Finite Group Databasebeta

← #28391712

Subgroups — #28391712

Order 14464.

290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#16813545C212yesmaximal
2#20298504C211yesmaximal, characteristic
3#20298360C212yesmaximal
4#20298353C211yesmaximal, characteristic
5C2×C4⋊Q8×C113C211yesmaximal, characteristic
6C22×Dic226C2211yescharacteristic
7C22×#11744751C2212yes—
8C2×C4⋊Dic113C2211yescharacteristic
9#16813545—24no—
10#16813529—21no—
11#16813529—21no—
12C22×Q8×C113—21no—
13C4⋊Q8×C113—24no—
14C2×C4⋊C4×C113—21no—
15C2×C4⋊C4×C113C2212yes—
16C2×C42×C113C2211yescharacteristic
17C2×Dic226—22no—
18C2×Dic226—22no—
19C2×Dic226—21no—
20C2×Dic226Q812yescomplemented
21C22×Dic113—21no—
22C22×Dic113—21no—
23C2×#11744751—22no—
24C2×#11744751—22no—
25C2×#11744751—22no—
26C4⋊Dic113—22no—
27C2×Q8×C113—24no—
28C2×Q8×C113—42no—
29C2×Q8×C113—42no—
30C22×C4×C113—22no—
31C22×C4×C113D411yescharacteristic
32C22×C4×C113D411yescharacteristic
33C22×C4×C113C2311yescharacteristic
34C4⋊C4×C113—24no—
35C4⋊C4×C113—22no—
36C4⋊C4×C113D414yes—
37C42×C113—22no—
38C23×C113C2×D411yescharacteristic
39Q8×C113—48no—
40C2×C4×C113—21no—
41C2×C4×C113—21no—
42C2×C4×C113—21no—
43C2×C4×C113—21no—
44C2×C4×C113—24no—
45C2×C4×C113—42no—
46C2×C4×C113—42no—
47C2×C4×C113SD1612yes—
48C2×C4×C113Q1612yes—
49C2×C4×C113C2×D412yes—
50C2×C4×C113C2×Q811yescharacteristic
51C2×C4×C113#4112yes—
52C2×C4×C113#4111yescharacteristic
53C2×Dic113—22no—
54C2×Dic113—41no—
55C2×Dic113—41no—
56C2×Dic113—41no—
57C2×Dic113—41no—
58C2×Dic113—41no—
59Dic226—24no—
60Dic226—42no—
61#11744751—42no—
62C22×C113#12011yescharacteristic
63C22×C113C22⋊Q811yescharacteristic
64C22×C113#12411yescharacteristic
65C22×C113C2×SD1611yescharacteristic
66C22×C113C2×Q1611yescharacteristic
67C22×C113AGL(1,ℤ/8)11yescharacteristic
68C22×C113#13711yescharacteristic
69C4×C113—22no—
70C4×C113—22no—
71C4×C113—44no—
72C4×C113C22⋊Q812yes—
73C4×C113#12412yes—
74Dic113—42no—
75Dic113—81no—
76C2×C113#39311yescharacteristic
77C2×C113#45011yescharacteristic
78C2×C113#45111yescharacteristic
79C2×C113#47511yescharacteristic
80C2×C113#47711yescharacteristic
81C2×C113#48711yescharacteristic
82C2×C113#48911yescharacteristic
83#2024—1131nomaximal, Sylow
84C113#202411yescharacteristic, complemented, Sylow
85C2×C4⋊Q8D11311yescharacteristic
86C2×#103—1132no—
87#391—1131no—
88#340—1132no—
89#336—1131no—
90C22×Q8—21no—
91C22×Q8—1131no—
92C22×C8—1132no—
93C4⋊Q8—24no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—1131no—
96C2×C4⋊C4C2×D11312yes—
97C2×C42C2×D11311yescharacteristic
98#103—2264no—
99#95—2261no—
100#95—2261no—
101C2×Q8—24no—
102C2×Q8—42no—
103C2×Q8—42no—
104C2×Q8—1132no—
105C2×Q8—2262no—
106C2×Q8—2262no—
107C2×Q8—2261no—
108C22×C4—22no—
109C22×C4—2261no—
110C22×C4—2261no—
111C22×C4C22⋊D11311yescharacteristic
112C22×C4C22⋊D11311yescharacteristic
113C22×C4C22×D11311yescharacteristic
114C2×C8—2262no—
115C2×C8—2262no—
116C2×C8—2262no—
117C4⋊C4—24no—
118C4⋊C4—22no—
119C4⋊C4—2262no—
120C4⋊C4C22⋊D11314yes—
121C42—22no—
122C23C2×C22⋊D11311yescharacteristic
123Q8—48no—
124Q8—4522no—
125Q8—2264no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—24no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—4521no—
134C2×C4—4521no—
135C2×C4—4521no—
136C2×C4—4521no—
137C2×C4—4521no—
138C2×C4—2262no—
139C2×C4#1426863512yes—
140C2×C4#1426863712yes—
141C2×C4C2×C22⋊D11312yes—
142C2×C4Q8×D11311yescharacteristic
143C2×C4#1426864812yes—
144C2×C4#1426864811yescharacteristic
145C8—4522no—
146C22#1681359111yescharacteristic
147C22#1681359811yescharacteristic
148C22#1681361111yescharacteristic
149C22C2×#1426863511yescharacteristic
150C22C2×#1426863711yescharacteristic
151C22#1681364811yescharacteristic
152C22#1681365311yescharacteristic
153C4—22no—
154C4—22no—
155C4—44no—
156C4—9041no—
157C4—4522no—
158C4#1681359812yes—
159C4#1681361112yes—
160C2#2029850911yescharacteristic
161C2#2029874911yescharacteristic
162C2#2029875411yescharacteristic
163C2#2029888011yescharacteristic
164C2#2029889011yescharacteristic
165C2#2029895011yescharacteristic
166C2#2029896011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingC2×C4⋊Q8×C113C2
socle, prime radicalC23×C113C2×D4
hypercenterC2×C4⋊Q8D113
hypocenterC113#2024
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
20. C2×Dic226Q8semidirect
84. C113#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#168135452
#202985042
#202983602
#202983532
C2×C4⋊Q8×C1132
#2024113