Group #28311127 — subgroups

Subgroups — #28311127

Order 13568.

478 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 148 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	C₂×C₄⋊#11719910	C₂	1	2	yes	maximal, complemented
2	C₂×#16811518	C₂	1	2	yes	maximal
3	#20289754	C₂	1	2	yes	maximal, complemented
4	C₂×#16810580	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11719910	C₂²	1	4	yes	—
6	C₄⋊#11719910	—	2	4	no	—
7	#16811518	—	2	4	no	—
8	C₂²×#11719912	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
10	C₂×#13133174	C₄	1	1	yes	characteristic
11	#16810580	—	2	4	no	—
12	C₂×#13133127	C₄	1	1	yes	characteristic
13	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
15	C₂×#97×C₅₃	C₄	1	1	yes	characteristic
16	C₂×#11719910	—	2	4	no	—
17	C₂×#11719910	—	2	4	no	—
18	C₂×#11719910	—	2	4	no	—
19	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
20	C₂×#11719912	—	2	2	no	—
21	C₂×#11719912	—	2	2	no	—
22	C₂×#11719912	—	2	2	no	—
23	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
24	C₂²×#88322	C₂³	1	1	yes	characteristic
25	C₂×C₈×D₅₃	—	2	2	no	—
26	C₂×C₈×D₅₃	—	2	2	no	—
27	C₂×C₈×D₅₃	D₄	1	2	yes	—
28	C₂×C₈×D₅₃	Q₈	1	2	yes	—
29	#13133174	—	2	2	no	—
30	#13133174	—	2	2	no	—
31	C₂×#11719919	C₈	1	2	yes	—
32	C₂×#11719921	C₈	1	2	yes	—
33	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
34	#13133127	—	2	2	no	—
35	C₄×#88322	D₄	1	4	yes	—
36	C₈×Dic₅₃	—	2	2	no	—
37	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
40	#97×C₅₃	—	2	2	no	—
41	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
42	C₂²×C₄×C₅₃	C₂×C₈	1	2	yes	—
43	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
44	C₂²×Dic₅₃	C₂×C₈	1	2	yes	—
45	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×D₅₃	—	2	1	no	—
47	C₂×C₄×D₅₃	—	2	1	no	—
48	C₂×C₄×D₅₃	—	2	1	no	—
49	C₂×C₄×D₅₃	—	2	1	no	—
50	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
51	C₂×C₄×D₅₃	M₁₆	1	2	yes	—
52	C₂×C₈×C₅₃	—	2	1	no	—
53	C₂×C₈×C₅₃	—	2	1	no	—
54	C₂×C₈×C₅₃	—	2	1	no	—
55	C₂×C₈×C₅₃	—	2	1	no	—
56	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
57	C₂×C₈×C₅₃	M₁₆	1	2	yes	—
58	C₄²×C₅₃	C₂²⋊C₄	1	2	yes	—
59	C₄²×C₅₃	M₁₆	1	2	yes	—
60	#11719921	—	2	4	no	—
61	#11719919	—	2	4	no	—
62	C₄×Dic₅₃	—	2	1	no	—
63	C₄×Dic₅₃	—	2	1	no	—
64	C₂×#88322	—	2	1	no	—
65	C₂×#88322	—	2	1	no	—
66	C₂×#88322	C₂²⋊C₄	1	2	yes	—
67	C₂×#88322	C₂×D₄	1	1	yes	characteristic
68	C₂×#88322	C₂×D₄	1	2	yes	—
69	C₂×#88322	C₂×Q₈	1	1	yes	characteristic
70	C₂×#88322	#41	1	2	yes	—
71	#11719912	—	2	8	no	—
72	C₈×D₅₃	—	2	4	no	—
73	C₈×D₅₃	—	2	4	no	—
74	#11719910	—	4	4	no	—
75	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
76	C₂²×D₅₃	—	2	1	no	—
77	C₂²×D₅₃	—	2	1	no	—
78	C₂²×D₅₃	—	2	4	no	—
79	C₂²×D₅₃	C₄⋊C₈	1	2	yes	—
80	C₂×C₄×C₅₃	—	2	4	no	—
81	C₂×C₄×C₅₃	C₂²⋊C₈	1	4	yes	—
82	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
85	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
86	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
87	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
88	C₂×Dic₅₃	—	2	1	no	—
89	C₂×Dic₅₃	—	2	1	no	—
90	C₂×Dic₅₃	—	2	2	no	—
91	C₂×Dic₅₃	—	2	4	no	—
92	C₂×Dic₅₃	C₄⋊C₈	1	2	yes	—
93	C₄×D₅₃	—	2	2	no	—
94	C₄×D₅₃	—	2	2	no	—
95	C₄×D₅₃	—	2	2	no	—
96	C₄×D₅₃	—	2	2	no	—
97	C₈×C₅₃	—	2	2	no	—
98	C₈×C₅₃	—	2	2	no	—
99	#88322	—	2	2	no	—
100	#88322	#121	1	2	yes	—
101	#88322	C₂²⋊Q₈	1	2	yes	—
102	#12784	—	53	1	no	maximal, Sylow
103	C₂²×C₅₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
104	C₂²×C₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic
105	C₂²×C₅₃	#431	1	1	yes	characteristic
106	C₂²×C₅₃	#504	1	4	yes	—
107	C₂×D₅₃	—	2	2	no	—
108	C₂×D₅₃	—	2	4	no	—
109	C₂×D₅₃	—	4	2	no	—
110	C₂×D₅₃	—	4	2	no	—
111	C₄×C₅₃	—	2	4	no	—
112	C₄×C₅₃	#380	1	1	yes	characteristic
113	C₄×C₅₃	#407	1	1	yes	characteristic
114	C₄×C₅₃	#423	1	1	yes	characteristic
115	C₄×C₅₃	#432	1	1	yes	characteristic
116	Dic₅₃	—	2	2	no	—
117	Dic₅₃	—	4	2	no	—
118	C₂×#405	—	53	1	no	—
119	C₂×C₄⋊C₁₆	—	53	2	no	—
120	C₂×C₂²⋊C₁₆	—	53	2	no	—
121	#1374	—	53	2	no	—
122	C₂×C₅₃	#1797	1	1	yes	characteristic
123	C₂×C₅₃	#2113	1	2	yes	—
124	C₂×C₅₃	#2151	1	2	yes	—
125	C₂×C₅₃	#2164	1	2	yes	—
126	D₅₃	—	4	2	no	—
127	C₂²×M₁₆	—	53	1	no	—
128	C₂³×C₈	—	53	1	no	—
129	C₂×#117	—	53	1	no	—
130	C₂²×C₁₆	—	53	4	no	—
131	#405	—	106	4	no	—
132	C₂×#97	—	53	1	no	—
133	C₂×#97	#6157	1	1	yes	characteristic
134	C₂×C₄×C₈	—	53	1	no	—
135	C₂×C₄×C₈	—	53	1	no	—
136	C₄⋊C₁₆	—	106	4	no	—
137	C₂²⋊C₁₆	—	106	4	no	—
138	C₅₃	#12784	1	1	yes	characteristic, complemented, Sylow
139	C₂³×C₄	—	53	1	no	—
140	C₂×M₁₆	—	106	2	no	—
141	C₂×M₁₆	—	106	2	no	—
142	C₂×M₁₆	—	106	2	no	—
143	C₂²×C₈	—	53	1	no	—
144	C₂²×C₈	—	53	1	no	—
145	C₂²×C₈	—	53	2	no	—
146	C₂²×C₈	—	53	2	no	—
147	C₂²×C₈	—	106	2	no	—
148	C₂²×C₈	—	106	2	no	—
149	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
150	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
151	#117	—	106	2	no	—
152	#117	—	106	2	no	—
153	C₂×C₄⋊C₄	—	53	2	no	—
154	C₂×C₂²⋊C₄	—	53	2	no	—
155	C₂×C₄²	—	53	1	no	—
156	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
157	C₂×C₁₆	—	106	4	no	—
158	C₂×C₁₆	—	106	4	no	—
159	C₂×C₁₆	—	106	4	no	—
160	#97	—	2	2	no	—
161	#97	—	106	2	no	—
162	C₄×C₈	—	53	4	no	—
163	C₄×C₈	—	106	2	no	—
164	C₂⁴	—	53	1	no	—
165	C₂²×C₄	—	53	1	no	—
166	C₂²×C₄	—	53	2	no	—
167	C₂²×C₄	—	53	2	no	—
168	C₂²×C₄	—	53	2	no	—
169	C₂²×C₄	—	106	1	no	—
170	C₂²×C₄	—	106	1	no	—
171	C₂²×C₄	—	106	1	no	—
172	C₂²×C₄	—	106	1	no	—
173	C₂²×C₄	D₅₃⋊C₈	1	2	yes	—
174	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
175	M₁₆	—	106	8	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	53	2	no	—
181	C₂×C₈	—	53	1	no	—
182	C₂×C₈	—	53	1	no	—
183	C₂×C₈	—	53	2	no	—
184	C₂×C₈	—	53	2	no	—
185	C₂×C₈	—	106	4	no	—
186	C₂×C₈	—	106	4	no	—
187	C₂×C₈	—	106	1	no	—
188	C₂×C₈	—	106	1	no	—
189	C₂×C₈	#11719936	1	2	yes	—
190	C₂×C₈	C₄⋊#6157	1	2	yes	—
191	C₄⋊C₄	—	106	4	no	—
192	C₂²⋊C₄	—	106	4	no	—
193	C₄²	—	106	1	no	—
194	C₄²	—	106	1	no	—
195	C₄²	#11719936	1	2	yes	—
196	C₄²	C₂²⋊#6157	1	2	yes	—
197	C₁₆	—	212	4	no	—
198	C₂³	—	53	2	no	—
199	C₂³	—	106	1	no	—
200	C₂³	—	106	1	no	—
201	C₂³	—	106	4	no	—
202	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	53	2	no	—
205	C₂×C₄	—	106	1	no	—
206	C₂×C₄	—	106	1	no	—
207	C₂×C₄	—	106	2	no	—
208	C₂×C₄	—	106	2	no	—
209	C₂×C₄	—	106	2	no	—
210	C₂×C₄	—	106	2	no	—
211	C₂×C₄	—	106	2	no	—
212	C₂×C₄	—	106	4	no	—
213	C₂×C₄	#13133274	1	4	yes	—
214	C₂×C₄	C₂×C₂²⋊#6157	1	1	yes	characteristic
215	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
216	C₂×C₄	#13133296	1	1	yes	characteristic
217	C₂×C₄	D₅₃⋊M₁₆	1	1	yes	characteristic
218	C₂×C₄	C₂×#11719936	1	1	yes	characteristic
219	C₂×C₄	C₂×#11719936	1	1	yes	characteristic
220	C₈	—	2	2	no	—
221	C₈	—	2	2	no	—
222	C₈	—	53	2	no	—
223	C₈	—	53	2	no	—
224	C₈	—	106	2	no	—
225	C₂²	—	106	2	no	—
226	C₂²	—	106	4	no	—
227	C₂²	—	212	2	no	—
228	C₂²	—	212	2	no	—
229	C₂²	C₂×#13133274	1	1	yes	characteristic
230	C₂²	D₅₃⋊(C₄⋊C₈)	1	1	yes	characteristic
231	C₂²	#16811642	1	1	yes	characteristic
232	C₂²	#16811682	1	4	yes	—
233	C₄	—	2	4	no	—
234	C₄	—	106	2	no	—
235	C₄	—	212	2	no	—
236	C₄	#16811565	1	1	yes	characteristic
237	C₄	#16811594	1	1	yes	characteristic
238	C₄	#16811627	1	1	yes	characteristic
239	C₄	#16811645	1	1	yes	characteristic
240	C₂	—	212	2	no	—
241	C₂	#20290570	1	1	yes	characteristic
242	C₂	#20290947	1	2	yes	—
243	C₂	#20291051	1	2	yes	—
244	C₂	#20291083	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#11719910

C₂

yes

maximal, complemented

C₂×#16811518

C₂

yes

maximal

#20289754

C₂

yes

maximal, complemented

C₂×#16810580

C₂

yes

maximal, characteristic

C₂²×#11719910

C₂²

yes

—

C₄⋊#11719910

—

#16811518

—

C₂²×#11719912

C₄

yes

characteristic

C₂²×C₈×D₅₃

C₂²

yes

characteristic

C₂×#13133174

C₄

yes

characteristic

#16810580

—

C₂×#13133127

C₄

yes

characteristic

C₂×C₄×#88322

C₂²

yes

characteristic

C₂×C₈×Dic₅₃

C₂²

yes

characteristic

C₂×#97×C₅₃

C₄

yes

—

—

—

C₂²×C₄×D₅₃

C₂×C₄

yes

—

—

—

C₂²×#88322

C₂×C₄

yes

characteristic

C₂²×#88322

C₂³

yes

characteristic

C₂×C₈×D₅₃

—

C₂×C₈×D₅₃

—

C₂×C₈×D₅₃

D₄

yes

—

C₂×C₈×D₅₃

Q₈

yes

—

#13133174

—

#13133174

—

C₂×#11719919

C₈

yes

—

C₂×#11719921

C₈

yes

—

C₂×C₄×Dic₅₃

C₂×C₄

yes

characteristic

#13133127

—

C₄×#88322

D₄

yes

—

C₈×Dic₅₃

—

C₂²×C₈×C₅₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₅₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₅₃

C₂×C₄

yes

characteristic

#97×C₅₃

—

C₂³×D₅₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₅₃

C₂×C₈

yes

—

C₂²×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂²×Dic₅₃

C₂×C₈

yes

—

C₂²×Dic₅₃

C₂×C₈

yes

characteristic

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

C₄⋊C₄

yes

—

C₂×C₄×D₅₃

M₁₆

yes

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₄⋊C₄

yes

—

C₂×C₈×C₅₃

M₁₆

yes

—

C₄²×C₅₃

C₂²⋊C₄

yes

—

C₄²×C₅₃

M₁₆

yes

—

#11719921

—

#11719919

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₂×#88322

—

C₂×#88322

—

C₂×#88322

C₂²⋊C₄

yes

—

C₂×#88322

C₂×D₄

yes

characteristic

C₂×#88322

C₂×D₄

yes

—

C₂×#88322

C₂×Q₈

yes

characteristic

C₂×#88322

#41

yes

—

#11719912

—

C₈×D₅₃

—

C₈×D₅₃

—

#11719910

—

C₂³×C₅₃

C₂²×C₈

yes

characteristic

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

C₄⋊C₈

yes

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂²⋊C₈

yes

—

C₂×C₄×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₃

#117

yes

characteristic

C₂×C₄×C₅₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₅₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₅₃

C₂×M₁₆

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

C₄⋊C₈

yes

—

C₄×D₅₃

—

C₄×D₅₃

—

C₄×D₅₃

—

C₄×D₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

#88322

—

100

#88322

#121

yes

—

101

#88322

C₂²⋊Q₈

yes

—

102

#12784

—

maximal, Sylow

103

C₂²×C₅₃

C₂×C₂²⋊C₈

yes

characteristic

104

C₂²×C₅₃

C₂×C₄⋊C₈

yes

characteristic

105

C₂²×C₅₃

#431

yes

characteristic

106

C₂²×C₅₃

#504

yes

—

107

C₂×D₅₃

—

108

C₂×D₅₃

—

109

C₂×D₅₃

—

110

C₂×D₅₃

—

111

C₄×C₅₃

—

112

C₄×C₅₃

#380

yes

characteristic

113

C₄×C₅₃

#407

yes

characteristic

114

C₄×C₅₃

#423

yes

characteristic

115

C₄×C₅₃

#432

yes

characteristic

116

Dic₅₃

—

117

Dic₅₃

—

118

C₂×#405

—

119

C₂×C₄⋊C₁₆

—

120

C₂×C₂²⋊C₁₆

—

121

#1374

—

122

C₂×C₅₃

#1797

yes

characteristic

123

C₂×C₅₃

#2113

yes

—

124

C₂×C₅₃

#2151

yes

—

125

C₂×C₅₃

#2164

yes

—

126

D₅₃

—

127

C₂²×M₁₆

—

128

C₂³×C₈

—

129

C₂×#117

—

130

C₂²×C₁₆

—

131

#405

—

106

—

132

C₂×#97

—

133

C₂×#97

#6157

yes

characteristic

134

C₂×C₄×C₈

—

135

C₂×C₄×C₈

—

136

C₄⋊C₁₆

—

106

—

137

C₂²⋊C₁₆

—

106

—

138

C₅₃

#12784

yes

characteristic, complemented, Sylow

139

C₂³×C₄

—

140

C₂×M₁₆

—

106

—

141

C₂×M₁₆

—

106

—

142

C₂×M₁₆

—

106

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

—

106

—

148

C₂²×C₈

—

106

—

149

C₂²×C₈

C₂×#6157

yes

characteristic

150

C₂²×C₈

C₂×#6157

yes

characteristic

151

#117

—

106

—

152

#117

—

106

—

153

C₂×C₄⋊C₄

—

154

C₂×C₂²⋊C₄

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂×#6157

yes

characteristic

157

C₂×C₁₆

—

106

—

158

C₂×C₁₆

—

106

—

159

C₂×C₁₆

—

106

—

160

#97

—

161

#97

—

106

—

162

C₄×C₈

—

163

C₄×C₈

—

106

—

164

C₂⁴

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

106

—

170

C₂²×C₄

—

106

—

171

C₂²×C₄

—

106

—

172

C₂²×C₄

—

106

—

173

C₂²×C₄

D₅₃⋊C₈

yes

—

174

C₂²×C₄

C₂²×#6157

yes

characteristic

175

M₁₆

—

106

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

106

—

186

C₂×C₈

—

106

—

187

C₂×C₈

—

106

—

188

C₂×C₈

—

106

—

189

C₂×C₈

#11719936

yes

—

190

C₂×C₈

C₄⋊#6157

yes

—

191

C₄⋊C₄

—

106

—

192

C₂²⋊C₄

—

106

—

193

C₄²

—

106

—

194

C₄²

—

106

—

195

C₄²

#11719936

yes

—

196

C₄²

C₂²⋊#6157

yes

—

197

C₁₆

—

212

—

198

C₂³

—

199

C₂³

—

106

—

200

C₂³

—

106

—

201

C₂³

—

106

—

202

C₂³

C₂×D₅₃⋊C₈

yes

characteristic

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

106

—

206

C₂×C₄

—

106

—

207

C₂×C₄

—

106

—

208

C₂×C₄

—

106

—

209

C₂×C₄

—

106

—

210

C₂×C₄

—

106

—

211

C₂×C₄

—

106

—

212

C₂×C₄

—

106

—

213

C₂×C₄

#13133274

yes

—

214

C₂×C₄

C₂×C₂²⋊#6157

yes

characteristic

215

C₂×C₄

C₂×C₄⋊#6157

yes

characteristic

216

C₂×C₄

#13133296

yes

characteristic

217

C₂×C₄

D₅₃⋊M₁₆

yes

characteristic

218

C₂×C₄

C₂×#11719936

yes

characteristic

219

C₂×C₄

C₂×#11719936

yes

characteristic

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

106

—

225

C₂²

—

106

—

226

C₂²

—

106

—

227

C₂²

—

212

—

228

C₂²

—

212

—

229

C₂²

C₂×#13133274

yes

characteristic

230

C₂²

D₅₃⋊(C₄⋊C₈)

yes

characteristic

231

C₂²

#16811642

yes

characteristic

232

C₂²

#16811682

yes

—

233

C₄

—

234

C₄

—

106

—

235

C₄

—

212

—

236

C₄

#16811565

yes

characteristic

237

C₄

#16811594

yes

characteristic

238

C₄

#16811627

yes

characteristic

239

C₄

#16811645

yes

characteristic

240

C₂

—

212

—

241

C₂

#20290570

yes

characteristic

242

C₂

#20290947

yes

—

243

C₂

#20291051

yes

—

244

C₂

#20291083

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#6157
commutator, socle	C₂³×C₅₃	C₂²×C₈
Fitting	C₂×#97×C₅₃	C₄
prime radical	C₂³×D₅₃	C₂×C₈
cosocle	C₂²×#88322	C₂³
hypercenter	C₂×#97	#6157
hypocenter	C₅₃	#12784
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×#6157

commutator, socle

C₂³×C₅₃

C₂²×C₈

Fitting

C₂×#97×C₅₃

C₄

prime radical

C₂³×D₅₃

C₂×C₈

cosocle

C₂²×#88322

C₂³

C₂×#97

C₅₃

G ▷ C₂³×C₅₃ ▷ C₅₃

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
1. C₂×C₄⋊#11719910	C₂	semidirect
3. #20289754	C₂	semidirect
138. C₅₃	#12784	semidirect

H ≅ G/N

type

1. C₂×C₄⋊#11719910

C₂

semidirect

3. #20289754

C₂

semidirect

138. C₅₃

#12784

semidirect

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

subgroup	index
C₂×C₄⋊#11719910	2
C₂×#16811518	2
#20289754	2
C₂×#16810580	2
#12784	53

subgroup

index

Subgroups — #28311127

Conjugacy classes of subgroups

Complements

Maximal subgroups