Finite Group Databasebeta

← C2×#11762954 #14537985

Subgroups — C2×#11762954 #14537985

Order 2176.

812 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 181 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×#63230C211yesmaximal, characteristic, complemented
2C22×#63228C211yesmaximal, characteristic, complemented
3C2×#10587616C211yesmaximal, characteristic, complemented
4#11762954C218yesmaximal, direct product factor
5C2×#10587506C211yesmaximal, characteristic, complemented
6C2×#10587503C211yesmaximal, characteristic, complemented
7C2×C22⋊#3622C211yesmaximal, characteristic, complemented
8C22×#41×C17C211yesmaximal, characteristic, complemented
9C2×#41×C17—24no—
10C2×#41×C17—24no—
11C2×#41×C17—22no—
12C2×#41×C17C2214yescomplemented
13C22×Q8×C17C2211yescharacteristic
14C22×D4×C17—21no—
15C22×D4×C17C2211yescharacteristic
16C23×C4×C17—21no—
17C23×C4×C17C2211yescharacteristic
18C22×C22⋊D17—21no—
19C22×D68C2211yescharacteristic
20C2×#63230—24no—
21C2×#63230C2214yescomplemented
22C2×#63228—24no—
23C2×#63228C2214yescomplemented
24#10587616—22no—
25#10587616C2214yescomplemented
26C2×#63227—21no—
27C2×C4⋊Dic17C2211yescharacteristic
28C22×#3622C2211yescharacteristic
29C22×#3622C2211yescharacteristic
30#10587506C2214yescomplemented
31#10587503C2214yescomplemented
32C22⋊#3622C2214yescomplemented
33C24×C17—21no—
34C24×C17D411yescharacteristic
35C23×D17—21no—
36#41×C17—216no—
37#41×C17—28no—
38#41×C17—28no—
39C2×Q8×C17—22no—
40C2×Q8×C17—21no—
41C2×Q8×C17D414yescomplemented
42C2×Q8×C17C2312yes—
43C2×D4×C17—28no—
44C2×D4×C17—24no—
45C2×D4×C17—21no—
46C2×D4×C17—22no—
47C2×D4×C17D414yescomplemented
48C2×D4×C17C2312yes—
49C22×C4×C17—28no—
50C22×C4×C17—21no—
51C22×C4×C17—24no—
52C22×C4×C17—22no—
53C22×C4×C17—22no—
54C22×C4×C17D411yescharacteristic
55C22×C4×C17D412yes—
56C22×C4×C17C2312yes—
57C22×C4×C17C2311yescharacteristic
58C2×C22⋊D17—24no—
59C2×C22⋊D17—44no—
60C22×Dic17—21no—
61C2×D68—22no—
62C2×D68—22no—
63C2×D68—21no—
64C2×D68C2312yes—
65#63230—28no—
66#63228—28no—
67#63227—24no—
68C4⋊Dic17—21no—
69C4⋊Dic17C2312yes—
70C2×#3622—22no—
71C2×#3622—22no—
72C2×#3622C2312yes—
73C2×#3622C2312yes—
74C23×C17—22no—
75C23×C17—24no—
76C23×C17—22no—
77C23×C17—22no—
78C23×C17—22no—
79C23×C17—42no—
80C23×C17—42no—
81C23×C17C2×D412yes—
82C23×C17C2×D411yescharacteristic
83C22×D17—22no—
84C22×D17—42no—
85C22×D17—42no—
86C22×D17—42no—
87Q8×C17—24no—
88Q8×C17—22no—
89Q8×C17C2×D414yescomplemented
90D4×C17—216no—
91D4×C17—24no—
92D4×C17—22no—
93D4×C17C2×D414yescomplemented
94C2×C4×C17—216no—
95C2×C4×C17—22no—
96C2×C4×C17—24no—
97C2×C4×C17—22no—
98C2×C4×C17—24no—
99C2×C4×C17—22no—
100C2×C4×C17—22no—
101C2×C4×C17C2×D412yes—
102C2×C4×C17C2×D411yescharacteristic
103C2×C4×C17C2×D412yes—
104C2×C4×C17C2×D412yes—
105C2×C4×C17C2411yescharacteristic
106C22⋊D17—48no—
107C2×Dic17—22no—
108C2×Dic17—42no—
109D68—22no—
110D68—22no—
111D68—42no—
112#3622—22no—
113#3622—22no—
114C2×#449—171nomaximal, Sylow
115C22×C17—22no—
116C22×C17—24no—
117C22×C17—22no—
118C22×C17—22no—
119C22×C17—42no—
120C22×C17—42no—
121C22×C17—44no—
122C22×C17—48no—
123C22×C17#12012yes—
124C22×C17#13512yes—
125C22×C17AGL(1,ℤ/8)12yes—
126C22×C17C22×D411yescharacteristic
127C2×D17—42no—
128C2×D17—42no—
129C2×D17—42no—
130C2×D17—84no—
131C4×C17—22no—
132C4×C17—24no—
133C4×C17#12012yes—
134C4×C17C22×D411yescharacteristic
135C4×C17C22×D411yescharacteristic
136Dic17—42no—
137C22×#41D1711yescharacteristic, complemented
138C22×SD16—171no—
139C22×D8—171no—
140C2×#121—171no—
141#449—178no—
142C2×#103—171no—
143C2×#102—171no—
144C2×C22⋊C8—171no—
145C2×C17—42no—
146C2×C17—44no—
147C2×C17#44914yescomplemented
148C2×C17C2×#12011yescharacteristic
149C2×C17C2×#13511yescharacteristic
150C2×C17C2×AGL(1,ℤ/8)11yescharacteristic
151D17—82no—
152C2×#41—24no—
153C2×#41—24no—
154C2×#41—22no—
155C2×#41C2×D1714yescomplemented
156C22×Q8C2×D1711yescharacteristic
157C22×D4—21no—
158C22×D4—171no—
159C22×D4—341no—
160C22×D4C2×D1711yescharacteristic
161C23×C4—21no—
162C23×C4C2×D1711yescharacteristic
163C2×SD16—174no—
164C2×SD16—344no—
165C2×D8—174no—
166C2×D8—344no—
167C22×C8—171no—
168C22×C8—171no—
169#121—174no—
170#121—342no—
171C2×C4⋊C4—171no—
172C2×C22⋊C4—341no—
173#103—174no—
174#102—174no—
175C22⋊C8—174no—
176C17C2×#44911yescharacteristic, complemented, Sylow
177C24—21no—
178C24—341no—
179C24C22⋊D1711yescharacteristic
180#41—216no—
181#41—28no—
182#41—28no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8C22⋊D1714yescomplemented
186C2×Q8C22×D1712yes—
187C2×D4—28no—
188C2×D4—24no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—172no—
192C2×D4—344no—
193C2×D4—342no—
194C2×D4—342no—
195C2×D4—341no—
196C2×D4—684no—
197C2×D4C22⋊D1714yescomplemented
198C2×D4C22×D1712yes—
199C22×C4—28no—
200C22×C4—21no—
201C22×C4—24no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—341no—
205C22×C4C22⋊D1712yes—
206C22×C4C22⋊D1711yescharacteristic
207C22×C4C22×D1712yes—
208C22×C4C22×D1711yescharacteristic
209SD16—348no—
210D8—348no—
211C2×C8—172no—
212C2×C8—172no—
213C2×C8—342no—
214C2×C8—342no—
215C4⋊C4—172no—
216C4⋊C4—341no—
217C22⋊C4—344no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—24no—
223C23—42no—
224C23—42no—
225C23—342no—
226C23—682no—
227C23—682no—
228C23—682no—
229C23C2×C22⋊D1712yes—
230C23C2×C22⋊D1711yescharacteristic
231Q8—22no—
232Q8—24no—
233Q8C2×C22⋊D1714yescomplemented
234D4—216no—
235D4—22no—
236D4—24no—
237D4—342no—
238D4—342no—
239D4—688no—
240D4—682no—
241D4C2×C22⋊D1714yescomplemented
242C2×C4—216no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—24no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—342no—
250C2×C4—682no—
251C2×C4C2×C22⋊D1712yes—
252C2×C4C2×C22⋊D1712yes—
253C2×C4C2×C22⋊D1712yes—
254C2×C4C2×C22⋊D1711yescharacteristic
255C2×C4C23×D1711yescharacteristic
256C8—342no—
257C8—342no—
258C22—22no—
259C22—24no—
260C22—22no—
261C22—22no—
262C22—44no—
263C22—48no—
264C22—42no—
265C22—42no—
266C22—682no—
267C22—682no—
268C22—682no—
269C22—1364no—
270C22#1058763512yes—
271C22#1058763612yes—
272C22#1058763912yes—
273C22C22×C22⋊D1711yescharacteristic
274C4—22no—
275C4—24no—
276C4—682no—
277C4#1058763912yes—
278C4C22×C22⋊D1711yescharacteristic
279C4C22×C22⋊D1711yescharacteristic
280C2—42no—
281C2—44no—
282C2—1362no—
283C2#1176295414yesdirect product factor
284C2C2×#1058763911yescharacteristic
285C2C2×#1058763611yescharacteristic
286C2C2×#1058763511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC22×#41×C17C2
socleC23×C17C2×D4
hypercenterC22×#41D17
hypocenterC17C2×#449
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#63230C2semidirect
2. C22×#63228C2semidirect
3. C2×#10587616C2semidirect
4. #11762954C2direct (N × H)
5. C2×#10587506C2semidirect
6. C2×#10587503C2semidirect
7. C2×C22⋊#3622C2semidirect
8. C22×#41×C17C2semidirect
12. C2×#41×C17C22semidirect
21. C2×#63230C22semidirect
23. C2×#63228C22semidirect
25. #10587616C22semidirect
30. #10587506C22semidirect
31. #10587503C22semidirect
32. C22⋊#3622C22semidirect
41. C2×Q8×C17D4semidirect
47. C2×D4×C17D4semidirect
89. Q8×C17C2×D4semidirect
93. D4×C17C2×D4semidirect
137. C22×#41D17semidirect
147. C2×C17#449semidirect
155. C2×#41C2×D17semidirect
176. C17C2×#449semidirect
185. C2×Q8C22⋊D17semidirect
197. C2×D4C22⋊D17semidirect
233. Q8C2×C22⋊D17semidirect
241. D4C2×C22⋊D17semidirect
283. C2#11762954direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#632302
C22×#632282
C2×#105876162
#117629542
C2×#105875062
C2×#105875032
C2×C22⋊#36222
C22×#41×C172
C2×#44917