Finite Group Databasebeta

← #28391615

Subgroups — #28391615

Order 14464.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#16813648C212yesmaximal, complemented
2#20299179C211yesmaximal, characteristic, complemented
3C2×#16813550C212yesmaximal, complemented
4#20298367C211yesmaximal, characteristic, complemented
5#390×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2212yes—
7#16813648—24no—
8#16813648—24no—
9C2×#14268635—22no—
10C2×#14268632—22no—
11C2×#14268631C2212yes—
12#16813602—22no—
13#16813597—22no—
14#16813596—22no—
15#16813550—24no—
16C22×D4×C113C2211yescharacteristic
17C2×C4⋊C4×C113C2211yescharacteristic
18C2×C22⋊C4×C113—22no—
19C2×C42×C113C2211yescharacteristic
20#14268647—22no—
21#14268647—22no—
22#14268647—22no—
23#14268647—22no—
24C2×Dic226D412yes—
25C2×D452—22no—
26C2×D452D412yes—
27C2×C22⋊D113—22no—
28C2×C4×D113—22no—
29#14268635—28no—
30#14268632—28no—
31#14268631—22no—
32#14268631D414yescomplemented
33C2×#11744751—22no—
34C4⋊Dic113—22no—
35#14268624—24no—
36C24×C113—21no—
37C2×D4×C113—22no—
38C2×D4×C113—22no—
39C2×D4×C113—21no—
40C2×D4×C113D412yescomplemented
41C22×C4×C113—21no—
42C22×C4×C113D412yes—
43C22×C4×C113C2311yescharacteristic
44C4⋊C4×C113—22no—
45C22⋊C4×C113—44no—
46C42×C113—22no—
47C23×C113—22no—
48C23×C113—42no—
49C23×C113—42no—
50C23×C113—41no—
51C23×C113—41no—
52C23×C113C2×D411yescharacteristic
53C22×D113—22no—
54D4×C113—24no—
55D4×C113—42no—
56C2×C4×C113—22no—
57C2×C4×C113—22no—
58C2×C4×C113—41no—
59C2×C4×C113—41no—
60C2×C4×C113—42no—
61C2×C4×C113C2×D412yes—
62C2×C4×C113C2×D412yes—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113#4111yescharacteristic
65C22⋊D113—42no—
66C22⋊D113—42no—
67C2×Dic113—22no—
68D452—22no—
69D452—22no—
70D452—82no—
71C4×D113—42no—
72C4×D113—42no—
73Dic226—22no—
74Dic226—22no—
75#11744751—24no—
76C22×C113—21no—
77C22×C113—21no—
78C22×C113—44no—
79C22×C113—42no—
80C22×C113—82no—
81C22×C113—81no—
82C22×C113—81no—
83C22×C113#12011yescharacteristic
84C22×C113#12111yescharacteristic
85C22×C113#12711yescharacteristic
86C2×D113—42no—
87C2×D113—42no—
88C2×D113—42no—
89C4×C113—42no—
90C4×C113—42no—
91C4×C113#12012yes—
92C4×C113#12112yes—
93Dic113—42no—
94C2×C113—21no—
95C2×C113—21no—
96C2×C113—82no—
97C2×C113#39211yescharacteristic
98C2×C113#45311yescharacteristic
99C2×C113#45411yescharacteristic
100D113—82no—
101#2006—1131nomaximal, Sylow
102C113#200611yescharacteristic, complemented, Sylow
103C2×AGL(1,ℤ/8)—1132no—
104#537—1131no—
105C2×#104—1132no—
106#390D11311yescharacteristic, complemented
107#343—1131no—
108C2×#41—1132no—
109C22×D4C2×D11311yescharacteristic
110AGL(1,ℤ/8)—2264no—
111AGL(1,ℤ/8)—2264no—
112C2×SD16—2262no—
113C2×D8—2262no—
114C2×M16—1132no—
115C22⋊Q8—2262no—
116#121—2262no—
117#121—2262no—
118C2×C4⋊C4C2×D11311yescharacteristic
119C2×C22⋊C4—22no—
120C2×C42C2×D11311yescharacteristic
121#104—2264no—
122C24—21no—
123#41—2262no—
124#41—2262no—
125#41—2262no—
126#41—2262no—
127C2×Q8—1132no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—21no—
131C2×D4—1132no—
132C2×D4—2262no—
133C2×D4—2262no—
134C2×D4D45212yescomplemented
135C22×C4—21no—
136C22×C4—2262no—
137C22×C4C22⋊D11312yes—
138C22×C4C22×D11311yescharacteristic
139SD16—2268no—
140D8—2268no—
141M16—1134no—
142M16—2262no—
143C2×C8—2262no—
144C4⋊C4—22no—
145C4⋊C4—2262no—
146C22⋊C4—44no—
147C22⋊C4—2264no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—2262no—
155C23C2×C22⋊D11311yescharacteristic
156Q8—2262no—
157Q8—2262no—
158D4—24no—
159D4—42no—
160D4—9042no—
161D4—4522no—
162D4—4522no—
163D4—2262no—
164D4—2262no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—4522no—
171C2×C4—4522no—
172C2×C4—2262no—
173C2×C4D4×D11312yes—
174C2×C4D4×D11312yes—
175C2×C4C2×D45211yescharacteristic
176C2×C4#1426864711yescharacteristic
177C8—2264no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—4522no—
186C22—4522no—
187C22—4522no—
188C22#1681359011yescharacteristic
189C22#1681359611yescharacteristic
190C22#1681361811yescharacteristic
191C4—42no—
192C4—42no—
193C4—4522no—
194C4#1681359212yes—
195C4#1681359512yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—9042no—
200C2#2029850711yescharacteristic
201C2#2029876511yescharacteristic
202C2#2029877011yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#390×C113C2
socleC22×C113#120
hypercenter#390D113
hypocenterC113#2006
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. #20299179C2semidirect
3. C2×#16813550C2semidirect
4. #20298367C2semidirect
5. #390×C113C2semidirect
32. #14268631D4semidirect
40. C2×D4×C113D4semidirect
102. C113#2006semidirect
106. #390D113semidirect
134. C2×D4D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
#202991792
C2×#168135502
#202983672
#390×C1132
#2006113