Finite Group Databasebeta

← #28389101

Subgroups — #28389101

Order 14464.

326 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 63 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#121×D113C211yesmaximal, characteristic
2#20298560C211yesmaximal, characteristic, complemented
3#20298460C211yesmaximal, characteristic, complemented
4#20298333C211yesmaximal, characteristic, complemented
5#20298332C211yesmaximal, characteristic, complemented
6#20298331C211yesmaximal, characteristic, complemented
7#327×C113C211yesmaximal, characteristic, complemented
8C2×D4×D113—21no—
9C2×D4×D113C411yescharacteristic, complemented
10C22×C4×D113C2211yescharacteristic
11C2×#14268630—21no—
12#16813597C411yescharacteristic, complemented
13#16813596C2211yescharacteristic
14#16813595—21no—
15#16813594—21no—
16#16813593C411yescharacteristic, complemented
17C4⋊C4×D113C411yescharacteristic, complemented
18C2×#14268624—21no—
19C22⋊C4×D113—21no—
20C22⋊#11744751C2211yescharacteristic, complemented
21#16813534—21no—
22#16813529—21no—
23#16813529C2211yescharacteristic, complemented
24#121×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic, complemented
26#95×C113C2211yescharacteristic, complemented
27C23×D113—21no—
28C23×D113D411yescharacteristic
29C2×D452—21no—
30C2×D452C2×C411yescharacteristic
31C2×C22⋊D113—21no—
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34D4×D113—42no—
35D4×D113—42no—
36D4×D113—42no—
37C22×Dic113—21no—
38C22×Dic113D411yescharacteristic
39C2×C4×D113—21no—
40C2×C4×D113—42no—
41C2×C4×D113C2×C411yescharacteristic
42C2×C4×D113C2×C411yescharacteristic
43C2×C4×D113D411yescharacteristic
44C2×C4×D113D411yescharacteristic
45#14268630—42no—
46C2×#11744751—21no—
47C4⋊Dic113C2×C411yescharacteristic
48#14268626—21no—
49C22⋊Dic113—21no—
50#14268624—21no—
51#14268624—21no—
52#14268624—42no—
53C2×D4×C113—21no—
54C2×D4×C113C2×C411yescharacteristic
55C22×C4×C113—21no—
56C22×C4×C113C2311yescharacteristic
57C2×C8×C113—21no—
58C4⋊C4×C113C2×C411yescharacteristic
59C22⋊C4×C113—21no—
60C23×C113—21no—
61C23×C113C2×D411yescharacteristic
62C22×D113—21no—
63C22×D113—21no—
64C22×D113—22no—
65C22×D113—21no—
66C22×D113—41no—
67C22×D113—42no—
68C22×D113—42no—
69C22×D113—42no—
70C22×D113C22⋊C411yescharacteristic
71C22×D113C22⋊C411yescharacteristic
72D4×C113—41no—
73D4×C113—41no—
74D4×C113—41no—
75C2×C4×C113—21no—
76C2×C4×C113—41no—
77C2×C4×C113—41no—
78C2×C4×C113—41no—
79C2×C4×C113—41no—
80C2×C4×C113C22×C411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C22⋊D113—42no—
83C22⋊D113—42no—
84C22⋊D113—41no—
85C22⋊D113—41no—
86C2×Dic113—21no—
87C2×Dic113—41no—
88C2×Dic113—41no—
89C2×Dic113—41no—
90C2×Dic113—41no—
91C2×Dic113C22⋊C411yescharacteristic
92C2×Dic113C22⋊C411yescharacteristic
93D452—41no—
94D452—42no—
95C4×D113—22no—
96C4×D113—22no—
97C4×D113—41no—
98C4×D113—41no—
99C4×D113—42no—
100C8×C113—41no—
101#11744751—41no—
102C22×C113—21no—
103C22×C113—21no—
104C22×C113—41no—
105C22×C113—41no—
106C22×C113—41no—
107C22×C113C2×C22⋊C411yescharacteristic
108C22×C113AGL(1,ℤ/8)11yescharacteristic
109C22×C113AGL(1,ℤ/8)11yescharacteristic
110C2×D113—21no—
111C2×D113—21no—
112C2×D113—21no—
113C2×D113—21no—
114C2×D113—21no—
115C2×D113—42no—
116C2×D113—42no—
117C2×D113—41no—
118C2×D113—41no—
119C2×D113—41no—
120C2×D113—84no—
121C2×D113#9912yes—
122C4×C113—21no—
123C4×C113—21no—
124C4×C113—41no—
125C4×C113—81no—
126Dic113—21no—
127Dic113—21no—
128Dic113—41no—
129Dic113—81no—
130C2×C113—21no—
131C2×C113—21no—
132C2×C113—81no—
133C2×C113C2×#9911yescharacteristic
134C2×C113#41811yescharacteristic
135C2×C113#42111yescharacteristic
136D113—22no—
137D113—41no—
138D113—81no—
139#1510—1131nomaximal, Sylow
140C113#151011yescharacteristic, complemented, Sylow
141C2×#121—1131no—
142#407—1131no—
143#381—1131no—
144#327—1131no—
145#327—1131no—
146#327—1131no—
147#327D11311yescharacteristic, complemented
148C22×D4—1131no—
149C22×D4—2261no—
150C23×C4—1131no—
151C2×M16—2261no—
152#121—1131no—
153#121—1131no—
154#121—1131no—
155#121—2261no—
156#121—2261no—
157#121C2×D11311yescharacteristic
158C2×C4⋊C4—1131no—
159C2×C22⋊C4—2261no—
160C2×C22⋊C4—2261no—
161C22⋊C8—1131no—
162C22⋊C8—2261no—
163C22⋊C8C2×D11311yescharacteristic, complemented
164#95—1131no—
165#95—2261no—
166#95C2×D11311yescharacteristic, complemented
167C24—1131no—
168C24—2261no—
169C2×D4—21no—
170C2×D4—1131no—
171C2×D4—4522no—
172C2×D4—4522no—
173C2×D4—4522no—
174C2×D4—2261no—
175C2×D4—2261no—
176C2×D4—2261no—
177C2×D4—2261no—
178C2×D4C4×D11311yescharacteristic
179C22×C4—21no—
180C22×C4—1131no—
181C22×C4—1131no—
182C22×C4—1131no—
183C22×C4—1131no—
184C22×C4—1131no—
185C22×C4—4522no—
186C22×C4—2261no—
187C22×C4—2261no—
188C22×C4C22×D11311yescharacteristic
189M16—4522no—
190C2×C8—21no—
191C2×C8—2261no—
192C4⋊C4—1131no—
193C4⋊C4—2261no—
194C4⋊C4C4×D11311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—4522no—
197C22⋊C4—2261no—
198C22⋊C4—2261no—
199C22⋊C4—2261no—
200C23—21no—
201C23—1131no—
202C23—1131no—
203C23—4521no—
204C23—4522no—
205C23—4522no—
206C23—4522no—
207C23—2262no—
208C23—2261no—
209C23—2261no—
210C23—2261no—
211C23D4×D11311yescharacteristic
212D4—41no—
213D4—41no—
214D4—41no—
215D4—4521no—
216D4—4522no—
217D4—4522no—
218D4—4521no—
219D4—4521no—
220D4—4522no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—1131no—
227C2×C4—1131no—
228C2×C4—4521no—
229C2×C4—4521no—
230C2×C4—4522no—
231C2×C4—4521no—
232C2×C4—4521no—
233C2×C4—4521no—
234C2×C4—4521no—
235C2×C4—2262no—
236C2×C4—2262no—
237C2×C4—2261no—
238C2×C4C2×C4×D11311yescharacteristic
239C2×C4D4×D11311yescharacteristic
240C8—41no—
241C8—4521no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—1132no—
248C22—9044no—
249C22—4522no—
250C22—4522no—
251C22—4521no—
252C22—4521no—
253C22—4521no—
254C22—2261no—
255C22—2261no—
256C22—2261no—
257C22—2261no—
258C22—2261no—
259C22C22⋊C4×D11311yescharacteristic
260C22#1681364611yescharacteristic
261C22#1681364911yescharacteristic
262C4—21no—
263C4—21no—
264C4—41no—
265C4—81no—
266C4—9041no—
267C4—4521no—
268C4—2261no—
269C4—2261no—
270C2—21no—
271C2—21no—
272C2—81no—
273C2—9041no—
274C2—4521no—
275C2—2262no—
276C2#99×D11311yescharacteristic
277C2#2029860111yescharacteristic
278C2#2029861311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#327×C113C2
socleC22×C113C2×C22⋊C4
prime radical#121×D113C2
cosocleC22×C4×C113C23
hypercenter#327D113
hypocenterC113#1510
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20298560C2semidirect
3. #20298460C2semidirect
4. #20298333C2semidirect
5. #20298332C2semidirect
6. #20298331C2semidirect
7. #327×C113C2semidirect
9. C2×D4×D113C4semidirect
12. #16813597C4semidirect
16. #16813593C4semidirect
17. C4⋊C4×D113C4semidirect
20. C22⋊#11744751C22semidirect
23. #16813529C22semidirect
25. C22⋊C8×C113C22semidirect
26. #95×C113C22semidirect
140. C113#1510semidirect
147. #327D113semidirect
163. C22⋊C8C2×D113semidirect
166. #95C2×D113semidirect

Maximal subgroups

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

subgroupindex
#121×D1132
#202985602
#202984602
#202983332
#202983322
#202983312
#327×C1132
#1510113