Subgroups — C₁₀₁×#8045 #38790196

Order 25856.

730 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#423×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₁₀₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1296	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₁₀₁	—	2	1	no	—
6	C₂³×C₈×C₁₀₁	—	2	1	no	—
7	C₂×#117×C₁₀₁	—	2	1	no	—
8	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
9	#423×C₁₀₁	—	2	2	no	—
10	#423×C₁₀₁	C₄	1	4	yes	complemented
11	C₂×C₄⋊C₈×C₁₀₁	—	2	1	no	—
12	C₂×C₄⋊C₈×C₁₀₁	—	2	2	no	—
13	C₂×C₄⋊C₈×C₁₀₁	—	2	1	no	—
14	C₂×C₄⋊C₈×C₁₀₁	C₄	1	4	yes	complemented
15	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
17	#384×C₁₀₁	C₂²	1	2	yes	—
18	#382×C₁₀₁	—	2	1	no	—
19	#380×C₁₀₁	—	2	1	no	—
20	#380×C₁₀₁	C₄	1	2	yes	—
21	C₄×C₄⋊C₄×C₁₀₁	—	2	1	no	—
22	C₄×C₄⋊C₄×C₁₀₁	C₄	1	2	yes	—
23	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
26	C₂×M₁₆×C₁₀₁	—	2	4	no	—
27	C₂×M₁₆×C₁₀₁	—	4	2	no	—
28	C₂×M₁₆×C₁₀₁	—	4	2	no	—
29	C₂²×C₈×C₁₀₁	—	2	4	no	—
30	C₂²×C₈×C₁₀₁	—	2	2	no	—
31	C₂²×C₈×C₁₀₁	—	2	2	no	—
32	C₂²×C₈×C₁₀₁	—	4	4	no	—
33	#117×C₁₀₁	—	4	2	no	—
34	#117×C₁₀₁	—	4	2	no	—
35	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
38	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
39	C₂×C₄²×C₁₀₁	—	2	2	no	—
40	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
46	C₂×C₄²×C₁₀₁	Q₈	1	2	yes	—
47	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
48	C₄⋊C₈×C₁₀₁	—	2	4	no	—
49	C₄⋊C₈×C₁₀₁	—	2	4	no	—
50	C₄⋊C₈×C₁₀₁	—	2	2	no	—
51	C₄⋊C₈×C₁₀₁	—	2	2	no	—
52	C₄⋊C₈×C₁₀₁	C₂×C₄	1	4	yes	—
53	C₄⋊C₈×C₁₀₁	C₂×C₄	1	4	yes	—
54	#95×C₁₀₁	—	2	2	no	—
55	#95×C₁₀₁	—	2	2	no	—
56	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₀₁	—	2	2	no	—
58	C₂²×C₄×C₁₀₁	—	2	2	no	—
59	C₂²×C₄×C₁₀₁	—	2	4	no	—
60	C₂²×C₄×C₁₀₁	—	4	2	no	—
61	C₂²×C₄×C₁₀₁	C₄²	1	2	yes	—
62	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₀₁	D₈	1	2	yes	—
71	C₂²×C₄×C₁₀₁	SD₁₆	1	2	yes	—
72	C₂²×C₄×C₁₀₁	SD₁₆	1	2	yes	—
73	C₂²×C₄×C₁₀₁	Q₁₆	1	2	yes	—
74	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
77	M₁₆×C₁₀₁	—	4	8	no	—
78	C₂×C₈×C₁₀₁	—	2	4	no	—
79	C₂×C₈×C₁₀₁	—	2	4	no	—
80	C₂×C₈×C₁₀₁	—	4	8	no	—
81	C₂×C₈×C₁₀₁	—	4	2	no	—
82	C₂×C₈×C₁₀₁	—	4	2	no	—
83	C₂×C₈×C₁₀₁	—	4	4	no	—
84	C₄⋊C₄×C₁₀₁	—	4	4	no	—
85	C₄⋊C₄×C₁₀₁	—	4	2	no	—
86	C₄⋊C₄×C₁₀₁	—	4	2	no	—
87	C₄⋊C₄×C₁₀₁	—	4	2	no	—
88	C₄⋊C₄×C₁₀₁	—	4	2	no	—
89	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
90	C₄²×C₁₀₁	—	4	4	no	—
91	C₄²×C₁₀₁	C₄²	1	2	yes	—
92	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
93	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₁₀₁	C₄⋊C₄	1	2	yes	—
95	C₄²×C₁₀₁	C₄⋊C₄	1	2	yes	—
96	C₄²×C₁₀₁	C₄⋊C₄	1	2	yes	—
97	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
98	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
101	C₂³×C₁₀₁	—	2	2	no	—
102	C₂³×C₁₀₁	—	2	2	no	—
103	C₂³×C₁₀₁	#95	1	2	yes	—
104	C₂³×C₁₀₁	#102	1	2	yes	—
105	C₂³×C₁₀₁	#103	1	2	yes	—
106	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₀₁	—	2	2	no	—
108	C₂×C₄×C₁₀₁	—	2	2	no	—
109	C₂×C₄×C₁₀₁	—	2	2	no	—
110	C₂×C₄×C₁₀₁	—	2	2	no	—
111	C₂×C₄×C₁₀₁	—	2	2	no	—
112	C₂×C₄×C₁₀₁	—	2	4	no	—
113	C₂×C₄×C₁₀₁	—	4	2	no	—
114	C₂×C₄×C₁₀₁	—	4	2	no	—
115	C₂×C₄×C₁₀₁	—	4	4	no	—
116	C₂×C₄×C₁₀₁	—	4	4	no	—
117	C₂×C₄×C₁₀₁	—	4	4	no	—
118	C₂×C₄×C₁₀₁	#95	1	2	yes	—
119	C₂×C₄×C₁₀₁	#95	1	2	yes	—
120	C₂×C₄×C₁₀₁	#95	1	2	yes	—
121	C₂×C₄×C₁₀₁	#102	1	2	yes	—
122	C₂×C₄×C₁₀₁	#102	1	4	yes	—
123	C₂×C₄×C₁₀₁	#103	1	2	yes	—
124	C₂×C₄×C₁₀₁	#103	1	4	yes	—
125	C₂×C₄×C₁₀₁	#106	1	4	yes	—
126	C₂×C₄×C₁₀₁	#107	1	4	yes	—
127	C₂×C₄×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
128	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₀₁	C₂×D₈	1	1	yes	characteristic
134	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
135	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
136	C₂×C₄×C₁₀₁	C₂×Q₁₆	1	1	yes	characteristic
137	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
138	C₂×C₄×C₁₀₁	#137	1	2	yes	—
139	C₈×C₁₀₁	—	4	4	no	—
140	C₈×C₁₀₁	—	4	4	no	—
141	C₂²×C₁₀₁	—	2	4	no	—
142	C₂²×C₁₀₁	—	2	4	no	—
143	C₂²×C₁₀₁	—	2	2	no	—
144	C₂²×C₁₀₁	—	2	2	no	—
145	C₂²×C₁₀₁	#340	1	4	yes	—
146	C₂²×C₁₀₁	C₂×#95	1	1	yes	characteristic
147	C₂²×C₁₀₁	#413	1	2	yes	—
148	C₂²×C₁₀₁	C₂×#102	1	1	yes	characteristic
149	C₂²×C₁₀₁	C₂×#103	1	1	yes	characteristic
150	C₂²×C₁₀₁	#417	1	2	yes	—
151	C₄×C₁₀₁	—	2	2	no	—
152	C₄×C₁₀₁	—	2	2	no	—
153	C₄×C₁₀₁	—	2	1	no	—
154	C₄×C₁₀₁	—	2	1	no	—
155	C₄×C₁₀₁	—	8	4	no	—
156	C₄×C₁₀₁	#340	1	4	yes	—
157	C₄×C₁₀₁	C₂×#102	1	1	yes	characteristic
158	C₄×C₁₀₁	C₂×#103	1	1	yes	characteristic
159	C₄×C₁₀₁	#418	1	1	yes	characteristic
160	C₄×C₁₀₁	#419	1	1	yes	characteristic
161	C₄×C₁₀₁	C₂×#106	1	1	yes	characteristic
162	C₄×C₁₀₁	C₂×#107	1	1	yes	characteristic
163	C₄×C₁₀₁	#428	1	2	yes	—
164	#8045	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₁₀₁	—	2	4	no	—
166	C₂×C₁₀₁	#1547	1	2	yes	—
167	C₂×C₁₀₁	#1550	1	2	yes	—
168	C₂×C₁₀₁	C₂×#340	1	1	yes	characteristic
169	C₂×C₁₀₁	#1736	1	1	yes	characteristic
170	C₂×C₁₀₁	#1742	1	1	yes	characteristic
171	C₂×#423	C₂×C₁₀₁	1	1	yes	characteristic
172	C₂²×C₄⋊C₈	C₂×C₁₀₁	1	1	yes	characteristic
173	#2285	C₂×C₁₀₁	1	1	yes	characteristic
174	#1296	C₂×C₁₀₁	1	4	yes	complemented
175	C₁₀₁	#8045	1	1	yes	characteristic, direct product factor, Sylow
176	C₂²×M₁₆	—	2	1	no	—
177	C₂³×C₈	—	2	1	no	—
178	C₂×#117	—	2	1	no	—
179	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
180	#423	—	2	2	no	—
181	#423	C₄×C₁₀₁	1	4	yes	complemented
182	C₂×C₄⋊C₈	—	2	1	no	—
183	C₂×C₄⋊C₈	—	2	2	no	—
184	C₂×C₄⋊C₈	—	2	1	no	—
185	C₂×C₄⋊C₈	C₄×C₁₀₁	1	4	yes	complemented
186	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
188	#384	C₂²×C₁₀₁	1	2	yes	—
189	#382	—	2	1	no	—
190	#380	—	2	1	no	—
191	#380	C₄×C₁₀₁	1	2	yes	—
192	C₄×C₄⋊C₄	—	2	1	no	—
193	C₄×C₄⋊C₄	C₄×C₁₀₁	1	2	yes	—
194	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
195	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
196	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
197	C₂×M₁₆	—	2	4	no	—
198	C₂×M₁₆	—	4	2	no	—
199	C₂×M₁₆	—	4	2	no	—
200	C₂²×C₈	—	2	4	no	—
201	C₂²×C₈	—	2	2	no	—
202	C₂²×C₈	—	2	2	no	—
203	C₂²×C₈	—	4	4	no	—
204	#117	—	4	2	no	—
205	#117	—	4	2	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	2	2	no	—
208	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
209	C₂×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₄²	—	2	2	no	—
211	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
212	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
213	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
214	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
215	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
216	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
217	C₂×C₄²	Q₈×C₁₀₁	1	2	yes	—
218	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
219	C₄⋊C₈	—	2	4	no	—
220	C₄⋊C₈	—	2	4	no	—
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	C₂×C₄×C₁₀₁	1	4	yes	—
224	C₄⋊C₈	C₂×C₄×C₁₀₁	1	4	yes	—
225	#95	—	2	2	no	—
226	#95	—	2	2	no	—
227	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	4	2	no	—
232	C₂²×C₄	C₄²×C₁₀₁	1	2	yes	—
233	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
234	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
235	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
236	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
237	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
238	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	2	yes	—
239	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	2	yes	—
240	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	2	yes	—
241	C₂²×C₄	D₈×C₁₀₁	1	2	yes	—
242	C₂²×C₄	SD₁₆×C₁₀₁	1	2	yes	—
243	C₂²×C₄	SD₁₆×C₁₀₁	1	2	yes	—
244	C₂²×C₄	Q₁₆×C₁₀₁	1	2	yes	—
245	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
246	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
247	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
248	M₁₆	—	4	8	no	—
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	4	8	no	—
252	C₂×C₈	—	4	2	no	—
253	C₂×C₈	—	4	2	no	—
254	C₂×C₈	—	4	4	no	—
255	C₄⋊C₄	—	4	4	no	—
256	C₄⋊C₄	—	4	2	no	—
257	C₄⋊C₄	—	4	2	no	—
258	C₄⋊C₄	—	4	2	no	—
259	C₄⋊C₄	—	4	2	no	—
260	C₂²⋊C₄	—	4	4	no	—
261	C₄²	—	4	4	no	—
262	C₄²	C₄²×C₁₀₁	1	2	yes	—
263	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
264	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
265	C₄²	C₄⋊C₄×C₁₀₁	1	2	yes	—
266	C₄²	C₄⋊C₄×C₁₀₁	1	2	yes	—
267	C₄²	C₄⋊C₄×C₁₀₁	1	2	yes	—
268	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
269	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
270	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
271	C₄²	C₂×Q₈×C₁₀₁	1	1	yes	characteristic
272	C₂³	—	2	2	no	—
273	C₂³	—	2	2	no	—
274	C₂³	#95×C₁₀₁	1	2	yes	—
275	C₂³	#102×C₁₀₁	1	2	yes	—
276	C₂³	#103×C₁₀₁	1	2	yes	—
277	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	4	4	no	—
287	C₂×C₄	—	4	4	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	#95×C₁₀₁	1	2	yes	—
290	C₂×C₄	#95×C₁₀₁	1	2	yes	—
291	C₂×C₄	#95×C₁₀₁	1	2	yes	—
292	C₂×C₄	#102×C₁₀₁	1	4	yes	—
293	C₂×C₄	#102×C₁₀₁	1	2	yes	—
294	C₂×C₄	#103×C₁₀₁	1	4	yes	—
295	C₂×C₄	#103×C₁₀₁	1	2	yes	—
296	C₂×C₄	#106×C₁₀₁	1	4	yes	—
297	C₂×C₄	#107×C₁₀₁	1	4	yes	—
298	C₂×C₄	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
299	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
300	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
301	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
302	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
303	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
304	C₂×C₄	C₂×D₈×C₁₀₁	1	1	yes	characteristic
305	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	1	yes	characteristic
306	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	1	yes	characteristic
307	C₂×C₄	C₂×Q₁₆×C₁₀₁	1	1	yes	characteristic
308	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
309	C₂×C₄	#137×C₁₀₁	1	2	yes	—
310	C₈	—	4	4	no	—
311	C₈	—	4	4	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	4	no	—
316	C₂²	#340×C₁₀₁	1	4	yes	—
317	C₂²	C₂×#95×C₁₀₁	1	1	yes	characteristic
318	C₂²	#413×C₁₀₁	1	2	yes	—
319	C₂²	C₂×#102×C₁₀₁	1	1	yes	characteristic
320	C₂²	C₂×#103×C₁₀₁	1	1	yes	characteristic
321	C₂²	#417×C₁₀₁	1	2	yes	—
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	1	no	—
325	C₄	—	2	1	no	—
326	C₄	—	8	4	no	—
327	C₄	#340×C₁₀₁	1	4	yes	—
328	C₄	C₂×#102×C₁₀₁	1	1	yes	characteristic
329	C₄	C₂×#103×C₁₀₁	1	1	yes	characteristic
330	C₄	#418×C₁₀₁	1	1	yes	characteristic
331	C₄	#419×C₁₀₁	1	1	yes	characteristic
332	C₄	C₂×#106×C₁₀₁	1	1	yes	characteristic
333	C₄	C₂×#107×C₁₀₁	1	1	yes	characteristic
334	C₄	#428×C₁₀₁	1	2	yes	—
335	C₂	—	2	4	no	—
336	C₂	C₁₀₁×#1547	1	2	yes	—
337	C₂	C₁₀₁×#1550	1	2	yes	—
338	C₂	C₂×#340×C₁₀₁	1	1	yes	characteristic
339	C₂	C₁₀₁×#1736	1	1	yes	characteristic
340	C₂	C₁₀₁×#1742	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₀₁×#1296	C₂	semidirect
10. #423×C₁₀₁	C₄	semidirect
14. C₂×C₄⋊C₈×C₁₀₁	C₄	semidirect
164. #8045	C₁₀₁	direct (N × H)
174. #1296	C₂×C₁₀₁	semidirect
175. C₁₀₁	#8045	direct (N × H)
181. #423	C₄×C₁₀₁	semidirect
185. C₂×C₄⋊C₈	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×#423×C₁₀₁	2
C₂²×C₄⋊C₈×C₁₀₁	2
C₁₀₁×#2285	2
C₁₀₁×#1296	2
#8045	101

Subgroups — C101×#8045 #38790196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#8045 #38790196