Finite Group Databasebeta

← C2×#19151845 #26029841

Subgroups — C2×#19151845 #26029841

Order 11392.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13083563C211yesmaximal, characteristic, complemented
2C22×#13083557C211yesmaximal, characteristic, complemented
3C2×#15667992C211yesmaximal, characteristic, complemented
4C2×#15667987C211yesmaximal, characteristic
5#19151845C218yesmaximal, direct product factor
6C2×#15667935C211yesmaximal, characteristic, complemented
7C2×#15667932C211yesmaximal, characteristic, complemented
8C2×#107×C89C211yesmaximal, characteristic, complemented
9C22×Dic178C2211yescharacteristic
10C22×D356—21no—
11C22×D356C2211yescharacteristic
12C22×C4×D89C2211yescharacteristic
13C2×#13083563—24no—
14C2×#13083563C2214yescomplemented
15C2×#13083557—24no—
16C2×#13083557C2214yescomplemented
17C22×#10623494C2211yescharacteristic
18#15667992—22no—
19#15667992C2214yescomplemented
20#15667987—22no—
21#15667987C2214yes—
22C2×C4⋊Dic89—21no—
23C2×#13083551—21no—
24C2×#13083551—21no—
25#15667935C2214yescomplemented
26#15667932C2214yescomplemented
27C22×C8×C89C2211yescharacteristic
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2211yescharacteristic
30#107×C89C2214yescomplemented
31C23×D89—21no—
32C23×D89D411yescharacteristic
33C2×Dic178—22no—
34C2×Dic178—22no—
35C2×Dic178—21no—
36C2×Dic178C2312yes—
37C2×D356—22no—
38C2×D356—22no—
39C2×D356—24no—
40C2×D356—21no—
41C2×D356—44no—
42C2×D356C2312yes—
43C22×Dic89—21no—
44C22×Dic89D411yescharacteristic
45C2×C4×D89—22no—
46C2×C4×D89—22no—
47C2×C4×D89D412yes—
48C2×C4×D89C2312yes—
49#13083563—28no—
50#13083557—28no—
51C2×#10623494—22no—
52C2×#10623494C2312yes—
53C4⋊Dic89—24no—
54#13083551—24no—
55#13083551—24no—
56C22×C4×C89—21no—
57C22×C4×C89—21no—
58C22×C4×C89C2311yescharacteristic
59C2×C8×C89D414yescomplemented
60C2×C8×C89C2312yes—
61C4⋊C4×C89—21no—
62C4⋊C4×C89—21no—
63C4⋊C4×C89C2312yes—
64C4⋊C4×C89C2312yes—
65C23×C89C2×D411yescharacteristic
66C22×D89—22no—
67C22×D89—22no—
68C22×D89—22no—
69C22×D89—22no—
70C22×D89—42no—
71C22×D89—42no—
72C22×D89—42no—
73C22×D89C2×D412yes—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—42no—
77C2×C4×C89—42no—
78C2×C4×C89C2×D411yescharacteristic
79C2×C4×C89C2×D412yes—
80C2×C4×C89#4112yes—
81C2×C4×C89C2411yescharacteristic
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—42no—
85C2×Dic89C2×D412yes—
86D356—22no—
87D356—22no—
88D356—48no—
89D356—42no—
90C4×D89—24no—
91C4×D89—22no—
92C4×D89—22no—
93Dic178—22no—
94Dic178—22no—
95Dic178—42no—
96C8×C89C2×D414yescomplemented
97#10623494—22no—
98C22×C89#12112yes—
99C22×C89AGL(1,ℤ/8)12yes—
100C22×C89#13712yes—
101C22×C89C22×D411yescharacteristic
102C2×D89—22no—
103C2×D89—22no—
104C2×D89—22no—
105C2×D89—44no—
106C2×D89—42no—
107C2×D89—42no—
108C2×D89—42no—
109C2×D89—84no—
110C4×C89—42no—
111C4×C89—42no—
112C4×C89#12112yes—
113C4×C89C22×D411yescharacteristic
114C4×C89C2×#4111yescharacteristic
115Dic89—22no—
116Dic89—42no—
117C2×C89#46814yescomplemented
118C2×C89C2×#12111yescharacteristic
119C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C89C2×#13711yescharacteristic
121D89—42no—
122D89—82no—
123C2×#468—891nomaximal, Sylow
124C89C2×#46811yescharacteristic, complemented, Sylow
125C22×SD16—891no—
126C22×M16—891no—
127C2×C22⋊Q8—891no—
128C2×#121—891no—
129#468—898no—
130C2×#107D8911yescharacteristic, complemented
131C2×#103—891no—
132C2×#102—891no—
133C22×Q8—891no—
134C22×D4—891no—
135C22×D4—1781no—
136C23×C4—891no—
137C2×SD16—894no—
138C2×SD16—1784no—
139C2×M16—894no—
140C2×M16—1784no—
141C22×C8—891no—
142C22×C8C2×D8911yescharacteristic
143C22⋊Q8—894no—
144C22⋊Q8—1782no—
145#121—894no—
146#121—1782no—
147C2×C4⋊C4—1781no—
148C2×C4⋊C4C2×D8911yescharacteristic
149C2×C4⋊C4C2×D8911yescharacteristic
150C2×C22⋊C4—1781no—
151C2×C22⋊C4—1781no—
152#107C2×D8914yescomplemented
153#103—894no—
154#102—894no—
155C24—891no—
156C24—1781no—
157C2×Q8—892no—
158C2×Q8—1782no—
159C2×Q8—1782no—
160C2×Q8—1781no—
161C2×D4—892no—
162C2×D4—3564no—
163C2×D4—1784no—
164C2×D4—1781no—
165C2×D4—1782no—
166C2×D4—1782no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—891no—
170C22×C4—892no—
171C22×C4—892no—
172C22×C4—1781no—
173C22×C4—1782no—
174C22×C4—1782no—
175C22×C4C22×D8911yescharacteristic
176SD16—1788no—
177M16—1788no—
178C2×C8—892no—
179C2×C8—1782no—
180C2×C8D35614yescomplemented
181C2×C8C22×D8912yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—1784no—
185C4⋊C4C22×D8912yes—
186C4⋊C4C22×D8912yes—
187C22⋊C4—1784no—
188C22⋊C4—1784no—
189C23—892no—
190C23—3562no—
191C23—3562no—
192C23—3562no—
193C23—1782no—
194C23—1782no—
195C23—1782no—
196C23—1782no—
197C23D4×D8911yescharacteristic
198Q8—3562no—
199Q8—1782no—
200Q8—1782no—
201D4—3568no—
202D4—3562no—
203D4—1782no—
204D4—1782no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—892no—
210C2×C4—3562no—
211C2×C4—1782no—
212C2×C4—1782no—
213C2×C4—1784no—
214C2×C4—1782no—
215C2×C4—1782no—
216C2×C4D4×D8911yescharacteristic
217C2×C4C2×D35612yes—
218C2×C4#1308357512yes—
219C2×C4C23×D8911yescharacteristic
220C8—1782no—
221C8C2×D35614yescomplemented
222C22—3564no—
223C22—3562no—
224C22—3562no—
225C22—3562no—
226C22—1782no—
227C22—1782no—
228C22—1782no—
229C22—7124no—
230C22#1566798712yes—
231C22#1566803612yes—
232C22#1566804412yes—
233C22C2×D4×D8911yescharacteristic
234C4—42no—
235C4—42no—
236C4—3562no—
237C4—1782no—
238C4#1566798712yes—
239C4C22×D35611yescharacteristic
240C4C2×#1308357511yescharacteristic
241C2—3562no—
242C2—7122no—
243C2#1915184514yesdirect product factor
244C2C2×#1566798711yescharacteristic
245C2C2×#1566803611yescharacteristic
246C2C2×#1566804411yescharacteristic
subgroupG/H
centerC23D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC2×#107×C89C2
socleC23×C89C2×D4
prime radicalC2×#15667987C2
hypercenterC2×#107D89
hypocenterC89C2×#468
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#13083563C2semidirect
2. C22×#13083557C2semidirect
3. C2×#15667992C2semidirect
5. #19151845C2direct (N × H)
6. C2×#15667935C2semidirect
7. C2×#15667932C2semidirect
8. C2×#107×C89C2semidirect
14. C2×#13083563C22semidirect
16. C2×#13083557C22semidirect
19. #15667992C22semidirect
25. #15667935C22semidirect
26. #15667932C22semidirect
30. #107×C89C22semidirect
59. C2×C8×C89D4semidirect
96. C8×C89C2×D4semidirect
117. C2×C89#468semidirect
124. C89C2×#468semidirect
130. C2×#107D89semidirect
152. #107C2×D89semidirect
180. C2×C8D356semidirect
221. C8C2×D356semidirect
243. C2#19151845direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130835632
C22×#130835572
C2×#156679922
C2×#156679872
#191518452
C2×#156679352
C2×#156679322
C2×#107×C892
C2×#46889