Finite Group Databasebeta

← #28405987

Subgroups — #28405987

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#20299621C211yesmaximal, characteristic, complemented
2#20299542C211yesmaximal, characteristic, complemented
3#20299452C212yesmaximal, complemented
4#20299450C212yesmaximal
5#20299135C211yesmaximal, characteristic
6C2×C4⋊#90673—21no—
7#16813689—21no—
8#16813679C2212yes—
9#16813677—21no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4C2212yes—
12#16813617—21no—
13#16813613C411yescharacteristic, complemented
14#16813611C411yescharacteristic, complemented
15#16813607—21no—
16#16813598C2211yescharacteristic
17#16813597C2211yescharacteristic
18C4×D452—21no—
19C4×D452C411yescharacteristic, complemented
20#16813579—21no—
21C42×D113C2211yescharacteristic
22C4×Q8×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24C2×#11744753—22no—
25C4⋊#90673—42no—
26C2×D452—21no—
27C2×D452C2×C411yescharacteristic
28C2×C4×D113—21no—
29C2×C4×D113D411yescharacteristic
30C2×C4×D113D411yescharacteristic
31C2×C4×D113C2311yescharacteristic
32C4⋊Dic113—21no—
33C4⋊Dic113C2×C411yescharacteristic
34#14268626—21no—
35#14268626—21no—
36#14268624—21no—
37#14268624—21no—
38#14268624—21no—
39#14268624—21no—
40#14268624—21no—
41C4×Dic113C2×C411yescharacteristic
42C4×Dic113D411yescharacteristic
43C4×Dic113D411yescharacteristic
44C2×Q8×C113C2×C411yescharacteristic
45C4⋊C4×C113—21no—
46C4⋊C4×C113C2×C411yescharacteristic
47C42×C113—21no—
48C42×C113C2×C411yescharacteristic
49C22×D113—21no—
50C22×D113C2×D411yescharacteristic
51C2×#90673—42no—
52C2×#90673—42no—
53C2×#90673—42no—
54Q8×C113—41no—
55C2×C4×C113—21no—
56C2×C4×C113—21no—
57C2×C4×C113C22⋊C411yescharacteristic
58C2×C4×C113C22⋊C411yescharacteristic
59C2×C4×C113C22×C411yescharacteristic
60C2×Dic113—21no—
61C2×Dic113C22⋊C411yescharacteristic
62C2×Dic113C22⋊C411yescharacteristic
63C2×Dic113C2×D411yescharacteristic
64D452—41no—
65D452—41no—
66D452—41no—
67C4×D113—21no—
68C4×D113—21no—
69C4×D113—41no—
70C4×D113—41no—
71C4×D113—42no—
72#11744753—42no—
73C22×C113C2×C22⋊C411yescharacteristic
74C2×D113—21no—
75C2×D113—21no—
76C2×D113—41no—
77C2×D113—41no—
78C2×D113—41no—
79C2×D113AGL(1,ℤ/8)11yescharacteristic
80C2×D113#13711yescharacteristic
81#90673—82no—
82C4×C113—21no—
83C4×C113—21no—
84C4×C113—21no—
85C4×C113—41no—
86C4×C113—41no—
87Dic113—21no—
88Dic113—21no—
89Dic113—21no—
90Dic113—41no—
91C2×C113#41011yescharacteristic
92C2×C113#41711yescharacteristic
93C2×C113#42111yescharacteristic
94D113—21no—
95D113—21no—
96D113—81no—
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—1131no—
107#123—2261no—
108C22⋊Q8—1131no—
109#121—1131no—
110C4×Q8#9067311yescharacteristic, complemented
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—1131no—
123C2×D4—2261no—
124C22×C4—1131no—
125C22×C4—1131no—
126C22×C4—1131no—
127C22×C4—2262no—
128C22×C4—2261no—
129C2×C8—2262no—
130C4⋊C4—21no—
131C4⋊C4—1131no—
132C4⋊C4—4522no—
133C4⋊C4—2261no—
134C4⋊C4—2261no—
135C4⋊C4—2261no—
136C4⋊C4C2×#9067311yescharacteristic
137C22⋊C4—2261no—
138C22⋊C4—2261no—
139C22⋊C4—2261no—
140C22⋊C4—2261no—
141C22⋊C4—2261no—
142C42—21no—
143C42—1131no—
144C42—1131no—
145C42—1131no—
146C42C2×#9067311yescharacteristic
147C23—1131no—
148C23—2261no—
149Q8—41no—
150D4—4521no—
151D4—4521no—
152D4—4521no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—1131no—
156C2×C4—1131no—
157C2×C4—1131no—
158C2×C4—4522no—
159C2×C4—4521no—
160C2×C4—4521no—
161C2×C4—4522no—
162C2×C4—4522no—
163C2×C4—4522no—
164C2×C4—2261no—
165C2×C4—2261no—
166C2×C4—2261no—
167C2×C4C22⋊#9067311yescharacteristic
168C2×C4C22⋊#9067311yescharacteristic
169C2×C4C22×#9067311yescharacteristic
170C8—4522no—
171C22—1131no—
172C22—1131no—
173C22—4521no—
174C22—4521no—
175C22—4521no—
176C22—2261no—
177C22—2261no—
178C22C2×C22⋊#9067311yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—9042no—
185C4—4521no—
186C4—2261no—
187C4—2261no—
188C4—2261no—
189C2—9041no—
190C2—2261no—
191C2—2261no—
192C2#2029957711yescharacteristic
193C2#2029958911yescharacteristic
194C2#2029959711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4×Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radical#16813597C22
cosocleC2×C4×D113C23
hypercenterC4×Q8#90673
hypocenterC113#1512
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #20299621C2semidirect
2. #20299542C2semidirect
3. #20299452C2semidirect
13. #16813613C4semidirect
14. #16813611C4semidirect
19. C4×D452C4semidirect
22. C4×Q8×C113C4semidirect
98. C113#1512semidirect
110. C4×Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202996212
#202995422
#202994522
#202994502
#202991352
#1512113