Finite Group Databasebeta

← #28389610

Subgroups — #28389610

Order 14464.

246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299179C211yesmaximal, characteristic
2#20298916C212yesmaximal, complemented
3#20298331C212yesmaximal, complemented
4#20298324C211yesmaximal, characteristic, complemented
5#400×C113C211yesmaximal, characteristic, complemented
6C2×#14268647—21no—
7#16813602—22no—
8#16813597—22no—
9#16813596—21no—
10#16813596C2212yes—
11#16813553—22no—
12#16813542—22no—
13C22⋊#11744751C2212yes—
14C2×C4⋊C4×C113C2211yescharacteristic
15C2×C4⋊C4×C113C2211yescharacteristic
16#95×C113—21no—
17#95×C113—21no—
18#95×C113C2211yescharacteristic
19#14268647—42no—
20#14268647—42no—
21C2×Dic226—21no—
22C2×D452—21no—
23C2×D452—21no—
24C2×D452D412yes—
25C2×C22⋊D113—22no—
26C2×C4×D113—22no—
27C2×#11744751—22no—
28C4⋊Dic113—21no—
29C4⋊Dic113D412yes—
30#14268624—22no—
31#14268624—22no—
32C22×C4×C113—21no—
33C22×C4×C113—21no—
34C22×C4×C113D411yescharacteristic
35C22×C4×C113D411yescharacteristic
36C22×C4×C113C2311yescharacteristic
37C4⋊C4×C113—22no—
38C4⋊C4×C113—22no—
39C23×C113C2×D411yescharacteristic
40C22×D113—22no—
41C2×C4×C113—21no—
42C2×C4×C113—21no—
43C2×C4×C113—21no—
44C2×C4×C113—41no—
45C2×C4×C113—41no—
46C2×C4×C113—41no—
47C2×C4×C113—41no—
48C2×C4×C113—42no—
49C2×C4×C113—41no—
50C2×C4×C113—41no—
51C2×C4×C113SD1612yes—
52C2×C4×C113C2×D412yes—
53C22⋊D113—42no—
54C22⋊D113—42no—
55C2×Dic113—22no—
56D452—42no—
57D452—42no—
58D452—81no—
59C4×D113—44no—
60Dic226—42no—
61#11744751—42no—
62C22×C113—21no—
63C22×C113—21no—
64C22×C113#12011yescharacteristic
65C22×C113C2×SD1611yescharacteristic
66C22×C113AGL(1,ℤ/8)11yescharacteristic
67C2×D113—42no—
68C2×D113—42no—
69C2×D113—42no—
70C4×C113—22no—
71C4×C113—22no—
72C4×C113—41no—
73C4×C113—81no—
74C4×C113—81no—
75Dic113—42no—
76C2×C113—21no—
77C2×C113—21no—
78C2×C113#45011yescharacteristic
79C2×C113#45411yescharacteristic
80C2×C113#45811yescharacteristic
81D113—82no—
82#1616—1131nomaximal, Sylow
83C113#161611yescharacteristic, complemented, Sylow
84#537—1131no—
85#481—1132no—
86#400D11311yescharacteristic, complemented
87#327—1132no—
88#324—1131no—
89C2×#41—2261no—
90C22⋊Q8—2262no—
91#121—1132no—
92#121—2262no—
93#121—2261no—
94C2×C4⋊C4C2×D11311yescharacteristic
95C2×C4⋊C4C2×D11311yescharacteristic
96#106—2262no—
97#102—2262no—
98C22⋊C8—1132no—
99#95—21no—
100#95—21no—
101#95C2×D11311yescharacteristic
102#41—4522no—
103#41—4522no—
104C2×Q8—2261no—
105C2×D4—1132no—
106C2×D4—2261no—
107C2×D4—2261no—
108C2×D4—2262no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—2262no—
112C22×C4C22⋊D11311yescharacteristic
113C22×C4C22⋊D11311yescharacteristic
114C22×C4C22×D11311yescharacteristic
115C2×C8—2262no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—1132no—
119C4⋊C4—2261no—
120C22⋊C4—2262no—
121C22⋊C4—2262no—
122C23—2262no—
123C23C2×C22⋊D11311yescharacteristic
124Q8—4522no—
125D4—9041no—
126D4—4522no—
127D4—4522no—
128D4—4522no—
129D4—4522no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—4524no—
141C2×C4—2262no—
142C2×C4#1426863412yes—
143C2×C4D4×D11312yes—
144C8—4522no—
145C22—21no—
146C22—21no—
147C22—4522no—
148C22—4522no—
149C22—4522no—
150C22#1681359011yescharacteristic
151C22C2×#1426863411yescharacteristic
152C22#1681364711yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—4522no—
159C2—21no—
160C2—21no—
161C2—9042no—
162C2#2029874811yescharacteristic
163C2#2029877011yescharacteristic
164C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#400×C113C2
socleC22×C113#120
prime radical#20299179C2
hypercenter#400D113
hypocenterC113#1616
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #20298916C2semidirect
3. #20298331C2semidirect
4. #20298324C2semidirect
5. #400×C113C2semidirect
83. C113#1616semidirect
86. #400D113semidirect

Maximal subgroups

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

subgroupindex
#202991792
#202989162
#202983312
#202983242
#400×C1132
#1616113