Subgroups — C₁₀₁×#22022 #38804173

Order 25856.

706 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#1984	C₂	1	2	yes	maximal
3	C₁₀₁×#1939	C₂	1	2	yes	maximal
4	C₁₀₁×#1917	C₂	1	4	yes	maximal
5	C₁₀₁×#1839	C₂	1	2	yes	maximal
6	C₁₀₁×#1831	C₂	1	2	yes	maximal
7	C₁₀₁×#1767	C₂	1	1	yes	maximal, characteristic
8	C₁₀₁×#1744	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₈×C₁₀₁	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₀₁	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	4	yes	—
14	C₂×#97×C₁₀₁	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₀₁	C₂²	1	2	yes	—
16	C₄×C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₁₀₁	C₄	1	2	yes	—
18	C₄×C₄⋊C₄×C₁₀₁	C₄	1	2	yes	—
19	C₄×C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
21	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₄³×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₄³×C₁₀₁	C₂²	1	2	yes	—
24	#336×C₁₀₁	C₂²	1	2	yes	—
25	#336×C₁₀₁	C₂²	1	4	yes	—
26	#336×C₁₀₁	C₂²	1	4	yes	—
27	#336×C₁₀₁	C₂²	1	4	yes	—
28	#336×C₁₀₁	C₂²	1	1	yes	characteristic
29	#336×C₁₀₁	C₂²	1	1	yes	characteristic
30	#336×C₁₀₁	C₂²	1	2	yes	—
31	C₂²×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
33	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
34	C₂²×C₈×C₁₀₁	C₂³	1	4	yes	—
35	C₄×Q₈×C₁₀₁	—	2	4	no	—
36	C₄×Q₈×C₁₀₁	—	2	4	no	—
37	C₄×Q₈×C₁₀₁	—	2	4	no	—
38	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₁₀₁	—	2	4	no	—
58	C₄⋊C₈×C₁₀₁	—	4	4	no	—
59	#97×C₁₀₁	—	4	2	no	—
60	C₄×C₈×C₁₀₁	—	2	4	no	—
61	#95×C₁₀₁	C₂×C₄	1	2	yes	—
62	#95×C₁₀₁	C₂×C₄	1	2	yes	—
63	#95×C₁₀₁	C₂×C₄	1	2	yes	—
64	C₂×Q₈×C₁₀₁	—	2	2	no	—
65	C₂×Q₈×C₁₀₁	—	2	2	no	—
66	C₂×Q₈×C₁₀₁	M₁₆	1	4	yes	—
67	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
68	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
71	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
73	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
78	C₂×C₈×C₁₀₁	—	2	2	no	—
79	C₂×C₈×C₁₀₁	—	2	2	no	—
80	C₂×C₈×C₁₀₁	—	2	4	no	—
81	C₂×C₈×C₁₀₁	—	2	4	no	—
82	C₂×C₈×C₁₀₁	—	2	2	no	—
83	C₂×C₈×C₁₀₁	—	2	2	no	—
84	C₂×C₈×C₁₀₁	—	2	2	no	—
85	C₂×C₈×C₁₀₁	—	2	2	no	—
86	C₂×C₈×C₁₀₁	—	2	4	no	—
87	C₄⋊C₄×C₁₀₁	—	2	4	no	—
88	C₄⋊C₄×C₁₀₁	—	2	2	no	—
89	C₄⋊C₄×C₁₀₁	—	2	4	no	—
90	C₄⋊C₄×C₁₀₁	—	2	4	no	—
91	C₄⋊C₄×C₁₀₁	—	2	2	no	—
92	C₄⋊C₄×C₁₀₁	M₁₆	1	4	yes	—
93	C₄²×C₁₀₁	—	2	4	no	—
94	C₄²×C₁₀₁	—	2	4	no	—
95	C₄²×C₁₀₁	—	2	2	no	—
96	C₄²×C₁₀₁	—	2	2	no	—
97	C₄²×C₁₀₁	—	2	2	no	—
98	C₄²×C₁₀₁	—	2	2	no	—
99	C₄²×C₁₀₁	—	2	4	no	—
100	C₄²×C₁₀₁	—	2	4	no	—
101	C₄²×C₁₀₁	—	2	4	no	—
102	C₄²×C₁₀₁	—	2	1	no	—
103	C₄²×C₁₀₁	—	2	2	no	—
104	C₄²×C₁₀₁	—	2	2	no	—
105	C₄²×C₁₀₁	—	2	2	no	—
106	C₄²×C₁₀₁	—	2	1	no	—
107	C₄²×C₁₀₁	#41	1	4	yes	—
108	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
109	Q₈×C₁₀₁	—	2	8	no	—
110	C₂×C₄×C₁₀₁	—	2	2	no	—
111	C₂×C₄×C₁₀₁	—	2	1	no	—
112	C₂×C₄×C₁₀₁	—	2	1	no	—
113	C₂×C₄×C₁₀₁	—	2	2	no	—
114	C₂×C₄×C₁₀₁	—	2	1	no	—
115	C₂×C₄×C₁₀₁	—	2	1	no	—
116	C₂×C₄×C₁₀₁	—	2	2	no	—
117	C₂×C₄×C₁₀₁	—	2	1	no	—
118	C₂×C₄×C₁₀₁	—	2	1	no	—
119	C₂×C₄×C₁₀₁	—	2	2	no	—
120	C₂×C₄×C₁₀₁	—	2	2	no	—
121	C₂×C₄×C₁₀₁	—	2	1	no	—
122	C₂×C₄×C₁₀₁	—	2	1	no	—
123	C₂×C₄×C₁₀₁	—	2	2	no	—
124	C₂×C₄×C₁₀₁	—	2	1	no	—
125	C₂×C₄×C₁₀₁	—	2	2	no	—
126	C₂×C₄×C₁₀₁	—	2	1	no	—
127	C₂×C₄×C₁₀₁	—	2	2	no	—
128	C₂×C₄×C₁₀₁	—	2	2	no	—
129	C₂×C₄×C₁₀₁	—	2	1	no	—
130	C₂×C₄×C₁₀₁	—	2	1	no	—
131	C₂×C₄×C₁₀₁	—	2	2	no	—
132	C₂×C₄×C₁₀₁	#117	1	2	yes	—
133	C₂×C₄×C₁₀₁	#117	1	2	yes	—
134	C₂×C₄×C₁₀₁	C₂×M₁₆	1	4	yes	—
135	C₂×C₄×C₁₀₁	C₂×M₁₆	1	4	yes	—
136	C₂×C₄×C₁₀₁	C₂×M₁₆	1	2	yes	—
137	C₂×C₄×C₁₀₁	C₂×M₁₆	1	2	yes	—
138	C₂×C₄×C₁₀₁	#131	1	2	yes	—
139	C₂×C₄×C₁₀₁	#131	1	2	yes	—
140	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
141	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂×C₄×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
143	C₂×C₄×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
144	C₈×C₁₀₁	—	4	2	no	—
145	C₈×C₁₀₁	—	4	2	no	—
146	C₈×C₁₀₁	—	4	4	no	—
147	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
148	C₂²×C₁₀₁	#519	1	1	yes	characteristic
149	C₂²×C₁₀₁	#520	1	1	yes	characteristic
150	C₂²×C₁₀₁	C₂²×M₁₆	1	1	yes	characteristic
151	C₂²×C₁₀₁	C₂²×M₁₆	1	1	yes	characteristic
152	C₂²×C₁₀₁	C₂×#131	1	1	yes	characteristic
153	C₂²×C₁₀₁	C₂×#131	1	1	yes	characteristic
154	C₄×C₁₀₁	—	2	4	no	—
155	C₄×C₁₀₁	—	2	2	no	—
156	C₄×C₁₀₁	—	2	2	no	—
157	C₄×C₁₀₁	—	2	2	no	—
158	C₄×C₁₀₁	—	2	4	no	—
159	C₄×C₁₀₁	—	4	2	no	—
160	C₄×C₁₀₁	—	4	1	no	—
161	C₄×C₁₀₁	—	4	1	no	—
162	C₄×C₁₀₁	—	4	2	no	—
163	C₄×C₁₀₁	#432	1	4	yes	—
164	C₄×C₁₀₁	#541	1	2	yes	—
165	C₄×C₁₀₁	#542	1	2	yes	—
166	#22022	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂×C₁₀₁	#2320	1	1	yes	characteristic
168	C₂×C₁₀₁	C₂×#432	1	1	yes	characteristic
169	C₂×C₁₀₁	#2922	1	1	yes	characteristic
170	C₂×C₁₀₁	#2984	1	1	yes	characteristic
171	C₂×C₁₀₁	#2984	1	1	yes	characteristic
172	C₂×C₁₀₁	#2990	1	1	yes	characteristic
173	C₂×C₁₀₁	#2991	1	1	yes	characteristic
174	C₄²×Q₈	C₂×C₁₀₁	1	1	yes	characteristic
175	#1984	C₂×C₁₀₁	1	2	yes	—
176	#1939	C₂×C₁₀₁	1	2	yes	—
177	#1917	C₂×C₁₀₁	1	4	yes	—
178	#1839	C₂×C₁₀₁	1	2	yes	—
179	#1831	C₂×C₁₀₁	1	2	yes	—
180	#1767	C₂×C₁₀₁	1	1	yes	characteristic
181	#1744	C₂×C₁₀₁	1	1	yes	characteristic
182	C₁₀₁	#22022	1	1	yes	characteristic, direct product factor, Sylow
183	C₂×C₄×Q₈	C₄×C₁₀₁	1	1	yes	characteristic
184	C₂×C₄×Q₈	C₄×C₁₀₁	1	1	yes	characteristic
185	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
186	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	4	yes	—
188	C₂×#97	C₂²×C₁₀₁	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₁₀₁	1	2	yes	—
190	C₄×C₄⋊C₄	C₄×C₁₀₁	1	1	yes	characteristic
191	C₄×C₄⋊C₄	C₄×C₁₀₁	1	2	yes	—
192	C₄×C₄⋊C₄	C₄×C₁₀₁	1	2	yes	—
193	C₄×C₄⋊C₄	C₄×C₁₀₁	1	1	yes	characteristic
194	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
195	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
196	C₄³	C₂²×C₁₀₁	1	2	yes	—
197	C₄³	C₂²×C₁₀₁	1	1	yes	characteristic
198	#336	C₂²×C₁₀₁	1	1	yes	characteristic
199	#336	C₂²×C₁₀₁	1	2	yes	—
200	#336	C₂²×C₁₀₁	1	4	yes	—
201	#336	C₂²×C₁₀₁	1	1	yes	characteristic
202	#336	C₂²×C₁₀₁	1	4	yes	—
203	#336	C₂²×C₁₀₁	1	4	yes	—
204	#336	C₂²×C₁₀₁	1	2	yes	—
205	C₂²×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
206	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
207	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
208	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
209	C₄×Q₈	—	2	4	no	—
210	C₄×Q₈	—	2	4	no	—
211	C₄×Q₈	—	2	4	no	—
212	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
213	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
215	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
219	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
222	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
226	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
227	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
230	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
231	C₄⋊C₈	—	2	4	no	—
232	C₄⋊C₈	—	4	4	no	—
233	#97	—	4	2	no	—
234	C₄×C₈	—	2	4	no	—
235	#95	C₂×C₄×C₁₀₁	1	2	yes	—
236	#95	C₂×C₄×C₁₀₁	1	2	yes	—
237	#95	C₂×C₄×C₁₀₁	1	2	yes	—
238	C₂×Q₈	—	2	2	no	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	M₁₆×C₁₀₁	1	4	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
243	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
244	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
245	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
246	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
251	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	4	no	—
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	M₁₆×C₁₀₁	1	4	yes	—
267	C₄²	—	2	4	no	—
268	C₄²	—	2	4	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	2	no	—
272	C₄²	—	2	2	no	—
273	C₄²	—	2	4	no	—
274	C₄²	—	2	4	no	—
275	C₄²	—	2	4	no	—
276	C₄²	—	2	1	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	2	2	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	2	1	no	—
281	C₄²	#41×C₁₀₁	1	4	yes	—
282	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
283	Q₈	—	2	8	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	#117×C₁₀₁	1	2	yes	—
307	C₂×C₄	#117×C₁₀₁	1	2	yes	—
308	C₂×C₄	C₂×M₁₆×C₁₀₁	1	4	yes	—
309	C₂×C₄	C₂×M₁₆×C₁₀₁	1	4	yes	—
310	C₂×C₄	C₂×M₁₆×C₁₀₁	1	2	yes	—
311	C₂×C₄	C₂×M₁₆×C₁₀₁	1	2	yes	—
312	C₂×C₄	#131×C₁₀₁	1	2	yes	—
313	C₂×C₄	#131×C₁₀₁	1	2	yes	—
314	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
315	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
316	C₂×C₄	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
317	C₂×C₄	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
318	C₈	—	4	2	no	—
319	C₈	—	4	2	no	—
320	C₈	—	4	4	no	—
321	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
322	C₂²	#519×C₁₀₁	1	1	yes	characteristic
323	C₂²	#520×C₁₀₁	1	1	yes	characteristic
324	C₂²	C₂²×M₁₆×C₁₀₁	1	1	yes	characteristic
325	C₂²	C₂²×M₁₆×C₁₀₁	1	1	yes	characteristic
326	C₂²	C₂×#131×C₁₀₁	1	1	yes	characteristic
327	C₂²	C₂×#131×C₁₀₁	1	1	yes	characteristic
328	C₄	—	2	4	no	—
329	C₄	—	2	2	no	—
330	C₄	—	2	2	no	—
331	C₄	—	2	2	no	—
332	C₄	—	2	4	no	—
333	C₄	—	4	2	no	—
334	C₄	—	4	1	no	—
335	C₄	—	4	1	no	—
336	C₄	—	4	2	no	—
337	C₄	#432×C₁₀₁	1	4	yes	—
338	C₄	#541×C₁₀₁	1	2	yes	—
339	C₄	#542×C₁₀₁	1	2	yes	—
340	C₂	C₁₀₁×#2320	1	1	yes	characteristic
341	C₂	C₂×#432×C₁₀₁	1	1	yes	characteristic
342	C₂	C₁₀₁×#2922	1	1	yes	characteristic
343	C₂	C₁₀₁×#2984	1	1	yes	characteristic
344	C₂	C₁₀₁×#2984	1	1	yes	characteristic
345	C₂	C₁₀₁×#2990	1	1	yes	characteristic
346	C₂	C₁₀₁×#2991	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
166. #22022	C₁₀₁	direct (N × H)
182. C₁₀₁	#22022	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×Q₈×C₁₀₁	2
C₁₀₁×#1984	2
C₁₀₁×#1939	2
C₁₀₁×#1917	2
C₁₀₁×#1839	2
C₁₀₁×#1831	2
C₁₀₁×#1767	2
C₁₀₁×#1744	2
#22022	101

Subgroups — C101×#22022 #38804173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#22022 #38804173