Group #34181189 — subgroups

Subgroups — #34181189

Order 20224.

486 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 155 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	#23763392	C₂	1	2	yes	maximal
2	#23762156	C₂	1	2	yes	maximal, complemented
3	#23761275	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic
5	#19098587	C₂²	1	4	yes	—
6	C₂×#14579078	—	2	2	no	—
7	#19098332	—	2	2	no	—
8	#19098314	—	2	2	no	—
9	#19098314	—	2	2	no	—
10	C₂³×C₈×C₇₉	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
12	C₈×D₄×C₇₉	—	2	2	no	—
13	C₈×D₄×C₇₉	—	2	2	no	—
14	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₈×C₇₉	C₄	1	2	yes	—
16	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#11929608	—	2	4	no	—
18	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
19	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
20	#14579078	—	4	4	no	—
21	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₇₉	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₇₉	—	2	2	no	—
24	C₂²×C₈×C₇₉	—	2	2	no	—
25	C₂²×C₈×C₇₉	—	4	4	no	—
26	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
29	C₄×D₄×C₇₉	—	2	2	no	—
30	C₄×D₄×C₇₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₇₉	Q₈	1	2	yes	—
33	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
34	C₄⋊C₈×C₇₉	—	2	2	no	—
35	C₂²⋊C₈×C₇₉	—	2	4	no	—
36	C₄×C₈×C₇₉	D₄	1	2	yes	—
37	C₄×C₈×C₇₉	D₄	1	2	yes	—
38	#11929608	—	4	4	no	—
39	#11929608	—	4	4	no	—
40	C₂×C₇₉⋊C₈	—	4	4	no	—
41	C₂⁴×C₇₉	C₄⋊C₄	1	2	yes	—
42	C₂×D₄×C₇₉	—	2	2	no	—
43	C₂×D₄×C₇₉	—	2	2	no	—
44	C₂×D₄×C₇₉	SD₁₆	1	4	yes	—
45	C₂²×C₄×C₇₉	—	2	2	no	—
46	C₂²×C₄×C₇₉	—	2	2	no	—
47	C₂²×C₄×C₇₉	—	4	2	no	—
48	C₂²×C₄×C₇₉	—	4	2	no	—
49	C₂²×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₈×C₇₉	—	2	2	no	—
54	C₂×C₈×C₇₉	—	2	2	no	—
55	C₂×C₈×C₇₉	—	4	1	no	—
56	C₂×C₈×C₇₉	—	4	2	no	—
57	C₂×C₈×C₇₉	—	4	4	no	—
58	C₂×C₈×C₇₉	—	4	4	no	—
59	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₄⋊C₄×C₇₉	—	2	2	no	—
63	C₂²⋊C₄×C₇₉	—	2	4	no	—
64	C₄²×C₇₉	C₂×D₄	1	2	yes	—
65	C₄²×C₇₉	#41	1	2	yes	—
66	C₂³×C₇₉	—	2	2	no	—
67	C₂³×C₇₉	—	2	2	no	—
68	C₂³×C₇₉	—	4	2	no	—
69	C₂³×C₇₉	—	4	2	no	—
70	C₂³×C₇₉	#106	1	4	yes	—
71	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
72	D₄×C₇₉	—	2	8	no	—
73	C₂×C₄×C₇₉	—	2	1	no	—
74	C₂×C₄×C₇₉	—	2	1	no	—
75	C₂×C₄×C₇₉	—	2	2	no	—
76	C₂×C₄×C₇₉	—	4	1	no	—
77	C₂×C₄×C₇₉	—	4	4	no	—
78	C₂×C₄×C₇₉	—	4	2	no	—
79	C₂×C₄×C₇₉	—	4	2	no	—
80	C₂×C₄×C₇₉	—	4	2	no	—
81	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
83	C₂×C₄×C₇₉	#121	1	2	yes	—
84	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
86	C₂×C₄×C₇₉	#135	1	2	yes	—
87	C₈×C₇₉	—	2	1	no	—
88	C₈×C₇₉	—	2	2	no	—
89	C₈×C₇₉	—	4	2	no	—
90	C₈×C₇₉	#100	1	2	yes	complemented
91	C₇₉⋊C₈	—	8	4	no	—
92	C₂²×C₇₉	—	2	1	no	—
93	C₂²×C₇₉	—	2	1	no	—
94	C₂²×C₇₉	—	2	4	no	—
95	C₂²×C₇₉	—	4	4	no	—
96	C₂²×C₇₉	—	4	4	no	—
97	C₂²×C₇₉	—	4	2	no	—
98	C₂²×C₇₉	—	4	2	no	—
99	C₂²×C₇₉	#380	1	1	yes	characteristic
100	C₂²×C₇₉	C₂×#106	1	1	yes	characteristic
101	C₂²×C₇₉	#427	1	1	yes	characteristic
102	C₄×C₇₉	—	2	1	no	—
103	C₄×C₇₉	—	2	2	no	—
104	C₄×C₇₉	—	4	2	no	—
105	C₄×C₇₉	C₂×#100	1	1	yes	characteristic
106	C₄×C₇₉	#413	1	1	yes	characteristic
107	C₄×C₇₉	#465	1	4	yes	—
108	#8614	—	79	1	no	maximal, Sylow
109	C₂×C₇₉	—	2	1	no	—
110	C₂×C₇₉	—	2	1	no	—
111	C₂×C₇₉	—	4	4	no	—
112	C₂×C₇₉	#1800	1	1	yes	characteristic
113	C₂×C₇₉	#1807	1	1	yes	characteristic
114	C₂×C₇₉	#1813	1	1	yes	characteristic
115	C₂×C₈×D₄	D₇₉	1	1	yes	characteristic
116	#1800	—	79	2	no	—
117	#1566	—	79	2	no	—
118	#1292	—	79	2	no	—
119	C₇₉	#8614	1	1	yes	characteristic, complemented, Sylow
120	C₂³×C₈	Dic₇₉	1	2	yes	—
121	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
122	C₈×D₄	—	2	2	no	—
123	C₈×D₄	—	2	2	no	—
124	#423	—	79	4	no	—
125	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
126	C₂×#100	—	158	2	no	—
127	C₂×C₂²⋊C₈	Dic₇₉	1	2	yes	—
128	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
129	#343	—	158	2	no	—
130	#334	—	158	2	no	—
131	#334	—	158	2	no	—
132	C₂²×D₄	D₃₁₆	1	1	yes	characteristic
133	C₂³×C₄	C₂×Dic₇₉	1	2	yes	—
134	C₂×M₁₆	—	158	4	no	—
135	C₂²×C₈	—	2	2	no	—
136	C₂²×C₈	—	2	2	no	—
137	C₂²×C₈	—	4	4	no	—
138	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
139	C₂²×C₈	C₂×Dic₇₉	1	2	yes	—
140	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
141	C₄×D₄	—	2	2	no	—
142	C₄×D₄	—	2	2	no	—
143	C₂×C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
144	C₂×C₂²⋊C₄	Dic₁₅₈	1	2	yes	—
145	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	158	4	no	—
148	C₄⋊C₈	—	158	4	no	—
149	#100	—	316	4	no	—
150	C₂²⋊C₈	—	2	4	no	—
151	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
152	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
153	C₂⁴	C₄⋊Dic₇₉	1	2	yes	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	2	no	—
156	C₂×D₄	#11929613	1	4	yes	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	4	2	no	—
160	C₂²×C₄	—	4	2	no	—
161	C₂²×C₄	C₄⋊Dic₇₉	1	2	yes	—
162	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
163	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
164	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
165	M₁₆	—	316	4	no	—
166	M₁₆	—	316	4	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	4	1	no	—
170	C₂×C₈	—	4	4	no	—
171	C₂×C₈	—	4	4	no	—
172	C₂×C₈	—	4	2	no	—
173	C₂×C₈	—	316	4	no	—
174	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
175	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
176	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
177	C₄⋊C₄	—	2	2	no	—
178	C₂²⋊C₄	—	2	4	no	—
179	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
180	C₄²	#11929624	1	2	yes	—
181	C₂³	—	2	2	no	—
182	C₂³	—	2	2	no	—
183	C₂³	—	4	2	no	—
184	C₂³	—	4	2	no	—
185	C₂³	#14579093	1	4	yes	—
186	C₂³	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
187	D₄	—	2	8	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
197	C₂×C₄	#14579120	1	1	yes	characteristic
198	C₂×C₄	#14579135	1	2	yes	—
199	C₂×C₄	#14579140	1	2	yes	—
200	C₂×C₄	C₂×#11929613	1	2	yes	—
201	C₂×C₄	#14579183	1	2	yes	—
202	C₈	—	2	1	no	—
203	C₈	—	2	2	no	—
204	C₈	—	4	2	no	—
205	C₈	—	632	4	no	—
206	C₈	#14579078	1	2	yes	complemented
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	4	no	—
210	C₂²	—	4	4	no	—
211	C₂²	—	4	4	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	#19098423	1	1	yes	characteristic
215	C₂²	C₂×#14579093	1	1	yes	characteristic
216	C₂²	#19098601	1	1	yes	characteristic
217	C₄	—	2	1	no	—
218	C₄	—	2	2	no	—
219	C₄	—	4	2	no	—
220	C₄	C₂×#14579078	1	1	yes	characteristic
221	C₄	#19098547	1	1	yes	characteristic
222	C₄	#19098792	1	4	yes	—
223	C₂	—	2	1	no	—
224	C₂	—	2	1	no	—
225	C₂	—	4	4	no	—
226	C₂	#23763392	1	1	yes	characteristic
227	C₂	#23763425	1	1	yes	characteristic
228	C₂	#23763450	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23763392

C₂

yes

maximal

#23762156

C₂

yes

maximal, complemented

#23761275

C₂

yes

maximal, complemented

C₂×C₈×D₄×C₇₉

C₂

yes

maximal, characteristic

#19098587

C₂²

yes

—

—

—

—

—

C₂³×C₈×C₇₉

C₄

yes

—

C₂×C₄×D₄×C₇₉

C₂²

yes

characteristic

C₈×D₄×C₇₉

—

C₈×D₄×C₇₉

—

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₇₉

C₄

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

#14579078

—

C₂²×D₄×C₇₉

D₄

yes

characteristic

C₂³×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂×C₄

yes

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×D₄×C₇₉

—

C₄×D₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₇₉

Q₈

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

D₄

yes

—

C₄×C₈×C₇₉

D₄

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂⁴×C₇₉

C₄⋊C₄

yes

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

SD₁₆

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₄⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

#106

yes

—

C₂³×C₇₉

C₂×C₄⋊C₄

yes

characteristic

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₉

C₂×SD₁₆

yes

—

C₂×C₄×C₇₉

#135

yes

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

#100

yes

complemented

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#380

yes

characteristic

100

C₂²×C₇₉

C₂×#106

yes

characteristic

101

C₂²×C₇₉

#427

yes

characteristic

102

C₄×C₇₉

—

103

C₄×C₇₉

—

104

C₄×C₇₉

—

105

C₄×C₇₉

C₂×#100

yes

characteristic

106

C₄×C₇₉

#413

yes

characteristic

107

C₄×C₇₉

#465

yes

—

108

#8614

—

maximal, Sylow

109

C₂×C₇₉

—

110

C₂×C₇₉

—

111

C₂×C₇₉

—

112

C₂×C₇₉

#1800

yes

characteristic

113

C₂×C₇₉

#1807

yes

characteristic

114

C₂×C₇₉

#1813

yes

characteristic

115

C₂×C₈×D₄

D₇₉

yes

characteristic

116

#1800

—

117

#1566

—

118

#1292

—

119

C₇₉

#8614

yes

characteristic, complemented, Sylow

120

C₂³×C₈

Dic₇₉

yes

—

121

C₂×C₄×D₄

C₂×D₇₉

yes

characteristic

122

C₈×D₄

—

123

C₈×D₄

—

124

#423

—

125

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

126

C₂×#100

—

158

—

127

C₂×C₂²⋊C₈

Dic₇₉

yes

—

128

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

129

#343

—

158

—

130

#334

—

158

—

131

#334

—

158

—

132

C₂²×D₄

D₃₁₆

yes

characteristic

133

C₂³×C₄

C₂×Dic₇₉

yes

—

134

C₂×M₁₆

—

158

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

C₂×Dic₇₉

yes

characteristic

139

C₂²×C₈

C₂×Dic₇₉

yes

—

140

C₂²×C₈

C₂×Dic₇₉

yes

characteristic

141

C₄×D₄

—

142

C₄×D₄

—

143

C₂×C₄⋊C₄

D₃₁₆

yes

characteristic

144

C₂×C₂²⋊C₄

Dic₁₅₈

yes

—

145

C₂×C₄²

C₂²×D₇₉

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

158

—

148

C₄⋊C₈

—

158

—

149

#100

—

316

—

150

C₂²⋊C₈

—

151

C₄×C₈

C₂²⋊D₇₉

yes

—

152

C₄×C₈

C₂²⋊D₇₉

yes

—

153

C₂⁴

C₄⋊Dic₇₉

yes

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

#11929613

yes

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

C₄⋊Dic₇₉

yes

—

162

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

163

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

164

C₂²×C₄

C₂×Dic₁₅₈

yes

characteristic

165

M₁₆

—

316

—

166

M₁₆

—

316

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

316

—

174

C₂×C₈

C₂²⋊Dic₇₉

yes

—

175

C₂×C₈

C₂²⋊Dic₇₉

yes

characteristic

176

C₂×C₈

C₂²⋊Dic₇₉

yes

characteristic

177

C₄⋊C₄

—

178

C₂²⋊C₄

—

179

C₄²

C₂×C₂²⋊D₇₉

yes

—

180

C₄²

#11929624

yes

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

#14579093

yes

—

186

C₂³

C₂×C₄⋊Dic₇₉

yes

characteristic

187

D₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

197

C₂×C₄

#14579120

yes

characteristic

198

C₂×C₄

#14579135

yes

—

199

C₂×C₄

#14579140

yes

—

200

C₂×C₄

C₂×#11929613

yes

—

201

C₂×C₄

#14579183

yes

—

202

C₈

—

203

C₈

—

204

C₈

—

205

C₈

—

632

—

206

C₈

#14579078

yes

complemented

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

#19098423

yes

characteristic

215

C₂²

C₂×#14579093

yes

characteristic

216

C₂²

#19098601

yes

characteristic

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

C₂×#14579078

yes

characteristic

221

C₄

#19098547

yes

characteristic

222

C₄

#19098792

yes

—

223

C₂

—

224

C₂

—

225

C₂

—

226

C₂

#23763392

yes

characteristic

227

C₂

#23763425

yes

characteristic

228

C₂

#23763450

yes

characteristic

	subgroup	G/H
center	C₂²	#19098423
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×C₈×D₄×C₇₉	C₂
socle	C₂²×C₇₉	#380
prime radical	C₂²×D₄×C₇₉	D₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₂×C₈×D₄	D₇₉
hypocenter	C₇₉	#8614
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×D₄

subgroup

G/H

center

C₂²

#19098423

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₂×C₈×D₄×C₇₉

C₂

socle

C₂²×C₇₉

#380

prime radical

C₂²×D₄×C₇₉

D₄

cosocle

C₂×C₄²×C₇₉

C₂³

hypercenter

C₂×C₈×D₄

D₇₉

hypocenter

C₇₉

#8614

LCS

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×D₄

N	H ≅ G/N	type
2. #23762156	C₂	semidirect
3. #23761275	C₂	semidirect
90. C₈×C₇₉	#100	semidirect
119. C₇₉	#8614	semidirect
206. C₈	#14579078	semidirect

H ≅ G/N

type

2. #23762156

C₂

semidirect

3. #23761275

C₂

semidirect

90. C₈×C₇₉

#100

semidirect

119. C₇₉

#8614

semidirect

206. C₈

#14579078

semidirect

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

subgroup	index
#23763392	2
#23762156	2
#23761275	2
C₂×C₈×D₄×C₇₉	2
#8614	79

subgroup

index

C₂×C₈×D₄×C₇₉

Subgroups — #34181189

Conjugacy classes of subgroups

Complements

Maximal subgroups