Finite Group Databasebeta

← #28392599

Subgroups — #28392599

Order 14464.

236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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#20299314C211yesmaximal, characteristic, complemented
2#20298771C212yesmaximal, complemented
3#20298397C211yesmaximal, characteristic, complemented
4#20298394C212yesmaximal, complemented
5#456×C113C211yesmaximal, characteristic, complemented
6#16813647—22no—
7#16813611—21no—
8#16813611C2212yes—
9#16813597—22no—
10C4×D452—21no—
11#16813580—22no—
12#16813549—22no—
13#16813541C2212yes—
142−1+4×C113C2211yescharacteristic
15#137×C113—21no—
16C4⋊Q8×C113C2211yescharacteristic
17#104×C113—21no—
18#101×C113C2211yescharacteristic
19C2×D452—21no—
20C2×D452—21no—
21C2×D452D412yes—
22C2×C4×D113—22no—
23#14268634—42no—
24#14268632—42no—
25#14268631—22no—
26C4⋊Dic113—21no—
27#14268624—22no—
28#14268624—22no—
29#14268624—22no—
30C4×Dic113—21no—
31C4×Dic113D412yes—
32#41×C113—22no—
33#41×C113—21no—
34#41×C113—41no—
35C2×Q8×C113—41no—
36C2×Q8×C113D411yescharacteristic
37C2×Q8×C113C2311yescharacteristic
38Q16×C113—41no—
39SD16×C113—41no—
40M16×C113—21no—
41C4⋊C4×C113—22no—
42C42×C113D411yescharacteristic
43C22×D113—22no—
44Q8×C113—21no—
45Q8×C113—22no—
46Q8×C113—41no—
47Q8×C113—41no—
48D4×C113—21no—
49D4×C113—22no—
50D4×C113—41no—
51C2×C4×C113—21no—
52C2×C4×C113—21no—
53C2×C4×C113—42no—
54C2×C4×C113—41no—
55C2×C4×C113C2×D412yes—
56C2×C4×C113C2×D411yescharacteristic
57C2×Dic113—22no—
58D452—42no—
59D452—42no—
60D452—81no—
61C4×D113—44no—
62C8×C113—41no—
63#11744751—42no—
64C22×C113—41no—
65C22×C113#12011yescharacteristic
66C2×D113—42no—
67C2×D113—42no—
68C2×D113—42no—
69C4×C113—22no—
70C4×C113—22no—
71C4×C113—21no—
72C4×C113—41no—
73C4×C113—41no—
74Dic113—42no—
75C2×C113—21no—
76C2×C113—81no—
77C2×C113B(4,𝔽2)11yescharacteristic
78D113—82no—
79#2204—1131nomaximal, Sylow
80C113#220411yescharacteristic, complemented, Sylow
81#555—1131no—
82#456D11311yescharacteristic, complemented
83#454—1132no—
84#356—1131no—
85#355—1132no—
862−1+4C2×D11311yescharacteristic
87#137—21no—
88AGL(1,ℤ/8)—2262no—
89C4⋊Q8C2×D11311yescharacteristic
90#124—1132no—
91#124—2261no—
92#121—2262no—
93C4×D4—2261no—
94#117—2262no—
95#104—21no—
96#104—2262no—
97#101—1132no—
98#101C2×D11311yescharacteristic
99#41—22no—
100#41—21no—
101#41—41no—
102C2×Q8—41no—
103C2×Q8C22⋊D11311yescharacteristic
104C2×Q8C22×D11311yescharacteristic
105C2×D4—1132no—
106C2×D4—2261no—
107C2×D4—2261no—
108C22×C4—2262no—
109Q16—41no—
110SD16—41no—
111SD16—4522no—
112D8—4522no—
113M16—21no—
114M16—2262no—
115C4⋊C4—22no—
116C4⋊C4—2261no—
117C22⋊C4—2262no—
118C22⋊C4—2262no—
119C22⋊C4—2262no—
120C42—1132no—
121C42—2261no—
122C42C22⋊D11311yescharacteristic
123C23—2262no—
124Q8—22no—
125Q8—21no—
126Q8—41no—
127Q8—41no—
128D4—22no—
129D4—21no—
130D4—41no—
131D4—9041no—
132D4—4522no—
133D4—4522no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—4524no—
139C2×C4—2262no—
140C2×C4D4×D11312yes—
141C2×C4C2×C22⋊D11311yescharacteristic
142C8—41no—
143C8—4522no—
144C22—41no—
145C22—4522no—
146C22—4522no—
147C22—4522no—
148C22#1681359011yescharacteristic
149C4—22no—
150C4—21no—
151C4—22no—
152C4—41no—
153C4—41no—
154C4—4522no—
155C2—21no—
156C2—81no—
157C2—9042no—
158C2#2029878411yescharacteristic
subgroupG/H
centerC2#20298784
commutator, cosocleC2×Q8×C113C23
FrattiniC2×Q8C22×D113
Fitting#456×C113C2
socleC2×C113B(4,𝔽2)
hypercenter#456D113
hypocenterC113#2204
LCSG ▷ C2×Q8×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #20299314C2semidirect
2. #20298771C2semidirect
3. #20298397C2semidirect
4. #20298394C2semidirect
5. #456×C113C2semidirect
80. C113#2204semidirect
82. #456D113semidirect

Maximal subgroups

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

subgroupindex
#202993142
#202987712
#202983972
#202983942
#456×C1132
#2204113