Finite Group Databasebeta

← #15773209

Subgroups — #15773209

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#13114569C211yesmaximal, characteristic
3#13112858C214yesmaximal
4C13×#1458C211yesmaximal, characteristic
5C2×C13×#117C2211yescharacteristic
6C2×#88180—21no—
7C2×#88123C411yescharacteristic, complemented
8C13×#431—21no—
9#11718873—21no—
10#11718647—21no—
11#11718640C412yescomplemented
12#11718610—21no—
13#11718608C2212yes—
14#11718597C411yescharacteristic, complemented
15#11718589—21no—
16C13×#324—21no—
17C13×#323C2212yes—
18#11718118—21no—
19#11718118C2212yes—
20C23×C4×C13D411yescharacteristic
21C22×Dic26C2×C412yes—
22C13×#117—41no—
23C13×#117—41no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C22⋊C4D411yescharacteristic
27C2×C13×C22⋊C4C2311yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13—22no—
32#88180—24no—
33#88180—42no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—41no—
38C2×#6101—22no—
39C2×C4×Dic13—41no—
40#88123—41no—
41#88123—41no—
42C13×C4⋊C8—41no—
43C13×C22⋊C8—22no—
44C4×C8×C13—41no—
45#88071—21no—
46#88071—22no—
47#88071—22no—
48#88071C2×C412yes—
49#11717—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13SD1612yes—
59C22×C4×C13Q1612yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—42no—
65C2×Dic26—42no—
66C2×Dic26—82no—
67C2×C8×C13—42no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C22⋊C4—41no—
71C13×C22⋊C4—41no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C22⋊Dic13—24no—
77C22⋊Dic13—42no—
78C22⋊Dic13—82no—
79C4⋊Dic13—42no—
80C4⋊Dic13—44no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—42no—
84#6101—82no—
85C4×Dic13—44no—
86#2628—131no—
87#1740—131no—
88#1458D1311yescharacteristic
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#9911yescharacteristic
112C2×C4×C13#9911yescharacteristic
113C2×C4×C13#10312yes—
114C2×C4×C13#10312yes—
115C2×C4×C13#10412yes—
116C2×Dic13—44no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—82no—
124C2×Dic13—82no—
125Dic26—84no—
126C8×C13—82no—
127C2×C4⋊Q8—131no—
128C2×#117—261no—
129C2×#117C2×D1311yescharacteristic
130#431—21no—
131#400—261no—
132#399—261no—
133#395—132no—
134#393—132no—
135#389—261no—
136#382—131no—
137#380—261no—
138#342—132no—
139#342—261no—
140#324—21no—
141#323C2×D1312yes—
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#32812yes—
160C4×C13#32812yes—
161Dic13—82no—
162Dic13—84no—
163Dic13—82no—
164C22×Q8—132no—
165C23×C4D5211yescharacteristic
166C4⋊Q8—521no—
167C4⋊Q8—521no—
168#117—41no—
169#117—41no—
170#117—264no—
171#117—522no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—262no—
176C2×C4⋊C4—521no—
177C2×C4⋊C4C4×D1311yescharacteristic
178C2×C4⋊C4C22⋊D1311yescharacteristic
179C2×C22⋊C4—262no—
180C2×C22⋊C4—262no—
181C2×C22⋊C4D5211yescharacteristic
182C2×C22⋊C4C22×D1311yescharacteristic
183C2×C42—521no—
184C2×C42C4×D1311yescharacteristic
185C2×C42C22⋊D1311yescharacteristic
186C4⋊C8—41no—
187C22⋊C8—22no—
188C4×C8—41no—
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×D5211yescharacteristic
201C2×Q8—522no—
202C2×Q8—1042no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—262no—
207C22×C4—262no—
208C22×C4—522no—
209C22×C4#609512yes—
210C22×C4Dic5212yes—
211C22×C4#610311yescharacteristic
212C22×C4#610311yescharacteristic
213C22×C4#610311yescharacteristic
214C22×C4#610311yescharacteristic
215C22×C4C2×C4×D1311yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217C2×C8—42no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—522no—
221C4⋊C4—524no—
222C4⋊C4—522no—
223C4⋊C4—521no—
224C4⋊C4—521no—
225C4⋊C4—1042no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—264no—
229C22⋊C4—522no—
230C22⋊C4—1042no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—524no—
236C13#1171711yescharacteristic, complemented, Sylow
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23C2×#609511yescharacteristic
242C23C2×Dic5211yescharacteristic
243C23C2×#610311yescharacteristic
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—524no—
260C2×C4—522no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—522no—
266C2×C4—1042no—
267C2×C4—1042no—
268C2×C4#8804611yescharacteristic
269C2×C4#8804611yescharacteristic
270C2×C4#8805612yes—
271C2×C4#8805612yes—
272C2×C4#8806512yes—
273C8—82no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22C2×#8804611yescharacteristic
284C22C2×#8805611yescharacteristic
285C22C2×#8806511yescharacteristic
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—1042no—
292C4—1044no—
293C4—1042no—
294C4#1171805912yes—
295C4#1171805912yes—
296C2—21no—
297C2—21no—
298C2—41no—
299C2—41no—
300C2C2×#1171805911yescharacteristic
301C2#1311648711yescharacteristic
302C2#1311651011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1458C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1458D13
hypocenterC13#11717
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
7. C2×#88123C4semidirect
11. #11718640C4semidirect
14. #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
#131145692
#131128582
C13×#14582
#1171713