Subgroups — C₁₀₁×#11209 #38793360

Order 25856.

842 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#423×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2296	C₂	1	1	yes	maximal, characteristic
3	C₂×#339×C₁₀₁	C₂	1	2	yes	maximal
4	C₂×#339×C₁₀₁	C₂	1	2	yes	maximal
5	C₄×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
7	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
11	#423×C₁₀₁	—	2	4	no	—
12	C₂×C₄⋊C₈×C₁₀₁	—	2	2	no	—
13	#389×C₁₀₁	C₄	1	2	yes	complemented
14	#389×C₁₀₁	C₄	1	2	yes	complemented
15	#385×C₁₀₁	—	2	2	no	—
16	C₄×C₄⋊C₄×C₁₀₁	—	2	2	no	—
17	C₂×#95×C₁₀₁	—	2	2	no	—
18	#339×C₁₀₁	—	2	4	no	—
19	#339×C₁₀₁	—	2	4	no	—
20	C₂³×C₄×C₁₀₁	—	2	2	no	—
21	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
22	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
23	C₂×M₁₆×C₁₀₁	—	2	2	no	—
24	C₂×M₁₆×C₁₀₁	—	2	2	no	—
25	C₂×M₁₆×C₁₀₁	—	2	2	no	—
26	C₂×M₁₆×C₁₀₁	—	2	2	no	—
27	C₂×M₁₆×C₁₀₁	—	2	2	no	—
28	C₂×M₁₆×C₁₀₁	D₄	1	4	yes	—
29	C₂²×C₈×C₁₀₁	—	2	2	no	—
30	#117×C₁₀₁	—	2	1	no	—
31	#117×C₁₀₁	—	2	1	no	—
32	#117×C₁₀₁	—	2	2	no	—
33	#117×C₁₀₁	—	2	2	no	—
34	#117×C₁₀₁	D₄	1	2	yes	—
35	#117×C₁₀₁	Q₈	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
42	C₂×C₄²×C₁₀₁	—	2	2	no	—
43	C₂×C₄²×C₁₀₁	—	2	1	no	—
44	C₂×C₄²×C₁₀₁	—	2	2	no	—
45	C₂×C₄²×C₁₀₁	—	2	2	no	—
46	C₂×C₄²×C₁₀₁	—	2	2	no	—
47	C₂×C₄²×C₁₀₁	—	2	2	no	—
48	C₂×C₄²×C₁₀₁	—	2	2	no	—
49	C₂×C₄²×C₁₀₁	—	2	1	no	—
50	C₂×C₄²×C₁₀₁	—	2	2	no	—
51	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
54	C₂×C₄²×C₁₀₁	Q₈	1	4	yes	—
55	C₄⋊C₈×C₁₀₁	—	2	8	no	—
56	#95×C₁₀₁	—	2	8	no	—
57	#95×C₁₀₁	—	2	2	no	—
58	#95×C₁₀₁	—	2	2	no	—
59	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₀₁	—	2	8	no	—
61	C₂²×C₄×C₁₀₁	—	2	2	no	—
62	C₂²×C₄×C₁₀₁	—	2	4	no	—
63	C₂²×C₄×C₁₀₁	—	2	4	no	—
64	C₂²×C₄×C₁₀₁	—	2	4	no	—
65	C₂²×C₄×C₁₀₁	—	2	2	no	—
66	C₂²×C₄×C₁₀₁	—	4	2	no	—
67	C₂²×C₄×C₁₀₁	—	4	4	no	—
68	C₂²×C₄×C₁₀₁	—	4	2	no	—
69	C₂²×C₄×C₁₀₁	—	4	2	no	—
70	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
75	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
78	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
79	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
81	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
82	M₁₆×C₁₀₁	—	2	4	no	—
83	M₁₆×C₁₀₁	—	2	4	no	—
84	M₁₆×C₁₀₁	—	4	2	no	—
85	M₁₆×C₁₀₁	—	4	2	no	—
86	C₂×C₈×C₁₀₁	—	2	4	no	—
87	C₂×C₈×C₁₀₁	—	4	2	no	—
88	C₂×C₈×C₁₀₁	—	4	2	no	—
89	C₄⋊C₄×C₁₀₁	—	2	2	no	—
90	C₄⋊C₄×C₁₀₁	—	2	4	no	—
91	C₄⋊C₄×C₁₀₁	—	4	4	no	—
92	C₄⋊C₄×C₁₀₁	—	4	4	no	—
93	C₄⋊C₄×C₁₀₁	C₄⋊C₄	1	4	yes	—
94	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
95	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
96	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
97	C₄²×C₁₀₁	—	2	2	no	—
98	C₄²×C₁₀₁	—	2	2	no	—
99	C₄²×C₁₀₁	—	2	2	no	—
100	C₄²×C₁₀₁	—	2	2	no	—
101	C₄²×C₁₀₁	—	2	2	no	—
102	C₄²×C₁₀₁	—	2	2	no	—
103	C₄²×C₁₀₁	—	2	4	no	—
104	C₄²×C₁₀₁	—	2	4	no	—
105	C₄²×C₁₀₁	—	4	1	no	—
106	C₄²×C₁₀₁	—	4	2	no	—
107	C₄²×C₁₀₁	—	4	1	no	—
108	C₄²×C₁₀₁	—	4	2	no	—
109	C₂³×C₁₀₁	—	2	2	no	—
110	C₂³×C₁₀₁	—	2	2	no	—
111	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂³×C₁₀₁	#121	1	1	yes	characteristic
113	C₂³×C₁₀₁	#121	1	2	yes	—
114	C₂³×C₁₀₁	C₂²⋊Q₈	1	1	yes	characteristic
115	C₂³×C₁₀₁	C₂²⋊Q₈	1	2	yes	—
116	C₂×C₄×C₁₀₁	—	2	2	no	—
117	C₂×C₄×C₁₀₁	—	2	2	no	—
118	C₂×C₄×C₁₀₁	—	2	8	no	—
119	C₂×C₄×C₁₀₁	—	2	4	no	—
120	C₂×C₄×C₁₀₁	—	2	2	no	—
121	C₂×C₄×C₁₀₁	—	2	2	no	—
122	C₂×C₄×C₁₀₁	—	2	2	no	—
123	C₂×C₄×C₁₀₁	—	4	8	no	—
124	C₂×C₄×C₁₀₁	—	4	8	no	—
125	C₂×C₄×C₁₀₁	—	4	8	no	—
126	C₂×C₄×C₁₀₁	—	4	4	no	—
127	C₂×C₄×C₁₀₁	—	4	4	no	—
128	C₂×C₄×C₁₀₁	—	4	2	no	—
129	C₂×C₄×C₁₀₁	—	4	2	no	—
130	C₂×C₄×C₁₀₁	—	4	2	no	—
131	C₂×C₄×C₁₀₁	—	4	2	no	—
132	C₂×C₄×C₁₀₁	—	4	2	no	—
133	C₂×C₄×C₁₀₁	#104	1	4	yes	—
134	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
136	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₁₀₁	C₄×Q₈	1	2	yes	—
138	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
139	C₂×C₄×C₁₀₁	#121	1	2	yes	—
140	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
141	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	2	yes	—
142	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₀₁	#123	1	2	yes	—
145	C₂×C₄×C₁₀₁	#123	1	1	yes	characteristic
146	C₂×C₄×C₁₀₁	#124	1	1	yes	characteristic
147	C₂×C₄×C₁₀₁	#125	1	2	yes	—
148	C₂×C₄×C₁₀₁	#125	1	2	yes	—
149	C₂×C₄×C₁₀₁	#126	1	2	yes	—
150	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	2	yes	—
151	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	1	yes	characteristic
152	C₈×C₁₀₁	—	4	4	no	—
153	C₂²×C₁₀₁	—	2	2	no	—
154	C₂²×C₁₀₁	—	2	2	no	—
155	C₂²×C₁₀₁	—	2	4	no	—
156	C₂²×C₁₀₁	—	2	2	no	—
157	C₂²×C₁₀₁	—	2	2	no	—
158	C₂²×C₁₀₁	#380	1	1	yes	characteristic
159	C₂²×C₁₀₁	#386	1	1	yes	characteristic
160	C₂²×C₁₀₁	#391	1	1	yes	characteristic
161	C₂²×C₁₀₁	#396	1	2	yes	—
162	C₂²×C₁₀₁	#398	1	2	yes	—
163	C₂²×C₁₀₁	C₂×#104	1	2	yes	—
164	C₂²×C₁₀₁	#421	1	2	yes	—
165	C₄×C₁₀₁	—	2	4	no	—
166	C₄×C₁₀₁	—	4	8	no	—
167	C₄×C₁₀₁	—	4	4	no	—
168	C₄×C₁₀₁	—	4	2	no	—
169	C₄×C₁₀₁	—	8	2	no	—
170	C₄×C₁₀₁	#387	1	2	yes	—
171	C₄×C₁₀₁	#389	1	2	yes	—
172	C₄×C₁₀₁	#394	1	1	yes	characteristic
173	C₄×C₁₀₁	#395	1	1	yes	characteristic
174	C₄×C₁₀₁	#398	1	1	yes	characteristic
175	C₄×C₁₀₁	#400	1	1	yes	characteristic
176	#11209	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×C₁₀₁	—	2	2	no	—
178	C₂×C₁₀₁	—	2	2	no	—
179	C₂×C₁₀₁	#1441	1	1	yes	characteristic
180	C₂×C₁₀₁	#1806	1	2	yes	—
181	C₂×C₁₀₁	#1871	1	2	yes	—
182	C₂×C₁₀₁	#1994	1	1	yes	characteristic
183	C₂×C₁₀₁	#1995	1	1	yes	characteristic
184	C₂×#423	C₂×C₁₀₁	1	1	yes	characteristic
185	#2296	C₂×C₁₀₁	1	1	yes	characteristic
186	C₂×#339	C₂×C₁₀₁	1	2	yes	—
187	C₂×#339	C₂×C₁₀₁	1	2	yes	—
188	C₄×#95	C₂×C₁₀₁	1	1	yes	characteristic
189	C₁₀₁	#11209	1	1	yes	characteristic, direct product factor, Sylow
190	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
191	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
192	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
193	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
194	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
195	#423	—	2	4	no	—
196	C₂×C₄⋊C₈	—	2	2	no	—
197	#389	C₄×C₁₀₁	1	2	yes	complemented
198	#389	C₄×C₁₀₁	1	2	yes	complemented
199	#385	—	2	2	no	—
200	C₄×C₄⋊C₄	—	2	2	no	—
201	C₂×#95	—	2	2	no	—
202	#339	—	2	4	no	—
203	#339	—	2	4	no	—
204	C₂³×C₄	—	2	2	no	—
205	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
206	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
207	C₂×M₁₆	—	2	2	no	—
208	C₂×M₁₆	—	2	2	no	—
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	—	2	2	no	—
212	C₂×M₁₆	D₄×C₁₀₁	1	4	yes	—
213	C₂²×C₈	—	2	2	no	—
214	#117	—	2	1	no	—
215	#117	—	2	1	no	—
216	#117	—	2	2	no	—
217	#117	—	2	2	no	—
218	#117	D₄×C₁₀₁	1	2	yes	—
219	#117	Q₈×C₁₀₁	1	2	yes	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
224	C₂×C₂²⋊C₄	—	2	1	no	—
225	C₂×C₂²⋊C₄	—	2	1	no	—
226	C₂×C₄²	—	2	1	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
238	C₂×C₄²	Q₈×C₁₀₁	1	4	yes	—
239	C₄⋊C₈	—	2	8	no	—
240	#95	—	2	8	no	—
241	#95	—	2	2	no	—
242	#95	—	2	2	no	—
243	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
244	C₂²×C₄	—	2	8	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	4	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
255	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
260	C₂²×C₄	C₂×Q₈×C₁₀₁	1	1	yes	characteristic
261	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
262	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
263	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
264	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
265	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
266	M₁₆	—	2	4	no	—
267	M₁₆	—	2	4	no	—
268	M₁₆	—	4	2	no	—
269	M₁₆	—	4	2	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	—	4	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	C₄⋊C₄×C₁₀₁	1	4	yes	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	4	2	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	2	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	4	no	—
288	C₄²	—	2	4	no	—
289	C₄²	—	4	1	no	—
290	C₄²	—	4	2	no	—
291	C₄²	—	4	1	no	—
292	C₄²	—	4	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
296	C₂³	#121×C₁₀₁	1	1	yes	characteristic
297	C₂³	#121×C₁₀₁	1	2	yes	—
298	C₂³	C₂²⋊Q₈×C₁₀₁	1	2	yes	—
299	C₂³	C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	4	8	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	8	no	—
310	C₂×C₄	—	4	8	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	#104×C₁₀₁	1	4	yes	—
318	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
319	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
320	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
321	C₂×C₄	C₄×Q₈×C₁₀₁	1	2	yes	—
322	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
323	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
324	C₂×C₄	#121×C₁₀₁	1	2	yes	—
325	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
326	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	2	yes	—
327	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	2	yes	—
328	C₂×C₄	#123×C₁₀₁	1	1	yes	characteristic
329	C₂×C₄	#123×C₁₀₁	1	2	yes	—
330	C₂×C₄	#124×C₁₀₁	1	1	yes	characteristic
331	C₂×C₄	#125×C₁₀₁	1	2	yes	—
332	C₂×C₄	#125×C₁₀₁	1	2	yes	—
333	C₂×C₄	#126×C₁₀₁	1	2	yes	—
334	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	1	yes	characteristic
335	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	2	yes	—
336	C₈	—	4	4	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	4	no	—
342	C₂²	#380×C₁₀₁	1	1	yes	characteristic
343	C₂²	#386×C₁₀₁	1	1	yes	characteristic
344	C₂²	#391×C₁₀₁	1	1	yes	characteristic
345	C₂²	#396×C₁₀₁	1	2	yes	—
346	C₂²	#398×C₁₀₁	1	2	yes	—
347	C₂²	C₂×#104×C₁₀₁	1	2	yes	—
348	C₂²	#421×C₁₀₁	1	2	yes	—
349	C₄	—	2	4	no	—
350	C₄	—	4	8	no	—
351	C₄	—	4	4	no	—
352	C₄	—	4	2	no	—
353	C₄	—	8	2	no	—
354	C₄	#387×C₁₀₁	1	2	yes	—
355	C₄	#389×C₁₀₁	1	2	yes	—
356	C₄	#394×C₁₀₁	1	1	yes	characteristic
357	C₄	#395×C₁₀₁	1	1	yes	characteristic
358	C₄	#398×C₁₀₁	1	1	yes	characteristic
359	C₄	#400×C₁₀₁	1	1	yes	characteristic
360	C₂	—	2	2	no	—
361	C₂	—	2	2	no	—
362	C₂	C₁₀₁×#1441	1	1	yes	characteristic
363	C₂	C₁₀₁×#1806	1	2	yes	—
364	C₂	C₁₀₁×#1871	1	2	yes	—
365	C₂	C₁₀₁×#1994	1	1	yes	characteristic
366	C₂	C₁₀₁×#1995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₀₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₁
socle	C₂³×C₁₀₁	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₀₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
13. #389×C₁₀₁	C₄	semidirect
14. #389×C₁₀₁	C₄	semidirect
176. #11209	C₁₀₁	direct (N × H)
189. C₁₀₁	#11209	direct (N × H)
197. #389	C₄×C₁₀₁	semidirect
198. #389	C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#423×C₁₀₁	2
C₁₀₁×#2296	2
C₂×#339×C₁₀₁	2
C₄×#95×C₁₀₁	2
#11209	101

Subgroups — C101×#11209 #38793360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#11209 #38793360