Finite Group Databasebeta

← #16778822

Subgroups — #16778822

Order 3328.

494 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130728C211yesmaximal, characteristic
2#13130693C211yesmaximal, characteristic
3#13129654C214yesmaximal, complemented
4#13123189C211yesmaximal, characteristic
5C2×#88151—21no—
6C2×C42×D13C2211yescharacteristic
7C2×#88123C411yescharacteristic
8C2×#88112—21no—
9C2×#88111—21no—
10C2×#88111—21no—
11C13×#384C411yescharacteristic
12#11718648—21no—
13#11718648C412yes—
14#11718646—21no—
15#11718646C2212yes—
16#11718635—21no—
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C22×C4×D13C2×C411yescharacteristic
21C22×C4×D13D411yescharacteristic
22C22×C4×D13D411yescharacteristic
23C22×Dic26—21no—
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C42×C13C2×C411yescharacteristic
30C2×#6103—22no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—22no—
33C2×C4⋊Dic13C2×C412yes—
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13C2311yescharacteristic
37#88151—44no—
38C42×D13—42no—
39#88123—42no—
40#88112—42no—
41#88111—42no—
42#88111—42no—
43#88071—22no—
44#88071—22no—
45#7725—131nomaximal, Sylow
46C23×D13C22⋊C411yescharacteristic
47C22×C4×C13—22no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13C22⋊C411yescharacteristic
53C22×Dic13C2×D411yescharacteristic
54C22×Dic13C2×D411yescharacteristic
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×C4×D13—22no—
59C2×C4×D13—41no—
60C2×C4×D13—41no—
61C2×C4×D13—41no—
62C2×C4×D13—41no—
63C2×C4×D13SD1612yes—
64C2×C4×D13Q1612yes—
65C2×Dic26—42no—
66C2×Dic26—42no—
67C2×Dic26—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C42×C13—22no—
78#6103—44no—
79C4⋊Dic13—42no—
80C4⋊Dic13—44no—
81C4⋊Dic13—42no—
82C4×Dic13—22no—
83C4×Dic13—41no—
84C4×Dic13—41no—
85#2857—131no—
86#1817—131no—
87#1797—131no—
88#1271—134no—
89C23×C13C2×C22⋊C411yescharacteristic
90C22×D13—21no—
91C22×D13—21no—
92C22×D13—21no—
93C22×D13—21no—
94C22×D13—21no—
95C22×D13—21no—
96C22×D13#10312yes—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13#9912yes—
107C2×C4×C13#10312yes—
108C2×C4×C13#13112yes—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13#10112yes—
119C2×Dic13C2×SD1611yescharacteristic
120C2×Dic13C2×Q1611yescharacteristic
121C2×Dic13AGL(1,ℤ/8)12yes—
122C4×D13—42no—
123C4×D13—42no—
124C4×D13—44no—
125C4×D13—44no—
126Dic26—84no—
127#1057—82no—
128#1057—82no—
129C2×C4⋊Q8—131no—
130C2×C22⋊Q8—261no—
131C22×C42—131no—
132C2×C4⋊C8—261no—
133C2×C22⋊C8—261no—
134C2×C22⋊C8—261no—
135#391—261no—
136#389—132no—
137#389—261no—
138#384#26111yescharacteristic
139#380—132no—
140#380—261no—
141#336—132no—
142#336—132no—
143#336—261no—
144C22×C13#40811yescharacteristic
145C22×C13C2×#9911yescharacteristic
146C22×C13C2×#10111yescharacteristic
147C22×C13C2×#10311yescharacteristic
148C22×C13#41811yescharacteristic
149C22×C13#42111yescharacteristic
150C22×C13#42111yescharacteristic
151C2×D13—22no—
152C2×D13—22no—
153C2×D13—22no—
154C2×D13—41no—
155C2×D13—41no—
156C2×D13—41no—
157C2×D13—41no—
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—22no—
161C4×C13—82no—
162Dic13—22no—
163Dic13—22no—
164Dic13—21no—
165Dic13—21no—
166Dic13—82no—
167C22×Q8—261no—
168C23×C4—131no—
169C23×C4—131no—
170C23×C4—131no—
171C22×C8—262no—
172C22×C8—262no—
173C4⋊Q8—522no—
174C22⋊Q8—524no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—132no—
178C2×C4⋊C4—262no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4C2×#26112yes—
181C2×C22⋊C4—262no—
182C2×C42—131no—
183C2×C42—131no—
184C2×C42—131no—
185C2×C42—522no—
186C2×C42C2×#26111yescharacteristic
187C4⋊C8—522no—
188C22⋊C8—522no—
189C22⋊C8—522no—
190#95—262no—
191#95—262no—
192C2×C13#147211yescharacteristic
193C2×C13#148111yescharacteristic
194C2×C13#149611yescharacteristic
195C2×C13#151011yescharacteristic
196C2×C13#152011yescharacteristic
197C2×C13#153711yescharacteristic
198C2×C13#154911yescharacteristic
199D13—42no—
200C24—131no—
201C2×Q8—522no—
202C2×Q8—522no—
203C2×Q8—522no—
204C22×C4—22no—
205C22×C4—131no—
206C22×C4—131no—
207C22×C4—131no—
208C22×C4—132no—
209C22×C4—132no—
210C22×C4—262no—
211C22×C4—262no—
212C22×C4—262no—
213C22×C4—262no—
214C22×C4—262no—
215C22×C4—521no—
216C22×C4—521no—
217C22×C4—521no—
218C22×C4—521no—
219C22×C4C22⋊#26111yescharacteristic
220C22×C4C22⋊#26111yescharacteristic
221C22×C4C22×#26111yescharacteristic
222C2×C8—522no—
223C2×C8—522no—
224C2×C8—522no—
225C2×C8—522no—
226C2×C8—522no—
227C2×C8—522no—
228C4⋊C4—24no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—522no—
232C4⋊C4—522no—
233C4⋊C4—524no—
234C22⋊C4—524no—
235C42—22no—
236C42—262no—
237C42—521no—
238C42—521no—
239C13#772511yescharacteristic, complemented, Sylow
240C23—132no—
241C23—261no—
242C23—261no—
243C23—261no—
244C23—261no—
245C23—261no—
246C23—261no—
247C23C2×C22⋊#26111yescharacteristic
248Q8—1044no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—132no—
259C2×C4—131no—
260C2×C4—131no—
261C2×C4—132no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—522no—
269C2×C4—522no—
270C2×C4—524no—
271C2×C4—524no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4#8810712yes—
276C2×C4#8811712yes—
277C2×C4#8823812yes—
278C8—1042no—
279C8—1042no—
280C22—262no—
281C22—262no—
282C22—262no—
283C22—521no—
284C22—521no—
285C22—521no—
286C22—521no—
287C22C2×#8810711yescharacteristic
288C22#1171913811yescharacteristic
289C22#1171914011yescharacteristic
290C22#1171914711yescharacteristic
291C22C2×#8811711yescharacteristic
292C22#1171915511yescharacteristic
293C22D13⋊#10111yescharacteristic
294C4—22no—
295C4—22no—
296C4—22no—
297C4—82no—
298C4—262no—
299C4—261no—
300C4—261no—
301C4—262no—
302C4—1042no—
303C2—522no—
304C2#1313011411yescharacteristic
305C2#1313014511yescharacteristic
306C2#1313019611yescharacteristic
307C2#1313024311yescharacteristic
308C2#1313027511yescharacteristic
309C2#1313032811yescharacteristic
310C2#1313035211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#7725
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #13129654C2semidirect
239. C13#7725semidirect

Maximal subgroups

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

subgroupindex
#131307282
#131306932
#131296542
#131231892
#772513