Finite Group Databasebeta

← #28389576

Subgroups — #28389576

Order 14464.

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

normal subgroups only

This group has 254 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#20298911C212yesmaximal, complemented
3#20298331C212yesmaximal, complemented
4#20298324C211yesmaximal, characteristic, complemented
5#398×C113C211yesmaximal, characteristic, complemented
6C2×#14268647—21no—
7#16813602—22no—
8#16813597—22no—
9#16813596—21no—
10#16813596C2212yes—
11#16813555—22no—
12#16813542—22no—
13C22⋊#11744751C2212yes—
14C2×C4⋊C4×C113—21no—
15C2×C4⋊C4×C113C2211yescharacteristic
16C2×C4⋊C4×C113C2211yescharacteristic
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—
39C4⋊C4×C113—42no—
40C23×C113C2×D411yescharacteristic
41C22×D113—22no—
42C2×C4×C113—21no—
43C2×C4×C113—21no—
44C2×C4×C113—22no—
45C2×C4×C113—21no—
46C2×C4×C113—41no—
47C2×C4×C113—41no—
48C2×C4×C113—41no—
49C2×C4×C113—41no—
50C2×C4×C113—41no—
51C2×C4×C113—41no—
52C2×C4×C113—41no—
53C2×C4×C113D812yes—
54C2×C4×C113C2×D412yes—
55C22⋊D113—42no—
56C22⋊D113—42no—
57C2×Dic113—22no—
58D452—42no—
59D452—42no—
60D452—81no—
61C4×D113—44no—
62Dic226—42no—
63#11744751—42no—
64C22×C113—21no—
65C22×C113—21no—
66C22×C113#12011yescharacteristic
67C22×C113C2×D811yescharacteristic
68C22×C113AGL(1,ℤ/8)11yescharacteristic
69C2×D113—42no—
70C2×D113—42no—
71C2×D113—42no—
72C4×C113—22no—
73C4×C113—22no—
74C4×C113—42no—
75C4×C113—41no—
76C4×C113—81no—
77Dic113—42no—
78C2×C113—21no—
79C2×C113—21no—
80C2×C113#44711yescharacteristic
81C2×C113#45611yescharacteristic
82C2×C113#45811yescharacteristic
83D113—82no—
84#1610—1131nomaximal, Sylow
85C113#161011yescharacteristic, complemented, Sylow
86#537—1131no—
87#480—1132no—
88#398D11311yescharacteristic, complemented
89#327—1132no—
90#324—1131no—
91C2×#41—2261no—
92C22⋊Q8—2262no—
93#121—1132no—
94#121—2262no—
95#121—2261no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4C2×D11311yescharacteristic
98C2×C4⋊C4C2×D11311yescharacteristic
99#107—2262no—
100#102—2262no—
101C22⋊C8—1132no—
102#95—21no—
103#95C2×D11311yescharacteristic
104#41—4522no—
105#41—4522no—
106C2×Q8—2261no—
107C2×D4—1132no—
108C2×D4—2261no—
109C2×D4—2261no—
110C2×D4—2262no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—2262no—
114C22×C4C22⋊D11311yescharacteristic
115C22×C4C22⋊D11311yescharacteristic
116C22×C4C22×D11311yescharacteristic
117C2×C8—2262no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—42no—
121C4⋊C4—1132no—
122C4⋊C4—2261no—
123C22⋊C4—2262no—
124C22⋊C4—2262no—
125C23—2262no—
126C23C2×C22⋊D11311yescharacteristic
127Q8—4522no—
128D4—9041no—
129D4—4522no—
130D4—4522no—
131D4—4522no—
132D4—4522no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—4524no—
145C2×C4—2262no—
146C2×C4#1426863212yes—
147C2×C4D4×D11312yes—
148C8—4522no—
149C22—21no—
150C22—21no—
151C22—4522no—
152C22—4522no—
153C22—4522no—
154C22#1681359011yescharacteristic
155C22C2×#1426863211yescharacteristic
156C22#1681364711yescharacteristic
157C4—22no—
158C4—22no—
159C4—42no—
160C4—41no—
161C4—81no—
162C4—4522no—
163C2—21no—
164C2—21no—
165C2—9042no—
166C2#2029873111yescharacteristic
167C2#2029878011yescharacteristic
168C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#398×C113C2
socleC22×C113#120
prime radical#20299179C2
hypercenter#398D113
hypocenterC113#1610
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #20298911C2semidirect
3. #20298331C2semidirect
4. #20298324C2semidirect
5. #398×C113C2semidirect
85. C113#1610semidirect
88. #398D113semidirect

Maximal subgroups

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

subgroupindex
#202991792
#202989112
#202983312
#202983242
#398×C1132
#1610113