Finite Group Databasebeta

← #16787731

Subgroups — #16787731

Order 3328.

448 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 88 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#13130535C211yesmaximal, characteristic
2#13130069C211yesmaximal, characteristic
3#13129833C214yesmaximal
4#13120658C211yesmaximal, characteristic
5C2×#88237—21no—
6C2×C13×C4⋊Q8C411yescharacteristic, complemented
7C2×#88126C2211yescharacteristic
8#11719119—21no—
9#11718892—21no—
10#11718890—21no—
11#11718653C2212yes—
12#11718648—21no—
13#11718643C412yescomplemented
14#11718634—21no—
15#11718597C411yescharacteristic, complemented
16#11718289—21no—
17#11718289C2212yes—
18#11718287C2212yes—
19#11718286—21no—
20C22×Q8×C13—21no—
21C22×C4×D13D411yescharacteristic
22C2×C22⋊#261—22no—
23#88237—24no—
24#88237—42no—
25C2×C4⋊#261—41no—
26C2×C4×#261—41no—
27C13×C4⋊Q8—41no—
28C13×C4⋊Q8—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C42×C13C2×C411yescharacteristic
32C2×#6103—22no—
33C2×#6103D411yescharacteristic
34C2×#6103C2311yescharacteristic
35C2×C4⋊Dic13—21no—
36C2×#6101—22no—
37C2×#6101C2×C411yescharacteristic
38C2×#6101D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40#88126—41no—
41#88126—41no—
42C22⋊#1057—22no—
43C4⋊#1057—41no—
44C4×#1057—41no—
45#88071—21no—
46#88071—22no—
47#88071—22no—
48#88071C2×C412yes—
49#11718—131nomaximal, Sylow
50C23×D13C2×D411yescharacteristic
51C22×#261—42no—
52C2×Q8×C13—42no—
53C2×Q8×C13—82no—
54C22×C4×C13—22no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×Dic13—22no—
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C2×C4×D13—21no—
63C2×C4×D13—21no—
64C2×C4×D13—22no—
65C2×C4×D13SD1612yes—
66C2×C4×D13Q1612yes—
67C22⋊#261—24no—
68C22⋊#261—42no—
69C2×#1057—42no—
70C4⋊#261—44no—
71C4×#261—44no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C42×C13—21no—
76C42×C13—21no—
77#6103—41no—
78#6103—41no—
79#6103—82no—
80C4⋊Dic13—42no—
81#6101—41no—
82#6101—41no—
83#6101—82no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86#2628—131no—
87#1740—131no—
88#1458—131no—
89#1352—134no—
90C23×C13C2×C22⋊C411yescharacteristic
91C22×D13—21no—
92C22×D13—21no—
93C22×D13—41no—
94C22×D13—41no—
95C22×D13C2×SD1611yescharacteristic
96C22×D13C2×Q1611yescharacteristic
97C2×#261—44no—
98C2×#261—82no—
99C2×#261—82no—
100Q8×C13—84no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13#9911yescharacteristic
109C2×C4×C13#9911yescharacteristic
110C2×C4×C13#10312yes—
111C2×C4×C13#10412yes—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13#10312yes—
122C4×D13—22no—
123C4×D13—22no—
124C4×D13—22no—
125C4×D13—22no—
126#1057—82no—
127C2×C4⋊Q8#26111yescharacteristic, complemented
128C2×#117—131no—
129C2×#117—261no—
130#431—261no—
131#400—132no—
132#399—132no—
133#395—261no—
134#393—261no—
135#389—261no—
136#382—131no—
137#380—261no—
138#342—132no—
139#342—261no—
140#324—261no—
141#323—132no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13C2×#9911yescharacteristic
145C22×C13C2×#10311yescharacteristic
146C22×C13C2×#10411yescharacteristic
147C2×D13—21no—
148C2×D13—21no—
149C2×D13—41no—
150C2×D13—41no—
151C2×D13—41no—
152C2×D13—41no—
153C2×D13—81no—
154#261—84no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—82no—
158C4×C13#32812yes—
159C4×C13#32812yes—
160Dic13—22no—
161Dic13—41no—
162Dic13—41no—
163Dic13—82no—
164C22×Q8—21no—
165C23×C4—131no—
166C4⋊Q8—41no—
167C4⋊Q8—41no—
168#117—264no—
169#117—521no—
170#117—521no—
171#117—522no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—262no—
177C2×C4⋊C4—521no—
178C2×C4⋊C4C2×#26112yes—
179C2×C22⋊C4—131no—
180C2×C22⋊C4—131no—
181C2×C22⋊C4—262no—
182C2×C22⋊C4—262no—
183C2×C42—131no—
184C2×C42—521no—
185C2×C42C2×#26111yescharacteristic
186C4⋊C8—521no—
187C22⋊C8—262no—
188C4×C8—521no—
189#95—132no—
190#95—262no—
191#95—262no—
192#95—261no—
193C2×C13—21no—
194C2×C13—21no—
195C2×C13C2×#32811yescharacteristic
196C2×C13#212311yescharacteristic
197C2×C13#212811yescharacteristic
198D13—41no—
199D13—41no—
200C24—131no—
201C2×Q8—42no—
202C2×Q8—82no—
203C22×C4—22no—
204C22×C4—131no—
205C22×C4—132no—
206C22×C4—132no—
207C22×C4—131no—
208C22×C4—131no—
209C22×C4—262no—
210C22×C4—261no—
211C22×C4—261no—
212C22×C4—262no—
213C22×C4—522no—
214C22×C4C22⋊#26111yescharacteristic
215C22×C4C22⋊#26111yescharacteristic
216C22×C4C22×#26111yescharacteristic
217C2×C8—522no—
218C4⋊C4—42no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—521no—
222C4⋊C4—521no—
223C4⋊C4—524no—
224C4⋊C4—522no—
225C4⋊C4—1042no—
226C22⋊C4—264no—
227C22⋊C4—521no—
228C22⋊C4—521no—
229C22⋊C4—522no—
230C22⋊C4—1042no—
231C42—21no—
232C42—21no—
233C42—261no—
234C42—261no—
235C42—524no—
236C13#1171811yescharacteristic, complemented, Sylow
237C23—131no—
238C23—131no—
239C23—261no—
240C23—261no—
241C23—521no—
242C23—521no—
243C23C2×C22⋊#26111yescharacteristic
244Q8—84no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—132no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—524no—
266C2×C4—522no—
267C2×C4—1042no—
268C2×C4—1042no—
269C2×C4#8811712yes—
270C2×C4#8811812yes—
271C2×C4#8811911yescharacteristic
272C2×C4#8811911yescharacteristic
273C8—1042no—
274C22—21no—
275C22—21no—
276C22—261no—
277C22—261no—
278C22—521no—
279C22—521no—
280C22—521no—
281C22—521no—
282C22—1041no—
283C22C2×#8811711yescharacteristic
284C22C2×#8811811yescharacteristic
285C22C2×#8811911yescharacteristic
286C4—41no—
287C4—41no—
288C4—82no—
289C4—262no—
290C4—521no—
291C4—521no—
292C4—1042no—
293C4—1044no—
294C4#1171829812yes—
295C4#1171829812yes—
296C2—21no—
297C2—21no—
298C2—521no—
299C2—521no—
300C2C2×#1171829811yescharacteristic
301C2#1313109811yescharacteristic
302C2#1313111511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×D13C2×D4
cosocleC2×#6103C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11718
LCSG ▷ C22×C4×C13 ▷ C23×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
6. C2×C13×C4⋊Q8C4semidirect
13. #11718643C4semidirect
15. #11718597C4semidirect
127. C2×C4⋊Q8#261semidirect
236. C13#11718semidirect

Maximal subgroups

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

subgroupindex
#131305352
#131300692
#131298332
#131206582
#1171813