Group #28363283 — subgroups

Subgroups — #28363283

Order 13952.

298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂×#16812664	C₂	1	1	yes	maximal, characteristic
2	C₂×#16812624	C₂	1	1	yes	maximal, characteristic
3	C₂×#16812622	C₂	1	1	yes	maximal, characteristic
4	#20294922	C₂	1	1	yes	maximal, characteristic
5	#20294788	C₂	1	1	yes	maximal, characteristic
6	#20294780	C₂	1	1	yes	maximal, characteristic
7	C₂×#107×C₁₀₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₂₁₈	C₂²	1	1	yes	characteristic
9	C₂²×#11724784	C₂²	1	1	yes	characteristic
10	#16812664	—	2	2	no	—
11	#16812664	—	2	2	no	—
12	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
13	C₂×#13182008	—	2	1	no	—
14	C₂×#13182008	—	2	1	no	—
15	C₂×C₄×Dic₁₀₉	—	2	1	no	—
16	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
17	#16812624	C₄	1	4	yes	complemented
18	#16812622	—	2	2	no	—
19	#16812606	—	2	1	no	—
20	C₂²×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
23	#107×C₁₀₉	—	2	2	no	—
24	C₂×Dic₂₁₈	—	2	1	no	—
25	C₂×Dic₂₁₈	—	2	1	no	—
26	C₂×Dic₂₁₈	—	2	1	no	—
27	C₂×Dic₂₁₈	C₂×C₄	1	2	yes	—
28	C₂×Dic₂₁₈	D₄	1	2	yes	—
29	C₂×Dic₂₁₈	Q₈	1	2	yes	—
30	C₂²×Dic₁₀₉	—	2	1	no	—
31	C₂²×Dic₁₀₉	—	2	1	no	—
32	C₂²×Dic₁₀₉	D₄	1	1	yes	characteristic
33	C₂²×Dic₁₀₉	D₄	1	1	yes	characteristic
34	C₂×#11724784	—	2	1	no	—
35	C₂×#11724784	—	2	1	no	—
36	C₂×#11724784	—	2	1	no	—
37	C₄⋊Dic₁₀₉	—	2	1	no	—
38	C₄⋊Dic₁₀₉	C₂×C₄	1	2	yes	—
39	#13182008	—	2	4	no	—
40	#13182008	—	4	2	no	—
41	C₄×Dic₁₀₉	—	2	4	no	—
42	C₄×Dic₁₀₉	—	2	1	no	—
43	C₄×Dic₁₀₉	—	2	1	no	—
44	C₂²×C₄×C₁₀₉	—	2	1	no	—
45	C₂²×C₄×C₁₀₉	—	2	1	no	—
46	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
47	C₂×C₈×C₁₀₉	—	2	1	no	—
48	C₂×C₈×C₁₀₉	—	2	1	no	—
49	C₂×C₈×C₁₀₉	C₂×C₄	1	2	yes	—
50	C₄⋊C₄×C₁₀₉	—	2	1	no	—
51	C₄⋊C₄×C₁₀₉	—	2	1	no	—
52	C₄⋊C₄×C₁₀₉	—	2	1	no	—
53	C₄⋊C₄×C₁₀₉	D₄	1	2	yes	—
54	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₀₉	—	2	2	no	—
56	C₂×C₄×C₁₀₉	—	4	1	no	—
57	C₂×C₄×C₁₀₉	—	4	1	no	—
58	C₂×C₄×C₁₀₉	—	4	1	no	—
59	C₂×C₄×C₁₀₉	—	4	1	no	—
60	C₂×C₄×C₁₀₉	—	4	1	no	—
61	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₄×C₁₀₉	#41	1	1	yes	characteristic
66	C₂×C₄×C₁₀₉	#41	1	1	yes	characteristic
67	C₂×Dic₁₀₉	—	2	2	no	—
68	C₂×Dic₁₀₉	—	2	1	no	—
69	C₂×Dic₁₀₉	—	2	2	no	—
70	C₂×Dic₁₀₉	—	2	2	no	—
71	C₂×Dic₁₀₉	—	2	1	no	—
72	C₂×Dic₁₀₉	—	2	2	no	—
73	C₂×Dic₁₀₉	—	2	1	no	—
74	C₂×Dic₁₀₉	—	2	1	no	—
75	C₂×Dic₁₀₉	—	2	1	no	—
76	C₂×Dic₁₀₉	—	4	1	no	—
77	C₂×Dic₁₀₉	—	4	1	no	—
78	C₂×Dic₁₀₉	Q₁₆	1	2	yes	—
79	Dic₂₁₈	—	2	2	no	—
80	Dic₂₁₈	—	2	2	no	—
81	Dic₂₁₈	—	2	2	no	—
82	Dic₂₁₈	C₄⋊C₄	1	4	yes	complemented
83	C₈×C₁₀₉	—	2	2	no	—
84	#11724784	—	4	1	no	—
85	C₂²×C₁₀₉	C₄×D₄	1	1	yes	characteristic
86	C₂²×C₁₀₉	#120	1	1	yes	characteristic
87	C₂²×C₁₀₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂²×C₁₀₉	C₂×Q₁₆	1	1	yes	characteristic
89	C₂²×C₁₀₉	#135	1	1	yes	characteristic
90	C₂²×C₁₀₉	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂²×C₁₀₉	#137	1	1	yes	characteristic
92	C₄×C₁₀₉	—	4	2	no	—
93	C₄×C₁₀₉	—	8	1	no	—
94	C₄×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
95	C₄×C₁₀₉	C₄×D₄	1	1	yes	characteristic
96	C₄×C₁₀₉	C₂²⋊Q₈	1	1	yes	characteristic
97	C₄×C₁₀₉	#123	1	1	yes	characteristic
98	Dic₁₀₉	—	2	4	no	—
99	Dic₁₀₉	—	2	2	no	—
100	Dic₁₀₉	—	4	2	no	—
101	Dic₁₀₉	—	4	1	no	—
102	C₂×C₁₀₉	#385	1	1	yes	characteristic
103	C₂×C₁₀₉	C₄×Q₁₆	1	1	yes	characteristic
104	C₂×C₁₀₉	#440	1	1	yes	characteristic
105	C₂×C₁₀₉	#449	1	1	yes	characteristic
106	C₂×C₁₀₉	#451	1	1	yes	characteristic
107	C₂×C₁₀₉	#477	1	1	yes	characteristic
108	C₂×C₁₀₉	#479	1	1	yes	characteristic
109	#1863	—	109	1	no	maximal, Sylow
110	C₁₀₉	#1863	1	1	yes	characteristic, complemented, Sylow
111	C₂×C₄×Q₈	—	109	1	no	—
112	C₂×#107	D₁₀₉	1	1	yes	characteristic
113	C₂×#103	—	109	1	no	—
114	C₂×#103	—	109	1	no	—
115	#389	—	109	1	no	—
116	#340	—	109	1	no	—
117	#336	—	109	1	no	—
118	C₂²×Q₈	—	109	1	no	—
119	C₂²×C₈	—	109	1	no	—
120	C₂²×C₈	C₂×D₁₀₉	1	1	yes	characteristic
121	C₄×Q₈	—	218	2	no	—
122	C₄×Q₈	—	218	2	no	—
123	C₂×C₄⋊C₄	—	109	1	no	—
124	C₂×C₄⋊C₄	—	218	1	no	—
125	C₂×C₄⋊C₄	—	218	1	no	—
126	C₂×C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic
127	C₂×C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic
128	C₂×C₄²	—	109	1	no	—
129	C₂×C₄²	—	218	1	no	—
130	#107	—	2	2	no	—
131	#103	—	109	4	no	—
132	#103	—	218	2	no	—
133	#95	—	218	1	no	—
134	C₂×Q₈	—	109	2	no	—
135	C₂×Q₈	—	109	2	no	—
136	C₂×Q₈	—	109	2	no	—
137	C₂×Q₈	—	218	1	no	—
138	C₂×Q₈	—	218	1	no	—
139	C₂×Q₈	—	218	1	no	—
140	C₂²×C₄	—	2	1	no	—
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	109	1	no	—
143	C₂²×C₄	—	109	1	no	—
144	C₂²×C₄	—	218	1	no	—
145	C₂²×C₄	—	218	1	no	—
146	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
147	C₂×C₈	—	2	1	no	—
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	218	1	no	—
150	C₂×C₈	—	218	1	no	—
151	C₂×C₈	—	218	1	no	—
152	C₂×C₈	C₄×D₁₀₉	1	2	yes	—
153	C₄⋊C₄	—	2	1	no	—
154	C₄⋊C₄	—	2	1	no	—
155	C₄⋊C₄	—	2	1	no	—
156	C₄⋊C₄	—	109	2	no	—
157	C₄⋊C₄	—	436	2	no	—
158	C₄⋊C₄	—	218	4	no	—
159	C₄⋊C₄	—	218	1	no	—
160	C₄⋊C₄	C₂²⋊D₁₀₉	1	2	yes	—
161	C₄²	—	218	4	no	—
162	C₄²	—	218	1	no	—
163	C₄²	—	218	1	no	—
164	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
165	Q₈	—	109	4	no	—
166	Q₈	—	218	2	no	—
167	Q₈	—	218	2	no	—
168	Q₈	—	218	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	4	1	no	—
171	C₂×C₄	—	4	1	no	—
172	C₂×C₄	—	4	1	no	—
173	C₂×C₄	—	4	1	no	—
174	C₂×C₄	—	4	1	no	—
175	C₂×C₄	—	109	2	no	—
176	C₂×C₄	—	436	1	no	—
177	C₂×C₄	—	436	1	no	—
178	C₂×C₄	—	218	2	no	—
179	C₂×C₄	—	218	1	no	—
180	C₂×C₄	—	218	1	no	—
181	C₂×C₄	—	218	1	no	—
182	C₂×C₄	—	218	2	no	—
183	C₂×C₄	—	218	1	no	—
184	C₂×C₄	—	218	2	no	—
185	C₂×C₄	—	218	2	no	—
186	C₂×C₄	—	218	1	no	—
187	C₂×C₄	C₂×C₄×D₁₀₉	1	1	yes	characteristic
188	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
189	C₂×C₄	C₂×C₂²⋊D₁₀₉	1	1	yes	characteristic
190	C₂×C₄	Q₈×D₁₀₉	1	1	yes	characteristic
191	C₂×C₄	#13182029	1	1	yes	characteristic
192	C₂×C₄	#13182030	1	1	yes	characteristic
193	C₈	—	2	2	no	—
194	C₈	—	436	1	no	—
195	C₂²	#16812661	1	1	yes	characteristic
196	C₂²	#16812667	1	1	yes	characteristic
197	C₂²	#16812677	1	1	yes	characteristic
198	C₂²	Q₁₆×D₁₀₉	1	1	yes	characteristic
199	C₂²	#16812718	1	1	yes	characteristic
200	C₂²	#16812723	1	1	yes	characteristic
201	C₂²	#16812731	1	1	yes	characteristic
202	C₄	—	4	2	no	—
203	C₄	—	8	1	no	—
204	C₄	—	436	1	no	—
205	C₄	—	436	2	no	—
206	C₄	—	218	2	no	—
207	C₄	—	218	4	no	—
208	C₄	C₄⋊C₄×D₁₀₉	1	1	yes	characteristic
209	C₄	C₄×C₂²⋊D₁₀₉	1	1	yes	characteristic
210	C₄	#16812675	1	1	yes	characteristic
211	C₄	#16812684	1	1	yes	characteristic
212	C₂	#20294897	1	1	yes	characteristic
213	C₂	#20295120	1	1	yes	characteristic
214	C₂	#20295125	1	1	yes	characteristic
215	C₂	#20295168	1	1	yes	characteristic
216	C₂	#20295180	1	1	yes	characteristic
217	C₂	#20295320	1	1	yes	characteristic
218	C₂	#20295332	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16812664

C₂

yes

maximal, characteristic

C₂×#16812624

C₂

yes

maximal, characteristic

C₂×#16812622

C₂

yes

maximal, characteristic

#20294922

C₂

yes

maximal, characteristic

#20294788

C₂

yes

maximal, characteristic

#20294780

C₂

yes

maximal, characteristic

C₂×#107×C₁₀₉

C₂

yes

maximal, characteristic

C₂²×Dic₂₁₈

C₂²

yes

characteristic

C₂²×#11724784

C₂²

yes

characteristic

#16812664

—

#16812664

—

C₂×C₄⋊Dic₁₀₉

C₂²

yes

characteristic

C₂×#13182008

—

C₂×#13182008

—

C₂×C₄×Dic₁₀₉

—

C₂×C₄×Dic₁₀₉

C₂²

yes

characteristic

#16812624

C₄

yes

complemented

#16812622

—

#16812606

—

C₂²×C₈×C₁₀₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₀₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₀₉

C₂²

yes

characteristic

#107×C₁₀₉

—

C₂×Dic₂₁₈

—

C₂×Dic₂₁₈

—

C₂×Dic₂₁₈

—

C₂×Dic₂₁₈

C₂×C₄

yes

—

C₂×Dic₂₁₈

D₄

yes

—

C₂×Dic₂₁₈

Q₈

yes

—

C₂²×Dic₁₀₉

—

C₂²×Dic₁₀₉

—

C₂²×Dic₁₀₉

D₄

yes

characteristic

C₂²×Dic₁₀₉

D₄

yes

—

—

—

C₄⋊Dic₁₀₉

—

C₄⋊Dic₁₀₉

C₂×C₄

yes

—

#13182008

—

#13182008

—

C₄×Dic₁₀₉

—

C₄×Dic₁₀₉

—

C₄×Dic₁₀₉

—

C₂²×C₄×C₁₀₉

—

C₂²×C₄×C₁₀₉

—

C₂²×C₄×C₁₀₉

C₂³

yes

characteristic

C₂×C₈×C₁₀₉

—

C₂×C₈×C₁₀₉

—

C₂×C₈×C₁₀₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

D₄

yes

—

C₂³×C₁₀₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₀₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₀₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₀₉

C₂×Q₈

yes

C₂×C₄×C₁₀₉

yes

C₂×C₄×C₁₀₉

yes

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

Q₁₆

yes

—

Dic₂₁₈

—

Dic₂₁₈

—

Dic₂₁₈

—

Dic₂₁₈

C₄⋊C₄

yes

complemented

C₈×C₁₀₉

—

#11724784

—

C₂²×C₁₀₉

C₄×D₄

yes

characteristic

C₂²×C₁₀₉

#120

yes

characteristic

C₂²×C₁₀₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₀₉

C₂×Q₁₆

yes

C₂²×C₁₀₉

yes

C₂²×C₁₀₉

yes

C₂²×C₁₀₉

yes

C₄×C₁₀₉

—

C₄×C₁₀₉

—

C₄×C₁₀₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₀₉

C₄×D₄

yes

characteristic

C₄×C₁₀₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₀₉

#123

yes

characteristic

Dic₁₀₉

—

Dic₁₀₉

—

100

Dic₁₀₉

—

101

Dic₁₀₉

—

102

C₂×C₁₀₉

#385

yes

characteristic

103

C₂×C₁₀₉

C₄×Q₁₆

yes

characteristic

104

C₂×C₁₀₉

#440

yes

characteristic

105

C₂×C₁₀₉

#449

yes

characteristic

106

C₂×C₁₀₉

#451

yes

characteristic

107

C₂×C₁₀₉

#477

yes

characteristic

108

C₂×C₁₀₉

#479

yes

characteristic

109

#1863

—

109

maximal, Sylow

110

C₁₀₉

#1863

yes

characteristic, complemented, Sylow

111

C₂×C₄×Q₈

—

109

—

112

C₂×#107

D₁₀₉

yes

characteristic

113

C₂×#103

—

109

—

114

C₂×#103

—

109

—

115

#389

—

109

—

116

#340

—

109

—

117

#336

—

109

—

118

C₂²×Q₈

—

109

—

119

C₂²×C₈

—

109

—

120

C₂²×C₈

C₂×D₁₀₉

yes

characteristic

121

C₄×Q₈

—

218

—

122

C₄×Q₈

—

218

—

123

C₂×C₄⋊C₄

—

109

—

124

C₂×C₄⋊C₄

—

218

—

125

C₂×C₄⋊C₄

—

218

—

126

C₂×C₄⋊C₄

C₂×D₁₀₉

yes

characteristic

127

C₂×C₄⋊C₄

C₂×D₁₀₉

yes

characteristic

128

C₂×C₄²

—

109

—

129

C₂×C₄²

—

218

—

130

#107

—

131

#103

—

109

—

132

#103

—

218

—

133

#95

—

218

—

134

C₂×Q₈

—

109

—

135

C₂×Q₈

—

109

—

136

C₂×Q₈

—

109

—

137

C₂×Q₈

—

218

—

138

C₂×Q₈

—

218

—

139

C₂×Q₈

—

218

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

109

—

143

C₂²×C₄

—

109

—

144

C₂²×C₄

—

218

—

145

C₂²×C₄

—

218

—

146

C₂²×C₄

C₂²×D₁₀₉

yes

characteristic

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

218

—

150

C₂×C₈

—

218

—

151

C₂×C₈

—

218

—

152

C₂×C₈

C₄×D₁₀₉

yes

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

109

—

157

C₄⋊C₄

—

436

—

158

C₄⋊C₄

—

218

—

159

C₄⋊C₄

—

218

—

160

C₄⋊C₄

C₂²⋊D₁₀₉

yes

—

161

C₄²

—

218

—

162

C₄²

—

218

—

163

C₄²

—

218

—

164

C₂³

D₄×D₁₀₉

yes

characteristic

165

Q₈

—

109

—

166

Q₈

—

218

—

167

Q₈

—

218

—

168

Q₈

—

218

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

109

—

176

C₂×C₄

—

436

—

177

C₂×C₄

—

436

—

178

C₂×C₄

—

218

—

179

C₂×C₄

—

218

—

180

C₂×C₄

—

218

—

181

C₂×C₄

—

218

—

182

C₂×C₄

—

218

—

183

C₂×C₄

—

218

—

184

C₂×C₄

—

218

—

185

C₂×C₄

—

218

—

186

C₂×C₄

—

218

—

187

C₂×C₄

C₂×C₄×D₁₀₉

yes

characteristic

188

C₂×C₄

D₄×D₁₀₉

yes

characteristic

189

C₂×C₄

C₂×C₂²⋊D₁₀₉

yes

characteristic

190

C₂×C₄

Q₈×D₁₀₉

yes

characteristic

191

C₂×C₄

#13182029

yes

characteristic

192

C₂×C₄

#13182030

yes

characteristic

193

C₈

—

194

C₈

—

436

—

195

C₂²

#16812661

yes

characteristic

196

C₂²

#16812667

yes

characteristic

197

C₂²

#16812677

yes

characteristic

198

C₂²

Q₁₆×D₁₀₉

yes

characteristic

199

C₂²

#16812718

yes

characteristic

200

C₂²

#16812723

yes

characteristic

201

C₂²

#16812731

yes

characteristic

202

C₄

—

203

C₄

—

204

C₄

—

436

—

205

C₄

—

436

—

206

C₄

—

218

—

207

C₄

—

218

—

208

C₄

C₄⋊C₄×D₁₀₉

yes

characteristic

209

C₄

C₄×C₂²⋊D₁₀₉

yes

characteristic

210

C₄

#16812675

yes

characteristic

211

C₄

#16812684

yes

characteristic

212

C₂

#20294897

yes

characteristic

213

C₂

#20295120

yes

characteristic

214

C₂

#20295125

yes

characteristic

215

C₂

#20295168

yes

characteristic

216

C₂

#20295180

yes

characteristic

217

C₂

#20295320

yes

characteristic

218

C₂

#20295332

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₀₉
commutator	C₂×C₄×C₁₀₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₀₉
Fitting	C₂×#107×C₁₀₉	C₂
socle, prime radical	C₂³×C₁₀₉	C₂×D₄
cosocle	C₂²×C₄×C₁₀₉	C₂³
hypercenter	C₂×#107	D₁₀₉
hypocenter	C₁₀₉	#1863
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₁₀₉

commutator

C₂×C₄×C₁₀₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₀₉

Fitting

C₂×#107×C₁₀₉

C₂

socle, prime radical

C₂³×C₁₀₉

C₂×D₄

cosocle

C₂²×C₄×C₁₀₉

C₂³

D₁₀₉

C₁₀₉

G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
17. #16812624	C₄	semidirect
82. Dic₂₁₈	C₄⋊C₄	semidirect
110. C₁₀₉	#1863	semidirect

H ≅ G/N

type

17. #16812624

C₄

semidirect

82. Dic₂₁₈

C₄⋊C₄

semidirect

110. C₁₀₉

#1863

semidirect

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

subgroup	index
C₂×#16812664	2
C₂×#16812624	2
C₂×#16812622	2
#20294922	2
#20294788	2
#20294780	2
C₂×#107×C₁₀₉	2
#1863	109

subgroup

index

C₂×#107×C₁₀₉

109

Subgroups — #28363283

Conjugacy classes of subgroups

Complements

Maximal subgroups