Subgroups — C₁₀₁×#10808 #38792959

Order 25856.

850 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#117×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#339×C₁₀₁	C₂	1	2	yes	maximal
3	C₂×#339×C₁₀₁	C₂	1	2	yes	maximal
4	C₁₀₁×#1728	C₂	1	1	yes	maximal, characteristic
5	C₄×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
7	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₄×C₄⋊C₄×C₁₀₁	C₄	1	2	yes	complemented
12	C₄×C₄⋊C₄×C₁₀₁	C₄	1	2	yes	complemented
13	C₄×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
14	#376×C₁₀₁	—	2	1	no	—
15	C₂×#95×C₁₀₁	—	2	2	no	—
16	C₄³×C₁₀₁	—	2	1	no	—
17	#339×C₁₀₁	—	2	4	no	—
18	#339×C₁₀₁	C₄	1	8	yes	complemented
19	#336×C₁₀₁	—	2	1	no	—
20	#336×C₁₀₁	—	2	1	no	—
21	C₂³×C₄×C₁₀₁	—	2	2	no	—
22	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
23	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
24	C₂×M₁₆×C₁₀₁	—	2	2	no	—
25	C₂×M₁₆×C₁₀₁	—	2	2	no	—
26	C₂×M₁₆×C₁₀₁	—	2	2	no	—
27	C₂×M₁₆×C₁₀₁	—	2	2	no	—
28	C₂×M₁₆×C₁₀₁	—	2	2	no	—
29	C₂×M₁₆×C₁₀₁	C₂×C₄	1	4	yes	—
30	C₂²×C₈×C₁₀₁	—	2	2	no	—
31	#117×C₁₀₁	—	2	2	no	—
32	#117×C₁₀₁	—	2	1	no	—
33	#117×C₁₀₁	—	2	1	no	—
34	#117×C₁₀₁	C₂×C₄	1	4	yes	—
35	#117×C₁₀₁	D₄	1	2	yes	—
36	#117×C₁₀₁	Q₈	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
42	C₂×C₄²×C₁₀₁	—	2	1	no	—
43	C₂×C₄²×C₁₀₁	—	2	1	no	—
44	C₂×C₄²×C₁₀₁	—	2	2	no	—
45	C₂×C₄²×C₁₀₁	—	2	2	no	—
46	C₂×C₄²×C₁₀₁	—	2	2	no	—
47	C₂×C₄²×C₁₀₁	—	2	2	no	—
48	C₂×C₄²×C₁₀₁	—	2	2	no	—
49	C₂×C₄²×C₁₀₁	—	2	2	no	—
50	C₂×C₄²×C₁₀₁	—	2	2	no	—
51	C₂×C₄²×C₁₀₁	—	2	2	no	—
52	C₂×C₄²×C₁₀₁	—	2	2	no	—
53	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
57	#95×C₁₀₁	—	2	8	no	—
58	#95×C₁₀₁	—	2	2	no	—
59	#95×C₁₀₁	—	2	2	no	—
60	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₀₁	—	2	8	no	—
62	C₂²×C₄×C₁₀₁	—	2	1	no	—
63	C₂²×C₄×C₁₀₁	—	2	1	no	—
64	C₂²×C₄×C₁₀₁	—	2	2	no	—
65	C₂²×C₄×C₁₀₁	—	2	4	no	—
66	C₂²×C₄×C₁₀₁	—	2	4	no	—
67	C₂²×C₄×C₁₀₁	—	2	4	no	—
68	C₂²×C₄×C₁₀₁	—	4	2	no	—
69	C₂²×C₄×C₁₀₁	—	4	4	no	—
70	C₂²×C₄×C₁₀₁	—	4	2	no	—
71	C₂²×C₄×C₁₀₁	—	4	2	no	—
72	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
73	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
82	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
83	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
84	M₁₆×C₁₀₁	—	2	4	no	—
85	M₁₆×C₁₀₁	—	2	4	no	—
86	M₁₆×C₁₀₁	—	4	2	no	—
87	M₁₆×C₁₀₁	—	4	2	no	—
88	C₂×C₈×C₁₀₁	—	2	4	no	—
89	C₂×C₈×C₁₀₁	—	4	2	no	—
90	C₂×C₈×C₁₀₁	—	4	2	no	—
91	C₄⋊C₄×C₁₀₁	—	2	1	no	—
92	C₄⋊C₄×C₁₀₁	—	2	1	no	—
93	C₄⋊C₄×C₁₀₁	—	2	2	no	—
94	C₄⋊C₄×C₁₀₁	C₄²	1	2	yes	—
95	C₄⋊C₄×C₁₀₁	C₄²	1	2	yes	—
96	C₄⋊C₄×C₁₀₁	C₄⋊C₄	1	4	yes	—
97	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
98	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
99	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
100	C₄²×C₁₀₁	—	2	2	no	—
101	C₄²×C₁₀₁	—	2	2	no	—
102	C₄²×C₁₀₁	—	2	4	no	—
103	C₄²×C₁₀₁	—	2	2	no	—
104	C₄²×C₁₀₁	—	2	2	no	—
105	C₄²×C₁₀₁	—	2	2	no	—
106	C₄²×C₁₀₁	—	2	2	no	—
107	C₄²×C₁₀₁	—	2	4	no	—
108	C₄²×C₁₀₁	—	2	4	no	—
109	C₄²×C₁₀₁	—	4	4	no	—
110	C₄²×C₁₀₁	—	4	4	no	—
111	C₄²×C₁₀₁	—	4	2	no	—
112	C₄²×C₁₀₁	—	4	2	no	—
113	C₂³×C₁₀₁	—	2	2	no	—
114	C₂³×C₁₀₁	—	2	2	no	—
115	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂³×C₁₀₁	C₄×D₄	1	2	yes	—
117	C₂³×C₁₀₁	#121	1	1	yes	characteristic
118	C₂³×C₁₀₁	C₂²⋊Q₈	1	1	yes	characteristic
119	C₂³×C₁₀₁	#123	1	2	yes	—
120	C₂×C₄×C₁₀₁	—	2	2	no	—
121	C₂×C₄×C₁₀₁	—	2	2	no	—
122	C₂×C₄×C₁₀₁	—	2	8	no	—
123	C₂×C₄×C₁₀₁	—	2	2	no	—
124	C₂×C₄×C₁₀₁	—	2	2	no	—
125	C₂×C₄×C₁₀₁	—	2	4	no	—
126	C₂×C₄×C₁₀₁	—	2	2	no	—
127	C₂×C₄×C₁₀₁	—	2	2	no	—
128	C₂×C₄×C₁₀₁	—	2	2	no	—
129	C₂×C₄×C₁₀₁	—	4	8	no	—
130	C₂×C₄×C₁₀₁	—	4	8	no	—
131	C₂×C₄×C₁₀₁	—	4	8	no	—
132	C₂×C₄×C₁₀₁	—	4	4	no	—
133	C₂×C₄×C₁₀₁	—	4	4	no	—
134	C₂×C₄×C₁₀₁	—	4	2	no	—
135	C₂×C₄×C₁₀₁	—	4	2	no	—
136	C₂×C₄×C₁₀₁	—	4	2	no	—
137	C₂×C₄×C₁₀₁	—	4	2	no	—
138	C₂×C₄×C₁₀₁	#104	1	4	yes	—
139	C₂×C₄×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
142	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
143	C₂×C₄×C₁₀₁	#117	1	2	yes	—
144	C₂×C₄×C₁₀₁	#117	1	2	yes	—
145	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
146	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
147	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₁₀₁	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₀₁	#123	1	2	yes	—
153	C₂×C₄×C₁₀₁	#124	1	2	yes	—
154	C₂×C₄×C₁₀₁	#125	1	2	yes	—
155	C₂×C₄×C₁₀₁	#126	1	2	yes	—
156	C₂×C₄×C₁₀₁	#126	1	2	yes	—
157	C₈×C₁₀₁	—	4	4	no	—
158	C₂²×C₁₀₁	—	2	2	no	—
159	C₂²×C₁₀₁	—	2	2	no	—
160	C₂²×C₁₀₁	—	2	4	no	—
161	C₂²×C₁₀₁	—	2	2	no	—
162	C₂²×C₁₀₁	—	2	2	no	—
163	C₂²×C₁₀₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₁₀₁	#380	1	1	yes	characteristic
165	C₂²×C₁₀₁	#381	1	1	yes	characteristic
166	C₂²×C₁₀₁	#387	1	2	yes	—
167	C₂²×C₁₀₁	#388	1	2	yes	—
168	C₂²×C₁₀₁	C₂×#104	1	2	yes	—
169	C₂²×C₁₀₁	#421	1	2	yes	—
170	C₄×C₁₀₁	—	2	4	no	—
171	C₄×C₁₀₁	—	4	8	no	—
172	C₄×C₁₀₁	—	4	4	no	—
173	C₄×C₁₀₁	—	4	2	no	—
174	C₄×C₁₀₁	—	4	2	no	—
175	C₄×C₁₀₁	—	4	2	no	—
176	C₄×C₁₀₁	#376	1	1	yes	characteristic
177	C₄×C₁₀₁	C₄×C₄⋊C₄	1	1	yes	characteristic
178	C₄×C₁₀₁	#382	1	1	yes	characteristic
179	C₄×C₁₀₁	#383	1	1	yes	characteristic
180	C₄×C₁₀₁	#387	1	2	yes	—
181	C₄×C₁₀₁	#388	1	2	yes	—
182	#10808	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₁₀₁	—	2	2	no	—
184	C₂×C₁₀₁	—	2	2	no	—
185	C₂×C₁₀₁	#1434	1	1	yes	characteristic
186	C₂×C₁₀₁	C₄×#104	1	1	yes	characteristic
187	C₂×C₁₀₁	#1759	1	1	yes	characteristic
188	C₂×C₁₀₁	#1806	1	2	yes	—
189	C₂×C₁₀₁	#1826	1	2	yes	—
190	C₄×#117	C₂×C₁₀₁	1	1	yes	characteristic
191	C₂×#339	C₂×C₁₀₁	1	2	yes	—
192	C₂×#339	C₂×C₁₀₁	1	2	yes	—
193	#1728	C₂×C₁₀₁	1	1	yes	characteristic
194	C₄×#95	C₂×C₁₀₁	1	1	yes	characteristic
195	C₁₀₁	#10808	1	1	yes	characteristic, direct product factor, Sylow
196	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
197	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
198	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
199	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
200	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
201	C₄×C₄⋊C₄	C₄×C₁₀₁	1	2	yes	complemented
202	C₄×C₄⋊C₄	C₄×C₁₀₁	1	2	yes	complemented
203	C₄×C₂²⋊C₄	—	2	2	no	—
204	#376	—	2	1	no	—
205	C₂×#95	—	2	2	no	—
206	C₄³	—	2	1	no	—
207	#339	—	2	4	no	—
208	#339	C₄×C₁₀₁	1	8	yes	complemented
209	#336	—	2	1	no	—
210	#336	—	2	1	no	—
211	C₂³×C₄	—	2	2	no	—
212	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
213	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	—	2	2	no	—
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	C₂×C₄×C₁₀₁	1	4	yes	—
220	C₂²×C₈	—	2	2	no	—
221	#117	—	2	2	no	—
222	#117	—	2	1	no	—
223	#117	—	2	1	no	—
224	#117	C₂×C₄×C₁₀₁	1	4	yes	—
225	#117	D₄×C₁₀₁	1	2	yes	—
226	#117	Q₈×C₁₀₁	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
230	C₂×C₂²⋊C₄	—	2	1	no	—
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	—
244	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
245	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
247	#95	—	2	8	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
263	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
266	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
268	C₂²×C₄	C₂×Q₈×C₁₀₁	1	1	yes	characteristic
269	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
270	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
271	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
272	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
273	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
274	M₁₆	—	2	4	no	—
275	M₁₆	—	2	4	no	—
276	M₁₆	—	4	2	no	—
277	M₁₆	—	4	2	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	4	2	no	—
280	C₂×C₈	—	4	2	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	1	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	C₄²×C₁₀₁	1	2	yes	—
285	C₄⋊C₄	C₄²×C₁₀₁	1	2	yes	—
286	C₄⋊C₄	C₄⋊C₄×C₁₀₁	1	4	yes	—
287	C₂²⋊C₄	—	2	4	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₂²⋊C₄	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	4	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	4	no	—
299	C₄²	—	4	4	no	—
300	C₄²	—	4	4	no	—
301	C₄²	—	4	2	no	—
302	C₄²	—	4	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
306	C₂³	C₄×D₄×C₁₀₁	1	2	yes	—
307	C₂³	#121×C₁₀₁	1	1	yes	characteristic
308	C₂³	C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
309	C₂³	#123×C₁₀₁	1	2	yes	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	8	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	#104×C₁₀₁	1	4	yes	—
329	C₂×C₄	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
331	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
332	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
333	C₂×C₄	#117×C₁₀₁	1	2	yes	—
334	C₂×C₄	#117×C₁₀₁	1	2	yes	—
335	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
336	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
337	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
338	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
339	C₂×C₄	C₄×Q₈×C₁₀₁	1	2	yes	—
340	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
341	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
342	C₂×C₄	#123×C₁₀₁	1	2	yes	—
343	C₂×C₄	#124×C₁₀₁	1	2	yes	—
344	C₂×C₄	#125×C₁₀₁	1	2	yes	—
345	C₂×C₄	#126×C₁₀₁	1	2	yes	—
346	C₂×C₄	#126×C₁₀₁	1	2	yes	—
347	C₈	—	4	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	C₄×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
354	C₂²	#380×C₁₀₁	1	1	yes	characteristic
355	C₂²	#381×C₁₀₁	1	1	yes	characteristic
356	C₂²	#387×C₁₀₁	1	2	yes	—
357	C₂²	#388×C₁₀₁	1	2	yes	—
358	C₂²	C₂×#104×C₁₀₁	1	2	yes	—
359	C₂²	#421×C₁₀₁	1	2	yes	—
360	C₄	—	2	4	no	—
361	C₄	—	4	8	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	4	no	—
365	C₄	—	4	2	no	—
366	C₄	#376×C₁₀₁	1	1	yes	characteristic
367	C₄	C₄×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
368	C₄	#382×C₁₀₁	1	1	yes	characteristic
369	C₄	#383×C₁₀₁	1	1	yes	characteristic
370	C₄	#387×C₁₀₁	1	2	yes	—
371	C₄	#388×C₁₀₁	1	2	yes	—
372	C₂	—	2	2	no	—
373	C₂	—	2	2	no	—
374	C₂	C₁₀₁×#1434	1	1	yes	characteristic
375	C₂	C₄×#104×C₁₀₁	1	1	yes	characteristic
376	C₂	C₁₀₁×#1759	1	1	yes	characteristic
377	C₂	C₁₀₁×#1806	1	2	yes	—
378	C₂	C₁₀₁×#1826	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
11. C₄×C₄⋊C₄×C₁₀₁	C₄	semidirect
12. C₄×C₄⋊C₄×C₁₀₁	C₄	semidirect
18. #339×C₁₀₁	C₄	semidirect
182. #10808	C₁₀₁	direct (N × H)
195. C₁₀₁	#10808	direct (N × H)
201. C₄×C₄⋊C₄	C₄×C₁₀₁	semidirect
202. C₄×C₄⋊C₄	C₄×C₁₀₁	semidirect
208. #339	C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×#117×C₁₀₁	2
C₂×#339×C₁₀₁	2
C₁₀₁×#1728	2
C₄×#95×C₁₀₁	2
#10808	101

Subgroups — C101×#10808 #38792959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#10808 #38792959