Finite Group Databasebeta

← #16790844

Subgroups — #16790844

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#13130777C211yesmaximal, characteristic
3#13130638C211yesmaximal, characteristic
4#13129917C212yesmaximal
5D13×#364C211yesmaximal, characteristic
6D13⋊#108C2211yescharacteristic
7C2×#88104—21no—
8C2×#88104C2212yes—
9#11719092C2211yescharacteristic
10#11719089—21no—
11#11719052—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
26C4⋊#1057—42no—
27#88104—22no—
28#88104—22no—
29#88104—41no—
30#88104—41no—
31#88104D411yescharacteristic
32#88104D411yescharacteristic
33#88103—21no—
34#88102—21no—
35#88101Q812yes—
36#88100—41no—
37C8×#261—41no—
38C13×M32C2×C412yes—
39C4×C8×C13C2×C411yescharacteristic
40C8×Dic13C2×C411yescharacteristic
41C8×Dic13Q811yescharacteristic
42#88052C2×C412yes—
43C4×#1055Q811yescharacteristic
44#88038—22no—
45C16×D13—22no—
46#13182—131nomaximal, Sylow
47C2×C4×D13—21no—
48C2×C4×D13C2×D411yescharacteristic
49C22⋊#261—41no—
50#6122—41no—
51C2×#1057—42no—
52C4⋊#261—22no—
53C4×#261—41no—
54#6118—21no—
55#6118—21no—
56#6118—42no—
57#6118—42no—
58D13⋊C8—41no—
59C2×C8×C13C4⋊C411yescharacteristic
60C2×C8×C13C22×C411yescharacteristic
61C42×C13C4⋊C411yescharacteristic
62C4×Dic13—21no—
63C4×Dic13C4⋊C411yescharacteristic
64C2×#1055C4⋊C411yescharacteristic
65C2×#1055C2×Q811yescharacteristic
66C8×D13D811yescharacteristic
67C8×D13D811yescharacteristic
68C8×D13Q1611yescharacteristic
69C8×D13Q1611yescharacteristic
70C8×D13C2×D411yescharacteristic
71C8×D13C2×Q811yescharacteristic
72C8×D13#4111yescharacteristic
73C8×D13#4111yescharacteristic
74C13×C16—22no—
75#6090—22no—
76#2161—132no—
77C2×#364—131no—
78#1848—131no—
79#1772—131no—
80#1389—132no—
81C22×D13#13711yescharacteristic
82C2×#261—42no—
83C2×C4×C13—21no—
84C2×C4×C13C2×C4⋊C411yescharacteristic
85C2×Dic13—21no—
86C2×Dic13AGL(1,ℤ/8)11yescharacteristic
87C4×D13—42no—
88C4×D13#12111yescharacteristic
89C4×D13C22⋊Q811yescharacteristic
90C4×D13C2×D811yescharacteristic
91C4×D13C2×Q1611yescharacteristic
92#1057—41no—
93#1057—41no—
94#1057—82no—
95C8×C13#10711yescharacteristic
96C8×C13#10711yescharacteristic
97C8×C13C4×D411yescharacteristic
98C8×C13C4×Q811yescharacteristic
99#1055#10711yescharacteristic
100#1055#10711yescharacteristic
101#1055#12511yescharacteristic
102#1055C4⋊Q811yescharacteristic
103C2×M32—132no—
104C2×#108—131no—
105C2×#108—132no—
106C2×#108—261no—
107#427—131no—
108#423—261no—
109#405—261no—
110C2×C4×C8—131no—
111#368—262no—
112#368—262no—
113#364—132no—
114#364—131no—
115#364#26111yescharacteristic, complemented
116#339—261no—
117C22×C13#42811yescharacteristic
118C2×D13—41no—
119C2×D13#46211yescharacteristic
120C2×D13#47411yescharacteristic
121#261—82no—
122C4×C13—22no—
123C4×C13#38911yescharacteristic
124C4×C13C2×#10711yescharacteristic
125Dic13—41no—
126Dic13#45911yescharacteristic
127Dic13#47711yescharacteristic
128C2×M16—261no—
129C2×M16—262no—
130C22×C8—131no—
131C22×C8—131no—
132#117—261no—
133C2×C42—131no—
134M32—132no—
135M32—262no—
136M32C2×#26112yes—
137C2×C16—262no—
138#108—131no—
139#108—131no—
140#108—261no—
141#108—262no—
142#108—262no—
143#108—521no—
144#108—521no—
145#107—261no—
146#106—132no—
147C4⋊C8—522no—
148#97—521no—
149C4×C8—131no—
150C4×C8—131no—
151C4×C8—131no—
152C4×C8—521no—
153C4×C8C2×#26111yescharacteristic
154C2×C13—21no—
155C2×C13#194711yescharacteristic
156D13—21no—
157D13—21no—
158C22×C4—131no—
159C22×C4—261no—
160M16—261no—
161M16—261no—
162M16—521no—
163M16—522no—
164M16—522no—
165C2×C8—131no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8—131no—
170C2×C8—131no—
171C2×C8—131no—
172C2×C8—131no—
173C2×C8—131no—
174C2×C8—131no—
175C2×C8—521no—
176C2×C8—522no—
177C2×C8C4⋊#26111yescharacteristic
178C2×C8C22×#26111yescharacteristic
179C4⋊C4—262no—
180C22⋊C4—521no—
181C42—131no—
182C42—261no—
183C42—521no—
184C42C4⋊#26111yescharacteristic
185C16—22no—
186C16—262no—
187C13#1318211yescharacteristic, complemented, Sylow
188C23—131no—
189C2×C4—21no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—131no—
194C2×C4—131no—
195C2×C4—261no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4C2×C4⋊#26111yescharacteristic
199C8—131no—
200C8—131no—
201C8—131no—
202C8—131no—
203C8—521no—
204C8—521no—
205C8—1042no—
206C8#8810211yescharacteristic
207C8#8810211yescharacteristic
208C8D4×#26111yescharacteristic
209C8Q8×#26111yescharacteristic
210C22—131no—
211C22—131no—
212C22—521no—
213C22#1171909811yescharacteristic
214C4—22no—
215C4—131no—
216C4—131no—
217C4—521no—
218C4—1042no—
219C4#1171908311yescharacteristic
220C4C2×#8810211yescharacteristic
221C2—21no—
222C2—261no—
223C2—261no—
224C2#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
115. #364#261semidirect
187. C13#13182semidirect

Maximal subgroups

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

subgroupindex
#131311922
#131307772
#131306382
#131299172
D13×#3642
#1318213