Finite Group Databasebeta

← #13125072

Subgroups — #13125072

Order 1664.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719438C211yesmaximal, characteristic
2#11719277C211yesmaximal, characteristic, complemented
3C13×#475C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718689C211yesmaximal, characteristic, complemented
6#11718528C211yesmaximal, characteristic, complemented
7#11718527C211yesmaximal, characteristic
8#11718514C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718501C211yesmaximal, characteristic, complemented
12#11718478C211yesmaximal, characteristic, complemented
13#11718469C211yesmaximal, characteristic, complemented
14#11718467C211yesmaximal, characteristic
15#11718451C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C13×C4⋊Q8C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19#88201—21no—
20#88200—21no—
21Q8×Dic13C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23C2×#6106C2211yescharacteristic
24C2×Dic52C2211yescharacteristic
25C2×#6095C2211yescharacteristic
26#88152—21no—
27#88151C2211yescharacteristic
28#88149C2211yescharacteristic
29#88148—21no—
30#88147C2211yescharacteristic
31#88146—21no—
32#88146C2211yescharacteristic
33#88141—21no—
34#88141C2211yescharacteristic
35#88141C2211yescharacteristic
36#88129C2211yescharacteristic
37#88126—21no—
38#88126C2211yescharacteristic
39C4×Dic26—21no—
40C4×Dic26C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×C4⋊C8C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46#88061C2211yescharacteristic
47#88060C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88055C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61Q8×D13—22no—
62Q8×D13—22no—
63C2×D52—21no—
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13C2311yescharacteristic
68C2×Dic26—21no—
69C2×Dic26C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C42×C13—21no—
79C42×C13C2311yescharacteristic
80#6107—22no—
81#6106—22no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103D411yescharacteristic
89#6103D411yescharacteristic
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101D411yescharacteristic
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106Dic52—22no—
107#6095—22no—
108#3121—131nomaximal, Sylow
109C22×D13—21no—
110C22×D13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—81no—
113Q8×C13#4112yes—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127D52—21no—
128D52—21no—
129D52—81no—
130C4×D13—24no—
131C4×D13—21no—
132C4×D13—21no—
133C4×D13—81no—
134Dic26—24no—
135Dic26—21no—
136Dic26—21no—
137Dic26—21no—
138Dic26#4112yes—
139C8×C13—21no—
140C8×C13—21no—
141#1055—21no—
142#1055—21no—
143#542—131no—
144#519—131no—
145#485—131no—
146#482—131no—
147#477—131no—
148#475D1311yescharacteristic, complemented
149#464—131no—
150#464—131no—
151#451—131no—
152#448—131no—
153#441—131no—
154#440—131no—
155C4×Q16—131no—
156C4×SD16—131no—
157#433—131no—
158C22×C13C22×D411yescharacteristic
159C2×D13—21no—
160C2×D13—21no—
161C2×D13—21no—
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#4111yescharacteristic
172C4×C13C2×#4111yescharacteristic
173Dic13—21no—
174Dic13—22no—
175Dic13—21no—
176Dic13—21no—
177Dic13—41no—
178Dic13—41no—
179C22×Q8—131no—
180C2×Q16—131no—
181C2×Q16—131no—
182C2×SD16—131no—
183C2×SD16—131no—
184C4⋊Q8C2×D1311yescharacteristic
185#126—261no—
186#124—131no—
187#124—261no—
188#123—261no—
189C22⋊Q8—131no—
190C22⋊Q8—261no—
191#121—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8—261no—
197C4×Q8—261no—
198C4×Q8C2×D1311yescharacteristic
199C4×D4—131no—
200#117—131no—
201#117—131no—
202#117—261no—
203#117—261no—
204#107—131no—
205#107—131no—
206#106C2×D1311yescharacteristic
207#106C2×D1311yescharacteristic
208C4⋊C8—131no—
209C4⋊C8C2×D1311yescharacteristic
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#103C2×D1311yescharacteristic
215#103C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218C22⋊C8—131no—
219C22⋊C8—131no—
220#97—131no—
221C4×C8—131no—
222C2×C13#52511yescharacteristic
223C2×C13#57711yescharacteristic
224C2×C13#57811yescharacteristic
225D13—41no—
226D13—81no—
227C2×Q8—21no—
228C2×Q8—131no—
229C2×Q8—131no—
230C2×Q8—261no—
231C2×Q8—262no—
232C2×Q8—262no—
233C2×Q8C22×D1311yescharacteristic
234C2×D4—131no—
235C2×D4—261no—
236C22×C4—131no—
237C22×C4—261no—
238C22×C4—261no—
239Q16—262no—
240Q16—262no—
241SD16—262no—
242SD16—262no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
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—131no—
261C22⋊C4—131no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C42—21no—
269C42—131no—
270C42—261no—
271C42—261no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42C22×D1311yescharacteristic
276C13#312111yescharacteristic, complemented, Sylow
277C23—131no—
278C23—261no—
279Q8—21no—
280Q8—81no—
281Q8—132no—
282Q8—264no—
283Q8—261no—
284Q8—261no—
285Q8—261no—
286Q8#613112yes—
287D4—261no—
288D4—261no—
289D4—1041no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—264no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—1041no—
304C2×C4D4×D1311yescharacteristic
305C2×C4D4×D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—21no—
309C8—261no—
310C8—261no—
311C22—261no—
312C22—261no—
313C22—261no—
314C22—521no—
315C22—521no—
316C22—521no—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—21no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—261no—
325C4—261no—
326C4—261no—
327C4—262no—
328C4—521no—
329C4—521no—
330C4C2×#613111yescharacteristic
331C4#41×D1311yescharacteristic
332C2—521no—
333C2—1041no—
334C2#1171933211yescharacteristic
335C2#1171946711yescharacteristic
336C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radical#88149C22
hypercenter#475D13
hypocenterC13#3121
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #11719277C2semidirect
3. C13×#475C2semidirect
4. #11718752C2semidirect
5. #11718689C2semidirect
6. #11718528C2semidirect
8. #11718514C2semidirect
9. #11718513C2semidirect
10. #11718506C2semidirect
11. #11718501C2semidirect
12. #11718478C2semidirect
13. #11718469C2semidirect
15. #11718451C2semidirect
148. #475D13semidirect
276. C13#3121semidirect

Maximal subgroups

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

subgroupindex
#117194382
#117192772
C13×#4752
#117187522
#117186892
#117185282
#117185272
#117185142
#117185132
#117185062
#117185012
#117184782
#117184692
#117184672
#117184512
#312113