Finite Group Databasebeta

← #28391623

Subgroups — #28391623

Order 14464.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16813655C212yesmaximal, complemented
2#20299179C211yesmaximal, characteristic
3C2×#16813548C212yesmaximal, complemented
4#20298503C211yesmaximal, characteristic, complemented
5#343×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2212yes—
7C22×Dic226C2211yescharacteristic
8#16813655—24no—
9#16813655—24no—
10C2×Dic452—22no—
11C2×#14268636—22no—
12#16813602—22no—
13#16813597—22no—
14#16813596—22no—
15C2×C4×Dic113C2211yescharacteristic
16#16813548—24no—
17#16813529—22no—
18C2×M16×C113C2212yes—
19C2×C4⋊C4×C113C2211yescharacteristic
20#14268647—22no—
21#14268647—22no—
22#14268647—22no—
23#14268647—22no—
24C2×Dic226—22no—
25C2×Dic226—22no—
26C2×Dic226—21no—
27C2×Dic226D412yes—
28C2×Dic226D412yescomplemented
29C2×D452—22no—
30C2×D452D412yes—
31C2×C22⋊D113—22no—
32C22×Dic113—21no—
33C22×Dic113—21no—
34C2×C4×D113—22no—
35Dic452—28no—
36#14268636—28no—
37C4⋊Dic113—22no—
38#14268624—24no—
39C4×Dic113—22no—
40C22×C4×C113D412yes—
41C22×C4×C113C2311yescharacteristic
42M16×C113—22no—
43M16×C113D414yescomplemented
44C2×C8×C113—22no—
45C4⋊C4×C113—22no—
46C23×C113C2×D411yescharacteristic
47C22×D113—22no—
48C2×C4×C113—22no—
49C2×C4×C113—42no—
50C2×C4×C113C2×D411yescharacteristic
51C2×C4×C113C2×D412yes—
52C2×C4×C113C2×D412yes—
53C2×C4×C113#4111yescharacteristic
54C22⋊D113—42no—
55C22⋊D113—42no—
56C2×Dic113—22no—
57C2×Dic113—22no—
58C2×Dic113—22no—
59C2×Dic113—41no—
60C2×Dic113—41no—
61C2×Dic113—41no—
62C2×Dic113—41no—
63D452—22no—
64D452—22no—
65D452—82no—
66C4×D113—42no—
67C4×D113—42no—
68Dic226—24no—
69Dic226—22no—
70Dic226—22no—
71Dic226—42no—
72C8×C113—24no—
73C22×C113—21no—
74C22×C113—21no—
75C22×C113#12011yescharacteristic
76C22×C113#12111yescharacteristic
77C22×C113#12711yescharacteristic
78C2×D113—42no—
79C2×D113—42no—
80C2×D113—42no—
81C4×C113—42no—
82C4×C113#12012yes—
83C4×C113#12112yes—
84Dic113—42no—
85Dic113—42no—
86Dic113—42no—
87C2×C113—21no—
88C2×C113—21no—
89C2×C113#39211yescharacteristic
90C2×C113#45511yescharacteristic
91C2×C113#45611yescharacteristic
92D113—82no—
93#2007—1131nomaximal, Sylow
94C113#200711yescharacteristic, complemented, Sylow
95C2×#137—1132no—
96#537—1131no—
97C2×#104—1132no—
98#391—1131no—
99#343D11311yescharacteristic, complemented
100C2×#41—1132no—
101C22×Q8—1131no—
102#137—2264no—
103#137—2264no—
104C2×Q16—2262no—
105C2×SD16—2262no—
106C2×M16C2×D11312yes—
107C22⋊Q8—2262no—
108#121—2262no—
109#121—2262no—
110C2×C4⋊C4C2×D11311yescharacteristic
111C2×C42—1131no—
112#104—2264no—
113#95—2262no—
114#41—2262no—
115#41—2262no—
116#41—2262no—
117#41—2262no—
118C2×Q8—1132no—
119C2×Q8—1132no—
120C2×Q8—2262no—
121C2×Q8—2262no—
122C2×Q8—2261no—
123C2×D4—1132no—
124C2×D4—2262no—
125C2×D4—2262no—
126C22×C4—2261no—
127C22×C4—2261no—
128C22×C4—2262no—
129C22×C4D45212yes—
130C22×C4C22×D11311yescharacteristic
131Q16—2268no—
132SD16—2268no—
133M16—22no—
134M16D45214yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—2262no—
138C22⋊C4—2264no—
139C42—2262no—
140C23—2262no—
141C23C2×D45211yescharacteristic
142Q8—4522no—
143Q8—2264no—
144Q8—2262no—
145Q8—2262no—
146D4—9042no—
147D4—4522no—
148D4—4522no—
149D4—2262no—
150D4—2262no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—4521no—
154C2×C4—4521no—
155C2×C4—4521no—
156C2×C4—4521no—
157C2×C4—4522no—
158C2×C4—4522no—
159C2×C4—2262no—
160C2×C4—2262no—
161C2×C4—2262no—
162C2×C4D4×D11311yescharacteristic
163C2×C4D4×D11312yes—
164C2×C4C2×D45212yes—
165C2×C4#1426864811yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—4522no—
170C22—4522no—
171C22—4522no—
172C22#1681359211yescharacteristic
173C22#1681359711yescharacteristic
174C22#1681361911yescharacteristic
175C4—42no—
176C4—4522no—
177C4—4522no—
178C4—4522no—
179C4#1681359212yes—
180C4#1681359712yes—
181C2—21no—
182C2—21no—
183C2—9042no—
184C2#2029850811yescharacteristic
185C2#2029877811yescharacteristic
186C2#2029878311yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#343×C113C2
socleC22×C113#120
prime radical#20299179C2
hypercenter#343D113
hypocenterC113#2007
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
3. C2×#16813548C2semidirect
4. #20298503C2semidirect
5. #343×C113C2semidirect
28. C2×Dic226D4semidirect
43. M16×C113D4semidirect
94. C113#2007semidirect
99. #343D113semidirect
134. M16D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
#202991792
C2×#168135482
#202985032
#343×C1132
#2007113