Subgroups — C₁₀₁×#22313 #38804464

Order 25856.

666 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#1985	C₂	1	2	yes	maximal
3	C₁₀₁×#1984	C₂	1	2	yes	maximal
4	C₁₀₁×#1940	C₂	1	2	yes	maximal
5	C₁₀₁×#1917	C₂	1	2	yes	maximal
6	C₁₀₁×#1916	C₂	1	2	yes	maximal
7	C₁₀₁×#1831	C₂	1	1	yes	maximal, characteristic
8	C₁₀₁×#1771	C₂	1	2	yes	maximal
9	C₁₀₁×#1745	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄⋊Q₈×C₁₀₁	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
12	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
15	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×#97×C₁₀₁	C₂²	1	2	yes	—
17	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₀₁	C₂²	1	2	yes	—
19	#391×C₁₀₁	C₄	1	2	yes	—
20	#389×C₁₀₁	C₄	1	2	yes	—
21	#389×C₁₀₁	C₄	1	1	yes	characteristic
22	#389×C₁₀₁	C₄	1	1	yes	characteristic
23	#384×C₁₀₁	C₄	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
27	C₄³×C₁₀₁	C₂²	1	1	yes	characteristic
28	#336×C₁₀₁	C₂²	1	2	yes	—
29	#336×C₁₀₁	C₂²	1	2	yes	—
30	#336×C₁₀₁	C₂²	1	2	yes	—
31	#336×C₁₀₁	C₂²	1	2	yes	—
32	#336×C₁₀₁	C₂²	1	2	yes	—
33	#336×C₁₀₁	C₂²	1	2	yes	—
34	#336×C₁₀₁	C₂²	1	1	yes	characteristic
35	#336×C₁₀₁	C₂²	1	2	yes	—
36	#336×C₁₀₁	C₂²	1	1	yes	characteristic
37	C₂²×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
42	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
43	C₄×Q₈×C₁₀₁	—	4	2	no	—
44	C₄×Q₈×C₁₀₁	—	4	2	no	—
45	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₁₀₁	—	2	4	no	—
64	C₄⋊C₈×C₁₀₁	—	4	2	no	—
65	C₄⋊C₈×C₁₀₁	—	4	2	no	—
66	#97×C₁₀₁	—	2	2	no	—
67	#97×C₁₀₁	—	4	2	no	—
68	#97×C₁₀₁	Q₈	1	4	yes	complemented
69	C₄×C₈×C₁₀₁	—	4	2	no	—
70	#95×C₁₀₁	C₂×C₄	1	2	yes	—
71	#95×C₁₀₁	C₂×C₄	1	2	yes	—
72	#95×C₁₀₁	C₂×C₄	1	2	yes	—
73	#95×C₁₀₁	C₂×C₄	1	2	yes	—
74	C₂×Q₈×C₁₀₁	—	2	4	no	—
75	C₂×Q₈×C₁₀₁	—	2	4	no	—
76	C₂×Q₈×C₁₀₁	—	4	2	no	—
77	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₁₀₁	—	2	2	no	—
89	C₂×C₈×C₁₀₁	—	2	2	no	—
90	C₂×C₈×C₁₀₁	—	2	2	no	—
91	C₂×C₈×C₁₀₁	—	2	2	no	—
92	C₂×C₈×C₁₀₁	—	2	2	no	—
93	C₂×C₈×C₁₀₁	—	2	2	no	—
94	C₂×C₈×C₁₀₁	—	2	2	no	—
95	C₂×C₈×C₁₀₁	—	2	2	no	—
96	C₂×C₈×C₁₀₁	—	2	2	no	—
97	C₂×C₈×C₁₀₁	—	2	2	no	—
98	C₂×C₈×C₁₀₁	—	2	2	no	—
99	C₂×C₈×C₁₀₁	C₂×Q₈	1	4	yes	—
100	C₄⋊C₄×C₁₀₁	—	2	4	no	—
101	C₄⋊C₄×C₁₀₁	—	2	2	no	—
102	C₄⋊C₄×C₁₀₁	—	4	2	no	—
103	C₄⋊C₄×C₁₀₁	—	4	1	no	—
104	C₄⋊C₄×C₁₀₁	—	4	1	no	—
105	C₄⋊C₄×C₁₀₁	—	4	2	no	—
106	C₄⋊C₄×C₁₀₁	—	4	2	no	—
107	C₄⋊C₄×C₁₀₁	—	4	2	no	—
108	C₄⋊C₄×C₁₀₁	M₁₆	1	4	yes	—
109	C₄²×C₁₀₁	—	2	2	no	—
110	C₄²×C₁₀₁	—	2	2	no	—
111	C₄²×C₁₀₁	—	2	2	no	—
112	C₄²×C₁₀₁	—	2	2	no	—
113	C₄²×C₁₀₁	—	2	2	no	—
114	C₄²×C₁₀₁	—	2	2	no	—
115	C₄²×C₁₀₁	—	2	2	no	—
116	C₄²×C₁₀₁	—	2	2	no	—
117	C₄²×C₁₀₁	—	4	1	no	—
118	C₄²×C₁₀₁	—	4	1	no	—
119	C₄²×C₁₀₁	C₂×Q₈	1	2	yes	—
120	C₄²×C₁₀₁	#41	1	2	yes	—
121	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
122	Q₈×C₁₀₁	—	4	8	no	—
123	C₂×C₄×C₁₀₁	—	2	1	no	—
124	C₂×C₄×C₁₀₁	—	2	2	no	—
125	C₂×C₄×C₁₀₁	—	2	1	no	—
126	C₂×C₄×C₁₀₁	—	2	1	no	—
127	C₂×C₄×C₁₀₁	—	2	1	no	—
128	C₂×C₄×C₁₀₁	—	2	1	no	—
129	C₂×C₄×C₁₀₁	—	2	2	no	—
130	C₂×C₄×C₁₀₁	—	2	1	no	—
131	C₂×C₄×C₁₀₁	—	2	1	no	—
132	C₂×C₄×C₁₀₁	—	2	1	no	—
133	C₂×C₄×C₁₀₁	—	2	1	no	—
134	C₂×C₄×C₁₀₁	—	2	2	no	—
135	C₂×C₄×C₁₀₁	—	2	2	no	—
136	C₂×C₄×C₁₀₁	—	2	2	no	—
137	C₂×C₄×C₁₀₁	—	2	1	no	—
138	C₂×C₄×C₁₀₁	—	2	2	no	—
139	C₂×C₄×C₁₀₁	—	2	1	no	—
140	C₂×C₄×C₁₀₁	—	2	2	no	—
141	C₂×C₄×C₁₀₁	—	2	1	no	—
142	C₂×C₄×C₁₀₁	—	2	1	no	—
143	C₂×C₄×C₁₀₁	—	2	1	no	—
144	C₂×C₄×C₁₀₁	—	2	2	no	—
145	C₂×C₄×C₁₀₁	—	2	2	no	—
146	C₂×C₄×C₁₀₁	—	2	2	no	—
147	C₂×C₄×C₁₀₁	—	2	2	no	—
148	C₂×C₄×C₁₀₁	C₄×Q₈	1	2	yes	—
149	C₂×C₄×C₁₀₁	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₁₀₁	C₂×M₁₆	1	2	yes	—
151	C₂×C₄×C₁₀₁	C₂×M₁₆	1	4	yes	—
152	C₂×C₄×C₁₀₁	#131	1	2	yes	—
153	C₂×C₄×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
156	C₂×C₄×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
157	C₈×C₁₀₁	—	2	4	no	—
158	C₈×C₁₀₁	—	4	2	no	—
159	C₈×C₁₀₁	—	4	2	no	—
160	C₈×C₁₀₁	—	4	2	no	—
161	C₂²×C₁₀₁	C₂×C₄×Q₈	1	1	yes	characteristic
162	C₂²×C₁₀₁	#518	1	1	yes	characteristic
163	C₂²×C₁₀₁	#519	1	1	yes	characteristic
164	C₂²×C₁₀₁	C₂²×M₁₆	1	1	yes	characteristic
165	C₂²×C₁₀₁	C₂×#131	1	1	yes	characteristic
166	C₂²×C₁₀₁	#568	1	1	yes	characteristic
167	C₂²×C₁₀₁	#568	1	1	yes	characteristic
168	C₄×C₁₀₁	—	2	2	no	—
169	C₄×C₁₀₁	—	2	2	no	—
170	C₄×C₁₀₁	—	2	4	no	—
171	C₄×C₁₀₁	—	2	2	no	—
172	C₄×C₁₀₁	—	2	2	no	—
173	C₄×C₁₀₁	—	4	2	no	—
174	C₄×C₁₀₁	—	4	1	no	—
175	C₄×C₁₀₁	—	4	2	no	—
176	C₄×C₁₀₁	—	4	2	no	—
177	C₄×C₁₀₁	—	4	1	no	—
178	C₄×C₁₀₁	#542	1	2	yes	—
179	C₄×C₁₀₁	#544	1	2	yes	—
180	#22313	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂×C₁₀₁	#2331	1	1	yes	characteristic
182	C₂×C₁₀₁	#2962	1	1	yes	characteristic
183	C₂×C₁₀₁	Q₈×M₁₆	1	1	yes	characteristic
184	C₂×C₁₀₁	#2974	1	1	yes	characteristic
185	C₂×C₁₀₁	#2980	1	1	yes	characteristic
186	C₂×C₁₀₁	#2983	1	1	yes	characteristic
187	C₂×C₁₀₁	#2985	1	1	yes	characteristic
188	C₄×C₄⋊Q₈	C₂×C₁₀₁	1	1	yes	characteristic
189	#1985	C₂×C₁₀₁	1	2	yes	—
190	#1984	C₂×C₁₀₁	1	2	yes	—
191	#1940	C₂×C₁₀₁	1	2	yes	—
192	#1917	C₂×C₁₀₁	1	2	yes	—
193	#1916	C₂×C₁₀₁	1	2	yes	—
194	#1831	C₂×C₁₀₁	1	1	yes	characteristic
195	#1771	C₂×C₁₀₁	1	2	yes	—
196	#1745	C₂×C₁₀₁	1	1	yes	characteristic
197	C₁₀₁	#22313	1	1	yes	characteristic, direct product factor, Sylow
198	C₂×C₄⋊Q₈	C₄×C₁₀₁	1	1	yes	characteristic
199	C₂×C₄×Q₈	C₂²×C₁₀₁	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
203	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic
204	C₂×#97	C₂²×C₁₀₁	1	2	yes	—
205	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₁₀₁	1	2	yes	—
207	#391	C₄×C₁₀₁	1	2	yes	—
208	#389	C₄×C₁₀₁	1	2	yes	—
209	#389	C₄×C₁₀₁	1	1	yes	characteristic
210	#389	C₄×C₁₀₁	1	1	yes	characteristic
211	#384	C₄×C₁₀₁	1	1	yes	characteristic
212	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
213	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
214	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
215	C₄³	C₂²×C₁₀₁	1	1	yes	characteristic
216	#336	C₂²×C₁₀₁	1	2	yes	—
217	#336	C₂²×C₁₀₁	1	1	yes	characteristic
218	#336	C₂²×C₁₀₁	1	1	yes	characteristic
219	#336	C₂²×C₁₀₁	1	2	yes	—
220	#336	C₂²×C₁₀₁	1	2	yes	—
221	#336	C₂²×C₁₀₁	1	2	yes	—
222	#336	C₂²×C₁₀₁	1	2	yes	—
223	#336	C₂²×C₁₀₁	1	2	yes	—
224	#336	C₂²×C₁₀₁	1	2	yes	—
225	C₂²×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
226	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
228	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
229	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
230	C₄⋊Q₈	—	2	4	no	—
231	C₄×Q₈	—	4	2	no	—
232	C₄×Q₈	—	4	2	no	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
242	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
243	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
248	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
249	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	4	2	no	—
253	C₄⋊C₈	—	4	2	no	—
254	#97	—	2	2	no	—
255	#97	—	4	2	no	—
256	#97	Q₈×C₁₀₁	1	4	yes	complemented
257	C₄×C₈	—	4	2	no	—
258	#95	C₂×C₄×C₁₀₁	1	2	yes	—
259	#95	C₂×C₄×C₁₀₁	1	2	yes	—
260	#95	C₂×C₄×C₁₀₁	1	2	yes	—
261	#95	C₂×C₄×C₁₀₁	1	2	yes	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	4	2	no	—
265	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₂×Q₈×C₁₀₁	1	4	yes	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	—	4	1	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	M₁₆×C₁₀₁	1	4	yes	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	C₂×Q₈×C₁₀₁	1	2	yes	—
308	C₄²	#41×C₁₀₁	1	2	yes	—
309	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
310	Q₈	—	4	8	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	C₄×Q₈×C₁₀₁	1	2	yes	—
337	C₂×C₄	C₄×Q₈×C₁₀₁	1	2	yes	—
338	C₂×C₄	C₂×M₁₆×C₁₀₁	1	2	yes	—
339	C₂×C₄	C₂×M₁₆×C₁₀₁	1	4	yes	—
340	C₂×C₄	#131×C₁₀₁	1	2	yes	—
341	C₂×C₄	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
343	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
344	C₂×C₄	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
345	C₈	—	2	4	no	—
346	C₈	—	4	2	no	—
347	C₈	—	4	2	no	—
348	C₈	—	4	2	no	—
349	C₂²	C₂×C₄×Q₈×C₁₀₁	1	1	yes	characteristic
350	C₂²	#518×C₁₀₁	1	1	yes	characteristic
351	C₂²	#519×C₁₀₁	1	1	yes	characteristic
352	C₂²	C₂²×M₁₆×C₁₀₁	1	1	yes	characteristic
353	C₂²	C₂×#131×C₁₀₁	1	1	yes	characteristic
354	C₂²	#568×C₁₀₁	1	1	yes	characteristic
355	C₂²	#568×C₁₀₁	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	1	no	—
366	C₄	#542×C₁₀₁	1	2	yes	—
367	C₄	#544×C₁₀₁	1	2	yes	—
368	C₂	C₁₀₁×#2331	1	1	yes	characteristic
369	C₂	C₁₀₁×#2962	1	1	yes	characteristic
370	C₂	Q₈×M₁₆×C₁₀₁	1	1	yes	characteristic
371	C₂	C₁₀₁×#2974	1	1	yes	characteristic
372	C₂	C₁₀₁×#2980	1	1	yes	characteristic
373	C₂	C₁₀₁×#2983	1	1	yes	characteristic
374	C₂	C₁₀₁×#2985	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
68. #97×C₁₀₁	Q₈	semidirect
180. #22313	C₁₀₁	direct (N × H)
197. C₁₀₁	#22313	direct (N × H)
256. #97	Q₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊Q₈×C₁₀₁	2
C₁₀₁×#1985	2
C₁₀₁×#1984	2
C₁₀₁×#1940	2
C₁₀₁×#1917	2
C₁₀₁×#1916	2
C₁₀₁×#1831	2
C₁₀₁×#1771	2
C₁₀₁×#1745	2
#22313	101

Subgroups — C101×#22313 #38804464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#22313 #38804464