Finite Group Databasebeta

← #13126697

Subgroups — #13126697

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D13C211yesmaximal, characteristic, complemented
2#11719212C211yesmaximal, characteristic
3C2×C13×#103C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5#11718775C211yesmaximal, characteristic, complemented
6C8×C22⋊D13C211yesmaximal, characteristic, complemented
7#11718632C211yesmaximal, characteristic, complemented
8#11718479C211yesmaximal, characteristic, complemented
9#11718468C211yesmaximal, characteristic, complemented
10#11718467C211yesmaximal, characteristic, complemented
11#11718466C211yesmaximal, characteristic, complemented
12D13×#103C211yesmaximal, characteristic, complemented
13#11718453C211yesmaximal, characteristic, complemented
14#11718452C211yesmaximal, characteristic, complemented
15#11718449C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C2×#6127—21no—
19C22×C8×C13C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21#88200—21no—
22#88200C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24#88198—21no—
25#88198C2211yescharacteristic
26C2×#6106C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28#88184C2211yescharacteristic
29#88183—21no—
30C4×C22⋊D13—21no—
31C4×C22⋊D13C2211yescharacteristic
32#88178—21no—
33#88178C2211yescharacteristic
34C2×#6095C2211yescharacteristic
35C2×C8×D13C2211yescharacteristic
36#88150—21no—
37#88149C2211yescharacteristic
38#88148—21no—
39#88147C2211yescharacteristic
40C4⋊C4×D13C2211yescharacteristic
41#88142C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88054C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88048C2211yescharacteristic
58#88048C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×Q8×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13D411yescharacteristic
69Q8×D13—22no—
70Q8×D13—41no—
71#6127—44no—
72C2×D52—21no—
73C2×D52C2311yescharacteristic
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13C2311yescharacteristic
78C2×Dic26—21no—
79C2×Dic26—21no—
80C2×Dic26C2311yescharacteristic
81C2×C8×C13—41no—
82C2×C8×C13C2311yescharacteristic
83C2×C8×C13C2311yescharacteristic
84C13×C4⋊C4—21no—
85C13×C4⋊C4C2311yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C22⋊Dic13—21no—
88C22⋊Dic13D411yescharacteristic
89#6106—22no—
90#6106—41no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103D411yescharacteristic
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101D411yescharacteristic
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6095—41no—
111C8×D13—41no—
112#3298—131nomaximal, Sylow
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119Q8×C13—42no—
120Q8×C13#4112yescomplemented
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C22⋊D13—42no—
132C22⋊D13SD1614yescomplemented
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139D52—21no—
140D52—21no—
141D52—42no—
142C4×D13—21no—
143C4×D13—21no—
144C4×D13—42no—
145C4×D13—42no—
146C4×D13—42no—
147Dic26—21no—
148Dic26—21no—
149Dic26—42no—
150Dic26—42no—
151C8×C13—21no—
152C8×C13—21no—
153#1055—21no—
154#1055—21no—
155D4×Q8—131no—
156#547—131no—
157#487—131no—
158#483—131no—
159#483—131no—
160#475—131no—
161#465—131no—
162#465—131no—
163#461—131no—
164#448—131no—
165#448—131no—
166C4×SD16—131no—
167C8×D4—131no—
168C2×#103—131no—
169C2×#103D1311yescharacteristic, complemented
170C22×C13—21no—
171C22×C13—21no—
172C22×C13C2×SD1612yes—
173C22×C13C22×D411yescharacteristic
174C2×D13—21no—
175C2×D13—21no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13C2×SD1612yes—
180C4×C13—22no—
181C4×C13—21no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13C2×#4111yescharacteristic
186C4×C13H(5,𝔽2)11yescharacteristic
187Dic13—21no—
188Dic13—21no—
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13C2×SD1612yes—
193C2×#41—261no—
194C22×Q8—131no—
195C22×Q8C2×D1311yescharacteristic
196C2×SD16—131no—
197C2×SD16—131no—
198C2×SD16—131no—
199C22×C8—131no—
200C22×C8C2×D1311yescharacteristic
201C4⋊Q8—131no—
202C4⋊Q8—131no—
203C4⋊Q8—261no—
204#123—261no—
205#123—261no—
206C22⋊Q8—131no—
207C22⋊Q8—131no—
208C22⋊Q8—261no—
209C22⋊Q8—261no—
210C22⋊Q8—261no—
211#121—131no—
212#121—131no—
213C4×Q8—131no—
214C4×D4—131no—
215C4×D4—131no—
216C4×D4—261no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4C2×D1311yescharacteristic
219#106—131no—
220#106—131no—
221#106—131no—
222C4⋊C8—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#103C2×D1311yescharacteristic
229#103C2×D1311yescharacteristic
230#103C2×D1311yescharacteristic
231#103C2×D1311yescharacteristic
232#102—131no—
233C22⋊C8—131no—
234C22⋊C8—131no—
235C4×C8—131no—
236C2×C13—22no—
237C2×C13#54611yescharacteristic
238C2×C13C22×SD1611yescharacteristic
239C2×C13#57811yescharacteristic
240D13—22no—
241D13—81no—
242#41—524no—
243C2×Q8—21no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—131no—
247C2×Q8—261no—
248C2×Q8—261no—
249C2×Q8—262no—
250C2×Q8—521no—
251C2×Q8C22×D1311yescharacteristic
252C2×Q8C22×D1311yescharacteristic
253C2×D4—131no—
254C2×D4—131no—
255C2×D4—261no—
256C2×D4—261no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—131no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4C22×D1311yescharacteristic
264SD16—262no—
265SD16—521no—
266SD16—521no—
267C2×C8—41no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8—521no—
271C2×C8C22×D1311yescharacteristic
272C2×C8C22×D1311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—131no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4C22×D1311yescharacteristic
285C4⋊C4C22×D1311yescharacteristic
286C22⋊C4—131no—
287C22⋊C4—131no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C42—131no—
294C42—261no—
295C13#329811yescharacteristic, complemented, Sylow
296C23—131no—
297C23—261no—
298C23D4×D1311yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—42no—
303Q8—261no—
304Q8—261no—
305Q8—522no—
306Q8—522no—
307Q8#612712yescomplemented
308D4—134no—
309D4—261no—
310D4—261no—
311D4—522no—
312D4—522no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—131no—
322C2×C4—131no—
323C2×C4—131no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4D4×D1311yescharacteristic
333C2×C4C23×D1311yescharacteristic
334C8—21no—
335C8—21no—
336C8—261no—
337C8—261no—
338C22—21no—
339C22—21no—
340C22—132no—
341C22—261no—
342C22—261no—
343C22—521no—
344C22—521no—
345C22—521no—
346C22SD16×D1312yes—
347C22C2×D4×D1311yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—132no—
354C4—261no—
355C4—261no—
356C4—521no—
357C4—521no—
358C4—521no—
359C4C2×#612711yescharacteristic
360C4#8825111yescharacteristic
361C2—22no—
362C2—262no—
363C2—1041no—
364C2#1171919511yescharacteristic
365C2C2×SD16×D1311yescharacteristic
366C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#103C2
socleC22×C13C22×D4
prime radical#11719212C2
hypercenterC2×#103D13
hypocenterC13#3298
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D13C2semidirect
3. C2×C13×#103C2semidirect
4. #11718888C2semidirect
5. #11718775C2semidirect
6. C8×C22⋊D13C2semidirect
7. #11718632C2semidirect
8. #11718479C2semidirect
9. #11718468C2semidirect
10. #11718467C2semidirect
11. #11718466C2semidirect
12. D13×#103C2semidirect
13. #11718453C2semidirect
14. #11718452C2semidirect
15. #11718449C2semidirect
120. Q8×C13#41semidirect
132. C22⋊D13SD16semidirect
169. C2×#103D13semidirect
295. C13#3298semidirect
307. Q8#6127semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D132
#117192122
C2×C13×#1032
#117188882
#117187752
C8×C22⋊D132
#117186322
#117184792
#117184682
#117184672
#117184662
D13×#1032
#117184532
#117184522
#117184492
#329813