Finite Group Databasebeta

← #28402392

Subgroups — #28402392

Order 14464.

462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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
1D4×D452C211yesmaximal, characteristic
2#20298946C211yesmaximal, characteristic, complemented
3#20298916C212yesmaximal, complemented
4#20298885C211yesmaximal, characteristic, complemented
5#20298829C212yesmaximal, complemented
6#20298798C211yesmaximal, characteristic, complemented
7#20298748C212yesmaximal, complemented
8C4×#14268634C211yesmaximal, characteristic, complemented
9D4×#11744751C211yesmaximal, characteristic, complemented
10C2×#16813542C212yesmaximal, complemented
11#554×C113C211yesmaximal, characteristic, complemented
12C22×D452C2212yes—
13C2×D4×D113—21no—
14C2×#14268634C2211yescharacteristic
15C2×#14268634C2212yescomplemented
16C22×#11744751C2212yescomplemented
17#16813619C2211yescharacteristic
18#16813597—21no—
19#16813596C2212yes—
20#16813592—22no—
21C4×D452C2211yescharacteristic
22#16813553C2212yescomplemented
23#16813553C2211yescharacteristic, complemented
24C4⋊#11744751C2211yescharacteristic, complemented
25#16813546C2211yescharacteristic, complemented
26#16813542C2211yescharacteristic
27#16813542C2212yes—
28#16813542C2212yescomplemented
29#16813542C2212yescomplemented
30#16813542C2212yescomplemented
31C22⋊#11744751C2212yescomplemented
32C4×#11744751C2211yescharacteristic, complemented
33C4⋊Q8×C113C2211yescharacteristic, complemented
34#125×C113—21no—
35C22⋊Q8×C113—22no—
36C22⋊Q8×C113C2212yescomplemented
37C4×Q8×C113C2211yescharacteristic, complemented
38C4×D4×C113—21no—
39C4×D4×C113C2211yescharacteristic
40C2×C4⋊C4×C113C2212yescomplemented
41C23×D113—22no—
42C2×D452—24no—
43C2×D452—22no—
44C2×D452—21no—
45C2×D452—21no—
46C2×D452—42no—
47C2×D452C2312yes—
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—22no—
50D4×D113—44no—
51C2×C4×D113—21no—
52#14268634—22no—
53#14268634—42no—
54C2×#11744751—42no—
55C2×#11744751C2311yescharacteristic
56C2×#11744751C2312yes—
57C2×#11744751C2311yescharacteristic
58C4⋊Dic113C2311yescharacteristic
59#14268624—21no—
60#14268624—22no—
61C2×Q8×C113—21no—
62C2×Q8×C113C2311yescharacteristic
63C2×D4×C113D411yescharacteristic
64C22×C4×C113—22no—
65C22×C4×C113C2312yes—
66C4⋊C4×C113—22no—
67C4⋊C4×C113—21no—
68C4⋊C4×C113—21no—
69C4⋊C4×C113—22no—
70C4⋊C4×C113D411yescharacteristic
71C4⋊C4×C113C2311yescharacteristic
72C4⋊C4×C113C2312yes—
73C22⋊C4×C113—22no—
74C22⋊C4×C113D412yes—
75C42×C113—21no—
76C42×C113C2311yescharacteristic
77C23×C113C2×D412yes—
78C22×D113—21no—
79C22×D113—22no—
80C22×D113—44no—
81C22×D113—44no—
82C22×D113—82no—
83Q8×C113—21no—
84Q8×C113—21no—
85Q8×C113—81no—
86D4×C113SD1614yescomplemented
87C2×C4×C113—22no—
88C2×C4×C113—22no—
89C2×C4×C113—21no—
90C2×C4×C113—21no—
91C2×C4×C113—22no—
92C2×C4×C113—82no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D412yes—
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2411yescharacteristic
97C22⋊D113—44no—
98C2×Dic113—21no—
99D452—22no—
100D452—21no—
101D452—22no—
102D452—44no—
103D452—42no—
104D452—81no—
105D452#4112yes—
106C4×D113—42no—
107#11744751—21no—
108#11744751—21no—
109#11744751—22no—
110C22×C113—22no—
111C22×C113—22no—
112C22×C113C2×SD1614yes—
113C22×C113C22×D411yescharacteristic
114C2×D113—22no—
115C2×D113—41no—
116C2×D113—41no—
117C2×D113—42no—
118C2×D113—42no—
119C2×D113—42no—
120C2×D113—88no—
121C4×C113—22no—
122C4×C113—21no—
123C4×C113—41no—
124C4×C113—41no—
125C4×C113—42no—
126C4×C113C2×SD1612yes—
127C4×C113C2×#4111yescharacteristic
128C4×C113H(5,𝔽2)11yescharacteristic
129Dic113—41no—
130C2×C113—24no—
131C2×C113#54611yescharacteristic
132C2×C113C22×SD1611yescharacteristic
133C2×C113#57611yescharacteristic
134D113—42no—
135D113—82no—
136#3295—1131nomaximal, Sylow
137C113#329511yescharacteristic, complemented, Sylow
138#554D11311yescharacteristic, complemented
139D42—1131no—
140#486—1131no—
141#481—1132no—
142#476—1131no—
143#465—1132no—
144#460—1131no—
145#450—1132no—
146C4×SD16—1131no—
147C8×D4—1131no—
148C2×#102—1132no—
149C22×D4—1132no—
150C22×D4—2261no—
151C2×SD16—1132no—
152C2×SD16—1131no—
153C22×C8—1132no—
154C4⋊Q8C2×D11311yescharacteristic, complemented
155#127—1131no—
156#125—21no—
157C22⋊Q8—22no—
158C22⋊Q8C2×D11312yescomplemented
159#121—1132no—
160#121—2261no—
161#120—2262no—
162C4×Q8C2×D11311yescharacteristic, complemented
163C4×D4—21no—
164C4×D4—1131no—
165C4×D4C2×D11311yescharacteristic
166C2×C4⋊C4C2×D11312yescomplemented
167#106—1131no—
168#106—1132no—
169C4⋊C8—1131no—
170#103—1131no—
171#102—1131no—
172#102—1132no—
173#102—1132no—
174#102—1132no—
175#102—1132no—
176C22⋊C8—1132no—
177C4×C8—1131no—
178C24—2262no—
179C2×Q8—21no—
180C2×Q8C22×D11311yescharacteristic
181C2×D4—1131no—
182C2×D4—1132no—
183C2×D4—4522no—
184C2×D4—4524no—
185C2×D4—2264no—
186C2×D4—2262no—
187C2×D4—2261no—
188C2×D4—2262no—
189C2×D4—2261no—
190C2×D4C22⋊D11311yescharacteristic
191C22×C4—22no—
192C22×C4—2261no—
193C22×C4C22×D11312yes—
194SD16—4522no—
195SD16—2262no—
196C2×C8—1131no—
197C2×C8—1131no—
198C2×C8—1132no—
199C2×C8—4522no—
200C4⋊C4—22no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—22no—
204C4⋊C4—1131no—
205C4⋊C4C22⋊D11311yescharacteristic
206C4⋊C4C22×D11311yescharacteristic
207C4⋊C4C22×D11312yes—
208C22⋊C4—22no—
209C22⋊C4—2261no—
210C22⋊C4—2262no—
211C22⋊C4C22⋊D11312yes—
212C42—21no—
213C42C22×D11311yescharacteristic
214C23—9042no—
215C23—4524no—
216C23—4524no—
217C23—2262no—
218C23—2261no—
219C23C2×C22⋊D11312yes—
220Q8—21no—
221Q8—21no—
222Q8—81no—
223D4—1132no—
224D4—9041no—
225D4—4524no—
226D4—4524no—
227D4—4522no—
228D4—2262no—
229D4—2262no—
230D4—2261no—
231D4#1426863414yescomplemented
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—82no—
238C2×C4—4522no—
239C2×C4—2261no—
240C2×C4C2×C22⋊D11311yescharacteristic
241C2×C4C2×C22⋊D11312yes—
242C2×C4C2×C22⋊D11311yescharacteristic
243C2×C4C23×D11311yescharacteristic
244C8—2261no—
245C8—2261no—
246C8—2262no—
247C22—22no—
248C22—22no—
249C22—9048no—
250C22—4522no—
251C22—4522no—
252C22—4522no—
253C22—4521no—
254C22—4521no—
255C22—2262no—
256C22C2×#1426863414yes—
257C22C22×C22⋊D11311yescharacteristic
258C4—21no—
259C4—22no—
260C4—41no—
261C4—42no—
262C4—41no—
263C4—4521no—
264C4C2×#1426863412yes—
265C4#41×D11311yescharacteristic
266C4#1681366811yescharacteristic
267C2—24no—
268C2—9042no—
269C2—4522no—
270C2#2029923611yescharacteristic
271C2C22×#1426863411yescharacteristic
272C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#554×C113C2
socleC22×C113C22×D4
prime radicalD4×D452C2
hypercenter#554D113
hypocenterC113#3295
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #20298946C2semidirect
3. #20298916C2semidirect
4. #20298885C2semidirect
5. #20298829C2semidirect
6. #20298798C2semidirect
7. #20298748C2semidirect
8. C4×#14268634C2semidirect
9. D4×#11744751C2semidirect
10. C2×#16813542C2semidirect
11. #554×C113C2semidirect
15. C2×#14268634C22semidirect
16. C22×#11744751C22semidirect
22. #16813553C22semidirect
23. #16813553C22semidirect
24. C4⋊#11744751C22semidirect
25. #16813546C22semidirect
28. #16813542C22semidirect
29. #16813542C22semidirect
30. #16813542C22semidirect
31. C22⋊#11744751C22semidirect
32. C4×#11744751C22semidirect
33. C4⋊Q8×C113C22semidirect
36. C22⋊Q8×C113C22semidirect
37. C4×Q8×C113C22semidirect
40. C2×C4⋊C4×C113C22semidirect
86. D4×C113SD16semidirect
137. C113#3295semidirect
138. #554D113semidirect
154. C4⋊Q8C2×D113semidirect
158. C22⋊Q8C2×D113semidirect
162. C4×Q8C2×D113semidirect
166. C2×C4⋊C4C2×D113semidirect
231. D4#14268634semidirect

Maximal subgroups

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

subgroupindex
D4×D4522
#202989462
#202989162
#202988852
#202988292
#202987982
#202987482
C4×#142686342
D4×#117447512
C2×#168135422
#554×C1132
#3295113