Finite Group Databasebeta

← #15757427

Subgroups — #15757427

Order 3328.

412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 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#13115665C211yesmaximal, characteristic
2#13113624C212yesmaximal, complemented
3#13113498C211yesmaximal, characteristic
4#13112668C212yesmaximal, complemented
5C13×#2979C211yesmaximal, characteristic
6C13×#532C2211yescharacteristic
7C13×#436—22no—
8C8×D4×C13—22no—
9C13×#431C2212yes—
10C13×#408—22no—
11C2×#88077—22no—
12C42×Dic13C2211yescharacteristic
13#11718586C2212yes—
14#11718585C2211yescharacteristic
15#11718138C411yescharacteristic, complemented
16#11718138C411yescharacteristic, complemented
17#11718136C412yescomplemented
18#11718072—22no—
19#11718071—22no—
20C2×C13×#41D412yes—
21C2×C13×M16—22no—
22C22×C8×C13—22no—
23C13×C4⋊Q8C2×C411yescharacteristic
24C13×#127C2×C411yescharacteristic
25C13×#124Q812yes—
26C13×#121—22no—
27C4×D4×C13—22no—
28C2×C42×C13C2311yescharacteristic
29C2×C4×Dic13—21no—
30C2×C4×Dic13—22no—
31C2×#6099—21no—
32C13×C4⋊C8D412yes—
33C13×C4⋊C8D412yes—
34C13×C22⋊C8—24no—
35C13×C22⋊C8—22no—
36C4×C8×C13—22no—
37#88077—44no—
38C22⋊#1055—22no—
39C4⋊#1055—22no—
40C4⋊#1055C2×C412yes—
41C4⋊#1055C2×C412yes—
42C4×#1055—22no—
43#8935—131nomaximal, Sylow
44C13×#41—42no—
45C13×#41—42no—
46C2×Q8×C13C4⋊C412yes—
47C2×D4×C13—22no—
48C2×D4×C13—22no—
49C2×D4×C13C4⋊C412yes—
50C22×C4×C13—22no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13#4112yes—
53C22×Dic13—41no—
54C13×M16—82no—
55C2×C8×C13—22no—
56C2×C8×C13—22no—
57C2×C8×C13—82no—
58C13×C4⋊C4—22no—
59C13×C22⋊C4—24no—
60C42×C13C22×C411yescharacteristic
61C42×C13C2×D412yes—
62C42×C13C2×Q811yescharacteristic
63C4×Dic13—22no—
64C4×Dic13—24no—
65C4×Dic13—42no—
66C4×Dic13—41no—
67#6099—42no—
68C2×#1055—22no—
69C2×#1055—22no—
70C2×#1055—41no—
71#2979D1311yescharacteristic
72#1962—131no—
73#1574—132no—
74#1543—131no—
75#1276—132no—
76C23×C13—22no—
77C23×C13#12311yescharacteristic
78Q8×C13—42no—
79D4×C13—42no—
80D4×C13—42no—
81D4×C13—42no—
82D4×C13—82no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13C2×C4⋊C411yescharacteristic
91C2×C4×C13C4×D412yes—
92C2×C4×C13#12011yescharacteristic
93C2×C4×C13C22⋊Q812yes—
94C2×Dic13—42no—
95C2×Dic13—44no—
96C8×C13—42no—
97C8×C13—42no—
98#1055—42no—
99#1055—42no—
100#1055—81no—
101#532C2×D1311yescharacteristic
102#436—22no—
103C8×D4—22no—
104#431—132no—
105#431C2×D1312yes—
106#423—131no—
107C2×#104—262no—
108#408—22no—
109C43—131no—
110#335—262no—
111#334—262no—
112#333—131no—
113#333—131no—
114#331—132no—
115C22×C13—21no—
116C22×C13—22no—
117C22×C13—42no—
118C22×C13—44no—
119C22×C13#38511yescharacteristic
120C4×C13—21no—
121C4×C13—22no—
122C4×C13—42no—
123C4×C13#44312yes—
124C4×C13#44412yes—
125C4×C13#45311yescharacteristic
126C4×C13#45511yescharacteristic
127Dic13—44no—
128C2×#41C22⋊D1312yes—
129C2×M16—22no—
130C2×M16—261no—
131C22×C8—22no—
132C4⋊Q8C4×D1311yescharacteristic
133#127C4×D1311yescharacteristic
134#124Dic2612yes—
135#121—22no—
136C4×D4—22no—
137C2×C42—262no—
138C2×C42—261no—
139C2×C42C22×D1311yescharacteristic
140C4⋊C8—132no—
141C4⋊C8—132no—
142C4⋊C8—262no—
143C4⋊C8C22⋊D1312yes—
144C4⋊C8C22⋊D1312yes—
145#104—524no—
146C22⋊C8—24no—
147C22⋊C8—22no—
148C22⋊C8—262no—
149C4×C8—22no—
150C4×C8—262no—
151C2×C13—41no—
152C2×C13—82no—
153C2×C13#185611yescharacteristic
154C2×C13#186612yes—
155#41—42no—
156#41—42no—
157C2×Q8#610112yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4#610112yes—
161C22×C4—22no—
162C22×C4—521no—
163C22×C4#612712yes—
164C22×C4C2×C22⋊D1311yescharacteristic
165M16—82no—
166M16—522no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—82no—
170C2×C8—262no—
171C2×C8—262no—
172C2×C8—521no—
173C4⋊C4—22no—
174C22⋊C4—24no—
175C42—262no—
176C42—264no—
177C42—522no—
178C42—521no—
179C42C2×Dic2611yescharacteristic
180C42C2×C4×D1311yescharacteristic
181C42C2×C22⋊D1312yes—
182C13#893511yescharacteristic, complemented, Sylow
183C23—22no—
184C23#8818311yescharacteristic
185Q8—42no—
186D4—42no—
187D4—42no—
188D4—42no—
189D4—82no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—522no—
198C2×C4—524no—
199C2×C4C2×#610111yescharacteristic
200C2×C4#8817812yes—
201C2×C4C4×C22⋊D1312yes—
202C2×C4#8820711yescharacteristic
203C8—42no—
204C8—42no—
205C8—522no—
206C8—522no—
207C8—1041no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—44no—
212C22#1171887111yescharacteristic
213C4—21no—
214C4—22no—
215C4—42no—
216C4—524no—
217C4#1171880512yes—
218C4#1171880612yes—
219C4#1171890211yescharacteristic
220C4#1171890311yescharacteristic
221C2—41no—
222C2—82no—
223C2#1311504611yescharacteristic
224C2#1311511112yes—
subgroupG/H
centerC2×C4#88207
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2979C2
socleC22×C13#385
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#2979D13
hypocenterC13#8935
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #13113624C2semidirect
4. #13112668C2semidirect
15. #11718138C4semidirect
16. #11718138C4semidirect
17. #11718136C4semidirect
182. C13#8935semidirect

Maximal subgroups

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

subgroupindex
#131156652
#131136242
#131134982
#131126682
C13×#29792
#893513