Finite Group Databasebeta

← #28392267

Subgroups — #28392267

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#20299173C211yesmaximal, characteristic
2#20298581C212yesmaximal
3#20298397C211yesmaximal, characteristic, complemented
4#20298396C212yesmaximal, complemented
5#356×C113C211yesmaximal, characteristic, complemented
6C2×#14268648C2211yescharacteristic
7C2×Q8×D113C411yescharacteristic
8M16×D113—22no—
9#16813620C2211yescharacteristic
10#16813611C411yescharacteristic
11#16813610C411yescharacteristic
12#16813607—22no—
13#16813600—22no—
14#16813579C411yescharacteristic
15#16813541C2212yes—
16#16813538—22no—
17C4⋊Q8×C113C2211yescharacteristic
18#101×C113C2212yes—
19#14268648—42no—
20C2×Dic226—21no—
21C2×Dic226C2×C411yescharacteristic
22Q8×D113—42no—
23C2×D452C2×C411yescharacteristic
24C2×D452D412yes—
25C2×C4×D113—21no—
26C2×C4×D113C2×C411yescharacteristic
27C2×C4×D113D412yes—
28#14268631—22no—
29#14268630—42no—
30C8×D113—42no—
31#14268626—22no—
32#14268626—21no—
33#14268624—21no—
34#14268624—22no—
35#14268624—22no—
36C4×Dic113C2×C411yescharacteristic
37C2×Q8×C113C2×C411yescharacteristic
38C2×Q8×C113C2311yescharacteristic
39M16×C113—22no—
40C4⋊C4×C113—22no—
41C42×C113C2×C411yescharacteristic
42C22×D113C22⋊C412yes—
43C22×D113C22⋊C411yescharacteristic
44Q8×C113—41no—
45Q8×C113—41no—
46C2×C4×C113—21no—
47C2×C4×C113—21no—
48C2×C4×C113C22×C411yescharacteristic
49C2×C4×C113C2×D412yes—
50C2×Dic113—21no—
51C2×Dic113—21no—
52C2×Dic113C22⋊C411yescharacteristic
53D452—41no—
54D452—42no—
55C4×D113—22no—
56C4×D113—22no—
57C4×D113—22no—
58C4×D113—42no—
59Dic226—42no—
60Dic226—41no—
61C8×C113—42no—
62#11744751—42no—
63C22×C113C2×C22⋊C411yescharacteristic
64C2×D113—21no—
65C2×D113—22no—
66C2×D113—42no—
67C2×D113—41no—
68C4×C113—22no—
69C4×C113—21no—
70C4×C113—41no—
71C4×C113—41no—
72Dic113—41no—
73Dic113—41no—
74Dic113#9912yes—
75C2×C113—21no—
76C2×C113C2×#9911yescharacteristic
77D113—41no—
78D113—42no—
79#2135—1131nomaximal, Sylow
80C113#213511yescharacteristic, complemented, Sylow
81#536—1131no—
82#413—1132no—
83#356—1131no—
84#356—1132no—
85#356D11311yescharacteristic, complemented
86C2×#41—1131no—
87C22×Q8—1131no—
88C2×M16—2262no—
89C4⋊Q8—1131no—
90C4⋊Q8C2×D11311yescharacteristic
91#124—1131no—
92#124—1131no—
93#123—2262no—
94C22⋊Q8—2262no—
95#117—1131no—
96#101—1132no—
97#101C2×D11312yes—
98#100—2262no—
99#41—4522no—
100C2×Q8—1131no—
101C2×Q8—4522no—
102C2×Q8—2261no—
103C2×Q8C4×D11311yescharacteristic
104C2×Q8C22×D11311yescharacteristic
105C2×D4—1131no—
106C2×D4—1132no—
107C22×C4—1131no—
108C22×C4—1132no—
109C22×C4—2261no—
110M16—22no—
111M16—4522no—
112M16—2262no—
113C2×C8—4522no—
114C4⋊C4—22no—
115C4⋊C4—2261no—
116C4⋊C4—2262no—
117C22⋊C4—2261no—
118C22⋊C4—2262no—
119C22⋊C4—2262no—
120C42—1131no—
121C42C4×D11311yescharacteristic
122C23—1132no—
123C23—1131no—
124Q8—41no—
125Q8—41no—
126Q8—4521no—
127Q8—4522no—
128D4—4522no—
129D4—4521no—
130C2×C4—21no—
131C2×C4—21no—
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—4522no—
144C22—4521no—
145C22—2261no—
146C22—2262no—
147C22C22⋊C4×D11311yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—1132no—
153C4—4521no—
154C4—4521no—
155C2—21no—
156C2—4521no—
157C2—4522no—
158C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC2×C4×C113C22×C4
FrattiniC2×Q8C22×D113
Fitting#356×C113C2
socleC2×C113C2×#99
prime radicalC2×#14268648C22
cosocleC2×Q8×C113C23
hypercenter#356D113
hypocenterC113#2135
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. #20298397C2semidirect
4. #20298396C2semidirect
5. #356×C113C2semidirect
80. C113#2135semidirect
85. #356D113semidirect

Maximal subgroups

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

subgroupindex
#202991732
#202985812
#202983972
#202983962
#356×C1132
#2135113