Subgroups — C₁₀₁×#23060 #38805211

Order 25856.

854 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#474×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2354	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#1934	C₂	1	2	yes	maximal
7	C₁₀₁×#1925	C₂	1	2	yes	maximal
8	C₁₀₁×#1918	C₂	1	2	yes	maximal, complemented
9	C₄×#107×C₁₀₁	C₂	1	2	yes	maximal, complemented
10	C₈×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₁₀₁	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₀₁	—	2	1	no	—
14	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₀₁	—	2	1	no	—
16	#474×C₁₀₁	C₄	1	8	yes	complemented
17	C₂×#107×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#107×C₁₀₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#102×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂×#102×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₀₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
25	#391×C₁₀₁	—	2	1	no	—
26	#390×C₁₀₁	C₂²	1	2	yes	—
27	#389×C₁₀₁	C₂²	1	2	yes	—
28	#388×C₁₀₁	—	2	2	no	—
29	#387×C₁₀₁	—	2	2	no	—
30	#384×C₁₀₁	C₂²	1	1	yes	characteristic
31	#380×C₁₀₁	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
36	#340×C₁₀₁	C₂²	1	1	yes	characteristic
37	#340×C₁₀₁	C₂²	1	2	yes	—
38	#340×C₁₀₁	C₂²	1	2	yes	—
39	#340×C₁₀₁	C₂²	1	2	yes	—
40	#340×C₁₀₁	C₂²	1	1	yes	characteristic
41	#336×C₁₀₁	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₀₁	—	2	1	no	—
43	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₀₁	—	2	1	no	—
45	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
48	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
49	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
50	C₄×Q₈×C₁₀₁	—	4	4	no	—
51	C₄×D₄×C₁₀₁	—	2	2	no	—
52	C₄×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
53	#117×C₁₀₁	—	4	4	no	—
54	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
68	C₂×C₄²×C₁₀₁	—	2	2	no	—
69	C₂×C₄²×C₁₀₁	—	2	2	no	—
70	C₂×C₄²×C₁₀₁	—	2	1	no	—
71	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
73	#107×C₁₀₁	—	2	4	no	—
74	#107×C₁₀₁	C₂×C₄	1	8	yes	—
75	C₄⋊C₈×C₁₀₁	C₂×C₄	1	4	yes	—
76	#102×C₁₀₁	—	2	2	no	—
77	#102×C₁₀₁	—	2	2	no	—
78	#102×C₁₀₁	C₂×C₄	1	8	yes	—
79	C₄×C₈×C₁₀₁	—	2	4	no	—
80	C₄×C₈×C₁₀₁	—	2	2	no	—
81	#95×C₁₀₁	—	2	2	no	—
82	#95×C₁₀₁	—	2	1	no	—
83	#95×C₁₀₁	—	2	2	no	—
84	#95×C₁₀₁	—	2	2	no	—
85	#95×C₁₀₁	D₄	1	2	yes	—
86	C₂⁴×C₁₀₁	—	2	1	no	—
87	C₂×Q₈×C₁₀₁	—	2	4	no	—
88	C₂×Q₈×C₁₀₁	—	4	2	no	—
89	C₂×Q₈×C₁₀₁	—	4	2	no	—
90	C₂×D₄×C₁₀₁	—	2	1	no	—
91	C₂×D₄×C₁₀₁	—	2	1	no	—
92	C₂×D₄×C₁₀₁	—	2	1	no	—
93	C₂×D₄×C₁₀₁	—	2	1	no	—
94	C₂×D₄×C₁₀₁	—	2	1	no	—
95	C₂×D₄×C₁₀₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₀₁	—	2	1	no	—
97	C₂²×C₄×C₁₀₁	—	2	1	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	4	no	—
100	C₂²×C₄×C₁₀₁	—	2	1	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	4	2	no	—
103	C₂²×C₄×C₁₀₁	—	4	2	no	—
104	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₀₁	—	2	2	no	—
110	C₂×C₈×C₁₀₁	—	2	1	no	—
111	C₂×C₈×C₁₀₁	—	2	2	no	—
112	C₂×C₈×C₁₀₁	—	2	1	no	—
113	C₂×C₈×C₁₀₁	—	2	1	no	—
114	C₂×C₈×C₁₀₁	—	2	1	no	—
115	C₂×C₈×C₁₀₁	—	2	1	no	—
116	C₂×C₈×C₁₀₁	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₁₀₁	#41	1	2	yes	—
118	C₄⋊C₄×C₁₀₁	—	2	4	no	—
119	C₄⋊C₄×C₁₀₁	—	2	2	no	—
120	C₄⋊C₄×C₁₀₁	—	2	1	no	—
121	C₄⋊C₄×C₁₀₁	—	2	2	no	—
122	C₄⋊C₄×C₁₀₁	—	2	1	no	—
123	C₄⋊C₄×C₁₀₁	—	2	1	no	—
124	C₄⋊C₄×C₁₀₁	—	2	2	no	—
125	C₄⋊C₄×C₁₀₁	—	2	1	no	—
126	C₄⋊C₄×C₁₀₁	—	2	2	no	—
127	C₄⋊C₄×C₁₀₁	—	4	2	no	—
128	C₄⋊C₄×C₁₀₁	—	4	4	no	—
129	C₄⋊C₄×C₁₀₁	—	8	1	no	—
130	C₄⋊C₄×C₁₀₁	D₈	1	4	yes	—
131	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
132	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₁₀₁	#41	1	2	yes	—
134	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
135	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
136	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
137	C₄²×C₁₀₁	—	2	2	no	—
138	C₄²×C₁₀₁	—	2	2	no	—
139	C₄²×C₁₀₁	—	4	4	no	—
140	C₄²×C₁₀₁	—	4	4	no	—
141	C₄²×C₁₀₁	—	4	2	no	—
142	C₄²×C₁₀₁	C₂²×C₄	1	2	yes	—
143	C₄²×C₁₀₁	#41	1	2	yes	—
144	C₂³×C₁₀₁	—	2	2	no	—
145	C₂³×C₁₀₁	—	4	1	no	—
146	C₂³×C₁₀₁	—	4	1	no	—
147	C₂³×C₁₀₁	—	4	1	no	—
148	C₂³×C₁₀₁	—	4	1	no	—
149	C₂³×C₁₀₁	—	4	1	no	—
150	C₂³×C₁₀₁	—	4	1	no	—
151	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₁₀₁	—	4	8	no	—
153	D₄×C₁₀₁	—	2	2	no	—
154	D₄×C₁₀₁	—	2	2	no	—
155	D₄×C₁₀₁	—	4	1	no	—
156	D₄×C₁₀₁	—	4	1	no	—
157	C₂×C₄×C₁₀₁	—	2	2	no	—
158	C₂×C₄×C₁₀₁	—	2	1	no	—
159	C₂×C₄×C₁₀₁	—	2	2	no	—
160	C₂×C₄×C₁₀₁	—	2	1	no	—
161	C₂×C₄×C₁₀₁	—	2	2	no	—
162	C₂×C₄×C₁₀₁	—	2	4	no	—
163	C₂×C₄×C₁₀₁	—	2	2	no	—
164	C₂×C₄×C₁₀₁	—	2	2	no	—
165	C₂×C₄×C₁₀₁	—	2	2	no	—
166	C₂×C₄×C₁₀₁	—	2	2	no	—
167	C₂×C₄×C₁₀₁	—	4	1	no	—
168	C₂×C₄×C₁₀₁	—	4	1	no	—
169	C₂×C₄×C₁₀₁	—	4	2	no	—
170	C₂×C₄×C₁₀₁	—	4	1	no	—
171	C₂×C₄×C₁₀₁	—	4	2	no	—
172	C₂×C₄×C₁₀₁	—	4	1	no	—
173	C₂×C₄×C₁₀₁	—	4	8	no	—
174	C₂×C₄×C₁₀₁	—	4	1	no	—
175	C₂×C₄×C₁₀₁	—	4	2	no	—
176	C₂×C₄×C₁₀₁	—	4	2	no	—
177	C₂×C₄×C₁₀₁	—	4	1	no	—
178	C₂×C₄×C₁₀₁	—	4	2	no	—
179	C₂×C₄×C₁₀₁	—	4	1	no	—
180	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₁₀₁	C₂×D₈	1	4	yes	—
183	C₂×C₄×C₁₀₁	C₂×D₈	1	2	yes	—
184	C₂×C₄×C₁₀₁	#135	1	2	yes	—
185	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
191	C₈×C₁₀₁	—	2	4	no	—
192	C₈×C₁₀₁	—	2	2	no	—
193	C₈×C₁₀₁	—	4	1	no	—
194	C₂²×C₁₀₁	—	4	2	no	—
195	C₂²×C₁₀₁	—	4	2	no	—
196	C₂²×C₁₀₁	—	4	2	no	—
197	C₂²×C₁₀₁	—	8	1	no	—
198	C₂²×C₁₀₁	—	8	1	no	—
199	C₂²×C₁₀₁	—	8	1	no	—
200	C₂²×C₁₀₁	—	8	1	no	—
201	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂²×C₁₀₁	#547	1	1	yes	characteristic
203	C₂²×C₁₀₁	#548	1	1	yes	characteristic
204	C₂²×C₁₀₁	C₂²×D₈	1	1	yes	characteristic
205	C₂²×C₁₀₁	C₂×#135	1	1	yes	characteristic
206	C₂²×C₁₀₁	#577	1	1	yes	characteristic
207	C₂²×C₁₀₁	#578	1	1	yes	characteristic
208	C₄×C₁₀₁	—	2	4	no	—
209	C₄×C₁₀₁	—	2	2	no	—
210	C₄×C₁₀₁	—	4	2	no	—
211	C₄×C₁₀₁	—	4	2	no	—
212	C₄×C₁₀₁	—	4	2	no	—
213	C₄×C₁₀₁	—	4	4	no	—
214	C₄×C₁₀₁	—	8	1	no	—
215	C₄×C₁₀₁	—	8	2	no	—
216	C₄×C₁₀₁	C₄×D₈	1	4	yes	—
217	C₄×C₁₀₁	C₄×#41	1	1	yes	characteristic
218	C₄×C₁₀₁	#519	1	1	yes	characteristic
219	C₄×C₁₀₁	#552	1	1	yes	characteristic
220	C₄×C₁₀₁	#556	1	1	yes	characteristic
221	#23060	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂×C₁₀₁	—	8	2	no	—
223	C₂×C₁₀₁	#2362	1	1	yes	characteristic
224	C₂×C₁₀₁	C₂×C₄×D₈	1	1	yes	characteristic
225	C₂×C₁₀₁	#2947	1	1	yes	characteristic
226	C₂×C₁₀₁	#3334	1	1	yes	characteristic
227	C₂×C₁₀₁	#3340	1	1	yes	characteristic
228	C₂×C₁₀₁	#3358	1	1	yes	characteristic
229	C₂×C₁₀₁	#3364	1	1	yes	characteristic
230	C₂×#474	C₂×C₁₀₁	1	1	yes	characteristic
231	#2365	C₂×C₁₀₁	1	1	yes	characteristic, complemented
232	#2354	C₂×C₁₀₁	1	1	yes	characteristic
233	#1990	C₂×C₁₀₁	1	1	yes	characteristic, complemented
234	#1947	C₂×C₁₀₁	1	1	yes	characteristic, complemented
235	#1934	C₂×C₁₀₁	1	2	yes	—
236	#1925	C₂×C₁₀₁	1	2	yes	—
237	#1918	C₂×C₁₀₁	1	2	yes	complemented
238	C₄×#107	C₂×C₁₀₁	1	2	yes	complemented
239	C₈×C₄⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic, complemented
240	C₄×#102	C₂×C₁₀₁	1	1	yes	characteristic
241	C₁₀₁	#23060	1	1	yes	characteristic, direct product factor, Sylow
242	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
243	C₂×C₄×Q₈	—	2	1	no	—
244	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
245	C₂×#117	—	2	1	no	—
246	#474	C₄×C₁₀₁	1	8	yes	complemented
247	C₂×#107	C₂²×C₁₀₁	1	2	yes	—
248	C₂×#107	C₂²×C₁₀₁	1	2	yes	—
249	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
250	C₂×#102	C₂²×C₁₀₁	1	1	yes	characteristic
251	C₂×#102	C₂²×C₁₀₁	1	1	yes	characteristic
252	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
253	C₂×C₄×C₈	C₂²×C₁₀₁	1	2	yes	—
254	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
255	#391	—	2	1	no	—
256	#390	C₂²×C₁₀₁	1	2	yes	—
257	#389	C₂²×C₁₀₁	1	2	yes	—
258	#388	—	2	2	no	—
259	#387	—	2	2	no	—
260	#384	C₂²×C₁₀₁	1	1	yes	characteristic
261	#380	—	2	1	no	—
262	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
263	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
264	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
265	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
266	#340	C₂²×C₁₀₁	1	1	yes	characteristic
267	#340	C₂²×C₁₀₁	1	2	yes	—
268	#340	C₂²×C₁₀₁	1	2	yes	—
269	#340	C₂²×C₁₀₁	1	2	yes	—
270	#340	C₂²×C₁₀₁	1	1	yes	characteristic
271	#336	C₂²×C₁₀₁	1	2	yes	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
277	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
280	C₄×Q₈	—	4	4	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
283	#117	—	4	4	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
302	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
303	#107	—	2	4	no	—
304	#107	C₂×C₄×C₁₀₁	1	8	yes	—
305	C₄⋊C₈	C₂×C₄×C₁₀₁	1	4	yes	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	C₂×C₄×C₁₀₁	1	8	yes	—
309	C₄×C₈	—	2	4	no	—
310	C₄×C₈	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	D₄×C₁₀₁	1	2	yes	—
316	C₂⁴	—	2	1	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	C₂²×C₄×C₁₀₁	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	C₂²×C₄×C₁₀₁	1	4	yes	—
347	C₂×C₈	#41×C₁₀₁	1	2	yes	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	8	1	no	—
360	C₄⋊C₄	D₈×C₁₀₁	1	4	yes	—
361	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
362	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
363	C₄⋊C₄	#41×C₁₀₁	1	2	yes	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	8	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	4	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	2	no	—
372	C₄²	C₂²×C₄×C₁₀₁	1	2	yes	—
373	C₄²	#41×C₁₀₁	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
382	Q₈	—	4	8	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
412	C₂×C₄	C₂×D₈×C₁₀₁	1	4	yes	—
413	C₂×C₄	C₂×D₈×C₁₀₁	1	2	yes	—
414	C₂×C₄	#135×C₁₀₁	1	2	yes	—
415	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
419	C₂×C₄	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
420	C₂×C₄	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
421	C₈	—	2	4	no	—
422	C₈	—	2	2	no	—
423	C₈	—	4	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
432	C₂²	#547×C₁₀₁	1	1	yes	characteristic
433	C₂²	#548×C₁₀₁	1	1	yes	characteristic
434	C₂²	C₂²×D₈×C₁₀₁	1	1	yes	characteristic
435	C₂²	C₂×#135×C₁₀₁	1	1	yes	characteristic
436	C₂²	#577×C₁₀₁	1	1	yes	characteristic
437	C₂²	#578×C₁₀₁	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	2	no	—
446	C₄	C₄×D₈×C₁₀₁	1	4	yes	—
447	C₄	C₄×#41×C₁₀₁	1	1	yes	characteristic
448	C₄	#519×C₁₀₁	1	1	yes	characteristic
449	C₄	#552×C₁₀₁	1	1	yes	characteristic
450	C₄	#556×C₁₀₁	1	1	yes	characteristic
451	C₂	—	8	2	no	—
452	C₂	C₁₀₁×#2362	1	1	yes	characteristic
453	C₂	C₂×C₄×D₈×C₁₀₁	1	1	yes	characteristic
454	C₂	C₁₀₁×#2947	1	1	yes	characteristic
455	C₂	C₁₀₁×#3334	1	1	yes	characteristic
456	C₂	C₁₀₁×#3340	1	1	yes	characteristic
457	C₂	C₁₀₁×#3358	1	1	yes	characteristic
458	C₂	C₁₀₁×#3364	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2365	C₂	semidirect
4. C₁₀₁×#1990	C₂	semidirect
5. C₁₀₁×#1947	C₂	semidirect
8. C₁₀₁×#1918	C₂	semidirect
9. C₄×#107×C₁₀₁	C₂	semidirect
10. C₈×C₄⋊C₄×C₁₀₁	C₂	semidirect
16. #474×C₁₀₁	C₄	semidirect
221. #23060	C₁₀₁	direct (N × H)
231. #2365	C₂×C₁₀₁	semidirect
233. #1990	C₂×C₁₀₁	semidirect
234. #1947	C₂×C₁₀₁	semidirect
237. #1918	C₂×C₁₀₁	semidirect
238. C₄×#107	C₂×C₁₀₁	semidirect
239. C₈×C₄⋊C₄	C₂×C₁₀₁	semidirect
241. C₁₀₁	#23060	direct (N × H)
246. #474	C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#474×C₁₀₁	2
C₁₀₁×#2365	2
C₁₀₁×#2354	2
C₁₀₁×#1990	2
C₁₀₁×#1947	2
C₁₀₁×#1934	2
C₁₀₁×#1925	2
C₁₀₁×#1918	2
C₄×#107×C₁₀₁	2
C₈×C₄⋊C₄×C₁₀₁	2
C₄×#102×C₁₀₁	2
#23060	101

Subgroups — C101×#23060 #38805211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23060 #38805211