Finite Group Databasebeta

← #15773207

Subgroups — #15773207

Order 3328.

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

normal subgroups only

This group has 448 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#13120657C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112856C214yesmaximal
4C13×#1740C211yesmaximal, characteristic
5C2×C13×#117—21no—
6C2×C13×#117C2211yescharacteristic
7C2×#88123C411yescharacteristic, complemented
8#11718873—21no—
9#11718647—21no—
10#11718640C412yescomplemented
11#11718610—21no—
12#11718608C2212yes—
13#11718597C411yescharacteristic, complemented
14#11718589—21no—
15#11718586—21no—
16C13×#342—21no—
17C13×#342C2212yes—
18#11718120—21no—
19#11718117C2212yes—
20C23×C4×C13D411yescharacteristic
21C22×Dic26C2×C412yes—
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⋊Dic13—21no—
39C2×#6101—22no—
40#88123—41no—
41#88123—41no—
42#88071—21no—
43#88071—22no—
44#88071—22no—
45#88071C2×C412yes—
46C22⋊#1055—22no—
47C4⋊#1055—41no—
48C4×#1055—41no—
49#11717—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—42no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13SD1612yes—
60C22×C4×C13Q1612yes—
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—22no—
64C22×Dic13—22no—
65C2×Dic26—42no—
66C2×Dic26—82no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—44no—
70C13×C22⋊C4—24no—
71C13×C22⋊C4—41no—
72C13×C22⋊C4—41no—
73C13×C22⋊C4—42no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—44no—
79C22⋊Dic13—82no—
80C4⋊Dic13—42no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—42no—
84#6101—82no—
85C2×#1055—42no—
86#2628—131no—
87#1740D1311yescharacteristic
88#1458—131no—
89#1351—134no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13C2×C22⋊C411yescharacteristic
95C23×C13C2×SD1611yescharacteristic
96C23×C13C2×Q1611yescharacteristic
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—44no—
112C2×C4×C13—82no—
113C2×C4×C13—82no—
114C2×C4×C13#9911yescharacteristic
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#10312yes—
117C2×C4×C13#10312yes—
118C2×C4×C13#10412yes—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125Dic26—84no—
126#1055—82no—
127C2×C4⋊Q8—131no—
128C2×#117—21no—
129C2×#117C2×D1311yescharacteristic
130#431—261no—
131#400—261no—
132#399—261no—
133#395—132no—
134#393—132no—
135#389—261no—
136#382—131no—
137#380—261no—
138#342—21no—
139#342C2×D1312yes—
140#324—261no—
141#323—132no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—81no—
151C22×C13C2×#9911yescharacteristic
152C22×C13C2×#10311yescharacteristic
153C22×C13C2×#10411yescharacteristic
154C4×C13—22no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—84no—
160C4×C13#32812yes—
161C4×C13#32812yes—
162Dic13—82no—
163Dic13—82no—
164C22×Q8—132no—
165C23×C4C22⋊D1311yescharacteristic
166C4⋊Q8—521no—
167C4⋊Q8—521no—
168#117—24no—
169#117—41no—
170#117—41no—
171#117—42no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—262no—
177C2×C4⋊C4C4×D1311yescharacteristic
178C2×C4⋊C4D5211yescharacteristic
179C2×C22⋊C4—22no—
180C2×C22⋊C4—262no—
181C2×C22⋊C4C22⋊D1311yescharacteristic
182C2×C22⋊C4C22×D1311yescharacteristic
183C2×C42—41no—
184C2×C42C4×D1311yescharacteristic
185C2×C42D5211yescharacteristic
186C4⋊C8—521no—
187C22⋊C8—262no—
188C4×C8—521no—
189#95—132no—
190#95—262no—
191#95—261no—
192#95—262no—
193C2×C13—21no—
194C2×C13—21no—
195C2×C13—41no—
196C2×C13—41no—
197C2×C13C2×#32811yescharacteristic
198C2×C13#212211yescharacteristic
199C2×C13#212911yescharacteristic
200C24C2×C22⋊D1311yescharacteristic
201C2×Q8—522no—
202C2×Q8—1042no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—42no—
207C22×C4—262no—
208C22×C4—262no—
209C22×C4#610311yescharacteristic
210C22×C4#610311yescharacteristic
211C22×C4#610311yescharacteristic
212C22×C4#610311yescharacteristic
213C22×C4#610512yes—
214C22×C4#610712yes—
215C22×C4C2×C4×D1311yescharacteristic
216C22×C4C2×D5211yescharacteristic
217C2×C8—522no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—44no—
221C4⋊C4—522no—
222C4⋊C4—522no—
223C4⋊C4—521no—
224C4⋊C4—521no—
225C4⋊C4—1042no—
226C22⋊C4—24no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—42no—
230C22⋊C4—1042no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—44no—
236C13#1171711yescharacteristic, complemented, Sylow
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23C2×#610311yescharacteristic
242C23C2×#610511yescharacteristic
243C23C2×#610711yescharacteristic
244Q8—1044no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—44no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4—522no—
268C2×C4#8804512yes—
269C2×C4#8804611yescharacteristic
270C2×C4#8804611yescharacteristic
271C2×C4#8805012yes—
272C2×C4#8805012yes—
273C8—1042no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22C2×#8804511yescharacteristic
284C22C2×#8804611yescharacteristic
285C22C2×#8805011yescharacteristic
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—84no—
292C4—1042no—
293C4—1042no—
294C4#1171804412yes—
295C4#1171804412yes—
296C2—21no—
297C2—21no—
298C2—41no—
299C2—41no—
300C2C2×#1171804411yescharacteristic
301C2#1311648511yescharacteristic
302C2#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#11717
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
7. C2×#88123C4semidirect
10. #11718640C4semidirect
13. #11718597C4semidirect
236. C13#11717semidirect

Maximal subgroups

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

subgroupindex
#131206572
#131131502
#131128562
C13×#17402
#1171713