Group #34193073 — subgroups

Subgroups — #34193073

Order 20224.

294 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 87 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	#23764372	C₂	1	1	yes	maximal, characteristic
2	#23763574	C₂	1	1	yes	maximal, characteristic
3	#23762086	C₂	1	1	yes	maximal, characteristic
4	#23762080	C₂	1	1	yes	maximal, characteristic
5	#23761258	C₂	1	1	yes	maximal, characteristic
6	#23761244	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1286	C₂	1	1	yes	maximal, characteristic
8	C₂×#14579161	C₂²	1	1	yes	characteristic
9	#19098616	C₂²	1	1	yes	characteristic
10	C₂×#14579096	—	2	1	no	—
11	C₂×#14579096	—	2	1	no	—
12	#19098587	C₂²	1	1	yes	characteristic
13	C₂×#14579072	C₂²	1	1	yes	characteristic
14	#19098325	—	2	1	no	—
15	#19098325	—	2	1	no	—
16	#19098311	—	2	2	no	—
17	#19098308	—	2	2	no	—
18	#431×C₇₉	C₂²	1	1	yes	characteristic
19	#423×C₇₉	C₂²	1	1	yes	characteristic
20	#382×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×Dic₁₅₈	—	2	1	no	—
22	C₂×#11929608	—	2	1	no	—
23	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
24	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
25	#14579161	—	2	1	no	—
26	#14579161	—	2	1	no	—
27	#14579161	—	2	1	no	—
28	#14579161	D₄	1	2	yes	—
29	C₂×C₄⋊Dic₇₉	—	2	1	no	—
30	C₂×C₄⋊Dic₇₉	—	2	1	no	—
31	#14579096	—	4	2	no	—
32	#14579096	—	4	2	no	—
33	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
34	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
35	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
36	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
37	#14579072	—	2	1	no	—
38	#14579072	—	2	1	no	—
39	C₄×C₇₉⋊C₈	—	2	1	no	—
40	C₂×M₁₆×C₇₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
42	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₉	—	2	1	no	—
44	C₄⋊C₈×C₇₉	—	2	1	no	—
45	C₄⋊C₈×C₇₉	—	2	1	no	—
46	C₂²⋊C₈×C₇₉	—	2	1	no	—
47	C₄×C₈×C₇₉	—	2	1	no	—
48	#95×C₇₉	—	2	1	no	—
49	#95×C₇₉	—	2	1	no	—
50	C₂×Dic₁₅₈	—	2	2	no	—
51	C₂×Dic₁₅₈	—	4	1	no	—
52	C₂×Dic₁₅₈	—	8	2	no	—
53	C₂²×Dic₇₉	—	4	1	no	—
54	#11929608	—	4	1	no	—
55	#11929608	—	4	1	no	—
56	C₂×C₇₉⋊C₈	—	2	1	no	—
57	C₂×C₇₉⋊C₈	—	2	1	no	—
58	C₂×C₇₉⋊C₈	—	2	1	no	—
59	C₂×C₇₉⋊C₈	—	2	1	no	—
60	C₂×C₇₉⋊C₈	—	4	1	no	—
61	C₂×C₇₉⋊C₈	—	4	1	no	—
62	C₂×C₇₉⋊C₈	SD₁₆	1	2	yes	—
63	C₂×C₇₉⋊C₈	Q₁₆	1	2	yes	—
64	C₄⋊Dic₇₉	—	2	2	no	—
65	C₄⋊Dic₇₉	—	2	2	no	—
66	C₄⋊Dic₇₉	—	4	1	no	—
67	C₄⋊Dic₇₉	—	4	1	no	—
68	C₂²×C₄×C₇₉	—	4	1	no	—
69	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
71	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
72	M₁₆×C₇₉	—	4	1	no	—
73	M₁₆×C₇₉	—	4	1	no	—
74	C₂×C₈×C₇₉	—	4	1	no	—
75	C₂×C₈×C₇₉	—	4	1	no	—
76	C₄⋊C₄×C₇₉	—	4	1	no	—
77	C₄⋊C₄×C₇₉	—	4	1	no	—
78	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₇₉	#41	1	1	yes	characteristic
80	C₄²×C₇₉	#41	1	1	yes	characteristic
81	C₄²×C₇₉	#41	1	1	yes	characteristic
82	C₂³×C₇₉	#124	1	1	yes	characteristic
83	C₂×C₄×C₇₉	—	4	1	no	—
84	C₂×C₄×C₇₉	—	4	1	no	—
85	C₂×C₄×C₇₉	—	8	1	no	—
86	C₂×C₄×C₇₉	—	8	1	no	—
87	C₂×C₄×C₇₉	—	8	1	no	—
88	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
90	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
91	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
92	C₂×C₄×C₇₉	#126	1	1	yes	characteristic
93	C₂×C₄×C₇₉	#126	1	1	yes	characteristic
94	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
95	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
96	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
98	C₂×Dic₇₉	—	4	2	no	—
99	C₂×Dic₇₉	—	8	2	no	—
100	Dic₁₅₈	—	8	2	no	—
101	Dic₁₅₈	—	8	2	no	—
102	C₈×C₇₉	—	8	1	no	—
103	C₈×C₇₉	—	8	1	no	—
104	C₇₉⋊C₈	—	2	2	no	—
105	C₇₉⋊C₈	—	2	2	no	—
106	C₇₉⋊C₈	—	8	1	no	—
107	C₇₉⋊C₈	—	8	1	no	—
108	C₂²×C₇₉	—	2	1	no	—
109	C₂²×C₇₉	—	2	1	no	—
110	C₂²×C₇₉	#397	1	1	yes	characteristic
111	C₂²×C₇₉	#487	1	1	yes	characteristic
112	C₂²×C₇₉	#489	1	1	yes	characteristic
113	C₄×C₇₉	—	2	1	no	—
114	C₄×C₇₉	—	2	1	no	—
115	C₄×C₇₉	—	2	1	no	—
116	C₄×C₇₉	—	2	1	no	—
117	C₄×C₇₉	—	16	1	no	—
118	C₄×C₇₉	#460	1	1	yes	characteristic
119	C₄×C₇₉	#462	1	1	yes	characteristic
120	C₄×C₇₉	#483	1	1	yes	characteristic
121	C₄×C₇₉	#484	1	1	yes	characteristic
122	Dic₇₉	—	8	2	no	—
123	#10633	—	79	1	no	maximal, Sylow
124	C₂×C₇₉	—	2	1	no	—
125	C₂×C₇₉	—	2	1	no	—
126	C₂×C₇₉	#2072	1	1	yes	characteristic
127	C₂×C₇₉	#2081	1	1	yes	characteristic
128	C₂×C₇₉	#2082	1	1	yes	characteristic
129	#1993	—	79	1	no	—
130	#1849	—	79	1	no	—
131	#1549	—	79	1	no	—
132	#1548	—	79	1	no	—
133	#1286	—	79	1	no	—
134	#1286	D₇₉	1	1	yes	characteristic
135	#1281	—	79	1	no	—
136	C₇₉	#10633	1	1	yes	characteristic, complemented, Sylow
137	C₂×C₄⋊Q₈	—	79	1	no	—
138	#431	—	79	1	no	—
139	#431	C₂×D₇₉	1	1	yes	characteristic
140	C₂×#108	—	158	1	no	—
141	C₂×#108	—	158	1	no	—
142	#423	—	79	1	no	—
143	#423	C₂×D₇₉	1	1	yes	characteristic
144	C₂×#97	—	79	1	no	—
145	#382	C₂×D₇₉	1	1	yes	characteristic
146	#340	—	158	1	no	—
147	#340	—	158	1	no	—
148	#333	—	158	2	no	—
149	#332	—	158	2	no	—
150	C₂²×Q₈	—	158	1	no	—
151	C₂×M₁₆	—	2	1	no	—
152	C₂×M₁₆	—	158	1	no	—
153	C₂²×C₈	—	79	1	no	—
154	C₂²×C₈	—	79	1	no	—
155	C₄⋊Q₈	—	79	2	no	—
156	C₄⋊Q₈	—	158	1	no	—
157	C₄⋊Q₈	—	158	1	no	—
158	C₄⋊Q₈	—	158	1	no	—
159	C₂×C₄⋊C₄	—	2	1	no	—
160	C₂×C₄⋊C₄	—	158	1	no	—
161	C₂×C₄⋊C₄	—	158	1	no	—
162	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
163	#108	—	316	2	no	—
164	#108	—	316	2	no	—
165	C₄⋊C₈	—	2	1	no	—
166	C₄⋊C₈	—	2	1	no	—
167	C₄⋊C₈	—	2	1	no	—
168	C₄⋊C₈	—	158	1	no	—
169	C₄⋊C₈	—	158	1	no	—
170	C₄⋊C₈	—	158	1	no	—
171	C₂²⋊C₈	—	2	1	no	—
172	C₂²⋊C₈	—	158	1	no	—
173	#97	—	158	1	no	—
174	#97	—	158	1	no	—
175	C₄×C₈	—	2	1	no	—
176	C₄×C₈	—	158	1	no	—
177	#95	—	2	1	no	—
178	#95	—	2	1	no	—
179	C₂×Q₈	—	316	1	no	—
180	C₂×Q₈	—	632	2	no	—
181	C₂×Q₈	—	158	2	no	—
182	C₂²×C₄	—	4	1	no	—
183	C₂²×C₄	—	316	1	no	—
184	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
185	C₂²×C₄	#11929623	1	1	yes	characteristic
186	C₂²×C₄	#11929624	1	1	yes	characteristic
187	M₁₆	—	4	1	no	—
188	M₁₆	—	4	1	no	—
189	M₁₆	—	316	1	no	—
190	M₁₆	—	316	1	no	—
191	C₂×C₈	—	4	1	no	—
192	C₂×C₈	—	4	1	no	—
193	C₂×C₈	—	316	1	no	—
194	C₂×C₈	—	316	1	no	—
195	C₂×C₈	—	79	2	no	—
196	C₂×C₈	—	79	2	no	—
197	C₂×C₈	—	158	1	no	—
198	C₂×C₈	—	158	1	no	—
199	C₂×C₈	—	158	1	no	—
200	C₂×C₈	—	158	1	no	—
201	C₄⋊C₄	—	4	1	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₄⋊C₄	—	316	1	no	—
204	C₄⋊C₄	—	316	1	no	—
205	C₄⋊C₄	—	158	2	no	—
206	C₄⋊C₄	—	158	2	no	—
207	C₄²	D₄×D₇₉	1	1	yes	characteristic
208	C₄²	#11929624	1	1	yes	characteristic
209	C₄²	#11929624	1	1	yes	characteristic
210	C₄²	#11929625	1	1	yes	characteristic
211	C₂³	#14579147	1	1	yes	characteristic
212	Q₈	—	632	2	no	—
213	Q₈	—	632	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	8	1	no	—
217	C₂×C₄	—	8	1	no	—
218	C₂×C₄	—	8	1	no	—
219	C₂×C₄	—	316	2	no	—
220	C₂×C₄	—	632	2	no	—
221	C₂×C₄	#14579134	1	1	yes	characteristic
222	C₂×C₄	#14579143	1	1	yes	characteristic
223	C₂×C₄	#14579146	1	1	yes	characteristic
224	C₂×C₄	#14579146	1	1	yes	characteristic
225	C₂×C₄	#14579155	1	1	yes	characteristic
226	C₂×C₄	#14579156	1	1	yes	characteristic
227	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
228	C₂×C₄	Q₁₆×D₇₉	1	1	yes	characteristic
229	C₂×C₄	#14579185	1	1	yes	characteristic
230	C₂×C₄	#14579190	1	1	yes	characteristic
231	C₈	—	8	1	no	—
232	C₈	—	8	1	no	—
233	C₈	—	632	1	no	—
234	C₈	—	632	1	no	—
235	C₈	—	158	2	no	—
236	C₈	—	158	2	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#19098492	1	1	yes	characteristic
240	C₂²	#19098912	1	1	yes	characteristic
241	C₂²	#19098921	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	16	1	no	—
247	C₄	—	632	2	no	—
248	C₄	#19098762	1	1	yes	characteristic
249	C₄	#19098772	1	1	yes	characteristic
250	C₄	#19098895	1	1	yes	characteristic
251	C₄	#19098900	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	#23764812	1	1	yes	characteristic
255	C₂	#23764863	1	1	yes	characteristic
256	C₂	#23764869	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764372

C₂

yes

maximal, characteristic

#23763574

C₂

yes

maximal, characteristic

#23762086

C₂

yes

maximal, characteristic

#23762080

C₂

yes

maximal, characteristic

#23761258

C₂

yes

maximal, characteristic

#23761244

C₂

yes

maximal, characteristic

C₇₉×#1286

C₂

yes

maximal, characteristic

C₂×#14579161

C₂²

yes

characteristic

#19098616

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#14579072

C₂²

yes

—

—

—

—

#431×C₇₉

C₂²

yes

characteristic

#423×C₇₉

C₂²

yes

characteristic

#382×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

—

C₂×#11929608

—

C₂²×C₇₉⋊C₈

D₄

yes

characteristic

C₂²×C₇₉⋊C₈

D₄

yes

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

#14579096

—

#14579096

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₂×M₁₆×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

—

#95×C₇₉

—

#95×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

SD₁₆

yes

—

C₂×C₇₉⋊C₈

Q₁₆

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

C₂²×C₄×C₇₉

yes

C₂²×C₄×C₇₉

yes

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₄²×C₇₉

yes

C₄²×C₇₉

yes

C₂³×C₇₉

yes

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

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₁₆

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×Dic₇₉

—

C₂×Dic₇₉

—

100

Dic₁₅₈

—

101

Dic₁₅₈

—

102

C₈×C₇₉

—

103

C₈×C₇₉

—

104

C₇₉⋊C₈

—

105

C₇₉⋊C₈

—

106

C₇₉⋊C₈

—

107

C₇₉⋊C₈

—

108

C₂²×C₇₉

—

109

C₂²×C₇₉

—

110

C₂²×C₇₉

#397

yes

characteristic

111

C₂²×C₇₉

#487

yes

characteristic

112

C₂²×C₇₉

#489

yes

characteristic

113

C₄×C₇₉

—

114

C₄×C₇₉

—

115

C₄×C₇₉

—

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

#460

yes

characteristic

119

C₄×C₇₉

#462

yes

characteristic

120

C₄×C₇₉

#483

yes

characteristic

121

C₄×C₇₉

#484

yes

characteristic

122

Dic₇₉

—

123

#10633

—

maximal, Sylow

124

C₂×C₇₉

—

125

C₂×C₇₉

—

126

C₂×C₇₉

#2072

yes

characteristic

127

C₂×C₇₉

#2081

yes

characteristic

128

C₂×C₇₉

#2082

yes

characteristic

129

#1993

—

130

#1849

—

131

#1549

—

132

#1548

—

133

#1286

—

134

#1286

D₇₉

yes

characteristic

135

#1281

—

136

C₇₉

#10633

yes

characteristic, complemented, Sylow

137

C₂×C₄⋊Q₈

—

138

#431

—

139

#431

C₂×D₇₉

yes

characteristic

140

C₂×#108

—

158

—

141

C₂×#108

—

158

—

142

#423

—

143

#423

C₂×D₇₉

yes

characteristic

144

C₂×#97

—

145

#382

C₂×D₇₉

yes

characteristic

146

#340

—

158

—

147

#340

—

158

—

148

#333

—

158

—

149

#332

—

158

—

150

C₂²×Q₈

—

158

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

158

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

158

—

157

C₄⋊Q₈

—

158

—

158

C₄⋊Q₈

—

158

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

158

—

161

C₂×C₄⋊C₄

—

158

—

162

C₂×C₄²

C₂²×D₇₉

yes

characteristic

163

#108

—

316

—

164

#108

—

316

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

158

—

169

C₄⋊C₈

—

158

—

170

C₄⋊C₈

—

158

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

158

—

173

#97

—

158

—

174

#97

—

158

—

175

C₄×C₈

—

176

C₄×C₈

—

158

—

177

#95

—

178

#95

—

179

C₂×Q₈

—

316

—

180

C₂×Q₈

—

632

—

181

C₂×Q₈

—

158

—

182

C₂²×C₄

—

183

C₂²×C₄

—

316

—

184

C₂²×C₄

D₄×D₇₉

yes

characteristic

185

C₂²×C₄

#11929623

yes

characteristic

186

C₂²×C₄

#11929624

yes

characteristic

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

316

—

190

M₁₆

—

316

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

316

—

194

C₂×C₈

—

316

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

158

—

198

C₂×C₈

—

158

—

199

C₂×C₈

—

158

—

200

C₂×C₈

—

158

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

316

—

204

C₄⋊C₄

—

316

—

205

C₄⋊C₄

—

158

—

206

C₄⋊C₄

—

158

—

207

C₄²

D₄×D₇₉

yes

characteristic

208

C₄²

#11929624

yes

characteristic

209

C₄²

#11929624

yes

characteristic

210

C₄²

#11929625

yes

characteristic

211

C₂³

#14579147

yes

characteristic

212

Q₈

—

632

—

213

Q₈

—

632

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

316

—

220

C₂×C₄

—

632

—

221

C₂×C₄

#14579134

yes

characteristic

222

C₂×C₄

#14579143

yes

characteristic

223

C₂×C₄

#14579146

yes

characteristic

224

C₂×C₄

#14579146

yes

characteristic

225

C₂×C₄

#14579155

yes

characteristic

226

C₂×C₄

#14579156

yes

characteristic

227

C₂×C₄

SD₁₆×D₇₉

yes

characteristic

228

C₂×C₄

Q₁₆×D₇₉

yes

characteristic

229

C₂×C₄

#14579185

yes

characteristic

230

C₂×C₄

#14579190

yes

characteristic

231

C₈

—

232

C₈

—

233

C₈

—

632

—

234

C₈

—

632

—

235

C₈

—

158

—

236

C₈

—

158

—

237

C₂²

—

238

C₂²

—

239

C₂²

#19098492

yes

characteristic

240

C₂²

#19098912

yes

characteristic

241

C₂²

#19098921

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

632

—

248

C₄

#19098762

yes

characteristic

249

C₄

#19098772

yes

characteristic

250

C₄

#19098895

yes

characteristic

251

C₄

#19098900

yes

characteristic

252

C₂

—

253

C₂

—

254

C₂

#23764812

yes

characteristic

255

C₂

#23764863

yes

characteristic

256

C₂

#23764869

yes

characteristic

	subgroup	G/H
center	C₂²	#19098492
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1286	C₂
socle	C₂²×C₇₉	#397
prime radical	C₂³×C₇₉	#124
hypercenter	#1286	D₇₉
hypocenter	C₇₉	#10633
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1286

subgroup

G/H

center

C₂²

#19098492

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1286

C₂

C₂²×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1286

N	H ≅ G/N	type
136. C₇₉	#10633	semidirect

H ≅ G/N

type

136. C₇₉

#10633

semidirect

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

subgroup	index
#23764372	2
#23763574	2
#23762086	2
#23762080	2
#23761258	2
#23761244	2
C₇₉×#1286	2
#10633	79

subgroup

index

C₇₉×#1286

Subgroups — #34193073

Conjugacy classes of subgroups

Complements

Maximal subgroups