Finite Group Databasebeta

← #28393834

Subgroups — #28393834

Order 14464.

560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4×C22⋊D113C211yesmaximal, characteristic
2C2×#16813581C211yesmaximal, characteristic, complemented
3#20298538C211yesmaximal, characteristic, complemented
4#20298535C211yesmaximal, characteristic, complemented
5#20298530C211yesmaximal, characteristic, complemented
6#20298525C211yesmaximal, characteristic, complemented
7#20298523C212yesmaximal, complemented
8#20298514C212yesmaximal
9C4×C4⋊Dic113C212yesmaximal, complemented
10C4×#14268624C212yesmaximal, complemented
11C4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
12C22×C22⋊D113C2211yescharacteristic
13C22×C4×D113C2211yescharacteristic
14C4×C22⋊D113—24no—
15#16813581—24no—
16C2×C4⋊Dic113C2212yes—
17C2×C4⋊Dic113C2212yes—
18C2×C4⋊Dic113C2211yescharacteristic
19C2×C4⋊Dic113C2211yescharacteristic
20C2×#14268626C2211yescharacteristic
21C2×C22⋊Dic113C2212yes—
22C2×C22⋊Dic113C2211yescharacteristic
23C2×#14268624C2212yes—
24C2×#14268624C2212yes—
25C2×#14268624C2211yescharacteristic
26C2×C4×Dic113C2212yes—
27C2×C4×Dic113C2211yescharacteristic
28#16813529C2212yes—
29#16813529C2212yes—
30#16813529C2212yes—
31#16813529C2212yes—
32C23×C4×C113C2211yescharacteristic
33C2×C22⋊C4×C113C2212yes—
34C2×C42×C113C2212yes—
35#95×C113C2211yescharacteristic
36#95×C113C2211yescharacteristic
37C23×D113C2311yescharacteristic
38C2×C22⋊D113—22no—
39C2×C22⋊D113—22no—
40C2×C22⋊D113—22no—
41C22×Dic113C2311yescharacteristic
42C22×Dic113C2312yes—
43C22×Dic113C2312yes—
44C22×Dic113C2311yescharacteristic
45C22×Dic113C2311yescharacteristic
46C2×C4×D113—22no—
47C2×C4×D113—24no—
48C4⋊Dic113—22no—
49C4⋊Dic113—22no—
50C4⋊Dic113—24no—
51C4⋊Dic113—24no—
52#14268626—22no—
53C22⋊Dic113—24no—
54C22⋊Dic113—22no—
55#14268624—24no—
56#14268624—22no—
57#14268624—24no—
58C4×Dic113—24no—
59C4×Dic113—22no—
60C24×C113C2311yescharacteristic
61C22×C4×C113—24no—
62C22×C4×C113D414yes—
63C22×C4×C113C2312yes—
64C22×C4×C113C2311yescharacteristic
65C22×C4×C113C2312yes—
66C22×C4×C113C2311yescharacteristic
67C22⋊C4×C113—24no—
68C42×C113—24no—
69C23×C113—22no—
70C23×C113—22no—
71C23×C113—21no—
72C23×C113—21no—
73C23×C113C2×D412yes—
74C23×C113C2411yescharacteristic
75C22×D113—21no—
76C22×D113—22no—
77C22×D113—22no—
78C22×D113—21no—
79C22×D113#4112yes—
80C2×C4×C113—22no—
81C2×C4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113—28no—
84C2×C4×C113—22no—
85C2×C4×C113—22no—
86C2×C4×C113—22no—
87C2×C4×C113C2×D412yes—
88C2×C4×C113C2×D412yes—
89C2×C4×C113#4114yes—
90C2×C4×C113#4114yes—
91C22⋊D113—28no—
92C2×Dic113—21no—
93C2×Dic113—21no—
94C2×Dic113—21no—
95C2×Dic113—22no—
96C2×Dic113—22no—
97C2×Dic113—21no—
98C2×Dic113—22no—
99C2×Dic113—22no—
100C2×Dic113—22no—
101C2×Dic113—22no—
102C2×Dic113—22no—
103C2×Dic113—22no—
104C2×Dic113#4112yes—
105C4×D113—44no—
106C22×C113—22no—
107C22×C113—22no—
108C22×C113—22no—
109C22×C113—42no—
110C22×C113—42no—
111C22×C113C22×D411yescharacteristic
112C22×C113C2×#4111yescharacteristic
113C22×C113C2×#4111yescharacteristic
114C22×C113C2×#4112yes—
115C22×C113C2×#4112yes—
116C2×D113—22no—
117C2×D113—24no—
118C2×D113—41no—
119C2×D113—42no—
120C2×D113—41no—
121C4×C113—22no—
122C4×C113—24no—
123C4×C113—42no—
124C4×C113#12314yes—
125Dic113—22no—
126Dic113—41no—
127Dic113—42no—
128Dic113—41no—
129Dic113—42no—
130C2×C113—42no—
131C2×C113C2×#12311yescharacteristic
132C2×C113#52511yescharacteristic
133C2×C113#52912yes—
134C2×C113#52912yes—
135C2×C113#53211yescharacteristic
136D113—42no—
137#2395—1131nomaximal, Sylow
138C113#239511yescharacteristic, complemented, Sylow
139C2×C4×D4—1131no—
140C2×#117—1131no—
141#400—1131no—
142#399—1131no—
143#398—1131no—
144#397—1132no—
145#397—1131no—
146#394—1132no—
147C4×C4⋊C4—1132no—
148C4×C22⋊C4—1132no—
149C4×C22⋊C4D11311yescharacteristic, complemented
150C22×D4—1131no—
151C23×C4—1131no—
152C23×C4C2×D11311yescharacteristic
153C4×D4—2264no—
154#117—2264no—
155C2×C4⋊C4—1131no—
156C2×C4⋊C4—1131no—
157C2×C4⋊C4—1131no—
158C2×C4⋊C4—1132no—
159C2×C4⋊C4—1132no—
160C2×C22⋊C4—1132no—
161C2×C22⋊C4—1131no—
162C2×C22⋊C4—1131no—
163C2×C22⋊C4—1132no—
164C2×C22⋊C4—1132no—
165C2×C22⋊C4C2×D11312yes—
166C2×C42—1132no—
167C2×C42—1131no—
168C2×C42C2×D11312yes—
169#95—1132no—
170#95—1132no—
171#95—1132no—
172#95—1132no—
173#95C2×D11311yescharacteristic
174#95C2×D11311yescharacteristic
175C24—1131no—
176C24C22×D11311yescharacteristic
177C2×D4—2262no—
178C2×D4—2262no—
179C2×D4—2262no—
180C22×C4—24no—
181C22×C4—1131no—
182C22×C4—1131no—
183C22×C4—1131no—
184C22×C4—1132no—
185C22×C4—1132no—
186C22×C4—2262no—
187C22×C4—2264no—
188C22×C4D45214yes—
189C22×C4C22×D11312yes—
190C22×C4C22×D11311yescharacteristic
191C22×C4C22×D11312yes—
192C22×C4C22×D11311yescharacteristic
193C4⋊C4—2264no—
194C4⋊C4—2262no—
195C4⋊C4—2262no—
196C4⋊C4—2262no—
197C4⋊C4—2264no—
198C22⋊C4—24no—
199C22⋊C4—2264no—
200C22⋊C4—2264no—
201C22⋊C4—2262no—
202C22⋊C4—2262no—
203C22⋊C4—2264no—
204C42—24no—
205C42—2264no—
206C42—2262no—
207C23—21no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—1132no—
212C23—2261no—
213C23—2261no—
214C23—2262no—
215C23—2262no—
216C23C2×D45212yes—
217C23C23×D11311yescharacteristic
218D4—2268no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—28no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—1132no—
227C2×C4—4524no—
228C2×C4—2261no—
229C2×C4—2262no—
230C2×C4—2262no—
231C2×C4—2261no—
232C2×C4—2262no—
233C2×C4—2262no—
234C2×C4—2262no—
235C2×C4—2262no—
236C2×C4—2262no—
237C2×C4—2262no—
238C2×C4—2261no—
239C2×C4—2261no—
240C2×C4C2×D45212yes—
241C2×C4C2×D45212yes—
242C2×C4#1426864614yes—
243C2×C4#1426864714yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—4521no—
250C22—4522no—
251C22—4521no—
252C22—2262no—
253C22—2264no—
254C22C22×D45211yescharacteristic
255C22#41×D11311yescharacteristic
256C22#41×D11311yescharacteristic
257C22C2×#1426864612yes—
258C22C2×#1426864712yes—
259C4—22no—
260C4—24no—
261C4—42no—
262C4—4521no—
263C4—4522no—
264C4—4521no—
265C4—4522no—
266C4—2262no—
267C4#1681360614yes—
268C2—42no—
269C2—4522no—
270C2C2×#1681360611yescharacteristic
271C2#2029911011yescharacteristic
272C2#2029912812yes—
273C2#2029913012yes—
274C2#2029914811yescharacteristic
subgroupG/H
centerC22×C4C22×D113
commutator, socle, cosocleC23×C113C24
FrattiniC23C23×D113
FittingC4×C22⋊C4×C113C2
prime radicalC22×C22⋊D113C22
hypercenterC4×C22⋊C4D113
hypocenterC113#2395
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16813581C2semidirect
3. #20298538C2semidirect
4. #20298535C2semidirect
5. #20298530C2semidirect
6. #20298525C2semidirect
7. #20298523C2semidirect
9. C4×C4⋊Dic113C2semidirect
10. C4×#14268624C2semidirect
11. C4×C22⋊C4×C113C2semidirect
138. C113#2395semidirect
149. C4×C22⋊C4D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1132
C2×#168135812
#202985382
#202985352
#202985302
#202985252
#202985232
#202985142
C4×C4⋊Dic1132
C4×#142686242
C4×C22⋊C4×C1132
#2395113