Subgroups — C₁₀₁×#17236 #38799387

Order 25856.

1034 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#1446	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#1446	C₂	1	2	yes	maximal
3	C₁₀₁×#1444	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1443	C₂	1	2	yes	maximal
5	C₁₀₁×#1443	C₂	1	2	yes	maximal
6	C₁₀₁×#1442	C₂	1	2	yes	maximal
7	C₁₀₁×#1442	C₂	1	1	yes	maximal, characteristic
8	C₁₀₁×#1442	C₂	1	2	yes	maximal
9	C₁₀₁×#1441	C₂	1	2	yes	maximal
10	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
16	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
17	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
19	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
20	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
23	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
27	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
28	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
29	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
30	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
31	C₂²×Q₈×C₁₀₁	—	2	4	no	—
32	C₂²×Q₈×C₁₀₁	—	2	2	no	—
33	C₂²×Q₈×C₁₀₁	—	4	2	no	—
34	C₂²×Q₈×C₁₀₁	—	4	1	no	—
35	C₂²×Q₈×C₁₀₁	—	4	1	no	—
36	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
47	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
48	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
49	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
52	#95×C₁₀₁	—	2	4	no	—
53	#95×C₁₀₁	—	2	4	no	—
54	#95×C₁₀₁	—	2	4	no	—
55	#95×C₁₀₁	—	2	2	no	—
56	#95×C₁₀₁	—	4	2	no	—
57	#95×C₁₀₁	—	4	2	no	—
58	#95×C₁₀₁	—	4	1	no	—
59	#95×C₁₀₁	—	4	2	no	—
60	#95×C₁₀₁	—	4	2	no	—
61	#95×C₁₀₁	—	4	2	no	—
62	#95×C₁₀₁	—	4	2	no	—
63	#95×C₁₀₁	—	4	1	no	—
64	#95×C₁₀₁	—	4	2	no	—
65	#95×C₁₀₁	—	4	2	no	—
66	#95×C₁₀₁	—	4	2	no	—
67	#95×C₁₀₁	—	4	2	no	—
68	#95×C₁₀₁	Q₈	1	4	yes	complemented
69	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
70	C₂×Q₈×C₁₀₁	—	4	8	no	—
71	C₂×Q₈×C₁₀₁	—	4	4	no	—
72	C₂×Q₈×C₁₀₁	—	4	8	no	—
73	C₂×Q₈×C₁₀₁	—	4	4	no	—
74	C₂×Q₈×C₁₀₁	—	4	4	no	—
75	C₂²×C₄×C₁₀₁	—	2	2	no	—
76	C₂²×C₄×C₁₀₁	—	2	2	no	—
77	C₂²×C₄×C₁₀₁	—	2	2	no	—
78	C₂²×C₄×C₁₀₁	—	2	2	no	—
79	C₂²×C₄×C₁₀₁	—	2	2	no	—
80	C₂²×C₄×C₁₀₁	—	2	2	no	—
81	C₂²×C₄×C₁₀₁	—	2	2	no	—
82	C₂²×C₄×C₁₀₁	—	2	2	no	—
83	C₂²×C₄×C₁₀₁	—	2	1	no	—
84	C₂²×C₄×C₁₀₁	—	2	2	no	—
85	C₂²×C₄×C₁₀₁	—	2	1	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	—	2	1	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	1	no	—
92	C₂²×C₄×C₁₀₁	—	2	2	no	—
93	C₂²×C₄×C₁₀₁	—	2	2	no	—
94	C₂²×C₄×C₁₀₁	—	2	2	no	—
95	C₂²×C₄×C₁₀₁	—	2	2	no	—
96	C₂²×C₄×C₁₀₁	—	2	1	no	—
97	C₂²×C₄×C₁₀₁	—	2	1	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	2	no	—
100	C₂²×C₄×C₁₀₁	—	2	2	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	2	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	2	2	no	—
108	C₂²×C₄×C₁₀₁	—	2	2	no	—
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	2	no	—
111	C₂²×C₄×C₁₀₁	—	2	2	no	—
112	C₂²×C₄×C₁₀₁	—	2	2	no	—
113	C₂²×C₄×C₁₀₁	—	2	2	no	—
114	C₂²×C₄×C₁₀₁	—	2	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	2	no	—
117	C₂²×C₄×C₁₀₁	—	2	2	no	—
118	C₂²×C₄×C₁₀₁	—	2	2	no	—
119	C₂²×C₄×C₁₀₁	—	2	2	no	—
120	C₂²×C₄×C₁₀₁	—	2	2	no	—
121	C₂²×C₄×C₁₀₁	—	2	2	no	—
122	C₂²×C₄×C₁₀₁	—	2	2	no	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	2	2	no	—
125	C₂²×C₄×C₁₀₁	—	2	2	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
129	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
130	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
131	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
132	C₄⋊C₄×C₁₀₁	—	4	8	no	—
133	C₄⋊C₄×C₁₀₁	—	4	4	no	—
134	C₄⋊C₄×C₁₀₁	—	4	4	no	—
135	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
136	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
137	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
138	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
139	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
140	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
141	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
143	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
144	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
145	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
146	Q₈×C₁₀₁	—	4	16	no	—
147	C₂×C₄×C₁₀₁	—	2	4	no	—
148	C₂×C₄×C₁₀₁	—	2	4	no	—
149	C₂×C₄×C₁₀₁	—	2	2	no	—
150	C₂×C₄×C₁₀₁	—	2	2	no	—
151	C₂×C₄×C₁₀₁	—	2	2	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	4	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	2	no	—
161	C₂×C₄×C₁₀₁	—	4	2	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	2	no	—
167	C₂×C₄×C₁₀₁	—	4	1	no	—
168	C₂×C₄×C₁₀₁	—	4	2	no	—
169	C₂×C₄×C₁₀₁	—	4	1	no	—
170	C₂×C₄×C₁₀₁	—	4	2	no	—
171	C₂×C₄×C₁₀₁	—	4	1	no	—
172	C₂×C₄×C₁₀₁	—	4	1	no	—
173	C₂×C₄×C₁₀₁	—	4	1	no	—
174	C₂×C₄×C₁₀₁	—	4	2	no	—
175	C₂×C₄×C₁₀₁	—	4	2	no	—
176	C₂×C₄×C₁₀₁	—	4	2	no	—
177	C₂×C₄×C₁₀₁	—	4	2	no	—
178	C₂×C₄×C₁₀₁	—	4	2	no	—
179	C₂×C₄×C₁₀₁	—	4	2	no	—
180	C₂×C₄×C₁₀₁	—	4	2	no	—
181	C₂×C₄×C₁₀₁	—	4	2	no	—
182	C₂×C₄×C₁₀₁	—	4	2	no	—
183	C₂×C₄×C₁₀₁	—	4	2	no	—
184	C₂×C₄×C₁₀₁	—	4	2	no	—
185	C₂×C₄×C₁₀₁	—	4	2	no	—
186	C₂×C₄×C₁₀₁	—	4	2	no	—
187	C₂×C₄×C₁₀₁	—	4	2	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	2	no	—
190	C₂×C₄×C₁₀₁	—	4	2	no	—
191	C₂×C₄×C₁₀₁	—	4	2	no	—
192	C₂×C₄×C₁₀₁	—	4	2	no	—
193	C₂×C₄×C₁₀₁	—	4	2	no	—
194	C₂×C₄×C₁₀₁	—	4	2	no	—
195	C₂×C₄×C₁₀₁	—	4	2	no	—
196	C₂×C₄×C₁₀₁	—	4	2	no	—
197	C₂×C₄×C₁₀₁	—	4	2	no	—
198	C₂×C₄×C₁₀₁	—	4	2	no	—
199	C₂×C₄×C₁₀₁	—	4	2	no	—
200	C₂×C₄×C₁₀₁	—	4	2	no	—
201	C₂×C₄×C₁₀₁	—	4	2	no	—
202	C₂×C₄×C₁₀₁	—	4	2	no	—
203	C₂×C₄×C₁₀₁	—	4	2	no	—
204	C₂²×C₁₀₁	#538	1	2	yes	—
205	C₂²×C₁₀₁	#538	1	2	yes	—
206	C₂²×C₁₀₁	#538	1	1	yes	characteristic
207	C₂²×C₁₀₁	#539	1	1	yes	characteristic
208	C₂²×C₁₀₁	#541	1	2	yes	—
209	C₂²×C₁₀₁	#542	1	2	yes	—
210	C₂²×C₁₀₁	#542	1	2	yes	—
211	C₂²×C₁₀₁	#544	1	2	yes	—
212	C₂²×C₁₀₁	#544	1	1	yes	characteristic
213	C₂²×C₁₀₁	#551	1	2	yes	—
214	C₂²×C₁₀₁	#551	1	1	yes	characteristic
215	C₂²×C₁₀₁	#554	1	2	yes	—
216	C₂²×C₁₀₁	#554	1	1	yes	characteristic
217	C₂²×C₁₀₁	#556	1	1	yes	characteristic
218	C₂²×C₁₀₁	#556	1	2	yes	—
219	C₂²×C₁₀₁	#557	1	1	yes	characteristic
220	C₂²×C₁₀₁	#560	1	1	yes	characteristic
221	C₂²×C₁₀₁	H(3,𝔽₄)	1	1	yes	characteristic
222	C₂²×C₁₀₁	#562	1	2	yes	—
223	C₂²×C₁₀₁	#562	1	2	yes	—
224	C₂²×C₁₀₁	#563	1	1	yes	characteristic
225	C₂²×C₁₀₁	#563	1	2	yes	—
226	C₂²×C₁₀₁	#563	1	1	yes	characteristic
227	C₄×C₁₀₁	—	4	2	no	—
228	C₄×C₁₀₁	—	4	4	no	—
229	C₄×C₁₀₁	—	4	2	no	—
230	C₄×C₁₀₁	—	4	2	no	—
231	C₄×C₁₀₁	—	4	4	no	—
232	C₄×C₁₀₁	—	8	2	no	—
233	C₄×C₁₀₁	—	8	2	no	—
234	C₄×C₁₀₁	—	8	2	no	—
235	C₄×C₁₀₁	—	8	2	no	—
236	#17236	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂×C₁₀₁	#2735	1	1	yes	characteristic
238	C₂×C₁₀₁	#2755	1	2	yes	—
239	C₂×C₁₀₁	#2759	1	2	yes	—
240	C₂×C₁₀₁	#2763	1	1	yes	characteristic
241	C₂×C₁₀₁	#2788	1	2	yes	—
242	C₂×C₁₀₁	#2789	1	1	yes	characteristic
243	C₂×C₁₀₁	#2805	1	1	yes	characteristic
244	C₂×C₁₀₁	#2824	1	1	yes	characteristic
245	C₂×C₁₀₁	#2831	1	2	yes	—
246	C₂×C₁₀₁	#2832	1	1	yes	characteristic
247	C₂×C₁₀₁	#2843	1	1	yes	characteristic
248	#1446	C₂×C₁₀₁	1	1	yes	characteristic
249	#1446	C₂×C₁₀₁	1	2	yes	—
250	#1444	C₂×C₁₀₁	1	1	yes	characteristic
251	#1443	C₂×C₁₀₁	1	2	yes	—
252	#1443	C₂×C₁₀₁	1	2	yes	—
253	#1442	C₂×C₁₀₁	1	2	yes	—
254	#1442	C₂×C₁₀₁	1	1	yes	characteristic
255	#1442	C₂×C₁₀₁	1	2	yes	—
256	#1441	C₂×C₁₀₁	1	2	yes	—
257	C₁₀₁	#17236	1	1	yes	characteristic, direct product factor, Sylow
258	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
262	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
263	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
264	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
265	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
266	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
267	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
268	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
269	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
270	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
271	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
272	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
273	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
274	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
275	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
276	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
277	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
278	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
279	C₂²×Q₈	—	2	4	no	—
280	C₂²×Q₈	—	2	2	no	—
281	C₂²×Q₈	—	4	2	no	—
282	C₂²×Q₈	—	4	1	no	—
283	C₂²×Q₈	—	4	1	no	—
284	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
285	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
287	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
288	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
292	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	4	2	no	—
295	C₂×C₄⋊C₄	—	4	2	no	—
296	C₂×C₄⋊C₄	—	4	1	no	—
297	C₂×C₄⋊C₄	—	4	1	no	—
298	C₂×C₄⋊C₄	—	4	2	no	—
299	C₂×C₄⋊C₄	—	4	2	no	—
300	#95	—	2	4	no	—
301	#95	—	2	4	no	—
302	#95	—	2	4	no	—
303	#95	—	2	2	no	—
304	#95	—	4	2	no	—
305	#95	—	4	2	no	—
306	#95	—	4	1	no	—
307	#95	—	4	2	no	—
308	#95	—	4	2	no	—
309	#95	—	4	2	no	—
310	#95	—	4	2	no	—
311	#95	—	4	1	no	—
312	#95	—	4	2	no	—
313	#95	—	4	2	no	—
314	#95	—	4	2	no	—
315	#95	—	4	2	no	—
316	#95	Q₈×C₁₀₁	1	4	yes	complemented
317	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
318	C₂×Q₈	—	4	8	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×Q₈	—	4	8	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
376	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
377	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
378	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
379	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
380	C₄⋊C₄	—	4	8	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
384	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
385	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
386	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
387	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
388	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
389	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
390	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
391	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
392	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
393	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
394	Q₈	—	4	16	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂²	#538×C₁₀₁	1	2	yes	—
453	C₂²	#538×C₁₀₁	1	1	yes	characteristic
454	C₂²	#538×C₁₀₁	1	2	yes	—
455	C₂²	#539×C₁₀₁	1	1	yes	characteristic
456	C₂²	#541×C₁₀₁	1	2	yes	—
457	C₂²	#542×C₁₀₁	1	2	yes	—
458	C₂²	#542×C₁₀₁	1	2	yes	—
459	C₂²	#544×C₁₀₁	1	2	yes	—
460	C₂²	#544×C₁₀₁	1	1	yes	characteristic
461	C₂²	#551×C₁₀₁	1	2	yes	—
462	C₂²	#551×C₁₀₁	1	1	yes	characteristic
463	C₂²	#554×C₁₀₁	1	2	yes	—
464	C₂²	#554×C₁₀₁	1	1	yes	characteristic
465	C₂²	#556×C₁₀₁	1	1	yes	characteristic
466	C₂²	#556×C₁₀₁	1	2	yes	—
467	C₂²	#557×C₁₀₁	1	1	yes	characteristic
468	C₂²	#560×C₁₀₁	1	1	yes	characteristic
469	C₂²	H(3,𝔽₄)×C₁₀₁	1	1	yes	characteristic
470	C₂²	#562×C₁₀₁	1	2	yes	—
471	C₂²	#562×C₁₀₁	1	2	yes	—
472	C₂²	#563×C₁₀₁	1	2	yes	—
473	C₂²	#563×C₁₀₁	1	1	yes	characteristic
474	C₂²	#563×C₁₀₁	1	1	yes	characteristic
475	C₄	—	4	4	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	2	no	—
482	C₄	—	8	2	no	—
483	C₄	—	8	2	no	—
484	C₂	C₁₀₁×#2735	1	1	yes	characteristic
485	C₂	C₁₀₁×#2755	1	2	yes	—
486	C₂	C₁₀₁×#2759	1	2	yes	—
487	C₂	C₁₀₁×#2763	1	1	yes	characteristic
488	C₂	C₁₀₁×#2788	1	2	yes	—
489	C₂	C₁₀₁×#2789	1	1	yes	characteristic
490	C₂	C₁₀₁×#2805	1	1	yes	characteristic
491	C₂	C₁₀₁×#2824	1	1	yes	characteristic
492	C₂	C₁₀₁×#2831	1	2	yes	—
493	C₂	C₁₀₁×#2832	1	1	yes	characteristic
494	C₂	C₁₀₁×#2843	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
68. #95×C₁₀₁	Q₈	semidirect
236. #17236	C₁₀₁	direct (N × H)
257. C₁₀₁	#17236	direct (N × H)
316. #95	Q₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#1446	2
C₁₀₁×#1444	2
C₁₀₁×#1443	2
C₁₀₁×#1442	2
C₁₀₁×#1441	2
#17236	101

Subgroups — C101×#17236 #38799387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17236 #38799387