Finite Group Databasebeta

← #13125206

Subgroups — #13125206

Order 1664.

372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C13×#544C211yesmaximal, characteristic, complemented
2#11719231C211yesmaximal, characteristic
3#11718754C212yesmaximal, complemented
4#11718750C212yesmaximal, complemented
5#11718730C212yesmaximal, complemented
6#11718729C212yesmaximal, complemented
7#11718665C211yesmaximal, characteristic, complemented
8#11718663C211yesmaximal, characteristic
9#11718658C211yesmaximal, characteristic, complemented
10C2×#88050C211yesmaximal, characteristic, complemented
11#11718627C211yesmaximal, characteristic
12C2×#6127C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C13×C4⋊Q8—21no—
15C13×C4⋊Q8C2212yes—
16C13×#125—21no—
17C13×#125C2212yes—
18C13×C22⋊Q8—22no—
19C13×#117C2211yescharacteristic
20C13×#117C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×#6099C2211yescharacteristic
23C22×#1055C2211yescharacteristic
24#88151—21no—
25#88151—21no—
26#88140—22no—
27#88129C2212yes—
28#88123C2212yes—
29#88050C2211yescharacteristic
30#88050C2211yescharacteristic
31#88050C2212yes—
32#88050C2212yes—
33#88050C2212yes—
34#88050C2212yes—
35#88050C2212yes—
36#88049C2211yescharacteristic
37#88049C2211yescharacteristic
38#88049C2212yes—
39#88043C2212yes—
40C4×#1055C2212yes—
41C2×Q8×C13—22no—
42C22×C4×C13—21no—
43C22×C4×C13C2311yescharacteristic
44C2×C22⋊D13—21no—
45C22×Dic13—21no—
46#6127—22no—
47#6127—22no—
48C2×D52C2311yescharacteristic
49C2×C4×D13—21no—
50C2×Dic26—22no—
51C2×Dic26—22no—
52C2×Dic26—21no—
53C2×Dic26C2311yescharacteristic
54C2×Dic26C2312yes—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4D411yescharacteristic
60C13×C4⋊C4D411yescharacteristic
61C13×C4⋊C4C2312yes—
62C13×C4⋊C4C2311yescharacteristic
63C13×C4⋊C4C2311yescharacteristic
64C13×C22⋊C4—21no—
65C13×C22⋊C4D412yes—
66C42×C13—21no—
67C42×C13C2312yes—
68#6103—22no—
69#6103—22no—
70C4⋊Dic13—22no—
71C4⋊Dic13—22no—
72#6099—22no—
73C2×#1055—22no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2311yescharacteristic
76C2×#1055C2312yes—
77#3137—131nomaximal, Sylow
78C23×C13C2×D411yescharacteristic
79C22×D13—21no—
80Q8×C13—82no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—81no—
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×D412yes—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13#4112yes—
89C2×C4×C13#4112yes—
90C2×C4×C13C2411yescharacteristic
91C22⋊D13—42no—
92C2×Dic13—21no—
93C2×Dic13—22no—
94C2×Dic13—42no—
95D52—21no—
96D52—21no—
97C4×D13—42no—
98Dic26—22no—
99Dic26—22no—
100Dic26—21no—
101Dic26—21no—
102Dic26—42no—
103#1055—21no—
104#1055—21no—
105#1055—22no—
106#544D1311yescharacteristic, complemented
107#536—131no—
108#491—132no—
109#489—132no—
110#488—132no—
111#487—132no—
112#419—131no—
113#417—131no—
114#416—131no—
115C2×#103—131no—
116#405—131no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13#12412yes—
120C22×C13C22×D411yescharacteristic
121C2×D13—41no—
122C2×D13—41no—
123C2×D13—41no—
124C4×C13—22no—
125C4×C13—22no—
126C4×C13—42no—
127C4×C13—41no—
128C4×C13—41no—
129C4×C13#12412yes—
130C4×C13C2×#4111yescharacteristic
131C4×C13C2×#4111yescharacteristic
132Dic13—42no—
133Dic13—41no—
134C2×#41—131no—
135C22×Q8—131no—
136C2×M16—131no—
137C22×C8—131no—
138C4⋊Q8—21no—
139C4⋊Q8—132no—
140C4⋊Q8C2×D1312yes—
141#125—21no—
142#125C2×D1312yes—
143#124—132no—
144#123—262no—
145C22⋊Q8—22no—
146C22⋊Q8—261no—
147C22⋊Q8—261no—
148#117C2×D1311yescharacteristic
149#117C2×D1311yescharacteristic
150C2×C4⋊C4C2×D1311yescharacteristic
151#103—132no—
152#103—132no—
153#103—131no—
154#103—131no—
155#103—132no—
156#103—132no—
157#103—132no—
158#102—131no—
159#102—131no—
160#102—132no—
161#97—132no—
162C4×C8—132no—
163C2×C13—22no—
164C2×C13C2×#12411yescharacteristic
165C2×C13#57711yescharacteristic
166C2×C13#57811yescharacteristic
167D13—81no—
168#41—262no—
169#41—262no—
170C2×Q8—22no—
171C2×Q8—132no—
172C2×Q8—131no—
173C2×Q8—261no—
174C2×Q8—262no—
175C2×Q8—262no—
176C2×D4—131no—
177C2×D4—261no—
178C22×C4—21no—
179C22×C4—261no—
180C22×C4—261no—
181C22×C4C22×D1311yescharacteristic
182M16—262no—
183C2×C8—131no—
184C2×C8—132no—
185C2×C8—131no—
186C2×C8—262no—
187C4⋊C4—21no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—262no—
192C4⋊C4—262no—
193C4⋊C4C22⋊D1311yescharacteristic
194C4⋊C4C22⋊D1311yescharacteristic
195C4⋊C4C22×D1312yes—
196C4⋊C4C22×D1311yescharacteristic
197C4⋊C4C22×D1311yescharacteristic
198C22⋊C4—21no—
199C22⋊C4—262no—
200C22⋊C4—262no—
201C22⋊C4C22⋊D1312yes—
202C42—21no—
203C42C22×D1312yes—
204C13#313711yescharacteristic, complemented, Sylow
205C23—261no—
206C23C2×C22⋊D1311yescharacteristic
207Q8—82no—
208Q8—262no—
209Q8—262no—
210Q8—261no—
211Q8—261no—
212Q8—522no—
213D4—261no—
214D4—261no—
215D4—522no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—81no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4#613112yes—
225C2×C4#613112yes—
226C2×C4C2×C22⋊D1312yes—
227C2×C4C2×C22⋊D1312yes—
228C2×C4C2×C22⋊D1311yescharacteristic
229C2×C4C23×D1311yescharacteristic
230C8—261no—
231C8—261no—
232C8—262no—
233C22—21no—
234C22—21no—
235C22—521no—
236C22—521no—
237C22—521no—
238C22#8820112yes—
239C22C22×C22⋊D1311yescharacteristic
240C4—22no—
241C4—22no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—521no—
246C4—522no—
247C4#8820112yes—
248C4C2×#613111yescharacteristic
249C4C2×#613111yescharacteristic
250C2—22no—
251C2—1041no—
252C2C2×#8820111yescharacteristic
253C2#1171954111yescharacteristic
254C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#544C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#544D13
hypocenterC13#3137
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C13×#544C2semidirect
3. #11718754C2semidirect
4. #11718750C2semidirect
5. #11718730C2semidirect
6. #11718729C2semidirect
7. #11718665C2semidirect
9. #11718658C2semidirect
10. C2×#88050C2semidirect
106. #544D13semidirect
204. C13#3137semidirect

Maximal subgroups

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

subgroupindex
C13×#5442
#117192312
#117187542
#117187502
#117187302
#117187292
#117186652
#117186632
#117186582
C2×#880502
#117186272
#313713