Finite Group Databasebeta

← #28391029

Subgroups — #28391029

Order 14464.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16813603C211yesmaximal, characteristic
2C2×#16813578C211yesmaximal, characteristic, complemented
3C2×#16813537C211yesmaximal, characteristic
4#20298459C211yesmaximal, characteristic, complemented
5#20298364C211yesmaximal, characteristic, complemented
6#20298364C211yesmaximal, characteristic, complemented
7C2×#99×C113C211yesmaximal, characteristic
8C23×Dic113C2211yescharacteristic
9#16813603—21no—
10#16813603—21no—
11#16813603—22no—
12#16813578—22no—
13#16813578—22no—
14C2×#14268626—21no—
15C2×#14268626C412yescomplemented
16C2×C22⋊Dic113C412yescomplemented
17C2×C22⋊Dic113C2211yescharacteristic
18C2×C22⋊Dic113C2211yescharacteristic
19C2×C22⋊Dic113C2211yescharacteristic
20C2×C4×Dic113—21no—
21#16813537—22no—
22#16813529—22no—
23C22×D4×C113C2211yescharacteristic
24C2×C22⋊C4×C113C2211yescharacteristic
25C2×C22⋊C4×C113C2211yescharacteristic
26#99×C113—22no—
27C22×Dic113—21no—
28C22×Dic113—21no—
29C22×Dic113—21no—
30C22×Dic113—21no—
31C22×Dic113—21no—
32C22×Dic113—21no—
33C22×Dic113C2×C412yes—
34C22×Dic113C2×C412yes—
35C22×Dic113D411yescharacteristic
36C22×Dic113D411yescharacteristic
37C22×Dic113D412yes—
38#14268626—24no—
39#14268626—22no—
40#14268626—22no—
41C22⋊Dic113—21no—
42C22⋊Dic113—21no—
43C22⋊Dic113—21no—
44C22⋊Dic113—22no—
45C22⋊Dic113—22no—
46C22⋊Dic113—21no—
47C22⋊Dic113—21no—
48C22⋊Dic113D412yes—
49C4×Dic113—24no—
50C24×C113C2×C411yescharacteristic
51C24×C113C2311yescharacteristic
52C2×D4×C113—21no—
53C2×D4×C113—21no—
54C2×D4×C113—21no—
55C2×D4×C113—21no—
56C2×D4×C113—21no—
57C2×D4×C113—21no—
58C22×C4×C113—21no—
59C22×C4×C113—21no—
60C22×C4×C113C2×C411yescharacteristic
61C22⋊C4×C113—21no—
62C22⋊C4×C113—21no—
63C22⋊C4×C113—21no—
64C22⋊C4×C113D412yes—
65C23×C113—21no—
66C23×C113—21no—
67C23×C113—21no—
68C23×C113—42no—
69C23×C113—42no—
70C23×C113C22×C411yescharacteristic
71C23×C113C2×D411yescharacteristic
72C23×C113C2×D411yescharacteristic
73C23×C113C2×D411yescharacteristic
74C23×C113C2×D411yescharacteristic
75C23×C113#4111yescharacteristic
76C23×C113#4111yescharacteristic
77D4×C113—41no—
78D4×C113—41no—
79D4×C113—41no—
80D4×C113—41no—
81C2×C4×C113—21no—
82C2×C4×C113—21no—
83C2×C4×C113—21no—
84C2×C4×C113—22no—
85C2×C4×C113—42no—
86C2×C4×C113—42no—
87C2×C4×C113—41no—
88C2×Dic113—22no—
89C2×Dic113—22no—
90C2×Dic113—21no—
91C2×Dic113—21no—
92C2×Dic113—22no—
93C2×Dic113—22no—
94C2×Dic113—21no—
95C2×Dic113—21no—
96C2×Dic113—22no—
97C2×Dic113—22no—
98C2×Dic113—42no—
99C2×Dic113—42no—
100C2×Dic113—42no—
101C2×Dic113—41no—
102C2×Dic113C22⋊C412yes—
103C2×Dic113C22⋊C412yes—
104C22×C113—22no—
105C22×C113—22no—
106C22×C113—22no—
107C22×C113—41no—
108C22×C113—41no—
109C22×C113—41no—
110C22×C113—41no—
111C22×C113—41no—
112C22×C113—42no—
113C22×C113—81no—
114C22×C113—81no—
115C22×C113C2×C22⋊C411yescharacteristic
116C22×C113C4×D411yescharacteristic
117C22×C113C4×D411yescharacteristic
118C22×C113#12011yescharacteristic
119C22×C113#12111yescharacteristic
120C22×C113#12111yescharacteristic
121C22×C113#12311yescharacteristic
122C4×C113—42no—
123C4×C113—41no—
124C4×C113—81no—
125Dic113—22no—
126Dic113—22no—
127Dic113—42no—
128Dic113—42no—
129Dic113—81no—
130C2×C113—21no—
131C2×C113—21no—
132C2×C113—21no—
133C2×C113—21no—
134C2×C113—21no—
135C2×C113—21no—
136C2×C113—81no—
137C2×C113#38611yescharacteristic
138C2×C113#41012yes—
139#1899—1131nomaximal, Sylow
140C113#189911yescharacteristic, complemented, Sylow
141C2×#123—1131no—
142C2×#117—1131no—
143C2×#99—1131no—
144C2×#99D11311yescharacteristic
145#381—1131no—
146#342—1131no—
147#342—1131no—
148C22×D4C2×D11311yescharacteristic
149C23×C4—1131no—
150#123—2262no—
151#123—2261no—
152#123—2261no—
153#117—2262no—
154#117—2262no—
155C2×C4⋊C4—1132no—
156C2×C4⋊C4—2261no—
157C2×C22⋊C4—1131no—
158C2×C22⋊C4—1132no—
159C2×C22⋊C4—1131no—
160C2×C22⋊C4—1131no—
161C2×C22⋊C4C2×D11311yescharacteristic
162C2×C22⋊C4C2×D11311yescharacteristic
163C2×C42—2261no—
164#99—22no—
165#99—2262no—
166#95—2262no—
167C24C4×D11311yescharacteristic
168C24C22×D11311yescharacteristic
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—1132no—
178C22×C4—1132no—
179C22×C4—1131no—
180C22×C4—1131no—
181C22×C4—1132no—
182C22×C4—2261no—
183C22×C4—2261no—
184C22×C4—2261no—
185C22×C4—2261no—
186C22×C4—2261no—
187C22×C4—2261no—
188C22×C4C4×D11311yescharacteristic
189C4⋊C4—2262no—
190C4⋊C4—2262no—
191C4⋊C4—2264no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—1132no—
196C22⋊C4—2262no—
197C22⋊C4—2262no—
198C22⋊C4—2261no—
199C22⋊C4—2261no—
200C22⋊C4—2261no—
201C22⋊C4—2261no—
202C22⋊C4—2261no—
203C22⋊C4C22⋊D11312yes—
204C42—2264no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—42no—
209C23—42no—
210C23C2×C4×D11311yescharacteristic
211C23D4×D11311yescharacteristic
212C23D4×D11311yescharacteristic
213C23D4×D11311yescharacteristic
214C23C2×C22⋊D11311yescharacteristic
215C23#1426864611yescharacteristic
216C23#1426864711yescharacteristic
217D4—41no—
218D4—41no—
219D4—41no—
220D4—41no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—1132no—
229C2×C4—1132no—
230C2×C4—4522no—
231C2×C4—4521no—
232C2×C4—4522no—
233C2×C4—4522no—
234C2×C4—2262no—
235C2×C4—2262no—
236C2×C4—2262no—
237C2×C4—2262no—
238C2×C4—2261no—
239C2×C4—2261no—
240C2×C4—2262no—
241C2×C4—2262no—
242C2×C4—2261no—
243C2×C4—2261no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—81no—
254C22—81no—
255C22C22⋊C4×D11311yescharacteristic
256C22#1681358211yescharacteristic
257C22C4×C22⋊D11311yescharacteristic
258C22#1681359011yescharacteristic
259C22#1681359311yescharacteristic
260C22#1681359511yescharacteristic
261C22#1681360411yescharacteristic
262C4—42no—
263C4—41no—
264C4—81no—
265C4—9041no—
266C4—4522no—
267C4—4522no—
268C4—2262no—
269C4—2262no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—81no—
277C2#2029847411yescharacteristic
278C2#2029857012yes—
subgroupG/H
centerC22C22⋊C4×D113
commutatorC23×C113C22×C4
FrattiniC24C22×D113
FittingC2×#99×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×D4×C113C22
cosocleC24×C113C23
hypercenterC2×#99D113
hypocenterC113#1899
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#16813578C2semidirect
4. #20298459C2semidirect
5. #20298364C2semidirect
6. #20298364C2semidirect
15. C2×#14268626C4semidirect
16. C2×C22⋊Dic113C4semidirect
140. C113#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#168136032
C2×#168135782
C2×#168135372
#202984592
#202983642
C2×#99×C1132
#1899113