Subgroups — C₁₀₁×#23918 #38806069

Order 25856.

2596 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₀₁	C₂	1	2	yes	maximal, complemented
2	C₂×#447×C₁₀₁	C₂	1	4	yes	maximal, complemented
3	C₁₀₁×#1999	C₂	1	4	yes	maximal, complemented
4	C₁₀₁×#1874	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1779	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₀₁	—	2	2	no	—
7	C₂³×D₄×C₁₀₁	C₂²	1	2	yes	complemented
8	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×D₈×C₁₀₁	C₂²	1	4	yes	complemented
10	C₂×#121×C₁₀₁	—	2	2	no	—
11	C₂×#121×C₁₀₁	—	2	2	no	—
12	C₂×#121×C₁₀₁	—	2	16	no	—
13	C₂×#121×C₁₀₁	C₂²	1	4	yes	—
14	C₂×#121×C₁₀₁	C₂²	1	4	yes	complemented
15	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
16	C₂²×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
17	#447×C₁₀₁	—	2	16	no	—
18	C₂×#102×C₁₀₁	C₂²	1	8	yes	complemented
19	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	4	yes	complemented
20	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	complemented
21	#340×C₁₀₁	C₂²	1	4	yes	complemented
22	C₂⁵×C₁₀₁	—	2	2	no	—
23	C₂⁵×C₁₀₁	D₄	1	1	yes	characteristic
24	C₂²×D₄×C₁₀₁	—	2	16	no	—
25	C₂²×D₄×C₁₀₁	—	2	4	no	—
26	C₂²×D₄×C₁₀₁	—	2	4	no	—
27	C₂²×D₄×C₁₀₁	—	2	8	no	—
28	C₂²×D₄×C₁₀₁	—	2	2	no	—
29	C₂²×D₄×C₁₀₁	—	2	8	no	—
30	C₂²×D₄×C₁₀₁	—	4	4	no	—
31	C₂²×D₄×C₁₀₁	—	4	8	no	—
32	C₂²×D₄×C₁₀₁	—	4	8	no	—
33	C₂²×D₄×C₁₀₁	C₂³	1	4	yes	—
34	C₂³×C₄×C₁₀₁	—	2	2	no	—
35	C₂³×C₄×C₁₀₁	—	2	8	no	—
36	C₂³×C₄×C₁₀₁	—	4	2	no	—
37	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
38	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
41	C₂×D₈×C₁₀₁	—	2	16	no	—
42	C₂×D₈×C₁₀₁	—	4	4	no	—
43	C₂²×C₈×C₁₀₁	C₂³	1	4	yes	—
44	#121×C₁₀₁	—	2	16	no	—
45	#121×C₁₀₁	—	2	16	no	—
46	#121×C₁₀₁	—	2	8	no	—
47	#121×C₁₀₁	—	2	8	no	—
48	#121×C₁₀₁	—	2	8	no	—
49	#121×C₁₀₁	D₄	1	16	yes	complemented
50	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
53	C₂×C₂²⋊C₄×C₁₀₁	—	2	16	no	—
54	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
56	#102×C₁₀₁	—	2	16	no	—
57	C₂²⋊C₈×C₁₀₁	—	2	8	no	—
58	C₂²⋊C₈×C₁₀₁	—	4	2	no	—
59	C₂⁴×C₁₀₁	—	2	4	no	—
60	C₂⁴×C₁₀₁	—	2	4	no	—
61	C₂⁴×C₁₀₁	—	2	8	no	—
62	C₂⁴×C₁₀₁	—	2	4	no	—
63	C₂⁴×C₁₀₁	—	4	1	no	—
64	C₂⁴×C₁₀₁	—	4	1	no	—
65	C₂⁴×C₁₀₁	—	4	4	no	—
66	C₂⁴×C₁₀₁	—	4	4	no	—
67	C₂⁴×C₁₀₁	—	4	4	no	—
68	C₂⁴×C₁₀₁	—	4	4	no	—
69	C₂⁴×C₁₀₁	—	4	4	no	—
70	C₂⁴×C₁₀₁	—	4	4	no	—
71	C₂⁴×C₁₀₁	D₈	1	4	yes	complemented
72	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
73	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
74	C₂×D₄×C₁₀₁	—	2	8	no	—
75	C₂×D₄×C₁₀₁	—	2	16	no	—
76	C₂×D₄×C₁₀₁	—	2	16	no	—
77	C₂×D₄×C₁₀₁	—	2	8	no	—
78	C₂×D₄×C₁₀₁	—	2	4	no	—
79	C₂×D₄×C₁₀₁	—	2	8	no	—
80	C₂×D₄×C₁₀₁	—	4	32	no	—
81	C₂×D₄×C₁₀₁	—	4	4	no	—
82	C₂×D₄×C₁₀₁	—	4	64	no	—
83	C₂×D₄×C₁₀₁	—	4	8	no	—
84	C₂×D₄×C₁₀₁	—	4	8	no	—
85	C₂×D₄×C₁₀₁	—	4	8	no	—
86	C₂×D₄×C₁₀₁	—	4	8	no	—
87	C₂×D₄×C₁₀₁	—	4	4	no	—
88	C₂×D₄×C₁₀₁	C₂×D₄	1	8	yes	complemented
89	C₂²×C₄×C₁₀₁	—	2	4	no	—
90	C₂²×C₄×C₁₀₁	—	2	4	no	—
91	C₂²×C₄×C₁₀₁	—	2	8	no	—
92	C₂²×C₄×C₁₀₁	—	2	4	no	—
93	C₂²×C₄×C₁₀₁	—	2	4	no	—
94	C₂²×C₄×C₁₀₁	—	2	4	no	—
95	C₂²×C₄×C₁₀₁	—	2	4	no	—
96	C₂²×C₄×C₁₀₁	—	2	4	no	—
97	C₂²×C₄×C₁₀₁	—	2	2	no	—
98	C₂²×C₄×C₁₀₁	—	4	1	no	—
99	C₂²×C₄×C₁₀₁	—	4	2	no	—
100	C₂²×C₄×C₁₀₁	—	4	16	no	—
101	C₂²×C₄×C₁₀₁	—	4	4	no	—
102	C₂²×C₄×C₁₀₁	—	4	4	no	—
103	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₀₁	C₂×D₄	1	8	yes	—
106	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
107	D₈×C₁₀₁	—	4	16	no	—
108	C₂×C₈×C₁₀₁	—	2	8	no	—
109	C₂×C₈×C₁₀₁	—	2	4	no	—
110	C₄⋊C₄×C₁₀₁	—	2	8	no	—
111	C₄⋊C₄×C₁₀₁	—	2	4	no	—
112	C₄⋊C₄×C₁₀₁	C₂×D₄	1	8	yes	complemented
113	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
114	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
115	C₂³×C₁₀₁	—	2	2	no	—
116	C₂³×C₁₀₁	—	2	2	no	—
117	C₂³×C₁₀₁	—	2	2	no	—
118	C₂³×C₁₀₁	—	2	2	no	—
119	C₂³×C₁₀₁	—	2	2	no	—
120	C₂³×C₁₀₁	—	2	1	no	—
121	C₂³×C₁₀₁	—	2	2	no	—
122	C₂³×C₁₀₁	—	2	1	no	—
123	C₂³×C₁₀₁	—	2	16	no	—
124	C₂³×C₁₀₁	—	2	8	no	—
125	C₂³×C₁₀₁	—	4	4	no	—
126	C₂³×C₁₀₁	—	4	4	no	—
127	C₂³×C₁₀₁	—	4	4	no	—
128	C₂³×C₁₀₁	—	4	8	no	—
129	C₂³×C₁₀₁	—	4	16	no	—
130	C₂³×C₁₀₁	—	4	16	no	—
131	C₂³×C₁₀₁	—	4	16	no	—
132	C₂³×C₁₀₁	—	4	4	no	—
133	C₂³×C₁₀₁	—	4	4	no	—
134	C₂³×C₁₀₁	—	4	4	no	—
135	C₂³×C₁₀₁	—	4	4	no	—
136	C₂³×C₁₀₁	—	4	4	no	—
137	C₂³×C₁₀₁	—	4	4	no	—
138	C₂³×C₁₀₁	—	8	8	no	—
139	C₂³×C₁₀₁	—	8	8	no	—
140	C₂³×C₁₀₁	—	8	8	no	—
141	C₂³×C₁₀₁	—	8	8	no	—
142	C₂³×C₁₀₁	#120	1	4	yes	—
143	C₂³×C₁₀₁	C₂×D₈	1	2	yes	—
144	C₂³×C₁₀₁	C₂×D₈	1	4	yes	—
145	C₂³×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	—
146	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
147	D₄×C₁₀₁	—	2	16	no	—
148	D₄×C₁₀₁	—	4	16	no	—
149	D₄×C₁₀₁	—	4	32	no	—
150	D₄×C₁₀₁	—	4	32	no	—
151	D₄×C₁₀₁	—	4	8	no	—
152	C₂×C₄×C₁₀₁	—	2	2	no	—
153	C₂×C₄×C₁₀₁	—	2	2	no	—
154	C₂×C₄×C₁₀₁	—	2	16	no	—
155	C₂×C₄×C₁₀₁	—	2	2	no	—
156	C₂×C₄×C₁₀₁	—	2	8	no	—
157	C₂×C₄×C₁₀₁	—	2	1	no	—
158	C₂×C₄×C₁₀₁	—	4	4	no	—
159	C₂×C₄×C₁₀₁	—	4	8	no	—
160	C₂×C₄×C₁₀₁	—	4	16	no	—
161	C₂×C₄×C₁₀₁	—	4	4	no	—
162	C₂×C₄×C₁₀₁	—	4	4	no	—
163	C₂×C₄×C₁₀₁	—	4	4	no	—
164	C₂×C₄×C₁₀₁	#120	1	4	yes	—
165	C₂×C₄×C₁₀₁	C₂²×D₄	1	4	yes	—
166	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
167	C₈×C₁₀₁	—	4	4	no	—
168	C₂²×C₁₀₁	—	2	4	no	—
169	C₂²×C₁₀₁	—	2	4	no	—
170	C₂²×C₁₀₁	—	2	4	no	—
171	C₂²×C₁₀₁	—	2	4	no	—
172	C₂²×C₁₀₁	—	2	4	no	—
173	C₂²×C₁₀₁	—	2	4	no	—
174	C₂²×C₁₀₁	—	2	2	no	—
175	C₂²×C₁₀₁	—	2	4	no	—
176	C₂²×C₁₀₁	—	4	16	no	—
177	C₂²×C₁₀₁	—	4	1	no	—
178	C₂²×C₁₀₁	—	4	1	no	—
179	C₂²×C₁₀₁	—	4	2	no	—
180	C₂²×C₁₀₁	—	4	8	no	—
181	C₂²×C₁₀₁	—	4	8	no	—
182	C₂²×C₁₀₁	—	4	8	no	—
183	C₂²×C₁₀₁	—	8	32	no	—
184	C₂²×C₁₀₁	—	8	4	no	—
185	C₂²×C₁₀₁	—	8	4	no	—
186	C₂²×C₁₀₁	—	8	4	no	—
187	C₂²×C₁₀₁	—	8	4	no	—
188	C₂²×C₁₀₁	#447	1	8	yes	complemented
189	C₂²×C₁₀₁	C₂×#120	1	2	yes	—
190	C₂²×C₁₀₁	#534	1	1	yes	characteristic
191	C₂²×C₁₀₁	C₂²×D₈	1	1	yes	characteristic
192	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
193	C₂²×C₁₀₁	#575	1	1	yes	characteristic
194	C₄×C₁₀₁	—	2	4	no	—
195	C₄×C₁₀₁	—	4	1	no	—
196	C₄×C₁₀₁	—	4	8	no	—
197	C₄×C₁₀₁	D₄²	1	4	yes	—
198	#23918	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂×C₁₀₁	—	2	8	no	—
200	C₂×C₁₀₁	—	4	2	no	—
201	C₂×C₁₀₁	—	8	8	no	—
202	C₂×C₁₀₁	#2403	1	1	yes	characteristic
203	C₂×C₁₀₁	C₂×#447	1	2	yes	—
204	C₂×C₁₀₁	#3006	1	2	yes	—
205	C₂×C₁₀₁	#3186	1	1	yes	characteristic
206	C₂×C₁₀₁	#3192	1	1	yes	characteristic
207	C₂²×#121	C₂×C₁₀₁	1	2	yes	complemented
208	C₂×#447	C₂×C₁₀₁	1	4	yes	complemented
209	#1999	C₂×C₁₀₁	1	4	yes	complemented
210	#1874	C₂×C₁₀₁	1	4	yes	complemented
211	#1779	C₂×C₁₀₁	1	1	yes	characteristic, complemented
212	C₁₀₁	#23918	1	1	yes	characteristic, direct product factor, Sylow
213	C₂³×D₄	—	2	2	no	—
214	C₂³×D₄	C₂²×C₁₀₁	1	2	yes	complemented
215	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
216	C₂²×D₈	C₂²×C₁₀₁	1	4	yes	complemented
217	C₂×#121	—	2	2	no	—
218	C₂×#121	—	2	2	no	—
219	C₂×#121	—	2	16	no	—
220	C₂×#121	C₂²×C₁₀₁	1	4	yes	—
221	C₂×#121	C₂²×C₁₀₁	1	4	yes	complemented
222	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	complemented
223	C₂²×C₂²⋊C₄	—	2	2	no	—
224	#447	—	2	16	no	—
225	C₂×#102	C₂²×C₁₀₁	1	8	yes	complemented
226	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	4	yes	complemented
227	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	complemented
228	#340	C₂²×C₁₀₁	1	4	yes	complemented
229	C₂⁵	—	2	2	no	—
230	C₂⁵	D₄×C₁₀₁	1	1	yes	characteristic
231	C₂²×D₄	—	2	16	no	—
232	C₂²×D₄	—	2	4	no	—
233	C₂²×D₄	—	2	4	no	—
234	C₂²×D₄	—	2	8	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	—	2	8	no	—
237	C₂²×D₄	—	4	4	no	—
238	C₂²×D₄	—	4	8	no	—
239	C₂²×D₄	—	4	8	no	—
240	C₂²×D₄	C₂³×C₁₀₁	1	4	yes	—
241	C₂³×C₄	—	2	2	no	—
242	C₂³×C₄	—	2	8	no	—
243	C₂³×C₄	—	4	2	no	—
244	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
245	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
248	C₂×D₈	—	2	16	no	—
249	C₂×D₈	—	4	4	no	—
250	C₂²×C₈	C₂³×C₁₀₁	1	4	yes	—
251	#121	—	2	16	no	—
252	#121	—	2	16	no	—
253	#121	—	2	8	no	—
254	#121	—	2	8	no	—
255	#121	—	2	8	no	—
256	#121	D₄×C₁₀₁	1	16	yes	complemented
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	8	no	—
259	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	4	yes	—
260	C₂×C₂²⋊C₄	—	2	16	no	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	#102	—	2	16	no	—
264	C₂²⋊C₈	—	2	8	no	—
265	C₂²⋊C₈	—	4	2	no	—
266	C₂⁴	—	2	4	no	—
267	C₂⁴	—	2	4	no	—
268	C₂⁴	—	2	8	no	—
269	C₂⁴	—	2	4	no	—
270	C₂⁴	—	4	1	no	—
271	C₂⁴	—	4	1	no	—
272	C₂⁴	—	4	4	no	—
273	C₂⁴	—	4	4	no	—
274	C₂⁴	—	4	4	no	—
275	C₂⁴	—	4	4	no	—
276	C₂⁴	—	4	4	no	—
277	C₂⁴	—	4	4	no	—
278	C₂⁴	D₈×C₁₀₁	1	4	yes	complemented
279	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
280	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	16	no	—
283	C₂×D₄	—	2	16	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	4	32	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	—	4	64	no	—
290	C₂×D₄	—	4	8	no	—
291	C₂×D₄	—	4	8	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	8	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	C₂×D₄×C₁₀₁	1	8	yes	complemented
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	16	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₀₁	1	8	yes	—
313	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
314	D₈	—	4	16	no	—
315	C₂×C₈	—	2	8	no	—
316	C₂×C₈	—	2	4	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	C₂×D₄×C₁₀₁	1	8	yes	complemented
320	C₂²⋊C₄	—	2	16	no	—
321	C₂²⋊C₄	—	2	16	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	16	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	4	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	4	16	no	—
337	C₂³	—	4	16	no	—
338	C₂³	—	4	16	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	4	no	—
345	C₂³	—	8	8	no	—
346	C₂³	—	8	8	no	—
347	C₂³	—	8	8	no	—
348	C₂³	—	8	8	no	—
349	C₂³	#120×C₁₀₁	1	4	yes	—
350	C₂³	C₂×D₈×C₁₀₁	1	2	yes	—
351	C₂³	C₂×D₈×C₁₀₁	1	4	yes	—
352	C₂³	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	—
353	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
354	D₄	—	2	16	no	—
355	D₄	—	4	16	no	—
356	D₄	—	4	32	no	—
357	D₄	—	4	32	no	—
358	D₄	—	4	8	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	16	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	16	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	#120×C₁₀₁	1	4	yes	—
372	C₂×C₄	C₂²×D₄×C₁₀₁	1	4	yes	—
373	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
374	C₈	—	4	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	4	16	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	8	32	no	—
391	C₂²	—	8	4	no	—
392	C₂²	—	8	4	no	—
393	C₂²	—	8	4	no	—
394	C₂²	—	8	4	no	—
395	C₂²	#447×C₁₀₁	1	8	yes	complemented
396	C₂²	C₂×#120×C₁₀₁	1	2	yes	—
397	C₂²	#534×C₁₀₁	1	1	yes	characteristic
398	C₂²	C₂²×D₈×C₁₀₁	1	1	yes	characteristic
399	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
400	C₂²	#575×C₁₀₁	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	8	no	—
404	C₄	D₄²×C₁₀₁	1	4	yes	—
405	C₂	—	2	8	no	—
406	C₂	—	4	2	no	—
407	C₂	—	8	8	no	—
408	C₂	C₁₀₁×#2403	1	1	yes	characteristic
409	C₂	C₂×#447×C₁₀₁	1	2	yes	—
410	C₂	C₁₀₁×#3006	1	2	yes	—
411	C₂	C₁₀₁×#3186	1	1	yes	characteristic
412	C₂	C₁₀₁×#3192	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#121×C₁₀₁	C₂	semidirect
2. C₂×#447×C₁₀₁	C₂	semidirect
3. C₁₀₁×#1999	C₂	semidirect
4. C₁₀₁×#1874	C₂	semidirect
5. C₁₀₁×#1779	C₂	semidirect
7. C₂³×D₄×C₁₀₁	C₂²	semidirect
9. C₂²×D₈×C₁₀₁	C₂²	semidirect
14. C₂×#121×C₁₀₁	C₂²	semidirect
15. C₂²×C₄⋊C₄×C₁₀₁	C₂²	semidirect
18. C₂×#102×C₁₀₁	C₂²	semidirect
19. C₂×C₂²⋊C₈×C₁₀₁	C₂²	semidirect
20. C₂×C₂²⋊C₈×C₁₀₁	C₂²	semidirect
21. #340×C₁₀₁	C₂²	semidirect
49. #121×C₁₀₁	D₄	semidirect
71. C₂⁴×C₁₀₁	D₈	semidirect
88. C₂×D₄×C₁₀₁	C₂×D₄	semidirect
112. C₄⋊C₄×C₁₀₁	C₂×D₄	semidirect
188. C₂²×C₁₀₁	#447	semidirect
198. #23918	C₁₀₁	direct (N × H)
207. C₂²×#121	C₂×C₁₀₁	semidirect
208. C₂×#447	C₂×C₁₀₁	semidirect
209. #1999	C₂×C₁₀₁	semidirect
210. #1874	C₂×C₁₀₁	semidirect
211. #1779	C₂×C₁₀₁	semidirect
212. C₁₀₁	#23918	direct (N × H)
214. C₂³×D₄	C₂²×C₁₀₁	semidirect
216. C₂²×D₈	C₂²×C₁₀₁	semidirect
221. C₂×#121	C₂²×C₁₀₁	semidirect
222. C₂²×C₄⋊C₄	C₂²×C₁₀₁	semidirect
225. C₂×#102	C₂²×C₁₀₁	semidirect
226. C₂×C₂²⋊C₈	C₂²×C₁₀₁	semidirect
227. C₂×C₂²⋊C₈	C₂²×C₁₀₁	semidirect
228. #340	C₂²×C₁₀₁	semidirect
256. #121	D₄×C₁₀₁	semidirect
278. C₂⁴	D₈×C₁₀₁	semidirect
295. C₂×D₄	C₂×D₄×C₁₀₁	semidirect
319. C₄⋊C₄	C₂×D₄×C₁₀₁	semidirect
395. C₂²	#447×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₁₀₁	2
C₂×#447×C₁₀₁	2
C₁₀₁×#1999	2
C₁₀₁×#1874	2
C₁₀₁×#1779	2
#23918	101

Subgroups — C101×#23918 #38806069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23918 #38806069