Finite Group Databasebeta

← #13127741

Subgroups — #13127741

Order 1664.

340 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719427C211yesmaximal, characteristic, complemented
2#11719244C211yesmaximal, characteristic
3C13×#474C211yesmaximal, characteristic
4#11718741C211yesmaximal, characteristic, complemented
5#11718679C211yesmaximal, characteristic
6#11718538C211yesmaximal, characteristic, complemented
7#11718537C211yesmaximal, characteristic, complemented
8#11718536C211yesmaximal, characteristic, complemented
9#11718535C211yesmaximal, characteristic, complemented
10#11718490C211yesmaximal, characteristic, complemented
11#11718489C211yesmaximal, characteristic, complemented
12#11718422C211yesmaximal, characteristic
13#11718420C211yesmaximal, characteristic
14#11718419C211yesmaximal, characteristic
15#11718418C211yesmaximal, characteristic
16C13×C4⋊Q8C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic
18#88198—21no—
19#88198—21no—
20D4×Dic13C2211yescharacteristic
21D4×Dic13C2211yescharacteristic
22C2×#6105C2211yescharacteristic
23#88178—21no—
24C2×#6101—21no—
25#88144C2211yescharacteristic
26#88142—21no—
27#88142C2211yescharacteristic
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×#107C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#102C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88072C2211yescharacteristic
44#88058C2211yescharacteristic
45#88057C2211yescharacteristic
46#88056C2211yescharacteristic
47#88056C2211yescharacteristic
48#88055C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88050C2211yescharacteristic
53#88048C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×Dic13—21no—
63C22×Dic13—21no—
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×Dic26—21no—
67C2×Dic26D411yescharacteristic
68C2×Dic26C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C22⋊C4—21no—
76C42×C13C2311yescharacteristic
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79#6105Q814yescomplemented
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#3385—131nomaximal, Sylow
104C23×C13—21no—
105Q8×C13—81no—
106D4×C13—21no—
107D4×C13C2×Q812yes—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—81no—
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2411yescharacteristic
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—42no—
120C2×Dic13—81no—
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125Dic26—21no—
126Dic26—22no—
127Dic26—81no—
128Dic26—81no—
129Dic26—81no—
130Dic26C2×Q812yes—
131C8×C13—21no—
132C8×C13—21no—
133#1055—21no—
134#1055C2×Q812yes—
135Q82—131no—
136#554—131no—
137#501—131no—
138#501—131no—
139#500—131no—
140#479—131no—
141#479—131no—
142#477—131no—
143#476—131no—
144#474—131no—
145#474D1311yescharacteristic
146#446—131no—
147#440—131no—
148#440—131no—
149C4×SD16—131no—
150C22×C13—22no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13C22×D411yescharacteristic
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13C22×Q811yescharacteristic
160C4×C132−1+411yescharacteristic
161Dic13—22no—
162Dic13—21no—
163Dic13—21no—
164Dic13—21no—
165Dic13—41no—
166Dic13—41no—
167Dic13—41no—
168Dic13#13712yes—
169C2×SD16—131no—
170C4⋊Q8—131no—
171C4⋊Q8—131no—
172C4⋊Q8—131no—
173C4⋊Q8—261no—
174C4⋊Q8—261no—
175C4⋊Q8—261no—
176C4⋊Q8C2×D1311yescharacteristic
177#125—131no—
178#125—131no—
179C22⋊Q8—261no—
180C22⋊Q8—261no—
181C22⋊Q8—261no—
182C4×Q8—131no—
183C4×Q8—131no—
184C4×Q8—131no—
185C4×Q8—131no—
186C4×Q8—261no—
187C4×D4—131no—
188C4×D4—131no—
189C4×D4C2×D1311yescharacteristic
190C2×C4⋊C4—261no—
191#107—131no—
192#107—131no—
193#107—131no—
194#107—131no—
195#107C2×D1311yescharacteristic
196#107C2×D1311yescharacteristic
197#106—131no—
198#106—131no—
199#106—131no—
200C4⋊C8—131no—
201C4⋊C8—131no—
202C4⋊C8C2×D1311yescharacteristic
203#103—131no—
204#103—131no—
205#103—131no—
206#102—131no—
207#102C2×D1311yescharacteristic
208#102C2×D1311yescharacteristic
209#97—131no—
210#97—131no—
211C4×C8—131no—
212C2×C13—42no—
213C2×C13D4×Q811yescharacteristic
214C2×C13C2×#13711yescharacteristic
215C2×C13#57611yescharacteristic
216C2×Q8—21no—
217C2×Q8—131no—
218C2×Q8—131no—
219C2×Q8—261no—
220C2×Q8—261no—
221C2×Q8—261no—
222C2×D4C22×D1311yescharacteristic
223C22×C4—21no—
224C22×C4—261no—
225C22×C4—261no—
226SD16—134no—
227C2×C8—131no—
228C2×C8—131no—
229C2×C8C22×D1311yescharacteristic
230C2×C8C22×D1311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—131no—
233C4⋊C4—131no—
234C4⋊C4—131no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—131no—
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⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4C22×D1311yescharacteristic
249C4⋊C4C22×D1311yescharacteristic
250C4⋊C4C22×D1311yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C42—131no—
255C42—131no—
256C42—261no—
257C42—261no—
258C42—261no—
259C42C22×D1311yescharacteristic
260C13#338511yescharacteristic, complemented, Sylow
261C23—21no—
262Q8—81no—
263Q8—132no—
264Q8—262no—
265Q8—261no—
266Q8—1041no—
267Q8—1041no—
268Q8—1041no—
269D4—21no—
270D4Q8×D1312yes—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—81no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—131no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—522no—
284C2×C4—1041no—
285C2×C4D4×D1311yescharacteristic
286C2×C4D4×D1311yescharacteristic
287C2×C4C23×D1311yescharacteristic
288C8—21no—
289C8—21no—
290C8—132no—
291C8—261no—
292C22—22no—
293C22—41no—
294C22—41no—
295C22C2×D4×D1311yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—132no—
302C4—261no—
303C4—261no—
304C4—261no—
305C4—262no—
306C4—521no—
307C4—521no—
308C4—521no—
309C4C2×Q8×D1311yescharacteristic
310C4#8825711yescharacteristic
311C2—42no—
312C2#1171933711yescharacteristic
313C2#1171946211yescharacteristic
314C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#474D13
hypocenterC13#3385
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719427C2semidirect
4. #11718741C2semidirect
6. #11718538C2semidirect
7. #11718537C2semidirect
8. #11718536C2semidirect
9. #11718535C2semidirect
10. #11718490C2semidirect
11. #11718489C2semidirect
79. #6105Q8semidirect
260. C13#3385semidirect

Maximal subgroups

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

subgroupindex
#117194272
#117192442
C13×#4742
#117187412
#117186792
#117185382
#117185372
#117185362
#117185352
#117184902
#117184892
#117184222
#117184202
#117184192
#117184182
#338513