Finite Group Databasebeta

← #15773107

Subgroups — #15773107

Order 3328.

468 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 107 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#13120602C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112835C214yesmaximal
4C13×#1740C211yesmaximal, characteristic
5C2×C13×#117—21no—
6C2×C13×#117C2211yescharacteristic
7C2×#88178—21no—
8C2×#88123C411yescharacteristic, complemented
9#11718644—21no—
10#11718644C412yescomplemented
11#11718614—21no—
12#11718614C2212yes—
13#11718597C411yescharacteristic, complemented
14#11718590—21no—
15#11718586—21no—
16C13×#342—21no—
17C13×#342C2212yes—
18#11718120—21no—
19#11718117C2212yes—
20C23×C4×C13D411yescharacteristic
21C22×Dic26—21no—
22C13×#117—24no—
23C13×#117—41no—
24C13×#117—41no—
25C13×#117—42no—
26C2×C13×C4⋊C4—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C13×C22⋊C4C2311yescharacteristic
32C2×C42×C13—41no—
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C22⋊Dic13—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13C2×C412yes—
39#88178—42no—
40#88178—42no—
41C2×#6101—22no—
42#88123—41no—
43#88123—41no—
44#88071—22no—
45#88071—21no—
46#88071—22no—
47#88071C2×C412yes—
48C22⋊#1055—22no—
49C4⋊#1055—41no—
50C4×#1055—41no—
51#11694—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—42no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13D812yes—
62C22×C4×C13SD1612yes—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×Dic13—22no—
66C22×Dic13—22no—
67C2×Dic26—41no—
68C2×Dic26—41no—
69C2×Dic26—42no—
70C2×Dic26—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—44no—
74C13×C22⋊C4—24no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—42no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—44no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C4⋊Dic13—42no—
86C4⋊Dic13—42no—
87C4⋊Dic13—42no—
88#6101—44no—
89C2×#1055—42no—
90#2621—131no—
91#1740D1311yescharacteristic
92#1458—131no—
93#1344—134no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13C2×C22⋊C411yescharacteristic
99C23×C13C2×D811yescharacteristic
100C23×C13C2×SD1611yescharacteristic
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—44no—
116C2×C4×C13—82no—
117C2×C4×C13—82no—
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13#9911yescharacteristic
120C2×C4×C13#10212yes—
121C2×C4×C13#10212yes—
122C2×C4×C13#10412yes—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129Dic26—82no—
130Dic26—82no—
131#1055—82no—
132C2×C4⋊Q8—131no—
133C2×C22⋊Q8—261no—
134C2×#117—21no—
135C2×#117C2×D1311yescharacteristic
136#431—261no—
137#398—132no—
138#398—261no—
139#397—132no—
140#397—261no—
141#391—261no—
142#382—131no—
143#342—21no—
144#342C2×D1312yes—
145#324—261no—
146#323—132no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—81no—
156C22×C13C2×#9911yescharacteristic
157C22×C13C2×#10211yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C4×C13—22no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—84no—
165C4×C13#32712yes—
166C4×C13#32712yes—
167Dic13—82no—
168Dic13—82no—
169C22×Q8—261no—
170C23×C4C22⋊D1311yescharacteristic
171C4⋊Q8—521no—
172C4⋊Q8—521no—
173C22⋊Q8—522no—
174C22⋊Q8—522no—
175#117—24no—
176#117—41no—
177#117—41no—
178#117—42no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—132no—
181C2×C4⋊C4—262no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4C4×D1311yescharacteristic
185C2×C4⋊C4D5211yescharacteristic
186C2×C22⋊C4—22no—
187C2×C22⋊C4—262no—
188C2×C22⋊C4C22⋊D1311yescharacteristic
189C2×C22⋊C4C22×D1311yescharacteristic
190C2×C42—41no—
191C2×C42C4×D1311yescharacteristic
192C2×C42D5211yescharacteristic
193C4⋊C8—521no—
194C22⋊C8—262no—
195C4×C8—521no—
196#95—132no—
197#95—261no—
198#95—262no—
199#95—262no—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13—41no—
203C2×C13—41no—
204C2×C13C2×#32711yescharacteristic
205C2×C13#212311yescharacteristic
206C2×C13#212911yescharacteristic
207C24C2×C22⋊D1311yescharacteristic
208C2×Q8—522no—
209C2×Q8—521no—
210C2×Q8—521no—
211C2×Q8—522no—
212C22×C4—22no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—42no—
216C22×C4—262no—
217C22×C4—262no—
218C22×C4#610311yescharacteristic
219C22×C4#610311yescharacteristic
220C22×C4#610311yescharacteristic
221C22×C4#610311yescharacteristic
222C22×C4#610412yes—
223C22×C4#610612yes—
224C22×C4C2×C4×D1311yescharacteristic
225C22×C4C2×D5211yescharacteristic
226C2×C8—522no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—44no—
230C4⋊C4—522no—
231C4⋊C4—522no—
232C4⋊C4—524no—
233C4⋊C4—522no—
234C22⋊C4—24no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—42no—
238C22⋊C4—522no—
239C22⋊C4—522no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—44no—
245C13#1169411yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23C2×#610311yescharacteristic
251C23C2×#610411yescharacteristic
252C23C2×#610611yescharacteristic
253Q8—1042no—
254Q8—1042no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—44no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4—522no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4#8804512yes—
279C2×C4#8804611yescharacteristic
280C2×C4#8804611yescharacteristic
281C2×C4#8804912yes—
282C2×C4#8804912yes—
283C8—1042no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22C2×#8804511yescharacteristic
294C22C2×#8804611yescharacteristic
295C22C2×#8804911yescharacteristic
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—84no—
302C4—1042no—
303C4—1042no—
304C4#1171804312yes—
305C4#1171804312yes—
306C2—21no—
307C2—21no—
308C2—41no—
309C2—41no—
310C2C2×#1171804311yescharacteristic
311C2#1311648911yescharacteristic
312C2#1311651011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1740C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1740D13
hypocenterC13#11694
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1740

Complements

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

NH ≅ G/Ntype
8. C2×#88123C4semidirect
10. #11718644C4semidirect
13. #11718597C4semidirect
245. C13#11694semidirect

Maximal subgroups

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

subgroupindex
#131206022
#131131502
#131128352
C13×#17402
#1169413