Finite Group Databasebeta

← #28391018

Subgroups — #28391018

Order 14464.

442 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 105 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, complemented
2C2×#16813549C212yesmaximal, complemented
3#20298562C211yesmaximal, characteristic, complemented
4#20298357C212yesmaximal, complemented
5#525×C113C211yesmaximal, characteristic
6C23×Dic113—21no—
7C2×#14268631C2212yes—
8C2×C4×Dic113—24no—
9C2×C4×Dic113—21no—
10C2×C4×Dic113C2212yes—
11#16813549—24no—
12C22⋊#11744751—22no—
13C2×#41×C113C2211yescharacteristic
14C23×C4×C113C2211yescharacteristic
15#123×C113—21no—
16C22⋊Q8×C113C412yescomplemented
17#121×C113C412yescomplemented
18#120×C113—21no—
19C4×D4×C113—22no—
20#117×C113C2211yescharacteristic
21C22×Dic113—24no—
22C22×Dic113—28no—
23C22×Dic113—22no—
24#14268631—22no—
25#14268631—22no—
26C2×#11744751—22no—
27C4×Dic113—24no—
28C4×Dic113—22no—
29C4×Dic113D414yescomplemented
30C24×C113D411yescharacteristic
31#41×C113—22no—
32#41×C113—22no—
33C2×Q8×C113C2×C411yescharacteristic, complemented
34C2×D4×C113—22no—
35C2×D4×C113—21no—
36C2×D4×C113C2×C411yescharacteristic, complemented
37C22×C4×C113—22no—
38C22×C4×C113—22no—
39C22×C4×C113—21no—
40C22×C4×C113C2×C412yes—
41C22×C4×C113D411yescharacteristic
42C22×C4×C113D412yes—
43C22×C4×C113C2311yescharacteristic
44C4⋊C4×C113—22no—
45C4⋊C4×C113C2×C412yescomplemented
46C22⋊C4×C113—22no—
47C22⋊C4×C113—21no—
48C22⋊C4×C113—22no—
49C42×C113—21no—
50C23×C113—24no—
51C23×C113—21no—
52C23×C113—21no—
53C23×C113—21no—
54C23×C113C22⋊C412yes—
55C23×C113C2×D411yescharacteristic
56Q8×C113—22no—
57D4×C113—22no—
58D4×C113—44no—
59D4×C113—41no—
60D4×C113—41no—
61C2×C4×C113—21no—
62C2×C4×C113—21no—
63C2×C4×C113—24no—
64C2×C4×C113—24no—
65C2×C4×C113—22no—
66C2×C4×C113—21no—
67C2×C4×C113—42no—
68C2×C4×C113C22⋊C412yes—
69C2×C4×C113C22×C411yescharacteristic
70C2×C4×C113C2×D412yes—
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113#4112yes—
73C2×Dic113—216no—
74C2×Dic113—28no—
75C2×Dic113—24no—
76#11744751—42no—
77C22×C113—24no—
78C22×C113—24no—
79C22×C113—22no—
80C22×C113—22no—
81C22×C113—22no—
82C22×C113—41no—
83C22×C113—42no—
84C22×C113#10414yescomplemented
85C22×C113C2×C22⋊C411yescharacteristic
86C22×C113#12011yescharacteristic
87C22×C113#12311yescharacteristic
88C4×C113—22no—
89C4×C113—41no—
90C4×C113—42no—
91C4×C113C4×D412yes—
92C4×C113#12112yes—
93Dic113—28no—
94C2×C113—21no—
95C2×C113—24no—
96C2×C113—21no—
97C2×C113—81no—
98C2×C113#38611yescharacteristic
99C2×C113C2×#10412yes—
100#1896—1131nomaximal, Sylow
101C113#189611yescharacteristic, complemented, Sylow
102#525D11311yescharacteristic
103C22×C42—1131no—
104C2×#104—1132no—
105#407—1131no—
106#339—1132no—
107C2×#41C2×D11311yescharacteristic
108C23×C4—2261no—
109C23×C4C2×D11311yescharacteristic
110C2×M16—1132no—
111#123—21no—
112C22⋊Q8Dic11312yescomplemented
113#121Dic11312yescomplemented
114#120—21no—
115C4×D4—22no—
116#117C2×D11311yescharacteristic
117C2×C42—1132no—
118C2×C42—2264no—
119C2×C42—2261no—
120#104—2264no—
121C22⋊C8—2262no—
122C24C22⋊D11311yescharacteristic
123#41—22no—
124#41—22no—
125C2×Q8C2×Dic11311yescharacteristic, complemented
126C2×D4—22no—
127C2×D4—21no—
128C2×D4C2×Dic11311yescharacteristic, complemented
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—2264no—
133C22×C4—2268no—
134C22×C4—2262no—
135C22×C4C2×Dic11312yes—
136C22×C4C22⋊D11311yescharacteristic
137C22×C4C22⋊D11312yes—
138C22×C4C22×D11311yescharacteristic
139M16—2262no—
140M16—2262no—
141C2×C8—2262no—
142C4⋊C4—22no—
143C4⋊C4C2×Dic11312yescomplemented
144C22⋊C4—22no—
145C22⋊C4—21no—
146C22⋊C4—22no—
147C42—21no—
148C42—1134no—
149C42—2264no—
150C42—2262no—
151C23—21no—
152C23—21no—
153C23—24no—
154C23—21no—
155C23C22⋊Dic11312yes—
156C23C2×C22⋊D11311yescharacteristic
157Q8—22no—
158D4—22no—
159D4—41no—
160D4—41no—
161D4—44no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—22616no—
170C2×C4—2268no—
171C2×C4—2264no—
172C2×C4C22⋊Dic11312yes—
173C2×C4C22×Dic11311yescharacteristic
174C2×C4D4×D11312yes—
175C2×C4C2×C22⋊D11311yescharacteristic
176C2×C4#1426864612yes—
177C8—4522no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—42no—
184C22—41no—
185C22#1681354914yescomplemented
186C22C2×C22⋊Dic11311yescharacteristic
187C22#1681359011yescharacteristic
188C22#1681360311yescharacteristic
189C4—22no—
190C4—42no—
191C4—41no—
192C4—2268no—
193C4D4×Dic11312yes—
194C4#1681359412yes—
195C2—21no—
196C2—21no—
197C2—24no—
198C2—81no—
199C2#2029847811yescharacteristic
200C2C2×#1681354912yes—
subgroupG/H
centerC2×C4C2×C22⋊D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting, prime radical#525×C113C2
socleC22×C113C2×C22⋊C4
cosocleC22×C4×C113C23
hypercenter#525D113
hypocenterC113#1896
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic113C2semidirect
2. C2×#16813549C2semidirect
3. #20298562C2semidirect
4. #20298357C2semidirect
16. C22⋊Q8×C113C4semidirect
17. #121×C113C4semidirect
29. C4×Dic113D4semidirect
33. C2×Q8×C113C2×C4semidirect
36. C2×D4×C113C2×C4semidirect
45. C4⋊C4×C113C2×C4semidirect
84. C22×C113#104semidirect
101. C113#1896semidirect
112. C22⋊Q8Dic113semidirect
113. #121Dic113semidirect
125. C2×Q8C2×Dic113semidirect
128. C2×D4C2×Dic113semidirect
143. C4⋊C4C2×Dic113semidirect
185. C22#16813549semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1132
C2×#168135492
#202985622
#202983572
#525×C1132
#1896113