Finite Group Databasebeta

← #28390761

Subgroups — #28390761

Order 14464.

360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C22×C4⋊Dic113C211yesmaximal, characteristic
2C2×#16813555C212yesmaximal, complemented
3C2×C22⋊#11744751C211yesmaximal, characteristic
4#20298360C212yesmaximal, complemented
5#380×C113C211yesmaximal, characteristic
6C23×Dic113—21no—
7C22×#11744751C2212yes—
8C2×C4⋊Dic113—24no—
9C2×C4⋊Dic113—21no—
10C2×C4⋊Dic113C2212yes—
11#16813555—24no—
12C22⋊#11744751C414yescomplemented
13C23×C4×C113C2211yescharacteristic
14C2×C4⋊C4×C113C2211yescharacteristic
15C2×C4⋊C4×C113C2211yescharacteristic
16C2×C22⋊C4×C113—21no—
17#95×C113—21no—
18C22×Dic113—24no—
19C22×Dic113—22no—
20C22×Dic113—42no—
21C22×Dic113—42no—
22C2×#11744751—22no—
23C2×#11744751—22no—
24C2×#11744751C2×C414yescomplemented
25C4⋊Dic113—24no—
26C4⋊Dic113—22no—
27C4⋊Dic113D414yes—
28C24×C113D411yescharacteristic
29C22×C4×C113—22no—
30C22×C4×C113—22no—
31C22×C4×C113—21no—
32C22×C4×C113—21no—
33C22×C4×C113C2×C412yes—
34C22×C4×C113D411yescharacteristic
35C22×C4×C113Q812yes—
36C22×C4×C113C2311yescharacteristic
37C4⋊C4×C113—22no—
38C4⋊C4×C113—22no—
39C22⋊C4×C113—42no—
40C23×C113—21no—
41C23×C113—21no—
42C23×C113—21no—
43C23×C113—21no—
44C23×C113C4⋊C412yes—
45C23×C113D812yes—
46C23×C113Q1612yes—
47C23×C113C2×D411yescharacteristic
48C2×C4×C113—21no—
49C2×C4×C113—21no—
50C2×C4×C113—24no—
51C2×C4×C113—24no—
52C2×C4×C113—41no—
53C2×C4×C113—41no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113—41no—
58C2×C4×C113C4⋊C412yes—
59C2×C4×C113C22×C411yescharacteristic
60C2×C4×C113C2×D412yes—
61C2×C4×C113C2×Q811yescharacteristic
62C2×C4×C113#4112yes—
63C2×Dic113—24no—
64C2×Dic113—48no—
65C2×Dic113—42no—
66C2×Dic113—42no—
67#11744751—24no—
68C22×C113—22no—
69C22×C113—22no—
70C22×C113—22no—
71C22×C113—22no—
72C22×C113—22no—
73C22×C113—22no—
74C22×C113#10714yescomplemented
75C22×C113C2×C4⋊C411yescharacteristic
76C22×C113#12011yescharacteristic
77C22×C113#12311yescharacteristic
78C22×C113C2×D811yescharacteristic
79C22×C113C2×Q1611yescharacteristic
80C22×C113AGL(1,ℤ/8)11yescharacteristic
81C22×C113#13711yescharacteristic
82C4×C113—22no—
83C4×C113—81no—
84C4×C113—81no—
85C4×C113C4×D412yes—
86C4×C113C22⋊Q812yes—
87Dic113—44no—
88C2×C113—24no—
89C2×C113#38511yescharacteristic
90C2×C113C2×#10711yescharacteristic
91C2×C113#42811yescharacteristic
92C2×C113#44711yescharacteristic
93C2×C113#45111yescharacteristic
94C2×C113#48011yescharacteristic
95C2×C113#48411yescharacteristic
96#1852—1131nomaximal, Sylow
97C113#185211yescharacteristic, complemented, Sylow
98C22×C4⋊C4—1131no—
99C2×#107—1132no—
100C2×C22⋊C8—1131no—
101#380D11311yescharacteristic
102#340—1132no—
103C23×C4—2261no—
104C23×C4C2×D11311yescharacteristic
105C22×C8—1132no—
106C2×C4⋊C4—1132no—
107C2×C4⋊C4—2264no—
108C2×C4⋊C4—2261no—
109C2×C4⋊C4C2×D11311yescharacteristic
110C2×C4⋊C4C2×D11311yescharacteristic
111C2×C22⋊C4—21no—
112#107—2264no—
113C22⋊C8—1134no—
114#95—21no—
115C24C22⋊D11311yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—4522no—
121C22×C4—4522no—
122C22×C4—2264no—
123C22×C4—2262no—
124C22×C4Dic22612yes—
125C22×C4C4×D11312yes—
126C22×C4C22⋊D11311yescharacteristic
127C22×C4C22×D11311yescharacteristic
128C2×C8—1134no—
129C2×C8—2262no—
130C2×C8—2262no—
131C4⋊C4—22no—
132C4⋊C4—22no—
133C4⋊C4—1134no—
134C4⋊C4—2264no—
135C4⋊C4—2262no—
136C22⋊C4—42no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23#1426862612yes—
142C23#1426863212yes—
143C23#1426863712yes—
144C23C2×C22⋊D11311yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—4528no—
156C2×C4—4522no—
157C2×C4—4522no—
158C2×C4—2264no—
159C2×C4#1426862612yes—
160C2×C4C2×C4×D11311yescharacteristic
161C2×C4D4×D11312yes—
162C2×C4C2×Dic22611yescharacteristic
163C2×C4#1426864612yes—
164C8—2264no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#1681355514yescomplemented
172C22C2×#1426862611yescharacteristic
173C22#1681359011yescharacteristic
174C22#1681360311yescharacteristic
175C22C2×#1426863211yescharacteristic
176C22C2×#1426863711yescharacteristic
177C22#1681364711yescharacteristic
178C22#1681365211yescharacteristic
179C4—22no—
180C4—81no—
181C4—81no—
182C4—4524no—
183C4#1681358212yes—
184C4#1681359912yes—
185C2—24no—
186C2#2029847011yescharacteristic
187C2C2×#1681355511yescharacteristic
188C2#2029864111yescharacteristic
189C2#2029873111yescharacteristic
190C2#2029875311yescharacteristic
191C2#2029890911yescharacteristic
192C2#2029893111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#380×C113C2
socleC23×C113C2×D4
prime radicalC24×C113D4
cosocleC22×C4×C113C23
hypercenter#380D113
hypocenterC113#1852
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#16813555C2semidirect
4. #20298360C2semidirect
12. C22⋊#11744751C4semidirect
24. C2×#11744751C2×C4semidirect
74. C22×C113#107semidirect
97. C113#1852semidirect
171. C22#16813555semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic1132
C2×#168135552
C2×C22⋊#117447512
#202983602
#380×C1132
#1852113