Group #27179575 — subgroups

Subgroups — #27179575

Order 12928.

764 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13108074	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×D₁₀₁	C₂	1	2	yes	maximal, complemented
3	#20265142	C₂	1	8	yes	maximal, complemented
4	#20265141	C₂	1	1	yes	maximal, characteristic, complemented
5	#20265140	C₂	1	2	yes	maximal, complemented
6	#407×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13108074	—	2	8	no	—
8	C₂×#13108074	C₄	1	4	yes	—
9	C₂×#13108074	C₂²	1	4	yes	—
10	C₂²×Dic₂₀₂	C₄	1	1	yes	characteristic
11	C₂²×D₄₀₄	C₄	1	1	yes	characteristic
12	C₂²×C₂²⋊D₁₀₁	C₄	1	1	yes	characteristic
13	C₂²×C₂²⋊D₁₀₁	C₄	1	1	yes	characteristic
14	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×#13108058	C₂²	1	2	yes	—
17	C₂×#13108057	C₂²	1	4	yes	complemented
18	M₁₆×D₁₀₁	—	2	8	no	—
19	C₂×C₈×D₁₀₁	C₂²	1	4	yes	complemented
20	C₂²⋊#11717579	C₂²	1	4	yes	complemented
21	#15692167	C₂²	1	8	yes	complemented
22	C₂³×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂×M₁₆×C₁₀₁	C₂²	1	2	yes	—
24	C₂²⋊C₈×C₁₀₁	C₂²	1	4	yes	complemented
25	C₂³×D₁₀₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×D₁₀₁	C₂×C₄	1	1	yes	characteristic
27	#13108074	—	2	16	no	—
28	#13108074	—	2	8	no	—
29	#13108074	—	2	8	no	—
30	C₂×Dic₂₀₂	—	2	4	no	—
31	C₂×Dic₂₀₂	C₂×C₄	1	4	yes	—
32	C₂×D₄₀₄	—	2	4	no	—
33	C₂×D₄₀₄	C₂×C₄	1	4	yes	—
34	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
35	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
36	C₂×C₂²⋊D₁₀₁	C₂×C₄	1	4	yes	—
37	C₂×C₂²⋊D₁₀₁	C₂×C₄	1	4	yes	—
38	C₂²×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×D₁₀₁	—	2	4	no	—
41	C₂×C₄×D₁₀₁	C₂×C₄	1	2	yes	—
42	C₂×C₄×D₁₀₁	C₂×C₄	1	2	yes	—
43	C₂×C₄×D₁₀₁	D₄	1	8	yes	—
44	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
45	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
46	#13108058	—	2	4	no	—
47	#13108057	—	2	8	no	—
48	C₂×#11717579	C₂³	1	4	yes	—
49	C₈×D₁₀₁	—	2	8	no	—
50	C₂⁴×C₁₀₁	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₀₁	—	2	4	no	—
52	C₂²×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
54	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
55	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
56	M₁₆×C₁₀₁	—	2	4	no	—
57	C₂×C₈×C₁₀₁	C₂³	1	4	yes	—
58	C₂³×C₁₀₁	—	2	2	no	—
59	C₂³×C₁₀₁	—	4	2	no	—
60	C₂³×C₁₀₁	C₂²×C₄	1	2	yes	—
61	C₂³×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×D₁₀₁	—	2	2	no	—
63	C₂²×D₁₀₁	—	4	2	no	—
64	C₂²×D₁₀₁	—	4	2	no	—
65	C₂²×D₁₀₁	C₂²⋊C₄	1	4	yes	—
66	C₂²×D₁₀₁	C₂²×C₄	1	2	yes	—
67	C₂²×D₁₀₁	C₂²×C₄	1	2	yes	—
68	C₂×C₄×C₁₀₁	—	2	2	no	—
69	C₂×C₄×C₁₀₁	—	2	4	no	—
70	C₂×C₄×C₁₀₁	—	2	4	no	—
71	C₂×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
74	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
75	C₂²⋊D₁₀₁	—	2	8	no	—
76	C₂²⋊D₁₀₁	—	2	8	no	—
77	C₂×Dic₁₀₁	—	2	2	no	—
78	C₂×Dic₁₀₁	C₂²⋊C₄	1	4	yes	—
79	C₂×Dic₁₀₁	C₂²×C₄	1	2	yes	—
80	C₂×Dic₁₀₁	C₂²×C₄	1	2	yes	—
81	D₄₀₄	—	2	8	no	—
82	C₄×D₁₀₁	—	2	4	no	—
83	C₄×D₁₀₁	—	2	4	no	—
84	C₄×D₁₀₁	C₂²⋊C₄	1	8	yes	—
85	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
86	C₄×D₁₀₁	C₂×D₄	1	4	yes	—
87	Dic₂₀₂	—	2	8	no	—
88	C₈×C₁₀₁	—	2	4	no	—
89	#11717579	—	2	4	no	—
90	C₂²×C₁₀₁	—	2	2	no	—
91	C₂²×C₁₀₁	—	2	2	no	—
92	C₂²×C₁₀₁	—	2	4	no	—
93	C₂²×C₁₀₁	—	4	4	no	—
94	C₂²×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
95	C₂²×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
96	C₂×D₁₀₁	—	2	4	no	—
97	C₂×D₁₀₁	—	2	2	no	—
98	C₂×D₁₀₁	—	2	4	no	—
99	C₂×D₁₀₁	—	4	4	no	—
100	C₂×D₁₀₁	—	4	4	no	—
101	C₂×D₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
102	C₄×C₁₀₁	—	2	2	no	—
103	C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
104	C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
105	Dic₁₀₁	—	2	2	no	—
106	Dic₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
107	C₂×C₁₀₁	—	2	2	no	—
108	C₂×C₁₀₁	—	4	2	no	—
109	C₂×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₁₀₁	#568	1	2	yes	—
111	D₁₀₁	—	2	4	no	—
112	D₁₀₁	—	4	2	no	—
113	#2879	—	101	1	no	maximal, Sylow
114	C₁₀₁	#2879	1	1	yes	characteristic, complemented, Sylow
115	C₂²×#41	—	101	1	no	—
116	C₂²×M₁₆	—	101	2	no	—
117	#408	—	101	8	no	—
118	#407	—	101	1	no	—
119	#407	—	101	2	no	—
120	#407	D₁₀₁	1	1	yes	characteristic, complemented
121	C₂×#41	—	101	4	no	—
122	C₂×#41	—	101	4	no	—
123	C₂×#41	—	202	8	no	—
124	C₂²×Q₈	—	101	1	no	—
125	C₂²×D₄	—	101	1	no	—
126	C₂²×D₄	—	101	1	no	—
127	C₂²×D₄	—	101	1	no	—
128	C₂³×C₄	—	101	1	no	—
129	C₂³×C₄	—	101	1	no	—
130	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic
131	C₂×M₁₆	—	101	2	no	—
132	C₂×M₁₆	—	101	4	no	—
133	C₂×M₁₆	—	202	8	no	—
134	C₂×M₁₆	C₂×D₁₀₁	1	2	yes	—
135	C₂²×C₈	—	101	4	no	—
136	C₂²⋊C₈	—	101	4	no	—
137	C₂²⋊C₈	—	101	8	no	—
138	C₂²⋊C₈	C₂×D₁₀₁	1	4	yes	complemented
139	C₂⁴	—	101	1	no	—
140	C₂⁴	—	101	1	no	—
141	C₂⁴	C₄×D₁₀₁	1	1	yes	characteristic
142	#41	—	202	8	no	—
143	#41	—	202	8	no	—
144	#41	—	202	16	no	—
145	C₂×Q₈	—	101	4	no	—
146	C₂×Q₈	—	202	4	no	—
147	C₂×D₄	—	101	4	no	—
148	C₂×D₄	—	101	4	no	—
149	C₂×D₄	—	101	4	no	—
150	C₂×D₄	—	202	4	no	—
151	C₂×D₄	—	202	4	no	—
152	C₂×D₄	—	202	4	no	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	—	101	1	no	—
155	C₂²×C₄	—	101	2	no	—
156	C₂²×C₄	—	101	8	no	—
157	C₂²×C₄	—	101	2	no	—
158	C₂²×C₄	—	101	1	no	—
159	C₂²×C₄	—	101	2	no	—
160	C₂²×C₄	—	101	2	no	—
161	C₂²×C₄	—	202	4	no	—
162	C₂²×C₄	C₄×D₁₀₁	1	1	yes	characteristic
163	C₂²×C₄	C₄×D₁₀₁	1	2	yes	—
164	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
165	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
166	M₁₆	—	2	4	no	—
167	M₁₆	—	202	8	no	—
168	M₁₆	—	202	4	no	—
169	C₂×C₈	—	101	4	no	—
170	C₂×C₈	—	202	8	no	—
171	C₂×C₈	C₂²×D₁₀₁	1	4	yes	—
172	C₂³	—	2	2	no	—
173	C₂³	—	4	2	no	—
174	C₂³	—	101	4	no	—
175	C₂³	—	101	2	no	—
176	C₂³	—	101	2	no	—
177	C₂³	—	404	2	no	—
178	C₂³	—	404	2	no	—
179	C₂³	—	202	2	no	—
180	C₂³	C₂×C₄×D₁₀₁	1	2	yes	—
181	C₂³	C₂×C₄×D₁₀₁	1	1	yes	characteristic
182	Q₈	—	202	8	no	—
183	D₄	—	202	8	no	—
184	D₄	—	202	8	no	—
185	D₄	—	202	8	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	101	2	no	—
190	C₂×C₄	—	101	4	no	—
191	C₂×C₄	—	101	4	no	—
192	C₂×C₄	—	101	4	no	—
193	C₂×C₄	—	101	8	no	—
194	C₂×C₄	—	101	2	no	—
195	C₂×C₄	—	202	2	no	—
196	C₂×C₄	—	202	4	no	—
197	C₂×C₄	—	202	4	no	—
198	C₂×C₄	C₂×C₄×D₁₀₁	1	2	yes	—
199	C₂×C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
200	C₂×C₄	D₄×D₁₀₁	1	4	yes	—
201	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
202	C₈	—	2	4	no	—
203	C₈	—	202	4	no	—
204	C₂²	—	2	2	no	—
205	C₂²	—	2	2	no	—
206	C₂²	—	2	4	no	—
207	C₂²	—	4	4	no	—
208	C₂²	—	101	4	no	—
209	C₂²	—	404	4	no	—
210	C₂²	—	404	4	no	—
211	C₂²	—	202	2	no	—
212	C₂²	—	202	4	no	—
213	C₂²	—	202	4	no	—
214	C₂²	C₂²⋊C₄×D₁₀₁	1	2	yes	—
215	C₂²	C₂²×C₄×D₁₀₁	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	101	4	no	—
218	C₄	—	202	2	no	—
219	C₄	C₂²⋊C₄×D₁₀₁	1	2	yes	—
220	C₄	C₂×D₄×D₁₀₁	1	2	yes	—
221	C₂	—	2	2	no	—
222	C₂	—	4	2	no	—
223	C₂	—	404	2	no	—
224	C₂	—	202	4	no	—
225	C₂	C₂×C₂²⋊C₄×D₁₀₁	1	1	yes	characteristic
226	C₂	#20265943	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#13108074

C₂

yes

maximal, characteristic

C₂×M₁₆×D₁₀₁

C₂

yes

maximal, complemented

#20265142

C₂

yes

maximal, complemented

#20265141

C₂

yes

maximal, characteristic, complemented

#20265140

C₂

yes

maximal, complemented

#407×C₁₀₁

C₂

yes

maximal, characteristic, complemented

C₂×#13108074

—

C₂×#13108074

C₄

yes

—

C₂×#13108074

C₂²

yes

—

C₂²×Dic₂₀₂

C₄

yes

characteristic

C₂²×D₄₀₄

C₄

yes

characteristic

C₂²×C₂²⋊D₁₀₁

C₄

yes

characteristic

C₂²×C₂²⋊D₁₀₁

C₄

yes

characteristic

C₂²×C₄×D₁₀₁

C₂²

yes

characteristic

C₂²×C₄×D₁₀₁

C₂²

yes

characteristic

C₂×#13108058

C₂²

yes

—

C₂×#13108057

C₂²

yes

complemented

M₁₆×D₁₀₁

—

C₂×C₈×D₁₀₁

C₂²

yes

complemented

C₂²⋊#11717579

C₂²

yes

complemented

#15692167

C₂²

yes

complemented

C₂³×C₄×C₁₀₁

C₂²

yes

characteristic

C₂×M₁₆×C₁₀₁

C₂²

yes

—

C₂²⋊C₈×C₁₀₁

C₂²

yes

complemented

C₂³×D₁₀₁

C₂×C₄

yes

characteristic

C₂³×D₁₀₁

C₂×C₄

yes

—

—

—

C₂×Dic₂₀₂

—

C₂×Dic₂₀₂

C₂×C₄

yes

—

C₂×D₄₀₄

—

C₂×D₄₀₄

C₂×C₄

yes

—

C₂×C₂²⋊D₁₀₁

—

C₂×C₂²⋊D₁₀₁

—

C₂×C₂²⋊D₁₀₁

C₂×C₄

yes

—

C₂×C₂²⋊D₁₀₁

C₂×C₄

yes

—

C₂²×Dic₁₀₁

C₂×C₄

yes

characteristic

C₂²×Dic₁₀₁

C₂×C₄

yes

characteristic

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

C₂×C₄

yes

—

C₂×C₄×D₁₀₁

C₂×C₄

yes

—

C₂×C₄×D₁₀₁

D₄

yes

—

C₂×C₄×D₁₀₁

C₂³

yes

—

C₂×C₄×D₁₀₁

C₂³

yes

—

#13108058

—

#13108057

—

C₂×#11717579

C₂³

yes

—

C₈×D₁₀₁

—

C₂⁴×C₁₀₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₀₁

—

C₂²×C₄×C₁₀₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₀₁

C₂×C₄

yes

—

C₂²×C₄×C₁₀₁

C₂³

yes

—

C₂²×C₄×C₁₀₁

C₂³

yes

characteristic

M₁₆×C₁₀₁

—

C₂×C₈×C₁₀₁

C₂³

yes

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

C₂²×C₄

yes

—

C₂³×C₁₀₁

C₂²×C₄

yes

characteristic

C₂²×D₁₀₁

—

C₂²×D₁₀₁

—

C₂²×D₁₀₁

—

C₂²×D₁₀₁

C₂²⋊C₄

yes

—

C₂²×D₁₀₁

C₂²×C₄

yes

—

C₂²×D₁₀₁

C₂²×C₄

yes

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

C₂²×C₄

yes

—

C₂×C₄×C₁₀₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₀₁

C₂×D₄

yes

—

C₂×C₄×C₁₀₁

C₂⁴

yes

characteristic

C₂²⋊D₁₀₁

—

C₂²⋊D₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

C₂²⋊C₄

yes

—

C₂×Dic₁₀₁

C₂²×C₄

yes

—

C₂×Dic₁₀₁

C₂²×C₄

yes

—

D₄₀₄

—

C₄×D₁₀₁

—

C₄×D₁₀₁

—

C₄×D₁₀₁

C₂²⋊C₄

yes

—

C₄×D₁₀₁

C₂×D₄

yes

—

C₄×D₁₀₁

C₂×D₄

yes

—

Dic₂₀₂

—

C₈×C₁₀₁

—

#11717579

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

C₂×C₂²⋊C₄

yes

—

C₂²×C₁₀₁

C₂³×C₄

yes

characteristic

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₂×D₁₀₁

—

100

C₂×D₁₀₁

—

101

C₂×D₁₀₁

C₂×C₂²⋊C₄

yes

—

102

C₄×C₁₀₁

—

103

C₄×C₁₀₁

C₂×C₂²⋊C₄

yes

—

104

C₄×C₁₀₁

C₂²×D₄

yes

—

105

Dic₁₀₁

—

106

Dic₁₀₁

C₂×C₂²⋊C₄

yes

—

107

C₂×C₁₀₁

—

108

C₂×C₁₀₁

—

109

C₂×C₁₀₁

C₂²×C₂²⋊C₄

yes

characteristic

110

C₂×C₁₀₁

#568

yes

—

111

D₁₀₁

—

112

D₁₀₁

—

113

#2879

—

101

maximal, Sylow

114

C₁₀₁

#2879

yes

characteristic, complemented, Sylow

115

C₂²×#41

—

101

—

116

C₂²×M₁₆

—

101

—

117

#408

—

101

—

118

#407

—

101

—

119

#407

—

101

—

120

#407

D₁₀₁

yes

characteristic, complemented

121

C₂×#41

—

101

—

122

C₂×#41

—

101

—

123

C₂×#41

—

202

—

124

C₂²×Q₈

—

101

—

125

C₂²×D₄

—

101

—

126

C₂²×D₄

—

101

—

127

C₂²×D₄

—

101

—

128

C₂³×C₄

—

101

—

129

C₂³×C₄

—

101

—

130

C₂³×C₄

C₂×D₁₀₁

yes

characteristic

131

C₂×M₁₆

—

101

—

132

C₂×M₁₆

—

101

—

133

C₂×M₁₆

—

202

—

134

C₂×M₁₆

C₂×D₁₀₁

yes

—

135

C₂²×C₈

—

101

—

136

C₂²⋊C₈

—

101

—

137

C₂²⋊C₈

—

101

—

138

C₂²⋊C₈

C₂×D₁₀₁

yes

complemented

139

C₂⁴

—

101

—

140

C₂⁴

—

101

—

141

C₂⁴

C₄×D₁₀₁

yes

characteristic

142

#41

—

202

—

143

#41

—

202

—

144

#41

—

202

—

145

C₂×Q₈

—

101

—

146

C₂×Q₈

—

202

—

147

C₂×D₄

—

101

—

148

C₂×D₄

—

101

—

149

C₂×D₄

—

101

—

150

C₂×D₄

—

202

—

151

C₂×D₄

—

202

—

152

C₂×D₄

—

202

—

153

C₂²×C₄

—

154

C₂²×C₄

—

101

—

155

C₂²×C₄

—

101

—

156

C₂²×C₄

—

101

—

157

C₂²×C₄

—

101

—

158

C₂²×C₄

—

101

—

159

C₂²×C₄

—

101

—

160

C₂²×C₄

—

101

—

161

C₂²×C₄

—

202

—

162

C₂²×C₄

C₄×D₁₀₁

yes

characteristic

163

C₂²×C₄

C₄×D₁₀₁

yes

—

164

C₂²×C₄

C₂²×D₁₀₁

yes

—

165

C₂²×C₄

C₂²×D₁₀₁

yes

characteristic

166

M₁₆

—

167

M₁₆

—

202

—

168

M₁₆

—

202

—

169

C₂×C₈

—

101

—

170

C₂×C₈

—

202

—

171

C₂×C₈

C₂²×D₁₀₁

yes

—

172

C₂³

—

173

C₂³

—

174

C₂³

—

101

—

175

C₂³

—

101

—

176

C₂³

—

101

—

177

C₂³

—

404

—

178

C₂³

—

404

—

179

C₂³

—

202

—

180

C₂³

C₂×C₄×D₁₀₁

yes

—

181

C₂³

C₂×C₄×D₁₀₁

yes

characteristic

182

Q₈

—

202

—

183

D₄

—

202

—

184

D₄

—

202

—

185

D₄

—

202

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

101

—

190

C₂×C₄

—

101

—

191

C₂×C₄

—

101

—

192

C₂×C₄

—

101

—

193

C₂×C₄

—

101

—

194

C₂×C₄

—

101

—

195

C₂×C₄

—

202

—

196

C₂×C₄

—

202

—

197

C₂×C₄

—

202

—

198

C₂×C₄

C₂×C₄×D₁₀₁

yes

—

199

C₂×C₄

C₂×C₄×D₁₀₁

yes

characteristic

200

C₂×C₄

D₄×D₁₀₁

yes

—

201

C₂×C₄

C₂³×D₁₀₁

yes

characteristic

202

C₈

—

203

C₈

—

202

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

101

—

209

C₂²

—

404

—

210

C₂²

—

404

—

211

C₂²

—

202

—

212

C₂²

—

202

—

213

C₂²

—

202

—

214

C₂²

C₂²⋊C₄×D₁₀₁

yes

—

215

C₂²

C₂²×C₄×D₁₀₁

yes

characteristic

216

C₄

—

217

C₄

—

101

—

218

C₄

—

202

—

219

C₄

C₂²⋊C₄×D₁₀₁

yes

—

220

C₄

C₂×D₄×D₁₀₁

yes

—

221

C₂

—

222

C₂

—

223

C₂

—

404

—

224

C₂

—

202

—

225

C₂

C₂×C₂²⋊C₄×D₁₀₁

yes

characteristic

226

C₂

#20265943

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₀₁
commutator, socle	C₂²×C₁₀₁	C₂³×C₄
Fitting	#407×C₁₀₁	C₂
prime radical	C₂²×#13108074	C₂
cosocle	C₂×C₄×C₁₀₁	C₂⁴
hypercenter	#407	D₁₀₁
hypocenter	C₁₀₁	#2879
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ #407

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₀₁

commutator, socle

C₂²×C₁₀₁

C₂³×C₄

Fitting

#407×C₁₀₁

C₂

prime radical

C₂²×#13108074

C₂

cosocle

C₂×C₄×C₁₀₁

C₂⁴

D₁₀₁

C₁₀₁

G ▷ C₂²×C₁₀₁ ▷ C₁₀₁

C₁ ◁ C₂×C₄ ◁ #407

N	H ≅ G/N	type
2. C₂×M₁₆×D₁₀₁	C₂	semidirect
3. #20265142	C₂	semidirect
4. #20265141	C₂	semidirect
5. #20265140	C₂	semidirect
6. #407×C₁₀₁	C₂	semidirect
17. C₂×#13108057	C₂²	semidirect
19. C₂×C₈×D₁₀₁	C₂²	semidirect
20. C₂²⋊#11717579	C₂²	semidirect
21. #15692167	C₂²	semidirect
24. C₂²⋊C₈×C₁₀₁	C₂²	semidirect
114. C₁₀₁	#2879	semidirect
120. #407	D₁₀₁	semidirect
138. C₂²⋊C₈	C₂×D₁₀₁	semidirect

H ≅ G/N

type

2. C₂×M₁₆×D₁₀₁

C₂

semidirect

3. #20265142

C₂

semidirect

4. #20265141

C₂

semidirect

5. #20265140

C₂

semidirect

6. #407×C₁₀₁

C₂

semidirect

17. C₂×#13108057

C₂²

semidirect

19. C₂×C₈×D₁₀₁

C₂²

semidirect

20. C₂²⋊#11717579

C₂²

semidirect

21. #15692167

C₂²

semidirect

24. C₂²⋊C₈×C₁₀₁

C₂²

semidirect

114. C₁₀₁

#2879

semidirect

120. #407

D₁₀₁

semidirect

138. C₂²⋊C₈

C₂×D₁₀₁

semidirect

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

subgroup	index
C₂²×#13108074	2
C₂×M₁₆×D₁₀₁	2
#20265142	2
#20265141	2
#20265140	2
#407×C₁₀₁	2
#2879	101

subgroup

index

C₂×M₁₆×D₁₀₁

#407×C₁₀₁

101

Subgroups — #27179575

Conjugacy classes of subgroups

Complements

Maximal subgroups