Finite Group Databasebeta

← #28391244

Subgroups — #28391244

Order 14464.

216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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#20298647C211yesmaximal, characteristic, complemented
2#20298616C211yesmaximal, characteristic
3C2×#16813550C211yesmaximal, characteristic
4#20298580C211yesmaximal, characteristic
5C4×#14268631C211yesmaximal, characteristic, complemented
6#20298368C211yesmaximal, characteristic, complemented
7#339×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9C2×#14268631C2211yescharacteristic
10C2×#14268631C2211yescharacteristic
11C2×#14268631C2211yescharacteristic
12#16813558—22no—
13#16813550—22no—
14#16813550—21no—
15#16813550—21no—
16#16813540C412yescomplemented
17#16813538C412yescomplemented
18#16813533—21no—
19C4×#11744751—21no—
20C2×M16×C113C2211yescharacteristic
21#117×C113C2211yescharacteristic
22C2×C42×C113C2211yescharacteristic
23#14268647—21no—
24#14268647—21no—
25#14268647—21no—
26#14268647—21no—
27C2×Dic226C2×C411yescharacteristic
28C2×D452C2×C411yescharacteristic
29C2×C22⋊D113—21no—
30C2×C4×D113—21no—
31#14268631—21no—
32#14268631—21no—
33#14268631—21no—
34#14268631—21no—
35#14268631C2×C412yes—
36#14268631D412yes—
37C2×#11744751—21no—
38C2×#11744751—21no—
39C2×#11744751—21no—
40C22×C4×C113—21no—
41C22×C4×C113C2311yescharacteristic
42M16×C113—21no—
43M16×C113C2×C412yes—
44C2×C8×C113—21no—
45C4⋊C4×C113—21no—
46C22⋊C4×C113—21no—
47C42×C113—21no—
48C42×C113—21no—
49C42×C113D411yescharacteristic
50C42×C113D411yescharacteristic
51C23×C113#4111yescharacteristic
52C22×D113—21no—
53C2×C4×C113—21no—
54C2×C4×C113—21no—
55C2×C4×C113—42no—
56C2×C4×C113—41no—
57C2×C4×C113C22×C411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113#4111yescharacteristic
61C2×C4×C113#4111yescharacteristic
62C2×C4×C113#4111yescharacteristic
63C22⋊D113—41no—
64C22⋊D113—41no—
65C2×Dic113—21no—
66D452—21no—
67D452—21no—
68C4×D113—41no—
69C4×D113—41no—
70Dic226—21no—
71Dic226—21no—
72C8×C113—22no—
73#11744751—22no—
74#11744751—22no—
75#11744751—41no—
76C22×C113—41no—
77C22×C113#11711yescharacteristic
78C22×C113#12311yescharacteristic
79C22×C113#12411yescharacteristic
80C2×D113—41no—
81C2×D113—81no—
82C4×C113—22no—
83C4×C113—41no—
84C4×C113—81no—
85C4×C113C4×D411yescharacteristic
86C4×C113C4×D411yescharacteristic
87C4×C113#12111yescharacteristic
88C4×C113#12611yescharacteristic
89Dic113—41no—
90C2×C113—21no—
91C2×C113—21no—
92C2×C113—21no—
93C2×C113#38811yescharacteristic
94D113—81no—
95#1932—1131nomaximal, Sylow
96C113#193211yescharacteristic, complemented, Sylow
97#430—1131no—
98#421—1131no—
99C2×#104—1131no—
100#413—1131no—
101C4×M16—1131no—
102#344—1131no—
103#339D11311yescharacteristic, complemented
104C2×#41—1131no—
105C2×M16—1131no—
106C2×M16—1131no—
107C2×M16—1131no—
108C2×M16C2×D11311yescharacteristic
109#117C2×D11311yescharacteristic
110C2×C42C2×D11311yescharacteristic
111#108—2262no—
112#104—2262no—
113#104—2261no—
114#104—2261no—
115#101—1132no—
116#100—1132no—
117#97—2261no—
118C4×C8—2261no—
119#41—2261no—
120#41—2261no—
121#41—2261no—
122#41—2261no—
123C2×Q8—1131no—
124C2×D4—1131no—
125C2×D4—2261no—
126C22×C4—21no—
127C22×C4—2261no—
128C22×C4C22×D11311yescharacteristic
129M16—21no—
130M16—1132no—
131M16—1132no—
132M16—2261no—
133M16—2261no—
134M16—2261no—
135M16—2261no—
136M16C4×D11312yes—
137C2×C8—21no—
138C2×C8—2261no—
139C2×C8—2261no—
140C2×C8—2261no—
141C4⋊C4—21no—
142C22⋊C4—21no—
143C42—21no—
144C42—21no—
145C42D45211yescharacteristic
146C42D45211yescharacteristic
147C23—2261no—
148C23#1426864611yescharacteristic
149Q8—2261no—
150Q8—2261no—
151D4—4521no—
152D4—4521no—
153D4—2261no—
154D4—2261no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—41no—
159C2×C4—4521no—
160C2×C4—4521no—
161C2×C4—2261no—
162C2×C4C2×C4×D11311yescharacteristic
163C2×C4D4×D11311yescharacteristic
164C2×C4C2×D45211yescharacteristic
165C2×C4#1426864611yescharacteristic
166C2×C4#1426864711yescharacteristic
167C2×C4#1426864811yescharacteristic
168C8—22no—
169C8—4521no—
170C8—2262no—
171C8—2262no—
172C22—41no—
173C22—9041no—
174C22—4521no—
175C22#1681358011yescharacteristic
176C22#1681360611yescharacteristic
177C22#1681360811yescharacteristic
178C4—22no—
179C4—41no—
180C4—81no—
181C4—4521no—
182C4#1681358211yescharacteristic
183C4C4×D45211yescharacteristic
184C4#1681359711yescharacteristic
185C4#1681361711yescharacteristic
186C2—21no—
187C2—21no—
188C2—21no—
189C2—9041no—
190C2#2029849011yescharacteristic
subgroupG/H
centerC4#16813597
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#339×C113C2
socleC2×C113#388
prime radicalC2×#14268647C22
cosocleC22×C4×C113C23
hypercenter#339D113
hypocenterC113#1932
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #20298647C2semidirect
5. C4×#14268631C2semidirect
6. #20298368C2semidirect
7. #339×C113C2semidirect
16. #16813540C4semidirect
17. #16813538C4semidirect
96. C113#1932semidirect
103. #339D113semidirect

Maximal subgroups

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

subgroupindex
#202986472
#202986162
C2×#168135502
#202985802
C4×#142686312
#202983682
#339×C1132
#1932113