Finite Group Databasebeta

← #16787253

Subgroups — #16787253

Order 3328.

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

normal subgroups only

This group has 374 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
1#13130098C211yesmaximal, characteristic
2#13130078C211yesmaximal, characteristic
3#13129779C214yesmaximal
4#13120045C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Dic26C2211yescharacteristic
7#11719130—21no—
8#11719125—21no—
9#11718890—21no—
10#11718890—21no—
11#11718637C2212yes—
12#11718635C412yes—
13#11718634—21no—
14#11718634—21no—
15C4×C4⋊Dic13C411yescharacteristic
16#11718286—21no—
17#11718286—21no—
18#11718285C2212yes—
19#11718285C2212yes—
20C22×Q8×C13—21no—
21C22×Dic26C2×C411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C42×C13C2×C411yescharacteristic
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13C2311yescharacteristic
29C2×#6101—22no—
30C2×#6101—22no—
31C2×#6101D411yescharacteristic
32C2×#6101D411yescharacteristic
33C2×C4×Dic13C2×C412yes—
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C4×Dic26—41no—
37C4×Dic26—41no—
38C22⋊#1057—22no—
39C22⋊#1057—22no—
40#88112—41no—
41#88110—41no—
42C4⋊#1057—41no—
43C4×#1057—41no—
44#88071—21no—
45#88071—22no—
46#88071—22no—
47#11574—131nomaximal, Sylow
48C2×Q8×C13—42no—
49C2×Q8×C13—82no—
50C22×C4×C13—22no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—22no—
55C22×Dic13C22⋊C411yescharacteristic
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C2×D411yescharacteristic
58C22×Dic13C2×D411yescharacteristic
59C2×Dic26—22no—
60C2×Dic26—22no—
61C2×Dic26—41no—
62C2×#1057—42no—
63C2×#1057—42no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C42×C13—21no—
68C42×C13—21no—
69C4⋊Dic13—24no—
70C4⋊Dic13—41no—
71#6101—41no—
72#6101—41no—
73#6101—82no—
74#6101—82no—
75C4×Dic13—21no—
76C4×Dic13—21no—
77C4×Dic13—21no—
78C4×Dic13—21no—
79C4×Dic13—24no—
80#2567—131no—
81#1467—131no—
82#1461—131no—
83#1325—134no—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—84no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13#9911yescharacteristic
95C2×C4×C13#9911yescharacteristic
96C2×C4×C13#13112yes—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—24no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13#10112yes—
110Dic26—44no—
111#1057—82no—
112#1057—82no—
113C2×C4⋊Q8#26111yescharacteristic
114C2×C4×Q8—131no—
115#432—261no—
116#431—261no—
117#395—261no—
118#395—261no—
119#391—132no—
120#389—261no—
121#389—261no—
122#384—132no—
123C4×C4⋊C4—131no—
124#324—132no—
125#324—132no—
126#324—261no—
127#324—261no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13#40811yescharacteristic
131C22×C13C2×#9911yescharacteristic
132C22×C13C2×#10111yescharacteristic
133C4×C13—21no—
134C4×C13—22no—
135C4×C13—41no—
136C4×C13—82no—
137C4×C13#35612yes—
138Dic13—22no—
139Dic13—44no—
140Dic13—41no—
141Dic13—41no—
142Dic13—41no—
143C22×Q8—21no—
144C22×Q8—131no—
145C4⋊Q8—41no—
146C4⋊Q8—41no—
147C4×Q8—521no—
148C4×Q8—521no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—131no—
152C2×C4⋊C4—131no—
153C2×C4⋊C4—261no—
154C2×C4⋊C4—262no—
155C2×C4⋊C4—262no—
156C2×C4⋊C4C2×#26112yes—
157C2×C42—131no—
158C2×C42—131no—
159C2×C42—132no—
160C2×C42C2×#26111yescharacteristic
161C4⋊C8—521no—
162C4⋊C8—521no—
163C22⋊C8—262no—
164C22⋊C8—262no—
165#97—521no—
166C4×C8—521no—
167#95—262no—
168#95—262no—
169#95—261no—
170C2×C13—21no—
171C2×C13—21no—
172C2×C13#147211yescharacteristic
173C2×C13#212811yescharacteristic
174C2×C13C2×#35611yescharacteristic
175C2×Q8—42no—
176C2×Q8—82no—
177C2×Q8—262no—
178C2×Q8—262no—
179C2×Q8—521no—
180C22×C4—22no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—262no—
186C22×C4C22⋊#26111yescharacteristic
187C22×C4C22⋊#26111yescharacteristic
188C22×C4C22×#26111yescharacteristic
189C2×C8—522no—
190C2×C8—522no—
191C4⋊C4—42no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—264no—
195C4⋊C4—521no—
196C4⋊C4—521no—
197C4⋊C4—521no—
198C4⋊C4—1042no—
199C4⋊C4—1042no—
200C42—21no—
201C42—21no—
202C42—261no—
203C42—261no—
204C42—261no—
205C42—261no—
206C42—264no—
207C13#1157411yescharacteristic, complemented, Sylow
208C23C2×C22⋊#26111yescharacteristic
209Q8—84no—
210Q8—524no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—132no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—264no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—261no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4—521no—
231C2×C4—521no—
232C2×C4#8811911yescharacteristic
233C2×C4#8811911yescharacteristic
234C2×C4#8824012yes—
235C8—1042no—
236C8—1042no—
237C22—21no—
238C22—21no—
239C22#1171915911yescharacteristic
240C22D13⋊#10111yescharacteristic
241C22C2×#8811911yescharacteristic
242C4—21no—
243C4—22no—
244C4—41no—
245C4—82no—
246C4—262no—
247C4—524no—
248C4—521no—
249C4—521no—
250C4—521no—
251C4#1171830112yes—
252C2—21no—
253C2—21no—
254C2#1313011611yescharacteristic
255C2#1313111511yescharacteristic
256C2C2×#1171830111yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11574
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
207. C13#11574semidirect

Maximal subgroups

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

subgroupindex
#131300982
#131300782
#131297792
#131200452
#1157413