Finite Group Databasebeta

← C2×#11746822 #14478208

Subgroups — C2×#11746822 #14478208

Order 1920.

880 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C2×#91256C212yesmaximal, complemented
2C2×C16×D15C211yesmaximal, characteristic, complemented
3C2×C5×D48C211yesmaximal, characteristic, complemented
4C2×C3×D80C211yesmaximal, characteristic, complemented
5C2×#90937C212yesmaximal, complemented
6#11746822C218yesmaximal, direct product factor
7C2×D5×D16—31nomaximal, Hall
8C2×#6777—22no—
9C2×C8×D15C2211yescharacteristic
10C2×C5×D24C2212yescomplemented
11C2×C3×D40C2212yescomplemented
12C2×#6652—22no—
13#91256—24no—
14#91256C2218yescomplemented
15C2×C3×C5×C16C2211yescharacteristic, complemented
16C2×C3⋊#672C2211yescharacteristic, complemented
17C16×D15C2214yescomplemented
18C5×D48C2214yescomplemented
19C3×D80C2214yescomplemented
20#90937C2218yescomplemented
21C2×D3×D16—51nomaximal, Hall
22C2×D5×D8—32no—
23C2×C5×D16—31no—
24C2×#3958—32no—
25D5×D16—38no—
26C2×D80D311yescharacteristic, complemented
27C2×D5×C16—31no—
28C22×D3×D5—42no—
29C2×C4×D15D411yescharacteristic
30C2×C5×D12—22no—
31C2×C3×D20—22no—
32C2×#1201—42no—
33#6777—28no—
34#6777—44no—
35C2×C3×C5×C8C2311yescharacteristic
36C2×C3⋊#168D411yescharacteristic
37C8×D15D412yes—
38C8×D15C2312yes—
39C5×D24—22no—
40C5×D24C2314yescomplemented
41C3×D40—22no—
42C3×D40C2314yescomplemented
43#6652—28no—
44C3×C5×C16C2312yescomplemented
45C3⋊#672C2312yescomplemented
46C2×D3×D8—52no—
47C2×C3×D16—51no—
48C2×#826—52no—
49D3×D16—58no—
50C2×D48D511yescharacteristic, complemented
51C2×D3×C16—51no—
52C2×D4×D5—62no—
53C2×C5×D8—32no—
54C2×#686—62no—
55D5×D8—38no—
56D5×D8—64no—
57C2×D40C2×D312yescomplemented
58C2×C8×D5—31no—
59C5×D16—34no—
60C2×C5×C16C2×D311yescharacteristic, complemented
61#3958—38no—
62C2×#672—31no—
63D80C2×D314yescomplemented
64D5×C16—34no—
65C22×D16—151noSylow
66C22×D15D811yescharacteristic
67C22×C5×D3—42no—
68C22×C3×D5—42no—
69C2×D3×D5—48no—
70C2×D3×D5—88no—
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×Dic15D811yescharacteristic
73C4×D15D812yes—
74C4×D15C2×D412yes—
75C5×D12—24no—
76C5×D12—42no—
77C3×D20—24no—
78C3×D20—42no—
79#1201—48no—
80C3×C5×C8C2×D411yescharacteristic
81C3×C5×C8C2411yescharacteristic
82C3⋊#168C2×D412yes—
83C2×D3×D4—102no—
84C2×C3×D8—52no—
85C2×#213—102no—
86D3×D8—58no—
87D3×D8—104no—
88C2×D24C2×D512yescomplemented
89C2×D3×C8—51no—
90C3×D16—54no—
91C2×C3×C16C2×D511yescharacteristic, complemented
92#826—58no—
93C2×C3⋊C16—51no—
94D48C2×D514yescomplemented
95D3×C16—54no—
96C23×D5—122no—
97C2×C5×D4—62no—
98C2×C22⋊D5—122no—
99D4×D5—68no—
100D4×D5—124no—
101C2×D20—22no—
102C2×C4×D5—31no—
103C5×D8—34no—
104C5×D8—62no—
105C2×C5×C8C22×D311yescharacteristic
106#686—68no—
107C2×#168—31no—
108D40—22no—
109D40C22×D314yescomplemented
110C8×D5—32no—
111C8×D5—32no—
112C5×C16C22×D312yescomplemented
113#672—32no—
114C22×D8—152no—
115C2×D16—31no—
116C2×D16—51no—
117C2×D16—158no—
118C2×D16—152no—
119C22×C16—151no—
120C22×C3×C5C2×D811yescharacteristic
121C2×D15D1614yescomplemented
122C2×D15C2×D812yes—
123C2×C5×D3—44no—
124C2×C5×D3—84no—
125C2×C3×D5—44no—
126C2×C3×D5—84no—
127D3×D5—816no—
128C3×C4×C5C2×D811yescharacteristic
129C3×C4×C5C22×D411yescharacteristic
130Dic15C2×D812yes—
131C23×D3—202no—
132C2×C3×D4—102no—
133C2×#67—202no—
134D3×D4—108no—
135D3×D4—204no—
136C2×D12—22no—
137C2×C4×D3—51no—
138C3×D8—54no—
139C3×D8—102no—
140C2×C3×C8C22×D511yescharacteristic
141#213—108no—
142C2×C3⋊C8—51no—
143D24—22no—
144D24C22×D514yescomplemented
145D3×C8—52no—
146D3×C8—52no—
147C3×C16C22×D512yescomplemented
148C3⋊C16—52no—
149C23×C5—122no—
150C22×D5—31no—
151C22×D5—42no—
152C22×D5—128no—
153C22×D5—248no—
154C5×D4—64no—
155C5×D4—122no—
156C2×C4×C5D3×D411yescharacteristic
157C22⋊D5—128no—
158C2×Dic5—31no—
159D20—24no—
160D20—42no—
161C4×D5—32no—
162C4×D5—32no—
163C5×C8D3×D411yescharacteristic
164C5×C8C23×D311yescharacteristic
165#168—32no—
166C22×D4—302no—
167C2×D8—32no—
168C2×D8—52no—
169C2×D8—158no—
170C2×D8—304no—
171C2×D8—302no—
172C22×C8—151no—
173D16—34no—
174D16—54no—
175D16—158no—
176C2×C16—151no—
177C2×C16—154no—
178C2×C16D3×D511yescharacteristic, complemented
179C2×C3×C5C2×D1612yescomplemented
180C2×C3×C5C22×D811yescharacteristic
181D15C2×D1614yescomplemented
182C3×D5—84no—
183C5×D3—84no—
184C23×C3—202no—
185C22×D3—42no—
186C22×D3—51no—
187C22×D3—208no—
188C22×D3—408no—
189C3×D4—104no—
190C3×D4—202no—
191C2×C3×C4D4×D511yescharacteristic
192#67—208no—
193C2×Dic3—51no—
194D12—24no—
195D12—42no—
196C4×D3—52no—
197C4×D3—52no—
198C3×C8D4×D511yescharacteristic
199C3×C8C23×D511yescharacteristic
200C3⋊C8—52no—
201C22×C5—124no—
202C22×C5—244no—
203C22×C5D3×D811yescharacteristic
204C2×D5—34no—
205C2×D5—32no—
206C2×D5—44no—
207C2×D5—84no—
208C2×D5—2416no—
209C4×C5D3×D811yescharacteristic
210C4×C5C2×D3×D411yescharacteristic
211Dic5—32no—
212C24—602no—
213C2×D4—62no—
214C2×D4—102no—
215C2×D4—308no—
216C2×D4—604no—
217C2×D4—602no—
218C22×C4—151no—
219D8—34no—
220D8—54no—
221D8—62no—
222D8—102no—
223D8—308no—
224C2×C8—151no—
225C2×C8—152no—
226C2×C8—152no—
227C2×C8C2×D3×D511yescharacteristic
228C16—152no—
229C16C2×D3×D512yescomplemented
230C3×C5C22×D1611yescharacteristic, complemented, Hall
231C22×C3—204no—
232C22×C3—404no—
233C22×C3D5×D811yescharacteristic
234C2×D3—44no—
235C2×D3—52no—
236C2×D3—54no—
237C2×D3—84no—
238C2×D3—4016no—
239C3×C4D5×D811yescharacteristic
240C3×C4C2×D4×D511yescharacteristic
241Dic3—52no—
242C2×C5—244no—
243C2×C5D3×D1612yescomplemented
244C2×C5C2×D3×D811yescharacteristic
245D5—34no—
246D5—84no—
247C23—122no—
248C23—151no—
249C23—202no—
250C23—608no—
251C23—1208no—
252D4—64no—
253D4—104no—
254D4—122no—
255D4—202no—
256D4—608no—
257C2×C4—151no—
258C2×C4—152no—
259C2×C4—152no—
260C2×C4#677711yescharacteristic
261C8—152no—
262C8#677711yescharacteristic
263C8C22×D3×D511yescharacteristic
264C2×C3—404no—
265C2×C3D5×D1612yescomplemented
266C2×C3C2×D5×D811yescharacteristic
267D3—54no—
268D3—84no—
269C5C2×D3×D1611yescharacteristic, complemented, Sylow
270C22—124no—
271C22—154no—
272C22—152no—
273C22—204no—
274C22—244no—
275C22—404no—
276C22—12016no—
277C22#9125611yescharacteristic
278C4—152no—
279C4#9125611yescharacteristic
280C4C2×#677711yescharacteristic
281C3C2×D5×D1611yescharacteristic, complemented, Sylow
282C2—154no—
283C2—244no—
284C2—404no—
285C2#1174682212yesdirect product factor
286C2C2×#9125611yescharacteristic
subgroupG/H
centerC22#91256
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
hypercenterC2×C16D3×D5
hypocenterC3×C5C22×D16
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×#91256C2semidirect
2. C2×C16×D15C2semidirect
3. C2×C5×D48C2semidirect
4. C2×C3×D80C2semidirect
5. C2×#90937C2semidirect
6. #11746822C2direct (N × H)
10. C2×C5×D24C22semidirect
11. C2×C3×D40C22semidirect
14. #91256C22semidirect
15. C2×C3×C5×C16C22semidirect
16. C2×C3⋊#672C22semidirect
17. C16×D15C22semidirect
18. C5×D48C22semidirect
19. C3×D80C22semidirect
20. #90937C22semidirect
26. C2×D80D3semidirect
40. C5×D24C23semidirect
42. C3×D40C23semidirect
44. C3×C5×C16C23semidirect
45. C3⋊#672C23semidirect
50. C2×D48D5semidirect
57. C2×D40C2×D3semidirect
60. C2×C5×C16C2×D3semidirect
63. D80C2×D3semidirect
88. C2×D24C2×D5semidirect
91. C2×C3×C16C2×D5semidirect
94. D48C2×D5semidirect
109. D40C22×D3semidirect
112. C5×C16C22×D3semidirect
121. C2×D15D16semidirect
144. D24C22×D5semidirect
147. C3×C16C22×D5semidirect
178. C2×C16D3×D5semidirect
179. C2×C3×C5C2×D16semidirect
181. D15C2×D16semidirect
229. C16C2×D3×D5semidirect
230. C3×C5C22×D16semidirect
243. C2×C5D3×D16semidirect
265. C2×C3D5×D16semidirect
269. C5C2×D3×D16semidirect
281. C3C2×D5×D16semidirect
285. C2#11746822direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#912562
C2×C16×D152
C2×C5×D482
C2×C3×D802
C2×#909372
#117468222
C2×D5×D163
C2×D3×D165