Finite Group Databasebeta

← #28389136

Subgroups — #28389136

Order 14464.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#20299150C211yesmaximal, characteristic
2#20298648C211yesmaximal, characteristic
3#20298462C211yesmaximal, characteristic
4#20298336C211yesmaximal, characteristic
5#20298335C211yesmaximal, characteristic
6#20298334C211yesmaximal, characteristic
7#328×C113C211yesmaximal, characteristic
8#16813621C411yescharacteristic, complemented
9#16813620C411yescharacteristic, complemented
10#16813612—21no—
11#16813601C2211yescharacteristic
12#16813599—21no—
13Q8×Dic113C411yescharacteristic, complemented
14#16813587—21no—
15#16813587C411yescharacteristic, complemented
16#16813578—21no—
17C2×#14268626—21no—
18C2×C4×Dic113C2211yescharacteristic
19#16813551—21no—
20C22⋊#11744751C2211yescharacteristic
21C8×Dic113—21no—
22#16813529—21no—
23#16813529C2211yescharacteristic
24C22⋊Q8×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C2×Dic226—21no—
28C2×Dic226C2×C411yescharacteristic
29C22×Dic113—21no—
30C22×Dic113D411yescharacteristic
31C22×Dic113D411yescharacteristic
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113C2×C411yescharacteristic
35#14268626—21no—
36#14268626—21no—
37#14268626—21no—
38#14268626—21no—
39#14268626—21no—
40#14268626—42no—
41C22⋊Dic113—21no—
42C4×Dic113—21no—
43C4×Dic113—21no—
44C4×Dic113C2×C411yescharacteristic
45C4×Dic113C2×C411yescharacteristic
46C4×Dic113D411yescharacteristic
47C4×Dic113D411yescharacteristic
48C2×Q8×C113C2×C411yescharacteristic
49C22×C4×C113—21no—
50C22×C4×C113C2311yescharacteristic
51C2×C8×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113C2×C411yescharacteristic
54C22⋊C4×C113—21no—
55C23×C113C2×D411yescharacteristic
56Q8×C113—41no—
57C2×C4×C113—21no—
58C2×C4×C113—21no—
59C2×C4×C113—41no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113C22×C411yescharacteristic
64C2×C4×C113C2×D411yescharacteristic
65C2×Dic113—21no—
66C2×Dic113—21no—
67C2×Dic113—41no—
68C2×Dic113—41no—
69C2×Dic113—41no—
70C2×Dic113—41no—
71C2×Dic113C22⋊C411yescharacteristic
72C2×Dic113C22⋊C411yescharacteristic
73C2×Dic113C22⋊C411yescharacteristic
74C2×Dic113C22⋊C411yescharacteristic
75C2×Dic113SD1612yes—
76C2×Dic113Q1612yes—
77Dic226—42no—
78Dic226—41no—
79C8×C113—41no—
80#11744751—41no—
81C22×C113—21no—
82C22×C113—21no—
83C22×C113C2×C22⋊C411yescharacteristic
84C22×C113C2×SD1611yescharacteristic
85C22×C113C2×Q1611yescharacteristic
86C4×C113—21no—
87C4×C113—21no—
88C4×C113—41no—
89C4×C113—41no—
90C4×C113—81no—
91Dic113—21no—
92Dic113—21no—
93Dic113—41no—
94Dic113—41no—
95Dic113—81no—
96Dic113#10312yes—
97Dic113#10312yes—
98C2×C113—21no—
99C2×C113—21no—
100C2×C113#41011yescharacteristic
101C2×C113C2×#10311yescharacteristic
102C2×C113#42111yescharacteristic
103#1518—1131nomaximal, Sylow
104C113#151811yescharacteristic, complemented, Sylow
105#533—1131no—
106#431—1131no—
107#382—1131no—
108#328—1131no—
109#328—1131no—
110#328—1131no—
111#328D11311yescharacteristic
112C4⋊Q8—1131no—
113C4⋊Q8—1131no—
114#125—2261no—
115C22⋊Q8—1131no—
116C22⋊Q8—2261no—
117C22⋊Q8C2×D11311yescharacteristic
118C4×Q8—1131no—
119C4×Q8—1131no—
120C4×Q8—2261no—
121#117—2261no—
122C2×C4⋊C4—2261no—
123C2×C42—1131no—
124C4⋊C8—2261no—
125C22⋊C8—1131no—
126C22⋊C8C2×D11311yescharacteristic
127C4×C8—2261no—
128#95—1131no—
129#95—2261no—
130#95C2×D11311yescharacteristic
131C2×Q8—1131no—
132C2×Q8—2261no—
133C2×Q8C4×D11311yescharacteristic
134C22×C4—21no—
135C22×C4—1131no—
136C22×C4—1131no—
137C22×C4—2261no—
138C22×C4C22×D11311yescharacteristic
139C2×C8—21no—
140C2×C8—2261no—
141C4⋊C4—21no—
142C4⋊C4—1131no—
143C4⋊C4—4522no—
144C4⋊C4—2261no—
145C4⋊C4—2261no—
146C4⋊C4—2261no—
147C4⋊C4—2261no—
148C4⋊C4—2261no—
149C4⋊C4—2261no—
150C4⋊C4C4×D11311yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2261no—
153C42—1131no—
154C42—1131no—
155C42—1131no—
156C42—1131no—
157C42—2261no—
158C42—2261no—
159C23D4×D11311yescharacteristic
160Q8—41no—
161Q8—4521no—
162Q8—4522no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—1131no—
170C2×C4—1131no—
171C2×C4—1132no—
172C2×C4—1132no—
173C2×C4—1131no—
174C2×C4—1131no—
175C2×C4—4521no—
176C2×C4—4521no—
177C2×C4—4521no—
178C2×C4—4521no—
179C2×C4—2261no—
180C2×C4—2261no—
181C2×C4C2×C4×D11311yescharacteristic
182C2×C4D4×D11311yescharacteristic
183C8—41no—
184C8—4521no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D11311yescharacteristic
188C22SD16×D11311yescharacteristic
189C22Q16×D11311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—1132no—
196C4—1132no—
197C4—9041no—
198C4—4521no—
199C4—4521no—
200C4—2261no—
201C4—2261no—
202C2—21no—
203C2—21no—
204C2#2029857011yescharacteristic
205C2#103×D11311yescharacteristic
206C2#2029861311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#328×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC23×C113C2×D4
cosocleC22×C4×C113C23
hypercenter#328D113
hypocenterC113#1518
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
8. #16813621C4semidirect
9. #16813620C4semidirect
13. Q8×Dic113C4semidirect
15. #16813587C4semidirect
104. C113#1518semidirect

Maximal subgroups

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

subgroupindex
#202991502
#202986482
#202984622
#202983362
#202983352
#202983342
#328×C1132
#1518113