Finite Group Databasebeta

← #13130817

Subgroups — #13130817

Order 1664.

376 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#6118C211yesmaximal, characteristic, complemented
2#11719332C211yesmaximal, characteristic
3C2×#88118C212yesmaximal, complemented
4C4×C22⋊#261C211yesmaximal, characteristic, complemented
5#11718247C212yesmaximal, complemented
6C2×#6131C2211yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C22×#1057—21no—
10C2×C4×#261C2212yes—
11C2×#6118—21no—
12C2×#6118—24no—
13C2×#6118C2212yes—
14C13×C22⋊Q8C411yescharacteristic, complemented
15#88200C411yescharacteristic, complemented
16#88184C411yescharacteristic, complemented
17#88149C411yescharacteristic, complemented
18#88148—21no—
19#88147—21no—
20#88146C2211yescharacteristic
21#88136—21no—
22#88135—21no—
23#88118—24no—
24(C2×#261)⋊C4—21no—
25C23×D13D411yescharacteristic
26C22×#261—22no—
27C2×Q8×C13C2×C411yescharacteristic
28C22×C4×C13C2×C411yescharacteristic
29C2×C22⋊D13—21no—
30C22×Dic13D411yescharacteristic
31#6131—22no—
32#6131—22no—
33C2×D52—21no—
34C2×D52—21no—
35C2×D52C2×C411yescharacteristic
36C2×C4×D13—22no—
37C2×C4×D13—22no—
38C2×C4×D13—21no—
39C2×C4×D13C2×C411yescharacteristic
40C2×C4×D13D411yescharacteristic
41C2×C4×D13D411yescharacteristic
42C2×C4×D13C2311yescharacteristic
43C22⋊#261—24no—
44C2×#1057—24no—
45C2×#1057—22no—
46C4×#261—22no—
47C4×#261—22no—
48#6118—24no—
49#6118—22no—
50#6118D414yescomplemented
51C13×C4⋊C4—21no—
52C13×C4⋊C4C2×C411yescharacteristic
53C13×C22⋊C4—21no—
54#6103—21no—
55#6103—21no—
56#6103—21no—
57#6103—21no—
58C4⋊Dic13C2×C411yescharacteristic
59#6101—21no—
60C4×Dic13—21no—
61#1871—131nomaximal, Sylow
62C23×C13C22⋊C411yescharacteristic
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—21no—
66C22×D13—41no—
67C22×D13C22⋊C411yescharacteristic
68C22×D13C2×D411yescharacteristic
69C2×#261—24no—
70C2×#261—42no—
71C2×#261—42no—
72Q8×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13C22⋊C411yescharacteristic
77C2×C4×C13C22×C411yescharacteristic
78C22⋊D13—42no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13C22⋊C411yescharacteristic
83C2×Dic13C2×D411yescharacteristic
84D52—22no—
85D52—42no—
86D52—42no—
87C4×D13—22no—
88C4×D13—22no—
89C4×D13—21no—
90C4×D13—21no—
91C4×D13—41no—
92C4×D13—41no—
93C4×D13C2×D412yes—
94C4×D13#4112yes—
95#1057—24no—
96C22×M16—131no—
97#525—131no—
98C2×#104—132no—
99C4×C22⋊C4—131no—
100#339—132no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13#10412yescomplemented
104C22×C13C2×C22⋊C411yescharacteristic
105C2×D13—21no—
106C2×D13—21no—
107C2×D13—21no—
108C2×D13—21no—
109C2×D13—21no—
110C2×D13—44no—
111C2×D13—41no—
112C2×D13—41no—
113C2×D13—41no—
114C2×D13#12112yes—
115#261—44no—
116C4×C13—21no—
117C4×C13—41no—
118C4×C13—41no—
119C4×C13C4×D412yes—
120Dic13—21no—
121Dic13—41no—
122Dic13#12011yescharacteristic
123Dic13#12311yescharacteristic
124C2×#41—131no—
125C23×C4—131no—
126C2×M16—132no—
127C2×M16—264no—
128C2×M16—261no—
129C22×C8—261no—
130#123—261no—
131C22⋊Q8—131no—
132C22⋊Q8#26111yescharacteristic, complemented
133#121—131no—
134#121—131no—
135#120—261no—
136C4×D4—261no—
137C4×D4—261no—
138#117—131no—
139C2×C22⋊C4—261no—
140C2×C42—132no—
141#104—264no—
142#95—261no—
143C2×C13—22no—
144C2×C13#38611yescharacteristic
145C2×C13C2×#10411yescharacteristic
146C2×C13#42111yescharacteristic
147D13—22no—
148D13—41no—
149D13—81no—
150C24—131no—
151#41—262no—
152#41—262no—
153C2×Q8C2×#26111yescharacteristic
154C2×D4—131no—
155C2×D4—261no—
156C2×D4—261no—
157C2×D4—261no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—131no—
163C22×C4—262no—
164C22×C4—262no—
165C22×C4—261no—
166C22×C4—262no—
167C22×C4C2×#26111yescharacteristic
168M16—134no—
169M16—262no—
170M16—264no—
171C2×C8—262no—
172C2×C8—264no—
173C4⋊C4—21no—
174C4⋊C4—131no—
175C4⋊C4—261no—
176C4⋊C4C2×#26111yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—261no—
179C22⋊C4—261no—
180C22⋊C4—261no—
181C22⋊C4—264no—
182C22⋊C4—261no—
183C42—261no—
184C42—262no—
185C42—262no—
186C13#187111yescharacteristic, complemented, Sylow
187C23—131no—
188C23—131no—
189C23—262no—
190C23—262no—
191C23—261no—
192C23—521no—
193C23C22⋊#26111yescharacteristic
194Q8—22no—
195D4—262no—
196D4—522no—
197D4—522no—
198D4—522no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—131no—
203C2×C4—132no—
204C2×C4—132no—
205C2×C4—131no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—262no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—262no—
212C2×C4—264no—
213C2×C4—261no—
214C2×C4—521no—
215C2×C4—521no—
216C2×C4—522no—
217C2×C4—522no—
218C2×C4C22⋊#26111yescharacteristic
219C2×C4C22×#26111yescharacteristic
220C8—264no—
221C22—21no—
222C22—21no—
223C22—132no—
224C22—261no—
225C22—261no—
226C22—261no—
227C22—261no—
228C22—261no—
229C22—524no—
230C22—521no—
231C22—521no—
232C22—521no—
233C22#8811812yescomplemented
234C22C2×C22⋊#26111yescharacteristic
235C4—21no—
236C4—41no—
237C4—41no—
238C4—131no—
239C4—131no—
240C4—261no—
241C4—524no—
242C4—521no—
243C4D4×#26112yes—
244C2—22no—
245C2—262no—
246C2—521no—
247C2—1041no—
248C2#1171915011yescharacteristic
249C2C2×#8811811yescharacteristic
250C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C22⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radical#11719332C2
cosocleC2×C4×D13C23
hypercenterC22⋊Q8#261
hypocenterC13#1871
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#6118C2semidirect
3. C2×#88118C2semidirect
4. C4×C22⋊#261C2semidirect
5. #11718247C2semidirect
14. C13×C22⋊Q8C4semidirect
15. #88200C4semidirect
16. #88184C4semidirect
17. #88149C4semidirect
50. #6118D4semidirect
103. C22×C13#104semidirect
132. C22⋊Q8#261semidirect
186. C13#1871semidirect
233. C22#88118semidirect

Maximal subgroups

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

subgroupindex
C22×#61182
#117193322
C2×#881182
C4×C22⋊#2612
#117182472
#187113