Subgroups — C₁₀₁×#21302 #38803453

Order 25856.

1170 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1985	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1984	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1729	C₂	1	4	yes	maximal
7	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₀₁	C₂²	1	2	yes	—
9	#533×C₁₀₁	—	2	4	no	—
10	#533×C₁₀₁	—	2	4	no	—
11	C₂×C₄⋊Q₈×C₁₀₁	C₄	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₀₁	C₄	1	1	yes	characteristic
13	C₂×#125×C₁₀₁	C₄	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₁₀₁	C₄	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₁₀₁	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#117×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₀₁	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
23	C₄×M₁₆×C₁₀₁	—	2	4	no	—
24	C₂×#97×C₁₀₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₀₁	C₂²	1	2	yes	—
26	#336×C₁₀₁	C₂²	1	16	yes	—
27	C₂²×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
28	C₂²×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
32	C₂×M₁₆×C₁₀₁	—	2	4	no	—
33	C₂×M₁₆×C₁₀₁	—	2	4	no	—
34	C₂×M₁₆×C₁₀₁	Q₈	1	8	yes	complemented
35	C₂²×C₈×C₁₀₁	—	2	4	no	—
36	C₂²×C₈×C₁₀₁	—	2	8	no	—
37	C₂²×C₈×C₁₀₁	C₂³	1	4	yes	—
38	C₂²×C₈×C₁₀₁	C₂³	1	4	yes	—
39	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
40	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
41	#125×C₁₀₁	—	2	8	no	—
42	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
43	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
44	C₄×Q₈×C₁₀₁	—	2	4	no	—
45	C₄×Q₈×C₁₀₁	—	2	4	no	—
46	C₄×Q₈×C₁₀₁	—	2	4	no	—
47	C₄×Q₈×C₁₀₁	—	2	4	no	—
48	#117×C₁₀₁	—	2	4	no	—
49	#117×C₁₀₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₀₁	D₄	1	4	yes	—
60	C₂×C₄²×C₁₀₁	D₄	1	4	yes	—
61	C₂×C₄²×C₁₀₁	C₂³	1	4	yes	—
62	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₁₀₁	—	2	4	no	—
65	C₄⋊C₈×C₁₀₁	—	2	4	no	—
66	#97×C₁₀₁	—	2	4	no	—
67	C₄×C₈×C₁₀₁	—	2	4	no	—
68	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
69	C₂×Q₈×C₁₀₁	—	2	4	no	—
70	C₂×Q₈×C₁₀₁	—	2	4	no	—
71	C₂×Q₈×C₁₀₁	—	2	8	no	—
72	C₂×Q₈×C₁₀₁	—	4	4	no	—
73	C₂²×C₄×C₁₀₁	—	2	4	no	—
74	C₂²×C₄×C₁₀₁	—	4	2	no	—
75	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
76	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
77	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
87	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
88	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
89	M₁₆×C₁₀₁	—	2	16	no	—
90	C₂×C₈×C₁₀₁	—	2	4	no	—
91	C₂×C₈×C₁₀₁	—	2	4	no	—
92	C₂×C₈×C₁₀₁	—	2	4	no	—
93	C₂×C₈×C₁₀₁	—	2	8	no	—
94	C₂×C₈×C₁₀₁	—	4	8	no	—
95	C₂×C₈×C₁₀₁	C₂×Q₈	1	8	yes	—
96	C₄⋊C₄×C₁₀₁	—	2	4	no	—
97	C₄⋊C₄×C₁₀₁	—	2	4	no	—
98	C₄⋊C₄×C₁₀₁	—	2	8	no	—
99	C₄⋊C₄×C₁₀₁	—	2	8	no	—
100	C₄⋊C₄×C₁₀₁	—	2	4	no	—
101	C₄⋊C₄×C₁₀₁	—	2	4	no	—
102	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
103	C₄²×C₁₀₁	—	2	4	no	—
104	C₄²×C₁₀₁	—	2	4	no	—
105	C₄²×C₁₀₁	C₂²⋊C₄	1	4	yes	—
106	C₄²×C₁₀₁	C₂²⋊C₄	1	4	yes	—
107	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
108	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
109	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
110	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
111	C₂³×C₁₀₁	—	2	2	no	—
112	C₂³×C₁₀₁	—	2	2	no	—
113	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
114	C₂³×C₁₀₁	C₄×Q₈	1	4	yes	—
115	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
116	Q₈×C₁₀₁	—	4	8	no	—
117	Q₈×C₁₀₁	—	4	8	no	—
118	C₂×C₄×C₁₀₁	—	2	2	no	—
119	C₂×C₄×C₁₀₁	—	2	2	no	—
120	C₂×C₄×C₁₀₁	—	2	2	no	—
121	C₂×C₄×C₁₀₁	—	2	8	no	—
122	C₂×C₄×C₁₀₁	—	2	4	no	—
123	C₂×C₄×C₁₀₁	—	2	4	no	—
124	C₂×C₄×C₁₀₁	—	2	8	no	—
125	C₂×C₄×C₁₀₁	—	2	8	no	—
126	C₂×C₄×C₁₀₁	—	4	4	no	—
127	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
128	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
129	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
132	C₂×C₄×C₁₀₁	C₄×Q₈	1	4	yes	—
133	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	8	yes	—
134	C₂×C₄×C₁₀₁	#124	1	4	yes	—
135	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	4	yes	—
136	C₂×C₄×C₁₀₁	#131	1	4	yes	—
137	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₀₁	C₂²×Q₈	1	2	yes	—
140	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
141	C₈×C₁₀₁	—	2	8	no	—
142	C₈×C₁₀₁	—	4	4	no	—
143	C₂²×C₁₀₁	—	2	2	no	—
144	C₂²×C₁₀₁	—	2	2	no	—
145	C₂²×C₁₀₁	—	2	8	no	—
146	C₂²×C₁₀₁	#391	1	4	yes	—
147	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₁₀₁	C₂×C₄×Q₈	1	2	yes	—
149	C₂²×C₁₀₁	C₂×#131	1	2	yes	—
150	C₂²×C₁₀₁	#568	1	2	yes	—
151	C₄×C₁₀₁	—	2	2	no	—
152	C₄×C₁₀₁	—	2	2	no	—
153	C₄×C₁₀₁	—	2	2	no	—
154	C₄×C₁₀₁	—	4	4	no	—
155	C₄×C₁₀₁	—	4	4	no	—
156	C₄×C₁₀₁	#391	1	4	yes	—
157	C₄×C₁₀₁	#408	1	4	yes	—
158	C₄×C₁₀₁	C₂×C₂²⋊Q₈	1	2	yes	—
159	C₄×C₁₀₁	C₂×#124	1	1	yes	characteristic
160	C₄×C₁₀₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
161	#21302	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂×C₁₀₁	—	2	4	no	—
163	C₂×C₁₀₁	C₂×#391	1	1	yes	characteristic
164	C₂×C₁₀₁	C₂×#408	1	1	yes	characteristic
165	C₂×C₁₀₁	#2879	1	1	yes	characteristic
166	C₂×C₁₀₁	#2962	1	4	yes	—
167	C₂×#533	C₂×C₁₀₁	1	1	yes	characteristic
168	C₂²×C₄⋊C₈	C₂×C₁₀₁	1	1	yes	characteristic
169	C₂×C₄×M₁₆	C₂×C₁₀₁	1	1	yes	characteristic
170	#1985	C₂×C₁₀₁	1	4	yes	complemented
171	#1984	C₂×C₁₀₁	1	4	yes	complemented
172	#1729	C₂×C₁₀₁	1	4	yes	—
173	C₁₀₁	#21302	1	1	yes	characteristic, direct product factor, Sylow
174	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
175	C₂³×C₈	C₂²×C₁₀₁	1	2	yes	—
176	#533	—	2	4	no	—
177	#533	—	2	4	no	—
178	C₂×C₄⋊Q₈	C₄×C₁₀₁	1	1	yes	characteristic
179	C₂×C₄⋊Q₈	C₄×C₁₀₁	1	1	yes	characteristic
180	C₂×#125	C₄×C₁₀₁	1	2	yes	—
181	C₂×C₂²⋊Q₈	C₄×C₁₀₁	1	2	yes	—
182	C₂×C₂²⋊Q₈	C₄×C₁₀₁	1	2	yes	—
183	C₂×C₄×Q₈	C₂²×C₁₀₁	1	2	yes	—
184	C₂×C₄×Q₈	C₂²×C₁₀₁	1	2	yes	—
185	C₂×#117	C₂²×C₁₀₁	1	2	yes	—
186	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
187	C₂×C₄⋊C₈	—	2	4	no	—
188	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
190	C₄×M₁₆	—	2	4	no	—
191	C₂×#97	C₂²×C₁₀₁	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₁₀₁	1	2	yes	—
193	#336	C₂²×C₁₀₁	1	16	yes	—
194	C₂²×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
195	C₂²×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
196	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
197	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
198	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
199	C₂×M₁₆	—	2	4	no	—
200	C₂×M₁₆	—	2	4	no	—
201	C₂×M₁₆	Q₈×C₁₀₁	1	8	yes	complemented
202	C₂²×C₈	—	2	4	no	—
203	C₂²×C₈	—	2	8	no	—
204	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
205	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
206	C₄⋊Q₈	—	2	4	no	—
207	C₄⋊Q₈	—	2	4	no	—
208	#125	—	2	8	no	—
209	C₂²⋊Q₈	—	2	8	no	—
210	C₂²⋊Q₈	—	2	8	no	—
211	C₄×Q₈	—	2	4	no	—
212	C₄×Q₈	—	2	4	no	—
213	C₄×Q₈	—	2	4	no	—
214	C₄×Q₈	—	2	4	no	—
215	#117	—	2	4	no	—
216	#117	—	2	4	no	—
217	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
222	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
224	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
226	C₂×C₄²	D₄×C₁₀₁	1	4	yes	—
227	C₂×C₄²	D₄×C₁₀₁	1	4	yes	—
228	C₂×C₄²	C₂³×C₁₀₁	1	4	yes	—
229	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
231	C₄⋊C₈	—	2	4	no	—
232	C₄⋊C₈	—	2	4	no	—
233	#97	—	2	4	no	—
234	C₄×C₈	—	2	4	no	—
235	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
236	C₂×Q₈	—	2	4	no	—
237	C₂×Q₈	—	2	4	no	—
238	C₂×Q₈	—	2	8	no	—
239	C₂×Q₈	—	4	4	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
243	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
244	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
245	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
246	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
247	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
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	C₂×D₄×C₁₀₁	1	2	yes	—
252	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
253	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
254	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
255	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
256	M₁₆	—	2	16	no	—
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	8	no	—
261	C₂×C₈	—	4	8	no	—
262	C₂×C₈	C₂×Q₈×C₁₀₁	1	8	yes	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	8	no	—
266	C₄⋊C₄	—	2	8	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₂²⋊C₄	—	2	8	no	—
270	C₄²	—	2	4	no	—
271	C₄²	—	2	4	no	—
272	C₄²	C₂²⋊C₄×C₁₀₁	1	4	yes	—
273	C₄²	C₂²⋊C₄×C₁₀₁	1	4	yes	—
274	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
275	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
276	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
277	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	2	no	—
280	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
281	C₂³	C₄×Q₈×C₁₀₁	1	4	yes	—
282	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
283	Q₈	—	4	8	no	—
284	Q₈	—	4	8	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	8	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
295	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
296	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
297	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
298	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
299	C₂×C₄	C₄×Q₈×C₁₀₁	1	4	yes	—
300	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	8	yes	—
301	C₂×C₄	#124×C₁₀₁	1	4	yes	—
302	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	4	yes	—
303	C₂×C₄	#131×C₁₀₁	1	4	yes	—
304	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
306	C₂×C₄	C₂²×Q₈×C₁₀₁	1	2	yes	—
307	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
308	C₈	—	2	8	no	—
309	C₈	—	4	4	no	—
310	C₂²	—	2	8	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	2	no	—
313	C₂²	#391×C₁₀₁	1	4	yes	—
314	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
315	C₂²	C₂×C₄×Q₈×C₁₀₁	1	2	yes	—
316	C₂²	C₂×#131×C₁₀₁	1	2	yes	—
317	C₂²	#568×C₁₀₁	1	2	yes	—
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	2	2	no	—
321	C₄	—	4	4	no	—
322	C₄	—	4	4	no	—
323	C₄	#391×C₁₀₁	1	4	yes	—
324	C₄	#408×C₁₀₁	1	4	yes	—
325	C₄	C₂×C₂²⋊Q₈×C₁₀₁	1	2	yes	—
326	C₄	C₂×#124×C₁₀₁	1	1	yes	characteristic
327	C₄	C₂×C₄⋊Q₈×C₁₀₁	1	1	yes	characteristic
328	C₂	—	2	4	no	—
329	C₂	C₂×#391×C₁₀₁	1	1	yes	characteristic
330	C₂	C₂×#408×C₁₀₁	1	1	yes	characteristic
331	C₂	C₁₀₁×#2879	1	1	yes	characteristic
332	C₂	C₁₀₁×#2962	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
socle	C₂³×C₁₀₁	C₂³×C₄
prime radical	C₂⁴×C₁₀₁	C₂²×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
4. C₁₀₁×#1985	C₂	semidirect
5. C₁₀₁×#1984	C₂	semidirect
34. C₂×M₁₆×C₁₀₁	Q₈	semidirect
161. #21302	C₁₀₁	direct (N × H)
170. #1985	C₂×C₁₀₁	semidirect
171. #1984	C₂×C₁₀₁	semidirect
173. C₁₀₁	#21302	direct (N × H)
201. C₂×M₁₆	Q₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₀₁	2
C₂²×C₄⋊C₈×C₁₀₁	2
C₂×C₄×M₁₆×C₁₀₁	2
C₁₀₁×#1985	2
C₁₀₁×#1984	2
C₁₀₁×#1729	2
#21302	101

Subgroups — C101×#21302 #38803453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#21302 #38803453