Finite Group Databasebeta

← #16790843

Subgroups — #16790843

Order 3328.

280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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#13131192C212yesmaximal
2#13130776C211yesmaximal, characteristic
3#13130638C211yesmaximal, characteristic
4#13129917C212yesmaximal
5D13×#364C211yesmaximal, characteristic
6D13⋊#108C2211yescharacteristic
7C2×#88104C2212yes—
8C2×#88103—21no—
9#11719092C2211yescharacteristic
10#11719089—21no—
11#11719053—21no—
12D13×M32C2212yes—
13C4×C8×D13C2211yescharacteristic
14#11718234—21no—
15#11718224—22no—
16#11718223—22no—
17C13×#364C411yescharacteristic, complemented
18#11718103C412yescomplemented
19#11718055C411yescharacteristic, complemented
20#88237—21no—
21D13⋊M16—21no—
22C2×#6118—22no—
23C2×C8×D13D411yescharacteristic
24C2×C8×D13C2311yescharacteristic
25C42×D13D411yescharacteristic
26#88112—42no—
27#88104—22no—
28#88104—22no—
29#88104D412yes—
30#88103—21no—
31#88103—41no—
32#88103—41no—
33#88102—21no—
34#88101Q812yes—
35#88100—41no—
36C8×#261—41no—
37C13×M32C2×C412yes—
38C4×C8×C13C2×C411yescharacteristic
39C8×Dic13C2×C411yescharacteristic
40C8×Dic13Q811yescharacteristic
41#88052C2×C412yes—
42C4×#1055Q811yescharacteristic
43#88038—22no—
44C16×D13—22no—
45#13182—131nomaximal, Sylow
46C2×C4×D13—21no—
47C2×C4×D13C2×D411yescharacteristic
48C22⋊#261—41no—
49#6122—41no—
50C2×#1057—42no—
51C4⋊#261—22no—
52C4×#261—41no—
53#6118—22no—
54#6118—42no—
55#6118—42no—
56D13⋊C8—41no—
57C2×C8×C13C4⋊C411yescharacteristic
58C2×C8×C13C22×C411yescharacteristic
59C42×C13C4⋊C411yescharacteristic
60C4×Dic13—21no—
61C4×Dic13C4⋊C411yescharacteristic
62C2×#1055C4⋊C411yescharacteristic
63C2×#1055C2×Q811yescharacteristic
64C8×D13D811yescharacteristic
65C8×D13D811yescharacteristic
66C8×D13Q1611yescharacteristic
67C8×D13Q1611yescharacteristic
68C8×D13C2×D411yescharacteristic
69C8×D13C2×Q811yescharacteristic
70C8×D13#4111yescharacteristic
71C8×D13#4111yescharacteristic
72C13×C16—22no—
73#6090—22no—
74#2161—132no—
75C2×#364—131no—
76#1848—131no—
77#1772—131no—
78#1389—132no—
79C22×D13#13711yescharacteristic
80C2×#261—42no—
81C2×C4×C13—21no—
82C2×C4×C13C2×C4⋊C411yescharacteristic
83C2×Dic13—21no—
84C2×Dic13AGL(1,ℤ/8)11yescharacteristic
85C4×D13—42no—
86C4×D13#12111yescharacteristic
87C4×D13C22⋊Q811yescharacteristic
88C4×D13C2×D811yescharacteristic
89C4×D13C2×Q1611yescharacteristic
90#1057—42no—
91#1057—82no—
92C8×C13#10711yescharacteristic
93C8×C13#10711yescharacteristic
94C8×C13C4×D411yescharacteristic
95C8×C13C4×Q811yescharacteristic
96#1055#10711yescharacteristic
97#1055#10711yescharacteristic
98#1055#12511yescharacteristic
99#1055C4⋊Q811yescharacteristic
100C2×M32—132no—
101C2×#108—131no—
102C2×#108—132no—
103C2×#108—261no—
104#427—131no—
105#423—261no—
106#405—261no—
107C2×C4×C8—131no—
108#368—262no—
109#368—262no—
110#364—132no—
111#364—131no—
112#364#26111yescharacteristic, complemented
113#339—261no—
114C22×C13#42811yescharacteristic
115C2×D13—41no—
116C2×D13#46211yescharacteristic
117C2×D13#47411yescharacteristic
118#261—82no—
119C4×C13—41no—
120C4×C13#38911yescharacteristic
121C4×C13C2×#10711yescharacteristic
122Dic13—22no—
123Dic13#45911yescharacteristic
124Dic13#47711yescharacteristic
125C2×M16—261no—
126C2×M16—262no—
127C22×C8—131no—
128C22×C8—131no—
129#117—261no—
130C2×C42—131no—
131M32—132no—
132M32—262no—
133M32C2×#26112yes—
134C2×C16—262no—
135#108—132no—
136#108—261no—
137#108—262no—
138#108—262no—
139#108—521no—
140#108—521no—
141#107—261no—
142#106—132no—
143C4⋊C8—522no—
144#97—521no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8—131no—
148C4×C8—521no—
149C4×C8C2×#26111yescharacteristic
150C2×C13—21no—
151C2×C13#194711yescharacteristic
152D13—21no—
153D13—21no—
154C22×C4—131no—
155C22×C4—261no—
156M16—262no—
157M16—521no—
158M16—522no—
159M16—522no—
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—131no—
169C2×C8—131no—
170C2×C8—521no—
171C2×C8—522no—
172C2×C8C4⋊#26111yescharacteristic
173C2×C8C22×#26111yescharacteristic
174C4⋊C4—262no—
175C22⋊C4—521no—
176C42—131no—
177C42—261no—
178C42—521no—
179C42C4⋊#26111yescharacteristic
180C16—22no—
181C16—262no—
182C13#1318211yescharacteristic, complemented, Sylow
183C23—131no—
184C2×C4—21no—
185C2×C4—131no—
186C2×C4—131no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—261no—
191C2×C4—522no—
192C2×C4—522no—
193C2×C4C2×C4⋊#26111yescharacteristic
194C8—131no—
195C8—131no—
196C8—131no—
197C8—131no—
198C8—522no—
199C8—1042no—
200C8#8810211yescharacteristic
201C8#8810211yescharacteristic
202C8D4×#26111yescharacteristic
203C8Q8×#26111yescharacteristic
204C22—131no—
205C22—131no—
206C22—521no—
207C22#1171909811yescharacteristic
208C4—41no—
209C4—131no—
210C4—131no—
211C4—262no—
212C4—1042no—
213C4#1171908311yescharacteristic
214C4C2×#8810211yescharacteristic
215C2—21no—
216C2—261no—
217C2—261no—
218C2#1313094711yescharacteristic
subgroupG/H
centerC2#13130947
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#364C4
socleC2×C13#1947
prime radicalC22×D13#137
cosocleC2×C8×D13C23
hypercenter#364#261
hypocenterC13#13182
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
17. C13×#364C4semidirect
18. #11718103C4semidirect
19. #11718055C4semidirect
112. #364#261semidirect
182. C13#13182semidirect

Maximal subgroups

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

subgroupindex
#131311922
#131307762
#131306382
#131299172
D13×#3642
#1318213