Finite Group Databasebeta

← #28389611

Subgroups — #28389611

Order 14464.

246 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 57 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#20298914C212yesmaximal, complemented
2#20298537C211yesmaximal, characteristic, complemented
3#20298332C212yesmaximal, complemented
4#20298324C211yesmaximal, characteristic, complemented
5#537×C113C211yesmaximal, characteristic
6C2×C4⋊Dic113C2211yescharacteristic
7#16813553—22no—
8#16813543—22no—
9C22⋊#11744751C2212yes—
10#16813529—21no—
11#16813529—21no—
12#16813529C2211yescharacteristic
13C2×#41×C113—21no—
14C22⋊Q8×C113—22no—
15#121×C113—22no—
16#121×C113—21no—
17#121×C113C2212yes—
18C2×C4⋊C4×C113C2211yescharacteristic
19C22×Dic113—21no—
20C22×Dic113—21no—
21C2×#11744751—22no—
22C4⋊Dic113—22no—
23#41×C113—42no—
24#41×C113—42no—
25C2×Q8×C113—21no—
26C2×D4×C113—21no—
27C2×D4×C113—22no—
28C2×D4×C113—21no—
29C2×D4×C113D412yes—
30C22×C4×C113—22no—
31C22×C4×C113D411yescharacteristic
32C22×C4×C113D411yescharacteristic
33C22×C4×C113C2311yescharacteristic
34C4⋊C4×C113—21no—
35C4⋊C4×C113—22no—
36C4⋊C4×C113D412yes—
37C22⋊C4×C113—22no—
38C22⋊C4×C113—22no—
39C23×C113—22no—
40C23×C113C2×D411yescharacteristic
41Q8×C113—42no—
42D4×C113—42no—
43D4×C113—42no—
44D4×C113—42no—
45D4×C113—42no—
46D4×C113—81no—
47C2×C4×C113—21no—
48C2×C4×C113—21no—
49C2×C4×C113—21no—
50C2×C4×C113—22no—
51C2×C4×C113—41no—
52C2×C4×C113—44no—
53C2×C4×C113—41no—
54C2×C4×C113SD1612yes—
55C2×C4×C113C2×D412yes—
56C2×Dic113—41no—
57C2×Dic113—41no—
58C2×Dic113—42no—
59C2×Dic113—41no—
60C2×Dic113—41no—
61#11744751—42no—
62C22×C113—21no—
63C22×C113—21no—
64C22×C113—42no—
65C22×C113—42no—
66C22×C113—42no—
67C22×C113#12011yescharacteristic
68C22×C113C2×SD1611yescharacteristic
69C22×C113AGL(1,ℤ/8)11yescharacteristic
70C4×C113—22no—
71C4×C113—22no—
72C4×C113—42no—
73C4×C113—41no—
74Dic113—81no—
75Dic113—81no—
76C2×C113—21no—
77C2×C113—21no—
78C2×C113—82no—
79C2×C113#45011yescharacteristic
80C2×C113#45411yescharacteristic
81C2×C113#45811yescharacteristic
82#1616—1131nomaximal, Sylow
83C113#161611yescharacteristic, complemented, Sylow
84#537D11311yescharacteristic
85#481—1132no—
86#400—1131no—
87#327—1132no—
88#324—1131no—
89C2×#41—21no—
90C22⋊Q8—22no—
91#121—22no—
92#121—21no—
93#121C2×D11312yes—
94C2×C4⋊C4—1131no—
95C2×C4⋊C4C2×D11311yescharacteristic
96#106—2262no—
97#102—2262no—
98C22⋊C8—1132no—
99#95—1131no—
100#95—2261no—
101#95—2261no—
102#41—42no—
103#41—42no—
104C2×Q8—21no—
105C2×D4—21no—
106C2×D4—22no—
107C2×D4—21no—
108C2×D4C22⋊D11312yes—
109C22×C4—22no—
110C22×C4—2261no—
111C22×C4—2261no—
112C22×C4C22⋊D11311yescharacteristic
113C22×C4C22⋊D11311yescharacteristic
114C22×C4C22×D11311yescharacteristic
115C2×C8—2262no—
116C4⋊C4—21no—
117C4⋊C4—22no—
118C4⋊C4—2262no—
119C4⋊C4C22⋊D11312yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C23—22no—
123C23C2×C22⋊D11311yescharacteristic
124Q8—42no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—44no—
136C2×C4—41no—
137C2×C4—4521no—
138C2×C4—4521no—
139C2×C4—4522no—
140C2×C4—4521no—
141C2×C4—4521no—
142C2×C4#1426863512yes—
143C2×C4C2×C22⋊D11312yes—
144C8—4522no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22#1681359111yescharacteristic
151C22C2×#1426863511yescharacteristic
152C22#1681364811yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—42no—
157C4—9041no—
158C4—9041no—
159C2—21no—
160C2—21no—
161C2—82no—
162C2#2029874911yescharacteristic
163C2#2029877111yescharacteristic
164C2#2029878811yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting, prime radical#537×C113C2
socleC22×C113#120
hypercenter#537D113
hypocenterC113#1616
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #20298914C2semidirect
2. #20298537C2semidirect
3. #20298332C2semidirect
4. #20298324C2semidirect
83. C113#1616semidirect

Maximal subgroups

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

subgroupindex
#202989142
#202985372
#202983322
#202983242
#537×C1132
#1616113