Finite Group Databasebeta

← #13127557

Subgroups — #13127557

Order 1664.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719432C211yesmaximal, characteristic, complemented
2#11719273C211yesmaximal, characteristic, complemented
3C13×#477C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718687C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718550C211yesmaximal, characteristic, complemented
8#11718536C211yesmaximal, characteristic, complemented
9#11718533C211yesmaximal, characteristic
10#11718505C211yesmaximal, characteristic
11#11718489C211yesmaximal, characteristic, complemented
12#11718480C211yesmaximal, characteristic
13#11718479C211yesmaximal, characteristic, complemented
14#11718456C211yesmaximal, characteristic, complemented
15#11718453C211yesmaximal, characteristic, complemented
16C2×Q8×D13—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19#88201C2211yescharacteristic
20#88200—21no—
21#88198C2211yescharacteristic
22C2×#6106C2211yescharacteristic
23C2×D104C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25#88152—21no—
26#88150—21no—
27#88150—21no—
28#88150—21no—
29#88147C2211yescharacteristic
30#88147C2211yescharacteristic
31#88147C2211yescharacteristic
32#88142C2211yescharacteristic
33#88142C2211yescharacteristic
34#88141C2211yescharacteristic
35#88130—21no—
36#88129C2211yescharacteristic
37C4×D52C2211yescharacteristic
38#88126—21no—
39C4×Dic26C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45#88075C2211yescharacteristic
46#88061C2211yescharacteristic
47#88056C2211yescharacteristic
48#88055C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61Q8×D13—44no—
62C2×D52C2311yescharacteristic
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×Dic26—21no—
69C2×Dic26—21no—
70C2×Dic26D411yescharacteristic
71C2×Dic26C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C42×C13—21no—
80C42×C13C2311yescharacteristic
81#6106—22no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90C4⋊Dic13D411yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104D104—22no—
105#6095—22no—
106#3367—131nomaximal, Sylow
107C22×D13—21no—
108C22×D13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—42no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125D52—21no—
126D52—21no—
127D52—21no—
128D52#4112yes—
129C4×D13—42no—
130C4×D13—42no—
131C4×D13—42no—
132C4×D13—42no—
133Dic26—22no—
134Dic26—21no—
135Dic26—21no—
136Dic26—42no—
137Dic26—42no—
138C8×C13—21no—
139C8×C13—21no—
140#1055—21no—
141#1055—21no—
142#556—131no—
143D4×Q8—131no—
144#489—131no—
145#489—131no—
146#487—131no—
147#477—131no—
148#477D1311yescharacteristic, complemented
149#474—131no—
150#463—131no—
151#463—131no—
152#461—131no—
153#446—131no—
154#440—131no—
155#440—131no—
156C4×D8—131no—
157C22×C13C22×D411yescharacteristic
158C2×D13—22no—
159C2×D13—41no—
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—41no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13C2×#4111yescharacteristic
171C4×C132−1+411yescharacteristic
172Dic13—21no—
173Dic13—21no—
174Dic13—21no—
175Dic13—41no—
176Dic13—41no—
177Dic13AGL(1,ℤ/8)12yes—
178C22×Q8—261no—
179C2×SD16—131no—
180C2×SD16—131no—
181C2×D8—131no—
182C4⋊Q8—131no—
183C4⋊Q8—131no—
184C4⋊Q8—131no—
185C4⋊Q8C2×D1311yescharacteristic
186#126—261no—
187#126—261no—
188#124—131no—
189#124—131no—
190C22⋊Q8—261no—
191C22⋊Q8—261no—
192C22⋊Q8—261no—
193C22⋊Q8—261no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8C2×D1311yescharacteristic
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—131no—
201#117—261no—
202#107—131no—
203#107C2×D1311yescharacteristic
204#107C2×D1311yescharacteristic
205C4⋊C8—131no—
206C4⋊C8—131no—
207C4⋊C8C2×D1311yescharacteristic
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103C2×D1311yescharacteristic
213#103C2×D1311yescharacteristic
214#102—131no—
215#102—131no—
216#102—131no—
217#102—131no—
218#97—131no—
219#97—131no—
220C4×C8—131no—
221C2×C13#54811yescharacteristic
222C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
223C2×C13#57811yescharacteristic
224D13—42no—
225D13—81no—
226C2×Q8—21no—
227C2×Q8—131no—
228C2×Q8—131no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×Q8—524no—
232C2×Q8C22×D1311yescharacteristic
233C2×D4—131no—
234C2×D4—131no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239SD16—262no—
240SD16—262no—
241D8—262no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8C22×D1311yescharacteristic
245C2×C8C22×D1311yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4C22×D1311yescharacteristic
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C42—21no—
269C42—131no—
270C42—131no—
271C42—261no—
272C42C22×D1311yescharacteristic
273C13#336711yescharacteristic, complemented, Sylow
274C23—261no—
275C23—261no—
276Q8—21no—
277Q8—21no—
278Q8—42no—
279Q8—262no—
280Q8—261no—
281Q8—261no—
282Q8—522no—
283Q8—522no—
284D4—132no—
285D4—261no—
286D4—261no—
287D4—261no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4D4×D1311yescharacteristic
303C2×C4D4×D1311yescharacteristic
304C2×C4C23×D1311yescharacteristic
305C8—21no—
306C8—21no—
307C8—261no—
308C8—261no—
309C22—262no—
310C22—521no—
311C22—521no—
312C22—521no—
313C22—521no—
314C22—521no—
315C22C2×D4×D1311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—132no—
323C4—261no—
324C4—261no—
325C4—261no—
326C4—521no—
327C4—521no—
328C4#8825411yescharacteristic
329C4#41×D1311yescharacteristic
330C2—522no—
331C2—1041no—
332C2#1171933811yescharacteristic
333C2#1171947111yescharacteristic
334C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#477C2
socleC22×C13C22×D4
prime radicalC2×D104C22
hypercenter#477D13
hypocenterC13#3367
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #11719432C2semidirect
2. #11719273C2semidirect
3. C13×#477C2semidirect
4. #11718750C2semidirect
5. #11718687C2semidirect
6. #11718551C2semidirect
7. #11718550C2semidirect
8. #11718536C2semidirect
11. #11718489C2semidirect
13. #11718479C2semidirect
14. #11718456C2semidirect
15. #11718453C2semidirect
148. #477D13semidirect
273. C13#3367semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117192732
C13×#4772
#117187502
#117186872
#117185512
#117185502
#117185362
#117185332
#117185052
#117184892
#117184802
#117184792
#117184562
#117184532
#336713