Finite Group Databasebeta

← #28389140

Subgroups — #28389140

Order 14464.

340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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
2C22⋊C8×D113C211yesmaximal, characteristic, complemented
3#20298457C211yesmaximal, 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×C8×D113—21no—
12#16813597C411yescharacteristic, complemented
13#16813596C2211yescharacteristic
14#16813595—21no—
15#16813594—21no—
16#16813593C411yescharacteristic, complemented
17C2×#14268626—21no—
18C4⋊C4×D113C411yescharacteristic, complemented
19C2×#14268624—21no—
20C22⋊C4×D113—21no—
21C22⋊#11744751C2211yescharacteristic, complemented
22#16813534—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
45C2×#11744751—21no—
46C8×D113—42no—
47C4⋊Dic113C2×C411yescharacteristic
48#14268626—21no—
49#14268626—42no—
50C22⋊Dic113—21no—
51#14268624—21no—
52#14268624—21no—
53#14268624—42no—
54C2×D4×C113—21no—
55C2×D4×C113C2×C411yescharacteristic
56C22×C4×C113—21no—
57C22×C4×C113C2311yescharacteristic
58C2×C8×C113—21no—
59C4⋊C4×C113C2×C411yescharacteristic
60C22⋊C4×C113—21no—
61C23×C113—21no—
62C23×C113C2×D411yescharacteristic
63C22×D113—21no—
64C22×D113—41no—
65C22×D113—41no—
66C22×D113—42no—
67C22×D113—42no—
68C22×D113—42no—
69C22×D113C22⋊C411yescharacteristic
70C22×D113C22⋊C411yescharacteristic
71C22×D113D812yes—
72C22×D113SD1612yes—
73D4×C113—41no—
74D4×C113—41no—
75D4×C113—41no—
76C2×C4×C113—21no—
77C2×C4×C113—41no—
78C2×C4×C113—41no—
79C2×C4×C113—41no—
80C2×C4×C113—41no—
81C2×C4×C113C22×C411yescharacteristic
82C2×C4×C113C2×D411yescharacteristic
83C22⋊D113—41no—
84C22⋊D113—41no—
85C22⋊D113—42no—
86C22⋊D113—42no—
87C2×Dic113—22no—
88C2×Dic113—21no—
89C2×Dic113—41no—
90C2×Dic113—41no—
91C2×Dic113—41no—
92C2×Dic113C22⋊C411yescharacteristic
93C2×Dic113C22⋊C411yescharacteristic
94D452—41no—
95D452—42no—
96C4×D113—22no—
97C4×D113—22no—
98C4×D113—41no—
99C4×D113—41no—
100C4×D113—42no—
101C8×C113—41no—
102#11744751—41no—
103C22×C113—21no—
104C22×C113—21no—
105C22×C113—41no—
106C22×C113—41no—
107C22×C113—41no—
108C22×C113C2×C22⋊C411yescharacteristic
109C22×C113C2×D811yescharacteristic
110C22×C113C2×SD1611yescharacteristic
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#10212yes—
122C2×D113#10212yes—
123C4×C113—21no—
124C4×C113—21no—
125C4×C113—41no—
126C4×C113—81no—
127Dic113—21no—
128Dic113—41no—
129Dic113—81no—
130Dic113#9912yes—
131C2×C113—21no—
132C2×C113—21no—
133C2×C113—81no—
134C2×C113C2×#9911yescharacteristic
135C2×C113C2×#10211yescharacteristic
136C2×C113#42111yescharacteristic
137D113—22no—
138D113—22no—
139D113—81no—
140#1519—1131nomaximal, Sylow
141C113#151911yescharacteristic, complemented, Sylow
142C2×#121—1131no—
143C2×C22⋊C8—1131no—
144#380—1131no—
145#327—1131no—
146#327—1131no—
147#327—1131no—
148#327D11311yescharacteristic, complemented
149C22×D4—1131no—
150C22×D4—2261no—
151C23×C4—1131no—
152C22×C8—2261no—
153#121—1131no—
154#121—1131no—
155#121—1131no—
156#121—2261no—
157#121—2261no—
158#121C2×D11311yescharacteristic
159C2×C4⋊C4—1131no—
160C2×C4⋊C4—2261no—
161C2×C22⋊C4—2261no—
162C2×C22⋊C4—2261no—
163C22⋊C8—1131no—
164C22⋊C8—2261no—
165C22⋊C8C2×D11311yescharacteristic, complemented
166#95—1131no—
167#95C2×D11311yescharacteristic, complemented
168C24—1131no—
169C24—2261no—
170C2×D4—21no—
171C2×D4—1131no—
172C2×D4—4522no—
173C2×D4—4522no—
174C2×D4—4522no—
175C2×D4—2261no—
176C2×D4—2261no—
177C2×D4—2261no—
178C2×D4—2261no—
179C2×D4C4×D11311yescharacteristic
180C22×C4—21no—
181C22×C4—1131no—
182C22×C4—1131no—
183C22×C4—1131no—
184C22×C4—1131no—
185C22×C4—1131no—
186C22×C4—4522no—
187C22×C4—2261no—
188C22×C4—2261no—
189C22×C4C22×D11311yescharacteristic
190C2×C8—21no—
191C2×C8—4522no—
192C2×C8—2261no—
193C4⋊C4—1131no—
194C4⋊C4—4522no—
195C4⋊C4—2261no—
196C4⋊C4C4×D11311yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—4522no—
199C22⋊C4—2261no—
200C22⋊C4—2261no—
201C22⋊C4—2261no—
202C23—21no—
203C23—1132no—
204C23—1132no—
205C23—1131no—
206C23—1131no—
207C23—4521no—
208C23—4521no—
209C23—4522no—
210C23—4522no—
211C23—4522no—
212C23—2261no—
213C23D4×D11311yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—4521no—
218D4—4522no—
219D4—4522no—
220D4—4522no—
221D4—4521no—
222D4—4521no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—1131no—
229C2×C4—1131no—
230C2×C4—4521no—
231C2×C4—4521no—
232C2×C4—4522no—
233C2×C4—4521no—
234C2×C4—4521no—
235C2×C4—4521no—
236C2×C4—2262no—
237C2×C4—2262no—
238C2×C4—2262no—
239C2×C4—2261no—
240C2×C4C2×C4×D11311yescharacteristic
241C2×C4D4×D11311yescharacteristic
242C8—41no—
243C8—4521no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—1132no—
250C22—1132no—
251C22—9044no—
252C22—4522no—
253C22—4522no—
254C22—4521no—
255C22—4521no—
256C22—4521no—
257C22—2261no—
258C22—2261no—
259C22—2261no—
260C22—2261no—
261C22C22⋊C4×D11311yescharacteristic
262C22D8×D11311yescharacteristic
263C22SD16×D11311yescharacteristic
264C4—21no—
265C4—21no—
266C4—41no—
267C4—81no—
268C4—1132no—
269C4—9041no—
270C4—4521no—
271C4—2261no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—9041no—
276C2—2262no—
277C2—2262no—
278C2#99×D11311yescharacteristic
279C2#102×D11311yescharacteristic
280C2#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#1519
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. C22⋊C8×D113C2semidirect
3. #20298457C2semidirect
4. #20298333C2semidirect
5. #20298332C2semidirect
6. #20298331C2semidirect
7. #327×C113C2semidirect
9. C2×D4×D113C4semidirect
12. #16813597C4semidirect
16. #16813593C4semidirect
18. C4⋊C4×D113C4semidirect
21. C22⋊#11744751C22semidirect
23. #16813529C22semidirect
25. C22⋊C8×C113C22semidirect
26. #95×C113C22semidirect
141. C113#1519semidirect
148. #327D113semidirect
165. C22⋊C8C2×D113semidirect
167. #95C2×D113semidirect

Maximal subgroups

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

subgroupindex
#121×D1132
C22⋊C8×D1132
#202984572
#202983332
#202983322
#202983312
#327×C1132
#1519113