Finite Group Databasebeta

← #13127791

Subgroups — #13127791

Order 1664.

348 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719435C211yesmaximal, characteristic, complemented
2#11719395C211yesmaximal, characteristic, complemented
3C13×#501C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718727C211yesmaximal, characteristic, complemented
6#11718552C211yesmaximal, characteristic, complemented
7#11718551C211yesmaximal, characteristic, complemented
8#11718537C211yesmaximal, characteristic, complemented
9#11718533C211yesmaximal, characteristic
10#11718532C211yesmaximal, characteristic, complemented
11#11718532C211yesmaximal, characteristic, complemented
12#11718530C211yesmaximal, characteristic
13#11718519C211yesmaximal, characteristic, complemented
14#11718372C211yesmaximal, characteristic
15#11718362C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#125C2211yescharacteristic
18#88200—21no—
19#88200—21no—
20C2×D104C2211yescharacteristic
21#88151—21no—
22#88151—21no—
23#88150—21no—
24#88150—21no—
25#88147C2211yescharacteristic
26#88147C2211yescharacteristic
27#88147C2211yescharacteristic
28#88147C2211yescharacteristic
29C4⋊C4×D13—21no—
30C4⋊C4×D13—21no—
31#88144C2211yescharacteristic
32#88144C2211yescharacteristic
33#88144C2211yescharacteristic
34#88142C2211yescharacteristic
35C4×D52C2211yescharacteristic
36C4×D52C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38C13×#107C2211yescharacteristic
39C13×#107C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#97C2211yescharacteristic
43#88061C2211yescharacteristic
44#88061C2211yescharacteristic
45#88057C2211yescharacteristic
46#88055C2211yescharacteristic
47#88054C2211yescharacteristic
48#88054C2211yescharacteristic
49C8×Dic13C2211yescharacteristic
50#88049C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D52C2311yescharacteristic
61C2×D52C2311yescharacteristic
62C2×C4×D13—21no—
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×Dic26—21no—
69C2×Dic26D411yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C42×C13C2311yescharacteristic
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13D411yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101D411yescharacteristic
97#6101D411yescharacteristic
98C4×Dic13C2311yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102D104Q814yescomplemented
103#3389—131nomaximal, Sylow
104C22×D13—21no—
105C22×D13—21no—
106Q8×C13—81no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2411yescharacteristic
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13C2×D411yescharacteristic
117C2×Dic13C2×D411yescharacteristic
118C2×Dic13C2×D411yescharacteristic
119C2×Dic13C2×D411yescharacteristic
120D52—21no—
121D52—21no—
122D52C2×Q812yes—
123D52C2×Q812yes—
124C4×D13—42no—
125C4×D13—42no—
126C4×D13—81no—
127C4×D13—81no—
128C4×D13—81no—
129C4×D13—81no—
130Dic26—41no—
131Dic26—81no—
132C8×C13—21no—
133C8×C13C2×Q812yes—
134#1055—21no—
135#1055—21no—
136#554—131no—
137#554—131no—
138#501—131no—
139#501D1311yescharacteristic, complemented
140#499—131no—
141#478—131no—
142#478—131no—
143#478—131no—
144#478—131no—
145#474—131no—
146#474—131no—
147#446—131no—
148#442—131no—
149#442—131no—
150C4×D8—131no—
151C22×C13C22×D411yescharacteristic
152C2×D13—22no—
153C2×D13—22no—
154C2×D13—41no—
155C2×D13—41no—
156C2×D13—41no—
157C2×D13—41no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13C22×Q811yescharacteristic
165C4×C132−1+411yescharacteristic
166Dic13—21no—
167Dic13—21no—
168Dic13—21no—
169Dic13—21no—
170Dic13—41no—
171Dic13—41no—
172C2×D8—131no—
173C4⋊Q8—131no—
174C4⋊Q8C2×D1311yescharacteristic
175#125—131no—
176#125—131no—
177#125—131no—
178#125C2×D1311yescharacteristic
179C22⋊Q8—261no—
180C22⋊Q8—261no—
181C22⋊Q8—261no—
182C22⋊Q8—261no—
183C22⋊Q8—261no—
184C22⋊Q8—261no—
185C4×Q8—131no—
186C4×D4—131no—
187C4×D4—131no—
188C4×D4—131no—
189C4×D4—131no—
190C4×D4—131no—
191C4×D4—131no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194#107—131no—
195#107—131no—
196#107—131no—
197#107C2×D1311yescharacteristic
198#107C2×D1311yescharacteristic
199#106—131no—
200#106—131no—
201#106C2×D1311yescharacteristic
202#106C2×D1311yescharacteristic
203C4⋊C8—131no—
204C4⋊C8—131no—
205C4⋊C8—131no—
206#102—131no—
207#102—131no—
208#102—131no—
209#102—131no—
210#102—131no—
211#102—131no—
212#97—131no—
213#97C2×D1311yescharacteristic
214C4×C8—131no—
215C2×C13D4×Q811yescharacteristic
216C2×C13#57511yescharacteristic
217C2×C13#57611yescharacteristic
218D13—42no—
219D13—42no—
220C2×Q8—21no—
221C2×Q8—131no—
222C2×Q8—261no—
223C2×D4—131no—
224C2×D4—131no—
225C22×C4—261no—
226C22×C4—261no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—261no—
231D8—134no—
232C2×C8—131no—
233C2×C8—131no—
234C2×C8C22×D1311yescharacteristic
235C2×C8C22×D1311yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—131no—
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4C22×D1311yescharacteristic
252C4⋊C4C22×D1311yescharacteristic
253C4⋊C4C22×D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C22⋊C4—261no—
256C22⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C42—131no—
262C42—131no—
263C42C22×D1311yescharacteristic
264C13#338911yescharacteristic, complemented, Sylow
265C23—261no—
266C23—261no—
267Q8—81no—
268Q8—521no—
269Q8—1041no—
270D4—132no—
271D4—132no—
272D4—261no—
273D4—261no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—522no—
285C2×C4—522no—
286C2×C4—1041no—
287C2×C4—1041no—
288C2×C4—1041no—
289C2×C4—1041no—
290C2×C4D4×D1311yescharacteristic
291C2×C4D4×D1311yescharacteristic
292C2×C4C23×D1311yescharacteristic
293C8—21no—
294C8—261no—
295C8—261no—
296C8Q8×D1312yes—
297C22—262no—
298C22—262no—
299C22—521no—
300C22—521no—
301C22—521no—
302C22—521no—
303C22C2×D4×D1311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—261no—
311C4—261no—
312C4—261no—
313C4—261no—
314C4—521no—
315C4—521no—
316C4C2×Q8×D1311yescharacteristic
317C4#8825411yescharacteristic
318C2—522no—
319C2—522no—
320C2#1171943211yescharacteristic
321C2#1171947911yescharacteristic
322C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radicalC2×D104C22
hypercenter#501D13
hypocenterC13#3389
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
2. #11719395C2semidirect
3. C13×#501C2semidirect
4. #11718748C2semidirect
5. #11718727C2semidirect
6. #11718552C2semidirect
7. #11718551C2semidirect
8. #11718537C2semidirect
10. #11718532C2semidirect
11. #11718532C2semidirect
13. #11718519C2semidirect
15. #11718362C2semidirect
102. D104Q8semidirect
139. #501D13semidirect
264. C13#3389semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117193952
C13×#5012
#117187482
#117187272
#117185522
#117185512
#117185372
#117185332
#117185322
#117185302
#117185192
#117183722
#117183622
#338913