Finite Group Databasebeta

← #28389129

Subgroups — #28389129

Order 14464.

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

normal subgroups only

This group has 284 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#20299111C211yesmaximal, characteristic
2C22⋊C8×D113C211yesmaximal, characteristic, complemented
3#20298460C211yesmaximal, characteristic, complemented
4#20298335C211yesmaximal, characteristic, complemented
5#20298333C211yesmaximal, characteristic, complemented
6#20298331C211yesmaximal, characteristic, complemented
7#328×C113C211yesmaximal, characteristic, complemented
8C2×#14268648C411yescharacteristic, complemented
9C22×C4×D113C2211yescharacteristic
10C2×C8×D113—21no—
11#16813607—21no—
12#16813598C411yescharacteristic, complemented
13#16813597C411yescharacteristic, complemented
14#16813596C2211yescharacteristic
15#16813592—21no—
16#16813584—21no—
17#16813582—21no—
18#16813580C411yescharacteristic, complemented
19C2×#14268624—21no—
20C22⋊#11744751C2211yescharacteristic
21#16813534—21no—
22#16813529—21no—
23#16813529C2211yescharacteristic
24C22⋊Q8×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C23×D113D411yescharacteristic
28#14268648—42no—
29C2×D452—21no—
30C2×D452—21no—
31C2×D452C2×C411yescharacteristic
32C2×C22⋊D113—21no—
33C22×Dic113—21no—
34C22×Dic113D411yescharacteristic
35C2×C4×D113—21no—
36C2×C4×D113—42no—
37C2×C4×D113C2×C411yescharacteristic
38C2×C4×D113C2×C411yescharacteristic
39C2×C4×D113D411yescharacteristic
40C2×C4×D113D411yescharacteristic
41C2×#11744751—21no—
42C8×D113—42no—
43C4⋊Dic113C2×C411yescharacteristic
44#14268626—21no—
45#14268624—21no—
46#14268624—21no—
47#14268624—21no—
48#14268624—21no—
49#14268624—42no—
50C4×Dic113—21no—
51C2×Q8×C113C2×C411yescharacteristic
52C22×C4×C113—21no—
53C22×C4×C113C2311yescharacteristic
54C2×C8×C113—21no—
55C4⋊C4×C113—21no—
56C4⋊C4×C113C2×C411yescharacteristic
57C22⋊C4×C113—21no—
58C23×C113C2×D411yescharacteristic
59C22×D113—21no—
60C22×D113—21no—
61C22×D113—22no—
62C22×D113—21no—
63C22×D113—41no—
64C22×D113C22⋊C411yescharacteristic
65C22×D113C22⋊C411yescharacteristic
66Q8×C113—41no—
67C2×C4×C113—21no—
68C2×C4×C113—21no—
69C2×C4×C113—41no—
70C2×C4×C113—41no—
71C2×C4×C113—41no—
72C2×C4×C113—41no—
73C2×C4×C113C22×C411yescharacteristic
74C2×C4×C113C2×D411yescharacteristic
75C22⋊D113—41no—
76C22⋊D113—41no—
77C2×Dic113—21no—
78C2×Dic113—41no—
79C2×Dic113—41no—
80C2×Dic113—41no—
81C2×Dic113—41no—
82C2×Dic113C22⋊C411yescharacteristic
83C2×Dic113C22⋊C411yescharacteristic
84D452—41no—
85D452—42no—
86D452—42no—
87C4×D113—22no—
88C4×D113—22no—
89C4×D113—41no—
90C4×D113—41no—
91C4×D113—42no—
92C8×C113—41no—
93#11744751—41no—
94C22×C113—21no—
95C22×C113—21no—
96C22×C113C2×C22⋊C411yescharacteristic
97C22×C113#13511yescharacteristic
98C22×C113#13511yescharacteristic
99C2×D113—21no—
100C2×D113—21no—
101C2×D113—21no—
102C2×D113—21no—
103C2×D113—21no—
104C2×D113—42no—
105C2×D113—42no—
106C2×D113—41no—
107C2×D113—41no—
108C2×D113—41no—
109C2×D113#9912yes—
110C4×C113—21no—
111C4×C113—21no—
112C4×C113—41no—
113C4×C113—41no—
114C4×C113—81no—
115Dic113—21no—
116Dic113—21no—
117Dic113—41no—
118Dic113—81no—
119C2×C113—21no—
120C2×C113—21no—
121C2×C113C2×#9911yescharacteristic
122C2×C113#41611yescharacteristic
123C2×C113#42111yescharacteristic
124D113—22no—
125D113—41no—
126D113—81no—
127#1516—1131nomaximal, Sylow
128C113#151611yescharacteristic, complemented, Sylow
129#525—1131no—
130C2×C22⋊C8—1131no—
131#381—1131no—
132#328—1131no—
133#328D11311yescharacteristic, complemented
134#327—1131no—
135#327—1131no—
136C2×#41—1131no—
137C23×C4—1131no—
138C22×C8—2261no—
139#123—2261no—
140C22⋊Q8—1131no—
141C22⋊Q8C2×D11311yescharacteristic
142#121—1131no—
143#121—1131no—
144#120—2261no—
145C4×D4—2261no—
146C4×D4—2261no—
147#117—1131no—
148C2×C22⋊C4—2261no—
149C22⋊C8—1131no—
150C22⋊C8—2261no—
151C22⋊C8C2×D11311yescharacteristic
152#95—1131no—
153#95—2261no—
154#95C2×D11311yescharacteristic
155C24—1131no—
156#41—4522no—
157C2×Q8C4×D11311yescharacteristic
158C2×D4—1131no—
159C2×D4—2261no—
160C2×D4—2261no—
161C2×D4—2261no—
162C22×C4—21no—
163C22×C4—1131no—
164C22×C4—1131no—
165C22×C4—1131no—
166C22×C4—1131no—
167C22×C4—1131no—
168C22×C4—4522no—
169C22×C4—2261no—
170C22×C4—2261no—
171C22×C4C22×D11311yescharacteristic
172C2×C8—21no—
173C2×C8—4522no—
174C2×C8—2261no—
175C4⋊C4—21no—
176C4⋊C4—1131no—
177C4⋊C4—2261no—
178C4⋊C4C4×D11311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—4522no—
181C22⋊C4—2261no—
182C22⋊C4—2261no—
183C22⋊C4—2261no—
184C22⋊C4—2261no—
185C42—2261no—
186C23—1131no—
187C23—1131no—
188C23—4521no—
189C23—2262no—
190C23—2261no—
191C23—2261no—
192C23—2261no—
193C23D4×D11311yescharacteristic
194Q8—41no—
195D4—4521no—
196D4—4522no—
197D4—4522no—
198D4—4521no—
199D4—4521no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—1131no—
207C2×C4—1131no—
208C2×C4—4521no—
209C2×C4—4521no—
210C2×C4—4522no—
211C2×C4—4521no—
212C2×C4—4521no—
213C2×C4—4521no—
214C2×C4—4521no—
215C2×C4—2262no—
216C2×C4—2262no—
217C2×C4—2261no—
218C2×C4C2×C4×D11311yescharacteristic
219C2×C4D4×D11311yescharacteristic
220C8—41no—
221C8—4521no—
222C22—21no—
223C22—21no—
224C22—1132no—
225C22—4522no—
226C22—4522no—
227C22—4521no—
228C22—4521no—
229C22—4521no—
230C22—2261no—
231C22—2261no—
232C22—2261no—
233C22—2261no—
234C22—2261no—
235C22C22⋊C4×D11311yescharacteristic
236C22#1681364311yescharacteristic
237C22#1681364511yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—81no—
243C4—9041no—
244C4—4521no—
245C4—2261no—
246C4—2261no—
247C2—21no—
248C2—21no—
249C2—9041no—
250C2—4521no—
251C2—2262no—
252C2#99×D11311yescharacteristic
253C2#2029859311yescharacteristic
254C2#2029861311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#328×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299111C2
cosocleC22×C4×C113C23
hypercenter#328D113
hypocenterC113#1516
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D113C2semidirect
3. #20298460C2semidirect
4. #20298335C2semidirect
5. #20298333C2semidirect
6. #20298331C2semidirect
7. #328×C113C2semidirect
8. C2×#14268648C4semidirect
12. #16813598C4semidirect
13. #16813597C4semidirect
18. #16813580C4semidirect
128. C113#1516semidirect
133. #328D113semidirect

Maximal subgroups

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

subgroupindex
#202991112
C22⋊C8×D1132
#202984602
#202983352
#202983332
#202983312
#328×C1132
#1516113