Finite Group Databasebeta

← #28389579

Subgroups — #28389579

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#20298912C212yesmaximal, complemented
3#20298528C211yesmaximal, characteristic, complemented
4#20298333C212yesmaximal, complemented
5#324×C113C211yesmaximal, characteristic, complemented
6C2×#14268647—21no—
7#16813602—22no—
8#16813597—22no—
9#16813596—21no—
10#16813596C2212yes—
11C2×C4⋊Dic113C2211yescharacteristic
12C2×#14268626—21no—
13#16813556—22no—
14#16813544—22no—
15#16813529—21no—
16#16813529C2211yescharacteristic
17C2×C4⋊C4×C113C2211yescharacteristic
18C22⋊C8×C113C2212yes—
19#14268647—42no—
20#14268647—42no—
21C2×Dic226—21no—
22C2×D452—21no—
23C2×D452—21no—
24C2×D452D412yes—
25C2×C22⋊D113—22no—
26C22×Dic113—21no—
27C22×Dic113—21no—
28C2×C4×D113—22no—
29C4⋊Dic113—21no—
30C4⋊Dic113—22no—
31C4⋊Dic113D412yes—
32#14268626—42no—
33#14268624—22no—
34#14268624—22no—
35C22×C4×C113D411yescharacteristic
36C22×C4×C113D411yescharacteristic
37C22×C4×C113C2311yescharacteristic
38C2×C8×C113—22no—
39C4⋊C4×C113—22no—
40C23×C113C2×D411yescharacteristic
41C22×D113—22no—
42C2×C4×C113—21no—
43C2×C4×C113—21no—
44C2×C4×C113—21no—
45C2×C4×C113—41no—
46C2×C4×C113—41no—
47C2×C4×C113D812yes—
48C2×C4×C113C2×D412yes—
49C22⋊D113—42no—
50C22⋊D113—42no—
51C2×Dic113—22no—
52C2×Dic113—22no—
53C2×Dic113—41no—
54C2×Dic113—41no—
55C2×Dic113—41no—
56C2×Dic113—41no—
57C2×Dic113—41no—
58D452—42no—
59D452—42no—
60D452—81no—
61C4×D113—44no—
62Dic226—42no—
63C8×C113—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—41no—
75Dic113—42no—
76Dic113—42no—
77Dic113—81no—
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#398—1131no—
89#327—1132no—
90#324D11311yescharacteristic, complemented
91C2×#41—2261no—
92C22⋊Q8—2262no—
93#121—1132no—
94#121—2262no—
95#121—2261no—
96C2×C4⋊C4—1131no—
97C2×C4⋊C4—2261no—
98C2×C4⋊C4C2×D11311yescharacteristic
99#107—2262no—
100#102—2262no—
101C22⋊C8C2×D11312yes—
102#95—1131no—
103#95—2261no—
104#41—4522no—
105#41—4522no—
106C2×Q8—2261no—
107C2×D4—1132no—
108C2×D4—2261no—
109C2×D4—2261no—
110C2×D4—2262no—
111C22×C4—2262no—
112C22×C4—2261no—
113C22×C4—2261no—
114C22×C4D45211yescharacteristic
115C22×C4D45211yescharacteristic
116C22×C4C22×D11311yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—1132no—
120C4⋊C4—4522no—
121C4⋊C4—2261no—
122C4⋊C4—2262no—
123C22⋊C4—2262no—
124C22⋊C4—2262no—
125C23—2262no—
126C23C2×D45211yescharacteristic
127Q8—4522no—
128D4—9041no—
129D4—4522no—
130D4—4522no—
131D4—4522no—
132D4—4522no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—4524no—
139C2×C4—4521no—
140C2×C4—4521no—
141C2×C4—4521no—
142C2×C4—4521no—
143C2×C4—4521no—
144C2×C4—2262no—
145C2×C4—2262no—
146C2×C4D90412yes—
147C2×C4D4×D11312yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—4522no—
152C22—4522no—
153C22—4522no—
154C22#1681359211yescharacteristic
155C22C2×D90411yescharacteristic
156C22#1681365011yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—9041no—
161C4—4522no—
162C4—4522no—
163C2—21no—
164C2—21no—
165C2—9042no—
166C2#2029873411yescharacteristic
167C2#2029878311yescharacteristic
168C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113#120
prime radical#20299179C2
hypercenter#324D113
hypocenterC113#1610
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20298912C2semidirect
3. #20298528C2semidirect
4. #20298333C2semidirect
5. #324×C113C2semidirect
85. C113#1610semidirect
90. #324D113semidirect

Maximal subgroups

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

subgroupindex
#202991792
#202989122
#202985282
#202983332
#324×C1132
#1610113