Finite Group Databasebeta

← #28402930

Subgroups — #28402930

Order 14464.

388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299309C211yesmaximal, characteristic, complemented
2#20299251C211yesmaximal, characteristic
3#20298930C212yesmaximal, complemented
4#20298918C212yesmaximal, complemented
5#20298885C211yesmaximal, characteristic, complemented
6#20298880C211yesmaximal, characteristic, complemented
7#20298828C212yesmaximal, complemented
8C4×#14268636C211yesmaximal, characteristic, complemented
9C8×D452C211yesmaximal, characteristic, complemented
10#106×D113C212yesmaximal, complemented
11#498×C113C211yesmaximal, characteristic, complemented
12C2×#14268648—21no—
13C2×#14268636C2211yescharacteristic
14C2×C8×D113C2212yes—
15#16813613—21no—
16#16813607—22no—
17#16813602C2212yes—
18#16813598—21no—
19#16813598—22no—
20#16813597C2212yes—
21C4×Dic226C2211yescharacteristic
22C4×D452C2211yescharacteristic
23C4×D452C2211yescharacteristic
24#16813584—21no—
25C4⋊C4×D113C2212yes—
26C4⋊C4×D113C2212yes—
27#16813554C2211yescharacteristic
28#16813553C2212yes—
29#16813553C2212yes—
30C4⋊#11744751C2211yescharacteristic
31#16813547C2211yescharacteristic
32#16813545C2212yes—
33#16813544C2211yescharacteristic
34#16813542C2212yes—
35#16813534C2212yes—
36C4⋊Q8×C113C2211yescharacteristic
37C4⋊Q8×C113C2211yescharacteristic
38#106×C113C2212yes—
39#106×C113C2212yes—
40C4×C8×C113C2211yescharacteristic
41#14268648—44no—
42C2×Dic226C2311yescharacteristic
43C2×D452—22no—
44C2×D452D411yescharacteristic
45C2×D452C2311yescharacteristic
46C2×C4×D113—22no—
47C2×C4×D113—21no—
48C2×C4×D113—22no—
49C2×C4×D113C2312yes—
50#14268636—22no—
51C2×#11744751C2312yes—
52C8×D113—24no—
53C4⋊Dic113—22no—
54C4⋊Dic113D411yescharacteristic
55C4⋊Dic113C2311yescharacteristic
56C4⋊Dic113C2311yescharacteristic
57#14268626—21no—
58#14268626—22no—
59#14268626—22no—
60#14268624—22no—
61#14268624—21no—
62#14268624—22no—
63#14268624D412yes—
64C4×Dic113—21no—
65C2×Q8×C113—21no—
66C2×Q8×C113—21no—
67C2×C8×C113C2311yescharacteristic
68C2×C8×C113C2311yescharacteristic
69C4⋊C4×C113—21no—
70C4⋊C4×C113—21no—
71C4⋊C4×C113C2312yes—
72C4⋊C4×C113C2312yes—
73C42×C113C2311yescharacteristic
74C22×D113—21no—
75C22×D113C2×D412yes—
76Q8×C113—42no—
77Q8×C113—81no—
78C2×C4×C113—22no—
79C2×C4×C113—22no—
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2411yescharacteristic
83C2×Dic113—21no—
84C2×Dic113—21no—
85C2×Dic113—21no—
86C2×Dic113C2×D412yes—
87D452—21no—
88D452—21no—
89D452—44no—
90D452SD1614yescomplemented
91C4×D113—22no—
92C4×D113—22no—
93C4×D113—44no—
94C4×D113—42no—
95C4×D113—82no—
96Dic226—21no—
97Dic226—21no—
98C8×C113—21no—
99C8×C113#4112yescomplemented
100#11744751—22no—
101C22×C113C22×D411yescharacteristic
102C2×D113—22no—
103C2×D113—22no—
104C2×D113—41no—
105C2×D113—41no—
106C2×D113—41no—
107C2×D113C2×SD1614yes—
108C4×C113—21no—
109C4×C113—42no—
110C4×C113—42no—
111C4×C113C2×SD1612yes—
112C4×C113C2×#4111yescharacteristic
113C4×C1132−1+411yescharacteristic
114Dic113—22no—
115Dic113—41no—
116Dic113—41no—
117Dic113—41no—
118C2×C113#54711yescharacteristic
119C2×C113C22×SD1611yescharacteristic
120C2×C113#57711yescharacteristic
121D113—24no—
122D113—81no—
123#3335—1131nomaximal, Sylow
124C113#333511yescharacteristic, complemented, Sylow
125#554—1131no—
126#547—1131no—
127#498D11311yescharacteristic, complemented
128#483—1132no—
129#481—1132no—
130#476—1131no—
131#475—1131no—
132#465—1132no—
133C4×SD16—1131no—
134C8×D4—1131no—
135C2×#106—1132no—
136C2×#41—2261no—
137C2×SD16—1131no—
138C22×C8—1132no—
139C4⋊Q8C2×D11311yescharacteristic
140C4⋊Q8C2×D11311yescharacteristic
141#125—2261no—
142#123—2262no—
143C22⋊Q8—1132no—
144C22⋊Q8—2262no—
145C22⋊Q8—2261no—
146#121—1132no—
147C4×Q8—1131no—
148C4×D4—1131no—
149C4×D4—1131no—
150C4×D4—2261no—
151C2×C4⋊C4—1132no—
152C2×C4⋊C4—1132no—
153#106—1131no—
154#106—1132no—
155#106—1132no—
156#106C2×D11312yes—
157#106C2×D11312yes—
158C4⋊C8—1131no—
159#103—1131no—
160#103—1132no—
161#102—1131no—
162#102—1132no—
163C22⋊C8—1132no—
164C4×C8C2×D11311yescharacteristic
165#41—4524no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—1131no—
169C2×D4—1131no—
170C2×D4—1131no—
171C2×D4—2262no—
172C22×C4—1132no—
173C22×C4—2262no—
174C22×C4—2262no—
175C22×C4—2261no—
176SD16—2262no—
177C2×C8—1132no—
178C2×C8—2264no—
179C2×C8C22×D11311yescharacteristic
180C2×C8C22×D11311yescharacteristic
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—1131no—
184C4⋊C4—1131no—
185C4⋊C4—1131no—
186C4⋊C4—2262no—
187C4⋊C4—2262no—
188C4⋊C4—2262no—
189C4⋊C4—2261no—
190C4⋊C4C22×D11312yes—
191C4⋊C4C22×D11312yes—
192C22⋊C4—1132no—
193C22⋊C4—2262no—
194C22⋊C4—2262no—
195C22⋊C4—2261no—
196C42—2261no—
197C42C22×D11311yescharacteristic
198C23—1132no—
199C23—2261no—
200Q8—42no—
201Q8—81no—
202Q8—2261no—
203Q8—2261no—
204D4—1134no—
205D4—4524no—
206D4—2261no—
207D4—2261no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—1132no—
211C2×C4—9042no—
212C2×C4—4524no—
213C2×C4—4522no—
214C2×C4—2261no—
215C2×C4—2261no—
216C2×C4—2261no—
217C2×C4—2262no—
218C2×C4—2262no—
219C2×C4D4×D11311yescharacteristic
220C2×C4D4×D11311yescharacteristic
221C2×C4C23×D11311yescharacteristic
222C8—21no—
223C8—2262no—
224C8#1426864812yescomplemented
225C22—1134no—
226C22—4521no—
227C22—4521no—
228C22—4521no—
229C22—2262no—
230C22—2262no—
231C22C2×D4×D11311yescharacteristic
232C4—21no—
233C4—42no—
234C4—42no—
235C4—4521no—
236C4—4521no—
237C4—4521no—
238C4—2262no—
239C4SD16×D11312yes—
240C4C2×#1426864811yescharacteristic
241C4#1681367011yescharacteristic
242C2—9041no—
243C2—2264no—
244C2#2029925111yescharacteristic
245C2C2×SD16×D11311yescharacteristic
246C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#498×C113C2
socleC22×C113C22×D4
prime radical#20299251C2
hypercenter#498D113
hypocenterC113#3335
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #20299309C2semidirect
3. #20298930C2semidirect
4. #20298918C2semidirect
5. #20298885C2semidirect
6. #20298880C2semidirect
7. #20298828C2semidirect
8. C4×#14268636C2semidirect
9. C8×D452C2semidirect
10. #106×D113C2semidirect
11. #498×C113C2semidirect
90. D452SD16semidirect
99. C8×C113#41semidirect
124. C113#3335semidirect
127. #498D113semidirect
224. C8#14268648semidirect

Maximal subgroups

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

subgroupindex
#202993092
#202992512
#202989302
#202989182
#202988852
#202988802
#202988282
C4×#142686362
C8×D4522
#106×D1132
#498×C1132
#3335113