Finite Group Databasebeta

← #28391616

Subgroups — #28391616

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×#16813647C212yesmaximal, complemented
2C2×#16813549C212yesmaximal, complemented
3#20298499C211yesmaximal, characteristic, complemented
4#20298367C211yesmaximal, characteristic, complemented
5#537×C113C211yesmaximal, characteristic, complemented
6C22×D452C2211yescharacteristic
7#16813647—24no—
8#16813647—24no—
9C2×#14268634—22no—
10C2×#14268632—22no—
11C2×#14268631C2212yes—
12C2×#14268624—22no—
13C2×C4×Dic113C2211yescharacteristic
14#16813549—24no—
15C2×#41×C113C2212yes—
16C22⋊Q8×C113—22no—
17#121×C113—22no—
18#121×C113—22no—
19C2×C4⋊C4×C113C2211yescharacteristic
20C23×D113—21no—
21C2×D452—22no—
22C2×D452—22no—
23C2×D452—21no—
24C2×D452D412yescomplemented
25C22×Dic113—21no—
26#14268634—28no—
27#14268632—28no—
28#14268631—22no—
29#14268631D414yescomplemented
30C2×#11744751—22no—
31#14268624—44no—
32C4×Dic113—22no—
33#41×C113—22no—
34#41×C113—22no—
35#41×C113—22no—
36#41×C113—22no—
37C2×Q8×C113D412yes—
38C2×D4×C113—22no—
39C2×D4×C113—22no—
40C2×D4×C113D412yes—
41C22×C4×C113—22no—
42C22×C4×C113D412yes—
43C22×C4×C113C2311yescharacteristic
44C4⋊C4×C113—22no—
45C4⋊C4×C113—22no—
46C22⋊C4×C113—24no—
47C23×C113—22no—
48C23×C113C2×D411yescharacteristic
49C22×D113—22no—
50C22×D113—42no—
51C22×D113—42no—
52C22×D113—41no—
53C22×D113—41no—
54Q8×C113—22no—
55Q8×C113—22no—
56D4×C113—22no—
57D4×C113—22no—
58D4×C113—42no—
59D4×C113—42no—
60D4×C113—82no—
61C2×C4×C113—22no—
62C2×C4×C113—22no—
63C2×C4×C113—42no—
64C2×C4×C113—42no—
65C2×C4×C113—42no—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113C2×D412yes—
68C2×C4×C113C2×D412yes—
69C2×C4×C113#4111yescharacteristic
70C2×Dic113—22no—
71C2×Dic113—41no—
72C2×Dic113—41no—
73D452—24no—
74D452—42no—
75#11744751—24no—
76C22×C113—21no—
77C22×C113—21no—
78C22×C113—42no—
79C22×C113—42no—
80C22×C113—42no—
81C22×C113#12011yescharacteristic
82C22×C113#12111yescharacteristic
83C22×C113#12711yescharacteristic
84C2×D113—44no—
85C2×D113—42no—
86C2×D113—82no—
87C2×D113—81no—
88C2×D113—81no—
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#537D11311yescharacteristic, complemented
105C2×#104—1132no—
106#390—1131no—
107#343—1131no—
108C2×#41C2×D11312yes—
109C22×D4—1131no—
110AGL(1,ℤ/8)—2264no—
111AGL(1,ℤ/8)—2264no—
112C2×SD16—2262no—
113C2×D8—2262no—
114C2×M16—1132no—
115C22⋊Q8—22no—
116#121—22no—
117#121—22no—
118C2×C4⋊C4C2×D11311yescharacteristic
119C2×C22⋊C4—2262no—
120C2×C42—1131no—
121#104—2264no—
122C24—2261no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D11312yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—1132no—
131C2×D4—2262no—
132C2×D4—2262no—
133C2×D4—2261no—
134C2×D4C22⋊D11312yes—
135C22×C4—22no—
136C22×C4—2261no—
137C22×C4C22⋊D11312yes—
138C22×C4C22×D11311yescharacteristic
139SD16—2268no—
140D8—2268no—
141M16—1134no—
142M16—2262no—
143C2×C8—2262no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—4524no—
148C42—2262no—
149C23—22no—
150C23—4522no—
151C23—4522no—
152C23—4521no—
153C23—4521no—
154C23—2262no—
155C23C2×C22⋊D11311yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—4522no—
164D4—2264no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—4521no—
171C2×C4—4521no—
172C2×C4—2262no—
173C2×C4D4×D11311yescharacteristic
174C2×C4D4×D11312yes—
175C2×C4C2×C22⋊D11312yes—
176C2×C4#1426864611yescharacteristic
177C8—2264no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—9042no—
184C22—9041no—
185C22—9041no—
186C22—4524no—
187C22—4522no—
188C22#1681359111yescharacteristic
189C22#1681359311yescharacteristic
190C22#1681361811yescharacteristic
191C4—42no—
192C4—42no—
193C4—4522no—
194C4#1681359012yes—
195C4#1681359412yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—9042no—
200C2#2029850611yescharacteristic
201C2#2029876611yescharacteristic
202C2#2029877111yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#537×C113C2
socleC22×C113#120
hypercenter#537D113
hypocenterC113#2006
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#16813647C2semidirect
2. C2×#16813549C2semidirect
3. #20298499C2semidirect
4. #20298367C2semidirect
5. #537×C113C2semidirect
24. C2×D452D4semidirect
29. #14268631D4semidirect
102. C113#2006semidirect
104. #537D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136472
C2×#168135492
#202984992
#202983672
#537×C1132
#2006113