Finite Group Databasebeta

← #28391618

Subgroups — #28391618

Order 14464.

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

normal subgroups only

This group has 406 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×#16813650C212yesmaximal, complemented
2#20299179C211yesmaximal, characteristic, complemented
3C2×#16813548C212yesmaximal, complemented
4#20298499C211yesmaximal, characteristic, complemented
5#343×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2212yes—
7C22×D452C2211yescharacteristic
8#16813650—24no—
9#16813650—24no—
10C2×#14268636—22no—
11C2×D904—22no—
12#16813602—22no—
13#16813597—22no—
14#16813596—22no—
15C2×#14268624—22no—
16C2×C4×Dic113C2211yescharacteristic
17#16813548—24no—
18C2×M16×C113C2212yes—
19C2×C4⋊C4×C113C2211yescharacteristic
20C23×D113—21no—
21#14268647—22no—
22#14268647—22no—
23#14268647—22no—
24#14268647—22no—
25C2×Dic226D412yes—
26C2×D452—22no—
27C2×D452—22no—
28C2×D452—21no—
29C2×D452—22no—
30C2×D452D412yes—
31C2×D452D412yescomplemented
32C2×C22⋊D113—22no—
33C22×Dic113—21no—
34C2×C4×D113—22no—
35#14268636—28no—
36D904—28no—
37C4⋊Dic113—22no—
38#14268624—24no—
39#14268624—44no—
40C4×Dic113—22no—
41C22×C4×C113D412yes—
42C22×C4×C113C2311yescharacteristic
43M16×C113—22no—
44M16×C113D414yescomplemented
45C2×C8×C113—22no—
46C4⋊C4×C113—22no—
47C23×C113C2×D411yescharacteristic
48C22×D113—22no—
49C22×D113—22no—
50C22×D113—42no—
51C22×D113—42no—
52C22×D113—41no—
53C22×D113—41no—
54C2×C4×C113—22no—
55C2×C4×C113—42no—
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×D412yes—
58C2×C4×C113C2×D412yes—
59C2×C4×C113#4111yescharacteristic
60C22⋊D113—42no—
61C22⋊D113—42no—
62C2×Dic113—22no—
63C2×Dic113—22no—
64C2×Dic113—41no—
65C2×Dic113—41no—
66D452—22no—
67D452—24no—
68D452—22no—
69D452—42no—
70D452—82no—
71C4×D113—42no—
72C4×D113—42no—
73Dic226—22no—
74Dic226—22no—
75C8×C113—24no—
76C22×C113—21no—
77C22×C113—21no—
78C22×C113#12011yescharacteristic
79C22×C113#12111yescharacteristic
80C22×C113#12711yescharacteristic
81C2×D113—44no—
82C2×D113—42no—
83C2×D113—42no—
84C2×D113—42no—
85C2×D113—42no—
86C2×D113—82no—
87C2×D113—81no—
88C2×D113—81no—
89C4×C113—42no—
90C4×C113#12012yes—
91C4×C113#12112yes—
92Dic113—42no—
93Dic113—42no—
94C2×C113—21no—
95C2×C113—21no—
96C2×C113#39211yescharacteristic
97C2×C113#45311yescharacteristic
98C2×C113#45411yescharacteristic
99D113—82no—
100D113—82no—
101#2006—1131nomaximal, Sylow
102C113#200611yescharacteristic, complemented, Sylow
103C2×AGL(1,ℤ/8)—1132no—
104#537—1131no—
105C2×#104—1132no—
106#390—1131no—
107#343D11311yescharacteristic, complemented
108C2×#41—1132no—
109C22×D4—1131no—
110AGL(1,ℤ/8)—2264no—
111AGL(1,ℤ/8)—2264no—
112C2×SD16—2262no—
113C2×D8—2262no—
114C2×M16C2×D11312yes—
115C22⋊Q8—2262no—
116#121—2262no—
117#121—2262no—
118C2×C4⋊C4C2×D11311yescharacteristic
119C2×C22⋊C4—2262no—
120C2×C42—1131no—
121#104—2264no—
122C24—2261no—
123#41—2262no—
124#41—2262no—
125#41—2262no—
126#41—2262no—
127C2×Q8—1132no—
128C2×D4—1132no—
129C2×D4—1132no—
130C2×D4—2262no—
131C2×D4—2262no—
132C2×D4—2262no—
133C2×D4—2262no—
134C2×D4—2261no—
135C22×C4—2261no—
136C22×C4—2262no—
137C22×C4D45212yes—
138C22×C4C22×D11311yescharacteristic
139SD16—2268no—
140D8—2268no—
141M16—22no—
142M16D45214yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—2262no—
146C22⋊C4—4524no—
147C22⋊C4—2264no—
148C42—2262no—
149C23—4522no—
150C23—4522no—
151C23—4521no—
152C23—4521no—
153C23—2262no—
154C23—2262no—
155C23C2×D45211yescharacteristic
156Q8—2262no—
157Q8—2262no—
158D4—9042no—
159D4—4522no—
160D4—4522no—
161D4—4522no—
162D4—2262no—
163D4—2264no—
164D4—2262no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—4521no—
168C2×C4—4521no—
169C2×C4—4522no—
170C2×C4—4522no—
171C2×C4—2262no—
172C2×C4—2262no—
173C2×C4D4×D11311yescharacteristic
174C2×C4D4×D11312yes—
175C2×C4C2×D45212yes—
176C2×C4#1426864811yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—9042no—
181C22—9041no—
182C22—9041no—
183C22—4524no—
184C22—4522no—
185C22—4522no—
186C22—4522no—
187C22—4522no—
188C22#1681359211yescharacteristic
189C22#1681359711yescharacteristic
190C22#1681361911yescharacteristic
191C4—42no—
192C4—4522no—
193C4—4522no—
194C4#1681359212yes—
195C4#1681359712yes—
196C2—21no—
197C2—21no—
198C2—9042no—
199C2—9042no—
200C2#2029850811yescharacteristic
201C2#2029876811yescharacteristic
202C2#2029877311yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#343×C113C2
socleC22×C113#120
hypercenter#343D113
hypocenterC113#2006
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×#16813650C2semidirect
2. #20299179C2semidirect
3. C2×#16813548C2semidirect
4. #20298499C2semidirect
5. #343×C113C2semidirect
31. C2×D452D4semidirect
44. M16×C113D4semidirect
102. C113#2006semidirect
107. #343D113semidirect
142. M16D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
#202991792
C2×#168135482
#202984992
#343×C1132
#2006113