Finite Group Databasebeta

← #13125202

Subgroups — #13125202

Order 1664.

372 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719429C211yesmaximal, characteristic
2#11719394C211yesmaximal, characteristic, complemented
3C13×#491C211yesmaximal, characteristic, complemented
4#11718742C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718465C211yesmaximal, characteristic
7#11718464C211yesmaximal, characteristic
8#11718463C211yesmaximal, characteristic, complemented
9D13×#103C211yesmaximal, characteristic, complemented
10#11718461C211yesmaximal, characteristic, complemented
11#11718458C211yesmaximal, characteristic, complemented
12#11718456C211yesmaximal, characteristic, complemented
13#11718453C211yesmaximal, characteristic, complemented
14#11718375C211yesmaximal, characteristic, complemented
15#11718369C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C13×#125C2211yescharacteristic
20#88201C2211yescharacteristic
21#88198C2211yescharacteristic
22C2×#6094C2211yescharacteristic
23C2×C8×D13C2211yescharacteristic
24#88151—21no—
25#88150—21no—
26#88150—21no—
27#88150—21no—
28#88148—21no—
29#88148—21no—
30#88146C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32#88144C2211yescharacteristic
33#88143—21no—
34#88142—21no—
35#88142C2211yescharacteristic
36#88129C2211yescharacteristic
37#88126C2211yescharacteristic
38#88123C2211yescharacteristic
39C13×#103C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#97C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88055C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88049C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61#6131—22no—
62#6131—22no—
63Q8×D13—22no—
64Q8×D13—22no—
65C2×D52—21no—
66C2×D52C2311yescharacteristic
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×Dic26C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C42×C13C2311yescharacteristic
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103D411yescharacteristic
90#6103D411yescharacteristic
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101#6101D411yescharacteristic
102C4×Dic13—21no—
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—22no—
107C8×D13—22no—
108#3137—131nomaximal, Sylow
109C22×D13—21no—
110C22×D13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128D52—21no—
129D52—21no—
130D52—42no—
131C4×D13—42no—
132C4×D13—42no—
133C4×D13—81no—
134C4×D13#4112yes—
135C4×D13#4112yes—
136Dic26—21no—
137Dic26—21no—
138Dic26—42no—
139Dic26—81no—
140Dic26—81no—
141C8×C13—21no—
142C8×C13—21no—
143#1055—21no—
144#1055—21no—
145#544—131no—
146#536—131no—
147#491—131no—
148#491D1311yescharacteristic, complemented
149#489—131no—
150#489—131no—
151#488—131no—
152#488—131no—
153#487—131no—
154#487—131no—
155#419—131no—
156#417—131no—
157#416—131no—
158C2×#103—131no—
159#405—131no—
160C22×C13C22×D411yescharacteristic
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—41no—
164C2×D13—41no—
165C2×D13—41no—
166C2×D13#12412yes—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13C2×#4111yescharacteristic
174C4×C13C2×#4111yescharacteristic
175Dic13—21no—
176Dic13—21no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180Dic13#12412yes—
181C2×#41—131no—
182C22×Q8—131no—
183C2×M16—131no—
184C22×C8—131no—
185C4⋊Q8—131no—
186C4⋊Q8—131no—
187C4⋊Q8—131no—
188C4⋊Q8—261no—
189C4⋊Q8C2×D1311yescharacteristic
190#125—131no—
191#125—261no—
192#125C2×D1311yescharacteristic
193#124—131no—
194#124—131no—
195#123—261no—
196#123—261no—
197C22⋊Q8—261no—
198C22⋊Q8—261no—
199C22⋊Q8—261no—
200C22⋊Q8—261no—
201#117—131no—
202#117—131no—
203C2×C4⋊C4—131no—
204#103—131no—
205#103—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103C2×D1311yescharacteristic
213#103C2×D1311yescharacteristic
214#103C2×D1311yescharacteristic
215#103C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#97—131no—
221#97C2×D1311yescharacteristic
222C4×C8—131no—
223C4×C8—131no—
224C2×C13C2×#12411yescharacteristic
225C2×C13#57711yescharacteristic
226C2×C13#57811yescharacteristic
227D13—22no—
228D13—81no—
229#41—262no—
230#41—262no—
231C2×Q8—131no—
232C2×Q8—261no—
233C2×Q8—261no—
234C2×Q8—262no—
235C2×Q8—262no—
236C2×Q8—261no—
237C2×Q8C22×D1311yescharacteristic
238C2×Q8C22×D1311yescharacteristic
239C2×D4—131no—
240C2×D4—261no—
241C22×C4—131no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—261no—
245M16—262no—
246C2×C8—131no—
247C2×C8—131no—
248C2×C8—262no—
249C2×C8C22×D1311yescharacteristic
250C2×C8C22×D1311yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4C22×D1311yescharacteristic
267C4⋊C4C22×D1311yescharacteristic
268C22⋊C4—131no—
269C22⋊C4—131no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C42—131no—
276C42—261no—
277C42C22×D1311yescharacteristic
278C13#313711yescharacteristic, complemented, Sylow
279C23—131no—
280C23—261no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—261no—
286Q8—261no—
287Q8—522no—
288Q8—1041no—
289Q8—1041no—
290D4—261no—
291D4—261no—
292D4—522no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—131no—
298C2×C4—132no—
299C2×C4—132no—
300C2×C4—131no—
301C2×C4—131no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—522no—
306C2×C4—522no—
307C2×C4—1041no—
308C2×C4D4×D1311yescharacteristic
309C2×C4D4×D1311yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—21no—
312C8—21no—
313C8—261no—
314C8—261no—
315C22—132no—
316C22—261no—
317C22—261no—
318C22—521no—
319C22—521no—
320C22—521no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—132no—
329C4—261no—
330C4—261no—
331C4—521no—
332C4—521no—
333C4—521no—
334C4#41×D1311yescharacteristic
335C4#41×D1311yescharacteristic
336C2—262no—
337C2—1041no—
338C2D13×#12411yescharacteristic
339C2#1171948311yescharacteristic
340C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#491C2
socleC22×C13C22×D4
prime radicalC2×#6131C22
hypercenter#491D13
hypocenterC13#3137
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #11719394C2semidirect
3. C13×#491C2semidirect
4. #11718742C2semidirect
5. #11718729C2semidirect
8. #11718463C2semidirect
9. D13×#103C2semidirect
10. #11718461C2semidirect
11. #11718458C2semidirect
12. #11718456C2semidirect
13. #11718453C2semidirect
14. #11718375C2semidirect
15. #11718369C2semidirect
148. #491D13semidirect
278. C13#3137semidirect

Maximal subgroups

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

subgroupindex
#117194292
#117193942
C13×#4912
#117187422
#117187292
#117184652
#117184642
#117184632
D13×#1032
#117184612
#117184582
#117184562
#117184532
#117183752
#117183692
#313713