Finite Group Databasebeta

← #13127706

Subgroups — #13127706

Order 1664.

338 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719390C211yesmaximal, characteristic, complemented
2#11719244C211yesmaximal, characteristic
3C13×#478C211yesmaximal, characteristic
4#11718725C211yesmaximal, characteristic, complemented
5C4×#6105C211yesmaximal, characteristic
6#11718539C211yesmaximal, characteristic, complemented
7#11718536C211yesmaximal, characteristic, complemented
8#11718518C211yesmaximal, characteristic, complemented
9#11718516C211yesmaximal, characteristic, complemented
10#11718491C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718424C211yesmaximal, characteristic
13#11718420C211yesmaximal, characteristic
14#11718419C211yesmaximal, characteristic
15#11718419C211yesmaximal, characteristic
16C13×#125C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic
18D4×Dic13C2211yescharacteristic
19D4×Dic13C2211yescharacteristic
20C2×#6105C2211yescharacteristic
21#88178—21no—
22C2×#6101—21no—
23#88144C2211yescharacteristic
24#88144C2211yescharacteristic
25#88143—21no—
26#88143—21no—
27#88142—21no—
28#88142C2211yescharacteristic
29#88142C2211yescharacteristic
30#88141—21no—
31#88141C2211yescharacteristic
32#88141C2211yescharacteristic
33#88132—21no—
34#88132—21no—
35#88124C2211yescharacteristic
36C4×Dic26C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38C13×#107C2211yescharacteristic
39C13×#106C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#102C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88072C2211yescharacteristic
44#88058C2211yescharacteristic
45#88057C2211yescharacteristic
46#88056C2211yescharacteristic
47#88056C2211yescharacteristic
48#88054C2211yescharacteristic
49#88054C2211yescharacteristic
50C8×Dic13C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88050C2211yescharacteristic
53#88048C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×D4×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C22×Dic13—21no—
62C22×Dic13—21no—
63C2×Dic26—21no—
64C2×Dic26—21no—
65C2×Dic26D411yescharacteristic
66C2×Dic26C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4C2311yescharacteristic
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C42×C13C2311yescharacteristic
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78#6105Q814yescomplemented
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13D411yescharacteristic
82C4⋊Dic13C2311yescharacteristic
83C4⋊Dic13C2311yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85#6101—21no—
86#6101—21no—
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101D411yescharacteristic
95#6101D411yescharacteristic
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13C2311yescharacteristic
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#3381—131nomaximal, Sylow
104C23×C13—21no—
105D4×C13—21no—
106D4×C13C2×Q812yes—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—81no—
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2411yescharacteristic
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—42no—
119C2×Dic13—81no—
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124Dic26—21no—
125Dic26—22no—
126Dic26—42no—
127Dic26—81no—
128Dic26C2×Q812yes—
129C8×C13—21no—
130C8×C13—21no—
131#1055—21no—
132#1055C2×Q812yes—
133#557—131no—
134#554—131no—
135#499—131no—
136#499—131no—
137#498—131no—
138#479—131no—
139#479—131no—
140#478—131no—
141#478D1311yescharacteristic
142#477—131no—
143#474—131no—
144C8×Q8—131no—
145C4×SD16—131no—
146C4×SD16—131no—
147C4×SD16—131no—
148C22×C13—22no—
149C22×C13—41no—
150C22×C13—41no—
151C22×C13C22×D411yescharacteristic
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13C22×Q811yescharacteristic
158C4×C132−1+411yescharacteristic
159Dic13—22no—
160Dic13—21no—
161Dic13—21no—
162Dic13—21no—
163Dic13—41no—
164Dic13—41no—
165Dic13—41no—
166Dic13#13512yes—
167C2×SD16—131no—
168C4⋊Q8—131no—
169C4⋊Q8—131no—
170C4⋊Q8—261no—
171#125—131no—
172#125—131no—
173#125—131no—
174#125—261no—
175#125—261no—
176#125C2×D1311yescharacteristic
177C22⋊Q8—261no—
178C22⋊Q8—261no—
179C22⋊Q8—261no—
180C4×Q8—131no—
181C4×Q8—131no—
182C4×Q8—131no—
183C4×Q8—131no—
184C4×Q8—261no—
185C4×D4—131no—
186C4×D4—131no—
187C4×D4C2×D1311yescharacteristic
188C2×C4⋊C4—261no—
189#107—131no—
190#107—131no—
191#107—131no—
192#107C2×D1311yescharacteristic
193#106—131no—
194#106—131no—
195#106—131no—
196#106—131no—
197#106C2×D1311yescharacteristic
198C4⋊C8—131no—
199C4⋊C8—131no—
200C4⋊C8C2×D1311yescharacteristic
201#103—131no—
202#103—131no—
203#103—131no—
204#102—131no—
205#102C2×D1311yescharacteristic
206#102C2×D1311yescharacteristic
207C4×C8—131no—
208C4×C8—131no—
209C4×C8—131no—
210C2×C13—42no—
211C2×C13D4×Q811yescharacteristic
212C2×C13C2×#13511yescharacteristic
213C2×C13#57711yescharacteristic
214C2×Q8—131no—
215C2×Q8—131no—
216C2×Q8—261no—
217C2×Q8—261no—
218C2×D4C22×D1311yescharacteristic
219C22×C4—21no—
220C22×C4—261no—
221C22×C4—261no—
222SD16—134no—
223C2×C8—131no—
224C2×C8—131no—
225C2×C8C22×D1311yescharacteristic
226C2×C8C22×D1311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—131no—
230C4⋊C4—131no—
231C4⋊C4—131no—
232C4⋊C4—131no—
233C4⋊C4—131no—
234C4⋊C4—131no—
235C4⋊C4—261no—
236C4⋊C4—261no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4C22×D1311yescharacteristic
247C4⋊C4C22×D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—261no—
251C22⋊C4—261no—
252C42—131no—
253C42—131no—
254C42—261no—
255C42—261no—
256C42—261no—
257C42C22×D1311yescharacteristic
258C13#338111yescharacteristic, complemented, Sylow
259C23—21no—
260Q8—132no—
261Q8—262no—
262Q8—261no—
263Q8—522no—
264Q8—1041no—
265D4—21no—
266D4Q8×D1312yes—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—81no—
271C2×C4—131no—
272C2×C4—131no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—522no—
280C2×C4—1041no—
281C2×C4D4×D1311yescharacteristic
282C2×C4D4×D1311yescharacteristic
283C2×C4C23×D1311yescharacteristic
284C8—21no—
285C8—21no—
286C8—132no—
287C8—261no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22C2×D4×D1311yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—132no—
298C4—261no—
299C4—261no—
300C4—261no—
301C4—262no—
302C4—521no—
303C4—521no—
304C4—521no—
305C4C2×Q8×D1311yescharacteristic
306C4#8825711yescharacteristic
307C2—42no—
308C2#1171933711yescharacteristic
309C2D13×#13511yescharacteristic
310C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#478C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#478D13
hypocenterC13#3381
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #11719390C2semidirect
4. #11718725C2semidirect
6. #11718539C2semidirect
7. #11718536C2semidirect
8. #11718518C2semidirect
9. #11718516C2semidirect
10. #11718491C2semidirect
11. #11718490C2semidirect
78. #6105Q8semidirect
258. C13#3381semidirect

Maximal subgroups

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

subgroupindex
#117193902
#117192442
C13×#4782
#117187252
C4×#61052
#117185392
#117185362
#117185182
#117185162
#117184912
#117184902
#117184242
#117184202
#117184192
#338113