Finite Group Databasebeta

← #13115072

Subgroups — #13115072

Order 1664.

286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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#11719209C211yesmaximal, characteristic
2C2×#88065C211yesmaximal, characteristic
3#11718794C211yesmaximal, characteristic
4#11718782C211yesmaximal, characteristic, complemented
5#11718638C211yesmaximal, characteristic, complemented
6C13×#343C211yesmaximal, characteristic, complemented
7#11718147C211yesmaximal, characteristic, complemented
8C2×#6127C2211yescharacteristic
9C2×C13×M16C2211yescharacteristic
10C2×C13×M16C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C4×C22⋊D13—22no—
13#88180C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4×Dic13C2211yescharacteristic
16#88147—21no—
17#88146—21no—
18C4⋊C4×D13—21no—
19#88141—21no—
20#88071—22no—
21#88065C414yescomplemented
22#88061—21no—
23#88058—21no—
24#88057—21no—
25#88056—21no—
26C22×C4×C13D412yes—
27C22×C4×C13C2311yescharacteristic
28C2×C22⋊D13—21no—
29C22×Dic13—21no—
30C22×Dic13—21no—
31#6127—21no—
32#6127—21no—
33#6127C2×C412yes—
34#6127Q812yes—
35C2×D52D411yescharacteristic
36C2×C4×D13—21no—
37C2×C4×D13—22no—
38C2×Dic26D411yescharacteristic
39C13×M16—21no—
40C13×M16—21no—
41C13×M16—21no—
42C13×M16C2×C412yescomplemented
43C2×C8×C13—21no—
44C2×C8×C13—21no—
45C13×C4⋊C4—21no—
46C13×C4⋊C4—21no—
47C22⋊Dic13—21no—
48#6103—22no—
49C4⋊Dic13—21no—
50C4⋊Dic13—21no—
51C4⋊Dic13D411yescharacteristic
52C4⋊Dic13D411yescharacteristic
53#6101—22no—
54C4×Dic13—22no—
55C4×Dic13—21no—
56C4×Dic13—21no—
57C4×Dic13C2×C412yescomplemented
58#1860—131nomaximal, Sylow
59C23×C13C2×D411yescharacteristic
60C22×D13—21no—
61C2×C4×C13—22no—
62C2×C4×C13—42no—
63C2×C4×C13C22×C411yescharacteristic
64C2×C4×C13C2×D411yescharacteristic
65C2×C4×C13C2×D411yescharacteristic
66C2×C4×C13C2×Q811yescharacteristic
67C2×C4×C13#4111yescharacteristic
68C2×C4×C13#4111yescharacteristic
69C22⋊D13—22no—
70C22⋊D13—22no—
71C2×Dic13—21no—
72C2×Dic13—22no—
73C2×Dic13—21no—
74C2×Dic13—21no—
75C2×Dic13—41no—
76C2×Dic13—41no—
77C2×Dic13—42no—
78C2×Dic13—41no—
79D52—21no—
80D52C4⋊C412yes—
81C4×D13—22no—
82C4×D13—22no—
83C4×D13—82no—
84Dic26—21no—
85Dic26C4⋊C412yes—
86C8×C13—22no—
87C8×C13—41no—
88#520—131no—
89#428—131no—
90C2×#104—131no—
91#417—131no—
92#382—131no—
93#343D1311yescharacteristic, complemented
94#339—131no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13C4×D411yescharacteristic
98C22×C13#12011yescharacteristic
99C22×C13C22⋊Q811yescharacteristic
100C2×D13—22no—
101C2×D13—41no—
102C2×D13—41no—
103C4×C13—42no—
104C4×C13C2×C4⋊C411yescharacteristic
105C4×C13C4×D411yescharacteristic
106C4×C13C22⋊Q811yescharacteristic
107C4×C13#12311yescharacteristic
108Dic13—22no—
109Dic13—42no—
110Dic13—41no—
111Dic13—41no—
112Dic13—81no—
113C2×#41—131no—
114C2×M16C2×D1311yescharacteristic
115C2×M16C2×D1311yescharacteristic
116C4×Q8—261no—
117C4×D4—261no—
118C4×D4—262no—
119#117—131no—
120#117—261no—
121C2×C4⋊C4—131no—
122C2×C4⋊C4—261no—
123C2×C4⋊C4C2×D1311yescharacteristic
124C2×C42—131no—
125#107—261no—
126#106—261no—
127#104—134no—
128#103—261no—
129#102—261no—
130#95—262no—
131C2×C13—21no—
132C2×C13—21no—
133C2×C13#38511yescharacteristic
134C2×C13#45411yescharacteristic
135C2×C13#45511yescharacteristic
136D13—42no—
137#41—132no—
138#41—132no—
139#41—261no—
140#41—261no—
141C2×Q8—131no—
142C2×D4—131no—
143C2×D4—261no—
144C22×C4—262no—
145C22×C4—261no—
146C22×C4—261no—
147C22×C4—261no—
148C22×C4D5212yes—
149C22×C4C22×D1311yescharacteristic
150M16—21no—
151M16—21no—
152M16—21no—
153M16C4×D1312yescomplemented
154C2×C8—21no—
155C2×C8—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—131no—
159C4⋊C4—131no—
160C4⋊C4—262no—
161C4⋊C4—261no—
162C4⋊C4—261no—
163C22⋊C4—262no—
164C22⋊C4—261no—
165C42—132no—
166C42—262no—
167C42—261no—
168C42—261no—
169C13#186011yescharacteristic, complemented, Sylow
170C23—261no—
171C23C2×D5211yescharacteristic
172Q8—132no—
173Q8—261no—
174D4—132no—
175D4—262no—
176D4—262no—
177D4—261no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—261no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—261no—
185C2×C4—261no—
186C2×C4—521no—
187C2×C4—521no—
188C2×C4—522no—
189C2×C4—521no—
190C2×C4—1042no—
191C2×C4C2×C4×D1311yescharacteristic
192C2×C4#612711yescharacteristic
193C2×C4D4×D1311yescharacteristic
194C2×C4D4×D1311yescharacteristic
195C2×C4#612911yescharacteristic
196C2×C4Q8×D1311yescharacteristic
197C8—22no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—262no—
202C22—521no—
203C22—521no—
204C22C4×D5211yescharacteristic
205C22#8813611yescharacteristic
206C22#8815111yescharacteristic
207C4—42no—
208C4—262no—
209C4—522no—
210C4—521no—
211C4—521no—
212C4—1041no—
213C4#8813511yescharacteristic
214C4#8813711yescharacteristic
215C4C4⋊C4×D1311yescharacteristic
216C4#8815011yescharacteristic
217C2—21no—
218C2—21no—
219C2—522no—
220C2#1171832911yescharacteristic
221C2#1171840711yescharacteristic
222C2#1171841411yescharacteristic
subgroupG/H
centerC22#88136
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#343C2
socleC22×C13#120
prime radicalC2×#6127C22
cosocleC22×C4×C13C23
hypercenter#343D13
hypocenterC13#1860
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
4. #11718782C2semidirect
5. #11718638C2semidirect
6. C13×#343C2semidirect
7. #11718147C2semidirect
21. #88065C4semidirect
42. C13×M16C2×C4semidirect
57. C4×Dic13C2×C4semidirect
93. #343D13semidirect
153. M16C4×D13semidirect
169. C13#1860semidirect

Maximal subgroups

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

subgroupindex
#117192092
C2×#880652
#117187942
#117187822
#117186382
C13×#3432
#117181472
#186013