Finite Group Databasebeta

← #13127789

Subgroups — #13127789

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#11719244C211yesmaximal, characteristic, complemented
3C13×#474C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718675C211yesmaximal, characteristic
6#11718552C211yesmaximal, characteristic, complemented
7#11718551C211yesmaximal, characteristic, complemented
8#11718539C211yesmaximal, characteristic, complemented
9#11718537C211yesmaximal, characteristic, complemented
10#11718508C211yesmaximal, characteristic, complemented
11#11718489C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic
13#11718427C211yesmaximal, characteristic, complemented
14#11718424C211yesmaximal, characteristic, complemented
15#11718417C211yesmaximal, characteristic
16C13×C4⋊Q8C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic
18#88200—21no—
19#88200—21no—
20D4×Dic13C2211yescharacteristic
21D4×Dic13C2211yescharacteristic
22C2×#6104C2211yescharacteristic
23#88178—21no—
24C2×#6101—21no—
25#88151—21no—
26#88147C2211yescharacteristic
27#88147C2211yescharacteristic
28C4⋊C4×D13—21no—
29#88144C2211yescharacteristic
30#88144C2211yescharacteristic
31#88144C2211yescharacteristic
32#88142C2211yescharacteristic
33#88132—21no—
34#88132—21no—
35C4×D52C2211yescharacteristic
36#88124C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38C13×#107C2211yescharacteristic
39C13×#107C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#102C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88072C2211yescharacteristic
44#88061C2211yescharacteristic
45#88061C2211yescharacteristic
46#88058C2211yescharacteristic
47#88057C2211yescharacteristic
48#88055C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88049C2211yescharacteristic
53#88048C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×Dic13—21no—
63C22×Dic13—21no—
64C2×D52C2311yescharacteristic
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⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C42×C13C2311yescharacteristic
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80#6104Q814yescomplemented
81#6103—21no—
82#6103—21no—
83#6103—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13D411yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98#6101D411yescharacteristic
99C4×Dic13C2311yescharacteristic
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#3389—131nomaximal, Sylow
104C23×C13—21no—
105C22×D13—21no—
106Q8×C13—81no—
107D4×C13—21no—
108D4×C13C2×Q812yes—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—81no—
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2411yescharacteristic
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
125D52—21no—
126D52C2×Q812yes—
127C4×D13—42no—
128C4×D13—81no—
129C4×D13—81no—
130Dic26—41no—
131Dic26—81no—
132C8×C13—21no—
133C8×C13—21no—
134#1055—21no—
135#1055C2×Q812yes—
136#554—131no—
137#554—131no—
138#501—131no—
139#501—131no—
140#499—131no—
141#478—131no—
142#478—131no—
143#478—131no—
144#478—131no—
145#474—131no—
146#474D1311yescharacteristic, complemented
147#446—131no—
148#442—131no—
149#442—131no—
150C4×D8—131no—
151C22×C13—22no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13C22×D411yescharacteristic
155C2×D13—22no—
156C2×D13—41no—
157C2×D13—41no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13C22×Q811yescharacteristic
164C4×C132−1+411yescharacteristic
165Dic13—21no—
166Dic13—21no—
167Dic13—21no—
168Dic13—21no—
169Dic13—41no—
170Dic13—41no—
171Dic13—41no—
172C2×D8—131no—
173C4⋊Q8—131no—
174C4⋊Q8C2×D1311yescharacteristic
175#125—131no—
176#125—131no—
177#125—131no—
178#125—131no—
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×D4C2×D1311yescharacteristic
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#106—131no—
202#106—131no—
203C4⋊C8—131no—
204C4⋊C8—131no—
205C4⋊C8C2×D1311yescharacteristic
206#102—131no—
207#102—131no—
208#102—131no—
209#102—131no—
210#102C2×D1311yescharacteristic
211#102C2×D1311yescharacteristic
212#97—131no—
213#97—131no—
214C4×C8—131no—
215C2×C13—42no—
216C2×C13D4×Q811yescharacteristic
217C2×C13#57511yescharacteristic
218C2×C13#57611yescharacteristic
219D13—42no—
220C2×Q8—21no—
221C2×Q8—131no—
222C2×Q8—261no—
223C2×D4—131no—
224C2×D4C22×D1311yescharacteristic
225C22×C4—21no—
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—131no—
238C4⋊C4—131no—
239C4⋊C4—131no—
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4C22×D1311yescharacteristic
253C4⋊C4C22×D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C22⋊C4—21no—
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—21no—
266C23—261no—
267Q8—81no—
268Q8—521no—
269Q8—1041no—
270D4—21no—
271D4—132no—
272D4—261no—
273D4Q8×D1312yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—81no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—1041no—
288C2×C4—1041no—
289C2×C4—1041no—
290C2×C4D4×D1311yescharacteristic
291C2×C4D4×D1311yescharacteristic
292C2×C4C23×D1311yescharacteristic
293C8—21no—
294C8—21no—
295C8—132no—
296C8—261no—
297C22—22no—
298C22—41no—
299C22—41no—
300C22—262no—
301C22—521no—
302C22—521no—
303C22C2×D4×D1311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—261no—
310C4—261no—
311C4—261no—
312C4—261no—
313C4—521no—
314C4—521no—
315C4—521no—
316C4C2×Q8×D1311yescharacteristic
317C4#8825711yescharacteristic
318C2—42no—
319C2—522no—
320C2#1171933711yescharacteristic
321C2#1171946211yescharacteristic
322C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#474D13
hypocenterC13#3389
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. #11719435C2semidirect
2. #11719244C2semidirect
3. C13×#474C2semidirect
4. #11718741C2semidirect
6. #11718552C2semidirect
7. #11718551C2semidirect
8. #11718539C2semidirect
9. #11718537C2semidirect
10. #11718508C2semidirect
11. #11718489C2semidirect
13. #11718427C2semidirect
14. #11718424C2semidirect
80. #6104Q8semidirect
146. #474D13semidirect
264. C13#3389semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117192442
C13×#4742
#117187412
#117186752
#117185522
#117185512
#117185392
#117185372
#117185082
#117184892
#117184462
#117184272
#117184242
#117184172
#338913