Finite Group Databasebeta

← #16789636

Subgroups — #16789636

Order 3328.

296 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 110 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#13131056C212yesmaximal
2C4×#88098C211yesmaximal, characteristic
3#13130638C211yesmaximal, characteristic
4#13129888C212yesmaximal
5D13×#364C211yesmaximal, characteristic
6D13⋊#108C411yescharacteristic
7#11719092C411yescharacteristic
8#11719089C2212yes—
9C2×#88098C2211yescharacteristic
10C2×#88098C2211yescharacteristic
11D13×M32C2212yes—
12C4×C8×D13C2211yescharacteristic
13#11718258C412yescomplemented
14#11718234C412yes—
15C4×#6092C412yescomplemented
16#11718218—22no—
17#11718217—22no—
18C13×#364C411yescharacteristic, complemented
19#11718103C412yescomplemented
20#11718055C411yescharacteristic, complemented
21#88237C2×C412yes—
22D13⋊M16C2×C412yes—
23C2×C8×D13C2×C411yescharacteristic
24C2×C8×D13C2311yescharacteristic
25C42×D13C2×C411yescharacteristic
26C2×#6092C2×C412yes—
27C2×#6092C2×C412yes—
28#88104—21no—
29#88103—21no—
30#88102—21no—
31#88101—21no—
32#88100—22no—
33C8×#261—22no—
34#88098—21no—
35#88098—21no—
36#88098D412yes—
37#88098Q812yes—
38C13×M32C2×C412yes—
39C4×C8×C13C2×C411yescharacteristic
40C8×Dic13C2×C411yescharacteristic
41C8×Dic13C2×C411yescharacteristic
42#88052C2×C412yes—
43C4×#1055C2×C411yescharacteristic
44#88038—22no—
45C16×D13—22no—
46#12667—131nomaximal, Sylow
47C2×C4×D13—21no—
48C2×C4×D13C22×C411yescharacteristic
49C22⋊#261—22no—
50#6122—22no—
51C4⋊#261—22no—
52C4×#261—22no—
53#6118—22no—
54D13⋊C8—22no—
55C2×C8×C13C4211yescharacteristic
56C2×C8×C13C22×C411yescharacteristic
57C42×C13C4211yescharacteristic
58C4×Dic13—21no—
59C4×Dic13C4211yescharacteristic
60C2×#1055C4211yescharacteristic
61C2×#1055C22×C411yescharacteristic
62C8×D13M1611yescharacteristic
63C8×D13M1611yescharacteristic
64C8×D13M1611yescharacteristic
65C8×D13M1611yescharacteristic
66C8×D13C2×D411yescharacteristic
67C8×D13C2×Q811yescharacteristic
68C8×D13#4111yescharacteristic
69C8×D13#4111yescharacteristic
70#6092—22no—
71#6092C4⋊C414yes—
72C13×C16—22no—
73#6090—22no—
74C2×#364—131no—
75#2110—132no—
76C4×M32—131no—
77#1772—131no—
78#1378—132no—
79C22×D13#13111yescharacteristic
80C2×#261—42no—
81C2×C4×C13—21no—
82C2×C4×C13C2×C4211yescharacteristic
83C2×Dic13—21no—
84C2×Dic13#13111yescharacteristic
85C4×D13—42no—
86C4×D13C4×D411yescharacteristic
87C4×D13C4×Q811yescharacteristic
88C4×D13C2×M1611yescharacteristic
89C4×D13C2×M1611yescharacteristic
90#1057—42no—
91C8×C13#9711yescharacteristic
92C8×C13#9711yescharacteristic
93C8×C13C4×D411yescharacteristic
94C8×C13C4×Q811yescharacteristic
95#1055#9711yescharacteristic
96#1055#9711yescharacteristic
97#1055C2×C4⋊C411yescharacteristic
98#1055#11711yescharacteristic
99C2×M32—131no—
100C2×M32—131no—
101C2×M32—132no—
102C2×#108—131no—
103#427—131no—
104#405—132no—
105C2×C4×C8—131no—
106#364—132no—
107#364—131no—
108#364#26111yescharacteristic, complemented
109#347—262no—
110#347—262no—
111#346—132no—
112C4×C16—132no—
113#339—132no—
114C22×C13#40511yescharacteristic
115C2×D13—41no—
116C2×D13#43611yescharacteristic
117C2×D13#44611yescharacteristic
118#261—82no—
119C4×C13—22no—
120C4×C13C4×C4⋊C411yescharacteristic
121C4×C13C2×#9711yescharacteristic
122Dic13—41no—
123Dic13#43611yescharacteristic
124Dic13#44611yescharacteristic
125C2×M16—132no—
126C22×C8—131no—
127C22×C8—131no—
128#117—132no—
129C2×C42—131no—
130M32—132no—
131M32—132no—
132M32—132no—
133M32—262no—
134M32—261no—
135M32—261no—
136M32C2×#26112yes—
137C2×C16—132no—
138C2×C16—132no—
139C2×C16—262no—
140#108—261no—
141#108—261no—
142#107—261no—
143#106—261no—
144#97—262no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8—131no—
148C4×C8—262no—
149C4×C8C2×#26111yescharacteristic
150C2×C13—21no—
151C2×C13#177011yescharacteristic
152D13—21no—
153D13—21no—
154C22×C4—131no—
155C22×C4—261no—
156M16—262no—
157M16—262no—
158C2×C8—131no—
159C2×C8—131no—
160C2×C8—131no—
161C2×C8—131no—
162C2×C8—131no—
163C2×C8—131no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—262no—
169C2×C8C4×#26111yescharacteristic
170C2×C8C22×#26111yescharacteristic
171C4⋊C4—262no—
172C22⋊C4—262no—
173C42—131no—
174C42—261no—
175C42—262no—
176C42C4×#26111yescharacteristic
177C16—22no—
178C16—134no—
179C16—262no—
180C16—262no—
181C13#1266711yescharacteristic, complemented, Sylow
182C23—131no—
183C2×C4—21no—
184C2×C4—131no—
185C2×C4—131no—
186C2×C4—131no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—261no—
190C2×C4—522no—
191C2×C4—522no—
192C2×C4C2×C4×#26111yescharacteristic
193C8—131no—
194C8—131no—
195C8—131no—
196C8—131no—
197C8—522no—
198C8#8810011yescharacteristic
199C8#8810011yescharacteristic
200C8D4×#26111yescharacteristic
201C8Q8×#26111yescharacteristic
202C22—131no—
203C22—131no—
204C22—521no—
205C22#1171909911yescharacteristic
206C4—22no—
207C4—131no—
208C4—131no—
209C4—521no—
210C4—1042no—
211C4C4⋊C4×#26111yescharacteristic
212C4C2×#8810011yescharacteristic
213C2—21no—
214C2—261no—
215C2—261no—
216C2#1313063311yescharacteristic
subgroupG/H
centerC4C4⋊C4×#261
commutatorC2×C4×C13C2×C42
FrattiniC2×C8C22×#261
FittingC13×#364C4
socleC2×C13#1770
prime radicalC22×D13#131
cosocleC2×C8×D13C23
hypercenter#364#261
hypocenterC13#12667
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
13. #11718258C4semidirect
15. C4×#6092C4semidirect
18. C13×#364C4semidirect
19. #11718103C4semidirect
20. #11718055C4semidirect
108. #364#261semidirect
181. C13#12667semidirect

Maximal subgroups

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

subgroupindex
#131310562
C4×#880982
#131306382
#131298882
D13×#3642
#1266713