Finite Group Databasebeta

← #16787748

Subgroups — #16787748

Order 3328.

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

normal subgroups only

This group has 432 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#13130541C211yesmaximal, characteristic
2#13130069C211yesmaximal, characteristic
3#13129835C214yesmaximal, complemented
4#13120658C211yesmaximal, characteristic
5C2×D13⋊M16—21no—
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×#88126C2211yescharacteristic
8#11719119—21no—
9#11718892—21no—
10#11718890—21no—
11#11718653C412yes—
12#11718648—21no—
13#11718643C2212yes—
14#11718634—21no—
15#11718597C411yescharacteristic
16#11718291—21no—
17#11718291C2212yes—
18#11718287—21no—
19#11718286C2212yes—
20C22×Q8×C13—21no—
21C22×C4×D13D411yescharacteristic
22C2×#6122—22no—
23D13⋊M16—24no—
24D13⋊M16—42no—
25C2×#6118—41no—
26C2×D13⋊C8—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×#6103C2×C411yescharacteristic
34C2×#6103D411yescharacteristic
35C2×C4⋊Dic13—21no—
36C2×#6101—22no—
37C2×#6101D411yescharacteristic
38C2×#6101C2311yescharacteristic
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#11723—131nomaximal, Sylow
50C23×D13C22⋊C411yescharacteristic
51C2×Q8×C13—42no—
52C2×Q8×C13—82no—
53C22×C4×C13—22no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×Dic13—22no—
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×C4×D13—22no—
64C2×C4×D13SD1612yes—
65C2×C4×D13Q1612yes—
66#6122—24no—
67#6122—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70#6118—44no—
71D13⋊C8—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#1742—131no—
88#1458—131no—
89#1353—134no—
90C23×C13C2×C22⋊C411yescharacteristic
91C22×D13—21no—
92C22×D13—21no—
93C22×D13—41no—
94C22×D13—41no—
95C22×D13#10312yes—
96Q8×C13—84no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13#9911yescharacteristic
105C2×C4×C13#9911yescharacteristic
106C2×C4×C13#10312yes—
107C2×C4×C13#10412yes—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13C2×SD1611yescharacteristic
118C2×Dic13C2×Q1611yescharacteristic
119C4×D13—22no—
120C4×D13—22no—
121C4×D13—22no—
122C4×D13—22no—
123#1057—44no—
124#1057—82no—
125C22×M16—261no—
126C2×C4⋊Q8#26111yescharacteristic
127C2×#117—131no—
128#431—261no—
129#400—132no—
130#399—132no—
131#395—261no—
132#393—261no—
133#389—261no—
134#382—131no—
135#380—261no—
136#343—132no—
137#343—261no—
138#324—132no—
139#323—261no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13C2×#9911yescharacteristic
143C22×C13C2×#10311yescharacteristic
144C22×C13C2×#10411yescharacteristic
145C2×D13—22no—
146C2×D13—41no—
147C2×D13—41no—
148C2×D13—42no—
149C2×D13—81no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13—82no—
153C4×C13#32812yes—
154C4×C13#32812yes—
155Dic13—21no—
156Dic13—21no—
157Dic13—41no—
158Dic13—41no—
159Dic13—82no—
160C22×Q8—21no—
161C23×C4—131no—
162C2×M16—262no—
163C2×M16—264no—
164C2×M16—522no—
165C2×M16—521no—
166C22×C8—521no—
167C4⋊Q8—41no—
168C4⋊Q8—41no—
169#117—521no—
170#117—521no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—262no—
176C2×C4⋊C4C2×#26112yes—
177C2×C22⋊C4—131no—
178C2×C22⋊C4—131no—
179C2×C22⋊C4—262no—
180C2×C42—131no—
181C2×C42C2×#26111yescharacteristic
182C4⋊C8—521no—
183C22⋊C8—262no—
184C4×C8—521no—
185#95—132no—
186#95—262no—
187#95—262no—
188#95—261no—
189C2×C13—21no—
190C2×C13—21no—
191C2×C13C2×#32811yescharacteristic
192C2×C13#212311yescharacteristic
193C2×C13#213411yescharacteristic
194D13—42no—
195C24—131no—
196C2×Q8—42no—
197C2×Q8—82no—
198C22×C4—22no—
199C22×C4—131no—
200C22×C4—132no—
201C22×C4—132no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—262no—
205C22×C4—261no—
206C22×C4—261no—
207C22×C4—262no—
208C22×C4C22⋊#26111yescharacteristic
209C22×C4C22⋊#26111yescharacteristic
210C22×C4C22×#26111yescharacteristic
211M16—264no—
212M16—522no—
213M16—524no—
214C2×C8—524no—
215C2×C8—522no—
216C2×C8—522no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—521no—
221C4⋊C4—521no—
222C4⋊C4—522no—
223C4⋊C4—1042no—
224C22⋊C4—521no—
225C22⋊C4—521no—
226C22⋊C4—1042no—
227C42—21no—
228C42—21no—
229C42—261no—
230C42—261no—
231C13#1172311yescharacteristic, complemented, Sylow
232C23—132no—
233C23—261no—
234C23—261no—
235C23—521no—
236C23—521no—
237C23C2×C22⋊#26111yescharacteristic
238Q8—84no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—131no—
247C2×C4—131no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—522no—
259C2×C4—522no—
260C2×C4—522no—
261C2×C4#8811712yes—
262C2×C4#8811812yes—
263C2×C4#8811911yescharacteristic
264C2×C4#8811911yescharacteristic
265C8—524no—
266C8—1042no—
267C22—21no—
268C22—21no—
269C22—262no—
270C22—522no—
271C22—521no—
272C22—521no—
273C22—1041no—
274C22C2×#8811711yescharacteristic
275C22C2×#8811811yescharacteristic
276C22C2×#8811911yescharacteristic
277C4—41no—
278C4—41no—
279C4—82no—
280C4—261no—
281C4—261no—
282C4—521no—
283C4—521no—
284C4—1042no—
285C4#1171829812yes—
286C4#1171829812yes—
287C2—21no—
288C2—21no—
289C2—522no—
290C2C2×#1171829811yescharacteristic
291C2#1313109811yescharacteristic
292C2#1313113511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×D13C22⋊C4
cosocleC2×#6101C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11723
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
3. #13129835C2semidirect
231. C13#11723semidirect

Maximal subgroups

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

subgroupindex
#131305412
#131300692
#131298352
#131206582
#1172313