Finite Group Databasebeta

← #13115136

Subgroups — #13115136

Order 1664.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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#11719496C211yesmaximal, characteristic
2C22×#6099C211yesmaximal, characteristic, complemented
3C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#88045C212yesmaximal, complemented
5#11718115C212yesmaximal, complemented
6C23×C4×C13C2211yescharacteristic
7C2×#6127C2211yescharacteristic
8C2×C13×C22⋊C4—21no—
9C2×C42×C13C2212yes—
10#88207—21no—
11#88184C411yescharacteristic, complemented
12#88184C411yescharacteristic, complemented
13#88183—21no—
14C4×C22⋊D13—21no—
15C4×C22⋊D13—21no—
16#88180C2211yescharacteristic
17#88178C411yescharacteristic, complemented
18#88178C411yescharacteristic, complemented
19C2×#6099—21no—
20C2×#6099—24no—
21C2×#6099C2212yes—
22C22×#1055—21no—
23C13×#95—21no—
24#88045—24no—
25C24×C13D411yescharacteristic
26C22×C4×C13—22no—
27C22×C4×C13—22no—
28C22×C4×C13—22no—
29C22×C4×C13C2×C411yescharacteristic
30C22×C4×C13C2×C411yescharacteristic
31C22×C4×C13D411yescharacteristic
32C22×C4×C13D411yescharacteristic
33C22×C4×C13D411yescharacteristic
34C22×C4×C13C2311yescharacteristic
35C2×C22⋊D13—21no—
36C2×C22⋊D13—21no—
37C2×C22⋊D13—21no—
38#6127—22no—
39#6127—22no—
40C2×D52C2×C411yescharacteristic
41C2×C4×D13—21no—
42C2×Dic26C2×C411yescharacteristic
43C13×C22⋊C4—24no—
44C42×C13—22no—
45C42×C13—22no—
46C22⋊Dic13—21no—
47C22⋊Dic13—21no—
48C22⋊Dic13—21no—
49#6103—21no—
50#6103—21no—
51C4⋊Dic13C2×C411yescharacteristic
52C4⋊Dic13C2×C411yescharacteristic
53#6101—21no—
54#6101—21no—
55C4×Dic13—21no—
56#6099—24no—
57#6099—22no—
58#6099D414yescomplemented
59C2×#1055—24no—
60C2×#1055—22no—
61#1871—131nomaximal, Sylow
62C23×C13—22no—
63C23×C13—22no—
64C23×C13—41no—
65C23×C13C22⋊C411yescharacteristic
66C23×C13C22⋊C411yescharacteristic
67C23×C13C2×D411yescharacteristic
68C22×D13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—24no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13C22⋊C411yescharacteristic
80C2×C4×C13C22⋊C411yescharacteristic
81C2×C4×C13C22×C411yescharacteristic
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13#4112yes—
85C22⋊D13—42no—
86C22⋊D13—42no—
87C22⋊D13—42no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91D52—22no—
92C4×D13—41no—
93C4×D13—41no—
94Dic26—22no—
95#1055—24no—
96C22×M16—131no—
97#525—131no—
98C2×#104—132no—
99C4×C22⋊C4D1311yescharacteristic, complemented
100#339—132no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13—21no—
105C22×C13—21no—
106C22×C13—21no—
107C22×C13—21no—
108C22×C13—44no—
109C22×C13#10412yescomplemented
110C22×C13C2×C22⋊C411yescharacteristic
111C22×C13#12112yes—
112C2×D13—41no—
113C2×D13—41no—
114C2×D13—41no—
115C4×C13—21no—
116C4×C13—21no—
117C4×C13—44no—
118C4×C13C4×D412yes—
119C4×C13#12011yescharacteristic
120C4×C13#12311yescharacteristic
121Dic13—41no—
122Dic13—41no—
123Dic13—41no—
124C2×#41—131no—
125C23×C4C2×D1311yescharacteristic
126C2×M16—132no—
127C2×M16—264no—
128C2×M16—261no—
129C22×C8—261no—
130#123—261no—
131C22⋊Q8—131no—
132C22⋊Q8—131no—
133#121—131no—
134#121—131no—
135#120—261no—
136C4×D4—261no—
137C4×D4—261no—
138#117—131no—
139C2×C22⋊C4—21no—
140C2×C42C2×D1312yes—
141#104—264no—
142#95—21no—
143C2×C13—22no—
144C2×C13—22no—
145C2×C13—41no—
146C2×C13#38611yescharacteristic
147C2×C13C2×#10411yescharacteristic
148C2×C13#42111yescharacteristic
149D13—81no—
150C24C22⋊D1311yescharacteristic
151#41—262no—
152#41—262no—
153C2×Q8—131no—
154C2×D4—131no—
155C2×D4—261no—
156C2×D4—261no—
157C2×D4—261no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—261no—
162C22×C4C4×D1311yescharacteristic
163C22×C4C4×D1311yescharacteristic
164C22×C4D5211yescharacteristic
165C22×C4D5211yescharacteristic
166C22×C4C22⋊D1311yescharacteristic
167C22×C4C22×D1311yescharacteristic
168M16—134no—
169M16—264no—
170M16—262no—
171C2×C8—264no—
172C2×C8—262no—
173C4⋊C4—131no—
174C4⋊C4—131no—
175C4⋊C4—261no—
176C4⋊C4—261no—
177C22⋊C4—24no—
178C22⋊C4—261no—
179C22⋊C4—261no—
180C22⋊C4—261no—
181C22⋊C4—261no—
182C22⋊C4—261no—
183C42—22no—
184C42—22no—
185C42—261no—
186C13#187111yescharacteristic, complemented, Sylow
187C23—22no—
188C23—22no—
189C23—41no—
190C23—261no—
191C23#610311yescharacteristic
192C23#610311yescharacteristic
193C23C2×C22⋊D1311yescharacteristic
194Q8—262no—
195D4—262no—
196D4—522no—
197D4—522no—
198D4—522no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—261no—
212C2×C4—521no—
213C2×C4—521no—
214C2×C4#610311yescharacteristic
215C2×C4#610311yescharacteristic
216C2×C4C2×C4×D1311yescharacteristic
217C2×C4C2×D5211yescharacteristic
218C2×C4D4×D1312yes—
219C2×C4#612912yes—
220C8—264no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—521no—
230C22—521no—
231C22—521no—
232C22#8804512yescomplemented
233C22C2×#610311yescharacteristic
234C22#8819312yes—
235C4—21no—
236C4—21no—
237C4—44no—
238C4—521no—
239C4—521no—
240C4—521no—
241C4#8813512yes—
242C4#8813611yescharacteristic
243C4#8814011yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—1041no—
248C2C2×#8804511yescharacteristic
249C2#1171861911yescharacteristic
250C2#1171866611yescharacteristic
subgroupG/H
centerC2×C4C2×D52
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC4×C13×C22⋊C4C2
socleC22×C13C2×C22⋊C4
prime radical#11719496C2
cosocleC22×C4×C13C23
hypercenterC4×C22⋊C4D13
hypocenterC13#1871
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#6099C2semidirect
3. C4×C13×C22⋊C4C2semidirect
4. C2×#88045C2semidirect
5. #11718115C2semidirect
11. #88184C4semidirect
12. #88184C4semidirect
17. #88178C4semidirect
18. #88178C4semidirect
58. #6099D4semidirect
99. C4×C22⋊C4D13semidirect
109. C22×C13#104semidirect
186. C13#1871semidirect
232. C22#88045semidirect

Maximal subgroups

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

subgroupindex
#117194962
C22×#60992
C4×C13×C22⋊C42
C2×#880452
#117181152
#187113