Finite Group Databasebeta

← #28391400

Subgroups — #28391400

Order 14464.

360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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#20299144C211yesmaximal, characteristic
2#20298621C211yesmaximal, characteristic, complemented
3C2×#16813550C211yesmaximal, characteristic, complemented
4C2×#16813549C211yesmaximal, characteristic, complemented
5C2×#16813548C211yesmaximal, characteristic, complemented
6C42×Dic113C211yesmaximal, characteristic, complemented
7C2×#104×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9C2×#14268631C2211yescharacteristic
10#16813620C411yescharacteristic, complemented
11#16813618C411yescharacteristic, complemented
12#16813611C411yescharacteristic, complemented
13#16813609C411yescharacteristic, complemented
14#16813594—22no—
15C4×C22⋊D113—22no—
16C2×C4×Dic113—22no—
17C2×C4×Dic113C2211yescharacteristic
18C2×C4×Dic113C2211yescharacteristic
19#16813551—22no—
20#16813550—22no—
21#16813549—22no—
22#16813548—22no—
23C2×#41×C113C2211yescharacteristic
24C2×M16×C113C2211yescharacteristic
25C2×C42×C113C2211yescharacteristic
26#104×C113—22no—
27#14268647—21no—
28#14268647—21no—
29#14268647—21no—
30#14268647—21no—
31C2×Dic226C2×C411yescharacteristic
32C2×D452C2×C411yescharacteristic
33C2×C22⋊D113—21no—
34C2×C22⋊D113—22no—
35C22×Dic113—21no—
36C22×Dic113D412yes—
37C2×C4×D113—21no—
38#14268631—21no—
39#14268631—21no—
40C2×#11744751—21no—
41#14268626—22no—
42C22⋊Dic113—22no—
43#14268624—22no—
44C4×Dic113—28no—
45C4×Dic113—21no—
46C4×Dic113C2×C411yescharacteristic
47C4×Dic113C2×C411yescharacteristic
48C4×Dic113D412yes—
49C4×Dic113D412yescomplemented
50#41×C113—21no—
51#41×C113—21no—
52#41×C113—21no—
53#41×C113—21no—
54C2×Q8×C113C2×C411yescharacteristic
55C2×D4×C113—21no—
56C2×D4×C113C2×C411yescharacteristic
57C22×C4×C113—21no—
58C22×C4×C113—21no—
59C22×C4×C113C2311yescharacteristic
60M16×C113—21no—
61M16×C113—21no—
62C2×C8×C113—21no—
63C42×C113—21no—
64C42×C113D412yescomplemented
65C23×C113—21no—
66C23×C113C2×D411yescharacteristic
67C22×D113—21no—
68Q8×C113—21no—
69Q8×C113—21no—
70D4×C113—21no—
71D4×C113—21no—
72D4×C113—41no—
73D4×C113—41no—
74C2×C4×C113—24no—
75C2×C4×C113—22no—
76C2×C4×C113—21no—
77C2×C4×C113—41no—
78C2×C4×C113—41no—
79C2×C4×C113C22×C411yescharacteristic
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113#4111yescharacteristic
84C2×C4×C113#4111yescharacteristic
85C22⋊D113—41no—
86C22⋊D113—41no—
87C22⋊D113—44no—
88C2×Dic113—24no—
89C2×Dic113—22no—
90C2×Dic113—24no—
91C2×Dic113—21no—
92C2×Dic113C22⋊C412yes—
93C2×Dic113C22⋊C412yes—
94D452—21no—
95D452—21no—
96C4×D113—41no—
97C4×D113—41no—
98Dic226—21no—
99Dic226—21no—
100C8×C113—41no—
101#11744751—41no—
102C22×C113—22no—
103C22×C113—41no—
104C22×C113—42no—
105C22×C113C2×C22⋊C411yescharacteristic
106C22×C113#12111yescharacteristic
107C22×C113#12111yescharacteristic
108C2×D113—41no—
109C2×D113—42no—
110C4×C113—24no—
111C4×C113—41no—
112C4×C113C4×D411yescharacteristic
113C4×C113C4×D411yescharacteristic
114C4×C113#12411yescharacteristic
115C4×C113#12711yescharacteristic
116Dic113—24no—
117Dic113—22no—
118Dic113—41no—
119Dic113#10414yescomplemented
120C2×C113—21no—
121C2×C113—21no—
122C2×C113—81no—
123C2×C113#39011yescharacteristic
124C2×C113C2×#10412yes—
125D113—81no—
126#1962—1131nomaximal, Sylow
127C113#196211yescharacteristic, complemented, Sylow
128#532—1131no—
129#423—1131no—
130C2×#104—1131no—
131C2×#104—1131no—
132C2×#104—1131no—
133C2×#104D11311yescharacteristic, complemented
134C43—1131no—
135C2×#41—1131no—
136C2×#41C2×D11311yescharacteristic
137C2×M16—1131no—
138C2×M16C2×D11311yescharacteristic
139C4⋊Q8—1131no—
140#127—1131no—
141#124—1131no—
142#124—1131no—
143#121—2262no—
144C4×D4—2262no—
145C2×C42—1131no—
146C2×C42—1131no—
147C2×C42—2262no—
148C2×C42C2×D11311yescharacteristic
149C4⋊C8—2262no—
150#104—22no—
151#104—2262no—
152#104—2262no—
153#104—2262no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—2261no—
159#41—2261no—
160#41—2261no—
161#41—2261no—
162C2×Q8—1131no—
163C2×Q8C4×D11311yescharacteristic
164C2×D4—21no—
165C2×D4—1131no—
166C2×D4—2262no—
167C2×D4—2261no—
168C2×D4C4×D11311yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—1132no—
172C22×C4—2261no—
173C22×C4—2261no—
174C22×C4C22×D11311yescharacteristic
175M16—21no—
176M16—21no—
177M16—2261no—
178M16—2261no—
179C2×C8—21no—
180C2×C8—2261no—
181C4⋊C4—2262no—
182C22⋊C4—2262no—
183C22⋊C4—2262no—
184C42—21no—
185C42—1131no—
186C42—1131no—
187C42—1132no—
188C42—1132no—
189C42—2268no—
190C42—2261no—
191C42C22⋊D11312yescomplemented
192C23—21no—
193C23—2261no—
194C23D4×D11311yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—2261no—
198Q8—2261no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—4524no—
204D4—4521no—
205D4—4521no—
206D4—2261no—
207D4—2261no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—1132no—
214C2×C4—1132no—
215C2×C4—4521no—
216C2×C4—4521no—
217C2×C4—2264no—
218C2×C4—2261no—
219C2×C4—2264no—
220C2×C4—2262no—
221C2×C4C2×C4×D11311yescharacteristic
222C2×C4D4×D11311yescharacteristic
223C2×C4D4×D11311yescharacteristic
224C2×C4C2×C22⋊D11311yescharacteristic
225C2×C4#1426864611yescharacteristic
226C2×C4#1426864711yescharacteristic
227C8—41no—
228C8—4521no—
229C22—22no—
230C22—41no—
231C22—42no—
232C22—4521no—
233C22—4522no—
234C22C22⋊C4×D11311yescharacteristic
235C22#1681359411yescharacteristic
236C22#1681359511yescharacteristic
237C4—24no—
238C4—41no—
239C4—1134no—
240C4—4521no—
241C4—2264no—
242C4—2262no—
243C4#1681358211yescharacteristic
244C4C4×C22⋊D11311yescharacteristic
245C4#1681360811yescharacteristic
246C4#1681361811yescharacteristic
247C2—21no—
248C2—21no—
249C2—81no—
250C2—9041no—
251C2#2029849811yescharacteristic
252C2#104×D11312yes—
subgroupG/H
centerC2×C4D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#104×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299144C2
cosocleC22×C4×C113C23
hypercenterC2×#104D113
hypocenterC113#1962
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #20298621C2semidirect
3. C2×#16813550C2semidirect
4. C2×#16813549C2semidirect
5. C2×#16813548C2semidirect
6. C42×Dic113C2semidirect
7. C2×#104×C113C2semidirect
10. #16813620C4semidirect
11. #16813618C4semidirect
12. #16813611C4semidirect
13. #16813609C4semidirect
49. C4×Dic113D4semidirect
64. C42×C113D4semidirect
119. Dic113#104semidirect
127. C113#1962semidirect
133. C2×#104D113semidirect
191. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202991442
#202986212
C2×#168135502
C2×#168135492
C2×#168135482
C42×Dic1132
C2×#104×C1132
#1962113