Finite Group Databasebeta

← C2×#19151829 #26029814

Subgroups — C2×#19151829 #26029814

Order 11392.

564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13083561C211yesmaximal, characteristic, complemented
2C23×#10623494C211yesmaximal, characteristic, complemented
3C2×#15667986C211yesmaximal, characteristic
4#19151829C218yesmaximal, direct product factor
5C2×#15667943C211yesmaximal, characteristic, complemented
6C2×#15667936C211yesmaximal, characteristic, complemented
7C2×#15667932C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C89C211yesmaximal, characteristic, complemented
9C22×D356C2211yescharacteristic
10C22×C22⋊D89—21no—
11C2×#13083561—24no—
12C2×#13083561C2214yescomplemented
13C22×#10623494—24no—
14C22×#10623494C2211yescharacteristic
15C22×#10623494C2211yescharacteristic
16C22×#10623494C2214yescomplemented
17#15667986—22no—
18#15667986C2214yes—
19C2×C4⋊Dic89C2211yescharacteristic
20C2×#13083551—21no—
21#15667943C2214yescomplemented
22#15667936C2214yescomplemented
23#15667932C2214yescomplemented
24C22×Q8×C89C2211yescharacteristic
25C23×C4×C89C2211yescharacteristic
26C22⋊Q8×C89—22no—
27C22⋊Q8×C89C2214yescomplemented
28C2×C4⋊C4×C89—21no—
29C2×C4⋊C4×C89C2211yescharacteristic
30C2×C22⋊C4×C89—21no—
31C23×D89—21no—
32C2×D356—22no—
33C2×D356—22no—
34C2×D356—21no—
35C2×D356C2312yes—
36C2×C22⋊D89—24no—
37C2×C22⋊D89—44no—
38C22×Dic89—21no—
39#13083561—28no—
40C2×#10623494—22no—
41C2×#10623494—28no—
42C2×#10623494D414yescomplemented
43C2×#10623494C2312yes—
44C2×#10623494C2312yes—
45C4⋊Dic89—21no—
46C4⋊Dic89C2312yes—
47#13083551—24no—
48C24×C89D411yescharacteristic
49C2×Q8×C89—21no—
50C2×Q8×C89—22no—
51C2×Q8×C89—22no—
52C2×Q8×C89C2312yes—
53C22×C4×C89—22no—
54C22×C4×C89—22no—
55C22×C4×C89—21no—
56C22×C4×C89—21no—
57C22×C4×C89D412yes—
58C22×C4×C89D411yescharacteristic
59C22×C4×C89C2312yes—
60C22×C4×C89C2311yescharacteristic
61C4⋊C4×C89—24no—
62C4⋊C4×C89—21no—
63C4⋊C4×C89C2312yes—
64C22⋊C4×C89—24no—
65C23×C89—22no—
66C23×C89—22no—
67C23×C89SD1614yescomplemented
68C23×C89C2×D412yes—
69C23×C89C2×D411yescharacteristic
70C22×D89—22no—
71C22×D89—42no—
72C22×D89—42no—
73C22×D89—42no—
74Q8×C89—22no—
75Q8×C89—22no—
76Q8×C89—42no—
77C2×C4×C89—22no—
78C2×C4×C89—24no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—22no—
83C2×C4×C89—42no—
84C2×C4×C89—42no—
85C2×C4×C89C2×D412yes—
86C2×C4×C89C2×D412yes—
87C2×C4×C89C2×D411yescharacteristic
88C2×C4×C89#4112yes—
89C2×C4×C89C2411yescharacteristic
90C22⋊D89—48no—
91C2×Dic89—22no—
92C2×Dic89—42no—
93D356—22no—
94D356—22no—
95D356—42no—
96#10623494—22no—
97#10623494C2×D414yescomplemented
98C22×C89—22no—
99C22×C89—22no—
100C22×C89—28no—
101C22×C89#12112yes—
102C22×C89C2×SD1612yes—
103C22×C89C2×SD1614yescomplemented
104C22×C89#13512yes—
105C22×C89C22×D411yescharacteristic
106C2×D89—42no—
107C2×D89—42no—
108C2×D89—42no—
109C2×D89—84no—
110C4×C89—22no—
111C4×C89—42no—
112C4×C89—42no—
113C4×C89#12112yes—
114C4×C89C22×D411yescharacteristic
115C4×C89C2×#4111yescharacteristic
116Dic89—42no—
117C2×C89—24no—
118C2×C89#46514yescomplemented
119C2×C89C2×#12111yescharacteristic
120C2×C89C22×SD1611yescharacteristic
121C2×C89C2×#13511yescharacteristic
122D89—82no—
123C2×#465—891nomaximal, Sylow
124C89C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—891no—
126C23×C8—891no—
127C2×C22⋊Q8D8911yescharacteristic, complemented
128C2×#121—891no—
129#465—898no—
130C2×#106—891no—
131C2×#103—891no—
132C2×#102—891no—
133C22×Q8C2×D8911yescharacteristic
134C22×D4—891no—
135C22×D4—1781no—
136C23×C4C2×D8911yescharacteristic
137C2×SD16—894no—
138C2×SD16—1784no—
139C22×C8—891no—
140C22×C8—891no—
141C22×C8—894no—
142C22×C8—1784no—
143C22⋊Q8—22no—
144C22⋊Q8C2×D8914yescomplemented
145#121—894no—
146#121—1782no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—891no—
149C2×C4⋊C4C2×D8911yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—1781no—
152#106—894no—
153#103—894no—
154#102—894no—
155C24—1781no—
156C24C22⋊D8911yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D8912yes—
161C2×D4—892no—
162C2×D4—3564no—
163C2×D4—1784no—
164C2×D4—1782no—
165C2×D4—1781no—
166C2×D4—1782no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—1781no—
172C22×C4C22⋊D8912yes—
173C22×C4C22⋊D8911yescharacteristic
174C22×C4C22×D8912yes—
175C22×C4C22×D8911yescharacteristic
176SD16—1788no—
177C2×C8—894no—
178C2×C8—892no—
179C2×C8—892no—
180C2×C8—1788no—
181C2×C8—1782no—
182C4⋊C4—24no—
183C4⋊C4—21no—
184C4⋊C4—892no—
185C4⋊C4—1781no—
186C4⋊C4C22×D8912yes—
187C22⋊C4—24no—
188C22⋊C4—1784no—
189C23—22no—
190C23—22no—
191C23—3562no—
192C23—3562no—
193C23—3562no—
194C23—1782no—
195C23#1308356114yescomplemented
196C23C2×C22⋊D8912yes—
197C23C2×C22⋊D8911yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—3568no—
202D4—3562no—
203D4—1782no—
204D4—1782no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—3562no—
214C2×C4—1782no—
215C2×C4D4×D8912yes—
216C2×C4C2×C22⋊D8912yes—
217C2×C4C2×C22⋊D8911yescharacteristic
218C2×C4#1308357312yes—
219C2×C4C23×D8911yescharacteristic
220C8—894no—
221C8—1782no—
222C22—28no—
223C22—22no—
224C22—22no—
225C22—3562no—
226C22—3562no—
227C22—3562no—
228C22—7124no—
229C22#1566798412yes—
230C22C2×#1308356112yes—
231C22C2×#1308356114yescomplemented
232C22#1566803212yes—
233C22C22×C22⋊D8911yescharacteristic
234C4—22no—
235C4—42no—
236C4—42no—
237C4—3562no—
238C4#1566798412yes—
239C4C2×D4×D8911yescharacteristic
240C4C2×#1308357311yescharacteristic
241C2—24no—
242C2—7122no—
243C2#1915182914yesdirect product factor
244C2C2×#1566798411yescharacteristic
245C2C22×#1308356111yescharacteristic
246C2C2×#1566803211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC2×C22⋊Q8×C89C2
socleC23×C89C2×D4
prime radicalC2×#15667986C2
hypercenterC2×C22⋊Q8D89
hypocenterC89C2×#465
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13083561C2semidirect
2. C23×#10623494C2semidirect
4. #19151829C2direct (N × H)
5. C2×#15667943C2semidirect
6. C2×#15667936C2semidirect
7. C2×#15667932C2semidirect
8. C2×C22⋊Q8×C89C2semidirect
12. C2×#13083561C22semidirect
16. C22×#10623494C22semidirect
21. #15667943C22semidirect
22. #15667936C22semidirect
23. #15667932C22semidirect
27. C22⋊Q8×C89C22semidirect
42. C2×#10623494D4semidirect
67. C23×C89SD16semidirect
97. #10623494C2×D4semidirect
103. C22×C89C2×SD16semidirect
118. C2×C89#465semidirect
124. C89C2×#465semidirect
127. C2×C22⋊Q8D89semidirect
144. C22⋊Q8C2×D89semidirect
195. C23#13083561semidirect
231. C22C2×#13083561semidirect
243. C2#19151829direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130835612
C23×#106234942
C2×#156679862
#191518292
C2×#156679432
C2×#156679362
C2×#156679322
C2×C22⋊Q8×C892
C2×#46589