Subgroups — C₁₀₁×#14682 #38796833

Order 25856.

2430 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#382×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×#380×C₁₀₁	C₂	1	2	yes	maximal
4	C₁₀₁×C₄⋊#95	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1434	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×C₂²⋊#95	C₂	1	4	yes	maximal
7	C₂⁴×C₄×C₁₀₁	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	4	yes	—
10	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
11	C₂²×C₄²×C₁₀₁	—	2	8	no	—
12	C₂²×C₄²×C₁₀₁	C₄	1	8	yes	complemented
13	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
16	#382×C₁₀₁	—	2	8	no	—
17	#380×C₁₀₁	—	2	8	no	—
18	C₂×#95×C₁₀₁	C₂²	1	8	yes	—
19	C₂×#95×C₁₀₁	C₂²	1	8	yes	—
20	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
21	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
22	C₂³×C₄×C₁₀₁	—	2	8	no	—
23	C₂³×C₄×C₁₀₁	—	2	8	no	—
24	C₂³×C₄×C₁₀₁	—	2	4	no	—
25	C₂³×C₄×C₁₀₁	—	2	8	no	—
26	C₂³×C₄×C₁₀₁	—	2	4	no	—
27	C₂³×C₄×C₁₀₁	C₂×C₄	1	8	yes	—
28	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
29	C₂³×C₄×C₁₀₁	D₄	1	4	yes	—
30	C₂³×C₄×C₁₀₁	Q₈	1	4	yes	—
31	C₂³×C₄×C₁₀₁	C₂³	1	8	yes	—
32	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
37	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
38	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
39	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
40	C₂×C₂²⋊C₄×C₁₀₁	—	2	16	no	—
41	C₂×C₄²×C₁₀₁	—	2	8	no	—
42	C₂×C₄²×C₁₀₁	—	2	4	no	—
43	C₂×C₄²×C₁₀₁	—	2	32	no	—
44	C₂×C₄²×C₁₀₁	C₂×C₄	1	8	yes	—
45	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₁₀₁	D₄	1	8	yes	—
48	#95×C₁₀₁	—	2	8	no	—
49	#95×C₁₀₁	—	2	16	no	—
50	#95×C₁₀₁	—	2	16	no	—
51	C₂⁴×C₁₀₁	—	2	2	no	—
52	C₂⁴×C₁₀₁	—	2	2	no	—
53	C₂⁴×C₁₀₁	—	2	4	no	—
54	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
55	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
56	C₂⁴×C₁₀₁	C₂×Q₈	1	2	yes	—
57	C₂⁴×C₁₀₁	#41	1	8	yes	—
58	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
59	C₂²×C₄×C₁₀₁	—	2	64	no	—
60	C₂²×C₄×C₁₀₁	—	2	16	no	—
61	C₂²×C₄×C₁₀₁	—	2	2	no	—
62	C₂²×C₄×C₁₀₁	—	2	4	no	—
63	C₂²×C₄×C₁₀₁	—	2	2	no	—
64	C₂²×C₄×C₁₀₁	—	2	4	no	—
65	C₂²×C₄×C₁₀₁	—	2	4	no	—
66	C₂²×C₄×C₁₀₁	—	2	4	no	—
67	C₂²×C₄×C₁₀₁	—	2	16	no	—
68	C₂²×C₄×C₁₀₁	—	2	8	no	—
69	C₂²×C₄×C₁₀₁	—	2	16	no	—
70	C₂²×C₄×C₁₀₁	—	2	8	no	—
71	C₂²×C₄×C₁₀₁	—	2	16	no	—
72	C₂²×C₄×C₁₀₁	—	2	16	no	—
73	C₂²×C₄×C₁₀₁	—	2	8	no	—
74	C₂²×C₄×C₁₀₁	—	2	8	no	—
75	C₂²×C₄×C₁₀₁	—	2	16	no	—
76	C₂²×C₄×C₁₀₁	—	2	16	no	—
77	C₂²×C₄×C₁₀₁	—	2	8	no	—
78	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	16	yes	—
79	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₀₁	C₂×D₄	1	8	yes	—
84	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₁₀₁	#41	1	8	yes	—
90	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
91	C₄⋊C₄×C₁₀₁	—	4	16	no	—
92	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
93	C₄²×C₁₀₁	—	2	16	no	—
94	C₄²×C₁₀₁	—	2	8	no	—
95	C₄²×C₁₀₁	C₂²⋊C₄	1	16	yes	complemented
96	C₂³×C₁₀₁	—	2	2	no	—
97	C₂³×C₁₀₁	—	2	2	no	—
98	C₂³×C₁₀₁	—	2	4	no	—
99	C₂³×C₁₀₁	—	2	4	no	—
100	C₂³×C₁₀₁	—	2	4	no	—
101	C₂³×C₁₀₁	—	2	16	no	—
102	C₂³×C₁₀₁	—	2	16	no	—
103	C₂³×C₁₀₁	—	2	4	no	—
104	C₂³×C₁₀₁	—	2	4	no	—
105	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
106	C₂³×C₁₀₁	#117	1	8	yes	—
107	C₂³×C₁₀₁	#124	1	8	yes	—
108	C₂³×C₁₀₁	#125	1	8	yes	—
109	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
110	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
111	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
112	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
113	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
114	C₂³×C₁₀₁	C₂×#41	1	4	yes	—
115	C₂³×C₁₀₁	C₂×#41	1	4	yes	—
116	C₂×C₄×C₁₀₁	—	2	64	no	—
117	C₂×C₄×C₁₀₁	—	2	2	no	—
118	C₂×C₄×C₁₀₁	—	2	4	no	—
119	C₂×C₄×C₁₀₁	—	2	2	no	—
120	C₂×C₄×C₁₀₁	—	2	4	no	—
121	C₂×C₄×C₁₀₁	—	2	4	no	—
122	C₂×C₄×C₁₀₁	—	2	4	no	—
123	C₂×C₄×C₁₀₁	—	2	4	no	—
124	C₂×C₄×C₁₀₁	—	2	4	no	—
125	C₂×C₄×C₁₀₁	—	2	16	no	—
126	C₂×C₄×C₁₀₁	—	2	16	no	—
127	C₂×C₄×C₁₀₁	—	2	32	no	—
128	C₂×C₄×C₁₀₁	—	4	8	no	—
129	C₂×C₄×C₁₀₁	—	4	16	no	—
130	C₂×C₄×C₁₀₁	—	4	8	no	—
131	C₂×C₄×C₁₀₁	—	4	16	no	—
132	C₂×C₄×C₁₀₁	—	4	8	no	—
133	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	8	yes	—
134	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
136	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₁₀₁	#117	1	8	yes	—
138	C₂×C₄×C₁₀₁	#117	1	4	yes	—
139	C₂×C₄×C₁₀₁	#121	1	8	yes	—
140	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	8	yes	—
141	C₂²×C₁₀₁	—	2	16	no	—
142	C₂²×C₁₀₁	—	2	16	no	—
143	C₂²×C₁₀₁	—	2	4	no	—
144	C₂²×C₁₀₁	—	2	8	no	—
145	C₂²×C₁₀₁	—	2	8	no	—
146	C₂²×C₁₀₁	—	2	4	no	—
147	C₂²×C₁₀₁	#382	1	8	yes	complemented
148	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₁₀₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
151	C₂²×C₁₀₁	C₂×#117	1	2	yes	—
152	C₂²×C₁₀₁	C₂×#117	1	2	yes	—
153	C₂²×C₁₀₁	C₂×#121	1	2	yes	—
154	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	2	yes	—
155	C₂²×C₁₀₁	#525	1	8	yes	—
156	C₂²×C₁₀₁	C₂×#124	1	2	yes	—
157	C₂²×C₁₀₁	C₂×#125	1	2	yes	—
158	C₂²×C₁₀₁	#529	1	8	yes	—
159	C₂²×C₁₀₁	#532	1	2	yes	—
160	C₂²×C₁₀₁	#533	1	2	yes	—
161	C₄×C₁₀₁	—	2	4	no	—
162	C₄×C₁₀₁	—	2	8	no	—
163	C₄×C₁₀₁	—	2	8	no	—
164	C₄×C₁₀₁	—	8	8	no	—
165	C₄×C₁₀₁	#380	1	8	yes	—
166	#14682	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂×C₁₀₁	—	2	8	no	—
168	C₂×C₁₀₁	C₂×#380	1	1	yes	characteristic
169	C₂×C₁₀₁	#2280	1	2	yes	—
170	C₂×C₁₀₁	C₂×#382	1	1	yes	characteristic
171	C₂×C₁₀₁	#2283	1	2	yes	—
172	C₂×C₁₀₁	#2285	1	1	yes	characteristic
173	C₂×C₁₀₁	#2850	1	4	yes	—
174	C₂×C₁₀₁	#2851	1	4	yes	—
175	C₂³×C₄²	C₂×C₁₀₁	1	1	yes	characteristic
176	C₂×#382	C₂×C₁₀₁	1	2	yes	complemented
177	C₂×#380	C₂×C₁₀₁	1	2	yes	—
178	C₄⋊#95	C₂×C₁₀₁	1	2	yes	complemented
179	#1434	C₂×C₁₀₁	1	4	yes	complemented
180	C₂²⋊#95	C₂×C₁₀₁	1	4	yes	—
181	C₁₀₁	#14682	1	1	yes	characteristic, direct product factor, Sylow
182	C₂⁴×C₄	C₂²×C₁₀₁	1	2	yes	—
183	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	4	yes	—
185	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
186	C₂²×C₄²	—	2	8	no	—
187	C₂²×C₄²	C₄×C₁₀₁	1	8	yes	complemented
188	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
189	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
190	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
191	#382	—	2	8	no	—
192	#380	—	2	8	no	—
193	C₂×#95	C₂²×C₁₀₁	1	8	yes	—
194	C₂×#95	C₂²×C₁₀₁	1	8	yes	—
195	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
196	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
197	C₂³×C₄	—	2	8	no	—
198	C₂³×C₄	—	2	8	no	—
199	C₂³×C₄	—	2	4	no	—
200	C₂³×C₄	—	2	8	no	—
201	C₂³×C₄	—	2	4	no	—
202	C₂³×C₄	C₂×C₄×C₁₀₁	1	8	yes	—
203	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
204	C₂³×C₄	D₄×C₁₀₁	1	4	yes	—
205	C₂³×C₄	Q₈×C₁₀₁	1	4	yes	—
206	C₂³×C₄	C₂³×C₁₀₁	1	8	yes	—
207	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
208	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
209	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
210	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
211	C₂×C₄⋊C₄	—	2	8	no	—
212	C₂×C₄⋊C₄	—	2	8	no	—
213	C₂×C₄⋊C₄	—	2	8	no	—
214	C₂×C₂²⋊C₄	—	2	8	no	—
215	C₂×C₂²⋊C₄	—	2	16	no	—
216	C₂×C₄²	—	2	8	no	—
217	C₂×C₄²	—	2	4	no	—
218	C₂×C₄²	—	2	32	no	—
219	C₂×C₄²	C₂×C₄×C₁₀₁	1	8	yes	—
220	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	—
221	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	—
222	C₂×C₄²	D₄×C₁₀₁	1	8	yes	—
223	#95	—	2	8	no	—
224	#95	—	2	16	no	—
225	#95	—	2	16	no	—
226	C₂⁴	—	2	2	no	—
227	C₂⁴	—	2	2	no	—
228	C₂⁴	—	2	4	no	—
229	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
230	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
231	C₂⁴	C₂×Q₈×C₁₀₁	1	2	yes	—
232	C₂⁴	#41×C₁₀₁	1	8	yes	—
233	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
234	C₂²×C₄	—	2	64	no	—
235	C₂²×C₄	—	2	16	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	16	no	—
243	C₂²×C₄	—	2	8	no	—
244	C₂²×C₄	—	2	16	no	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	16	no	—
247	C₂²×C₄	—	2	16	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	2	16	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	16	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
258	C₂²×C₄	C₂×D₄×C₁₀₁	1	8	yes	—
259	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
260	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
261	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
262	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
263	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
264	C₂²×C₄	#41×C₁₀₁	1	8	yes	—
265	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
266	C₄⋊C₄	—	4	16	no	—
267	C₂²⋊C₄	—	4	16	no	—
268	C₄²	—	2	16	no	—
269	C₄²	—	2	8	no	—
270	C₄²	C₂²⋊C₄×C₁₀₁	1	16	yes	complemented
271	C₂³	—	2	2	no	—
272	C₂³	—	2	2	no	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	4	no	—
275	C₂³	—	2	4	no	—
276	C₂³	—	2	16	no	—
277	C₂³	—	2	16	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	4	no	—
280	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
281	C₂³	#117×C₁₀₁	1	8	yes	—
282	C₂³	#124×C₁₀₁	1	8	yes	—
283	C₂³	#125×C₁₀₁	1	8	yes	—
284	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
285	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
286	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
287	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
288	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
289	C₂³	C₂×#41×C₁₀₁	1	4	yes	—
290	C₂³	C₂×#41×C₁₀₁	1	4	yes	—
291	C₂×C₄	—	2	64	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	16	no	—
301	C₂×C₄	—	2	16	no	—
302	C₂×C₄	—	2	32	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	4	16	no	—
305	C₂×C₄	—	4	8	no	—
306	C₂×C₄	—	4	16	no	—
307	C₂×C₄	—	4	8	no	—
308	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	8	yes	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
310	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
311	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	4	yes	—
312	C₂×C₄	#117×C₁₀₁	1	8	yes	—
313	C₂×C₄	#117×C₁₀₁	1	4	yes	—
314	C₂×C₄	#121×C₁₀₁	1	8	yes	—
315	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	8	yes	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	8	no	—
318	C₂²	—	2	8	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	16	no	—
321	C₂²	—	2	16	no	—
322	C₂²	#382×C₁₀₁	1	8	yes	complemented
323	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
324	C₂²	C₂²×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
325	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
326	C₂²	C₂×#117×C₁₀₁	1	2	yes	—
327	C₂²	C₂×#117×C₁₀₁	1	2	yes	—
328	C₂²	C₂×#121×C₁₀₁	1	2	yes	—
329	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	2	yes	—
330	C₂²	#525×C₁₀₁	1	8	yes	—
331	C₂²	C₂×#124×C₁₀₁	1	2	yes	—
332	C₂²	C₂×#125×C₁₀₁	1	2	yes	—
333	C₂²	#529×C₁₀₁	1	8	yes	—
334	C₂²	#532×C₁₀₁	1	2	yes	—
335	C₂²	#533×C₁₀₁	1	2	yes	—
336	C₄	—	2	4	no	—
337	C₄	—	2	8	no	—
338	C₄	—	2	8	no	—
339	C₄	—	8	8	no	—
340	C₄	#380×C₁₀₁	1	8	yes	—
341	C₂	—	2	8	no	—
342	C₂	C₂×#380×C₁₀₁	1	1	yes	characteristic
343	C₂	C₁₀₁×#2280	1	2	yes	—
344	C₂	C₂×#382×C₁₀₁	1	1	yes	characteristic
345	C₂	C₁₀₁×#2283	1	2	yes	—
346	C₂	C₁₀₁×#2285	1	1	yes	characteristic
347	C₂	C₁₀₁×#2850	1	4	yes	—
348	C₂	C₁₀₁×#2851	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#382×C₁₀₁	C₂	semidirect
4. C₁₀₁×C₄⋊#95	C₂	semidirect
5. C₁₀₁×#1434	C₂	semidirect
12. C₂²×C₄²×C₁₀₁	C₄	semidirect
95. C₄²×C₁₀₁	C₂²⋊C₄	semidirect
147. C₂²×C₁₀₁	#382	semidirect
166. #14682	C₁₀₁	direct (N × H)
176. C₂×#382	C₂×C₁₀₁	semidirect
178. C₄⋊#95	C₂×C₁₀₁	semidirect
179. #1434	C₂×C₁₀₁	semidirect
181. C₁₀₁	#14682	direct (N × H)
187. C₂²×C₄²	C₄×C₁₀₁	semidirect
270. C₄²	C₂²⋊C₄×C₁₀₁	semidirect
322. C₂²	#382×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄²×C₁₀₁	2
C₂×#382×C₁₀₁	2
C₂×#380×C₁₀₁	2
C₁₀₁×C₄⋊#95	2
C₁₀₁×#1434	2
C₁₀₁×C₂²⋊#95	2
#14682	101

Subgroups — C101×#14682 #38796833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#14682 #38796833