Finite Group Databasebeta

← #28406578

Subgroups — #28406578

Order 14464.

332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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#20299678C211yesmaximal, characteristic, complemented
2#20299596C212yesmaximal, complemented
3#20299579C211yesmaximal, characteristic, complemented
4#20299469C212yesmaximal, complemented
5#20299147C211yesmaximal, characteristic
6#16813710—24no—
7D113⋊M16—22no—
8D113⋊M16C2212yes—
9#16813701C2212yes—
10#16813686—24no—
11#16813681—22no—
12C2×#14268648C2211yescharacteristic
13C2×#14268646C2211yescharacteristic
14#16813620C411yescharacteristic, complemented
15#16813618C411yescharacteristic, complemented
16#16813610C411yescharacteristic, complemented
17#16813595—22no—
18#16813582—22no—
19C42×D113C2211yescharacteristic
20#124×C113C411yescharacteristic, complemented
21#14268657—24no—
22#14268657D414yescomplemented
23#14268656—22no—
24#14268655—24no—
25#14268655—22no—
26C4⋊#90673—22no—
27C22⋊#90673—22no—
28C4×#90673—22no—
29#14268648—22no—
30#14268648—22no—
31#14268646—22no—
32#14268646—22no—
33C2×Dic226C2×C411yescharacteristic
34C2×D452C2×C411yescharacteristic
35C2×D452D412yes—
36C2×C22⋊D113—22no—
37C2×C22⋊D113—21no—
38C22×Dic113—21no—
39C2×C4×D113—21no—
40C2×C4×D113D412yes—
41C2×C4×D113C2311yescharacteristic
42#14268626—22no—
43#14268624—22no—
44C4×Dic113—21no—
45C4×Dic113C2×C411yescharacteristic
46C2×Q8×C113C2×C411yescharacteristic
47C2×D4×C113C2×C411yescharacteristic
48C22⋊C4×C113—22no—
49C42×C113C2×C411yescharacteristic
50C23×C113—21no—
51C22×D113C22⋊C412yes—
52C22×D113C2×D411yescharacteristic
53C2×#90673—42no—
54Q8×C113—22no—
55D4×C113—22no—
56C2×C4×C113—21no—
57C2×C4×C113C22⋊C412yes—
58C2×C4×C113C22×C411yescharacteristic
59C22⋊D113—44no—
60C22⋊D113—42no—
61C2×Dic113—21no—
62C2×Dic113—21no—
63C2×Dic113—41no—
64C2×Dic113—41no—
65C2×Dic113C2×D411yescharacteristic
66D452—24no—
67D452—22no—
68C4×D113—22no—
69C4×D113—22no—
70C4×D113—42no—
71C4×D113C2×D412yes—
72C4×D113#4112yes—
73Dic226—22no—
74#11744753—24no—
75C22×C113—42no—
76C22×C113—41no—
77C22×C113C2×C22⋊C411yescharacteristic
78C2×D113—22no—
79C2×D113—41no—
80C2×D113—42no—
81C2×D113#12112yes—
82#90673—82no—
83C4×C113—22no—
84C4×C113—41no—
85C4×C113C4×D412yes—
86Dic113—22no—
87Dic113—41no—
88Dic113#12011yescharacteristic
89Dic113#12311yescharacteristic
90C2×C113—21no—
91C2×C113—81no—
92C2×C113#38611yescharacteristic
93D113—22no—
94D113—42no—
95#1884—1131nomaximal, Sylow
96C113#188411yescharacteristic, complemented, Sylow
97#568—1131no—
98#532—1131no—
99#421—1132no—
100#410—1131no—
101#339—1132no—
102C2×#41—1131no—
103C2×#41—1131no—
104#131—2264no—
105C2×M16—1132no—
106C2×M16—2262no—
107C4⋊Q8—1131no—
108#127—1131no—
109#124—1131no—
110#124#9067311yescharacteristic, complemented
111#121—2262no—
112C4×D4—2262no—
113#117—1132no—
114C2×C42—1131no—
115#104—2264no—
116#99—2262no—
117#41—2262no—
118#41—2262no—
119#41—2262no—
120#41—2262no—
121C2×Q8—1131no—
122C2×Q8C2×#9067311yescharacteristic
123C2×D4—1132no—
124C2×D4—1131no—
125C2×D4—2262no—
126C2×D4—2261no—
127C2×D4C2×#9067311yescharacteristic
128C22×C4—1131no—
129C22×C4—1132no—
130C22×C4—2261no—
131C22×C4—2261no—
132M16—1134no—
133M16—2262no—
134M16—2264no—
135C2×C8—2262no—
136C2×C8—2264no—
137C4⋊C4—2262no—
138C4⋊C4—2262no—
139C22⋊C4—22no—
140C22⋊C4—2262no—
141C22⋊C4—2262no—
142C42—1131no—
143C42—2261no—
144C42—2262no—
145C42C2×#9067311yescharacteristic
146C23—21no—
147C23—1131no—
148C23—1132no—
149Q8—22no—
150Q8—2262no—
151D4—22no—
152D4—4522no—
153D4—4524no—
154D4—2264no—
155D4—2262no—
156C2×C4—21no—
157C2×C4—1131no—
158C2×C4—1132no—
159C2×C4—1132no—
160C2×C4—4522no—
161C2×C4—4521no—
162C2×C4—4521no—
163C2×C4—4522no—
164C2×C4—2262no—
165C2×C4—2262no—
166C2×C4—2261no—
167C2×C4—2261no—
168C2×C4C22⋊#9067312yes—
169C2×C4C22×#9067311yescharacteristic
170C8—2264no—
171C22—42no—
172C22—41no—
173C22—1132no—
174C22—4522no—
175C22—4521no—
176C22—2262no—
177C22C2×C22⋊#9067311yescharacteristic
178C4—22no—
179C4—41no—
180C4—1131no—
181C4—1131no—
182C4—9042no—
183C4—4521no—
184C4—2262no—
185C4D4×#9067312yes—
186C2—21no—
187C2—81no—
188C2—4522no—
189C2—2262no—
190C2#2029954611yescharacteristic
subgroupG/H
centerC2#20299546
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#124×C113C4
socleC2×C113#386
prime radical#20299147C2
cosocleC2×C4×D113C23
hypercenter#124#90673
hypocenterC113#1884
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20299678C2semidirect
2. #20299596C2semidirect
3. #20299579C2semidirect
4. #20299469C2semidirect
14. #16813620C4semidirect
15. #16813618C4semidirect
16. #16813610C4semidirect
20. #124×C113C4semidirect
22. #14268657D4semidirect
96. C113#1884semidirect
110. #124#90673semidirect

Maximal subgroups

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

subgroupindex
#202996782
#202995962
#202995792
#202994692
#202991472
#1884113