Finite Group Databasebeta

← #28400405

Subgroups — #28400405

Order 14464.

398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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
1#20299226C211yesmaximal, characteristic, complemented
2#20298898C212yesmaximal, complemented
3#20298898C212yesmaximal, complemented
4#20298888C212yesmaximal, complemented
5#20298878C212yesmaximal, complemented
6#20298641C211yesmaximal, characteristic, complemented
7#20298634C211yesmaximal, characteristic, complemented
8#20298625C211yesmaximal, characteristic, complemented
9#20298603C211yesmaximal, characteristic
10C2×#16813543C211yesmaximal, characteristic
11#518×C113C211yesmaximal, characteristic
12C2×#14268631C2211yescharacteristic
13C22×#11744751C2211yescharacteristic
14#16813622C2212yescomplemented
15#16813621—21no—
16#16813614C2212yescomplemented
17#16813613—21no—
18#16813599—22no—
19#16813581C2211yescharacteristic
20C2×C4⋊Dic113C2211yescharacteristic
21#16813555C2211yescharacteristic, complemented
22#16813555C2212yescomplemented
23#16813555C2211yescharacteristic, complemented
24#16813553C2211yescharacteristic, complemented
25#16813553C2212yescomplemented
26#16813553C2211yescharacteristic, complemented
27C4⋊#11744751C2212yescomplemented
28C4⋊#11744751C2212yescomplemented
29#16813543C2212yes—
30#16813543C2212yes—
31#16813543C2212yes—
32#16813543C2212yes—
33C22×D4×C113C2211yescharacteristic
34C4×D4×C113—21no—
35C4×D4×C113—21no—
36C4×D4×C113C2212yes—
37C4×D4×C113C2212yes—
38#117×C113C2211yescharacteristic
39#117×C113C2211yescharacteristic
40C2×C22⋊C4×C113—22no—
41C2×Dic226—22no—
42C22×Dic113—21no—
43#14268631—22no—
44C2×#11744751—22no—
45C2×#11744751C2311yescharacteristic
46C2×#11744751C2311yescharacteristic
47C2×#11744751C2312yes—
48C4⋊Dic113—21no—
49C4⋊Dic113—22no—
50C4⋊Dic113C2312yes—
51C4⋊Dic113C2311yescharacteristic
52C4⋊Dic113C2311yescharacteristic
53#14268626—22no—
54#14268626—22no—
55C22⋊Dic113—21no—
56C4×Dic113—21no—
57C24×C113—21no—
58C2×D4×C113—21no—
59C2×D4×C113—22no—
60C2×D4×C113Q814yescomplemented
61C2×D4×C113C2312yes—
62C22×C4×C113—22no—
63C22×C4×C113—22no—
64C22×C4×C113C2311yescharacteristic
65C4⋊C4×C113D411yescharacteristic
66C4⋊C4×C113D411yescharacteristic
67C4⋊C4×C113C2311yescharacteristic
68C4⋊C4×C113C2311yescharacteristic
69C22⋊C4×C113—21no—
70C22⋊C4×C113—22no—
71C22⋊C4×C113—22no—
72C22⋊C4×C113D412yes—
73C42×C113—21no—
74C42×C113C2312yes—
75C23×C113—22no—
76C23×C113—24no—
77C23×C113—81no—
78C23×C113—81no—
79C23×C113C2×D411yescharacteristic
80D4×C113—24no—
81D4×C113—22no—
82D4×C113C2×Q814yes—
83C2×C4×C113—21no—
84C2×C4×C113—21no—
85C2×C4×C113—82no—
86C2×C4×C113—82no—
87C2×C4×C113C2×D412yes—
88C2×C4×C113C2×D412yes—
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2×Q812yes—
91C2×C4×C113#4112yes—
92C2×C4×C113C2411yescharacteristic
93C2×Dic113—21no—
94C2×Dic113—21no—
95C2×Dic113—22no—
96C2×Dic113—81no—
97Dic226—82no—
98#11744751—21no—
99#11744751—21no—
100#11744751—22no—
101C22×C113—21no—
102C22×C113—21no—
103C22×C113—24no—
104C22×C113—42no—
105C22×C113—42no—
106C22×C113—84no—
107C22×C113C22⋊Q812yes—
108C22×C113C22×D411yescharacteristic
109C4×C113—22no—
110C4×C113—22no—
111C4×C113—41no—
112C4×C113—41no—
113C4×C113C22⋊Q812yes—
114C4×C113C22×Q811yescharacteristic
115C4×C113C2×#4111yescharacteristic
116Dic113—41no—
117Dic113—42no—
118Dic113—41no—
119C2×C113—22no—
120C2×C113—44no—
121C2×C113C2×C22⋊Q811yescharacteristic
122C2×C113#57611yescharacteristic
123C2×C113#57711yescharacteristic
124#3081—1131nomaximal, Sylow
125C113#308111yescharacteristic, complemented, Sylow
126#544—1131no—
127#518D11311yescharacteristic
128#478—1132no—
129#478—1132no—
130#476—1132no—
131#474—1132no—
132#428—1131no—
133#427—1131no—
134#424—1131no—
135#418—1131no—
136C2×#102—1131no—
137C22×D4C2×D11311yescharacteristic
138C2×M16—1131no—
139C22×C8—1131no—
140C4⋊Q8—1132no—
141C4⋊Q8—2261no—
142#125—1132no—
143#125—2261no—
144C22⋊Q8—2262no—
145C4×D4—21no—
146C4×D4—21no—
147C4×D4C2×D11312yes—
148C4×D4C2×D11312yes—
149#117—1131no—
150#117C2×D11311yescharacteristic
151#117C2×D11311yescharacteristic
152C2×C4⋊C4—1131no—
153C2×C22⋊C4—22no—
154#107—1131no—
155#107—1131no—
156#107—1132no—
157#106—1131no—
158#106—1131no—
159#106—1132no—
160C4⋊C8—1132no—
161C4⋊C8—1132no—
162#102—1132no—
163#102—1132no—
164#102—1132no—
165#102—1132no—
166C24—21no—
167C2×Q8—2262no—
168C2×D4—21no—
169C2×D4—22no—
170C2×D4Dic22614yescomplemented
171C2×D4C22×D11312yes—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—2261no—
175C22×C4C22×D11311yescharacteristic
176M16—2262no—
177C2×C8—1131no—
178C2×C8—1132no—
179C2×C8—1131no—
180C2×C8—2262no—
181C4⋊C4—1132no—
182C4⋊C4—1131no—
183C4⋊C4—1131no—
184C4⋊C4—2261no—
185C4⋊C4—2262no—
186C4⋊C4—2262no—
187C4⋊C4—2262no—
188C4⋊C4C22⋊D11311yescharacteristic
189C4⋊C4C22⋊D11311yescharacteristic
190C4⋊C4C22×D11311yescharacteristic
191C4⋊C4C22×D11311yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—2261no—
196C22⋊C4C22⋊D11312yes—
197C42—21no—
198C42—2261no—
199C42C22×D11312yes—
200C23—22no—
201C23—24no—
202C23—81no—
203C23—81no—
204C23C2×C22⋊D11311yescharacteristic
205Q8—9042no—
206D4—24no—
207D4—22no—
208D4C2×Dic22614yes—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—9041no—
214C2×C4—2261no—
215C2×C4—2261no—
216C2×C4—2262no—
217C2×C4C2×C22⋊D11312yes—
218C2×C4C2×C22⋊D11312yes—
219C2×C4C2×C22⋊D11311yescharacteristic
220C2×C4C2×Dic22612yes—
221C2×C4#1426864712yes—
222C2×C4C23×D11311yescharacteristic
223C8—2261no—
224C8—2261no—
225C8—2262no—
226C22—21no—
227C22—21no—
228C22—24no—
229C22—42no—
230C22—42no—
231C22—84no—
232C22#1681360112yes—
233C22C22×C22⋊D11311yescharacteristic
234C4—22no—
235C4—22no—
236C4—41no—
237C4—41no—
238C4—4522no—
239C4—4521no—
240C4—4521no—
241C4#1681360112yes—
242C4C22×Dic22611yescharacteristic
243C4C2×#1426864711yescharacteristic
244C2—22no—
245C2—44no—
246C2C2×#1681360111yescharacteristic
247C2#2029940111yescharacteristic
248C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#518×C113C2
socleC22×C113C22×D4
prime radicalC22×D4×C113C22
hypercenter#518D113
hypocenterC113#3081
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #20299226C2semidirect
2. #20298898C2semidirect
3. #20298898C2semidirect
4. #20298888C2semidirect
5. #20298878C2semidirect
6. #20298641C2semidirect
7. #20298634C2semidirect
8. #20298625C2semidirect
14. #16813622C22semidirect
16. #16813614C22semidirect
21. #16813555C22semidirect
22. #16813555C22semidirect
23. #16813555C22semidirect
24. #16813553C22semidirect
25. #16813553C22semidirect
26. #16813553C22semidirect
27. C4⋊#11744751C22semidirect
28. C4⋊#11744751C22semidirect
60. C2×D4×C113Q8semidirect
125. C113#3081semidirect
170. C2×D4Dic226semidirect

Maximal subgroups

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

subgroupindex
#202992262
#202988982
#202988882
#202988782
#202986412
#202986342
#202986252
#202986032
C2×#168135432
#518×C1132
#3081113