Finite Group Databasebeta

← #28391115

Subgroups — #28391115

Order 14464.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#20299160C211yesmaximal, characteristic
2#20299071C211yesmaximal, characteristic, complemented
3C2×#16813536C211yesmaximal, characteristic, complemented
4C2×#16813536C211yesmaximal, characteristic, complemented
5C2×#16813536C211yesmaximal, characteristic, complemented
6#20298364C211yesmaximal, characteristic, complemented
7#342×C113C211yesmaximal, characteristic, complemented
8C22×C22⋊D113C2211yescharacteristic
9C22×C22⋊D113C2211yescharacteristic
10#16813606—21no—
11#16813606C412yescomplemented
12#16813596—22no—
13#16813592—21no—
14#16813592C412yescomplemented
15C4×C22⋊D113—22no—
16#16813582—22no—
17#16813578—21no—
18C2×C22⋊Dic113C2211yescharacteristic
19C2×C22⋊Dic113C2211yescharacteristic
20C22⋊C4×D113—21no—
21#16813536—22no—
22#16813536—22no—
23#16813536—22no—
24C2×C22⋊C4×C113C2211yescharacteristic
25C2×C22⋊C4×C113C2211yescharacteristic
26C2×C22⋊C4×C113C2211yescharacteristic
27C23×D113C2×C411yescharacteristic, complemented
28C23×D113D411yescharacteristic
29C2×D452—22no—
30C2×C22⋊D113—21no—
31C2×C22⋊D113—21no—
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34C2×C22⋊D113—21no—
35C2×C22⋊D113—21no—
36C2×C22⋊D113—21no—
37C2×C22⋊D113—21no—
38C2×C22⋊D113—21no—
39C2×C22⋊D113—21no—
40C2×C22⋊D113C2×C412yes—
41C2×C22⋊D113D412yes—
42C22×Dic113—21no—
43C22×Dic113—21no—
44C22×Dic113C2×C411yescharacteristic, complemented
45C22×Dic113D411yescharacteristic
46C2×C4×D113—22no—
47C4⋊Dic113—22no—
48#14268626—22no—
49C22⋊Dic113—21no—
50C22⋊Dic113—21no—
51C22⋊Dic113—21no—
52C22⋊Dic113D412yescomplemented
53#14268624—22no—
54#14268624—22no—
55#14268624—22no—
56C4×Dic113—22no—
57C24×C113C2311yescharacteristic
58C22×C4×C113—21no—
59C22×C4×C113—21no—
60C22×C4×C113—21no—
61C22⋊C4×C113—21no—
62C22⋊C4×C113—21no—
63C22⋊C4×C113—21no—
64C22⋊C4×C113—21no—
65C22⋊C4×C113C2×C412yescomplemented
66C22⋊C4×C113D412yescomplemented
67C23×C113—81no—
68C23×C113C22×C411yescharacteristic
69C23×C113C2×D411yescharacteristic
70C23×C113C2×D411yescharacteristic
71C23×C113C2×D411yescharacteristic
72C23×C113C2×D411yescharacteristic
73C23×C113#4111yescharacteristic
74C23×C113#4111yescharacteristic
75C22×D113—21no—
76C22×D113—21no—
77C22×D113—21no—
78C22×D113—21no—
79C22×D113—21no—
80C22×D113—81no—
81C22×D113—81no—
82C22×D113C22⋊C412yes—
83C2×C4×C113—22no—
84C2×C4×C113—22no—
85C2×C4×C113—41no—
86C2×C4×C113—81no—
87C2×C4×C113—81no—
88C2×C4×C113—81no—
89C22⋊D113—22no—
90C22⋊D113—22no—
91C22⋊D113—22no—
92C22⋊D113—22no—
93C22⋊D113—41no—
94C22⋊D113—41no—
95C22⋊D113—41no—
96C22⋊D113—41no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113—21no—
100C2×Dic113—21no—
101C2×Dic113—21no—
102C2×Dic113—22no—
103C2×Dic113—41no—
104C2×Dic113—81no—
105C2×Dic113—81no—
106C2×Dic113C22⋊C412yes—
107D452—82no—
108C4×D113—82no—
109C22×C113—41no—
110C22×C113—41no—
111C22×C113—41no—
112C22×C113—41no—
113C22×C113—41no—
114C22×C113—41no—
115C22×C113—41no—
116C22×C113C2×C22⋊C411yescharacteristic
117C22×C113C4×D411yescharacteristic
118C22×C113C4×D411yescharacteristic
119C22×C113#12011yescharacteristic
120C22×C113#12111yescharacteristic
121C22×C113#12111yescharacteristic
122C22×C113#12311yescharacteristic
123C2×D113—22no—
124C2×D113—42no—
125C2×D113—42no—
126C2×D113—42no—
127C2×D113—41no—
128C2×D113—81no—
129C2×D113—81no—
130C2×D113—81no—
131C4×C113—42no—
132C4×C113—42no—
133C4×C113—81no—
134Dic113—22no—
135Dic113—42no—
136Dic113—41no—
137Dic113—81no—
138C2×C113—21no—
139C2×C113—21no—
140C2×C113—21no—
141C2×C113—21no—
142C2×C113—21no—
143C2×C113—21no—
144C2×C113—21no—
145C2×C113#38611yescharacteristic
146D113—42no—
147D113—81no—
148#1913—1131nomaximal, Sylow
149C113#191311yescharacteristic, complemented, Sylow
150#534—1131no—
151#518—1131no—
152C2×#99—1131no—
153C2×#99—1131no—
154C2×#99—1131no—
155#342—1131no—
156#342D11311yescharacteristic, complemented
157C22×D4—1131no—
158C22×D4—1131no—
159#123—1132no—
160#123—2261no—
161#121—2262no—
162#120—1132no—
163#120—2261no—
164C4×D4—2262no—
165C4×D4—2262no—
166#117—2261no—
167C2×C22⋊C4—1131no—
168C2×C22⋊C4—1131no—
169C2×C22⋊C4—2261no—
170C2×C22⋊C4C2×D11311yescharacteristic
171C2×C22⋊C4C2×D11311yescharacteristic
172C2×C22⋊C4C2×D11311yescharacteristic
173#99—2262no—
174#99—2262no—
175#99—2262no—
176C24—1131no—
177C24—1131no—
178C24C22×D11311yescharacteristic
179C2×D4—1132no—
180C2×D4—1132no—
181C2×D4—2262no—
182C2×D4—2261no—
183C2×D4—2261no—
184C2×D4—2261no—
185C2×D4—2261no—
186C2×D4—2261no—
187C2×D4—2261no—
188C2×D4—2261no—
189C2×D4—2261no—
190C2×D4—2261no—
191C2×D4—2261no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—1131no—
196C22×C4—1131no—
197C22×C4—2262no—
198C22×C4—2261no—
199C22×C4—2261no—
200C4⋊C4—2262no—
201C4⋊C4—2262no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—21no—
206C22⋊C4—1132no—
207C22⋊C4—2262no—
208C22⋊C4—2262no—
209C22⋊C4—2262no—
210C22⋊C4—2261no—
211C22⋊C4—2261no—
212C22⋊C4—2261no—
213C22⋊C4C4×D11312yescomplemented
214C22⋊C4D45212yescomplemented
215C42—2262no—
216C23—81no—
217C23—1132no—
218C23—9041no—
219C23—9041no—
220C23—2261no—
221C23—2261no—
222C23—2261no—
223C23—2261no—
224C23—2261no—
225C23C2×C4×D11311yescharacteristic
226C23D4×D11311yescharacteristic
227C23D4×D11311yescharacteristic
228C23D4×D11311yescharacteristic
229C23C2×D45211yescharacteristic
230C23#1426864711yescharacteristic
231C23#1426864811yescharacteristic
232D4—9042no—
233D4—4521no—
234D4—4521no—
235D4—4521no—
236D4—4521no—
237D4—2262no—
238D4—2262no—
239D4—2262no—
240D4—2262no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—1132no—
248C2×C4—9042no—
249C2×C4—9041no—
250C2×C4—9041no—
251C2×C4—4521no—
252C2×C4—2261no—
253C2×C4—2261no—
254C2×C4—2261no—
255C2×C4—2262no—
256C2×C4—2261no—
257C2×C4—2261no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—9041no—
266C22—9041no—
267C22—9041no—
268C22—4522no—
269C22—4522no—
270C22—4522no—
271C22—4521no—
272C22—2262no—
273C22C22⋊C4×D11311yescharacteristic
274C22#1681358411yescharacteristic
275C22C4×D45211yescharacteristic
276C22#1681359211yescharacteristic
277C22#1681359511yescharacteristic
278C22#1681359711yescharacteristic
279C22#1681360711yescharacteristic
280C4—42no—
281C4—42no—
282C4—81no—
283C4—9041no—
284C4—4522no—
285C4—4521no—
286C4—2262no—
287C2—21no—
288C2—21no—
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2—21no—
294C2—9041no—
295C2—4522no—
296C2#2029847611yescharacteristic
subgroupG/H
centerC2#20298476
commutatorC23×C113C22×C4
FrattiniC24C22×D113
Fitting#342×C113C2
socleC2×C113#386
prime radical#20299160C2
cosocleC24×C113C23
hypercenter#342D113
hypocenterC113#1913
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #20299071C2semidirect
3. C2×#16813536C2semidirect
4. C2×#16813536C2semidirect
5. C2×#16813536C2semidirect
6. #20298364C2semidirect
7. #342×C113C2semidirect
11. #16813606C4semidirect
14. #16813592C4semidirect
27. C23×D113C2×C4semidirect
44. C22×Dic113C2×C4semidirect
52. C22⋊Dic113D4semidirect
65. C22⋊C4×C113C2×C4semidirect
66. C22⋊C4×C113D4semidirect
149. C113#1913semidirect
156. #342D113semidirect
213. C22⋊C4C4×D113semidirect
214. C22⋊C4D452semidirect

Maximal subgroups

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

subgroupindex
#202991602
#202990712
C2×#168135362
#202983642
#342×C1132
#1913113