Finite Group Databasebeta

← #28406581

Subgroups — #28406581

Order 14464.

444 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 68 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#20299665C211yesmaximal, characteristic, complemented
2#20299590C212yesmaximal, complemented
3D113⋊#100C211yesmaximal, characteristic, complemented
4#20299469C212yesmaximal, complemented
5#127×D113C211yesmaximal, characteristic
6D113⋊M16C2212yes—
7D4×#90673—24no—
8#16813701C2212yes—
9C2×C22⋊#90673—22no—
10#16813684—24no—
11#16813682—22no—
12C2×D4×D113—22no—
13C2×D4×D113C2211yescharacteristic
14C2×D4×D113C2211yescharacteristic
15#16813619C411yescharacteristic, complemented
16#16813618—22no—
17#16813618C411yescharacteristic, complemented
18#16813618C411yescharacteristic, complemented
19C42×D113C2211yescharacteristic
20#127×C113C411yescharacteristic, complemented
21C22×#90673—24no—
22#14268657—22no—
23#14268656—22no—
24#14268655—22no—
25C4⋊#90673D414yescomplemented
26C22⋊#90673—24no—
27C22⋊#90673—22no—
28C4×#90673—22no—
29C23×D113—21no—
30C23×D113D412yes—
31C2×D452—22no—
32C2×D452C2×C411yescharacteristic
33C2×D452C2×C411yescharacteristic, complemented
34C2×C22⋊D113—22no—
35C2×C22⋊D113—22no—
36C2×C22⋊D113—21no—
37C2×C22⋊D113D412yes—
38D4×D113—22no—
39D4×D113—22no—
40D4×D113—22no—
41D4×D113—22no—
42D4×D113—48no—
43C2×C4×D113—21no—
44C2×C4×D113C2311yescharacteristic
45C4×Dic113—21no—
46C4×Dic113C2×C411yescharacteristic, complemented
47C2×D4×C113—22no—
48C2×D4×C113C2×C411yescharacteristic
49C2×D4×C113C2×C411yescharacteristic, complemented
50C42×C113C2×C411yescharacteristic, complemented
51C23×C113—21no—
52C23×C113C22⋊C412yes—
53C22×D113—22no—
54C22×D113—22no—
55C22×D113—21no—
56C22×D113—44no—
57C22×D113—44no—
58C22×D113—41no—
59C22×D113—41no—
60C22×D113C22⋊C412yes—
61C22×D113C2×D411yescharacteristic
62C2×#90673—24no—
63C2×#90673—84no—
64D4×C113—22no—
65D4×C113—22no—
66D4×C113—44no—
67C2×C4×C113—21no—
68C2×C4×C113C22×C411yescharacteristic
69C22⋊D113—24no—
70C22⋊D113—44no—
71C22⋊D113—44no—
72C22⋊D113—42no—
73C2×Dic113—21no—
74C2×Dic113C2×D411yescharacteristic
75D452—22no—
76D452—22no—
77D452—44no—
78C4×D113—24no—
79C4×D113C2×D412yes—
80C4×D113#4112yes—
81#11744753—42no—
82C22×C113—22no—
83C22×C113—42no—
84C22×C113—42no—
85C22×C113—41no—
86C22×C113C2×C22⋊C411yescharacteristic
87C2×D113—22no—
88C2×D113—22no—
89C2×D113—44no—
90C2×D113—42no—
91C2×D113—42no—
92C2×D113—41no—
93C2×D113—82no—
94C2×D113—82no—
95C2×D113—82no—
96C2×D113#12011yescharacteristic
97C2×D113#12311yescharacteristic
98#90673—44no—
99C4×C113—22no—
100C4×C113C4×D412yes—
101Dic113—22no—
102Dic113#12112yes—
103C2×C113—21no—
104C2×C113—42no—
105C2×C113—81no—
106C2×C113#38611yescharacteristic
107D113—21no—
108D113—42no—
109D113—81no—
110D113#45312yes—
111#1887—1131nomaximal, Sylow
112C113#188711yescharacteristic, complemented, Sylow
113C2×#127—1131no—
114#518—1131no—
115#418—1132no—
116C2×#100—1131no—
117#339—1132no—
118C22×D4—1131no—
119C22×D4—1131no—
120C22×D4—2262no—
121C2×M16—1132no—
122#127—1131no—
123#127—1131no—
124#127—1131no—
125#127—2262no—
126#127#9067311yescharacteristic, complemented
127C4×D4—2264no—
128#117—1132no—
129C2×C22⋊C4—2262no—
130C2×C42—1131no—
131#102—2264no—
132#100—2262no—
133C24—1132no—
134C24—2261no—
135C2×D4—22no—
136C2×D4—1132no—
137C2×D4—1131no—
138C2×D4—1131no—
139C2×D4—4528no—
140C2×D4—2262no—
141C2×D4—2262no—
142C2×D4—2262no—
143C2×D4—2262no—
144C2×D4—2262no—
145C2×D4—2261no—
146C2×D4—2262no—
147C2×D4—2262no—
148C2×D4C2×#9067311yescharacteristic
149C2×D4C2×#9067311yescharacteristic, complemented
150C22×C4—1131no—
151C22×C4—2261no—
152C22×C4—2264no—
153M16—2262no—
154M16—2262no—
155C2×C8—2262no—
156C4⋊C4—1134no—
157C22⋊C4—2262no—
158C22⋊C4—2264no—
159C42—1131no—
160C42—2261no—
161C42—2262no—
162C42C2×#9067311yescharacteristic, complemented
163C23—21no—
164C23—1131no—
165C23—1132no—
166C23—4521no—
167C23—4521no—
168C23—4524no—
169C23—4524no—
170C23—2262no—
171C23—2262no—
172C23—2261no—
173C23C22⋊#9067312yes—
174D4—22no—
175D4—22no—
176D4—44no—
177D4—4524no—
178D4—4522no—
179D4—4524no—
180D4—4524no—
181D4—2264no—
182D4—2262no—
183D4—2262no—
184C2×C4—21no—
185C2×C4—1131no—
186C2×C4—1132no—
187C2×C4—1132no—
188C2×C4—9044no—
189C2×C4—2264no—
190C2×C4—2264no—
191C2×C4—2261no—
192C2×C4C22×#9067311yescharacteristic
193C8—4522no—
194C22—22no—
195C22—42no—
196C22—42no—
197C22—41no—
198C22—1131no—
199C22—1131no—
200C22—9042no—
201C22—9042no—
202C22—9042no—
203C22—4522no—
204C22—4522no—
205C22—4524no—
206C22—4521no—
207C22—2262no—
208C22—2262no—
209C22C2×C22⋊#9067311yescharacteristic
210C4—22no—
211C4—1132no—
212C4—4524no—
213C4—2262no—
214C4D4×#9067312yes—
215C2—21no—
216C2—42no—
217C2—81no—
218C2—1132no—
219C2—9041no—
220C2—4522no—
221C2—2261no—
222C2#2029954611yescharacteristic
subgroupG/H
centerC2#20299546
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#127×C113C4
socleC2×C113#386
prime radical#127×D113C2
cosocleC2×C4×D113C23
hypercenter#127#90673
hypocenterC113#1887
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20299665C2semidirect
2. #20299590C2semidirect
3. D113⋊#100C2semidirect
4. #20299469C2semidirect
15. #16813619C4semidirect
17. #16813618C4semidirect
18. #16813618C4semidirect
20. #127×C113C4semidirect
25. C4⋊#90673D4semidirect
33. C2×D452C2×C4semidirect
46. C4×Dic113C2×C4semidirect
49. C2×D4×C113C2×C4semidirect
50. C42×C113C2×C4semidirect
112. C113#1887semidirect
126. #127#90673semidirect
149. C2×D4C2×#90673semidirect
162. C42C2×#90673semidirect

Maximal subgroups

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

subgroupindex
#202996652
#202995902
D113⋊#1002
#202994692
#127×D1132
#1887113