Group #23776045 — subgroups

Subgroups — #23776045

Order 10112.

350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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	#19099273	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098917	C₂	1	2	yes	maximal, complemented
3	#19098913	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098870	C₂	1	2	yes	maximal, complemented
5	#19098853	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098775	C₂	1	2	yes	maximal
7	#19098765	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11929611	C₂	1	2	yes	maximal, complemented
10	C₄×#11929609	C₂	1	1	yes	maximal, characteristic
11	#556×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11929611	C₂²	1	2	yes	—
13	C₂×#11929609	C₂²	1	1	yes	characteristic
14	#14579161	C₂²	1	1	yes	characteristic
15	#14579153	C₂²	1	2	yes	—
16	#14579139	—	2	2	no	—
17	#14579137	—	2	1	no	—
18	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
19	C₄×D₃₁₆	C₂²	1	2	yes	—
20	C₄⋊C₄×D₇₉	—	2	1	no	—
21	#14579094	C₂²	1	1	yes	characteristic
22	#14579092	C₂²	1	2	yes	—
23	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
25	#14579085	C₂²	1	2	yes	—
26	#14579085	C₂²	1	2	yes	—
27	#14579085	C₂²	1	2	yes	—
28	#14579082	C₂²	1	1	yes	characteristic
29	#14579082	C₂²	1	2	yes	—
30	#14579081	C₂²	1	1	yes	characteristic
31	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	#126×C₇₉	—	2	2	no	—
35	#124×C₇₉	C₂²	1	2	yes	—
36	C₂²⋊Q₈×C₇₉	—	2	1	no	—
37	C₄×Q₈×C₇₉	C₂²	1	2	yes	—
38	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
40	#117×C₇₉	—	2	1	no	—
41	C₂×Dic₁₅₈	—	2	1	no	—
42	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
43	C₂×C₄×D₇₉	—	2	1	no	—
44	C₂×C₄×D₇₉	—	2	2	no	—
45	#11929611	—	2	4	no	—
46	#11929609	—	2	2	no	—
47	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
48	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
49	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
50	C₄⋊Dic₇₉	—	2	1	no	—
51	C₄⋊Dic₇₉	C₂³	1	2	yes	—
52	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
53	Dic₇₉⋊C₄	—	2	2	no	—
54	Dic₇₉⋊C₄	—	2	2	no	—
55	(C₂×D₇₉)⋊C₄	—	2	2	no	—
56	(C₂×D₇₉)⋊C₄	—	2	1	no	—
57	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
58	C₂×Q₈×C₇₉	C₂³	1	2	yes	—
59	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₇₉	—	2	1	no	—
61	C₄⋊C₄×C₇₉	—	2	1	no	—
62	C₄⋊C₄×C₇₉	—	2	2	no	—
63	C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
65	C₄⋊C₄×C₇₉	D₄	1	2	yes	—
66	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
67	C₂²⋊C₄×C₇₉	—	2	2	no	—
68	C₂²⋊C₄×C₇₉	—	2	1	no	—
69	C₂²⋊C₄×C₇₉	—	2	2	no	—
70	C₄²×C₇₉	—	2	2	no	—
71	C₄²×C₇₉	C₂³	1	1	yes	characteristic
72	C₄²×C₇₉	C₂³	1	2	yes	—
73	C₂³×C₇₉	—	2	1	no	—
74	C₂²×D₇₉	—	2	1	no	—
75	Q₈×C₇₉	—	2	2	no	—
76	Q₈×C₇₉	—	2	2	no	—
77	Q₈×C₇₉	—	2	2	no	—
78	D₄×C₇₉	—	2	1	no	—
79	D₄×C₇₉	—	2	1	no	—
80	C₂×C₄×C₇₉	—	2	1	no	—
81	C₂×C₄×C₇₉	—	2	2	no	—
82	C₂×C₄×C₇₉	—	4	2	no	—
83	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
86	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
88	C₂×Dic₇₉	—	2	1	no	—
89	C₂×Dic₇₉	—	2	2	no	—
90	D₃₁₆	—	2	1	no	—
91	D₃₁₆	#41	1	2	yes	—
92	C₄×D₇₉	—	4	2	no	—
93	C₄×D₇₉	—	8	2	no	—
94	Dic₁₅₈	—	8	1	no	—
95	C₇₉⋊C₈	—	2	1	no	—
96	C₇₉⋊C₈	—	2	2	no	—
97	C₇₉⋊C₈	—	2	1	no	—
98	C₂²×C₇₉	—	4	1	no	—
99	C₂²×C₇₉	—	4	1	no	—
100	C₂²×C₇₉	—	4	1	no	—
101	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
102	C₂×D₇₉	—	2	2	no	—
103	C₂×D₇₉	—	4	1	no	—
104	C₂×D₇₉	—	4	1	no	—
105	C₄×C₇₉	—	2	2	no	—
106	C₄×C₇₉	—	2	1	no	—
107	C₄×C₇₉	—	2	2	no	—
108	C₄×C₇₉	—	4	2	no	—
109	C₄×C₇₉	—	4	1	no	—
110	C₄×C₇₉	#135	1	2	yes	—
111	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
112	C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
113	Dic₇₉	—	4	1	no	—
114	Dic₇₉	—	4	2	no	—
115	C₂×C₇₉	—	8	1	no	—
116	C₂×C₇₉	#548	1	1	yes	characteristic
117	C₂×C₇₉	C₂×#135	1	1	yes	characteristic
118	C₂×C₇₉	#577	1	1	yes	characteristic
119	D₇₉	—	4	2	no	—
120	#3360	—	79	1	no	maximal, Sylow
121	C₇₉	#3360	1	1	yes	characteristic, complemented, Sylow
122	#556	D₇₉	1	1	yes	characteristic, complemented
123	#554	—	79	1	no	—
124	#488	—	79	2	no	—
125	#487	—	79	1	no	—
126	#479	—	79	2	no	—
127	#476	—	79	1	no	—
128	#463	—	79	2	no	—
129	#461	—	79	1	no	—
130	C₈×Q₈	—	79	1	no	—
131	C₄×SD₁₆	—	79	2	no	—
132	C₄×D₈	—	79	1	no	—
133	C₂×SD₁₆	—	79	2	no	—
134	C₂×D₈	—	79	1	no	—
135	C₄⋊Q₈	—	79	1	no	—
136	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
137	#126	—	2	2	no	—
138	#125	—	79	2	no	—
139	#124	C₂×D₇₉	1	2	yes	—
140	C₂²⋊Q₈	—	2	1	no	—
141	C₂²⋊Q₈	—	158	1	no	—
142	C₂²⋊Q₈	—	158	2	no	—
143	C₄×Q₈	C₂×D₇₉	1	2	yes	—
144	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
145	C₄×D₄	—	79	1	no	—
146	C₄×D₄	—	79	2	no	—
147	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
148	#117	—	2	1	no	—
149	C₂×C₄⋊C₄	—	158	1	no	—
150	#107	—	79	1	no	—
151	#106	—	79	2	no	—
152	C₄⋊C₈	—	79	1	no	—
153	C₄⋊C₈	—	79	2	no	—
154	#103	—	79	2	no	—
155	#103	—	79	2	no	—
156	#103	—	79	2	no	—
157	#102	—	79	1	no	—
158	#102	—	79	2	no	—
159	#102	—	79	1	no	—
160	C₄×C₈	—	79	1	no	—
161	C₄×C₈	—	79	2	no	—
162	C₂×Q₈	—	158	1	no	—
163	C₂×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
164	C₂×Q₈	C₂²×D₇₉	1	2	yes	—
165	C₂×D₄	—	79	1	no	—
166	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	158	1	no	—
169	C₂²×C₄	—	158	2	no	—
170	SD₁₆	—	158	4	no	—
171	D₈	—	158	2	no	—
172	C₂×C₈	—	79	1	no	—
173	C₂×C₈	—	79	2	no	—
174	C₂×C₈	—	79	1	no	—
175	C₄⋊C₄	—	2	1	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	1	no	—
178	C₄⋊C₄	—	79	2	no	—
179	C₄⋊C₄	—	79	1	no	—
180	C₄⋊C₄	—	158	2	no	—
181	C₄⋊C₄	—	158	2	no	—
182	C₄⋊C₄	—	158	1	no	—
183	C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
184	C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
185	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
186	C₂²⋊C₄	—	2	2	no	—
187	C₂²⋊C₄	—	2	1	no	—
188	C₂²⋊C₄	—	2	2	no	—
189	C₂²⋊C₄	—	158	1	no	—
190	C₂²⋊C₄	—	158	2	no	—
191	C₄²	—	2	2	no	—
192	C₄²	C₂²×D₇₉	1	1	yes	characteristic
193	C₄²	C₂²×D₇₉	1	2	yes	—
194	C₂³	—	2	1	no	—
195	C₂³	—	158	1	no	—
196	Q₈	—	2	2	no	—
197	Q₈	—	2	2	no	—
198	Q₈	—	2	2	no	—
199	Q₈	—	632	1	no	—
200	D₄	—	2	1	no	—
201	D₄	—	2	1	no	—
202	D₄	—	79	2	no	—
203	D₄	—	158	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	316	2	no	—
208	C₂×C₄	—	632	2	no	—
209	C₂×C₄	—	158	1	no	—
210	C₂×C₄	—	158	2	no	—
211	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
212	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
213	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
214	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
215	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
216	C₈	—	158	1	no	—
217	C₈	—	158	2	no	—
218	C₈	—	158	1	no	—
219	C₂²	—	4	1	no	—
220	C₂²	—	4	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	316	1	no	—
223	C₂²	—	316	1	no	—
224	C₂²	—	158	2	no	—
225	C₂²	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	2	1	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	1	no	—
231	C₄	—	316	1	no	—
232	C₄	—	316	2	no	—
233	C₄	#14579181	1	2	yes	—
234	C₄	#41×D₇₉	1	1	yes	characteristic
235	C₄	#14579208	1	1	yes	characteristic
236	C₂	—	8	1	no	—
237	C₂	—	316	2	no	—
238	C₂	#19099220	1	1	yes	characteristic
239	C₂	C₂×#14579181	1	1	yes	characteristic
240	C₂	#19099371	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099273

C₂

yes

maximal, characteristic, complemented

#19098917

C₂

yes

maximal, complemented

#19098913

C₂

yes

maximal, characteristic, complemented

#19098870

C₂

yes

maximal, complemented

#19098853

C₂

yes

maximal, characteristic, complemented

#19098775

C₂

yes

maximal

#19098765

C₂

yes

maximal, characteristic, complemented

Q₈×C₇₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#11929611

C₂

yes

maximal, complemented

C₄×#11929609

C₂

yes

maximal, characteristic

#556×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929611

C₂²

yes

—

C₂×#11929609

C₂²

yes

characteristic

#14579161

C₂²

yes

characteristic

#14579153

C₂²

yes

—

#14579139

—

#14579137

—

C₄×D₃₁₆

C₂²

yes

characteristic

C₄×D₃₁₆

C₂²

yes

—

C₄⋊C₄×D₇₉

—

#14579094

C₂²

yes

characteristic

#14579092

C₂²

yes

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579085

C₂²

yes

—

#14579085

C₂²

yes

—

#14579085

C₂²

yes

—

#14579082

C₂²

yes

characteristic

#14579082

C₂²

yes

—

#14579081

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#126×C₇₉

—

#124×C₇₉

C₂²

yes

—

C₂²⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

C₂²

yes

—

C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

C₂²

yes

characteristic

#117×C₇₉

—

C₂×Dic₁₅₈

—

C₂×D₃₁₆

C₂³

yes

characteristic

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

#11929611

—

#11929609

—

C₂×C₇₉⋊C₈

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

C₂³

yes

—

C₂×C₇₉⋊C₈

C₂³

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂³

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×Q₈×C₇₉

C₂³

yes

—

C₂×D₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

D₄

yes

—

C₄⋊C₄×C₇₉

C₂³

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂³

yes

—

C₂³×C₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

#41

yes

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

C₂²×D₄

yes

characteristic

102

C₂×D₇₉

—

103

C₂×D₇₉

—

104

C₂×D₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

#135

yes

—

111

C₄×C₇₉

C₂×#41

yes

characteristic

112

C₄×C₇₉

2₋¹⁺⁴

yes

characteristic

113

Dic₇₉

—

114

Dic₇₉

—

115

C₂×C₇₉

—

116

C₂×C₇₉

#548

yes

characteristic

117

C₂×C₇₉

C₂×#135

yes

characteristic

118

C₂×C₇₉

#577

yes

characteristic

119

D₇₉

—

120

#3360

—

maximal, Sylow

121

C₇₉

#3360

yes

characteristic, complemented, Sylow

122

#556

D₇₉

yes

characteristic, complemented

123

#554

—

124

#488

—

125

#487

—

126

#479

—

127

#476

—

128

#463

—

129

#461

—

130

C₈×Q₈

—

131

C₄×SD₁₆

—

132

C₄×D₈

—

133

C₂×SD₁₆

—

134

C₂×D₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

137

#126

—

138

#125

—

139

#124

C₂×D₇₉

yes

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

158

—

142

C₂²⋊Q₈

—

158

—

143

C₄×Q₈

C₂×D₇₉

yes

—

144

C₄×Q₈

C₂×D₇₉

yes

characteristic

145

C₄×D₄

—

146

C₄×D₄

—

147

C₄×D₄

C₂×D₇₉

yes

characteristic

148

#117

—

149

C₂×C₄⋊C₄

—

158

—

150

#107

—

151

#106

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#103

—

155

#103

—

156

#103

—

157

#102

—

158

#102

—

159

#102

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₂×Q₈

—

158

—

163

C₂×Q₈

C₂²⋊D₇₉

yes

characteristic

164

C₂×Q₈

C₂²×D₇₉

yes

—

165

C₂×D₄

—

166

C₂×D₄

C₂²×D₇₉

yes

characteristic

167

C₂²×C₄

—

168

C₂²×C₄

—

158

—

169

C₂²×C₄

—

158

—

170

SD₁₆

—

158

—

171

D₈

—

158

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

158

—

181

C₄⋊C₄

—

158

—

182

C₄⋊C₄

—

158

—

183

C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

184

C₄⋊C₄

C₂²⋊D₇₉

yes

—

185

C₄⋊C₄

C₂²×D₇₉

yes

characteristic

186

C₂²⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

189

C₂²⋊C₄

—

158

—

190

C₂²⋊C₄

—

158

—

191

C₄²

—

192

C₄²

C₂²×D₇₉

yes

characteristic

193

C₄²

C₂²×D₇₉

yes

—

194

C₂³

—

195

C₂³

—

158

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

Q₈

—

632

—

200

D₄

—

201

D₄

—

202

D₄

—

203

D₄

—

158

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

316

—

208

C₂×C₄

—

632

—

209

C₂×C₄

—

158

—

210

C₂×C₄

—

158

—

211

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

212

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

213

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

214

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

215

C₂×C₄

C₂³×D₇₉

yes

characteristic

216

C₈

—

158

—

217

C₈

—

158

—

218

C₈

—

158

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

316

—

223

C₂²

—

316

—

224

C₂²

—

158

—

225

C₂²

C₂²×C₂²⋊D₇₉

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

316

—

232

C₄

—

316

—

233

C₄

#14579181

yes

—

234

C₄

#41×D₇₉

yes

characteristic

235

C₄

#14579208

yes

characteristic

236

C₂

—

237

C₂

—

316

—

238

C₂

#19099220

yes

characteristic

239

C₂

C₂×#14579181

yes

characteristic

240

C₂

#19099371

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#556×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂×#11929609	C₂²
hypercenter	#556	D₇₉
hypocenter	C₇₉	#3360
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#556×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

C₂²

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

N	H ≅ G/N	type
1. #19099273	C₂	semidirect
2. #19098917	C₂	semidirect
3. #19098913	C₂	semidirect
4. #19098870	C₂	semidirect
5. #19098853	C₂	semidirect
7. #19098765	C₂	semidirect
8. Q₈×C₇₉⋊C₈	C₂	semidirect
9. C₄×#11929611	C₂	semidirect
11. #556×C₇₉	C₂	semidirect
121. C₇₉	#3360	semidirect
122. #556	D₇₉	semidirect

H ≅ G/N

type

1. #19099273

C₂

semidirect

2. #19098917

C₂

semidirect

3. #19098913

C₂

semidirect

4. #19098870

C₂

semidirect

5. #19098853

C₂

semidirect

7. #19098765

C₂

semidirect

8. Q₈×C₇₉⋊C₈

C₂

semidirect

9. C₄×#11929611

C₂

semidirect

11. #556×C₇₉

C₂

semidirect

121. C₇₉

#3360

semidirect

122. #556

D₇₉

semidirect

Subgroups — #23776045

Conjugacy classes of subgroups

Complements