Subgroups — C₁₀₁×#17397 #38799548

Order 25856.

1386 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₀₁	C₂	1	2	yes	maximal
3	C₁₀₁×#1472	C₂	1	8	yes	maximal, complemented
4	C₁₀₁×#1463	C₂	1	4	yes	maximal, complemented
5	C₂³×Q₈×C₁₀₁	C₄	1	1	yes	characteristic
6	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₀₁	—	2	2	no	—
8	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
9	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
10	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
11	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
12	C₂×C₂²⋊Q₈×C₁₀₁	C₄	1	4	yes	—
13	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₀₁	C₄	1	2	yes	—
17	#407×C₁₀₁	—	2	2	no	—
18	#407×C₁₀₁	—	2	2	no	—
19	#407×C₁₀₁	C₂²	1	4	yes	—
20	#407×C₁₀₁	C₂²	1	4	yes	—
21	C₂×C₂²⋊C₈×C₁₀₁	—	2	2	no	—
22	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	4	yes	—
23	#324×C₁₀₁	C₂²	1	16	yes	complemented
24	C₂⁵×C₁₀₁	C₂×C₄	1	1	yes	characteristic
25	C₂²×Q₈×C₁₀₁	—	2	2	no	—
26	C₂²×Q₈×C₁₀₁	—	2	1	no	—
27	C₂²×Q₈×C₁₀₁	—	2	1	no	—
28	C₂²×Q₈×C₁₀₁	—	4	4	no	—
29	C₂²×Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
30	C₂³×C₄×C₁₀₁	—	4	4	no	—
31	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
36	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
37	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
38	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
39	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₁₀₁	—	2	4	no	—
42	C₂×M₁₆×C₁₀₁	—	2	4	no	—
43	C₂×M₁₆×C₁₀₁	—	4	8	no	—
44	C₂²×C₈×C₁₀₁	—	2	4	no	—
45	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
46	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
47	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
48	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
49	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
50	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
51	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
52	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
61	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	—
65	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
66	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
67	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
68	C₂²⋊C₈×C₁₀₁	C₂³	1	8	yes	—
69	C₂⁴×C₁₀₁	—	2	4	no	—
70	C₂⁴×C₁₀₁	—	4	2	no	—
71	C₂⁴×C₁₀₁	—	4	2	no	—
72	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
73	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
76	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
77	C₂×Q₈×C₁₀₁	—	2	4	no	—
78	C₂×Q₈×C₁₀₁	—	2	4	no	—
79	C₂×Q₈×C₁₀₁	—	4	8	no	—
80	C₂×Q₈×C₁₀₁	—	4	4	no	—
81	C₂×Q₈×C₁₀₁	—	4	8	no	—
82	C₂×Q₈×C₁₀₁	—	4	4	no	—
83	C₂²×C₄×C₁₀₁	—	2	8	no	—
84	C₂²×C₄×C₁₀₁	—	2	4	no	—
85	C₂²×C₄×C₁₀₁	—	2	2	no	—
86	C₂²×C₄×C₁₀₁	—	2	2	no	—
87	C₂²×C₄×C₁₀₁	—	2	2	no	—
88	C₂²×C₄×C₁₀₁	—	2	2	no	—
89	C₂²×C₄×C₁₀₁	—	4	4	no	—
90	C₂²×C₄×C₁₀₁	—	4	4	no	—
91	C₂²×C₄×C₁₀₁	—	4	4	no	—
92	C₂²×C₄×C₁₀₁	—	4	4	no	—
93	C₂²×C₄×C₁₀₁	—	4	4	no	—
94	C₂²×C₄×C₁₀₁	—	4	2	no	—
95	C₂²×C₄×C₁₀₁	—	4	4	no	—
96	C₂²×C₄×C₁₀₁	—	4	4	no	—
97	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
115	M₁₆×C₁₀₁	—	4	8	no	—
116	M₁₆×C₁₀₁	—	4	8	no	—
117	C₂×C₈×C₁₀₁	—	2	8	no	—
118	C₂×C₈×C₁₀₁	—	4	8	no	—
119	C₄⋊C₄×C₁₀₁	—	2	4	no	—
120	C₄⋊C₄×C₁₀₁	—	2	4	no	—
121	C₄⋊C₄×C₁₀₁	—	2	8	no	—
122	C₄⋊C₄×C₁₀₁	—	2	8	no	—
123	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
124	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
125	C₂³×C₁₀₁	—	2	2	no	—
126	C₂³×C₁₀₁	—	2	2	no	—
127	C₂³×C₁₀₁	—	2	2	no	—
128	C₂³×C₁₀₁	—	2	4	no	—
129	C₂³×C₁₀₁	—	2	4	no	—
130	C₂³×C₁₀₁	—	2	4	no	—
131	C₂³×C₁₀₁	—	2	2	no	—
132	C₂³×C₁₀₁	—	2	4	no	—
133	C₂³×C₁₀₁	—	4	1	no	—
134	C₂³×C₁₀₁	—	4	1	no	—
135	C₂³×C₁₀₁	—	4	2	no	—
136	C₂³×C₁₀₁	—	4	1	no	—
137	C₂³×C₁₀₁	—	4	2	no	—
138	C₂³×C₁₀₁	—	4	1	no	—
139	C₂³×C₁₀₁	—	4	16	no	—
140	C₂³×C₁₀₁	#101	1	4	yes	—
141	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
146	Q₈×C₁₀₁	—	4	8	no	—
147	Q₈×C₁₀₁	—	4	8	no	—
148	C₂×C₄×C₁₀₁	—	2	4	no	—
149	C₂×C₄×C₁₀₁	—	2	2	no	—
150	C₂×C₄×C₁₀₁	—	2	4	no	—
151	C₂×C₄×C₁₀₁	—	2	4	no	—
152	C₂×C₄×C₁₀₁	—	2	4	no	—
153	C₂×C₄×C₁₀₁	—	2	4	no	—
154	C₂×C₄×C₁₀₁	—	2	4	no	—
155	C₂×C₄×C₁₀₁	—	2	4	no	—
156	C₂×C₄×C₁₀₁	—	2	4	no	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	—	2	8	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	2	no	—
161	C₂×C₄×C₁₀₁	—	4	1	no	—
162	C₂×C₄×C₁₀₁	—	4	2	no	—
163	C₂×C₄×C₁₀₁	—	4	2	no	—
164	C₂×C₄×C₁₀₁	—	4	2	no	—
165	C₂×C₄×C₁₀₁	—	4	1	no	—
166	C₂×C₄×C₁₀₁	—	4	4	no	—
167	C₂×C₄×C₁₀₁	—	4	4	no	—
168	C₂×C₄×C₁₀₁	—	4	4	no	—
169	C₂×C₄×C₁₀₁	—	4	4	no	—
170	C₂×C₄×C₁₀₁	—	4	4	no	—
171	C₂×C₄×C₁₀₁	#99	1	4	yes	—
172	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
176	C₈×C₁₀₁	—	4	8	no	—
177	C₂²×C₁₀₁	—	2	8	no	—
178	C₂²×C₁₀₁	—	2	1	no	—
179	C₂²×C₁₀₁	—	2	1	no	—
180	C₂²×C₁₀₁	—	2	2	no	—
181	C₂²×C₁₀₁	—	2	1	no	—
182	C₂²×C₁₀₁	—	2	1	no	—
183	C₂²×C₁₀₁	—	2	2	no	—
184	C₂²×C₁₀₁	—	2	1	no	—
185	C₂²×C₁₀₁	—	2	1	no	—
186	C₂²×C₁₀₁	—	2	2	no	—
187	C₂²×C₁₀₁	—	2	2	no	—
188	C₂²×C₁₀₁	—	2	2	no	—
189	C₂²×C₁₀₁	—	4	4	no	—
190	C₂²×C₁₀₁	—	4	8	no	—
191	C₂²×C₁₀₁	—	4	8	no	—
192	C₂²×C₁₀₁	—	4	4	no	—
193	C₂²×C₁₀₁	C₂×#99	1	2	yes	—
194	C₂²×C₁₀₁	C₂×#101	1	2	yes	—
195	C₂²×C₁₀₁	C₂×#101	1	4	yes	—
196	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₁₀₁	#568	1	2	yes	—
198	C₄×C₁₀₁	—	2	2	no	—
199	C₄×C₁₀₁	—	2	2	no	—
200	C₄×C₁₀₁	—	2	2	no	—
201	C₄×C₁₀₁	—	4	4	no	—
202	C₄×C₁₀₁	—	4	4	no	—
203	C₄×C₁₀₁	C₂×#99	1	4	yes	—
204	#17397	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂×C₁₀₁	—	2	2	no	—
206	C₂×C₁₀₁	—	2	2	no	—
207	C₂×C₁₀₁	—	2	2	no	—
208	C₂×C₁₀₁	—	2	4	no	—
209	C₂×C₁₀₁	—	4	2	no	—
210	C₂×C₁₀₁	#2879	1	1	yes	characteristic
211	C₂×C₁₀₁	C₂²×#99	1	1	yes	characteristic
212	C₂×C₁₀₁	C₂²×#101	1	1	yes	characteristic
213	C₂²×C₂²⋊Q₈	C₂×C₁₀₁	1	1	yes	characteristic
214	C₂×#407	C₂×C₁₀₁	1	2	yes	—
215	#1472	C₂×C₁₀₁	1	8	yes	complemented
216	#1463	C₂×C₁₀₁	1	4	yes	complemented
217	C₁₀₁	#17397	1	1	yes	characteristic, direct product factor, Sylow
218	C₂³×Q₈	C₄×C₁₀₁	1	1	yes	characteristic
219	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
220	C₂²×M₁₆	—	2	2	no	—
221	C₂×C₂²⋊Q₈	—	2	2	no	—
222	C₂×C₂²⋊Q₈	—	2	2	no	—
223	C₂×C₂²⋊Q₈	—	2	2	no	—
224	C₂×C₂²⋊Q₈	—	2	2	no	—
225	C₂×C₂²⋊Q₈	C₄×C₁₀₁	1	4	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	4	yes	—
227	C₂²×C₄⋊C₄	C₄×C₁₀₁	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
229	C₂²×C₂²⋊C₄	C₄×C₁₀₁	1	2	yes	—
230	#407	—	2	2	no	—
231	#407	—	2	2	no	—
232	#407	C₂²×C₁₀₁	1	4	yes	—
233	#407	C₂²×C₁₀₁	1	4	yes	—
234	C₂×C₂²⋊C₈	—	2	2	no	—
235	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	4	yes	—
236	#324	C₂²×C₁₀₁	1	16	yes	complemented
237	C₂⁵	C₂×C₄×C₁₀₁	1	1	yes	characteristic
238	C₂²×Q₈	—	2	2	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×Q₈	—	4	4	no	—
242	C₂²×Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
243	C₂³×C₄	—	4	4	no	—
244	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
245	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
246	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
247	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
248	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
249	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
250	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
251	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
252	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
254	C₂×M₁₆	—	2	4	no	—
255	C₂×M₁₆	—	2	4	no	—
256	C₂×M₁₆	—	4	8	no	—
257	C₂²×C₈	—	2	4	no	—
258	C₂²⋊Q₈	—	2	4	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	—	2	4	no	—
264	C₂²⋊Q₈	—	2	4	no	—
265	C₂²⋊Q₈	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	4	yes	—
274	C₂×C₂²⋊C₄	—	2	4	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	—
278	C₂²⋊C₈	—	2	4	no	—
279	C₂²⋊C₈	—	2	4	no	—
280	C₂²⋊C₈	—	2	4	no	—
281	C₂²⋊C₈	C₂³×C₁₀₁	1	8	yes	—
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	4	2	no	—
284	C₂⁴	—	4	2	no	—
285	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
286	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
287	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
288	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
289	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	4	8	no	—
293	C₂×Q₈	—	4	4	no	—
294	C₂×Q₈	—	4	8	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	4	4	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
311	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
312	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
313	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
314	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
315	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
316	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
318	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
319	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
320	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
328	M₁₆	—	4	8	no	—
329	M₁₆	—	4	8	no	—
330	C₂×C₈	—	2	8	no	—
331	C₂×C₈	—	4	8	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	16	no	—
353	C₂³	#101×C₁₀₁	1	4	yes	—
354	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
355	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
356	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
357	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
358	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
359	Q₈	—	4	8	no	—
360	Q₈	—	4	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	#99×C₁₀₁	1	4	yes	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
386	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
389	C₈	—	4	8	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	8	no	—
404	C₂²	—	4	8	no	—
405	C₂²	—	4	4	no	—
406	C₂²	C₂×#99×C₁₀₁	1	2	yes	—
407	C₂²	C₂×#101×C₁₀₁	1	2	yes	—
408	C₂²	C₂×#101×C₁₀₁	1	4	yes	—
409	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
410	C₂²	#568×C₁₀₁	1	2	yes	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	4	no	—
416	C₄	C₂×#99×C₁₀₁	1	4	yes	—
417	C₂	—	2	2	no	—
418	C₂	—	2	2	no	—
419	C₂	—	2	2	no	—
420	C₂	—	2	4	no	—
421	C₂	—	4	2	no	—
422	C₂	C₁₀₁×#2879	1	1	yes	characteristic
423	C₂	C₂²×#99×C₁₀₁	1	1	yes	characteristic
424	C₂	C₂²×#101×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂⁵×C₁₀₁	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂⁴×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₀₁×#1472	C₂	semidirect
4. C₁₀₁×#1463	C₂	semidirect
23. #324×C₁₀₁	C₂²	semidirect
204. #17397	C₁₀₁	direct (N × H)
215. #1472	C₂×C₁₀₁	semidirect
216. #1463	C₂×C₁₀₁	semidirect
217. C₁₀₁	#17397	direct (N × H)
236. #324	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₁₀₁	2
C₂×#407×C₁₀₁	2
C₁₀₁×#1472	2
C₁₀₁×#1463	2
#17397	101

Subgroups — C101×#17397 #38799548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17397 #38799548