	Dic₃₈₂	—	2	8	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	1	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	C₂²×C₄	1	2	yes	—
125	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
126	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
127	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
128	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
129	C₂×Dic₁₉₁	C₂×Q₈	1	2	yes	—
130	C₂×Dic₁₉₁	#41	1	2	yes	—
131	C₄×D₁₉₁	—	2	8	no	—
132	C₄×D₁₉₁	—	4	4	no	—
133	C₄×D₁₉₁	—	4	4	no	—
134	C₂³×C₁₉₁	C₂⁴	1	1	yes	characteristic
135	C₂×C₄×C₁₉₁	—	2	1	no	—
136	C₂×C₄×C₁₉₁	—	2	1	no	—
137	C₂×C₄×C₁₉₁	—	2	1	no	—
138	C₂×C₄×C₁₉₁	—	2	1	no	—
139	C₂×C₄×C₁₉₁	—	2	1	no	—
140	C₂×C₄×C₁₉₁	—	2	1	no	—
141	C₂×C₄×C₁₉₁	—	2	1	no	—
142	C₂×C₄×C₁₉₁	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
152	C₂×C₄×C₁₉₁	C₂²×C₄	1	2	yes	—
153	C₂×C₄×C₁₉₁	C₂²×C₄	1	2	yes	—
154	C₂×C₄×C₁₉₁	C₂×D₄	1	2	yes	—
155	C₂×C₄×C₁₉₁	C₂×Q₈	1	2	yes	—
156	C₂²×C₁₉₁	C₂³×C₄	1	1	yes	characteristic
157	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
158	C₂²×C₁₉₁	C₂²×Q₈	1	1	yes	characteristic
159	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
160	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
161	C₂²×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂²×C₁₉₁	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂×D₁₉₁	—	2	2	no	—
164	C₂×D₁₉₁	—	2	2	no	—
165	C₂×D₁₉₁	—	2	2	no	—
166	C₂×D₁₉₁	—	2	2	no	—
167	C₂×D₁₉₁	—	2	2	no	—
168	C₂×D₁₉₁	—	2	2	no	—
169	C₂×D₁₉₁	C₄×Q₈	1	4	yes	complemented
170	C₄×C₁₉₁	—	2	2	no	—
171	C₄×C₁₉₁	—	2	2	no	—
172	C₄×C₁₉₁	—	2	2	no	—
173	C₄×C₁₉₁	—	2	2	no	—
174	C₄×C₁₉₁	—	2	2	no	—
175	C₄×C₁₉₁	—	4	1	no	—
176	C₄×C₁₉₁	—	4	1	no	—
177	Dic₁₉₁	—	2	2	no	—
178	Dic₁₉₁	—	2	2	no	—
179	Dic₁₉₁	—	2	2	no	—
180	Dic₁₉₁	—	2	2	no	—
181	Dic₁₉₁	—	4	1	no	—
182	Dic₁₉₁	—	4	1	no	—
183	Dic₁₉₁	C₄×D₄	1	4	yes	—
184	C₂×C₁₉₁	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂×C₁₉₁	C₂×C₄×Q₈	1	1	yes	characteristic
186	C₂×C₁₉₁	#520	1	1	yes	characteristic
187	C₂×C₁₉₁	#546	1	1	yes	characteristic
188	C₂×C₁₉₁	D₄×Q₈	1	1	yes	characteristic
189	C₂×C₁₉₁	#552	1	1	yes	characteristic
190	C₂×C₁₉₁	#554	1	1	yes	characteristic
191	D₁₉₁	—	2	4	no	—
192	C₁₉₁	#2360	1	1	yes	characteristic, complemented, Sylow
193	#2360	—	191	1	no	maximal, Sylow
194	C₂×C₂²⋊Q₈	—	191	1	no	—
195	C₂×C₄×Q₈	—	191	1	no	—
196	C₂²×C₄⋊C₄	—	191	1	no	—
197	#391	—	191	1	no	—
198	#389	—	191	1	no	—
199	#389	—	191	1	no	—
200	#389	D₁₉₁	1	1	yes	characteristic, complemented
201	#387	—	191	1	no	—
202	#387	—	191	1	no	—
203	#385	—	191	1	no	—
204	#385	—	191	1	no	—
205	C₄×C₄⋊C₄	—	191	1	no	—
206	C₄×C₂²⋊C₄	—	191	1	no	—
207	C₄×C₂²⋊C₄	—	191	1	no	—
208	C₄×C₂²⋊C₄	—	191	1	no	—
209	C₂²×Q₈	—	191	1	no	—
210	C₂³×C₄	—	191	1	no	—
211	C₂³×C₄	—	191	1	no	—
212	C₂³×C₄	—	191	1	no	—
213	C₂²⋊Q₈	—	191	8	no	—
214	C₄×Q₈	—	382	4	no	—
215	C₂×C₄⋊C₄	—	382	4	no	—
216	C₂×C₄⋊C₄	—	191	1	no	—
217	C₂×C₄⋊C₄	—	191	1	no	—
218	C₂×C₄⋊C₄	—	191	1	no	—
219	C₂×C₄⋊C₄	—	191	1	no	—
220	C₂×C₄⋊C₄	—	191	1	no	—
221	C₂×C₄⋊C₄	—	191	1	no	—
222	C₂×C₄⋊C₄	—	191	1	no	—
223	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	191	1	no	—
228	C₂×C₂²⋊C₄	—	191	1	no	—
229	C₂×C₂²⋊C₄	—	191	1	no	—
230	C₂×C₂²⋊C₄	—	191	1	no	—
231	C₂×C₄²	—	191	1	no	—
232	C₂×C₄²	—	191	1	no	—
233	C₂×C₄²	—	191	1	no	—
234	C₂×C₄²	—	191	1	no	—
235	C₂×C₄²	—	191	1	no	—
236	C₂×C₄²	C₂×D₁₉₁	1	1	yes	characteristic
237	#95	—	191	1	no	—
238	#95	—	191	1	no	—
239	#95	—	191	1	no	—
240	#95	—	191	1	no	—
241	#95	—	191	1	no	—
242	#95	—	191	1	no	—
243	#95	—	191	1	no	—
244	#95	—	191	1	no	—
245	#95	C₂×D₁₉₁	1	1	yes	characteristic
246	#95	C₂×D₁₉₁	1	1	yes	characteristic
247	C₂⁴	—	191	1	no	—
248	C₂×Q₈	—	382	2	no	—
249	C₂×Q₈	—	382	2	no	—
250	C₂×Q₈	—	191	4	no	—
251	C₂²×C₄	—	382	2	no	—
252	C₂²×C₄	—	382	2	no	—
253	C₂²×C₄	—	382	2	no	—
254	C₂²×C₄	—	382	2	no	—
255	C₂²×C₄	—	382	2	no	—
256	C₂²×C₄	—	382	2	no	—
257	C₂²×C₄	—	191	1	no	—
258	C₂²×C₄	—	191	1	no	—
259	C₂²×C₄	—	191	1	no	—
260	C₂²×C₄	—	191	1	no	—
261	C₂²×C₄	—	191	1	no	—
262	C₂²×C₄	—	191	1	no	—
263	C₂²×C₄	—	191	4	no	—
264	C₂²×C₄	—	191	1	no	—
265	C₂²×C₄	—	764	1	no	—
266	C₂²×C₄	—	764	1	no	—
267	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
270	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
271	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	4	1	no	—
277	C₄⋊C₄	—	382	2	no	—
278	C₄⋊C₄	—	382	2	no	—
279	C₄⋊C₄	—	382	2	no	—
280	C₄⋊C₄	—	191	4	no	—
281	C₄⋊C₄	—	191	4	no	—
282	C₄⋊C₄	—	191	4	no	—
283	C₄⋊C₄	—	764	1	no	—
284	C₄⋊C₄	C₄×D₁₉₁	1	4	yes	complemented
285	C₂²⋊C₄	—	382	2	no	—
286	C₂²⋊C₄	—	191	4	no	—
287	C₂²⋊C₄	—	191	4	no	—
288	C₂²⋊C₄	—	191	4	no	—
289	C₄²	—	4	1	no	—
290	C₄²	—	382	2	no	—
291	C₄²	—	382	2	no	—
292	C₄²	—	382	2	no	—
293	C₄²	—	382	2	no	—
294	C₄²	—	764	1	no	—
295	C₂³	—	382	1	no	—
296	C₂³	—	382	1	no	—
297	C₂³	—	382	1	no	—
298	C₂³	—	382	1	no	—
299	C₂³	—	191	2	no	—
300	C₂³	—	191	2	no	—
301	C₂³	—	191	2	no	—
302	C₂³	C₂³×D₁₉₁	1	1	yes	characteristic
303	Q₈	—	382	8	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	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	—	382	8	no	—
321	C₂×C₄	—	382	1	no	—
322	C₂×C₄	—	382	1	no	—
323	C₂×C₄	—	382	1	no	—
324	C₂×C₄	—	382	1	no	—
325	C₂×C₄	—	382	1	no	—
326	C₂×C₄	—	382	1	no	—
327	C₂×C₄	—	382	1	no	—
328	C₂×C₄	—	382	1	no	—
329	C₂×C₄	—	382	1	no	—
330	C₂×C₄	—	382	1	no	—
331	C₂×C₄	—	382	1	no	—
332	C₂×C₄	—	382	1	no	—
333	C₂×C₄	—	382	1	no	—
334	C₂×C₄	—	382	1	no	—
335	C₂×C₄	—	191	2	no	—
336	C₂×C₄	—	191	2	no	—
337	C₂×C₄	—	191	2	no	—
338	C₂×C₄	—	191	2	no	—
339	C₂×C₄	—	191	2	no	—
340	C₂×C₄	—	191	2	no	—
341	C₂×C₄	—	191	2	no	—
342	C₂×C₄	—	764	4	no	—
343	C₂×C₄	—	764	4	no	—
344	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
345	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
346	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
347	C₂×C₄	D₄×D₁₉₁	1	2	yes	—
348	C₂×C₄	Q₈×D₁₉₁	1	2	yes	—
349	C₂²	—	382	2	no	—
350	C₂²	—	382	2	no	—
351	C₂²	—	382	2	no	—
352	C₂²	—	382	2	no	—
353	C₂²	—	382	2	no	—
354	C₂²	—	382	2	no	—
355	C₂²	—	191	4	no	—
356	C₂²	C₂²×C₄×D₁₉₁	1	1	yes	characteristic
357	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
358	C₂²	C₂×Q₈×D₁₉₁	1	1	yes	characteristic
359	C₂²	#41×D₁₉₁	1	1	yes	characteristic
360	C₂²	#41×D₁₉₁	1	1	yes	characteristic
361	C₂²	#20259367	1	1	yes	characteristic
362	C₂²	#20259370	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	382	2	no	—
371	C₄	—	382	2	no	—
372	C₄	—	382	2	no	—
373	C₄	—	382	2	no	—
374	C₄	—	191	4	no	—
375	C₄	—	764	1	no	—
376	C₄	—	764	1	no	—
377	C₂	—	382	4	no	—
378	C₂	C₄×D₄×D₁₉₁	1	1	yes	characteristic
379	C₂	C₄×Q₈×D₁₉₁	1	1	yes	characteristic
380	C₂	#27133144	1	1	yes	characteristic
381	C₂	#27133302	1	1	yes	characteristic
382	C₂	#27133328	1	1	yes	characteristic
383	C₂	#27133345	1	1	yes	characteristic
384	C₂	#27133367	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉₁
commutator	C₂²×C₁₉₁	C₂³×C₄
Fitting	#389×C₁₉₁	C₂
socle, cosocle	C₂³×C₁₉₁	C₂⁴
prime radical	C₂³×D₁₉₁	C₂³
hypercenter	#389	D₁₉₁
hypocenter	C₁₉₁	#2360
LCS	G ▷ C₂²×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂³ ◁ #389

Complements

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

N	H ≅ G/N	type
2. C₂×#20259287	C₂	semidirect
4. #27132567	C₂	semidirect
5. #27132560	C₂	semidirect
6. #27132558	C₂	semidirect
7. #27132549	C₂	semidirect
8. #27132544	C₂	semidirect
11. C₄×Dic₁₉₁⋊C₄	C₂	semidirect
15. #389×C₁₉₁	C₂	semidirect
20. #20259300	C₄	semidirect
57. C₂×Dic₃₈₂	C₂×C₄	semidirect
78. Dic₁₉₁⋊C₄	C₂×C₄	semidirect
79. Dic₁₉₁⋊C₄	C₂×C₄	semidirect
84. (C₂×D₁₉₁)⋊C₄	Q₈	semidirect
100. C₄⋊C₄×C₁₉₁	C₂×C₄	semidirect
169. C₂×D₁₉₁	C₄×Q₈	semidirect
192. C₁₉₁	#2360	semidirect
200. #389	D₁₉₁	semidirect
284. C₄⋊C₄	C₄×D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20259300	2
C₂×#20259287	2
C₂×C₄⋊C₄×D₁₉₁	2
#27132567	2
#27132560	2
#27132558	2
#27132549	2
#27132544	2
#27132534	2
C₄×Dic₁₉₁⋊C₄	2
C₄×(C₂×D₁₉₁)⋊C₄	2
#27132510	2
#389×C₁₉₁	2
#2360	191