Finite Group Databasebeta

← #16782470

Subgroups — #16782470

Order 3328.

482 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 118 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#13131683C211yesmaximal, characteristic
2#13130957C211yesmaximal, characteristic
3#13130389C212yesmaximal, complemented
4#13129669C212yesmaximal, complemented
5#100×Dic13C211yesmaximal, characteristic
6C2×D4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8C2×C22⋊#1057—22no—
9D4×#1057—22no—
10D4×#1057—22no—
11#11719119C2212yes—
12C2×C4⋊#1057C2211yescharacteristic
13C2×C4×#1057C2211yescharacteristic
14C2×C13×#100C411yescharacteristic
15C2×#88073C411yescharacteristic
16M16×Dic13C2212yes—
17#11718256—22no—
18#11718255—22no—
19#11718146C412yes—
20C22×D4×C13C2×C411yescharacteristic
21C23×Dic13D412yes—
22C22×#1057—21no—
23C22×#1057—22no—
24C22×#1057—22no—
25C22×#1057—21no—
26C2×C13×M16C2×C412yes—
27C2×C22⋊Dic13Q812yes—
28D4×Dic13—22no—
29D4×Dic13—22no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4×Dic13C2311yescharacteristic
32C2×#6099C2×C412yes—
33C22⋊#1057—24no—
34C22⋊#1057—22no—
35C22⋊#1057—44no—
36C4⋊#1057—22no—
37C4⋊#1057D412yes—
38C4⋊#1057D412yes—
39C4×#1057—22no—
40C4×#1057—22no—
41C13×#100—22no—
42#88073C814yescomplemented
43#88055—22no—
44C8×Dic13—22no—
45#8835—131nomaximal, Sylow
46C24×C13C4⋊C412yes—
47C2×D4×C13—22no—
48C2×D4×C13—22no—
49C2×D4×C13C2×C812yes—
50C2×D4×C13M1612yes—
51C22×C4×C13C22×C411yescharacteristic
52C22×Dic13—22no—
53C22×Dic13—22no—
54C22×Dic13—42no—
55C22×Dic13—42no—
56C22×Dic13C4⋊C412yes—
57C22×Dic13C2×D411yescharacteristic
58C22×Dic13C2×Q811yescharacteristic
59C2×#1057—22no—
60C2×#1057—22no—
61C2×#1057—22no—
62C2×#1057—41no—
63C2×#1057—41no—
64C2×#1057—42no—
65C2×#1057—41no—
66C2×#1057—82no—
67C2×#1057—82no—
68C13×M16—22no—
69C13×M16—22no—
70C2×C8×C13—22no—
71C22⋊Dic13—24no—
72C4⋊Dic13—22no—
73C4×Dic13C2×D412yes—
74C4×Dic13#4112yes—
75#6099—22no—
76#6099C2×C814yescomplemented
77C2×#1055—22no—
78#2972—131no—
79#1954—131no—
80C4×#100—131no—
81#1565—132no—
82#1278—132no—
83C23×C13—22no—
84C23×C13—22no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13C4⋊C814yes—
88C23×C13C2×C4⋊C411yescharacteristic
89D4×C13—24no—
90D4×C13—24no—
91C2×C4×C13C4×D412yes—
92C2×C4×C13C22×C811yescharacteristic
93C2×C4×C13C2×M1611yescharacteristic
94C2×C4×C13#13112yes—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—22no—
98C2×Dic13—41no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—82no—
103C2×Dic13#12011yescharacteristic
104C2×Dic13C22⋊Q812yes—
105C2×Dic13#12311yescharacteristic
106#1057—42no—
107#1057—42no—
108#1057—42no—
109#1057—81no—
110C8×C13—42no—
111#1055—24no—
112C2×C4×D4—131no—
113C8×D4—262no—
114C8×D4—262no—
115#431—132no—
116C2×C4⋊C8—131no—
117C2×#100—131no—
118C2×#100#26111yescharacteristic
119C2×C22⋊C8—262no—
120C2×C22⋊C8—262no—
121C4×M16—132no—
122C2×C4×C8—131no—
123#343—132no—
124#335—262no—
125#334—262no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—24no—
129C22×C13—44no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—82no—
133C22×C13#38511yescharacteristic
134C22×C13C2×C4⋊C811yescharacteristic
135C22×C13#42411yescharacteristic
136C4×C13C8×D412yes—
137C4×C13#43512yes—
138Dic13—21no—
139Dic13—22no—
140Dic13—42no—
141Dic13#45311yescharacteristic
142Dic13#45511yescharacteristic
143C22×D4C2×#26111yescharacteristic
144C23×C4—132no—
145C2×M16—132no—
146C2×M16C2×#26112yes—
147C22×C8—261no—
148C22×C8—262no—
149C22×C8—262no—
150C22×C8—261no—
151C4×D4—262no—
152C4×D4—262no—
153C2×C4⋊C4—131no—
154C2×C22⋊C4—132no—
155C2×C42—131no—
156C4⋊C8—132no—
157C4⋊C8—132no—
158C4⋊C8—262no—
159#100—22no—
160#100—134no—
161C22⋊C8—262no—
162C22⋊C8—264no—
163C22⋊C8—524no—
164#97—262no—
165C4×C8—262no—
166C4×C8—262no—
167C4×C8—262no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13—44no—
171C2×C13#185011yescharacteristic
172C2×C13#185611yescharacteristic
173C2×C13#185811yescharacteristic
174C24C4⋊#26112yes—
175C2×D4—22no—
176C2×D4—22no—
177C2×D4D13⋊C812yes—
178C2×D4#612212yes—
179C22×C4—131no—
180C22×C4—131no—
181C22×C4—132no—
182C22×C4—262no—
183C22×C4—262no—
184C22×C4—522no—
185C22×C4—522no—
186C22×C4C22×#26111yescharacteristic
187M16—22no—
188M16—22no—
189M16—134no—
190M16—262no—
191C2×C8—22no—
192C2×C8—262no—
193C2×C8—262no—
194C2×C8—262no—
195C2×C8—262no—
196C2×C8—521no—
197C2×C8—521no—
198C2×C8—521no—
199C2×C8—522no—
200C2×C8—1042no—
201C2×C8—1042no—
202C4⋊C4—262no—
203C22⋊C4—264no—
204C42—132no—
205C42—132no—
206C13#883511yescharacteristic, complemented, Sylow
207C23—22no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23#8811214yes—
212C23C2×C4⋊#26111yescharacteristic
213D4—24no—
214D4—24no—
215C2×C4—131no—
216C2×C4—132no—
217C2×C4—131no—
218C2×C4—261no—
219C2×C4—261no—
220C2×C4—262no—
221C2×C4—522no—
222C2×C4—522no—
223C2×C4—521no—
224C2×C4—522no—
225C2×C4—1042no—
226C2×C4C2×D13⋊C811yescharacteristic
227C2×C4#8823812yes—
228C2×C4D4×#26112yes—
229C2×C4C2×#612211yescharacteristic
230C8—42no—
231C8—264no—
232C8—522no—
233C8—522no—
234C8—522no—
235C8—1041no—
236C22—21no—
237C22—21no—
238C22—24no—
239C22—44no—
240C22—42no—
241C22—42no—
242C22—82no—
243C22#1171906711yescharacteristic
244C22#1171907011yescharacteristic
245C22C2×#8811211yescharacteristic
246C4—131no—
247C4—131no—
248C4—261no—
249C4—262no—
250C4—522no—
251C4#1171906312yes—
252C4#1171914412yes—
253C2—21no—
254C2—21no—
255C2—44no—
256C2#1313078011yescharacteristic
257C2#1313079111yescharacteristic
258C2#1313079311yescharacteristic
subgroupG/H
centerC22#11719070
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#100C4
socleC22×C13#385
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×#100#261
hypocenterC13#8835
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
3. #13130389C2semidirect
4. #13129669C2semidirect
42. #88073C8semidirect
76. #6099C2×C8semidirect
206. C13#8835semidirect

Maximal subgroups

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

subgroupindex
#131316832
#131309572
#131303892
#131296692
#100×Dic132
#883513