Finite Group Databasebeta

← C2×#19151708 #26029043

Subgroups — C2×#19151708 #26029043

Order 11392.

608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13083559C211yesmaximal, characteristic
2C2×C4×D356C211yesmaximal, characteristic, complemented
3#19151708C218yesmaximal, direct product factor
4C2×#15667943C211yesmaximal, characteristic, complemented
5C2×#15667933C211yesmaximal, characteristic, complemented
6C2×#15667932C211yesmaximal, characteristic, complemented
7C2×#15667923C211yesmaximal, characteristic, complemented
8C2×C4×D4×C89C211yesmaximal, characteristic, complemented
9C22×D356C2211yescharacteristic
10C22×C4×D89—21no—
11C2×#13083559C418yescomplemented
12C2×#13083559C2214yes—
13C22×#10623494C2211yescharacteristic
14C22×#10623494C2211yescharacteristic
15C4×D356—22no—
16C4×D356C2214yescomplemented
17C2×C4⋊Dic89C2211yescharacteristic
18C2×#13083551—21no—
19#15667943C2214yescomplemented
20#15667933C2214yescomplemented
21#15667932C2214yescomplemented
22#15667923C2214yescomplemented
23C22×D4×C89C2211yescharacteristic
24C23×C4×C89—21no—
25C4×D4×C89—22no—
26C4×D4×C89C2214yescomplemented
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C22⋊C4×C89—21no—
29C2×C42×C89C2211yescharacteristic
30C23×D89—21no—
31C2×D356—21no—
32C2×D356—22no—
33C2×D356C2×C414yescomplemented
34C2×D356C2312yes—
35C22×Dic89—21no—
36C2×C4×D89—24no—
37C2×C4×D89—44no—
38#13083559C2×C4116yescomplemented
39C2×#10623494—22no—
40C2×#10623494C2×C414yescomplemented
41C2×#10623494C2312yes—
42C2×#10623494C2312yes—
43C4⋊Dic89—21no—
44C4⋊Dic89C2312yes—
45#13083551—24no—
46C24×C89—21no—
47C2×D4×C89—21no—
48C2×D4×C89—22no—
49C2×D4×C89C2×C414yescomplemented
50C2×D4×C89C2312yes—
51C22×C4×C89—21no—
52C22×C4×C89—24no—
53C22×C4×C89—44no—
54C22×C4×C89D411yescharacteristic
55C22×C4×C89D411yescharacteristic
56C22×C4×C89C2311yescharacteristic
57C4⋊C4×C89—21no—
58C4⋊C4×C89C2312yes—
59C22⋊C4×C89—24no—
60C42×C89D412yes—
61C42×C89C2312yes—
62C23×C89—24no—
63C23×C89—22no—
64C23×C89—42no—
65C23×C89—42no—
66C23×C89C2×D411yescharacteristic
67C22×D89—24no—
68C22×D89—22no—
69C22×D89—42no—
70C22×D89—42no—
71D4×C89—24no—
72D4×C89—22no—
73D4×C89C22×C414yescomplemented
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—48no—
78C2×C4×C89—42no—
79C2×C4×C89C22×C412yes—
80C2×C4×C89C2×D412yes—
81C2×C4×C89C2×D412yes—
82C2×C4×C89C2×D411yescharacteristic
83C2×C4×C89#4112yes—
84C2×C4×C89C2411yescharacteristic
85C2×Dic89—22no—
86C2×Dic89—42no—
87D356—24no—
88D356—22no—
89D356C22×C414yescomplemented
90C4×D89—48no—
91#10623494—22no—
92#10623494C22×C414yescomplemented
93C22×C89—24no—
94C22×C89—42no—
95C22×C89—42no—
96C22×C89—48no—
97C22×C89C4×D412yes—
98C22×C89AGL(1,ℤ/8)12yes—
99C22×C89AGL(1,ℤ/8)12yes—
100C22×C89C22×D411yescharacteristic
101C2×D89—24no—
102C2×D89—42no—
103C2×D89—42no—
104C2×D89—48no—
105C4×C89—22no—
106C4×C89—22no—
107C4×C89—42no—
108C4×C89C4×D412yes—
109C4×C89C23×C411yescharacteristic
110C4×C89C2×#4111yescharacteristic
111Dic89—42no—
112C2×C89—44no—
113C2×C89#44214yescomplemented
114C2×C89C2×C4×D411yescharacteristic
115C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
116C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
117D89—44no—
118C2×#442—891nomaximal, Sylow
119C89C2×#44211yescharacteristic, complemented, Sylow
120C22×D8—891no—
121C2×C4×D4—891no—
122C2×C4×D4D8911yescharacteristic, complemented
123#442—898no—
124C2×#106—891no—
125C2×#102—891no—
126C2×#102—891no—
127C2×#97—891no—
128C22×D4—891no—
129C22×D4C2×D8911yescharacteristic
130C23×C4—21no—
131C23×C4—1781no—
132C2×D8—898no—
133C2×D8—894no—
134C22×C8—891no—
135C22×C8—891no—
136C4×D4—22no—
137C4×D4—894no—
138C4×D4—1782no—
139C4×D4C2×D8914yescomplemented
140C2×C4⋊C4—891no—
141C2×C4⋊C4C2×D8911yescharacteristic
142C2×C22⋊C4—21no—
143C2×C22⋊C4—1781no—
144C2×C42C2×D8911yescharacteristic
145#106—894no—
146#102—894no—
147#102—894no—
148#97—894no—
149C24—21no—
150C24—1781no—
151C2×D4—21no—
152C2×D4—22no—
153C2×D4—894no—
154C2×D4—892no—
155C2×D4—1781no—
156C2×D4—1782no—
157C2×D4C4×D8914yescomplemented
158C2×D4C22×D8912yes—
159C22×C4—21no—
160C22×C4—24no—
161C22×C4—44no—
162C22×C4—3564no—
163C22×C4—1781no—
164C22×C4—1784no—
165C22×C4C22⋊D8911yescharacteristic
166C22×C4C22⋊D8911yescharacteristic
167C22×C4C22×D8911yescharacteristic
168D8—8916no—
169C2×C8—894no—
170C2×C8—892no—
171C2×C8—892no—
172C2×C8—1782no—
173C4⋊C4—21no—
174C4⋊C4—892no—
175C4⋊C4—1781no—
176C4⋊C4C22×D8912yes—
177C22⋊C4—24no—
178C22⋊C4—1784no—
179C42C22⋊D8912yes—
180C42C22×D8912yes—
181C23—24no—
182C23—22no—
183C23—42no—
184C23—42no—
185C23—3562no—
186C23—3562no—
187C23—1784no—
188C23—1782no—
189C23C2×C22⋊D8911yescharacteristic
190D4—24no—
191D4—22no—
192D4—894no—
193D4—1784no—
194D4—1782no—
195D4C2×C4×D8914yescomplemented
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—48no—
200C2×C4—42no—
201C2×C4—3568no—
202C2×C4—3562no—
203C2×C4—1782no—
204C2×C4C2×C4×D8912yes—
205C2×C4C2×C22⋊D8912yes—
206C2×C4C2×C22⋊D8912yes—
207C2×C4C2×C22⋊D8911yescharacteristic
208C2×C4#1308357412yes—
209C2×C4C23×D8911yescharacteristic
210C8—894no—
211C8—1782no—
212C22—24no—
213C22—42no—
214C22—42no—
215C22—48no—
216C22—3562no—
217C22—3562no—
218C22—3568no—
219C22—1784no—
220C22C4×C22⋊D8912yes—
221C22#1566803712yes—
222C22#1566803812yes—
223C22C22×C22⋊D8911yescharacteristic
224C4—22no—
225C4—22no—
226C4—42no—
227C4—3562no—
228C4C4×C22⋊D8912yes—
229C4C22×C4×D8911yescharacteristic
230C4C2×#1308357411yescharacteristic
231C2—44no—
232C2—3564no—
233C2#1915170814yesdirect product factor
234C2C2×C4×C22⋊D8911yescharacteristic
235C2C2×#1566803711yescharacteristic
236C2C2×#1566803811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D89
commutatorC4×C89C23×C4
FrattiniC2×C4C23×D89
FittingC2×C4×D4×C89C2
socleC23×C89C2×D4
prime radicalC22×#13083559C2
cosocleC2×C4×C89C24
hypercenterC2×C4×D4D89
hypocenterC89C2×#442
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×D356C2semidirect
3. #19151708C2direct (N × H)
4. C2×#15667943C2semidirect
5. C2×#15667933C2semidirect
6. C2×#15667932C2semidirect
7. C2×#15667923C2semidirect
8. C2×C4×D4×C89C2semidirect
11. C2×#13083559C4semidirect
16. C4×D356C22semidirect
19. #15667943C22semidirect
20. #15667933C22semidirect
21. #15667932C22semidirect
22. #15667923C22semidirect
26. C4×D4×C89C22semidirect
33. C2×D356C2×C4semidirect
38. #13083559C2×C4semidirect
40. C2×#10623494C2×C4semidirect
49. C2×D4×C89C2×C4semidirect
73. D4×C89C22×C4semidirect
89. D356C22×C4semidirect
92. #10623494C22×C4semidirect
113. C2×C89#442semidirect
119. C89C2×#442semidirect
122. C2×C4×D4D89semidirect
139. C4×D4C2×D89semidirect
157. C2×D4C4×D89semidirect
195. D4C2×C4×D89semidirect
233. C2#19151708direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130835592
C2×C4×D3562
#191517082
C2×#156679432
C2×#156679332
C2×#156679322
C2×#156679232
C2×C4×D4×C892
C2×#44289