Finite Group Databasebeta

← #16789640

Subgroups — #16789640

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
2#13131043C211yesmaximal, 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#11718257C412yescomplemented
14#11718234C412yes—
15#11718231C412yescomplemented
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#88098D411yescharacteristic
37#88098D411yescharacteristic
38#88098Q812yes—
39C13×M32C2×C412yes—
40C4×C8×C13C2×C411yescharacteristic
41C8×Dic13C2×C411yescharacteristic
42C8×Dic13C2×C411yescharacteristic
43#88052C2×C412yes—
44C4×#1055C2×C411yescharacteristic
45#88038—22no—
46C16×D13—22no—
47#12667—131nomaximal, Sylow
48C2×C4×D13—21no—
49C2×C4×D13C22×C411yescharacteristic
50C22⋊#261—22no—
51#6122—22no—
52C4⋊#261—22no—
53C4×#261—22no—
54#6118—22no—
55D13⋊C8—22no—
56C2×C8×C13C4211yescharacteristic
57C2×C8×C13C22×C411yescharacteristic
58C42×C13C4211yescharacteristic
59C4×Dic13—21no—
60C4×Dic13C4211yescharacteristic
61C2×#1055C4211yescharacteristic
62C2×#1055C22×C411yescharacteristic
63C8×D13M1611yescharacteristic
64C8×D13M1611yescharacteristic
65C8×D13M1611yescharacteristic
66C8×D13M1611yescharacteristic
67C8×D13C2×D411yescharacteristic
68C8×D13C2×Q811yescharacteristic
69C8×D13#4111yescharacteristic
70C8×D13#4111yescharacteristic
71#6092—22no—
72#6092C4⋊C412yes—
73#6092C4⋊C412yes—
74C13×C16—22no—
75#6090—22no—
76C2×#364—131no—
77#2110—132no—
78C4×M32—131no—
79#1772—131no—
80#1378—132no—
81C22×D13#13111yescharacteristic
82C2×#261—42no—
83C2×C4×C13—21no—
84C2×C4×C13C2×C4211yescharacteristic
85C2×Dic13—21no—
86C2×Dic13#13111yescharacteristic
87C4×D13—42no—
88C4×D13C4×D411yescharacteristic
89C4×D13C4×Q811yescharacteristic
90C4×D13C2×M1611yescharacteristic
91C4×D13C2×M1611yescharacteristic
92#1057—42no—
93C8×C13#9711yescharacteristic
94C8×C13#9711yescharacteristic
95C8×C13C4×D411yescharacteristic
96C8×C13C4×Q811yescharacteristic
97#1055#9711yescharacteristic
98#1055#9711yescharacteristic
99#1055C2×C4⋊C411yescharacteristic
100#1055#11711yescharacteristic
101C2×M32—131no—
102C2×M32—131no—
103C2×M32—132no—
104C2×#108—131no—
105#427—131no—
106#405—132no—
107C2×C4×C8—131no—
108#364—132no—
109#364—131no—
110#364#26111yescharacteristic, complemented
111#347—262no—
112#347—262no—
113#346—132no—
114C4×C16—132no—
115#339—132no—
116C22×C13#40511yescharacteristic
117C2×D13—41no—
118C2×D13#43611yescharacteristic
119C2×D13#44611yescharacteristic
120#261—82no—
121C4×C13—41no—
122C4×C13C4×C4⋊C411yescharacteristic
123C4×C13C2×#9711yescharacteristic
124Dic13—22no—
125Dic13#43611yescharacteristic
126Dic13#44611yescharacteristic
127C2×M16—132no—
128C22×C8—131no—
129C22×C8—131no—
130#117—132no—
131C2×C42—131no—
132M32—131no—
133M32—131no—
134M32—132no—
135M32—132no—
136M32—262no—
137M32—261no—
138M32—261no—
139M32C2×#26112yes—
140C2×C16—132no—
141C2×C16—132no—
142C2×C16—262no—
143#108—261no—
144#108—261no—
145#107—261no—
146#106—261no—
147#97—262no—
148C4×C8—131no—
149C4×C8—131no—
150C4×C8—131no—
151C4×C8—262no—
152C4×C8C2×#26111yescharacteristic
153C2×C13—21no—
154C2×C13#177011yescharacteristic
155D13—21no—
156D13—21no—
157C22×C4—131no—
158C22×C4—261no—
159M16—262no—
160M16—262no—
161C2×C8—131no—
162C2×C8—131no—
163C2×C8—131no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8—131no—
170C2×C8—131no—
171C2×C8—262no—
172C2×C8C4×#26111yescharacteristic
173C2×C8C22×#26111yescharacteristic
174C4⋊C4—262no—
175C22⋊C4—262no—
176C42—131no—
177C42—261no—
178C42—262no—
179C42C4×#26111yescharacteristic
180C16—22no—
181C16—132no—
182C16—132no—
183C16—262no—
184C16—262no—
185C13#1266711yescharacteristic, complemented, Sylow
186C23—131no—
187C2×C4—21no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—261no—
194C2×C4—522no—
195C2×C4—522no—
196C2×C4C2×C4×#26111yescharacteristic
197C8—131no—
198C8—131no—
199C8—131no—
200C8—131no—
201C8—522no—
202C8#8810011yescharacteristic
203C8#8810011yescharacteristic
204C8D4×#26111yescharacteristic
205C8Q8×#26111yescharacteristic
206C22—131no—
207C22—131no—
208C22—521no—
209C22#1171909911yescharacteristic
210C4—41no—
211C4—131no—
212C4—131no—
213C4—262no—
214C4—1042no—
215C4C4⋊C4×#26111yescharacteristic
216C4C2×#8810011yescharacteristic
217C2—21no—
218C2—261no—
219C2—261no—
220C2#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. #11718257C4semidirect
15. #11718231C4semidirect
18. C13×#364C4semidirect
19. #11718103C4semidirect
20. #11718055C4semidirect
110. #364#261semidirect
185. C13#12667semidirect

Maximal subgroups

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

subgroupindex
#131310562
#131310432
#131306382
#131298882
D13×#3642
#1266713