Group #22581657 — subgroups

Subgroups — #22581657

Order 8896.

228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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	#17984840	C₂	1	1	yes	maximal, characteristic, complemented
2	#17984832	C₂	1	1	yes	maximal, characteristic, complemented
3	#17984832	C₂	1	1	yes	maximal, characteristic, complemented
4	#17984820	C₂	1	1	yes	maximal, characteristic, complemented
5	#17984820	C₂	1	1	yes	maximal, characteristic, complemented
6	#17984819	C₂	1	1	yes	maximal, characteristic, complemented
7	#17984819	C₂	1	1	yes	maximal, characteristic, complemented
8	#17984818	C₂	1	1	yes	maximal, characteristic, complemented
9	#17984807	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂²⋊D₁₃₉	C₂	1	1	yes	maximal, characteristic
11	(C₂²⋊D₁₃₉)⋊C₄	C₂	1	1	yes	maximal, characteristic
12	(C₂²⋊D₁₃₉)⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂×Dic₁₃₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄⋊C₄×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Dic₂₇₈	C₂²	1	1	yes	characteristic
17	C₂×Dic₂₇₈	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×Dic₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
24	C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
25	C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
26	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
27	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
28	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
29	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
30	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
31	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
32	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
33	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
34	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
35	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
36	Dic₁₃₉⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
38	(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
40	(C₂×D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
42	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
43	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
50	C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
51	C₂²×D₁₃₉	C₂³	1	1	yes	characteristic
52	Dic₂₇₈	—	2	2	no	—
53	Dic₂₇₈	—	4	1	no	—
54	C₂²⋊D₁₃₉	Q₈	1	4	yes	complemented
55	C₂×Dic₁₃₉	—	2	2	no	—
56	C₂×Dic₁₃₉	—	4	1	no	—
57	C₂×Dic₁₃₉	C₂³	1	1	yes	characteristic
58	C₂×Dic₁₃₉	C₂³	1	1	yes	characteristic
59	C₂×Dic₁₃₉	C₂³	1	1	yes	characteristic
60	C₂×Dic₁₃₉	C₂³	1	1	yes	characteristic
61	C₂×Dic₁₃₉	C₂³	1	1	yes	characteristic
62	C₂×Dic₁₃₉	C₂³	1	1	yes	characteristic
63	C₂×Dic₁₃₉	C₂³	1	1	yes	characteristic
64	C₄×D₁₃₉	—	2	2	no	—
65	C₄×D₁₃₉	—	4	1	no	—
66	C₄×D₁₃₉	—	4	1	no	—
67	C₂³×C₁₃₉	C₂³	1	1	yes	characteristic
68	Q₈×C₁₃₉	—	4	1	no	—
69	C₂×C₄×C₁₃₉	—	4	1	no	—
70	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂²×C₁₃₉	—	2	1	no	—
77	C₂²×C₁₃₉	—	2	1	no	—
78	C₂²×C₁₃₉	C₂×Q₈	1	2	yes	—
79	C₂²×C₁₃₉	C₂⁴	1	1	yes	characteristic
80	C₂×D₁₃₉	—	2	1	no	—
81	C₂×D₁₃₉	—	2	1	no	—
82	C₂×D₁₃₉	C₂×Q₈	1	2	yes	—
83	C₄×C₁₃₉	—	2	1	no	—
84	C₄×C₁₃₉	—	2	1	no	—
85	C₄×C₁₃₉	—	2	1	no	—
86	C₄×C₁₃₉	—	2	1	no	—
87	C₄×C₁₃₉	—	2	1	no	—
88	C₄×C₁₃₉	—	2	1	no	—
89	Dic₁₃₉	—	2	1	no	—
90	Dic₁₃₉	—	2	1	no	—
91	Dic₁₃₉	—	2	1	no	—
92	Dic₁₃₉	—	2	1	no	—
93	Dic₁₃₉	—	2	1	no	—
94	Dic₁₃₉	C₂×Q₈	1	2	yes	—
95	Dic₁₃₉	#41	1	2	yes	—
96	C₂×C₁₃₉	—	2	2	no	—
97	C₂×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
98	C₂×C₁₃₉	C₂×#41	1	1	yes	characteristic
99	C₂×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
100	D₁₃₉	—	2	2	no	—
101	C₁₃₉	#554	1	1	yes	characteristic, complemented, Sylow
102	#554	—	139	1	no	maximal, Sylow
103	C₄⋊Q₈	—	139	1	no	—
104	#125	—	139	1	no	—
105	#125	—	139	1	no	—
106	C₂²⋊Q₈	—	139	1	no	—
107	C₂²⋊Q₈	—	139	1	no	—
108	C₂²⋊Q₈	—	139	1	no	—
109	C₂²⋊Q₈	—	139	1	no	—
110	C₂²⋊Q₈	—	139	1	no	—
111	C₂²⋊Q₈	D₁₃₉	1	1	yes	characteristic, complemented
112	C₄×Q₈	—	139	1	no	—
113	C₄×D₄	—	139	1	no	—
114	C₄×D₄	—	139	1	no	—
115	C₄×D₄	—	139	1	no	—
116	C₂×C₄⋊C₄	—	139	1	no	—
117	C₂×C₄⋊C₄	—	139	1	no	—
118	C₂×Q₈	—	139	1	no	—
119	C₂×Q₈	—	139	1	no	—
120	C₂×Q₈	C₂×D₁₃₉	1	1	yes	characteristic
121	C₂×D₄	—	139	1	no	—
122	C₂²×C₄	—	139	1	no	—
123	C₂²×C₄	—	139	1	no	—
124	C₂²×C₄	—	139	1	no	—
125	C₂²×C₄	—	139	1	no	—
126	C₂²×C₄	—	139	1	no	—
127	C₂²×C₄	C₂×D₁₃₉	1	1	yes	characteristic
128	C₄⋊C₄	—	139	1	no	—
129	C₄⋊C₄	—	139	1	no	—
130	C₄⋊C₄	—	139	1	no	—
131	C₄⋊C₄	—	139	1	no	—
132	C₄⋊C₄	—	139	1	no	—
133	C₄⋊C₄	—	139	1	no	—
134	C₄⋊C₄	—	139	1	no	—
135	C₄⋊C₄	—	139	1	no	—
136	C₄⋊C₄	—	139	1	no	—
137	C₄⋊C₄	—	139	1	no	—
138	C₄⋊C₄	—	139	1	no	—
139	C₄⋊C₄	—	139	1	no	—
140	C₄⋊C₄	—	139	1	no	—
141	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
142	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
143	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
144	C₂²⋊C₄	—	139	1	no	—
145	C₂²⋊C₄	—	139	1	no	—
146	C₂²⋊C₄	—	139	1	no	—
147	C₂²⋊C₄	—	139	1	no	—
148	C₂²⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
149	C₂²⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
150	C₄²	—	139	1	no	—
151	C₄²	—	139	1	no	—
152	C₄²	—	139	1	no	—
153	C₂³	—	139	1	no	—
154	C₂³	C₂²×D₁₃₉	1	1	yes	characteristic
155	Q₈	—	4	1	no	—
156	Q₈	—	278	2	no	—
157	Q₈	—	556	1	no	—
158	D₄	—	139	4	no	—
159	C₂×C₄	—	4	1	no	—
160	C₂×C₄	—	278	2	no	—
161	C₂×C₄	—	278	2	no	—
162	C₂×C₄	—	556	1	no	—
163	C₂×C₄	—	556	1	no	—
164	C₂×C₄	—	556	1	no	—
165	C₂×C₄	—	139	1	no	—
166	C₂×C₄	—	139	1	no	—
167	C₂×C₄	—	139	1	no	—
168	C₂×C₄	—	139	1	no	—
169	C₂×C₄	—	139	1	no	—
170	C₂×C₄	—	139	1	no	—
171	C₂×C₄	—	139	1	no	—
172	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
173	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
174	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
175	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
176	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
177	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
178	C₂²	—	2	1	no	—
179	C₂²	—	2	1	no	—
180	C₂²	—	278	1	no	—
181	C₂²	—	278	1	no	—
182	C₂²	—	139	2	no	—
183	C₂²	Q₈×D₁₃₉	1	2	yes	—
184	C₂²	C₂³×D₁₃₉	1	1	yes	characteristic
185	C₄	—	2	1	no	—
186	C₄	—	2	1	no	—
187	C₄	—	2	1	no	—
188	C₄	—	2	1	no	—
189	C₄	—	2	1	no	—
190	C₄	—	2	1	no	—
191	C₄	—	278	1	no	—
192	C₄	—	278	1	no	—
193	C₄	—	278	1	no	—
194	C₄	—	278	1	no	—
195	C₄	—	278	1	no	—
196	C₄	—	139	2	no	—
197	C₄	—	139	2	no	—
198	C₂	—	2	2	no	—
199	C₂	—	278	2	no	—
200	C₂	C₂×Q₈×D₁₃₉	1	1	yes	characteristic
201	C₂	#41×D₁₃₉	1	1	yes	characteristic
202	C₂	#17984887	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17984840

C₂

yes

maximal, characteristic, complemented

#17984832

C₂

yes

maximal, characteristic, complemented

#17984832

C₂

yes

maximal, characteristic, complemented

#17984820

C₂

yes

maximal, characteristic, complemented

#17984820

C₂

yes

maximal, characteristic, complemented

#17984819

C₂

yes

maximal, characteristic, complemented

#17984819

C₂

yes

maximal, characteristic, complemented

#17984818

C₂

yes

maximal, characteristic, complemented

#17984807

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊D₁₃₉

C₂

yes

maximal, characteristic

(C₂²⋊D₁₃₉)⋊C₄

C₂

yes

maximal, characteristic

(C₂²⋊D₁₃₉)⋊C₄

C₂

yes

maximal, characteristic

C₂×Dic₁₃₉⋊C₄

C₂

yes

maximal, characteristic, complemented

C₄⋊C₄×D₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂²⋊Q₈×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₇₈

C₂²

yes

characteristic

C₂×Dic₂₇₈

C₂²

yes

characteristic

C₂×C₂²⋊D₁₃₉

C₂²

yes

characteristic

C₂²×Dic₁₃₉

C₂²

yes

characteristic

C₂²×Dic₁₃₉

C₂²

yes

characteristic

C₂×C₄×D₁₃₉

C₂²

yes

characteristic

C₂×C₄×D₁₃₉

C₂²

yes

characteristic

C₂×C₄×D₁₃₉

C₂²

yes

characteristic

C₄⋊Dic₁₃₉

C₂²

yes

characteristic

C₄⋊Dic₁₃₉

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

C₂²

yes

characteristic

C₂²⋊Dic₁₃₉

C₂²

yes

characteristic

(C₂×D₁₃₉)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₃₉)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₃₉)⋊C₄

C₂²

yes

characteristic

C₄×Dic₁₃₉

C₂²

yes

characteristic

C₄×Dic₁₃₉

C₂²

yes

characteristic

C₄×Dic₁₃₉

C₂²

yes

characteristic

C₂×Q₈×C₁₃₉

C₂²

yes

characteristic

C₂²×C₄×C₁₃₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₃₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₃₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₃₉

C₂²

yes

characteristic

C₂²⋊C₄×C₁₃₉

C₂²

yes

characteristic

C₂²⋊C₄×C₁₃₉

C₂²

yes

characteristic

C₂²×D₁₃₉

C₂³

yes

characteristic

Dic₂₇₈

—

Dic₂₇₈

—

C₂²⋊D₁₃₉

Q₈

yes

complemented

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

C₂³

yes

characteristic

C₂×Dic₁₃₉

C₂³

yes

characteristic

C₂×Dic₁₃₉

C₂³

yes

characteristic

C₂×Dic₁₃₉

C₂³

yes

characteristic

C₂×Dic₁₃₉

C₂³

yes

characteristic

C₂×Dic₁₃₉

C₂³

yes

characteristic

C₂×Dic₁₃₉

C₂³

yes

characteristic

C₄×D₁₃₉

—

C₄×D₁₃₉

—

C₄×D₁₃₉

—

C₂³×C₁₃₉

C₂³

yes

characteristic

Q₈×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

C₂×Q₈

yes

—

C₂²×C₁₃₉

C₂⁴

yes

characteristic

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₂×D₁₃₉

C₂×Q₈

yes

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

C₂×Q₈

yes

—

Dic₁₃₉

#41

yes

—

C₂×C₁₃₉

—

C₂×C₁₃₉

C₂²×Q₈

yes

characteristic

C₂×C₁₃₉

C₂×#41

yes

characteristic

C₂×C₁₃₉

H(5,𝔽₂)

yes

characteristic

100

D₁₃₉

—

101

C₁₃₉

#554

yes

characteristic, complemented, Sylow

102

#554

—

139

maximal, Sylow

103

C₄⋊Q₈

—

139

—

104

#125

—

139

—

105

#125

—

139

—

106

C₂²⋊Q₈

—

139

—

107

C₂²⋊Q₈

—

139

—

108

C₂²⋊Q₈

—

139

—

109

C₂²⋊Q₈

—

139

—

110

C₂²⋊Q₈

—

139

—

111

C₂²⋊Q₈

D₁₃₉

yes

characteristic, complemented

112

C₄×Q₈

—

139

—

113

C₄×D₄

—

139

—

114

C₄×D₄

—

139

—

115

C₄×D₄

—

139

—

116

C₂×C₄⋊C₄

—

139

—

117

C₂×C₄⋊C₄

—

139

—

118

C₂×Q₈

—

139

—

119

C₂×Q₈

—

139

—

120

C₂×Q₈

C₂×D₁₃₉

yes

characteristic

121

C₂×D₄

—

139

—

122

C₂²×C₄

—

139

—

123

C₂²×C₄

—

139

—

124

C₂²×C₄

—

139

—

125

C₂²×C₄

—

139

—

126

C₂²×C₄

—

139

—

127

C₂²×C₄

C₂×D₁₃₉

yes

characteristic

128

C₄⋊C₄

—

139

—

129

C₄⋊C₄

—

139

—

130

C₄⋊C₄

—

139

—

131

C₄⋊C₄

—

139

—

132

C₄⋊C₄

—

139

—

133

C₄⋊C₄

—

139

—

134

C₄⋊C₄

—

139

—

135

C₄⋊C₄

—

139

—

136

C₄⋊C₄

—

139

—

137

C₄⋊C₄

—

139

—

138

C₄⋊C₄

—

139

—

139

C₄⋊C₄

—

139

—

140

C₄⋊C₄

—

139

—

141

C₄⋊C₄

C₂×D₁₃₉

yes

characteristic

142

C₄⋊C₄

C₂×D₁₃₉

yes

characteristic

143

C₄⋊C₄

C₂×D₁₃₉

yes

characteristic

144

C₂²⋊C₄

—

139

—

145

C₂²⋊C₄

—

139

—

146

C₂²⋊C₄

—

139

—

147

C₂²⋊C₄

—

139

—

148

C₂²⋊C₄

C₂×D₁₃₉

yes

characteristic

149

C₂²⋊C₄

C₂×D₁₃₉

yes

characteristic

150

C₄²

—

139

—

151

C₄²

—

139

—

152

C₄²

—

139

—

153

C₂³

—

139

—

154

C₂³

C₂²×D₁₃₉

yes

characteristic

155

Q₈

—

156

Q₈

—

278

—

157

Q₈

—

556

—

158

D₄

—

139

—

159

C₂×C₄

—

160

C₂×C₄

—

278

—

161

C₂×C₄

—

278

—

162

C₂×C₄

—

556

—

163

C₂×C₄

—

556

—

164

C₂×C₄

—

556

—

165

C₂×C₄

—

139

—

166

C₂×C₄

—

139

—

167

C₂×C₄

—

139

—

168

C₂×C₄

—

139

—

169

C₂×C₄

—

139

—

170

C₂×C₄

—

139

—

171

C₂×C₄

—

139

—

172

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

173

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

174

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

175

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

176

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

177

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

178

C₂²

—

179

C₂²

—

180

C₂²

—

278

—

181

C₂²

—

278

—

182

C₂²

—

139

—

183

C₂²

Q₈×D₁₃₉

yes

—

184

C₂²

C₂³×D₁₃₉

yes

characteristic

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

278

—

192

C₄

—

278

—

193

C₄

—

278

—

194

C₄

—

278

—

195

C₄

—

278

—

196

C₄

—

139

—

197

C₄

—

139

—

198

C₂

—

199

C₂

—

278

—

200

C₂

C₂×Q₈×D₁₃₉

yes

characteristic

201

C₂

#41×D₁₃₉

yes

characteristic

202

C₂

#17984887

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₃₉
commutator, socle	C₂²×C₁₃₉	C₂⁴
Fitting	C₂²⋊Q₈×C₁₃₉	C₂
hypercenter	C₂²⋊Q₈	D₁₃₉
hypocenter	C₁₃₉	#554
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×D₁₃₉

commutator, socle

C₂²×C₁₃₉

C₂⁴

Fitting

C₂²⋊Q₈×C₁₃₉

C₂

hypercenter

C₂²⋊Q₈

D₁₃₉

C₁₃₉

G ▷ C₂²×C₁₃₉ ▷ C₁₃₉

C₁ ◁ C₂² ◁ C₂²⋊Q₈

N	H ≅ G/N	type
1. #17984840	C₂	semidirect
2. #17984832	C₂	semidirect
3. #17984832	C₂	semidirect
4. #17984820	C₂	semidirect
5. #17984820	C₂	semidirect
6. #17984819	C₂	semidirect
7. #17984819	C₂	semidirect
8. #17984818	C₂	semidirect
9. #17984807	C₂	semidirect
13. C₂×Dic₁₃₉⋊C₄	C₂	semidirect
14. C₄⋊C₄×D₁₃₉	C₂	semidirect
15. C₂²⋊Q₈×C₁₃₉	C₂	semidirect
54. C₂²⋊D₁₃₉	Q₈	semidirect
101. C₁₃₉	#554	semidirect
111. C₂²⋊Q₈	D₁₃₉	semidirect

H ≅ G/N

type

1. #17984840

C₂

semidirect

2. #17984832

C₂

semidirect

3. #17984832

C₂

semidirect

4. #17984820

C₂

semidirect

5. #17984820

C₂

semidirect

6. #17984819

C₂

semidirect

7. #17984819

C₂

semidirect

8. #17984818

C₂

semidirect

9. #17984807

C₂

semidirect

13. C₂×Dic₁₃₉⋊C₄

C₂

semidirect

14. C₄⋊C₄×D₁₃₉

C₂

semidirect

15. C₂²⋊Q₈×C₁₃₉

C₂

semidirect

54. C₂²⋊D₁₃₉

Q₈

semidirect

101. C₁₃₉

#554

semidirect

111. C₂²⋊Q₈

D₁₃₉

semidirect

Subgroups — #22581657

Conjugacy classes of subgroups

Complements