Subgroups — C₁₀₁×#17526 #38799677

Order 25856.

990 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3483	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1496	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#1489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1488	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1484	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1480	C₂	1	2	yes	maximal, complemented
10	C₁₀₁×#1477	C₂	1	2	yes	maximal, complemented
11	C₁₀₁×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈²×C₁₀₁	C₄	1	1	yes	characteristic
13	#555×C₁₀₁	—	2	1	no	—
14	#555×C₁₀₁	—	2	2	no	—
15	#555×C₁₀₁	C₄	1	2	yes	—
16	#555×C₁₀₁	C₄	1	1	yes	characteristic
17	#550×C₁₀₁	—	2	1	no	—
18	#550×C₁₀₁	C₄	1	1	yes	characteristic
19	#550×C₁₀₁	C₄	1	2	yes	—
20	#550×C₁₀₁	C₄	1	1	yes	characteristic
21	#532×C₁₀₁	—	2	1	no	—
22	#532×C₁₀₁	—	2	2	no	—
23	#532×C₁₀₁	C₂²	1	2	yes	—
24	#532×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₄×#41×C₁₀₁	—	2	1	no	—
26	C₄×#41×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₄×#41×C₁₀₁	C₂²	1	2	yes	—
28	C₄×#41×C₁₀₁	C₂²	1	1	yes	characteristic
29	#446×C₁₀₁	—	2	1	no	—
30	#435×C₁₀₁	—	2	2	no	—
31	C₈×D₄×C₁₀₁	—	2	1	no	—
32	#433×C₁₀₁	—	2	2	no	—
33	#432×C₁₀₁	C₂²	1	2	yes	—
34	#431×C₁₀₁	C₂²	1	1	yes	characteristic
35	#431×C₁₀₁	C₂²	1	2	yes	—
36	#431×C₁₀₁	C₂²	1	2	yes	—
37	#424×C₁₀₁	—	2	1	no	—
38	#423×C₁₀₁	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
40	#408×C₁₀₁	—	2	1	no	—
41	C₄×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
44	Q₈⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
45	Q₈⋊C₈×C₁₀₁	C₂²	1	2	yes	—
46	D₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
47	D₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
48	D₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
49	D₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
50	D₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
51	D₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
52	D₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
53	C₂×#41×C₁₀₁	—	2	1	no	—
54	C₂×#41×C₁₀₁	—	2	2	no	—
55	C₂×#41×C₁₀₁	—	2	1	no	—
56	C₂×#41×C₁₀₁	C₂×C₄	1	1	yes	characteristic
57	C₂×#41×C₁₀₁	C₂×C₄	1	2	yes	—
58	C₂×#41×C₁₀₁	D₄	1	1	yes	characteristic
59	C₂×M₁₆×C₁₀₁	—	2	1	no	—
60	C₂×M₁₆×C₁₀₁	—	2	1	no	—
61	C₂²×C₈×C₁₀₁	—	2	1	no	—
62	C₂²×C₈×C₁₀₁	—	2	2	no	—
63	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
64	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
65	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
66	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
67	#127×C₁₀₁	—	2	1	no	—
68	#127×C₁₀₁	—	2	2	no	—
69	#127×C₁₀₁	C₂×C₄	1	2	yes	—
70	#127×C₁₀₁	C₂×C₄	1	1	yes	characteristic
71	#124×C₁₀₁	—	2	2	no	—
72	#124×C₁₀₁	—	2	2	no	—
73	#124×C₁₀₁	—	2	2	no	—
74	#124×C₁₀₁	—	2	1	no	—
75	#124×C₁₀₁	—	2	2	no	—
76	#121×C₁₀₁	—	2	1	no	—
77	#121×C₁₀₁	—	2	2	no	—
78	#121×C₁₀₁	—	2	1	no	—
79	#121×C₁₀₁	—	2	2	no	—
80	#121×C₁₀₁	—	2	2	no	—
81	#121×C₁₀₁	—	2	1	no	—
82	#121×C₁₀₁	—	2	2	no	—
83	#121×C₁₀₁	—	2	2	no	—
84	#121×C₁₀₁	—	2	2	no	—
85	#121×C₁₀₁	C₂×C₄	1	2	yes	—
86	#121×C₁₀₁	C₂×C₄	1	2	yes	—
87	#121×C₁₀₁	C₂×C₄	1	2	yes	—
88	C₄×Q₈×C₁₀₁	—	2	1	no	—
89	C₄×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
91	C₄×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₀₁	D₄	1	1	yes	characteristic
93	C₄×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₀₁	—	2	2	no	—
95	C₄×D₄×C₁₀₁	—	2	1	no	—
96	C₄×D₄×C₁₀₁	—	2	1	no	—
97	C₄×D₄×C₁₀₁	—	2	2	no	—
98	C₄×D₄×C₁₀₁	—	2	2	no	—
99	C₄×D₄×C₁₀₁	—	2	1	no	—
100	C₄×D₄×C₁₀₁	—	2	1	no	—
101	C₄×D₄×C₁₀₁	—	2	2	no	—
102	C₄×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
103	C₄×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
104	C₄×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
106	C₄×D₄×C₁₀₁	D₄	1	1	yes	characteristic
107	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
108	C₄×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
109	C₄×D₄×C₁₀₁	C₂³	1	2	yes	—
110	#117×C₁₀₁	—	2	2	no	—
111	#117×C₁₀₁	—	2	1	no	—
112	#117×C₁₀₁	—	2	1	no	—
113	#117×C₁₀₁	—	2	2	no	—
114	#117×C₁₀₁	C₂×C₄	1	1	yes	characteristic
115	#117×C₁₀₁	C₂×C₄	1	2	yes	—
116	#117×C₁₀₁	D₄	1	1	yes	characteristic
117	#117×C₁₀₁	D₄	1	2	yes	—
118	C₂×C₄²×C₁₀₁	—	2	1	no	—
119	C₂×C₄²×C₁₀₁	—	2	2	no	—
120	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
122	C₄⋊C₈×C₁₀₁	—	2	2	no	—
123	C₄⋊C₈×C₁₀₁	—	2	1	no	—
124	C₄⋊C₈×C₁₀₁	—	2	2	no	—
125	C₄⋊C₈×C₁₀₁	—	2	2	no	—
126	C₄⋊C₈×C₁₀₁	C₂³	1	1	yes	characteristic
127	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
128	C₄⋊C₈×C₁₀₁	C₂³	1	1	yes	characteristic
129	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
130	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
131	C₂²⋊C₈×C₁₀₁	—	2	1	no	—
132	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
133	#97×C₁₀₁	—	2	1	no	—
134	#97×C₁₀₁	—	2	2	no	—
135	C₄×C₈×C₁₀₁	—	2	1	no	—
136	C₄×C₈×C₁₀₁	—	2	1	no	—
137	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
140	#41×C₁₀₁	—	2	2	no	—
141	#41×C₁₀₁	—	2	4	no	—
142	#41×C₁₀₁	—	4	1	no	—
143	#41×C₁₀₁	—	4	2	no	—
144	#41×C₁₀₁	—	4	2	no	—
145	#41×C₁₀₁	—	4	4	no	—
146	#41×C₁₀₁	—	8	2	no	—
147	#41×C₁₀₁	—	8	1	no	—
148	#41×C₁₀₁	—	8	2	no	—
149	#41×C₁₀₁	—	8	1	no	—
150	C₂×Q₈×C₁₀₁	—	2	1	no	—
151	C₂×Q₈×C₁₀₁	—	2	2	no	—
152	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×D₄×C₁₀₁	—	2	1	no	—
155	C₂×D₄×C₁₀₁	—	2	2	no	—
156	C₂×D₄×C₁₀₁	—	2	2	no	—
157	C₂×D₄×C₁₀₁	—	2	2	no	—
158	C₂×D₄×C₁₀₁	—	2	2	no	—
159	C₂×D₄×C₁₀₁	—	2	2	no	—
160	C₂×D₄×C₁₀₁	—	2	1	no	—
161	C₂×D₄×C₁₀₁	—	2	1	no	—
162	C₂×D₄×C₁₀₁	—	2	2	no	—
163	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
165	C₂×D₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₁₀₁	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₁₀₁	—	2	1	no	—
168	C₂²×C₄×C₁₀₁	—	2	2	no	—
169	C₂²×C₄×C₁₀₁	—	2	2	no	—
170	C₂²×C₄×C₁₀₁	—	2	1	no	—
171	C₂²×C₄×C₁₀₁	—	2	1	no	—
172	C₂²×C₄×C₁₀₁	—	2	2	no	—
173	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
179	M₁₆×C₁₀₁	—	4	2	no	—
180	M₁₆×C₁₀₁	—	8	1	no	—
181	C₂×C₈×C₁₀₁	—	2	1	no	—
182	C₂×C₈×C₁₀₁	—	2	1	no	—
183	C₂×C₈×C₁₀₁	—	2	2	no	—
184	C₂×C₈×C₁₀₁	—	2	1	no	—
185	C₂×C₈×C₁₀₁	—	2	1	no	—
186	C₂×C₈×C₁₀₁	—	2	2	no	—
187	C₂×C₈×C₁₀₁	—	4	2	no	—
188	C₂×C₈×C₁₀₁	—	8	2	no	—
189	C₄⋊C₄×C₁₀₁	—	2	2	no	—
190	C₄⋊C₄×C₁₀₁	—	2	1	no	—
191	C₄⋊C₄×C₁₀₁	—	2	1	no	—
192	C₄⋊C₄×C₁₀₁	—	2	2	no	—
193	C₄⋊C₄×C₁₀₁	—	2	1	no	—
194	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
195	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
197	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
199	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
201	C₂²⋊C₄×C₁₀₁	—	2	1	no	—
202	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
203	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
204	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
205	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
206	C₂²⋊C₄×C₁₀₁	—	2	1	no	—
207	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
208	C₂²⋊C₄×C₁₀₁	—	2	1	no	—
209	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
210	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
211	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
212	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
213	C₄²×C₁₀₁	—	2	1	no	—
214	C₄²×C₁₀₁	—	2	2	no	—
215	C₄²×C₁₀₁	—	2	2	no	—
216	C₄²×C₁₀₁	—	2	1	no	—
217	C₄²×C₁₀₁	—	2	1	no	—
218	C₄²×C₁₀₁	C₂²×C₄	1	2	yes	—
219	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
220	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
222	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
224	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
225	C₂³×C₁₀₁	—	2	2	no	—
226	C₂³×C₁₀₁	—	2	1	no	—
227	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
229	Q₈×C₁₀₁	—	2	1	no	—
230	Q₈×C₁₀₁	—	2	2	no	—
231	Q₈×C₁₀₁	—	8	2	no	—
232	Q₈×C₁₀₁	—	8	1	no	—
233	Q₈×C₁₀₁	#131	1	2	yes	—
234	D₄×C₁₀₁	—	2	1	no	—
235	D₄×C₁₀₁	—	2	2	no	—
236	D₄×C₁₀₁	—	2	1	no	—
237	D₄×C₁₀₁	—	2	2	no	—
238	D₄×C₁₀₁	—	2	2	no	—
239	D₄×C₁₀₁	—	4	2	no	—
240	D₄×C₁₀₁	—	4	2	no	—
241	D₄×C₁₀₁	—	4	4	no	—
242	D₄×C₁₀₁	—	4	4	no	—
243	D₄×C₁₀₁	—	4	2	no	—
244	D₄×C₁₀₁	—	8	2	no	—
245	D₄×C₁₀₁	—	8	1	no	—
246	D₄×C₁₀₁	—	8	2	no	—
247	D₄×C₁₀₁	—	8	2	no	—
248	D₄×C₁₀₁	—	8	2	no	—
249	C₂×C₄×C₁₀₁	—	2	1	no	—
250	C₂×C₄×C₁₀₁	—	2	1	no	—
251	C₂×C₄×C₁₀₁	—	2	2	no	—
252	C₂×C₄×C₁₀₁	—	2	1	no	—
253	C₂×C₄×C₁₀₁	—	2	2	no	—
254	C₂×C₄×C₁₀₁	—	2	2	no	—
255	C₂×C₄×C₁₀₁	—	2	1	no	—
256	C₂×C₄×C₁₀₁	—	2	2	no	—
257	C₂×C₄×C₁₀₁	—	2	1	no	—
258	C₂×C₄×C₁₀₁	—	2	2	no	—
259	C₂×C₄×C₁₀₁	—	2	1	no	—
260	C₂×C₄×C₁₀₁	—	2	2	no	—
261	C₂×C₄×C₁₀₁	—	2	1	no	—
262	C₂×C₄×C₁₀₁	—	4	2	no	—
263	C₂×C₄×C₁₀₁	—	4	2	no	—
264	C₂×C₄×C₁₀₁	—	4	4	no	—
265	C₂×C₄×C₁₀₁	—	4	4	no	—
266	C₂×C₄×C₁₀₁	—	4	1	no	—
267	C₂×C₄×C₁₀₁	—	4	2	no	—
268	C₂×C₄×C₁₀₁	—	4	1	no	—
269	C₂×C₄×C₁₀₁	—	4	2	no	—
270	C₂×C₄×C₁₀₁	—	4	2	no	—
271	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
274	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
280	C₈×C₁₀₁	—	4	1	no	—
281	C₈×C₁₀₁	—	4	1	no	—
282	C₈×C₁₀₁	—	4	2	no	—
283	C₈×C₁₀₁	—	4	1	no	—
284	C₈×C₁₀₁	—	4	2	no	—
285	C₈×C₁₀₁	—	4	1	no	—
286	C₂²×C₁₀₁	—	2	1	no	—
287	C₂²×C₁₀₁	—	2	2	no	—
288	C₂²×C₁₀₁	—	2	2	no	—
289	C₂²×C₁₀₁	—	2	1	no	—
290	C₂²×C₁₀₁	—	2	1	no	—
291	C₂²×C₁₀₁	—	2	2	no	—
292	C₂²×C₁₀₁	—	4	2	no	—
293	C₂²×C₁₀₁	—	4	1	no	—
294	C₂²×C₁₀₁	—	4	2	no	—
295	C₂²×C₁₀₁	—	4	1	no	—
296	C₂²×C₁₀₁	—	4	2	no	—
297	C₂²×C₁₀₁	—	4	1	no	—
298	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
299	C₄×C₁₀₁	—	2	1	no	—
300	C₄×C₁₀₁	—	2	2	no	—
301	C₄×C₁₀₁	—	2	2	no	—
302	C₄×C₁₀₁	—	2	2	no	—
303	C₄×C₁₀₁	—	2	1	no	—
304	C₄×C₁₀₁	—	2	1	no	—
305	C₄×C₁₀₁	—	2	2	no	—
306	C₄×C₁₀₁	—	4	2	no	—
307	C₄×C₁₀₁	—	4	1	no	—
308	C₄×C₁₀₁	—	4	1	no	—
309	C₄×C₁₀₁	#421	1	2	yes	—
310	C₄×C₁₀₁	C₂×#131	1	1	yes	characteristic
311	C₄×C₁₀₁	#568	1	1	yes	characteristic
312	C₄×C₁₀₁	#576	1	1	yes	characteristic
313	C₄×C₁₀₁	#577	1	1	yes	characteristic
314	#17526	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂×C₁₀₁	—	4	1	no	—
316	C₂×C₁₀₁	—	4	2	no	—
317	C₂×C₁₀₁	—	8	2	no	—
318	C₂×C₁₀₁	—	8	1	no	—
319	C₂×C₁₀₁	#2880	1	1	yes	characteristic
320	C₂×C₁₀₁	#2897	1	1	yes	characteristic
321	C₂×C₁₀₁	C₂×#421	1	1	yes	characteristic
322	#3483	C₂×C₁₀₁	1	1	yes	characteristic
323	#2990	C₂×C₁₀₁	1	1	yes	characteristic, complemented
324	#2922	C₂×C₁₀₁	1	1	yes	characteristic, complemented
325	#1496	C₂×C₁₀₁	1	2	yes	complemented
326	#1492	C₂×C₁₀₁	1	1	yes	characteristic, complemented
327	#1489	C₂×C₁₀₁	1	1	yes	characteristic, complemented
328	#1488	C₂×C₁₀₁	1	2	yes	complemented
329	#1484	C₂×C₁₀₁	1	1	yes	characteristic, complemented
330	#1480	C₂×C₁₀₁	1	2	yes	complemented
331	#1477	C₂×C₁₀₁	1	2	yes	complemented
332	#1476	C₂×C₁₀₁	1	1	yes	characteristic, complemented
333	C₁₀₁	#17526	1	1	yes	characteristic, direct product factor, Sylow
334	Q₈²	C₄×C₁₀₁	1	1	yes	characteristic
335	#555	—	2	1	no	—
336	#555	—	2	2	no	—
337	#555	C₄×C₁₀₁	1	2	yes	—
338	#555	C₄×C₁₀₁	1	1	yes	characteristic
339	#550	—	2	1	no	—
340	#550	C₄×C₁₀₁	1	1	yes	characteristic
341	#550	C₄×C₁₀₁	1	2	yes	—
342	#550	C₄×C₁₀₁	1	1	yes	characteristic
343	#532	—	2	1	no	—
344	#532	—	2	2	no	—
345	#532	C₂²×C₁₀₁	1	2	yes	—
346	#532	C₂²×C₁₀₁	1	1	yes	characteristic
347	C₄×#41	—	2	1	no	—
348	C₄×#41	C₂²×C₁₀₁	1	1	yes	characteristic
349	C₄×#41	C₂²×C₁₀₁	1	2	yes	—
350	C₄×#41	C₂²×C₁₀₁	1	1	yes	characteristic
351	#446	—	2	1	no	—
352	#435	—	2	2	no	—
353	C₈×D₄	—	2	1	no	—
354	#433	—	2	2	no	—
355	#432	C₂²×C₁₀₁	1	2	yes	—
356	#431	C₂²×C₁₀₁	1	1	yes	characteristic
357	#431	C₂²×C₁₀₁	1	2	yes	—
358	#431	C₂²×C₁₀₁	1	2	yes	—
359	#424	—	2	1	no	—
360	#423	C₂²×C₁₀₁	1	1	yes	characteristic
361	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
362	#408	—	2	1	no	—
363	C₄×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
364	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
365	Q₈⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
366	Q₈⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
367	Q₈⋊C₈	C₂²×C₁₀₁	1	2	yes	—
368	D₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
369	D₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
370	D₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
371	D₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
372	D₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
373	D₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
374	D₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	1	no	—
378	C₂×#41	C₂×C₄×C₁₀₁	1	1	yes	characteristic
379	C₂×#41	C₂×C₄×C₁₀₁	1	2	yes	—
380	C₂×#41	D₄×C₁₀₁	1	1	yes	characteristic
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	2	2	no	—
385	C₄⋊Q₈	—	2	2	no	—
386	C₄⋊Q₈	—	2	1	no	—
387	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
388	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
389	#127	—	2	1	no	—
390	#127	—	2	2	no	—
391	#127	C₂×C₄×C₁₀₁	1	2	yes	—
392	#127	C₂×C₄×C₁₀₁	1	1	yes	characteristic
393	#124	—	2	2	no	—
394	#124	—	2	2	no	—
395	#124	—	2	2	no	—
396	#124	—	2	1	no	—
397	#124	—	2	2	no	—
398	#121	—	2	1	no	—
399	#121	—	2	2	no	—
400	#121	—	2	1	no	—
401	#121	—	2	2	no	—
402	#121	—	2	2	no	—
403	#121	—	2	1	no	—
404	#121	—	2	2	no	—
405	#121	—	2	2	no	—
406	#121	—	2	2	no	—
407	#121	C₂×C₄×C₁₀₁	1	2	yes	—
408	#121	C₂×C₄×C₁₀₁	1	2	yes	—
409	#121	C₂×C₄×C₁₀₁	1	2	yes	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
412	C₄×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
413	C₄×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
414	C₄×Q₈	D₄×C₁₀₁	1	1	yes	characteristic
415	C₄×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	2	no	—
424	C₄×D₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
425	C₄×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
426	C₄×D₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
427	C₄×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
428	C₄×D₄	D₄×C₁₀₁	1	1	yes	characteristic
429	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
430	C₄×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
431	C₄×D₄	C₂³×C₁₀₁	1	2	yes	—
432	#117	—	2	2	no	—
433	#117	—	2	1	no	—
434	#117	—	2	1	no	—
435	#117	—	2	2	no	—
436	#117	C₂×C₄×C₁₀₁	1	1	yes	characteristic
437	#117	C₂×C₄×C₁₀₁	1	2	yes	—
438	#117	D₄×C₁₀₁	1	1	yes	characteristic
439	#117	D₄×C₁₀₁	1	2	yes	—
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	—	2	2	no	—
442	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
444	C₄⋊C₈	—	2	2	no	—
445	C₄⋊C₈	—	2	1	no	—
446	C₄⋊C₈	—	2	2	no	—
447	C₄⋊C₈	—	2	2	no	—
448	C₄⋊C₈	C₂³×C₁₀₁	1	1	yes	characteristic
449	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
450	C₄⋊C₈	C₂³×C₁₀₁	1	1	yes	characteristic
451	C₂²⋊C₈	—	2	2	no	—
452	C₂²⋊C₈	—	2	2	no	—
453	C₂²⋊C₈	—	2	1	no	—
454	C₂²⋊C₈	—	2	2	no	—
455	#97	—	2	1	no	—
456	#97	—	2	2	no	—
457	C₄×C₈	—	2	1	no	—
458	C₄×C₈	—	2	1	no	—
459	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
460	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
461	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
462	#41	—	2	2	no	—
463	#41	—	2	4	no	—
464	#41	—	4	1	no	—
465	#41	—	4	2	no	—
466	#41	—	4	2	no	—
467	#41	—	4	4	no	—
468	#41	—	8	2	no	—
469	#41	—	8	1	no	—
470	#41	—	8	2	no	—
471	#41	—	8	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
475	C₂×Q₈	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
486	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
487	C₂×D₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
488	C₂×D₄	C₂²×C₄×C₁₀₁	1	2	yes	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
496	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
497	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
498	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
501	M₁₆	—	4	2	no	—
502	M₁₆	—	8	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	4	2	no	—
510	C₂×C₈	—	8	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
517	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
518	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
519	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
533	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
534	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	C₂²×C₄×C₁₀₁	1	2	yes	—
541	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
542	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
543	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
544	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
545	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
546	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
547	C₂³	—	2	2	no	—
548	C₂³	—	2	1	no	—
549	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
550	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
551	Q₈	—	2	2	no	—
552	Q₈	—	2	1	no	—
553	Q₈	—	8	2	no	—
554	Q₈	—	8	1	no	—
555	Q₈	#131×C₁₀₁	1	2	yes	—
556	D₄	—	2	2	no	—
557	D₄	—	2	1	no	—
558	D₄	—	2	2	no	—
559	D₄	—	2	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	4	no	—
564	D₄	—	4	4	no	—
565	D₄	—	4	2	no	—
566	D₄	—	8	2	no	—
567	D₄	—	8	1	no	—
568	D₄	—	8	2	no	—
569	D₄	—	8	2	no	—
570	D₄	—	8	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
594	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
595	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
596	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
597	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
598	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
599	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
600	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
602	C₈	—	4	1	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	2	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	2	no	—
607	C₈	—	4	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	1	no	—
620	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	#421×C₁₀₁	1	2	yes	—
632	C₄	C₂×#131×C₁₀₁	1	1	yes	characteristic
633	C₄	#568×C₁₀₁	1	1	yes	characteristic
634	C₄	#576×C₁₀₁	1	1	yes	characteristic
635	C₄	#577×C₁₀₁	1	1	yes	characteristic
636	C₂	—	4	1	no	—
637	C₂	—	4	2	no	—
638	C₂	—	8	2	no	—
639	C₂	—	8	1	no	—
640	C₂	C₁₀₁×#2880	1	1	yes	characteristic
641	C₂	C₁₀₁×#2897	1	1	yes	characteristic
642	C₂	C₂×#421×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
prime radical	C₁₀₁×#3483	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₁ ◁ C₄×#41×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2990	C₂	semidirect
3. C₁₀₁×#2922	C₂	semidirect
4. C₁₀₁×#1496	C₂	semidirect
5. C₁₀₁×#1492	C₂	semidirect
6. C₁₀₁×#1489	C₂	semidirect
7. C₁₀₁×#1488	C₂	semidirect
8. C₁₀₁×#1484	C₂	semidirect
9. C₁₀₁×#1480	C₂	semidirect
10. C₁₀₁×#1477	C₂	semidirect
11. C₁₀₁×#1476	C₂	semidirect
314. #17526	C₁₀₁	direct (N × H)
323. #2990	C₂×C₁₀₁	semidirect
324. #2922	C₂×C₁₀₁	semidirect
325. #1496	C₂×C₁₀₁	semidirect
326. #1492	C₂×C₁₀₁	semidirect
327. #1489	C₂×C₁₀₁	semidirect
328. #1488	C₂×C₁₀₁	semidirect
329. #1484	C₂×C₁₀₁	semidirect
330. #1480	C₂×C₁₀₁	semidirect
331. #1477	C₂×C₁₀₁	semidirect
332. #1476	C₂×C₁₀₁	semidirect
333. C₁₀₁	#17526	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₁×#3483	2
C₁₀₁×#2990	2
C₁₀₁×#2922	2
C₁₀₁×#1496	2
C₁₀₁×#1492	2
C₁₀₁×#1489	2
C₁₀₁×#1488	2
C₁₀₁×#1484	2
C₁₀₁×#1480	2
C₁₀₁×#1477	2
C₁₀₁×#1476	2
#17526	101

Subgroups — C101×#17526 #38799677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17526 #38799677