Finite Group Databasebeta

← #28388919

Subgroups — #28388919

Order 14464.

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

normal subgroups only

This group has 280 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
1C2×#16813604C211yesmaximal, characteristic
2#20298560C211yesmaximal, characteristic, complemented
3C22⋊C8×D113C211yesmaximal, characteristic, complemented
4#20298323C211yesmaximal, characteristic, complemented
5#20298323C211yesmaximal, characteristic, complemented
6#20298322C211yesmaximal, characteristic, complemented
7#323×C113C211yesmaximal, characteristic, complemented
8C22×C22⋊D113C411yescharacteristic
9C22×C4×D113C2211yescharacteristic
10C2×#14268630—21no—
11C2×C8×D113—21no—
12#16813604—21no—
13#16813604—21no—
14#16813604—21no—
15#16813604—21no—
16C2×C4⋊Dic113C411yescharacteristic
17C2×#14268626C2211yescharacteristic
18C2×C22⋊Dic113C411yescharacteristic
19C2×#14268624C411yescharacteristic
20C22⋊#11744751C2211yescharacteristic
21C22⋊#11744751C2211yescharacteristic
22#16813534—21no—
23#16813534—21no—
24C2×C22⋊C4×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26C22⋊C8×C113C2211yescharacteristic
27C23×D113C2×C411yescharacteristic
28C2×C22⋊D113—21no—
29C2×C22⋊D113—21no—
30C2×C22⋊D113—42no—
31C22×Dic113C2×C411yescharacteristic
32C22×Dic113C2×C411yescharacteristic
33C22×Dic113C2×C411yescharacteristic
34C2×C4×D113—42no—
35C2×C4×D113D411yescharacteristic
36C2×C4×D113D411yescharacteristic
37C2×C4×D113D411yescharacteristic
38C2×C4×D113D411yescharacteristic
39#14268630—42no—
40C2×#11744751—21no—
41C2×#11744751—21no—
42C8×D113—42no—
43C4⋊Dic113—21no—
44C4⋊Dic113—21no—
45#14268626—21no—
46#14268626—21no—
47C22⋊Dic113—21no—
48C22⋊Dic113—21no—
49#14268624—21no—
50#14268624—21no—
51C24×C113C2×C411yescharacteristic
52C22×C4×C113C2×C411yescharacteristic
53C22×C4×C113C2311yescharacteristic
54C2×C8×C113—21no—
55C2×C8×C113—21no—
56C22⋊C4×C113—21no—
57C22⋊C4×C113—21no—
58C23×C113—21no—
59C23×C113—21no—
60C23×C113—21no—
61C23×C113—41no—
62C23×C113—41no—
63C23×C113C22×C411yescharacteristic
64C22×D113—21no—
65C22×D113—21no—
66C22×D113—22no—
67C22×D113—41no—
68C22×D113C22⋊C411yescharacteristic
69C22×D113C22⋊C411yescharacteristic
70C2×C4×C113—21no—
71C2×C4×C113—41no—
72C2×C4×C113—41no—
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2×D411yescharacteristic
75C22⋊D113—42no—
76C22⋊D113—42no—
77C2×Dic113—21no—
78C2×Dic113—21no—
79C2×Dic113—21no—
80C2×Dic113—21no—
81C2×Dic113—41no—
82C2×Dic113—41no—
83C2×Dic113C22⋊C411yescharacteristic
84C2×Dic113C22⋊C411yescharacteristic
85C4×D113—22no—
86C4×D113—22no—
87C4×D113—41no—
88C4×D113—41no—
89C8×C113—41no—
90C8×C113—41no—
91#11744751—41no—
92#11744751—41no—
93C22×C113—21no—
94C22×C113—21no—
95C22×C113—41no—
96C22×C113—41no—
97C22×C113—41no—
98C22×C113—81no—
99C22×C113—81no—
100C22×C113C2×C22⋊C411yescharacteristic
101C22×C113#13111yescharacteristic
102C22×C113#13111yescharacteristic
103C2×D113—21no—
104C2×D113—21no—
105C2×D113—21no—
106C2×D113—21no—
107C2×D113—21no—
108C2×D113—42no—
109C2×D113—42no—
110C2×D113#9912yes—
111C4×C113—21no—
112C4×C113—21no—
113C4×C113—41no—
114Dic113—21no—
115Dic113—21no—
116Dic113—41no—
117Dic113—41no—
118C2×C113—21no—
119C2×C113—21no—
120C2×C113—81no—
121C2×C113#40811yescharacteristic
122C2×C113C2×#9911yescharacteristic
123C2×C113#41311yescharacteristic
124D113—22no—
125D113—41no—
126#1468—1131nomaximal, Sylow
127C113#146811yescharacteristic, complemented, Sylow
128C2×#123—1131no—
129#407—1131no—
130C2×C22⋊C8—1131no—
131#324—1131no—
132#324—1131no—
133#323—1131no—
134#323D11311yescharacteristic, complemented
135C22×D4—1131no—
136C23×C4—1131no—
137C2×M16—2261no—
138C22×C8—2261no—
139#123—2261no—
140#123—2261no—
141#123—2261no—
142#123—2261no—
143C2×C4⋊C4—1131no—
144C2×C4⋊C4—1131no—
145C2×C22⋊C4—1131no—
146C2×C22⋊C4—1131no—
147C2×C22⋊C4C2×D11311yescharacteristic
148C22⋊C8—1131no—
149C22⋊C8—1131no—
150C22⋊C8—2261no—
151C22⋊C8—2261no—
152C22⋊C8C2×D11311yescharacteristic
153C22⋊C8C2×D11311yescharacteristic
154C24—1131no—
155C24C4×D11311yescharacteristic
156C2×D4—4522no—
157C2×D4—2261no—
158C2×D4—2261no—
159C22×C4—1131no—
160C22×C4—1131no—
161C22×C4—1131no—
162C22×C4—1131no—
163C22×C4—1131no—
164C22×C4—1131no—
165C22×C4—1131no—
166C22×C4—4522no—
167C22×C4C4×D11311yescharacteristic
168C22×C4C22×D11311yescharacteristic
169M16—4522no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—4522no—
173C2×C8—2261no—
174C2×C8—2261no—
175C4⋊C4—2261no—
176C4⋊C4—2261no—
177C4⋊C4—2261no—
178C4⋊C4—2261no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—2261no—
182C22⋊C4—2261no—
183C22⋊C4—2261no—
184C22⋊C4—2261no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—41no—
190C23—1131no—
191C23—1131no—
192C23—4521no—
193C23—2262no—
194C23—2261no—
195C23—2261no—
196C23C2×C4×D11311yescharacteristic
197D4—4522no—
198D4—4522no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—1131no—
203C2×C4—1131no—
204C2×C4—4521no—
205C2×C4—4521no—
206C2×C4—4521no—
207C2×C4—4521no—
208C2×C4—2262no—
209C2×C4—2262no—
210C2×C4—2261no—
211C2×C4—2261no—
212C2×C4—2261no—
213C2×C4—2261no—
214C2×C4D4×D11311yescharacteristic
215C2×C4D4×D11311yescharacteristic
216C8—41no—
217C8—41no—
218C8—4521no—
219C8—4521no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22—1132no—
228C22—4522no—
229C22—4522no—
230C22—2261no—
231C22—2261no—
232C22—2261no—
233C22—2261no—
234C22—2261no—
235C22C22⋊C4×D11311yescharacteristic
236C22#1681362811yescharacteristic
237C22#1681363011yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—4521no—
242C4—4521no—
243C4—2261no—
244C4—2261no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—4521no—
249C2—2262no—
250C2#2029856311yescharacteristic
251C2#99×D11311yescharacteristic
252C2#2029857911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC23×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#323×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×C22⋊D113C4
cosocleC22×C4×C113C23
hypercenter#323D113
hypocenterC113#1468
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #20298560C2semidirect
3. C22⋊C8×D113C2semidirect
4. #20298323C2semidirect
5. #20298323C2semidirect
6. #20298322C2semidirect
7. #323×C113C2semidirect
127. C113#1468semidirect
134. #323D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136042
#202985602
C22⋊C8×D1132
#202983232
#202983222
#323×C1132
#1468113