Finite Group Databasebeta

← #28390593

Subgroups — #28390593

Order 14464.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#20299066C211yesmaximal, characteristic
2#20298621C211yesmaximal, characteristic, complemented
3C2×#16813550C211yesmaximal, characteristic
4C2×#16813548C211yesmaximal, characteristic
5C4×#14268626C211yesmaximal, characteristic, complemented
6#20298357C211yesmaximal, characteristic, complemented
7#339×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9C2×#14268631C2211yescharacteristic
10#16813587C411yescharacteristic, complemented
11#16813587C411yescharacteristic, complemented
12#16813584C411yescharacteristic, complemented
13#16813584C411yescharacteristic, complemented
14#16813582—21no—
15#16813582—21no—
16#16813579—21no—
17C2×#14268626—21no—
18C2×C4×Dic113C2211yescharacteristic
19C2×C4×Dic113C2211yescharacteristic
20C42×D113—21no—
21#16813551—21no—
22#16813551—21no—
23#16813550—22no—
24#16813548—22no—
25#16813529—21no—
26C2×M16×C113C2211yescharacteristic
27#117×C113C2211yescharacteristic
28C2×C42×C113C2211yescharacteristic
29#14268647—21no—
30#14268647—21no—
31#14268647D412yes—
32#14268647Q812yes—
33C2×Dic226C2×C411yescharacteristic
34C2×D452C2×C411yescharacteristic
35C2×C22⋊D113—21no—
36C22×Dic113—21no—
37C22×Dic113D411yescharacteristic
38C22×Dic113D411yescharacteristic
39C2×C4×D113—21no—
40C2×C4×D113—21no—
41C2×C4×D113—21no—
42#14268631—21no—
43#14268631—21no—
44C2×#11744751—21no—
45#14268626—24no—
46#14268626—21no—
47#14268626—21no—
48#14268624—21no—
49#14268624—21no—
50C4×Dic113—21no—
51C4×Dic113—21no—
52C4×Dic113—21no—
53C4×Dic113—21no—
54C4×Dic113C2×C411yescharacteristic
55C4×Dic113C2×C411yescharacteristic
56C4×Dic113D411yescharacteristic
57C4×Dic113D411yescharacteristic
58C22×C4×C113—21no—
59C22×C4×C113C2311yescharacteristic
60M16×C113—21no—
61M16×C113—21no—
62C2×C8×C113—21no—
63C4⋊C4×C113C2×C411yescharacteristic
64C4⋊C4×C113C2×C411yescharacteristic
65C22⋊C4×C113—21no—
66C42×C113—21no—
67C42×C113—21no—
68C42×C113—21no—
69C23×C113C2×D411yescharacteristic
70C22×D113—21no—
71C2×C4×C113—22no—
72C2×C4×C113—21no—
73C2×C4×C113—21no—
74C2×C4×C113—41no—
75C2×C4×C113—41no—
76C2×C4×C113C22×C411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2×D411yescharacteristic
79C2×C4×C113C2×Q811yescharacteristic
80C2×C4×C113#4111yescharacteristic
81C2×C4×C113#4111yescharacteristic
82C22⋊D113—22no—
83C22⋊D113—22no—
84C2×Dic113—21no—
85C2×Dic113—22no—
86C2×Dic113—22no—
87C2×Dic113—41no—
88C2×Dic113—41no—
89C2×Dic113—41no—
90C2×Dic113C22⋊C411yescharacteristic
91C2×Dic113C22⋊C411yescharacteristic
92C2×Dic113C22⋊C411yescharacteristic
93C2×Dic113C22⋊C411yescharacteristic
94D452—21no—
95D452C4⋊C412yescomplemented
96C4×D113—22no—
97C4×D113—22no—
98C4×D113—42no—
99C4×D113—42no—
100Dic226—21no—
101Dic226C4⋊C412yescomplemented
102C8×C113—41no—
103#11744751—41no—
104C22×C113—21no—
105C22×C113—21no—
106C22×C113C2×C22⋊C411yescharacteristic
107C22×C113#12111yescharacteristic
108C22×C113C22⋊Q811yescharacteristic
109C2×D113—22no—
110C2×D113—41no—
111C2×D113—41no—
112C4×C113—42no—
113C4×C113—41no—
114C4×C113—41no—
115C4×C113C2×C4⋊C411yescharacteristic
116C4×C113#11711yescharacteristic
117C4×C113#12111yescharacteristic
118C4×C113C22⋊Q811yescharacteristic
119Dic113—22no—
120Dic113—21no—
121Dic113—21no—
122Dic113—21no—
123Dic113—42no—
124Dic113#10412yescomplemented
125C2×C113—21no—
126C2×C113—21no—
127C2×C113#38011yescharacteristic
128C2×C113C2×#10411yescharacteristic
129C2×C113#42111yescharacteristic
130D113—42no—
131#1806—1131nomaximal, Sylow
132C113#180611yescharacteristic, complemented, Sylow
133C4×#41—1131no—
134#423—1131no—
135C2×#104—1131no—
136C2×#104—1131no—
137C4×C4⋊C4—1131no—
138#339—1131no—
139#339D11311yescharacteristic, complemented
140C2×#41—1131no—
141C2×M16—1131no—
142C2×M16C2×D11311yescharacteristic
143C4×Q8—1131no—
144C4×Q8—1131no—
145C4×D4—1131no—
146C4×D4—1131no—
147C4×D4—2261no—
148C4×D4—2261no—
149#117—2261no—
150#117C2×D11311yescharacteristic
151C2×C4⋊C4—2261no—
152C2×C42—1131no—
153C2×C42—1131no—
154C2×C42—2261no—
155C2×C42C2×D11311yescharacteristic
156C4⋊C8—2261no—
157C4⋊C8—2261no—
158#104—2262no—
159#104—2262no—
160#95—2261no—
161#41—1132no—
162#41—1132no—
163#41—2261no—
164#41—2261no—
165C2×Q8—1131no—
166C2×D4—1131no—
167C2×D4—2261no—
168C22×C4—21no—
169C22×C4—1131no—
170C22×C4—1131no—
171C22×C4—2261no—
172C22×C4—2261no—
173C22×C4—2261no—
174C22×C4—2261no—
175C22×C4C22×D11311yescharacteristic
176M16—21no—
177M16—21no—
178M16—2261no—
179M16—2261no—
180C2×C8—21no—
181C2×C8—2261no—
182C4⋊C4—2261no—
183C4⋊C4—2261no—
184C4⋊C4—2264no—
185C4⋊C4C4×D11311yescharacteristic
186C4⋊C4C4×D11311yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—2261no—
189C22⋊C4—2261no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—1131no—
194C42—1131no—
195C42—1131no—
196C42—1131no—
197C42—2261no—
198C42—2261no—
199C42—2261no—
200C42—2261no—
201C23—2261no—
202C23D4×D11311yescharacteristic
203Q8—1132no—
204Q8—2261no—
205D4—1132no—
206D4—2262no—
207D4—2262no—
208D4—2261no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1131no—
215C2×C4—1131no—
216C2×C4—1131no—
217C2×C4—1131no—
218C2×C4—4522no—
219C2×C4—4522no—
220C2×C4—4521no—
221C2×C4—4521no—
222C2×C4—4521no—
223C2×C4—2262no—
224C2×C4—2262no—
225C2×C4—2261no—
226C2×C4—2262no—
227C2×C4—2262no—
228C2×C4C2×C4×D11311yescharacteristic
229C2×C4D4×D11311yescharacteristic
230C2×C4D4×D11311yescharacteristic
231C2×C4Q8×D11311yescharacteristic
232C2×C4#1426864711yescharacteristic
233C2×C4#1426864711yescharacteristic
234C8—41no—
235C8—4521no—
236C22—21no—
237C22—21no—
238C22—4521no—
239C22—4521no—
240C22—2262no—
241C22C22⋊C4×D11311yescharacteristic
242C22#1681359511yescharacteristic
243C22#1681360011yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—1132no—
248C4—4522no—
249C4—2261no—
250C4—2261no—
251C4—2261no—
252C4—2262no—
253C4C4⋊C4×D11311yescharacteristic
254C4#1681357911yescharacteristic
255C4#1681359511yescharacteristic
256C4#1681360011yescharacteristic
257C2—21no—
258C2—21no—
259C2—4522no—
260C2#2029845711yescharacteristic
261C2#104×D11311yescharacteristic
262C2#2029861311yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#339×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC2×#14268647C22
cosocleC22×C4×C113C23
hypercenter#339D113
hypocenterC113#1806
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #20298621C2semidirect
5. C4×#14268626C2semidirect
6. #20298357C2semidirect
7. #339×C113C2semidirect
10. #16813587C4semidirect
11. #16813587C4semidirect
12. #16813584C4semidirect
13. #16813584C4semidirect
95. D452C4⋊C4semidirect
101. Dic226C4⋊C4semidirect
124. Dic113#104semidirect
132. C113#1806semidirect
139. #339D113semidirect

Maximal subgroups

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

subgroupindex
#202990662
#202986212
C2×#168135502
C2×#168135482
C4×#142686262
#202983572
#339×C1132
#1806113