Finite Group Databasebeta

← #13126696

Subgroups — #13126696

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
1#11719337C211yesmaximal, characteristic, complemented
2#11719316C211yesmaximal, characteristic
3C13×#465C211yesmaximal, characteristic, complemented
4#11718831C211yesmaximal, characteristic, complemented
5#11718823C211yesmaximal, characteristic, complemented
6C8×C22⋊D13C211yesmaximal, characteristic, complemented
7C2×#88056C211yesmaximal, characteristic, complemented
8#11718704C211yesmaximal, characteristic, complemented
9#11718701C211yesmaximal, characteristic, complemented
10#11718523C211yesmaximal, characteristic, complemented
11#11718515C211yesmaximal, characteristic, complemented
12D13×#103C211yesmaximal, characteristic, complemented
13#11718453C211yesmaximal, characteristic, complemented
14#11718439C211yesmaximal, characteristic, complemented
15#11718419C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×#6129—21no—
18C22×Dic26C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C22×C8×C13C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22C13×#121C2211yescharacteristic
23#88198C2211yescharacteristic
24#88192C2211yescharacteristic
25#88189—21no—
26D4×Dic13C2211yescharacteristic
27C2×#6105C2211yescharacteristic
28C2×#6105C2211yescharacteristic
29C4×C22⋊D13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×C8×D13C2211yescharacteristic
32#88151C2211yescharacteristic
33#88150—21no—
34C4⋊C4×D13C2211yescharacteristic
35#88142—21no—
36#88142C2211yescharacteristic
37#88141C2211yescharacteristic
38#88137—21no—
39#88135—21no—
40#88132—21no—
41#88132—21no—
42C13×#106C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#102C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88054C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88048C2211yescharacteristic
58#88048C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13D411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68Q8×D13—22no—
69Q8×D13—41no—
70#6129—44no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×Dic26—22no—
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26—41no—
79C2×Dic26C2311yescharacteristic
80C2×Dic26C2311yescharacteristic
81C13×SD16—41no—
82C2×C8×C13—41no—
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C13×C4⋊C4—21no—
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C22⋊C4—21no—
89C13×C22⋊C4—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13D411yescharacteristic
93#6105—22no—
94#6105—41no—
95#6103—21no—
96#6103D411yescharacteristic
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101D411yescharacteristic
107C4×Dic13—21no—
108C4×Dic13C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C8×D13—41no—
112#3298—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C22×D13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118D4×C13—21no—
119D4×C13—21no—
120D4×C13—42no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C22⋊D13—42no—
129C22⋊D13SD1614yescomplemented
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140C4×D13—21no—
141C4×D13—21no—
142C4×D13—42no—
143C4×D13—42no—
144Dic26—21no—
145Dic26—21no—
146Dic26—21no—
147Dic26—42no—
148Dic26—42no—
149Dic26—42no—
150Dic26#4112yescomplemented
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#465D1311yescharacteristic, complemented
163#461—131no—
164#448—131no—
165#448—131no—
166C4×SD16—131no—
167C8×D4—131no—
168C2×#103—131no—
169C2×#103—131no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13C2×SD1612yes—
176C22×C13C22×D411yescharacteristic
177C2×D13—21no—
178C2×D13—21no—
179C2×D13C2×SD1612yes—
180C4×C13—21no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13C2×#4111yescharacteristic
185C4×C13H(5,𝔽2)11yescharacteristic
186Dic13—22no—
187Dic13—21no—
188Dic13—21no—
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13C2×SD1612yes—
193C2×#41—261no—
194C22×Q8—131no—
195C22×Q8—131no—
196C2×SD16—131no—
197C2×SD16—131no—
198C2×SD16C2×D1311yescharacteristic
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—261no—
208C22⋊Q8—261no—
209C22⋊Q8—261no—
210C22⋊Q8C2×D1311yescharacteristic
211#121—131no—
212#121C2×D1311yescharacteristic
213C4×Q8—131no—
214C4×D4—131no—
215C4×D4—131no—
216C4×D4—261no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219#106—131no—
220#106—131no—
221#106C2×D1311yescharacteristic
222C4⋊C8—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#103—131no—
229#103—131no—
230#103—131no—
231#103C2×D1311yescharacteristic
232#102C2×D1311yescharacteristic
233C22⋊C8—131no—
234C22⋊C8—131no—
235C4×C8—131no—
236C2×C13—22no—
237C2×C13—81no—
238C2×C13#54611yescharacteristic
239C2×C13C22×SD1611yescharacteristic
240C2×C13#57811yescharacteristic
241D13—22no—
242#41—524no—
243C2×Q8—131no—
244C2×Q8—131no—
245C2×Q8—261no—
246C2×Q8—261no—
247C2×Q8—262no—
248C2×Q8—261no—
249C2×Q8—262no—
250C2×Q8—521no—
251C2×Q8—521no—
252C2×Q8C22×D1311yescharacteristic
253C2×D4—21no—
254C2×D4—131no—
255C2×D4—261no—
256C2×D4C22×D1311yescharacteristic
257C22×C4—131no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4C22×D1311yescharacteristic
264SD16—41no—
265SD16—262no—
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—21no—
287C22⋊C4—21no—
288C22⋊C4—131no—
289C22⋊C4—131no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C42—131no—
294C42—261no—
295C13#329811yescharacteristic, complemented, Sylow
296C23—21no—
297C23—131no—
298C23D4×D1311yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—132no—
302Q8—261no—
303Q8—261no—
304Q8—261no—
305Q8—522no—
306Q8—522no—
307Q8—522no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—134no—
312D4—522no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—131no—
319C2×C4—131no—
320C2×C4—131no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—522no—
328C2×C4—522no—
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—41no—
341C22—41no—
342C22—41no—
343C22—132no—
344C22—261no—
345C22—261no—
346C22SD16×D1312yes—
347C22C2×D4×D1311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—132no—
353C4—261no—
354C4—261no—
355C4—262no—
356C4—521no—
357C4—521no—
358C4—521no—
359C4#8825111yescharacteristic
360C4#41×D1311yescharacteristic
361C2—22no—
362C2—81no—
363C2—262no—
364C2#1171931511yescharacteristic
365C2C2×SD16×D1311yescharacteristic
366C2#1171947611yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
prime radical#11719316C2
hypercenter#465D13
hypocenterC13#3298
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11719337C2semidirect
3. C13×#465C2semidirect
4. #11718831C2semidirect
5. #11718823C2semidirect
6. C8×C22⋊D13C2semidirect
7. C2×#88056C2semidirect
8. #11718704C2semidirect
9. #11718701C2semidirect
10. #11718523C2semidirect
11. #11718515C2semidirect
12. D13×#103C2semidirect
13. #11718453C2semidirect
14. #11718439C2semidirect
15. #11718419C2semidirect
129. C22⋊D13SD16semidirect
150. Dic26#41semidirect
162. #465D13semidirect
295. C13#3298semidirect

Maximal subgroups

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

subgroupindex
#117193372
#117193162
C13×#4652
#117188312
#117188232
C8×C22⋊D132
C2×#880562
#117187042
#117187012
#117185232
#117185152
D13×#1032
#117184532
#117184392
#117184192
#329813