Finite Group Databasebeta

← #28392247

Subgroups — #28392247

Order 14464.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299168C211yesmaximal, characteristic
2#20298570C212yesmaximal
3#20298393C211yesmaximal, characteristic, complemented
4#20298392C212yesmaximal, complemented
5#354×C113C211yesmaximal, characteristic, complemented
6C2×#14268646C2211yescharacteristic
7C2×Q8×D113C411yescharacteristic, complemented
8#16813622C411yescharacteristic, complemented
9#16813620C411yescharacteristic, complemented
10#16813609C2211yescharacteristic
11#16813604—22no—
12#16813599—22no—
13#16813579C411yescharacteristic, complemented
14#16813578—22no—
15#16813537C2212yes—
16#16813536—22no—
17#124×C113C2211yescharacteristic
18#99×C113C2212yes—
19#14268646—42no—
20C2×Dic226—21no—
21C2×Dic226C2×C411yescharacteristic
22C2×Dic226C2×C411yescharacteristic
23Q8×D113—42no—
24C2×C22⋊D113D412yes—
25C22×Dic113D412yes—
26C2×C4×D113—21no—
27C2×C4×D113C2×C411yescharacteristic
28C4⋊Dic113—22no—
29#14268626—21no—
30#14268626—22no—
31#14268626—42no—
32C22⋊Dic113—22no—
33C22⋊Dic113—22no—
34#14268624—21no—
35C4×Dic113—42no—
36C4×Dic113C2×C411yescharacteristic
37C2×Q8×C113C2×C411yescharacteristic
38C2×D4×C113C2311yescharacteristic
39C22⋊C4×C113—22no—
40C22⋊C4×C113—22no—
41C42×C113C2×C411yescharacteristic
42C23×C113C2×D412yes—
43C22×D113C22⋊C411yescharacteristic
44Q8×C113—41no—
45D4×C113—41no—
46C2×C4×C113—21no—
47C2×C4×C113—21no—
48C2×C4×C113—42no—
49C2×C4×C113C22×C411yescharacteristic
50C22⋊D113—42no—
51C2×Dic113—22no—
52C2×Dic113—22no—
53C2×Dic113—21no—
54C2×Dic113—21no—
55C2×Dic113—42no—
56C2×Dic113C22⋊C412yes—
57C2×Dic113C22⋊C411yescharacteristic
58C4×D113—22no—
59C4×D113—42no—
60Dic226—41no—
61Dic226—42no—
62Dic226—41no—
63C22×C113—22no—
64C22×C113—42no—
65C22×C113C2×C22⋊C411yescharacteristic
66C2×D113—21no—
67C2×D113—41no—
68C4×C113—21no—
69C4×C113—41no—
70C4×C113—41no—
71C4×C113—82no—
72Dic113—22no—
73Dic113—41no—
74Dic113—41no—
75Dic113—82no—
76Dic113#9912yes—
77C2×C113—21no—
78C2×C113—42no—
79C2×C113C2×#9911yescharacteristic
80D113—41no—
81#2129—1131nomaximal, Sylow
82C113#212911yescharacteristic, complemented, Sylow
83#536—1131no—
84#410—1132no—
85#354—1131no—
86#354—1132no—
87#354D11311yescharacteristic, complemented
88C2×#41—1131no—
89C22×Q8—1131no—
90C4⋊Q8—1131no—
91C4⋊Q8—1131no—
92#124—1131no—
93#124C2×D11311yescharacteristic
94#123—2262no—
95C22⋊Q8—2262no—
96#117—1131no—
97#117—2262no—
98#99—1132no—
99#99—2262no—
100#99C2×D11312yes—
101#41—4522no—
102C2×Q8—1131no—
103C2×Q8—1131no—
104C2×Q8—4522no—
105C2×Q8—2261no—
106C2×Q8C4×D11311yescharacteristic
107C2×D4—1132no—
108C2×D4C22×D11311yescharacteristic
109C22×C4—1132no—
110C22×C4—1131no—
111C22×C4—2261no—
112C4⋊C4—4522no—
113C4⋊C4—2261no—
114C4⋊C4—2262no—
115C4⋊C4—2262no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—2261no—
119C22⋊C4—2262no—
120C22⋊C4—2262no—
121C42—1131no—
122C42—4522no—
123C42C4×D11311yescharacteristic
124C23—1131no—
125C23D4×D11312yes—
126Q8—41no—
127Q8—4521no—
128Q8—4521no—
129Q8—4522no—
130D4—41no—
131D4—4522no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—1131no—
136C2×C4—1132no—
137C2×C4—4522no—
138C2×C4—4522no—
139C2×C4—2262no—
140C2×C4—2262no—
141C2×C4—2262no—
142C2×C4—2261no—
143C2×C4—2261no—
144C2×C4C2×C4×D11311yescharacteristic
145C22—22no—
146C22—42no—
147C22—4521no—
148C22—2261no—
149C22C22⋊C4×D11311yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—1132no—
155C4—9042no—
156C4—4521no—
157C4—4521no—
158C4—2262no—
159C2—21no—
160C2—42no—
161C2—4521no—
162C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC2×C4×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#354×C113C2
socleC2×C113C2×#99
prime radicalC2×#14268646C22
cosocleC2×D4×C113C23
hypercenter#354D113
hypocenterC113#2129
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #20298393C2semidirect
4. #20298392C2semidirect
5. #354×C113C2semidirect
7. C2×Q8×D113C4semidirect
8. #16813622C4semidirect
9. #16813620C4semidirect
13. #16813579C4semidirect
82. C113#2129semidirect
87. #354D113semidirect

Maximal subgroups

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

subgroupindex
#202991682
#202985702
#202983932
#202983922
#354×C1132
#2129113