Finite Group Databasebeta

← #28406009

Subgroups — #28406009

Order 14464.

340 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 68 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×#16813679C211yesmaximal, characteristic, complemented
2#20299540C211yesmaximal, characteristic, complemented
3#20299450C212yesmaximal, complemented
4#20299449C212yesmaximal, complemented
5#121×D113C211yesmaximal, characteristic
6C22×#11744753—21no—
7C2×C4⋊#90673—21no—
8C2×C22⋊#90673—21no—
9#16813679—21no—
10#16813679C2212yescomplemented
11(C2×#90673)⋊C4C2212yescomplemented
12C2×D4×D113—21no—
13C2×D4×D113C411yescharacteristic, complemented
14C22×C4×D113C2211yescharacteristic
15#16813597C2211yescharacteristic
16#16813596C411yescharacteristic, complemented
17#16813595—21no—
18#16813594—21no—
19#16813593C2211yescharacteristic
20C4⋊C4×D113C411yescharacteristic, complemented
21C22⋊C4×D113—21no—
22#121×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24C2×#11744753—22no—
25C2×#11744753—42no—
26C4⋊#90673—42no—
27C22⋊#90673—42no—
28C23×D113—21no—
29C23×D113D411yescharacteristic
30C2×D452—21no—
31C2×D452C2×C411yescharacteristic
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34C2×C22⋊D113—21no—
35D4×D113—42no—
36D4×D113—42no—
37D4×D113—42no—
38C22×Dic113D411yescharacteristic
39C2×C4×D113—21no—
40C2×C4×D113—42no—
41C2×C4×D113C2×C411yescharacteristic
42C2×C4×D113D411yescharacteristic
43C2×C4×D113D411yescharacteristic
44C2×C4×D113C2311yescharacteristic
45C4⋊Dic113C2×C411yescharacteristic
46#14268626—21no—
47C22⋊Dic113—21no—
48#14268624—21no—
49#14268624—21no—
50C2×D4×C113—21no—
51C2×D4×C113C2×C411yescharacteristic
52C22×C4×C113C2×C411yescharacteristic
53C4⋊C4×C113C2×C411yescharacteristic
54C22⋊C4×C113—21no—
55C23×C113—21no—
56C23×C113C22⋊C411yescharacteristic
57C22×D113—21no—
58C22×D113—41no—
59C22×D113—41no—
60C22×D113—42no—
61C22×D113—42no—
62C22×D113—42no—
63C22×D113C22⋊C411yescharacteristic
64C22×D113D812yes—
65C22×D113SD1612yes—
66C22×D113C2×D411yescharacteristic
67C2×#90673—42no—
68C2×#90673—42no—
69C2×#90673—42no—
70D4×C113—41no—
71D4×C113—42no—
72C2×C4×C113—21no—
73C2×C4×C113—41no—
74C2×C4×C113C22⋊C411yescharacteristic
75C2×C4×C113C22×C411yescharacteristic
76C22⋊D113—42no—
77C22⋊D113—41no—
78C22⋊D113—41no—
79C22⋊D113—42no—
80C2×Dic113—22no—
81C2×Dic113—21no—
82C2×Dic113C22⋊C411yescharacteristic
83C2×Dic113C2×D411yescharacteristic
84D452—41no—
85D452—41no—
86D452—41no—
87C4×D113—22no—
88C4×D113—22no—
89C4×D113—41no—
90C4×D113—41no—
91C4×D113—42no—
92#11744753—42no—
93C22×C113—21no—
94C22×C113—21no—
95C22×C113—41no—
96C22×C113—41no—
97C22×C113—41no—
98C22×C113#10212yes—
99C22×C113C2×C22⋊C411yescharacteristic
100C2×D113—21no—
101C2×D113—21no—
102C2×D113—21no—
103C2×D113—21no—
104C2×D113—42no—
105C2×D113—42no—
106C2×D113—41no—
107C2×D113—41no—
108C2×D113—41no—
109C2×D113—84no—
110C2×D113#10212yes—
111C2×D113C2×D811yescharacteristic
112C2×D113C2×SD1611yescharacteristic
113#90673—82no—
114C4×C113—21no—
115C4×C113—21no—
116C4×C113—41no—
117Dic113—21no—
118Dic113—41no—
119Dic113#9912yes—
120C2×C113—22no—
121C2×C113—81no—
122C2×C113C2×#9911yescharacteristic
123C2×C113C2×#10211yescharacteristic
124C2×C113#42111yescharacteristic
125D113—21no—
126D113—22no—
127D113—21no—
128D113—81no—
129#1519—1131nomaximal, Sylow
130C113#151911yescharacteristic, complemented, Sylow
131C2×#121—1131no—
132C2×C22⋊C8—1131no—
133#380—1131no—
134#327—1132no—
135#327—1132no—
136C22×D4—1131no—
137C22×D4—2261no—
138C23×C4—1131no—
139C22×C8—2261no—
140#121—1131no—
141#121—1131no—
142#121—1131no—
143#121—2261no—
144#121—2261no—
145#121#9067311yescharacteristic, complemented
146C2×C4⋊C4—1131no—
147C2×C4⋊C4—2261no—
148C2×C22⋊C4—2261no—
149C2×C22⋊C4—2261no—
150C22⋊C8—1132no—
151C22⋊C8—2261no—
152#95—1132no—
153C24—1131no—
154C24—2261no—
155C2×D4—21no—
156C2×D4—1131no—
157C2×D4—4522no—
158C2×D4—4522no—
159C2×D4—4522no—
160C2×D4—2261no—
161C2×D4—2261no—
162C2×D4—2261no—
163C2×D4—2261no—
164C2×D4C2×#9067311yescharacteristic
165C22×C4—1131no—
166C22×C4—1131no—
167C22×C4—1131no—
168C22×C4—1131no—
169C22×C4—1131no—
170C22×C4—4522no—
171C22×C4—2261no—
172C22×C4—2262no—
173C22×C4C2×#9067311yescharacteristic
174C2×C8—4522no—
175C2×C8—2262no—
176C4⋊C4—1131no—
177C4⋊C4—4522no—
178C4⋊C4—2261no—
179C4⋊C4C2×#9067311yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—4522no—
182C22⋊C4—2261no—
183C22⋊C4—2261no—
184C22⋊C4—2261no—
185C23—21no—
186C23—1132no—
187C23—1132no—
188C23—1131no—
189C23—1131no—
190C23—4521no—
191C23—4521no—
192C23—4522no—
193C23—4522no—
194C23—4522no—
195C23—2261no—
196C23C22⋊#9067311yescharacteristic
197D4—41no—
198D4—42no—
199D4—4521no—
200D4—4521no—
201D4—4521no—
202D4—4522no—
203D4—4521no—
204D4—4521no—
205D4—4522no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—1131no—
209C2×C4—1131no—
210C2×C4—4521no—
211C2×C4—4521no—
212C2×C4—4522no—
213C2×C4—4522no—
214C2×C4—4522no—
215C2×C4—4522no—
216C2×C4—2262no—
217C2×C4—2262no—
218C2×C4—2262no—
219C2×C4—2261no—
220C2×C4C22⋊#9067311yescharacteristic
221C2×C4C22×#9067311yescharacteristic
222C8—4522no—
223C22—21no—
224C22—21no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—1131no—
229C22—1132no—
230C22—1131no—
231C22—9044no—
232C22—4522no—
233C22—4522no—
234C22—4521no—
235C22—4521no—
236C22—4521no—
237C22—2261no—
238C22—2261no—
239C22—2261no—
240C22—2261no—
241C22#1681368412yes—
242C22C2×C22⋊#9067311yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—1132no—
247C4—9042no—
248C4—4521no—
249C4—2261no—
250C2—22no—
251C2—81no—
252C2—9041no—
253C2—2261no—
254C2—2262no—
255C2—2261no—
256C2D113⋊#9911yescharacteristic
257C2C2×#1681368411yescharacteristic
258C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#121×C113C4
socleC22×C113C2×C22⋊C4
prime radical#121×D113C2
cosocleC2×C4×D113C23
hypercenter#121#90673
hypocenterC113#1519
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#16813679C2semidirect
2. #20299540C2semidirect
3. #20299450C2semidirect
4. #20299449C2semidirect
10. #16813679C22semidirect
11. (C2×#90673)⋊C4C22semidirect
13. C2×D4×D113C4semidirect
16. #16813596C4semidirect
20. C4⋊C4×D113C4semidirect
22. #121×C113C4semidirect
130. C113#1519semidirect
145. #121#90673semidirect

Maximal subgroups

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

subgroupindex
C2×#168136792
#202995402
#202994502
#202994492
#121×D1132
#1519113