Finite Group Databasebeta

← #13115218

Subgroups — #13115218

Order 1664.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#11719450C211yesmaximal, characteristic, complemented
2#11719182C211yesmaximal, characteristic
3#11718800C211yesmaximal, characteristic, complemented
4#11718667C211yesmaximal, characteristic, complemented
5#11718666C211yesmaximal, characteristic, complemented
6C13×#339C211yesmaximal, characteristic, complemented
7#11718115C211yesmaximal, characteristic, complemented
8C2×#6127C2211yescharacteristic
9C2×#6127C2211yescharacteristic
10C2×C13×M16C2211yescharacteristic
11C13×#117C2211yescharacteristic
12C2×C42×C13C2211yescharacteristic
13#88184—22no—
14#88180C2211yescharacteristic
15C2×#6099C2211yescharacteristic
16#88161—22no—
17M16×D13—22no—
18#88155—22no—
19#88129C411yescharacteristic, complemented
20#88129C411yescharacteristic, complemented
21#88128C411yescharacteristic, complemented
22C4×D52—22no—
23#88123C411yescharacteristic, complemented
24#88065—22no—
25#88046—22no—
26#88045—22no—
27C22×C4×C13—21no—
28C22×C4×C13C2311yescharacteristic
29C2×C22⋊D13—21no—
30C2×C22⋊D13D412yes—
31#6127—21no—
32#6127—21no—
33#6127—21no—
34#6127—21no—
35#6127—21no—
36#6127—21no—
37#6127—21no—
38#6127—21no—
39C2×D52—22no—
40C2×D52C2×C411yescharacteristic
41C2×D52C2×C411yescharacteristic
42C2×C4×D13—21no—
43C2×C4×D13D412yes—
44C2×Dic26C2×C411yescharacteristic
45C2×Dic26C2×C411yescharacteristic
46C13×M16—21no—
47C13×M16D412yescomplemented
48C2×C8×C13—21no—
49C13×C4⋊C4—21no—
50C13×C22⋊C4—21no—
51C42×C13—21no—
52C42×C13—21no—
53C42×C13C2×C411yescharacteristic
54C42×C13C2×C411yescharacteristic
55C22⋊Dic13—21no—
56#6103—22no—
57#6103—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13—21no—
60C4×Dic13—21no—
61#6099—21no—
62#6099D412yescomplemented
63C2×#1055—21no—
64#6094—24no—
65C8×D13—24no—
66#1884—131nomaximal, Sylow
67C23×C13C2×D411yescharacteristic
68C22×D13—21no—
69C22×D13C22⋊C412yes—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—42no—
73C2×C4×C13—41no—
74C2×C4×C13C22×C411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13#4111yescharacteristic
79C2×C4×C13#4111yescharacteristic
80C22⋊D13—22no—
81C22⋊D13—22no—
82C22⋊D13—41no—
83C22⋊D13—41no—
84C2×Dic13—21no—
85C2×Dic13—41no—
86C2×Dic13C22⋊C412yes—
87D52—21no—
88D52—21no—
89D52—21no—
90D52—21no—
91D52—44no—
92C4×D13—22no—
93C4×D13—22no—
94C4×D13—41no—
95C4×D13—41no—
96Dic26—21no—
97Dic26—21no—
98Dic26—21no—
99Dic26—21no—
100C8×C13—22no—
101#1055—22no—
102#568—131no—
103#532—131no—
104#421—131no—
105#421—131no—
106#410—131no—
107#339—131no—
108#339D1311yescharacteristic, complemented
109C22×C13—41no—
110C22×C13C2×C22⋊C411yescharacteristic
111C22×C13#12111yescharacteristic
112C22×C13#12111yescharacteristic
113C2×D13—22no—
114C2×D13—42no—
115C2×D13—42no—
116C2×D13—41no—
117C4×C13—22no—
118C4×C13—41no—
119C4×C13—81no—
120C4×C13C4×D411yescharacteristic
121C4×C13C4×D411yescharacteristic
122C4×C13#12011yescharacteristic
123C4×C13#12311yescharacteristic
124Dic13—22no—
125Dic13—41no—
126Dic13—81no—
127C2×#41—131no—
128C2×#41—131no—
129#131—262no—
130#131—262no—
131C2×M16—131no—
132C2×M16—262no—
133C2×M16C2×D1311yescharacteristic
134C4⋊Q8—131no—
135#127—131no—
136#124—131no—
137#124—131no—
138#121—262no—
139C4×D4—262no—
140#117—131no—
141#117C2×D1311yescharacteristic
142C2×C42C2×D1311yescharacteristic
143#104—262no—
144#104—262no—
145#99—262no—
146C2×C13—21no—
147C2×C13—21no—
148C2×C13—21no—
149C2×C13#38611yescharacteristic
150D13—42no—
151D13—81no—
152#41—261no—
153#41—261no—
154#41—261no—
155#41—261no—
156#41—261no—
157#41—261no—
158#41—261no—
159#41—261no—
160C2×Q8—131no—
161C2×Q8—131no—
162C2×D4—132no—
163C2×D4—131no—
164C2×D4—131no—
165C2×D4—262no—
166C2×D4—261no—
167C22×C4—21no—
168C22×C4—132no—
169C22×C4—261no—
170C22×C4C22×D1311yescharacteristic
171M16—21no—
172M16—132no—
173M16—264no—
174M16—261no—
175M16D5212yescomplemented
176C2×C8—21no—
177C2×C8—264no—
178C2×C8—261no—
179C4⋊C4—21no—
180C4⋊C4—262no—
181C4⋊C4—261no—
182C22⋊C4—21no—
183C22⋊C4—262no—
184C22⋊C4—262no—
185C22⋊C4—261no—
186C42—21no—
187C42—21no—
188C42—261no—
189C42C4×D1311yescharacteristic
190C42C4×D1311yescharacteristic
191C13#188411yescharacteristic, complemented, Sylow
192C23—132no—
193C23—261no—
194C23D4×D1311yescharacteristic
195Q8—261no—
196Q8—261no—
197Q8—261no—
198Q8—261no—
199D4—262no—
200D4—262no—
201D4—261no—
202D4—261no—
203D4—261no—
204D4—261no—
205D4—524no—
206D4—521no—
207D4—521no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—132no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—521no—
217C2×C4—521no—
218C2×C4—521no—
219C2×C4C2×C4×D1311yescharacteristic
220C2×C4C2×D5211yescharacteristic
221C2×C4#612711yescharacteristic
222C2×C4D4×D1311yescharacteristic
223C2×C4D4×D1311yescharacteristic
224C2×C4#613111yescharacteristic
225C8—22no—
226C8—262no—
227C22—41no—
228C22—262no—
229C22—522no—
230C22—522no—
231C22—521no—
232C22C22⋊C4×D1311yescharacteristic
233C22#8813811yescharacteristic
234C22#8814911yescharacteristic
235C4—22no—
236C4—41no—
237C4—81no—
238C4—262no—
239C4—521no—
240C4—1041no—
241C4C4×D5211yescharacteristic
242C4#8813611yescharacteristic
243C4#8814711yescharacteristic
244C4#8814811yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—522no—
249C2—1041no—
250C2#1171832611yescharacteristic
subgroupG/H
centerC4#88136
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#339C2
socleC2×C13#386
prime radical#11719182C2
cosocleC22×C4×C13C23
hypercenter#339D13
hypocenterC13#1884
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #11719450C2semidirect
3. #11718800C2semidirect
4. #11718667C2semidirect
5. #11718666C2semidirect
6. C13×#339C2semidirect
7. #11718115C2semidirect
19. #88129C4semidirect
20. #88129C4semidirect
21. #88128C4semidirect
23. #88123C4semidirect
47. C13×M16D4semidirect
62. #6099D4semidirect
108. #339D13semidirect
175. M16D52semidirect
191. C13#1884semidirect

Maximal subgroups

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

subgroupindex
#117194502
#117191822
#117188002
#117186672
#117186662
C13×#3392
#117181152
#188413