Group #23776384 — subgroups

Subgroups — #23776384

Order 10112.

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

normal subgroups only

This group has 360 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	#19099286	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098945	C₂	1	2	yes	maximal
3	#19098942	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098785	C₂	1	2	yes	maximal, complemented
5	#19098782	C₂	1	2	yes	maximal, complemented
6	#19098768	C₂	1	1	yes	maximal, characteristic, complemented
7	#19098765	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11929614	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×#11929614	C₂²	1	2	yes	—
13	C₂×#11929614	C₂²	1	2	yes	—
14	C₂×#11929612	C₂²	1	2	yes	—
15	C₂×#11929611	C₂²	1	2	yes	—
16	C₂×#11929609	C₂²	1	1	yes	characteristic
17	#14579161	C₂²	1	1	yes	characteristic
18	#14579156	—	2	2	no	—
19	#14579149	C₂²	1	2	yes	—
20	#14579137	—	2	1	no	—
21	C₄×Dic₁₅₈	C₂²	1	2	yes	—
22	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
23	#14579119	—	2	1	no	—
24	#14579094	C₂²	1	1	yes	characteristic
25	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
27	#14579085	C₂²	1	2	yes	—
28	#14579084	C₂²	1	2	yes	—
29	#14579082	C₂²	1	1	yes	characteristic
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	C₂³	1	2	yes	—
42	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
43	C₂×C₄×D₇₉	—	2	1	no	—
44	#11929614	—	2	4	no	—
45	#11929614	—	4	2	no	—
46	#11929612	—	4	2	no	—
47	#11929611	—	4	2	no	—
48	#11929609	—	2	2	no	—
49	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
50	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
51	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
52	C₄⋊Dic₇₉	—	2	1	no	—
53	C₄⋊Dic₇₉	—	2	1	no	—
54	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
55	Dic₇₉⋊C₄	—	2	2	no	—
56	(C₂×D₇₉)⋊C₄	—	2	2	no	—
57	(C₂×D₇₉)⋊C₄	—	2	1	no	—
58	(C₂×D₇₉)⋊C₄	—	2	2	no	—
59	C₄×Dic₇₉	—	2	2	no	—
60	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
61	C₂×Q₈×C₇₉	C₂³	1	2	yes	—
62	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₇₉	—	2	1	no	—
64	C₄⋊C₄×C₇₉	—	2	1	no	—
65	C₄⋊C₄×C₇₉	—	2	2	no	—
66	C₄⋊C₄×C₇₉	—	2	1	no	—
67	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
68	C₄⋊C₄×C₇₉	D₄	1	2	yes	—
69	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
70	C₂²⋊C₄×C₇₉	—	2	2	no	—
71	C₂²⋊C₄×C₇₉	—	2	1	no	—
72	C₂²⋊C₄×C₇₉	—	2	2	no	—
73	C₄²×C₇₉	—	2	2	no	—
74	C₄²×C₇₉	C₂³	1	1	yes	characteristic
75	C₄²×C₇₉	C₂³	1	2	yes	—
76	C₂³×C₇₉	—	2	1	no	—
77	C₂²×D₇₉	—	2	1	no	—
78	Q₈×C₇₉	—	2	2	no	—
79	Q₈×C₇₉	—	2	2	no	—
80	Q₈×C₇₉	—	2	2	no	—
81	D₄×C₇₉	—	2	1	no	—
82	D₄×C₇₉	—	2	1	no	—
83	C₂×C₄×C₇₉	—	2	1	no	—
84	C₂×C₄×C₇₉	—	2	2	no	—
85	C₂×C₄×C₇₉	—	4	2	no	—
86	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
87	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
88	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
91	C₂×Dic₇₉	—	2	1	no	—
92	C₂×Dic₇₉	—	2	2	no	—
93	D₃₁₆	—	2	1	no	—
94	D₃₁₆	—	2	1	no	—
95	C₄×D₇₉	—	4	2	no	—
96	Dic₁₅₈	—	2	2	no	—
97	Dic₁₅₈	—	2	2	no	—
98	C₇₉⋊C₈	—	2	2	no	—
99	C₇₉⋊C₈	—	2	1	no	—
100	C₇₉⋊C₈	#41	1	2	yes	—
101	C₂²×C₇₉	—	4	1	no	—
102	C₂²×C₇₉	—	4	1	no	—
103	C₂²×C₇₉	—	4	1	no	—
104	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
105	C₂×D₇₉	—	4	1	no	—
106	C₂×D₇₉	—	4	1	no	—
107	C₂×D₇₉	—	4	1	no	—
108	C₄×C₇₉	—	2	2	no	—
109	C₄×C₇₉	—	2	2	no	—
110	C₄×C₇₉	—	2	1	no	—
111	C₄×C₇₉	—	4	2	no	—
112	C₄×C₇₉	—	4	1	no	—
113	C₄×C₇₉	#135	1	2	yes	—
114	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
115	C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
116	Dic₇₉	—	4	2	no	—
117	Dic₇₉	—	4	1	no	—
118	C₂×C₇₉	—	8	1	no	—
119	C₂×C₇₉	#550	1	1	yes	characteristic
120	C₂×C₇₉	C₂×#135	1	1	yes	characteristic
121	C₂×C₇₉	#578	1	1	yes	characteristic
122	D₇₉	—	8	1	no	—
123	#3393	—	79	1	no	maximal, Sylow
124	C₇₉	#3393	1	1	yes	characteristic, complemented, Sylow
125	#556	—	79	1	no	—
126	#556	D₇₉	1	1	yes	characteristic, complemented
127	#495	—	79	2	no	—
128	#494	—	79	1	no	—
129	#464	—	79	2	no	—
130	#464	—	79	2	no	—
131	#461	—	79	1	no	—
132	#461	—	79	1	no	—
133	C₈×Q₈	—	79	1	no	—
134	C₄×Q₁₆	—	79	2	no	—
135	C₄×D₈	—	79	1	no	—
136	C₂×Q₁₆	—	79	2	no	—
137	C₂×Q₁₆	—	79	2	no	—
138	C₂×SD₁₆	—	79	2	no	—
139	C₂×SD₁₆	—	79	2	no	—
140	C₂×D₈	—	79	1	no	—
141	C₄⋊Q₈	—	79	1	no	—
142	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
143	#126	—	2	2	no	—
144	#126	—	158	2	no	—
145	#124	—	79	2	no	—
146	#124	C₂×D₇₉	1	2	yes	—
147	C₂²⋊Q₈	—	2	1	no	—
148	C₂²⋊Q₈	—	158	1	no	—
149	C₄×Q₈	—	79	2	no	—
150	C₄×Q₈	C₂×D₇₉	1	2	yes	—
151	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
152	C₄×D₄	—	79	1	no	—
153	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
154	#117	—	2	1	no	—
155	#117	—	158	1	no	—
156	#107	—	79	1	no	—
157	C₄⋊C₈	—	79	1	no	—
158	C₄⋊C₈	—	79	2	no	—
159	#103	—	79	2	no	—
160	#103	—	79	2	no	—
161	#102	—	79	1	no	—
162	#102	—	79	1	no	—
163	C₄×C₈	—	79	1	no	—
164	C₄×C₈	—	79	2	no	—
165	C₂×Q₈	—	79	2	no	—
166	C₂×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
167	C₂×Q₈	C₂²×D₇₉	1	2	yes	—
168	C₂×D₄	—	79	1	no	—
169	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	158	1	no	—
172	Q₁₆	—	316	2	no	—
173	Q₁₆	—	158	4	no	—
174	SD₁₆	—	316	2	no	—
175	SD₁₆	—	316	2	no	—
176	D₈	—	158	2	no	—
177	C₂×C₈	—	79	1	no	—
178	C₂×C₈	—	79	1	no	—
179	C₂×C₈	—	79	2	no	—
180	C₄⋊C₄	—	2	1	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	79	1	no	—
184	C₄⋊C₄	—	158	2	no	—
185	C₄⋊C₄	—	158	1	no	—
186	C₄⋊C₄	—	158	1	no	—
187	C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
188	C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
189	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
190	C₂²⋊C₄	—	2	2	no	—
191	C₂²⋊C₄	—	2	1	no	—
192	C₂²⋊C₄	—	2	2	no	—
193	C₂²⋊C₄	—	158	2	no	—
194	C₂²⋊C₄	—	158	1	no	—
195	C₂²⋊C₄	—	158	2	no	—
196	C₄²	—	2	2	no	—
197	C₄²	—	158	2	no	—
198	C₄²	C₂²×D₇₉	1	1	yes	characteristic
199	C₄²	C₂²×D₇₉	1	2	yes	—
200	C₂³	—	2	1	no	—
201	C₂³	—	158	1	no	—
202	Q₈	—	2	2	no	—
203	Q₈	—	2	2	no	—
204	Q₈	—	2	2	no	—
205	Q₈	—	158	2	no	—
206	Q₈	—	158	2	no	—
207	D₄	—	2	1	no	—
208	D₄	—	2	1	no	—
209	D₄	—	158	1	no	—
210	D₄	—	158	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	316	2	no	—
215	C₂×C₄	—	158	1	no	—
216	C₂×C₄	—	158	2	no	—
217	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
218	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
219	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
220	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
221	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
222	C₈	—	79	2	no	—
223	C₈	—	158	2	no	—
224	C₈	—	158	1	no	—
225	C₂²	—	4	1	no	—
226	C₂²	—	4	1	no	—
227	C₂²	—	4	1	no	—
228	C₂²	—	316	1	no	—
229	C₂²	—	316	1	no	—
230	C₂²	—	316	1	no	—
231	C₂²	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	2	no	—
236	C₄	—	4	1	no	—
237	C₄	—	316	2	no	—
238	C₄	—	316	1	no	—
239	C₄	#14579181	1	2	yes	—
240	C₄	#41×D₇₉	1	1	yes	characteristic
241	C₄	#14579207	1	1	yes	characteristic
242	C₂	—	8	1	no	—
243	C₂	—	632	1	no	—
244	C₂	#19099232	1	1	yes	characteristic
245	C₂	C₂×#14579181	1	1	yes	characteristic
246	C₂	#19099378	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099286

C₂

yes

maximal, characteristic, complemented

#19098945

C₂

yes

maximal

#19098942

C₂

yes

maximal, characteristic, complemented

#19098785

C₂

yes

maximal, complemented

#19098782

C₂

yes

maximal, complemented

#19098768

C₂

yes

maximal, characteristic, complemented

#19098765

C₂

yes

maximal, characteristic, complemented

Q₈×C₇₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#11929614

C₂

yes

maximal, complemented

C₄×#11929609

C₂

yes

maximal, characteristic

#556×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929614

C₂²

yes

—

C₂×#11929614

C₂²

yes

—

C₂×#11929612

C₂²

yes

—

C₂×#11929611

C₂²

yes

—

C₂×#11929609

C₂²

yes

characteristic

#14579161

C₂²

yes

characteristic

#14579156

—

#14579149

C₂²

yes

—

#14579137

—

C₄×Dic₁₅₈

C₂²

yes

—

C₄×D₃₁₆

C₂²

yes

characteristic

#14579119

—

#14579094

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579085

C₂²

yes

—

#14579084

C₂²

yes

—

#14579082

C₂²

yes

characteristic

#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

C₂³

yes

—

C₂×D₃₁₆

C₂³

yes

characteristic

C₂×C₄×D₇₉

—

—

—

—

—

—

C₂×C₇₉⋊C₈

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

C₂³

yes

—

C₂×C₇₉⋊C₈

C₂³

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

characteristic

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

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

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

100

C₇₉⋊C₈

#41

yes

—

101

C₂²×C₇₉

—

102

C₂²×C₇₉

—

103

C₂²×C₇₉

—

104

C₂²×C₇₉

C₂²×D₄

yes

characteristic

105

C₂×D₇₉

—

106

C₂×D₇₉

—

107

C₂×D₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

—

113

C₄×C₇₉

#135

yes

—

114

C₄×C₇₉

C₂×#41

yes

characteristic

115

C₄×C₇₉

H(5,𝔽₂)

yes

characteristic

116

Dic₇₉

—

117

Dic₇₉

—

118

C₂×C₇₉

—

119

C₂×C₇₉

#550

yes

characteristic

120

C₂×C₇₉

C₂×#135

yes

characteristic

121

C₂×C₇₉

#578

yes

characteristic

122

D₇₉

—

123

#3393

—

maximal, Sylow

124

C₇₉

#3393

yes

characteristic, complemented, Sylow

125

#556

—

126

#556

D₇₉

yes

characteristic, complemented

127

#495

—

128

#494

—

129

#464

—

130

#464

—

131

#461

—

132

#461

—

133

C₈×Q₈

—

134

C₄×Q₁₆

—

135

C₄×D₈

—

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×SD₁₆

—

139

C₂×SD₁₆

—

140

C₂×D₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

143

#126

—

144

#126

—

158

—

145

#124

—

146

#124

C₂×D₇₉

yes

—

147

C₂²⋊Q₈

—

148

C₂²⋊Q₈

—

158

—

149

C₄×Q₈

—

150

C₄×Q₈

C₂×D₇₉

yes

—

151

C₄×Q₈

C₂×D₇₉

yes

characteristic

152

C₄×D₄

—

153

C₄×D₄

C₂×D₇₉

yes

characteristic

154

#117

—

155

#117

—

158

—

156

#107

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

#103

—

160

#103

—

161

#102

—

162

#102

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₂×Q₈

—

166

C₂×Q₈

C₂²⋊D₇₉

yes

characteristic

167

C₂×Q₈

C₂²×D₇₉

yes

—

168

C₂×D₄

—

169

C₂×D₄

C₂²×D₇₉

yes

characteristic

170

C₂²×C₄

—

171

C₂²×C₄

—

158

—

172

Q₁₆

—

316

—

173

Q₁₆

—

158

—

174

SD₁₆

—

316

—

175

SD₁₆

—

316

—

176

D₈

—

158

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

158

—

185

C₄⋊C₄

—

158

—

186

C₄⋊C₄

—

158

—

187

C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

188

C₄⋊C₄

C₂²⋊D₇₉

yes

—

189

C₄⋊C₄

C₂²×D₇₉

yes

characteristic

190

C₂²⋊C₄

—

191

C₂²⋊C₄

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

158

—

194

C₂²⋊C₄

—

158

—

195

C₂²⋊C₄

—

158

—

196

C₄²

—

197

C₄²

—

158

—

198

C₄²

C₂²×D₇₉

yes

characteristic

199

C₄²

C₂²×D₇₉

yes

—

200

C₂³

—

201

C₂³

—

158

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

158

—

206

Q₈

—

158

—

207

D₄

—

208

D₄

—

209

D₄

—

158

—

210

D₄

—

158

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

316

—

215

C₂×C₄

—

158

—

216

C₂×C₄

—

158

—

217

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

218

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

219

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

220

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

221

C₂×C₄

C₂³×D₇₉

yes

characteristic

222

C₈

—

223

C₈

—

158

—

224

C₈

—

158

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

316

—

229

C₂²

—

316

—

230

C₂²

—

316

—

231

C₂²

C₂²×C₂²⋊D₇₉

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

316

—

238

C₄

—

316

—

239

C₄

#14579181

yes

—

240

C₄

#41×D₇₉

yes

characteristic

241

C₄

#14579207

yes

characteristic

242

C₂

—

243

C₂

—

632

—

244

C₂

#19099232

yes

characteristic

245

C₂

C₂×#14579181

yes

characteristic

246

C₂

#19099378

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	#3393
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. #19099286	C₂	semidirect
3. #19098942	C₂	semidirect
4. #19098785	C₂	semidirect
5. #19098782	C₂	semidirect
6. #19098768	C₂	semidirect
7. #19098765	C₂	semidirect
8. Q₈×C₇₉⋊C₈	C₂	semidirect
9. C₄×#11929614	C₂	semidirect
11. #556×C₇₉	C₂	semidirect
124. C₇₉	#3393	semidirect
126. #556	D₇₉	semidirect

H ≅ G/N

type

1. #19099286

C₂

semidirect

3. #19098942

C₂

semidirect

4. #19098785

C₂

semidirect

5. #19098782

C₂

semidirect

6. #19098768

C₂

semidirect

7. #19098765

C₂

semidirect

8. Q₈×C₇₉⋊C₈

C₂

semidirect

9. C₄×#11929614

C₂

semidirect

11. #556×C₇₉

C₂

semidirect

124. C₇₉

#3393

semidirect

126. #556

D₇₉

semidirect

Subgroups — #23776384

Conjugacy classes of subgroups

Complements