Finite Group Databasebeta

← #28406624

Subgroups — #28406624

Order 14464.

380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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#20299665C211yesmaximal, characteristic, complemented
2C2×#16813681C212yesmaximal, complemented
3D113⋊#99C211yesmaximal, characteristic, complemented
4#20299475C212yesmaximal, complemented
5#20299159C211yesmaximal, characteristic
6D4×#90673—24no—
7#16813701—21no—
8C2×C22⋊#90673—21no—
9C2×C22⋊#90673C2212yes—
10C2×C22⋊#90673C2212yes—
11#16813681—24no—
12#16813681—21no—
13#16813680—21no—
14C22×D452C2211yescharacteristic
15C2×D4×D113C2211yescharacteristic
16#16813607—21no—
17#16813605C411yescharacteristic, complemented
18#16813597—21no—
19#16813595—21no—
20#16813592—21no—
21#16813592C411yescharacteristic, complemented
22#16813590C411yescharacteristic, complemented
23C22⋊C4×D113C2211yescharacteristic
24#123×C113C411yescharacteristic, complemented
25C22×#90673—22no—
26C22×#90673—22no—
27C22×#90673—22no—
28C4⋊#90673—22no—
29C22⋊#90673—22no—
30C22⋊#90673—22no—
31C22⋊#90673—22no—
32C22⋊#90673—22no—
33C22⋊#90673D414yescomplemented
34C4×#90673—22no—
35C23×D113C2×C411yescharacteristic, complemented
36C23×D113D411yescharacteristic
37C23×D113C2311yescharacteristic
38C2×D452—21no—
39C2×D452—21no—
40C2×D452—22no—
41C2×D452—22no—
42C2×D452—21no—
43C2×D452D411yescharacteristic
44C2×C22⋊D113—21no—
45C2×C22⋊D113C2×C411yescharacteristic
46C2×C22⋊D113D411yescharacteristic
47D4×D113—22no—
48D4×D113—22no—
49C2×C4×D113—21no—
50C2×C4×D113D411yescharacteristic
51#14268626—21no—
52C22⋊Dic113C2×C411yescharacteristic, complemented
53#14268624—21no—
54#14268624—21no—
55#14268624—21no—
56#14268624—21no—
57C2×D4×C113C2×C411yescharacteristic
58C22×C4×C113C2×C411yescharacteristic, complemented
59C4⋊C4×C113—21no—
60C22⋊C4×C113—21no—
61C22⋊C4×C113C2×C411yescharacteristic, complemented
62C23×C113C22⋊C411yescharacteristic
63C23×C113C22×C411yescharacteristic
64C22×D113—21no—
65C22×D113—21no—
66C22×D113—21no—
67C22×D113—22no—
68C22×D113—81no—
69C22×D113—81no—
70C22×D113—81no—
71C22×D113C22⋊C411yescharacteristic
72C22×D113C2×D412yes—
73C22×D113C2×D411yescharacteristic
74C22×D113C2×D411yescharacteristic
75C22×D113#4112yes—
76C2×#90673—24no—
77C2×#90673—42no—
78C2×#90673—82no—
79C2×#90673—82no—
80C2×#90673—82no—
81D4×C113—22no—
82C2×C4×C113—21no—
83C2×C4×C113—21no—
84C2×C4×C113—22no—
85C2×C4×C113C22⋊C411yescharacteristic
86C22⋊D113—22no—
87C22⋊D113—22no—
88C22⋊D113—81no—
89C2×Dic113—21no—
90C2×Dic113C22⋊C411yescharacteristic
91D452—22no—
92D452—41no—
93D452—42no—
94D452—41no—
95D452—81no—
96C4×D113—21no—
97C4×D113—21no—
98C4×D113—81no—
99C22×C113—21no—
100C22×C113—41no—
101C22×C113—41no—
102C22×C113C2×C22⋊C411yescharacteristic
103C22×C113C4×D412yes—
104C2×D113—21no—
105C2×D113—41no—
106C2×D113—42no—
107C2×D113—42no—
108C2×D113—41no—
109C2×D113—42no—
110C2×D113—41no—
111C2×D113—41no—
112C2×D113—41no—
113C2×D113—41no—
114C2×D113—81no—
115C2×D113—82no—
116C2×D113#12011yescharacteristic
117C2×D113#12112yes—
118C2×D113#12311yescharacteristic
119#90673—44no—
120#90673—82no—
121C4×C113—21no—
122C4×C113—41no—
123C4×C113—41no—
124Dic113—21no—
125Dic113—41no—
126C2×C113—21no—
127C2×C113—22no—
128C2×C113—41no—
129C2×C113#38611yescharacteristic
130D113—21no—
131D113—22no—
132D113—21no—
133D113—41no—
134D113—81no—
135#1913—1131nomaximal, Sylow
136C113#191311yescharacteristic, complemented, Sylow
137#534—1131no—
138#518—1131no—
139C2×#99—1131no—
140C2×#99—1132no—
141#342—1132no—
142C22×D4—1131no—
143C22×D4—1131no—
144#123—1131no—
145#123—2261no—
146#123#9067311yescharacteristic, complemented
147#121—2261no—
148#121—2261no—
149#120—1131no—
150#120—1131no—
151#120—2261no—
152C4×D4—2264no—
153#117—2261no—
154C2×C22⋊C4—1132no—
155C2×C22⋊C4—1131no—
156C2×C22⋊C4—1132no—
157C2×C22⋊C4—2261no—
158#99—2264no—
159#99—2261no—
160#99—2261no—
161C24—1131no—
162C24—1131no—
163C24—1131no—
164C2×D4—1131no—
165C2×D4—1131no—
166C2×D4—1131no—
167C2×D4—2261no—
168C2×D4—2262no—
169C2×D4—2261no—
170C2×D4—2261no—
171C2×D4—2262no—
172C2×D4—2262no—
173C2×D4—2262no—
174C2×D4—2261no—
175C2×D4C2×#9067311yescharacteristic
176C22×C4—1131no—
177C22×C4—2261no—
178C22×C4—2262no—
179C22×C4—2262no—
180C22×C4—2262no—
181C22×C4C2×#9067311yescharacteristic, complemented
182C4⋊C4—21no—
183C4⋊C4—2261no—
184C4⋊C4—2262no—
185C22⋊C4—21no—
186C22⋊C4—1134no—
187C22⋊C4—1131no—
188C22⋊C4—2261no—
189C22⋊C4—2261no—
190C22⋊C4—2261no—
191C22⋊C4—2262no—
192C22⋊C4—2262no—
193C22⋊C4—2262no—
194C22⋊C4—2262no—
195C22⋊C4—2261no—
196C22⋊C4C2×#9067311yescharacteristic, complemented
197C42—2262no—
198C23—1131no—
199C23—1131no—
200C23—1132no—
201C23—1132no—
202C23—1131no—
203C23—9041no—
204C23—9041no—
205C23—9041no—
206C23—2261no—
207C23—2261no—
208C23—2262no—
209C23—2261no—
210C23C22⋊#9067311yescharacteristic
211C23C22×#9067311yescharacteristic
212D4—22no—
213D4—9041no—
214D4—9041no—
215D4—4522no—
216D4—4521no—
217D4—4521no—
218D4—2262no—
219D4—2262no—
220D4—2262no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—1131no—
225C2×C4—9041no—
226C2×C4—9042no—
227C2×C4—9042no—
228C2×C4—9042no—
229C2×C4—4522no—
230C2×C4—2261no—
231C2×C4—2261no—
232C2×C4—2264no—
233C2×C4—2261no—
234C2×C4C22⋊#9067311yescharacteristic
235C22—21no—
236C22—41no—
237C22—41no—
238C22—1132no—
239C22—1131no—
240C22—1131no—
241C22—9042no—
242C22—9041no—
243C22—4521no—
244C22—4521no—
245C22—4521no—
246C22—4521no—
247C22—4522no—
248C22—4522no—
249C22—4521no—
250C22—4522no—
251C22—4521no—
252C22—2261no—
253C22C2×C22⋊#9067311yescharacteristic
254C22D4×#9067312yes—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—9042no—
259C4—4521no—
260C4—4524no—
261C4—2261no—
262C2—21no—
263C2—22no—
264C2—41no—
265C2—9041no—
266C2—4521no—
267C2—2262no—
268C2—2261no—
269C2—2261no—
270C2#2029954611yescharacteristic
subgroupG/H
centerC2#20299546
commutatorC23×C113C22×C4
FrattiniC23C22×#90673
Fitting#123×C113C4
socleC2×C113#386
prime radical#20299159C2
cosocleC23×D113C23
hypercenter#123#90673
hypocenterC113#1913
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #20299665C2semidirect
2. C2×#16813681C2semidirect
3. D113⋊#99C2semidirect
4. #20299475C2semidirect
17. #16813605C4semidirect
21. #16813592C4semidirect
22. #16813590C4semidirect
24. #123×C113C4semidirect
33. C22⋊#90673D4semidirect
35. C23×D113C2×C4semidirect
52. C22⋊Dic113C2×C4semidirect
58. C22×C4×C113C2×C4semidirect
61. C22⋊C4×C113C2×C4semidirect
136. C113#1913semidirect
146. #123#90673semidirect
181. C22×C4C2×#90673semidirect
196. C22⋊C4C2×#90673semidirect

Maximal subgroups

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

subgroupindex
#202996652
C2×#168136812
D113⋊#992
#202994752
#202991592
#1913113