Finite Group Databasebeta

← #13115061

Subgroups — #13115061

Order 1664.

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

normal subgroups only

This group has 302 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
2C13×#384C211yesmaximal, characteristic, complemented
3#11718627C211yesmaximal, characteristic
4#11718625C211yesmaximal, characteristic, complemented
5C2×#88045C211yesmaximal, characteristic
6#11718122C211yesmaximal, characteristic, complemented
7#11718115C211yesmaximal, characteristic, complemented
8C2×#6127C2211yescharacteristic
9C2×C13×C4⋊C4—22no—
10C2×C13×C4⋊C4C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C42×C13C2211yescharacteristic
13C4×C22⋊D13—22no—
14#88180C2211yescharacteristic
15C2×#6099C2211yescharacteristic
16C2×#6099C2211yescharacteristic
17#88147—21no—
18#88146—21no—
19C4⋊C4×D13—21no—
20#88141—21no—
21#88050—21no—
22#88049—21no—
23#88048—21no—
24#88047—21no—
25#88045C414yescomplemented
26C22×C4×C13—21no—
27C22×C4×C13—21no—
28C22×C4×C13D412yes—
29C22×C4×C13C2311yescharacteristic
30C2×C22⋊D13—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×C4⋊C4—21no—
40C13×C4⋊C4—21no—
41C13×C4⋊C4—21no—
42C13×C4⋊C4—21no—
43C13×C4⋊C4—44no—
44C42×C13—21no—
45C42×C13C2×C412yescomplemented
46C22⋊Dic13—21no—
47#6103—22no—
48C4⋊Dic13D411yescharacteristic
49C4⋊Dic13D411yescharacteristic
50#6101—22no—
51C4×Dic13—22no—
52C4×Dic13—21no—
53#6099—21no—
54#6099—21no—
55#6099—21no—
56#6099C2×C412yescomplemented
57C2×#1055—21no—
58C2×#1055—21no—
59#1859—131nomaximal, Sylow
60C23×C13C2×D411yescharacteristic
61C22×D13—21no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—42no—
67C2×C4×C13—42no—
68C2×C4×C13—41no—
69C2×C4×C13C22×C411yescharacteristic
70C2×C4×C13C2×D411yescharacteristic
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×Q811yescharacteristic
73C2×C4×C13#4111yescharacteristic
74C2×C4×C13#4111yescharacteristic
75C22⋊D13—22no—
76C22⋊D13—22no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—21no—
80D52—21no—
81D52C4⋊C412yescomplemented
82C4×D13—22no—
83C4×D13—22no—
84C4×D13—82no—
85Dic26—21no—
86Dic26C4⋊C412yescomplemented
87#1055—22no—
88#1055—41no—
89#520—131no—
90#428—131no—
91C2×#104—131no—
92#417—131no—
93#384D1311yescharacteristic, complemented
94#343—131no—
95#339—131no—
96C22×C13—21no—
97C22×C13—21no—
98C22×C13C4×D411yescharacteristic
99C22×C13#12011yescharacteristic
100C22×C13C22⋊Q811yescharacteristic
101C2×D13—22no—
102C2×D13—41no—
103C2×D13—41no—
104C4×C13—24no—
105C4×C13—42no—
106C4×C13—81no—
107C4×C13C2×C4⋊C411yescharacteristic
108C4×C13C4×D411yescharacteristic
109C4×C13C22⋊Q811yescharacteristic
110C4×C13#12311yescharacteristic
111Dic13—22no—
112Dic13—41no—
113Dic13—41no—
114C2×#41—131no—
115C2×M16—131no—
116C2×M16—131no—
117C4×Q8—261no—
118C4×D4—261no—
119C4×D4—262no—
120#117—131no—
121#117—261no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—261no—
124C2×C4⋊C4C2×D1311yescharacteristic
125C2×C4⋊C4C2×D1311yescharacteristic
126C2×C42C2×D1311yescharacteristic
127#107—261no—
128#106—261no—
129#104—134no—
130#103—261no—
131#102—261no—
132C2×C13—21no—
133C2×C13—21no—
134C2×C13#38511yescharacteristic
135C2×C13#45311yescharacteristic
136C2×C13#45611yescharacteristic
137D13—42no—
138#41—132no—
139#41—132no—
140#41—261no—
141#41—261no—
142C2×Q8—131no—
143C2×D4—131no—
144C2×D4—261no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—262no—
148C22×C4—261no—
149C22×C4C22⋊D1312yes—
150C22×C4C22×D1311yescharacteristic
151M16—132no—
152M16—261no—
153M16—261no—
154M16—261no—
155C2×C8—261no—
156C2×C8—261no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—44no—
162C4⋊C4—131no—
163C4⋊C4—131no—
164C4⋊C4—262no—
165C22⋊C4—262no—
166C22⋊C4—261no—
167C42—21no—
168C42—262no—
169C42—261no—
170C42C4×D1312yescomplemented
171C13#185911yescharacteristic, complemented, Sylow
172C23—261no—
173C23C2×C22⋊D1311yescharacteristic
174Q8—132no—
175Q8—261no—
176D4—132no—
177D4—262no—
178D4—262no—
179D4—261no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—261no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—261no—
191C2×C4—261no—
192C2×C4—1042no—
193C2×C4C2×C4×D1311yescharacteristic
194C2×C4#612711yescharacteristic
195C2×C4D4×D1311yescharacteristic
196C2×C4D4×D1311yescharacteristic
197C2×C4Q8×D1311yescharacteristic
198C2×C4#613111yescharacteristic
199C8—262no—
200C8—521no—
201C22—21no—
202C22—21no—
203C22—262no—
204C22—521no—
205C22—521no—
206C22C4×C22⋊D1311yescharacteristic
207C22#8819111yescharacteristic
208C22#8820011yescharacteristic
209C4—24no—
210C4—42no—
211C4—81no—
212C4—262no—
213C4—521no—
214C4—521no—
215C4C4⋊C4×D1311yescharacteristic
216C4#8814711yescharacteristic
217C4#8814811yescharacteristic
218C4#8815011yescharacteristic
219C2—21no—
220C2—21no—
221C2—522no—
222C2#1171865011yescharacteristic
223C2#1171873811yescharacteristic
224C2#1171875611yescharacteristic
subgroupG/H
centerC22#88191
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#384C2
socleC22×C13#120
prime radicalC2×#6127C22
cosocleC22×C4×C13C23
hypercenter#384D13
hypocenterC13#1859
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C13×#384C2semidirect
4. #11718625C2semidirect
6. #11718122C2semidirect
7. #11718115C2semidirect
25. #88045C4semidirect
45. C42×C13C2×C4semidirect
56. #6099C2×C4semidirect
81. D52C4⋊C4semidirect
86. Dic26C4⋊C4semidirect
93. #384D13semidirect
170. C42C4×D13semidirect
171. C13#1859semidirect

Maximal subgroups

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

subgroupindex
#117192092
C13×#3842
#117186272
#117186252
C2×#880452
#117181222
#117181152
#185913