Finite Group Databasebeta

← #28392600

Subgroups — #28392600

Order 14464.

236 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 45 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#20298780C211yesmaximal, characteristic, complemented
2#20298770C212yesmaximal, complemented
3#20298397C211yesmaximal, characteristic, complemented
4#20298395C212yesmaximal, complemented
5#555×C113C211yesmaximal, characteristic, complemented
6#16813670C2211yescharacteristic
7#16813653—21no—
8#16813648—22no—
9#16813550—22no—
10#16813550—21no—
11#16813541C2212yes—
12#16813541C2211yescharacteristic
13C4⋊Q8×C113C2211yescharacteristic
14#124×C113—21no—
15#124×C113C2212yes—
16#121×C113—22no—
17C4×D4×C113—21no—
18#117×C113—22no—
19#14268648—41no—
20#14268647—22no—
21#14268647—21no—
22Q8×D113—41no—
23#14268637—41no—
24#14268635—42no—
25#14268634—41no—
26#14268632—42no—
27#14268631—22no—
28#14268631—21no—
29C2×Q8×C113D411yescharacteristic
30C2×Q8×C113C2311yescharacteristic
31C2×D4×C113—21no—
32C2×D4×C113—21no—
33C2×D4×C113D412yes—
34C22×C4×C113—22no—
35C4⋊C4×C113—21no—
36C4⋊C4×C113—22no—
37C22⋊C4×C113—22no—
38C22⋊C4×C113—22no—
39C22⋊C4×C113—22no—
40C42×C113—21no—
41C42×C113D412yes—
42C42×C113D411yescharacteristic
43C23×C113—22no—
44Q8×C113—41no—
45Q8×C113—41no—
46D4×C113—42no—
47D4×C113—42no—
48D4×C113—81no—
49C2×C4×C113—21no—
50C2×C4×C113—22no—
51C2×C4×C113—21no—
52C2×C4×C113—44no—
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D412yes—
55C22⋊D113—41no—
56D452—22no—
57D452—21no—
58C4×D113—42no—
59C4×D113—41no—
60Dic226—22no—
61Dic226—21no—
62#11744751—42no—
63#11744751—41no—
64C22×C113—42no—
65C22×C113—42no—
66C22×C113—42no—
67C22×C113#12011yescharacteristic
68C2×D113—41no—
69C4×C113—22no—
70C4×C113—22no—
71C4×C113—21no—
72C4×C113—42no—
73C4×C113—41no—
74Dic113—41no—
75C2×C113—21no—
76C2×C113—82no—
77C2×C113B(4,𝔽2)11yescharacteristic
78D113—81no—
79#2204—1131nomaximal, Sylow
80C113#220411yescharacteristic, complemented, Sylow
81#555D11311yescharacteristic, complemented
82#456—1131no—
83#454—1132no—
84#356—1131no—
85#355—1132no—
862−1+4—1131no—
87#137—2261no—
88AGL(1,ℤ/8)—2262no—
89C4⋊Q8C2×D11311yescharacteristic
90#124—21no—
91#124C2×D11312yes—
92#121—22no—
93C4×D4—21no—
94#117—22no—
95#104—2262no—
96#104—2261no—
97#101—1131no—
98#101—1132no—
99#41—4521no—
100#41—2262no—
101#41—2261no—
102C2×Q8—4521no—
103C2×Q8C22⋊D11311yescharacteristic
104C2×Q8C22×D11311yescharacteristic
105C2×D4—21no—
106C2×D4—21no—
107C2×D4C22⋊D11312yes—
108C22×C4—22no—
109Q16—4521no—
110SD16—4522no—
111SD16—4521no—
112D8—4522no—
113M16—2262no—
114M16—2261no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C42—21no—
121C42C22⋊D11312yes—
122C42C22⋊D11311yescharacteristic
123C23—22no—
124Q8—41no—
125Q8—41no—
126Q8—2262no—
127Q8—2261no—
128D4—42no—
129D4—42no—
130D4—81no—
131D4—4521no—
132D4—2262no—
133D4—2261no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—44no—
138C2×C4—4522no—
139C2×C4—4521no—
140C2×C4C2×C22⋊D11311yescharacteristic
141C2×C4C2×C22⋊D11312yes—
142C8—4522no—
143C8—4521no—
144C22—42no—
145C22—42no—
146C22—42no—
147C22—4521no—
148C22#1681359111yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—42no—
153C4—41no—
154C4—4521no—
155C2—21no—
156C2—82no—
157C2—9041no—
158C2#2029878511yescharacteristic
subgroupG/H
centerC2#20298785
commutator, cosocleC2×Q8×C113C23
FrattiniC2×Q8C22×D113
Fitting#555×C113C2
socleC2×C113B(4,𝔽2)
hypercenter#555D113
hypocenterC113#2204
LCSG ▷ C2×Q8×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #20298780C2semidirect
2. #20298770C2semidirect
3. #20298397C2semidirect
4. #20298395C2semidirect
5. #555×C113C2semidirect
80. C113#2204semidirect
81. #555D113semidirect

Maximal subgroups

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

subgroupindex
#202987802
#202987702
#202983972
#202983952
#555×C1132
#2204113