Subgroups — C₁₀₁×#14321 #38796472

Order 25856.

2174 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#392×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#390×C₁₀₁	C₂	1	3	yes	maximal, complemented
3	C₂×#388×C₁₀₁	C₂	1	3	yes	maximal, complemented
4	C₁₀₁×#1444	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1439	C₂	1	3	yes	maximal, complemented
6	C₁₀₁×#1438	C₂	1	3	yes	maximal, complemented
7	C₄×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₀₁	C₂²	1	3	yes	—
9	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	3	yes	—
11	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	3	yes	—
12	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	3	yes	—
13	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	3	yes	—
14	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	6	yes	—
15	C₂²×C₄²×C₁₀₁	C₂²	1	3	yes	—
16	#392×C₁₀₁	C₄	1	8	yes	complemented
17	#390×C₁₀₁	—	2	12	no	—
18	#388×C₁₀₁	—	2	12	no	—
19	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
20	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂⁵×C₁₀₁	C₂³	1	3	yes	—
24	C₂²×D₄×C₁₀₁	—	2	6	no	—
25	C₂²×D₄×C₁₀₁	—	2	6	no	—
26	C₂²×D₄×C₁₀₁	—	4	6	no	—
27	C₂²×D₄×C₁₀₁	—	4	6	no	—
28	C₂²×D₄×C₁₀₁	C₂×C₄	1	12	yes	—
29	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
30	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
33	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
36	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
37	C₂×C₄⋊C₄×C₁₀₁	—	4	6	no	—
38	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
39	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
40	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
41	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
42	C₂×C₂²⋊C₄×C₁₀₁	—	2	12	no	—
43	C₂×C₂²⋊C₄×C₁₀₁	—	2	12	no	—
44	C₂×C₂²⋊C₄×C₁₀₁	—	4	6	no	—
45	C₂×C₂²⋊C₄×C₁₀₁	—	4	6	no	—
46	C₂×C₂²⋊C₄×C₁₀₁	—	4	6	no	—
47	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	12	yes	—
48	C₂×C₄²×C₁₀₁	—	4	6	no	—
49	C₂×C₄²×C₁₀₁	D₄	1	12	yes	complemented
50	#95×C₁₀₁	—	2	6	no	—
51	#95×C₁₀₁	—	2	6	no	—
52	#95×C₁₀₁	—	2	6	no	—
53	#95×C₁₀₁	C₂×C₄	1	4	yes	—
54	C₂⁴×C₁₀₁	—	2	3	no	—
55	C₂⁴×C₁₀₁	—	2	6	no	—
56	C₂⁴×C₁₀₁	—	2	3	no	—
57	C₂⁴×C₁₀₁	—	2	6	no	—
58	C₂⁴×C₁₀₁	—	2	3	no	—
59	C₂⁴×C₁₀₁	—	2	6	no	—
60	C₂⁴×C₁₀₁	—	2	6	no	—
61	C₂⁴×C₁₀₁	—	2	3	no	—
62	C₂⁴×C₁₀₁	—	2	3	no	—
63	C₂⁴×C₁₀₁	—	2	3	no	—
64	C₂⁴×C₁₀₁	C₂²×C₄	1	6	yes	—
65	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
66	C₂×D₄×C₁₀₁	—	2	24	no	—
67	C₂×D₄×C₁₀₁	—	4	24	no	—
68	C₂×D₄×C₁₀₁	—	4	12	no	—
69	C₂×D₄×C₁₀₁	—	4	12	no	—
70	C₂×D₄×C₁₀₁	—	4	24	no	—
71	C₂²×C₄×C₁₀₁	—	2	3	no	—
72	C₂²×C₄×C₁₀₁	—	2	6	no	—
73	C₂²×C₄×C₁₀₁	—	2	6	no	—
74	C₂²×C₄×C₁₀₁	—	2	1	no	—
75	C₂²×C₄×C₁₀₁	—	2	3	no	—
76	C₂²×C₄×C₁₀₁	—	2	6	no	—
77	C₂²×C₄×C₁₀₁	—	2	3	no	—
78	C₂²×C₄×C₁₀₁	—	2	6	no	—
79	C₂²×C₄×C₁₀₁	—	2	3	no	—
80	C₂²×C₄×C₁₀₁	—	2	3	no	—
81	C₂²×C₄×C₁₀₁	—	2	3	no	—
82	C₂²×C₄×C₁₀₁	—	2	3	no	—
83	C₂²×C₄×C₁₀₁	—	2	6	no	—
84	C₂²×C₄×C₁₀₁	—	2	3	no	—
85	C₂²×C₄×C₁₀₁	—	2	3	no	—
86	C₂²×C₄×C₁₀₁	—	2	6	no	—
87	C₂²×C₄×C₁₀₁	—	2	3	no	—
88	C₂²×C₄×C₁₀₁	—	2	1	no	—
89	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₀₁	C₂²×C₄	1	6	yes	—
91	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
92	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
93	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
94	C₂²×C₄×C₁₀₁	#41	1	6	yes	—
95	C₄⋊C₄×C₁₀₁	—	4	12	no	—
96	C₄⋊C₄×C₁₀₁	—	4	4	no	—
97	C₂²⋊C₄×C₁₀₁	—	2	24	no	—
98	C₂²⋊C₄×C₁₀₁	—	4	12	no	—
99	C₂²⋊C₄×C₁₀₁	—	4	24	no	—
100	C₂²⋊C₄×C₁₀₁	—	4	12	no	—
101	C₄²×C₁₀₁	—	4	12	no	—
102	C₂³×C₁₀₁	—	2	6	no	—
103	C₂³×C₁₀₁	—	2	12	no	—
104	C₂³×C₁₀₁	—	2	6	no	—
105	C₂³×C₁₀₁	—	2	12	no	—
106	C₂³×C₁₀₁	—	2	6	no	—
107	C₂³×C₁₀₁	—	4	3	no	—
108	C₂³×C₁₀₁	—	4	3	no	—
109	C₂³×C₁₀₁	—	4	6	no	—
110	C₂³×C₁₀₁	—	4	3	no	—
111	C₂³×C₁₀₁	—	4	6	no	—
112	C₂³×C₁₀₁	—	4	6	no	—
113	C₂³×C₁₀₁	—	4	6	no	—
114	C₂³×C₁₀₁	—	4	3	no	—
115	C₂³×C₁₀₁	—	4	3	no	—
116	C₂³×C₁₀₁	—	4	3	no	—
117	C₂³×C₁₀₁	—	4	6	no	—
118	C₂³×C₁₀₁	—	4	6	no	—
119	C₂³×C₁₀₁	—	4	6	no	—
120	C₂³×C₁₀₁	—	4	6	no	—
121	C₂³×C₁₀₁	—	4	3	no	—
122	C₂³×C₁₀₁	—	4	6	no	—
123	C₂³×C₁₀₁	—	4	3	no	—
124	C₂³×C₁₀₁	—	4	6	no	—
125	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
126	C₂³×C₁₀₁	C₂²×D₄	1	3	yes	—
127	C₂³×C₁₀₁	C₂×#41	1	3	yes	—
128	C₂³×C₁₀₁	H(5,𝔽₂)	1	3	yes	—
129	C₂³×C₁₀₁	H(5,𝔽₂)	1	3	yes	—
130	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
131	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
132	D₄×C₁₀₁	—	4	48	no	—
133	C₂×C₄×C₁₀₁	—	2	12	no	—
134	C₂×C₄×C₁₀₁	—	2	6	no	—
135	C₂×C₄×C₁₀₁	—	2	6	no	—
136	C₂×C₄×C₁₀₁	—	2	6	no	—
137	C₂×C₄×C₁₀₁	—	2	6	no	—
138	C₂×C₄×C₁₀₁	—	2	12	no	—
139	C₂×C₄×C₁₀₁	—	2	6	no	—
140	C₂×C₄×C₁₀₁	—	2	6	no	—
141	C₂×C₄×C₁₀₁	—	2	6	no	—
142	C₂×C₄×C₁₀₁	—	2	6	no	—
143	C₂×C₄×C₁₀₁	—	4	1	no	—
144	C₂×C₄×C₁₀₁	—	4	3	no	—
145	C₂×C₄×C₁₀₁	—	4	6	no	—
146	C₂×C₄×C₁₀₁	—	4	6	no	—
147	C₂×C₄×C₁₀₁	—	4	3	no	—
148	C₂×C₄×C₁₀₁	—	4	1	no	—
149	C₂×C₄×C₁₀₁	—	4	3	no	—
150	C₂×C₄×C₁₀₁	—	4	6	no	—
151	C₂×C₄×C₁₀₁	—	4	6	no	—
152	C₂×C₄×C₁₀₁	—	4	3	no	—
153	C₂×C₄×C₁₀₁	—	4	3	no	—
154	C₂×C₄×C₁₀₁	—	4	3	no	—
155	C₂×C₄×C₁₀₁	C₄×D₄	1	12	yes	—
156	C₂×C₄×C₁₀₁	#127	1	4	yes	—
157	C₂²×C₁₀₁	—	4	6	no	—
158	C₂²×C₁₀₁	—	4	12	no	—
159	C₂²×C₁₀₁	—	4	6	no	—
160	C₂²×C₁₀₁	—	4	6	no	—
161	C₂²×C₁₀₁	—	4	12	no	—
162	C₂²×C₁₀₁	—	8	3	no	—
163	C₂²×C₁₀₁	—	8	3	no	—
164	C₂²×C₁₀₁	—	8	3	no	—
165	C₂²×C₁₀₁	—	8	6	no	—
166	C₂²×C₁₀₁	—	8	6	no	—
167	C₂²×C₁₀₁	—	8	3	no	—
168	C₂²×C₁₀₁	C₂×C₄×D₄	1	3	yes	—
169	C₂²×C₁₀₁	#518	1	3	yes	—
170	C₂²×C₁₀₁	#520	1	1	yes	characteristic
171	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
172	C₂²×C₁₀₁	#532	1	3	yes	—
173	C₂²×C₁₀₁	#534	1	3	yes	—
174	C₂²×C₁₀₁	#535	1	3	yes	—
175	C₂²×C₁₀₁	#535	1	3	yes	—
176	C₂²×C₁₀₁	#537	1	3	yes	—
177	C₂²×C₁₀₁	#538	1	6	yes	—
178	C₂²×C₁₀₁	#540	1	3	yes	—
179	C₂²×C₁₀₁	#542	1	3	yes	—
180	C₄×C₁₀₁	—	2	12	no	—
181	C₄×C₁₀₁	—	2	4	no	—
182	C₄×C₁₀₁	—	4	2	no	—
183	C₄×C₁₀₁	—	4	6	no	—
184	C₄×C₁₀₁	—	8	1	no	—
185	C₄×C₁₀₁	—	8	3	no	—
186	#14321	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂×C₁₀₁	—	8	6	no	—
188	C₂×C₁₀₁	C₄×#127	1	1	yes	characteristic
189	C₂×C₁₀₁	#2321	1	3	yes	—
190	C₂×C₁₀₁	#2324	1	3	yes	—
191	C₂×C₁₀₁	#2656	1	1	yes	characteristic
192	C₂×C₁₀₁	#2657	1	1	yes	characteristic
193	C₂×C₁₀₁	#2661	1	3	yes	—
194	C₂×C₁₀₁	#2662	1	3	yes	—
195	C₂×#392	C₂×C₁₀₁	1	1	yes	characteristic
196	C₂×#390	C₂×C₁₀₁	1	3	yes	complemented
197	C₂×#388	C₂×C₁₀₁	1	3	yes	complemented
198	#1444	C₂×C₁₀₁	1	1	yes	characteristic, complemented
199	#1439	C₂×C₁₀₁	1	3	yes	complemented
200	#1438	C₂×C₁₀₁	1	3	yes	complemented
201	C₄×#95	C₂×C₁₀₁	1	1	yes	characteristic, complemented
202	C₁₀₁	#14321	1	1	yes	characteristic, direct product factor, Sylow
203	C₂³×D₄	C₂²×C₁₀₁	1	3	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
205	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	3	yes	—
206	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
207	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
208	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
209	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	6	yes	—
210	C₂²×C₄²	C₂²×C₁₀₁	1	3	yes	—
211	#392	C₄×C₁₀₁	1	8	yes	complemented
212	#390	—	2	12	no	—
213	#388	—	2	12	no	—
214	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
215	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
216	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
217	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
218	C₂⁵	C₂³×C₁₀₁	1	3	yes	—
219	C₂²×D₄	—	2	6	no	—
220	C₂²×D₄	—	2	6	no	—
221	C₂²×D₄	—	4	6	no	—
222	C₂²×D₄	—	4	6	no	—
223	C₂²×D₄	C₂×C₄×C₁₀₁	1	12	yes	—
224	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
225	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
226	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
227	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
228	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
229	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
230	C₂×C₄⋊C₄	—	2	6	no	—
231	C₂×C₄⋊C₄	—	2	6	no	—
232	C₂×C₄⋊C₄	—	4	6	no	—
233	C₂×C₂²⋊C₄	—	2	6	no	—
234	C₂×C₂²⋊C₄	—	2	6	no	—
235	C₂×C₂²⋊C₄	—	2	6	no	—
236	C₂×C₂²⋊C₄	—	2	6	no	—
237	C₂×C₂²⋊C₄	—	2	12	no	—
238	C₂×C₂²⋊C₄	—	2	12	no	—
239	C₂×C₂²⋊C₄	—	4	6	no	—
240	C₂×C₂²⋊C₄	—	4	6	no	—
241	C₂×C₂²⋊C₄	—	4	6	no	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	12	yes	—
243	C₂×C₄²	—	4	6	no	—
244	C₂×C₄²	D₄×C₁₀₁	1	12	yes	complemented
245	#95	—	2	6	no	—
246	#95	—	2	6	no	—
247	#95	—	2	6	no	—
248	#95	C₂×C₄×C₁₀₁	1	4	yes	—
249	C₂⁴	—	2	3	no	—
250	C₂⁴	—	2	6	no	—
251	C₂⁴	—	2	3	no	—
252	C₂⁴	—	2	6	no	—
253	C₂⁴	—	2	3	no	—
254	C₂⁴	—	2	6	no	—
255	C₂⁴	—	2	6	no	—
256	C₂⁴	—	2	3	no	—
257	C₂⁴	—	2	3	no	—
258	C₂⁴	—	2	3	no	—
259	C₂⁴	C₂²×C₄×C₁₀₁	1	6	yes	—
260	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
261	C₂×D₄	—	2	24	no	—
262	C₂×D₄	—	4	24	no	—
263	C₂×D₄	—	4	12	no	—
264	C₂×D₄	—	4	12	no	—
265	C₂×D₄	—	4	24	no	—
266	C₂²×C₄	—	2	3	no	—
267	C₂²×C₄	—	2	6	no	—
268	C₂²×C₄	—	2	6	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	3	no	—
271	C₂²×C₄	—	2	6	no	—
272	C₂²×C₄	—	2	3	no	—
273	C₂²×C₄	—	2	6	no	—
274	C₂²×C₄	—	2	3	no	—
275	C₂²×C₄	—	2	3	no	—
276	C₂²×C₄	—	2	3	no	—
277	C₂²×C₄	—	2	3	no	—
278	C₂²×C₄	—	2	6	no	—
279	C₂²×C₄	—	2	3	no	—
280	C₂²×C₄	—	2	3	no	—
281	C₂²×C₄	—	2	6	no	—
282	C₂²×C₄	—	2	3	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₀₁	1	6	yes	—
286	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
287	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
288	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
289	C₂²×C₄	#41×C₁₀₁	1	6	yes	—
290	C₄⋊C₄	—	4	12	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₂²⋊C₄	—	2	24	no	—
293	C₂²⋊C₄	—	4	12	no	—
294	C₂²⋊C₄	—	4	24	no	—
295	C₂²⋊C₄	—	4	12	no	—
296	C₄²	—	4	12	no	—
297	C₂³	—	2	6	no	—
298	C₂³	—	2	12	no	—
299	C₂³	—	2	6	no	—
300	C₂³	—	2	12	no	—
301	C₂³	—	2	6	no	—
302	C₂³	—	4	3	no	—
303	C₂³	—	4	3	no	—
304	C₂³	—	4	6	no	—
305	C₂³	—	4	3	no	—
306	C₂³	—	4	6	no	—
307	C₂³	—	4	6	no	—
308	C₂³	—	4	6	no	—
309	C₂³	—	4	3	no	—
310	C₂³	—	4	3	no	—
311	C₂³	—	4	3	no	—
312	C₂³	—	4	6	no	—
313	C₂³	—	4	6	no	—
314	C₂³	—	4	6	no	—
315	C₂³	—	4	6	no	—
316	C₂³	—	4	3	no	—
317	C₂³	—	4	6	no	—
318	C₂³	—	4	3	no	—
319	C₂³	—	4	6	no	—
320	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
321	C₂³	C₂²×D₄×C₁₀₁	1	3	yes	—
322	C₂³	C₂×#41×C₁₀₁	1	3	yes	—
323	C₂³	H(5,𝔽₂)×C₁₀₁	1	3	yes	—
324	C₂³	H(5,𝔽₂)×C₁₀₁	1	3	yes	—
325	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
326	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
327	D₄	—	4	48	no	—
328	C₂×C₄	—	2	12	no	—
329	C₂×C₄	—	2	6	no	—
330	C₂×C₄	—	2	6	no	—
331	C₂×C₄	—	2	6	no	—
332	C₂×C₄	—	2	6	no	—
333	C₂×C₄	—	2	12	no	—
334	C₂×C₄	—	2	6	no	—
335	C₂×C₄	—	2	6	no	—
336	C₂×C₄	—	2	6	no	—
337	C₂×C₄	—	2	6	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	3	no	—
340	C₂×C₄	—	4	6	no	—
341	C₂×C₄	—	4	6	no	—
342	C₂×C₄	—	4	3	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	3	no	—
345	C₂×C₄	—	4	6	no	—
346	C₂×C₄	—	4	6	no	—
347	C₂×C₄	—	4	3	no	—
348	C₂×C₄	—	4	3	no	—
349	C₂×C₄	—	4	3	no	—
350	C₂×C₄	C₄×D₄×C₁₀₁	1	12	yes	—
351	C₂×C₄	#127×C₁₀₁	1	4	yes	—
352	C₂²	—	4	6	no	—
353	C₂²	—	4	12	no	—
354	C₂²	—	4	6	no	—
355	C₂²	—	4	6	no	—
356	C₂²	—	4	12	no	—
357	C₂²	—	8	3	no	—
358	C₂²	—	8	3	no	—
359	C₂²	—	8	3	no	—
360	C₂²	—	8	6	no	—
361	C₂²	—	8	6	no	—
362	C₂²	—	8	3	no	—
363	C₂²	C₂×C₄×D₄×C₁₀₁	1	3	yes	—
364	C₂²	#518×C₁₀₁	1	3	yes	—
365	C₂²	#520×C₁₀₁	1	1	yes	characteristic
366	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
367	C₂²	#532×C₁₀₁	1	3	yes	—
368	C₂²	#534×C₁₀₁	1	3	yes	—
369	C₂²	#535×C₁₀₁	1	3	yes	—
370	C₂²	#535×C₁₀₁	1	3	yes	—
371	C₂²	#537×C₁₀₁	1	3	yes	—
372	C₂²	#538×C₁₀₁	1	6	yes	—
373	C₂²	#540×C₁₀₁	1	3	yes	—
374	C₂²	#542×C₁₀₁	1	3	yes	—
375	C₄	—	2	4	no	—
376	C₄	—	2	12	no	—
377	C₄	—	4	6	no	—
378	C₄	—	4	2	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	3	no	—
381	C₂	—	8	6	no	—
382	C₂	C₄×#127×C₁₀₁	1	1	yes	characteristic
383	C₂	C₁₀₁×#2321	1	3	yes	—
384	C₂	C₁₀₁×#2324	1	3	yes	—
385	C₂	C₁₀₁×#2656	1	1	yes	characteristic
386	C₂	C₁₀₁×#2657	1	1	yes	characteristic
387	C₂	C₁₀₁×#2661	1	3	yes	—
388	C₂	C₁₀₁×#2662	1	3	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂×#392×C₁₀₁	C₂
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×#390×C₁₀₁	C₂	semidirect
3. C₂×#388×C₁₀₁	C₂	semidirect
4. C₁₀₁×#1444	C₂	semidirect
5. C₁₀₁×#1439	C₂	semidirect
6. C₁₀₁×#1438	C₂	semidirect
7. C₄×#95×C₁₀₁	C₂	semidirect
16. #392×C₁₀₁	C₄	semidirect
49. C₂×C₄²×C₁₀₁	D₄	semidirect
186. #14321	C₁₀₁	direct (N × H)
196. C₂×#390	C₂×C₁₀₁	semidirect
197. C₂×#388	C₂×C₁₀₁	semidirect
198. #1444	C₂×C₁₀₁	semidirect
199. #1439	C₂×C₁₀₁	semidirect
200. #1438	C₂×C₁₀₁	semidirect
201. C₄×#95	C₂×C₁₀₁	semidirect
202. C₁₀₁	#14321	direct (N × H)
211. #392	C₄×C₁₀₁	semidirect
244. C₂×C₄²	D₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#392×C₁₀₁	2
C₂×#390×C₁₀₁	2
C₂×#388×C₁₀₁	2
C₁₀₁×#1444	2
C₁₀₁×#1439	2
C₁₀₁×#1438	2
C₄×#95×C₁₀₁	2
#14321	101

Subgroups — C101×#14321 #38796472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#14321 #38796472