Finite Group Databasebeta

← #28405986

Subgroups — #28405986

Order 14464.

222 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 56 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#20299620C211yesmaximal, characteristic, complemented
2#20299542C211yesmaximal, characteristic, complemented
3#20299452C212yesmaximal, complemented
4#20299449C212yesmaximal
5#20299127C211yesmaximal, characteristic
6C2×C4⋊#90673—21no—
7C4⋊#11744753—21no—
8#16813679C2212yes—
9#16813677—21no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4C2212yes—
12#16813615—21no—
13#16813614C411yescharacteristic, complemented
14#16813604—21no—
15#16813598C2211yescharacteristic
16#16813593C2211yescharacteristic
17Q8×Dic113C411yescharacteristic, complemented
18D4×Dic113C411yescharacteristic, complemented
19#16813582—21no—
20#16813578—21no—
21C42×D113C2211yescharacteristic
22#124×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24C2×#11744753—22no—
25C4⋊#90673—42no—
26C2×C22⋊D113—21no—
27C22×Dic113—21no—
28C2×C4×D113D411yescharacteristic
29C2×C4×D113D411yescharacteristic
30C2×C4×D113C2311yescharacteristic
31C4⋊Dic113—21no—
32C4⋊Dic113C2×C411yescharacteristic
33C4⋊Dic113C2×C411yescharacteristic
34#14268626—21no—
35#14268626—21no—
36#14268626—21no—
37C22⋊Dic113—21no—
38C22⋊Dic113—21no—
39#14268624—21no—
40C4×Dic113—21no—
41C4×Dic113C2×C411yescharacteristic
42C4×Dic113D411yescharacteristic
43C4×Dic113D411yescharacteristic
44C2×Q8×C113C2×C411yescharacteristic
45C2×D4×C113C2×C411yescharacteristic
46C22⋊C4×C113—21no—
47C22⋊C4×C113—21no—
48C42×C113C2×C411yescharacteristic
49C23×C113—21no—
50C22×D113C2×D411yescharacteristic
51C2×#90673—42no—
52C2×#90673—42no—
53C2×#90673—42no—
54Q8×C113—41no—
55D4×C113—41no—
56C2×C4×C113—21no—
57C2×C4×C113C22⋊C411yescharacteristic
58C2×C4×C113C22⋊C411yescharacteristic
59C2×C4×C113C22×C411yescharacteristic
60C22⋊D113—41no—
61C22⋊D113—41no—
62C2×Dic113—21no—
63C2×Dic113—21no—
64C2×Dic113—42no—
65C2×Dic113C22⋊C411yescharacteristic
66C2×Dic113C22⋊C411yescharacteristic
67C2×Dic113C2×D411yescharacteristic
68C4×D113—21no—
69C4×D113—21no—
70C4×D113—41no—
71C4×D113—41no—
72#11744753—42no—
73C22×C113—41no—
74C22×C113—41no—
75C22×C113—41no—
76C22×C113C2×C22⋊C411yescharacteristic
77C2×D113—21no—
78C2×D113—21no—
79C2×D113AGL(1,ℤ/8)11yescharacteristic
80C2×D113#13711yescharacteristic
81#90673—82no—
82C4×C113—21no—
83C4×C113—21no—
84C4×C113—21no—
85C4×C113—41no—
86Dic113—21no—
87Dic113—21no—
88Dic113—21no—
89Dic113—41no—
90Dic113—41no—
91C2×C113—81no—
92C2×C113#41011yescharacteristic
93C2×C113#41711yescharacteristic
94C2×C113#42111yescharacteristic
95D113—21no—
96D113—21no—
97#1512—1131nomaximal, Sylow
98C113#151211yescharacteristic, complemented, Sylow
99#529—1131no—
100#432—1131no—
101#382—1131no—
102#328—1132no—
103#327—1132no—
104#126—2261no—
105#125—1131no—
106#124#9067311yescharacteristic, complemented
107#123—2261no—
108C22⋊Q8—1131no—
109#121—1131no—
110C4×Q8—1131no—
111C4×D4—1131no—
112C4×D4—2261no—
113#117—2261no—
114C2×C4⋊C4—2261no—
115C2×C42—1131no—
116C4⋊C8—2261no—
117C22⋊C8—1132no—
118#97—2261no—
119#95—1132no—
120#95—2261no—
121C2×Q8C2×#9067311yescharacteristic
122C2×D4—2261no—
123C2×D4C2×#9067311yescharacteristic
124C22×C4—1131no—
125C22×C4—1131no—
126C22×C4—1131no—
127C22×C4—2261no—
128C22×C4—2262no—
129C2×C8—2262no—
130C4⋊C4—1131no—
131C4⋊C4—1131no—
132C4⋊C4—4522no—
133C4⋊C4—2261no—
134C4⋊C4—2261no—
135C4⋊C4—2261no—
136C4⋊C4—2261no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—2261no—
140C22⋊C4—2261no—
141C22⋊C4—2261no—
142C42—1131no—
143C42—1131no—
144C42—1131no—
145C42—2261no—
146C42C2×#9067311yescharacteristic
147C23—21no—
148C23—1131no—
149Q8—41no—
150D4—41no—
151D4—4521no—
152D4—4521no—
153C2×C4—21no—
154C2×C4—1131no—
155C2×C4—1131no—
156C2×C4—1131no—
157C2×C4—4521no—
158C2×C4—4521no—
159C2×C4—4522no—
160C2×C4—4522no—
161C2×C4—4522no—
162C2×C4—4522no—
163C2×C4—2261no—
164C2×C4—2261no—
165C2×C4—2261no—
166C2×C4—2261no—
167C2×C4C22⋊#9067311yescharacteristic
168C2×C4C22⋊#9067311yescharacteristic
169C2×C4C22×#9067311yescharacteristic
170C8—4522no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—1131no—
175C22—1131no—
176C22—2261no—
177C22—2261no—
178C22C2×C22⋊#9067311yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—9042no—
184C4—4521no—
185C4—4521no—
186C4—2261no—
187C4—2261no—
188C4—2261no—
189C2—81no—
190C2—2261no—
191C2—2261no—
192C2#2029957811yescharacteristic
193C2#2029958911yescharacteristic
194C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#124×C113C4
socleC22×C113C2×C22⋊C4
prime radical#16813593C22
cosocleC2×C4×D113C23
hypercenter#124#90673
hypocenterC113#1512
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20299620C2semidirect
2. #20299542C2semidirect
3. #20299452C2semidirect
13. #16813614C4semidirect
17. Q8×Dic113C4semidirect
18. D4×Dic113C4semidirect
22. #124×C113C4semidirect
98. C113#1512semidirect
106. #124#90673semidirect

Maximal subgroups

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

subgroupindex
#202996202
#202995422
#202994522
#202994492
#202991272
#1512113