Finite Group Databasebeta

← #28392260

Subgroups — #28392260

Order 14464.

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

normal subgroups only

This group has 230 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#101×D113C212yesmaximal, complemented
3#20298396C212yesmaximal, complemented
4#20298395C211yesmaximal, characteristic, complemented
5#355×C113C211yesmaximal, characteristic, complemented
6C2×#14268646C411yescharacteristic
7C2×Q8×D113C2211yescharacteristic
8M16×D113—22no—
9#16813622C411yescharacteristic
10#16813620C2211yescharacteristic
11#16813609C411yescharacteristic
12#16813604—22no—
13#16813599—22no—
14#16813579C411yescharacteristic
15#16813541C2212yes—
16#16813540—22no—
17#124×C113C2211yescharacteristic
18#101×C113C2212yes—
19#14268646—42no—
20C2×Dic226C2×C411yescharacteristic
21C2×Dic226C2×C411yescharacteristic
22C2×Dic226D412yes—
23Q8×D113—42no—
24C2×C22⋊D113—21no—
25C22×Dic113—21no—
26C2×C4×D113C2×C411yescharacteristic
27C2×C4×D113D412yes—
28#14268631—22no—
29#14268630—42no—
30C8×D113—42no—
31C4⋊Dic113—22no—
32#14268626—22no—
33#14268626—21no—
34C22⋊Dic113—22no—
35#14268624—21no—
36C4×Dic113C2×C411yescharacteristic
37C2×Q8×C113C2311yescharacteristic
38C2×D4×C113C2×C411yescharacteristic
39M16×C113—22no—
40C22⋊C4×C113—22no—
41C42×C113C2×C411yescharacteristic
42C23×C113—21no—
43C22×D113C22⋊C411yescharacteristic
44Q8×C113—41no—
45D4×C113—41no—
46C2×C4×C113—21no—
47C2×C4×C113C22×C411yescharacteristic
48C2×C4×C113C2×D412yes—
49C22⋊D113—42no—
50C2×Dic113—21no—
51C2×Dic113—21no—
52C2×Dic113—42no—
53C2×Dic113C22⋊C412yes—
54C2×Dic113C22⋊C411yescharacteristic
55C4×D113—22no—
56C4×D113—22no—
57C4×D113—22no—
58Dic226—41no—
59Dic226—42no—
60Dic226—41no—
61C8×C113—42no—
62#11744751—42no—
63C22×C113—42no—
64C22×C113—41no—
65C22×C113C2×C22⋊C411yescharacteristic
66C2×D113—41no—
67C2×D113#9912yes—
68C4×C113—22no—
69C4×C113—21no—
70C4×C113—41no—
71Dic113—21no—
72Dic113—22no—
73Dic113—41no—
74Dic113—41no—
75C2×C113—21no—
76C2×C113—81no—
77C2×C113C2×#9911yescharacteristic
78D113—22no—
79#2133—1131nomaximal, Sylow
80C113#213311yescharacteristic, complemented, Sylow
81#536—1131no—
82C2×#101—1132no—
83#356—1132no—
84#355—1131no—
85#355D11311yescharacteristic, complemented
86C2×#41—1131no—
87C22×Q8—1131no—
88C2×M16—2262no—
89C4⋊Q8—1131no—
90C4⋊Q8—1131no—
91#124—1131no—
92#124C2×D11311yescharacteristic
93#123—2262no—
94C22⋊Q8—2262no—
95#117—1131no—
96#101—1132no—
97#101—2262no—
98#101C2×D11312yes—
99#41—4522no—
100C2×Q8—1131no—
101C2×Q8—1132no—
102C2×Q8—1131no—
103C2×Q8—4522no—
104C2×Q8C22×D11311yescharacteristic
105C2×D4—2261no—
106C2×D4C4×D11311yescharacteristic
107C22×C4—1131no—
108C22×C4—1132no—
109C22×C4—2261no—
110M16—22no—
111M16—4522no—
112M16—2262no—
113C2×C8—4522no—
114C4⋊C4—2261no—
115C4⋊C4—2262no—
116C4⋊C4—2262no—
117C22⋊C4—22no—
118C22⋊C4—2261no—
119C22⋊C4—2262no—
120C42—1131no—
121C42C4×D11311yescharacteristic
122C23—21no—
123C23—1131no—
124Q8—41no—
125Q8—4521no—
126Q8—4522no—
127Q8—4521no—
128D4—41no—
129D4—4522no—
130C2×C4—21no—
131C2×C4—1132no—
132C2×C4—1131no—
133C2×C4—4522no—
134C2×C4—2262no—
135C2×C4—2262no—
136C2×C4—2262no—
137C2×C4—2261no—
138C2×C4—2261no—
139C2×C4C2×C4×D11311yescharacteristic
140C2×C4D4×D11312yes—
141C8—42no—
142C8—4522no—
143C22—42no—
144C22—41no—
145C22—1132no—
146C22—4521no—
147C22C22⋊C4×D11311yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—4521no—
152C4—4521no—
153C4—2261no—
154C4—2262no—
155C2—21no—
156C2—81no—
157C2—2262no—
158C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC2×C4×C113C22×C4
FrattiniC2×Q8C22×D113
Fitting#355×C113C2
socleC2×C113C2×#99
prime radicalC2×#14268646C4
cosocleC2×Q8×C113C23
hypercenter#355D113
hypocenterC113#2133
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D113C2semidirect
3. #20298396C2semidirect
4. #20298395C2semidirect
5. #355×C113C2semidirect
80. C113#2133semidirect
85. #355D113semidirect

Maximal subgroups

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

subgroupindex
#202991682
#101×D1132
#202983962
#202983952
#355×C1132
#2133113