Subgroups — C₁₀₁×#17700 #38799851

Order 25856.

1016 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1544	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1543	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1542	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1540	C₂	1	4	yes	maximal, complemented
7	#533×C₁₀₁	C₂²	1	2	yes	—
8	#533×C₁₀₁	C₂²	1	1	yes	characteristic
9	#532×C₁₀₁	C₂²	1	1	yes	characteristic
10	#532×C₁₀₁	C₂²	1	2	yes	—
11	#529×C₁₀₁	—	2	2	no	—
12	#529×C₁₀₁	—	2	2	no	—
13	#529×C₁₀₁	C₄	1	4	yes	—
14	#525×C₁₀₁	—	2	2	no	—
15	#525×C₁₀₁	C₄	1	2	yes	—
16	C₄×#41×C₁₀₁	—	2	2	no	—
17	C₄×#41×C₁₀₁	C₄	1	2	yes	—
18	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
19	#431×C₁₀₁	—	2	2	no	—
20	#431×C₁₀₁	—	2	2	no	—
21	#431×C₁₀₁	C₂²	1	4	yes	—
22	#431×C₁₀₁	C₂²	1	4	yes	—
23	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	4	yes	—
24	C₂×C₂²⋊C₈×C₁₀₁	—	2	2	no	—
25	C₂×C₄×C₈×C₁₀₁	—	2	2	no	—
26	#333×C₁₀₁	C₂²	1	4	yes	complemented
27	#332×C₁₀₁	C₂²	1	8	yes	complemented
28	#331×C₁₀₁	C₂²	1	4	yes	complemented
29	C₂×#41×C₁₀₁	—	2	2	no	—
30	C₂×#41×C₁₀₁	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
33	C₂²×C₈×C₁₀₁	—	2	4	no	—
34	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
35	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
36	#127×C₁₀₁	C₂³	1	1	yes	characteristic
37	#126×C₁₀₁	—	2	4	no	—
38	#125×C₁₀₁	—	2	2	no	—
39	#125×C₁₀₁	C₂×C₄	1	2	yes	—
40	#124×C₁₀₁	—	2	2	no	—
41	#124×C₁₀₁	C₂×C₄	1	2	yes	—
42	#123×C₁₀₁	—	2	4	no	—
43	#123×C₁₀₁	—	2	2	no	—
44	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
45	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
46	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
47	#121×C₁₀₁	—	2	2	no	—
48	#121×C₁₀₁	—	2	2	no	—
49	#121×C₁₀₁	C₂×C₄	1	4	yes	—
50	#120×C₁₀₁	—	2	2	no	—
51	C₄×Q₈×C₁₀₁	—	2	2	no	—
52	C₄×Q₈×C₁₀₁	—	2	2	no	—
53	C₄×Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
54	C₄×D₄×C₁₀₁	—	2	4	no	—
55	C₄×D₄×C₁₀₁	—	2	4	no	—
56	C₄×D₄×C₁₀₁	—	2	4	no	—
57	C₄×D₄×C₁₀₁	—	2	2	no	—
58	C₄×D₄×C₁₀₁	—	2	2	no	—
59	C₄×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
60	#117×C₁₀₁	—	2	2	no	—
61	#117×C₁₀₁	—	2	4	no	—
62	#117×C₁₀₁	—	2	2	no	—
63	#117×C₁₀₁	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₀₁	—	2	2	no	—
65	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
68	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
69	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
70	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₁₀₁	—	2	4	no	—
73	C₄⋊C₈×C₁₀₁	C₂³	1	8	yes	—
74	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
75	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
76	C₄×C₈×C₁₀₁	—	2	4	no	—
77	C₄×C₈×C₁₀₁	—	2	4	no	—
78	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
79	#41×C₁₀₁	—	4	4	no	—
80	#41×C₁₀₁	—	4	8	no	—
81	C₂×Q₈×C₁₀₁	—	2	2	no	—
82	C₂×Q₈×C₁₀₁	C₂²×C₄	1	2	yes	—
83	C₂×D₄×C₁₀₁	—	2	2	no	—
84	C₂×D₄×C₁₀₁	—	2	4	no	—
85	C₂×D₄×C₁₀₁	—	2	2	no	—
86	C₂×D₄×C₁₀₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₀₁	—	2	8	no	—
88	C₂²×C₄×C₁₀₁	—	2	2	no	—
89	C₂²×C₄×C₁₀₁	—	2	4	no	—
90	C₂²×C₄×C₁₀₁	—	4	2	no	—
91	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₀₁	—	2	8	no	—
102	C₂×C₈×C₁₀₁	—	4	8	no	—
103	C₄⋊C₄×C₁₀₁	—	2	4	no	—
104	C₄⋊C₄×C₁₀₁	—	2	4	no	—
105	C₄⋊C₄×C₁₀₁	—	2	4	no	—
106	C₄⋊C₄×C₁₀₁	—	2	2	no	—
107	C₄⋊C₄×C₁₀₁	—	2	2	no	—
108	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
109	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
110	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
111	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
112	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
113	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
114	C₄²×C₁₀₁	—	2	4	no	—
115	C₄²×C₁₀₁	—	2	2	no	—
116	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
117	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
118	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
120	C₄²×C₁₀₁	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
123	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
124	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
125	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
126	C₂³×C₁₀₁	—	2	4	no	—
127	C₂³×C₁₀₁	—	2	2	no	—
128	C₂³×C₁₀₁	—	4	1	no	—
129	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
131	Q₈×C₁₀₁	—	4	2	no	—
132	Q₈×C₁₀₁	—	4	4	no	—
133	D₄×C₁₀₁	—	4	2	no	—
134	D₄×C₁₀₁	—	4	4	no	—
135	D₄×C₁₀₁	—	4	8	no	—
136	D₄×C₁₀₁	—	4	4	no	—
137	C₂×C₄×C₁₀₁	—	2	4	no	—
138	C₂×C₄×C₁₀₁	—	2	4	no	—
139	C₂×C₄×C₁₀₁	—	2	4	no	—
140	C₂×C₄×C₁₀₁	—	2	4	no	—
141	C₂×C₄×C₁₀₁	—	2	2	no	—
142	C₂×C₄×C₁₀₁	—	2	4	no	—
143	C₂×C₄×C₁₀₁	—	2	4	no	—
144	C₂×C₄×C₁₀₁	—	2	2	no	—
145	C₂×C₄×C₁₀₁	—	2	4	no	—
146	C₂×C₄×C₁₀₁	—	4	1	no	—
147	C₂×C₄×C₁₀₁	—	4	2	no	—
148	C₂×C₄×C₁₀₁	—	4	4	no	—
149	C₂×C₄×C₁₀₁	—	4	8	no	—
150	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₀₁	#135	1	8	yes	—
156	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
158	C₈×C₁₀₁	—	4	8	no	—
159	C₂²×C₁₀₁	—	2	2	no	—
160	C₂²×C₁₀₁	—	2	2	no	—
161	C₂²×C₁₀₁	—	2	1	no	—
162	C₂²×C₁₀₁	—	2	2	no	—
163	C₂²×C₁₀₁	—	4	4	no	—
164	C₂²×C₁₀₁	—	4	2	no	—
165	C₂²×C₁₀₁	—	4	4	no	—
166	C₂²×C₁₀₁	#416	1	4	yes	—
167	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₄×C₁₀₁	—	2	2	no	—
169	C₄×C₁₀₁	—	2	1	no	—
170	C₄×C₁₀₁	—	2	2	no	—
171	C₄×C₁₀₁	—	2	2	no	—
172	C₄×C₁₀₁	—	4	2	no	—
173	C₄×C₁₀₁	—	4	4	no	—
174	C₄×C₁₀₁	#413	1	2	yes	—
175	C₄×C₁₀₁	#416	1	4	yes	—
176	C₄×C₁₀₁	C₂×#135	1	4	yes	—
177	#17700	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₁₀₁	—	2	4	no	—
179	C₂×C₁₀₁	—	4	1	no	—
180	C₂×C₁₀₁	—	8	2	no	—
181	C₂×C₁₀₁	C₂×#413	1	1	yes	characteristic
182	C₂×C₁₀₁	C₂×#416	1	2	yes	—
183	#3444	C₂×C₁₀₁	1	1	yes	characteristic
184	C₂×#431	C₂×C₁₀₁	1	2	yes	complemented
185	#1544	C₂×C₁₀₁	1	2	yes	complemented
186	#1543	C₂×C₁₀₁	1	2	yes	complemented
187	#1542	C₂×C₁₀₁	1	4	yes	complemented
188	#1540	C₂×C₁₀₁	1	4	yes	complemented
189	C₁₀₁	#17700	1	1	yes	characteristic, direct product factor, Sylow
190	#533	C₂²×C₁₀₁	1	2	yes	—
191	#533	C₂²×C₁₀₁	1	1	yes	characteristic
192	#532	C₂²×C₁₀₁	1	1	yes	characteristic
193	#532	C₂²×C₁₀₁	1	2	yes	—
194	#529	—	2	2	no	—
195	#529	—	2	2	no	—
196	#529	C₄×C₁₀₁	1	4	yes	—
197	#525	—	2	2	no	—
198	#525	C₄×C₁₀₁	1	2	yes	—
199	C₄×#41	—	2	2	no	—
200	C₄×#41	C₄×C₁₀₁	1	2	yes	—
201	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
202	#431	—	2	2	no	—
203	#431	—	2	2	no	—
204	#431	C₂²×C₁₀₁	1	4	yes	—
205	#431	C₂²×C₁₀₁	1	4	yes	—
206	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	4	yes	—
207	C₂×C₂²⋊C₈	—	2	2	no	—
208	C₂×C₄×C₈	—	2	2	no	—
209	#333	C₂²×C₁₀₁	1	4	yes	complemented
210	#332	C₂²×C₁₀₁	1	8	yes	complemented
211	#331	C₂²×C₁₀₁	1	4	yes	complemented
212	C₂×#41	—	2	2	no	—
213	C₂×#41	C₂×C₄×C₁₀₁	1	2	yes	—
214	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
215	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
216	C₂²×C₈	—	2	4	no	—
217	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
218	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
219	#127	C₂³×C₁₀₁	1	1	yes	characteristic
220	#126	—	2	4	no	—
221	#125	—	2	2	no	—
222	#125	C₂×C₄×C₁₀₁	1	2	yes	—
223	#124	—	2	2	no	—
224	#124	C₂×C₄×C₁₀₁	1	2	yes	—
225	#123	—	2	4	no	—
226	#123	—	2	2	no	—
227	C₂²⋊Q₈	—	2	2	no	—
228	C₂²⋊Q₈	—	2	2	no	—
229	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
230	#121	—	2	2	no	—
231	#121	—	2	2	no	—
232	#121	C₂×C₄×C₁₀₁	1	4	yes	—
233	#120	—	2	2	no	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₄×Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
237	C₄×D₄	—	2	4	no	—
238	C₄×D₄	—	2	4	no	—
239	C₄×D₄	—	2	4	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
243	#117	—	2	2	no	—
244	#117	—	2	4	no	—
245	#117	—	2	2	no	—
246	#117	C₂×C₄×C₁₀₁	1	2	yes	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
249	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
250	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
251	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
252	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
253	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
254	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
255	C₄⋊C₈	—	2	4	no	—
256	C₄⋊C₈	C₂³×C₁₀₁	1	8	yes	—
257	C₂²⋊C₈	—	2	4	no	—
258	C₂²⋊C₈	—	2	4	no	—
259	C₄×C₈	—	2	4	no	—
260	C₄×C₈	—	2	4	no	—
261	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
262	#41	—	4	4	no	—
263	#41	—	4	8	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	C₂²×C₄×C₁₀₁	1	2	yes	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	C₂²×C₄×C₁₀₁	1	2	yes	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
275	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
276	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
277	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
278	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
284	C₂×C₈	—	2	8	no	—
285	C₂×C₈	—	4	8	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	2	4	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
300	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
301	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
302	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
303	C₄²	C₂²×C₄×C₁₀₁	1	2	yes	—
304	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
305	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
306	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
307	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
308	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
309	C₂³	—	2	4	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	4	1	no	—
312	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
313	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
314	Q₈	—	4	2	no	—
315	Q₈	—	4	4	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	4	no	—
318	D₄	—	4	8	no	—
319	D₄	—	4	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
338	C₂×C₄	#135×C₁₀₁	1	8	yes	—
339	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
341	C₈	—	4	8	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	4	4	no	—
349	C₂²	#416×C₁₀₁	1	4	yes	—
350	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	4	no	—
357	C₄	#413×C₁₀₁	1	2	yes	—
358	C₄	#416×C₁₀₁	1	4	yes	—
359	C₄	C₂×#135×C₁₀₁	1	4	yes	—
360	C₂	—	2	4	no	—
361	C₂	—	4	1	no	—
362	C₂	—	8	2	no	—
363	C₂	C₂×#413×C₁₀₁	1	1	yes	characteristic
364	C₂	C₂×#416×C₁₀₁	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₀₁	C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
prime radical	C₁₀₁×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₁₀₁	C₂	semidirect
3. C₁₀₁×#1544	C₂	semidirect
4. C₁₀₁×#1543	C₂	semidirect
5. C₁₀₁×#1542	C₂	semidirect
6. C₁₀₁×#1540	C₂	semidirect
26. #333×C₁₀₁	C₂²	semidirect
27. #332×C₁₀₁	C₂²	semidirect
28. #331×C₁₀₁	C₂²	semidirect
177. #17700	C₁₀₁	direct (N × H)
184. C₂×#431	C₂×C₁₀₁	semidirect
185. #1544	C₂×C₁₀₁	semidirect
186. #1543	C₂×C₁₀₁	semidirect
187. #1542	C₂×C₁₀₁	semidirect
188. #1540	C₂×C₁₀₁	semidirect
189. C₁₀₁	#17700	direct (N × H)
209. #333	C₂²×C₁₀₁	semidirect
210. #332	C₂²×C₁₀₁	semidirect
211. #331	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3444	2
C₂×#431×C₁₀₁	2
C₁₀₁×#1544	2
C₁₀₁×#1543	2
C₁₀₁×#1542	2
C₁₀₁×#1540	2
#17700	101

Subgroups — C101×#17700 #38799851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17700 #38799851