Finite Group Databasebeta

← #28389571

Subgroups — #28389571

Order 14464.

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

normal subgroups only

This group has 216 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#20298926C211yesmaximal, characteristic, complemented
2#20298909C211yesmaximal, characteristic
3#20298528C211yesmaximal, characteristic, complemented
4#20298335C211yesmaximal, characteristic, complemented
5#20298332C211yesmaximal, characteristic
6#20298324C211yesmaximal, characteristic, complemented
7#539×C113C211yesmaximal, characteristic
8C2×C4⋊Dic113C2211yescharacteristic
9C2×#14268626—21no—
10#16813555—21no—
11#16813553—21no—
12#16813546—21no—
13#16813543—21no—
14C22⋊#11744751C2211yescharacteristic
15C22⋊#11744751C2211yescharacteristic
16#16813529—21no—
17#16813529C2211yescharacteristic
18#126×C113—21no—
19#125×C113—21no—
20#123×C113—21no—
21#123×C113—21no—
22C22⋊Q8×C113—21no—
23C22⋊Q8×C113C2211yescharacteristic
24#121×C113C2211yescharacteristic
25C4×D4×C113—21no—
26C2×C4⋊C4×C113C2211yescharacteristic
27C22×Dic113—21no—
28C22×Dic113—21no—
29C2×#11744751—21no—
30C2×#11744751—21no—
31C4⋊Dic113—21no—
32C4⋊Dic113—21no—
33#14268626—42no—
34C2×Q8×C113D411yescharacteristic
35C2×D4×C113—21no—
36C2×D4×C113D411yescharacteristic
37C22×C4×C113—21no—
38C22×C4×C113D411yescharacteristic
39C22×C4×C113D411yescharacteristic
40C22×C4×C113C2311yescharacteristic
41C4⋊C4×C113—21no—
42C4⋊C4×C113—21no—
43C4⋊C4×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113D411yescharacteristic
48C4⋊C4×C113D411yescharacteristic
49C22⋊C4×C113—21no—
50C22⋊C4×C113—21no—
51C22⋊C4×C113—21no—
52C22⋊C4×C113—21no—
53C22⋊C4×C113—21no—
54C42×C113—21no—
55C23×C113—21no—
56C23×C113C2×D411yescharacteristic
57Q8×C113—41no—
58D4×C113—41no—
59D4×C113—41no—
60D4×C113—41no—
61C2×C4×C113—21no—
62C2×C4×C113—21no—
63C2×C4×C113—21no—
64C2×C4×C113—21no—
65C2×C4×C113—21no—
66C2×C4×C113—21no—
67C2×C4×C113—21no—
68C2×C4×C113—41no—
69C2×C4×C113—41no—
70C2×C4×C113—81no—
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113C2×D411yescharacteristic
73C2×Dic113—22no—
74C2×Dic113—41no—
75C2×Dic113—41no—
76C2×Dic113—41no—
77C2×Dic113—41no—
78C2×Dic113—41no—
79#11744751—41no—
80#11744751—41no—
81C22×C113—21no—
82C22×C113—21no—
83C22×C113—41no—
84C22×C113—41no—
85C22×C113—41no—
86C22×C113#12011yescharacteristic
87C22×C113#13511yescharacteristic
88C22×C113AGL(1,ℤ/8)11yescharacteristic
89C4×C113—21no—
90C4×C113—21no—
91C4×C113—41no—
92C4×C113—41no—
93C4×C113—41no—
94C4×C113—41no—
95C4×C113—41no—
96Dic113—42no—
97Dic113—81no—
98C2×C113—21no—
99C2×C113—21no—
100C2×C113—81no—
101C2×C113#44911yescharacteristic
102C2×C113#45611yescharacteristic
103C2×C113#45811yescharacteristic
104#1609—1131nomaximal, Sylow
105C113#160911yescharacteristic, complemented, Sylow
106#539D11311yescharacteristic
107#483—1131no—
108#480—1131no—
109#398—1131no—
110#328—1131no—
111#327—1131no—
112#324—1131no—
113#126—21no—
114#125—21no—
115#123—21no—
116#123—21no—
117C22⋊Q8—21no—
118C22⋊Q8C2×D11311yescharacteristic
119#121C2×D11311yescharacteristic
120C4×D4—21no—
121C2×C4⋊C4—1131no—
122C2×C4⋊C4—2261no—
123C2×C4⋊C4C2×D11311yescharacteristic
124#107—2261no—
125#106—2261no—
126#103—2261no—
127#102—2261no—
128C22⋊C8—1131no—
129C22⋊C8—1131no—
130#95—1131no—
131#95—2261no—
132C2×Q8C22⋊D11311yescharacteristic
133C2×D4—21no—
134C2×D4C22⋊D11311yescharacteristic
135C22×C4—21no—
136C22×C4—2261no—
137C22×C4—2261no—
138C22×C4C22⋊D11311yescharacteristic
139C22×C4C22⋊D11311yescharacteristic
140C22×C4C22×D11311yescharacteristic
141C2×C8—2261no—
142C2×C8—2261no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—4522no—
150C4⋊C4—2261no—
151C4⋊C4—2261no—
152C4⋊C4C22⋊D11311yescharacteristic
153C4⋊C4C22⋊D11311yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C42—21no—
160C23—21no—
161C23C2×C22⋊D11311yescharacteristic
162Q8—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—81no—
176C2×C4—4521no—
177C2×C4—4521no—
178C2×C4—4521no—
179C2×C4—4521no—
180C2×C4—4521no—
181C2×C4—2262no—
182C2×C4C2×C22⋊D11311yescharacteristic
183C2×C4C2×C22⋊D11311yescharacteristic
184C8—4521no—
185C8—4521no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1681359111yescharacteristic
192C22#1681364211yescharacteristic
193C22#1681364711yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—41no—
199C4—41no—
200C4—41no—
201C4—9041no—
202C4—4522no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#2029874311yescharacteristic
207C2#2029878111yescharacteristic
208C2#2029878811yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#539×C113C2
socleC22×C113#120
prime radical#121×C113C22
hypercenter#539D113
hypocenterC113#1609
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #20298926C2semidirect
3. #20298528C2semidirect
4. #20298335C2semidirect
6. #20298324C2semidirect
105. C113#1609semidirect

Maximal subgroups

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

subgroupindex
#202989262
#202989092
#202985282
#202983352
#202983322
#202983242
#539×C1132
#1609113