Finite Group Databasebeta

← #28389593

Subgroups — #28389593

Order 14464.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#20299160C211yesmaximal, characteristic
2#20298916C212yesmaximal, complemented
3#20298331C212yesmaximal, complemented
4#20298322C211yesmaximal, characteristic, complemented
5#399×C113C211yesmaximal, characteristic, complemented
6C22×C22⋊D113—21no—
7#16813606—22no—
8#16813596—21no—
9#16813596C2212yes—
10#16813592—22no—
11#16813553—22no—
12#16813542—22no—
13C22⋊#11744751C2212yescomplemented
14C2×C4⋊C4×C113—21no—
15C2×C4⋊C4×C113C2211yescharacteristic, complemented
16C2×C22⋊C4×C113—21no—
17C2×C22⋊C4×C113C2211yescharacteristic
18#95×C113C2211yescharacteristic, complemented
19C23×D113—21no—
20C2×D452—21no—
21C2×D452D412yes—
22C2×C22⋊D113—22no—
23C2×C22⋊D113—22no—
24C2×C22⋊D113—42no—
25C2×C22⋊D113—42no—
26C22×Dic113—21no—
27C2×#11744751—22no—
28C4⋊Dic113—21no—
29C4⋊Dic113D412yes—
30#14268624—22no—
31#14268624—22no—
32C24×C113D411yescharacteristic
33C22×C4×C113—21no—
34C22×C4×C113—21no—
35C22×C4×C113D411yescharacteristic
36C22×C4×C113C2311yescharacteristic
37C4⋊C4×C113—22no—
38C4⋊C4×C113—42no—
39C22⋊C4×C113—22no—
40C22⋊C4×C113—42no—
41C23×C113—21no—
42C23×C113—21no—
43C23×C113—41no—
44C23×C113—41no—
45C23×C113SD1612yes—
46C23×C113C2×D411yescharacteristic
47C22×D113—22no—
48C22×D113—42no—
49C22×D113—81no—
50C22×D113—81no—
51C2×C4×C113—22no—
52C2×C4×C113—21no—
53C2×C4×C113—41no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113—41no—
58C2×C4×C113—41no—
59C2×C4×C113—41no—
60C2×C4×C113C2×D412yes—
61C22⋊D113—44no—
62C22⋊D113—42no—
63C22⋊D113—42no—
64C2×Dic113—22no—
65C2×Dic113—42no—
66D452—42no—
67D452—81no—
68#11744751—42no—
69C22×C113—21no—
70C22×C113—21no—
71C22×C113—22no—
72C22×C113—42no—
73C22×C113—41no—
74C22×C113—41no—
75C22×C113—81no—
76C22×C113#12011yescharacteristic
77C22×C113C2×SD1611yescharacteristic
78C22×C113AGL(1,ℤ/8)11yescharacteristic
79C2×D113—42no—
80C2×D113—42no—
81C2×D113—42no—
82C2×D113—84no—
83C4×C113—22no—
84C4×C113—42no—
85C4×C113—41no—
86C4×C113—81no—
87Dic113—42no—
88C2×C113—21no—
89C2×C113—21no—
90C2×C113—42no—
91C2×C113#45011yescharacteristic
92C2×C113#45311yescharacteristic
93C2×C113#45811yescharacteristic
94D113—82no—
95#1613—1131nomaximal, Sylow
96C113#161311yescharacteristic, complemented, Sylow
97#534—1131no—
98#481—1132no—
99#399D11311yescharacteristic, complemented
100#327—1132no—
101#323—1131no—
102C22×D4—2261no—
103#123—2262no—
104#121—1132no—
105#121—2261no—
106#120—2262no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4C2×D11311yescharacteristic, complemented
109C2×C22⋊C4—21no—
110C2×C22⋊C4C2×D11311yescharacteristic
111#106—2262no—
112#102—2262no—
113C22⋊C8—1132no—
114#95C2×D11311yescharacteristic, complemented
115C24—2261no—
116C24C22⋊D11311yescharacteristic
117C2×D4—1132no—
118C2×D4—4522no—
119C2×D4—4522no—
120C2×D4—2261no—
121C2×D4—2262no—
122C2×D4—2262no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—2261no—
126C22×C4C22⋊D11311yescharacteristic
127C22×C4C22×D11311yescharacteristic
128C2×C8—2262no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—1132no—
132C4⋊C4—2261no—
133C22⋊C4—22no—
134C22⋊C4—42no—
135C22⋊C4—2262no—
136C22⋊C4—2262no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—9041no—
142C23—9041no—
143C23—4522no—
144C23—2262no—
145C23#1426863412yes—
146C23C2×C22⋊D11311yescharacteristic
147D4—9041no—
148D4—4522no—
149D4—4524no—
150D4—4522no—
151D4—4522no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—4522no—
162C2×C4—2262no—
163C2×C4D4×D11312yes—
164C8—4522no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—9044no—
173C22—4522no—
174C22—4522no—
175C22—4522no—
176C22#1681359011yescharacteristic
177C22C2×#1426863411yescharacteristic
178C22#1681364711yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—81no—
183C4—4522no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—9042no—
188C2#2029874811yescharacteristic
189C2#2029876511yescharacteristic
190C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#399×C113C2
socleC22×C113#120
prime radical#20299160C2
hypercenter#399D113
hypocenterC113#1613
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #20298916C2semidirect
3. #20298331C2semidirect
4. #20298322C2semidirect
5. #399×C113C2semidirect
13. C22⋊#11744751C22semidirect
15. C2×C4⋊C4×C113C22semidirect
18. #95×C113C22semidirect
96. C113#1613semidirect
99. #399D113semidirect
108. C2×C4⋊C4C2×D113semidirect
114. #95C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991602
#202989162
#202983312
#202983222
#399×C1132
#1613113