Finite Group Databasebeta

← #16790851

Subgroups — #16790851

Order 3328.

310 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 92 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
1D13⋊#365C212yesmaximal
2#13130771C211yesmaximal, characteristic
3#13130638C211yesmaximal, characteristic
4#13129908C212yesmaximal
5D13×#364C211yesmaximal, characteristic
6D13⋊#108C2211yescharacteristic
7#11719092C2211yescharacteristic
8C2×#88101—21no—
9C2×#88101C2212yes—
10#11719089—21no—
11#11719059—21no—
12D13×M32C2212yes—
13C4×C8×D13C2211yescharacteristic
14#11718234—21no—
15#11718220—22no—
16#11718219—22no—
17C13×#364C411yescharacteristic, complemented
18#11718103C412yescomplemented
19#11718055C411yescharacteristic, complemented
20#88237—21no—
21C2×C4⋊#261—22no—
22C2×C4⋊#261—42no—
23D13⋊M16—21no—
24C2×C8×D13D411yescharacteristic
25C2×C8×D13C2311yescharacteristic
26C42×D13D411yescharacteristic
27#88104—21no—
28#88103D412yes—
29#88102Q812yes—
30#88101—22no—
31#88101—21no—
32#88101—22no—
33#88101—41no—
34#88101—41no—
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#13186—131nomaximal, Sylow
46C22×#261—42no—
47C2×C4×D13—21no—
48C2×C4×D13C2×D411yescharacteristic
49C22⋊#261—41no—
50#6122—41no—
51C4⋊#261—22no—
52C4⋊#261—42no—
53C4⋊#261—42no—
54C4⋊#261—84no—
55C4×#261—41no—
56#6118—22no—
57D13⋊C8—41no—
58C2×C8×C13C4⋊C411yescharacteristic
59C2×C8×C13C22×C411yescharacteristic
60C42×C13C4⋊C411yescharacteristic
61C4×Dic13—21no—
62C4×Dic13C4⋊C411yescharacteristic
63C2×#1055C4⋊C411yescharacteristic
64C2×#1055C2×Q811yescharacteristic
65C8×D13SD1611yescharacteristic
66C8×D13SD1611yescharacteristic
67C8×D13SD1611yescharacteristic
68C8×D13SD1611yescharacteristic
69C8×D13C2×D411yescharacteristic
70C8×D13C2×Q811yescharacteristic
71C8×D13#4111yescharacteristic
72C8×D13#4111yescharacteristic
73C13×C16—22no—
74#6090—22no—
75C2×#365—132no—
76C2×#364—131no—
77#1844—131no—
78#1772—131no—
79#1386—132no—
80C22×D13AGL(1,ℤ/8)11yescharacteristic
81C2×#261—42no—
82C2×#261—84no—
83C2×#261—82no—
84C2×C4×C13—21no—
85C2×C4×C13C2×C4⋊C411yescharacteristic
86C2×Dic13—21no—
87C2×Dic13#13711yescharacteristic
88C4×D13—24no—
89C4×D13#12111yescharacteristic
90C4×D13C22⋊Q811yescharacteristic
91C4×D13C2×SD1611yescharacteristic
92C4×D13C2×SD1611yescharacteristic
93#1057—42no—
94C8×C13#10611yescharacteristic
95C8×C13#10611yescharacteristic
96C8×C13C4×D411yescharacteristic
97C8×C13C4×Q811yescharacteristic
98#1055#10611yescharacteristic
99#1055#10611yescharacteristic
100#1055#12511yescharacteristic
101#1055C4⋊Q811yescharacteristic
102C2×M32—132no—
103C2×#108—131no—
104#427—131no—
105C2×#106—132no—
106C2×#106—261no—
107#405—261no—
108C2×C4×C8—131no—
109#384—261no—
110#365—262no—
111#365—262no—
112#364—132no—
113#364—131no—
114#364#26111yescharacteristic, complemented
115#339—261no—
116C22×C13#42811yescharacteristic
117C2×D13—22no—
118C2×D13#46011yescharacteristic
119C2×D13#47611yescharacteristic
120#261—82no—
121#261—162no—
122C4×C13—22no—
123C4×C13#38911yescharacteristic
124C4×C13C2×#10611yescharacteristic
125Dic13—22no—
126Dic13#46111yescharacteristic
127Dic13#47511yescharacteristic
128C2×M16—261no—
129C22×C8—131no—
130C22×C8—131no—
131#117—261no—
132C2×C4⋊C4—262no—
133C2×C4⋊C4—522no—
134C2×C42—131no—
135M32—132no—
136M32—262no—
137M32C2×#26112yes—
138C2×C16—262no—
139#108—132no—
140#108—261no—
141#107—132no—
142#106—261no—
143#106—262no—
144#106—262no—
145#106—521no—
146#106—521no—
147#97—521no—
148C4×C8—131no—
149C4×C8—131no—
150C4×C8—131no—
151C4×C8—521no—
152C4×C8C2×#26111yescharacteristic
153C2×C13—21no—
154C2×C13#194811yescharacteristic
155D13—21no—
156D13#223012yes—
157C22×C4—131no—
158C22×C4—261no—
159C22×C4—522no—
160M16—262no—
161M16—521no—
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—131no—
172C2×C8—521no—
173C2×C8C4⋊#26111yescharacteristic
174C2×C8C22×#26111yescharacteristic
175C4⋊C4—262no—
176C4⋊C4—522no—
177C4⋊C4—522no—
178C4⋊C4—1044no—
179C22⋊C4—521no—
180C42—131no—
181C42—261no—
182C42—521no—
183C42C4⋊#26111yescharacteristic
184C16—22no—
185C16—262no—
186C13#1318611yescharacteristic, complemented, Sylow
187C23—131no—
188C2×C4—21no—
189C2×C4—131no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—131no—
194C2×C4—264no—
195C2×C4—261no—
196C2×C4—522no—
197C2×C4—1042no—
198C2×C4—1044no—
199C2×C4C2×C4⋊#26111yescharacteristic
200C8—131no—
201C8—131no—
202C8—131no—
203C8—131no—
204C8—522no—
205C8#8810111yescharacteristic
206C8#8810111yescharacteristic
207C8D4×#26111yescharacteristic
208C8Q8×#26111yescharacteristic
209C22—131no—
210C22—131no—
211C22—262no—
212C22#1171909811yescharacteristic
213C4—22no—
214C4—131no—
215C4—131no—
216C4—262no—
217C4—1042no—
218C4—2082no—
219C4#1171908311yescharacteristic
220C4C2×#8810111yescharacteristic
221C2—21no—
222C2—132no—
223C2—261no—
224C2#1313094811yescharacteristic
subgroupG/H
centerC2#13130948
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#364C4
socleC2×C13#1948
prime radicalC22×D13AGL(1,ℤ/8)
cosocleC2×C8×D13C23
hypercenter#364#261
hypocenterC13#13186
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
114. #364#261semidirect
186. C13#13186semidirect

Maximal subgroups

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

subgroupindex
D13⋊#3652
#131307712
#131306382
#131299082
D13×#3642
#1318613