Finite Group Databasebeta

← #28399826

Subgroups — #28399826

Order 14464.

806 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 169 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×#16813647C212yesmaximal, complemented
2C2×#16813596C211yesmaximal, characteristic, complemented
3#20298743C214yesmaximal, complemented
4#20298737C212yesmaximal, complemented
5#20298732C212yesmaximal, complemented
6#20298599C212yesmaximal, complemented
7#20298562C211yesmaximal, characteristic, complemented
8C22×#41×C113C211yesmaximal, characteristic, complemented
9C22×D452C2211yescharacteristic, complemented
10C22×C22⋊D113—21no—
11#16813647—28no—
12C2×#14268634C2214yescomplemented
13C2×#14268632C2214yescomplemented
14C2×#14268631C2212yescomplemented
15#16813596—21no—
16#16813596—21no—
17#16813596C2212yes—
18#16813596C2212yescomplemented
19C2×C4⋊Dic113C2211yescharacteristic, complemented
20C2×#14268624—21no—
21#16813546C2214yescomplemented
22#16813543C2214yescomplemented
23C22⋊#11744751C2212yescomplemented
24C22⋊#11744751C2212yescomplemented
25C2×#41×C113—28no—
26C2×#41×C113—21no—
27C2×#41×C113—21no—
28C2×#41×C113C2212yes—
29C2×#41×C113C2212yescomplemented
30C22×Q8×C113C2211yescharacteristic, complemented
31C22×D4×C113—21no—
32C22×D4×C113C2211yescharacteristic, complemented
33C23×C4×C113—21no—
34C23×C4×C113C2211yescharacteristic
35C23×D113—21no—
36C2×D452—24no—
37C2×D452—21no—
38C2×D452C2312yes—
39C2×C22⋊D113—22no—
40C2×C22⋊D113—22no—
41C2×C22⋊D113—44no—
42C22×Dic113—21no—
43#14268634—28no—
44#14268632—28no—
45#14268631—24no—
46C2×#11744751C2314yes—
47C4⋊Dic113—21no—
48C4⋊Dic113C2312yes—
49#14268624—22no—
50#14268624—22no—
51C24×C113—21no—
52C24×C113D411yescharacteristic
53#41×C113—28no—
54#41×C113—28no—
55#41×C113—24no—
56#41×C113—24no—
57#41×C113—24no—
58#41×C113D418yescomplemented
59C2×Q8×C113—24no—
60C2×Q8×C113—21no—
61C2×Q8×C113C2312yes—
62C2×D4×C113—28no—
63C2×D4×C113—22no—
64C2×D4×C113—22no—
65C2×D4×C113—24no—
66C2×D4×C113—21no—
67C2×D4×C113C2312yes—
68C22×C4×C113—28no—
69C22×C4×C113—21no—
70C22×C4×C113—22no—
71C22×C4×C113—22no—
72C22×C4×C113—24no—
73C22×C4×C113D411yescharacteristic
74C22×C4×C113D411yescharacteristic
75C22×C4×C113D411yescharacteristic
76C22×C4×C113C2311yescharacteristic
77C22×C4×C113C2311yescharacteristic
78C22×C4×C113C2311yescharacteristic
79C23×C113—24no—
80C23×C113—22no—
81C23×C113—22no—
82C23×C113—22no—
83C23×C113—41no—
84C23×C113—42no—
85C23×C113—42no—
86C23×C113C2×D411yescharacteristic
87C23×C113C2×D411yescharacteristic
88C23×C113C2×D411yescharacteristic
89C22×D113—22no—
90C22×D113—42no—
91C22×D113—42no—
92C22×D113—42no—
93Q8×C113—24no—
94Q8×C113—22no—
95Q8×C113C2×D414yescomplemented
96D4×C113—28no—
97D4×C113—24no—
98D4×C113—28no—
99D4×C113—22no—
100D4×C113C2×D414yescomplemented
101C2×C4×C113—24no—
102C2×C4×C113—28no—
103C2×C4×C113—22no—
104C2×C4×C113—22no—
105C2×C4×C113—22no—
106C2×C4×C113—28no—
107C2×C4×C113—22no—
108C2×C4×C113—22no—
109C2×C4×C113—22no—
110C2×C4×C113C2×D411yescharacteristic
111C2×C4×C113C2×D411yescharacteristic
112C2×C4×C113C2×D411yescharacteristic
113C2×C4×C113C2×D414yes—
114C2×C4×C113C2411yescharacteristic
115C22⋊D113—44no—
116C22⋊D113—44no—
117C2×Dic113—22no—
118C2×Dic113—42no—
119D452—24no—
120D452—42no—
121#11744751—24no—
122C22×C113—21no—
123C22×C113—21no—
124C22×C113—21no—
125C22×C113—21no—
126C22×C113—21no—
127C22×C113—24no—
128C22×C113—21no—
129C22×C113—21no—
130C22×C113—44no—
131C22×C113—48no—
132C22×C113—42no—
133C22×C113—42no—
134C22×C113#12012yes—
135C22×C113AGL(1,ℤ/8)12yescomplemented
136C22×C113C22×D411yescharacteristic
137C2×D113—42no—
138C2×D113—42no—
139C2×D113—42no—
140C2×D113—84no—
141C4×C113—21no—
142C4×C113—24no—
143C4×C113—21no—
144C4×C113#12012yes—
145C4×C113C22×D412yes—
146Dic113—42no—
147C2×C113—22no—
148C2×C113—22no—
149C2×C113—41no—
150C2×C113—44no—
151C2×C113C2×#12011yescharacteristic
152C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C113#57511yescharacteristic
154D113—82no—
155#3006—1131nomaximal, Sylow
156C113#300611yescharacteristic, complemented, Sylow
157C22×#41D11311yescharacteristic, complemented
158C2×AGL(1,ℤ/8)—1132no—
159C2×#121—1131no—
160#449—1134no—
161#448—1132no—
162#447—1132no—
163#417—1132no—
164#407—1131no—
165C2×#41—28no—
166C2×#41—21no—
167C2×#41—21no—
168C2×#41C2×D11312yes—
169C2×#41C2×D11312yescomplemented
170C22×Q8C2×D11311yescharacteristic, complemented
171C22×D4—21no—
172C22×D4—1131no—
173C22×D4—2261no—
174C22×D4C2×D11311yescharacteristic, complemented
175C23×C4—21no—
176C23×C4C2×D11311yescharacteristic
177AGL(1,ℤ/8)—2268no—
178C2×SD16—1134no—
179C2×D8—1134no—
180C2×M16—1132no—
181#121—1132no—
182#121—1132no—
183#121—2261no—
184#121—2261no—
185C2×C4⋊C4—1131no—
186C2×C22⋊C4—2261no—
187#103—1134no—
188#102—1134no—
189C22⋊C8—1132no—
190C22⋊C8—1132no—
191C24—21no—
192C24—2261no—
193C24C22⋊D11311yescharacteristic
194#41—28no—
195#41—28no—
196#41—24no—
197#41—24no—
198#41—24no—
199#41C22⋊D11318yescomplemented
200C2×Q8—24no—
201C2×Q8—21no—
202C2×Q8C22×D11312yes—
203C2×D4—28no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—24no—
207C2×D4—21no—
208C2×D4—1132no—
209C2×D4—4524no—
210C2×D4—2262no—
211C2×D4—2262no—
212C2×D4—2261no—
213C2×D4—2264no—
214C2×D4C22×D11312yes—
215C22×C4—28no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—2261no—
221C22×C4C22⋊D11311yescharacteristic
222C22×C4C22⋊D11311yescharacteristic
223C22×C4C22⋊D11311yescharacteristic
224C22×C4C22×D11311yescharacteristic
225C22×C4C22×D11311yescharacteristic
226C22×C4C22×D11311yescharacteristic
227SD16—2268no—
228D8—2268no—
229M16—2264no—
230C2×C8—1134no—
231C4⋊C4—1132no—
232C4⋊C4—2261no—
233C22⋊C4—2262no—
234C22⋊C4—2262no—
235C23—24no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—41no—
240C23—42no—
241C23—42no—
242C23—4522no—
243C23—4522no—
244C23—4522no—
245C23—2262no—
246C23C2×C22⋊D11311yescharacteristic
247C23C2×C22⋊D11311yescharacteristic
248C23C2×C22⋊D11311yescharacteristic
249Q8—24no—
250Q8—22no—
251Q8C2×C22⋊D11314yescomplemented
252D4—28no—
253D4—24no—
254D4—28no—
255D4—22no—
256D4—4524no—
257D4—4524no—
258D4—4522no—
259D4—2264no—
260D4C2×C22⋊D11314yescomplemented
261C2×C4—24no—
262C2×C4—28no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—28no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—4522no—
271C2×C4—2262no—
272C2×C4C2×C22⋊D11311yescharacteristic
273C2×C4C2×C22⋊D11311yescharacteristic
274C2×C4C2×C22⋊D11311yescharacteristic
275C2×C4C2×C22⋊D11314yes—
276C2×C4C23×D11311yescharacteristic
277C8—2264no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—24no—
284C22—21no—
285C22—21no—
286C22—44no—
287C22—48no—
288C22—42no—
289C22—42no—
290C22—9044no—
291C22—4522no—
292C22—4522no—
293C22—4522no—
294C22#1681359112yes—
295C22#1681364712yescomplemented
296C22C22×C22⋊D11311yescharacteristic
297C4—21no—
298C4—24no—
299C4—21no—
300C4—4522no—
301C4#1681359112yes—
302C4C22×C22⋊D11312yes—
303C2—22no—
304C2—22no—
305C2—41no—
306C2—44no—
307C2—9042no—
308C2C2×#1681359111yescharacteristic
309C2C2×#1681364711yescharacteristic
310C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×#41×C113C2
socleC22×C113C22×D4
hypercenterC22×#41D113
hypocenterC113#3006
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16813647C2semidirect
2. C2×#16813596C2semidirect
3. #20298743C2semidirect
4. #20298737C2semidirect
5. #20298732C2semidirect
6. #20298599C2semidirect
7. #20298562C2semidirect
8. C22×#41×C113C2semidirect
9. C22×D452C22semidirect
12. C2×#14268634C22semidirect
13. C2×#14268632C22semidirect
14. C2×#14268631C22semidirect
18. #16813596C22semidirect
19. C2×C4⋊Dic113C22semidirect
21. #16813546C22semidirect
22. #16813543C22semidirect
23. C22⋊#11744751C22semidirect
24. C22⋊#11744751C22semidirect
29. C2×#41×C113C22semidirect
30. C22×Q8×C113C22semidirect
32. C22×D4×C113C22semidirect
58. #41×C113D4semidirect
95. Q8×C113C2×D4semidirect
100. D4×C113C2×D4semidirect
135. C22×C113AGL(1,ℤ/8)semidirect
156. C113#3006semidirect
157. C22×#41D113semidirect
169. C2×#41C2×D113semidirect
170. C22×Q8C2×D113semidirect
174. C22×D4C2×D113semidirect
199. #41C22⋊D113semidirect
251. Q8C2×C22⋊D113semidirect
260. D4C2×C22⋊D113semidirect
295. C22#16813647semidirect

Maximal subgroups

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

subgroupindex
C2×#168136472
C2×#168135962
#202987432
#202987372
#202987322
#202985992
#202985622
C22×#41×C1132
#3006113