Group #34199214 — subgroups

Subgroups — #34199214

Order 20224.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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	#23773986	C₂	1	1	yes	maximal, characteristic
2	#23765199	C₂	1	1	yes	maximal, characteristic
3	#23761411	C₂	1	4	yes	maximal
4	C₇₉×#1834	C₂	1	1	yes	maximal, characteristic
5	#19099120	—	2	1	no	—
6	#19098968	C₄	1	1	yes	characteristic, complemented
7	#19098943	C₄	1	1	yes	characteristic, complemented
8	#19098914	—	2	1	no	—
9	#19098804	—	2	1	no	—
10	#19098804	C₂²	1	2	yes	—
11	C₄×Dic₃₁₆	—	2	1	no	—
12	C₄×Dic₃₁₆	C₄	1	2	yes	complemented
13	C₄⋊(C₇₉⋊C₁₆)	—	2	1	no	—
14	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	—
15	C₄×C₇₉⋊C₁₆	—	2	1	no	—
16	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	#384×C₇₉	—	2	1	no	—
18	#340×C₇₉	—	2	1	no	—
19	#340×C₇₉	C₂²	1	2	yes	—
20	C₂×Dic₃₁₆	—	2	1	no	—
21	C₂×Dic₃₁₆	C₂×C₄	1	2	yes	—
22	#14579161	—	2	1	no	—
23	#14579161	—	2	1	no	—
24	#14579153	—	4	1	no	—
25	#14579140	—	2	2	no	—
26	#14579140	—	4	1	no	—
27	C₄×Dic₁₅₈	—	2	2	no	—
28	C₄×Dic₁₅₈	—	4	1	no	—
29	#14579120	—	4	1	no	—
30	C₂×C₇₉⋊C₁₆	—	2	2	no	—
31	#14579095	—	2	1	no	—
32	#14579095	C₂×C₄	1	2	yes	—
33	#14579086	—	2	2	no	—
34	#14579086	—	2	2	no	—
35	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₇₉	—	4	1	no	—
39	C₂×C₄⋊C₄×C₇₉	—	4	1	no	—
40	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
45	C₂×Dic₁₅₈	—	2	2	no	—
46	C₂×Dic₁₅₈	—	4	1	no	—
47	Dic₃₁₆	—	4	2	no	—
48	Dic₃₁₆	—	4	2	no	—
49	C₄⋊Dic₇₉	—	2	2	no	—
50	C₄⋊Dic₇₉	—	4	1	no	—
51	C₄⋊Dic₇₉	—	4	1	no	—
52	C₄⋊Dic₇₉	—	4	1	no	—
53	Dic₇₉⋊C₄	—	4	2	no	—
54	Dic₇₉⋊C₄	—	4	2	no	—
55	C₂²⋊Dic₇₉	—	4	2	no	—
56	C₄×Dic₇₉	—	4	2	no	—
57	C₇₉⋊C₁₆	—	4	2	no	—
58	C₂²×C₄×C₇₉	—	4	2	no	—
59	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
60	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
61	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₇₉	—	4	1	no	—
63	C₂×C₈×C₇₉	—	4	1	no	—
64	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
68	C₄⋊C₄×C₇₉	—	4	2	no	—
69	C₄⋊C₄×C₇₉	—	4	2	no	—
70	C₄⋊C₄×C₇₉	—	8	2	no	—
71	C₄⋊C₄×C₇₉	—	8	2	no	—
72	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₄²×C₇₉	SD₁₆	1	1	yes	characteristic
75	C₄²×C₇₉	SD₁₆	1	1	yes	characteristic
76	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
77	C₂×C₄×C₇₉	—	2	2	no	—
78	C₂×C₄×C₇₉	—	2	1	no	—
79	C₂×C₄×C₇₉	—	2	1	no	—
80	C₂×C₄×C₇₉	—	8	2	no	—
81	C₂×C₄×C₇₉	—	8	2	no	—
82	C₂×C₄×C₇₉	—	8	2	no	—
83	C₂×C₄×C₇₉	#102	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#102	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#102	1	1	yes	characteristic
86	C₂×C₄×C₇₉	#102	1	1	yes	characteristic
87	C₂×C₄×C₇₉	SD₃₂	1	2	yes	—
88	C₂×C₄×C₇₉	Q₃₂	1	2	yes	—
89	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×Dic₇₉	—	4	2	no	—
92	C₂×Dic₇₉	—	4	2	no	—
93	Dic₁₅₈	—	4	2	no	—
94	Dic₁₅₈	—	4	2	no	—
95	Dic₁₅₈	—	8	2	no	—
96	C₈×C₇₉	—	2	1	no	—
97	C₈×C₇₉	—	2	1	no	—
98	C₈×C₇₉	—	2	1	no	—
99	C₈×C₇₉	—	2	1	no	—
100	C₂²×C₇₉	—	2	1	no	—
101	C₂²×C₇₉	—	2	1	no	—
102	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
103	C₂²×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
104	C₂²×C₇₉	C₂×Q₃₂	1	1	yes	characteristic
105	C₄×C₇₉	—	2	1	no	—
106	C₄×C₇₉	—	2	1	no	—
107	C₄×C₇₉	—	16	2	no	—
108	C₄×C₇₉	#358	1	2	yes	—
109	C₄×C₇₉	#358	1	2	yes	—
110	C₄×C₇₉	#360	1	2	yes	—
111	C₄×C₇₉	#410	1	1	yes	characteristic
112	C₄×C₇₉	#421	1	1	yes	characteristic
113	Dic₇₉	—	8	2	no	—
114	Dic₇₉	—	8	2	no	—
115	#11857	—	79	1	no	maximal, Sylow
116	C₂×C₇₉	—	2	1	no	—
117	C₂×C₇₉	—	2	1	no	—
118	C₂×C₇₉	#1517	1	1	yes	characteristic
119	C₂×C₇₉	C₂×#358	1	1	yes	characteristic
120	C₂×C₇₉	C₂×#360	1	1	yes	characteristic
121	#3170	—	79	1	no	—
122	#2162	—	79	1	no	—
123	#1834	D₇₉	1	1	yes	characteristic
124	#1348	—	79	4	no	—
125	C₇₉	#11857	1	1	yes	characteristic, complemented, Sylow
126	#533	—	158	1	no	—
127	#500	—	79	1	no	—
128	#494	—	79	1	no	—
129	#487	—	158	1	no	—
130	#467	—	79	2	no	—
131	#467	—	158	1	no	—
132	C₄×Q₁₆	—	79	2	no	—
133	C₄×Q₁₆	—	158	1	no	—
134	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
135	#384	—	2	1	no	—
136	C₄⋊C₁₆	—	158	1	no	—
137	C₂²⋊C₁₆	—	79	2	no	—
138	C₄×C₁₆	—	158	1	no	—
139	#340	—	2	1	no	—
140	#340	C₂×D₇₉	1	2	yes	—
141	C₂×Q₁₆	—	79	2	no	—
142	C₂×Q₁₆	—	158	1	no	—
143	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
144	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
145	C₄⋊Q₈	—	158	1	no	—
146	C₄⋊Q₈	—	158	1	no	—
147	#125	—	316	1	no	—
148	C₂²⋊Q₈	—	316	1	no	—
149	C₂²⋊Q₈	—	158	2	no	—
150	C₄×Q₈	—	316	1	no	—
151	C₄×Q₈	—	158	2	no	—
152	#117	—	316	1	no	—
153	C₂×C₄⋊C₄	—	2	2	no	—
154	C₂×C₄⋊C₄	—	4	1	no	—
155	C₂×C₄⋊C₄	—	4	1	no	—
156	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
157	C₂×C₁₆	—	158	2	no	—
158	#107	—	79	2	no	—
159	#107	—	158	1	no	—
160	#103	—	158	2	no	—
161	#103	—	158	2	no	—
162	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
163	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
164	C₄×C₈	D₃₁₆	1	1	yes	characteristic
165	C₄×C₈	D₃₁₆	1	1	yes	characteristic
166	C₂×Q₈	—	316	1	no	—
167	C₂×Q₈	—	158	2	no	—
168	C₂²×C₄	—	4	2	no	—
169	C₂²×C₄	#11929609	1	1	yes	characteristic
170	C₂²×C₄	#11929609	1	1	yes	characteristic
171	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
172	Q₁₆	—	316	2	no	—
173	Q₁₆	—	316	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
177	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
178	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
179	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	8	2	no	—
183	C₄⋊C₄	—	8	2	no	—
184	C₄⋊C₄	—	316	2	no	—
185	C₄⋊C₄	—	316	1	no	—
186	C₄⋊C₄	—	316	1	no	—
187	C₄⋊C₄	—	316	1	no	—
188	C₄⋊C₄	—	316	2	no	—
189	C₄⋊C₄	—	158	2	no	—
190	C₂²⋊C₄	—	316	2	no	—
191	C₄²	—	316	2	no	—
192	C₄²	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
193	C₄²	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
194	C₄²	#11929611	1	1	yes	characteristic
195	C₄²	#11929611	1	1	yes	characteristic
196	C₁₆	—	316	2	no	—
197	C₂³	C₂×#11929609	1	1	yes	characteristic
198	Q₈	—	316	2	no	—
199	Q₈	—	316	2	no	—
200	Q₈	—	632	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	8	2	no	—
205	C₂×C₄	—	8	2	no	—
206	C₂×C₄	—	8	2	no	—
207	C₂×C₄	—	316	2	no	—
208	C₂×C₄	—	316	2	no	—
209	C₂×C₄	#14579081	1	1	yes	characteristic
210	C₂×C₄	#14579081	1	1	yes	characteristic
211	C₂×C₄	#14579081	1	1	yes	characteristic
212	C₂×C₄	#14579081	1	1	yes	characteristic
213	C₂×C₄	#14579105	1	2	yes	—
214	C₂×C₄	#14579107	1	2	yes	—
215	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
216	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	2	1	no	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	—	2	1	no	—
223	C₂²	C₂×#14579081	1	1	yes	characteristic
224	C₂²	C₂×#14579105	1	1	yes	characteristic
225	C₂²	C₂×#14579107	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	16	2	no	—
229	C₄	—	632	2	no	—
230	C₄	—	632	2	no	—
231	C₄	#19098366	1	2	yes	—
232	C₄	#19098366	1	2	yes	—
233	C₄	#19098372	1	2	yes	—
234	C₄	#19098536	1	1	yes	characteristic
235	C₄	#19098581	1	1	yes	characteristic
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	#23761959	1	1	yes	characteristic
239	C₂	C₂×#19098366	1	1	yes	characteristic
240	C₂	C₂×#19098372	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23773986

C₂

yes

maximal, characteristic

#23765199

C₂

yes

maximal, characteristic

#23761411

C₂

yes

maximal

C₇₉×#1834

C₂

yes

maximal, characteristic

#19099120

—

#19098968

C₄

yes

characteristic, complemented

#19098943

C₄

yes

characteristic, complemented

#19098914

—

#19098804

—

#19098804

C₂²

yes

—

C₄×Dic₃₁₆

—

C₄×Dic₃₁₆

C₄

yes

complemented

C₄⋊(C₇₉⋊C₁₆)

—

C₂²⋊(C₇₉⋊C₁₆)

C₂²

yes

—

C₄×C₇₉⋊C₁₆

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#384×C₇₉

—

#340×C₇₉

—

#340×C₇₉

C₂²

yes

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

C₂×C₄

yes

—

—

—

—

—

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

#14579120

—

C₂×C₇₉⋊C₁₆

—

#14579095

—

#14579095

C₂×C₄

yes

—

#14579086

—

#14579086

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

D₈

yes

characteristic

C₂²×C₄×C₇₉

D₈

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂²⋊C₄

yes

characteristic

C₄²×C₇₉

C₂²⋊C₄

yes

characteristic

C₄²×C₇₉

SD₁₆

yes

characteristic

C₄²×C₇₉

SD₁₆

yes

characteristic

C₂³×C₇₉

C₂×D₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

SD₃₂

yes

—

C₂×C₄×C₇₉

Q₃₂

yes

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

—

102

C₂²×C₇₉

C₂×#102

yes

characteristic

103

C₂²×C₇₉

C₂×SD₃₂

yes

characteristic

104

C₂²×C₇₉

C₂×Q₃₂

yes

characteristic

105

C₄×C₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

#358

yes

—

109

C₄×C₇₉

#358

yes

—

110

C₄×C₇₉

#360

yes

—

111

C₄×C₇₉

#410

yes

characteristic

112

C₄×C₇₉

#421

yes

characteristic

113

Dic₇₉

—

114

Dic₇₉

—

115

#11857

—

maximal, Sylow

116

C₂×C₇₉

—

117

C₂×C₇₉

—

118

C₂×C₇₉

#1517

yes

characteristic

119

C₂×C₇₉

C₂×#358

yes

characteristic

120

C₂×C₇₉

C₂×#360

yes

characteristic

121

#3170

—

122

#2162

—

123

#1834

D₇₉

yes

characteristic

124

#1348

—

125

C₇₉

#11857

yes

characteristic, complemented, Sylow

126

#533

—

158

—

127

#500

—

128

#494

—

129

#487

—

158

—

130

#467

—

131

#467

—

158

—

132

C₄×Q₁₆

—

133

C₄×Q₁₆

—

158

—

134

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

135

#384

—

136

C₄⋊C₁₆

—

158

—

137

C₂²⋊C₁₆

—

138

C₄×C₁₆

—

158

—

139

#340

—

140

#340

C₂×D₇₉

yes

—

141

C₂×Q₁₆

—

142

C₂×Q₁₆

—

158

—

143

C₂²×C₈

C₂²⋊D₇₉

yes

characteristic

144

C₂²×C₈

C₂²×D₇₉

yes

characteristic

145

C₄⋊Q₈

—

158

—

146

C₄⋊Q₈

—

158

—

147

#125

—

316

—

148

C₂²⋊Q₈

—

316

—

149

C₂²⋊Q₈

—

158

—

150

C₄×Q₈

—

316

—

151

C₄×Q₈

—

158

—

152

#117

—

316

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

157

C₂×C₁₆

—

158

—

158

#107

—

159

#107

—

158

—

160

#103

—

158

—

161

#103

—

158

—

162

C₄×C₈

C₄×D₇₉

yes

characteristic

163

C₄×C₈

C₄×D₇₉

yes

characteristic

164

C₄×C₈

D₃₁₆

yes

characteristic

165

C₄×C₈

D₃₁₆

yes

characteristic

166

C₂×Q₈

—

316

—

167

C₂×Q₈

—

158

—

168

C₂²×C₄

—

169

C₂²×C₄

#11929609

yes

characteristic

170

C₂²×C₄

#11929609

yes

characteristic

171

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

172

Q₁₆

—

316

—

173

Q₁₆

—

316

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

177

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

178

C₂×C₈

C₂×C₄×D₇₉

yes

characteristic

179

C₂×C₈

C₂×D₃₁₆

yes

characteristic

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

316

—

185

C₄⋊C₄

—

316

—

186

C₄⋊C₄

—

316

—

187

C₄⋊C₄

—

316

—

188

C₄⋊C₄

—

316

—

189

C₄⋊C₄

—

158

—

190

C₂²⋊C₄

—

316

—

191

C₄²

—

316

—

192

C₄²

(C₂×D₇₉)⋊C₄

yes

characteristic

193

C₄²

(C₂×D₇₉)⋊C₄

yes

characteristic

194

C₄²

#11929611

yes

characteristic

195

C₄²

#11929611

yes

characteristic

196

C₁₆

—

316

—

197

C₂³

C₂×#11929609

yes

characteristic

198

Q₈

—

316

—

199

Q₈

—

316

—

200

Q₈

—

632

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

316

—

208

C₂×C₄

—

316

—

209

C₂×C₄

#14579081

yes

characteristic

210

C₂×C₄

#14579081

yes

characteristic

211

C₂×C₄

#14579081

yes

characteristic

212

C₂×C₄

#14579081

yes

characteristic

213

C₂×C₄

#14579105

yes

—

214

C₂×C₄

#14579107

yes

—

215

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

216

C₂×C₄

C₂×#11929611

yes

characteristic

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₂²

—

222

C₂²

—

223

C₂²

C₂×#14579081

yes

characteristic

224

C₂²

C₂×#14579105

yes

characteristic

225

C₂²

C₂×#14579107

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

632

—

230

C₄

—

632

—

231

C₄

#19098366

yes

—

232

C₄

#19098366

yes

—

233

C₄

#19098372

yes

—

234

C₄

#19098536

yes

characteristic

235

C₄

#19098581

yes

characteristic

236

C₂

—

237

C₂

—

238

C₂

#23761959

yes

characteristic

239

C₂

C₂×#19098366

yes

characteristic

240

C₂

C₂×#19098372

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#14579081
commutator	C₂×C₈×C₇₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#1834	C₂
socle	C₂²×C₇₉	C₂×#102
prime radical	C₂³×C₇₉	C₂×D₈
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	#1834	D₇₉
hypocenter	C₇₉	#11857
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1834

subgroup

G/H

center

C₂²

C₂×#14579081

commutator

C₂×C₈×C₇₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#1834

C₂

socle

C₂²×C₇₉

C₂×#102

prime radical

C₂³×C₇₉

C₂×D₈

cosocle

C₂²×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1834

N	H ≅ G/N	type
6. #19098968	C₄	semidirect
7. #19098943	C₄	semidirect
12. C₄×Dic₃₁₆	C₄	semidirect
125. C₇₉	#11857	semidirect

H ≅ G/N

type

6. #19098968

C₄

semidirect

7. #19098943

C₄

semidirect

12. C₄×Dic₃₁₆

C₄

semidirect

125. C₇₉

#11857

semidirect

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

subgroup	index
#23773986	2
#23765199	2
#23761411	2
C₇₉×#1834	2
#11857	79

subgroup

index

C₇₉×#1834

Subgroups — #34199214

Conjugacy classes of subgroups

Complements

Maximal subgroups