Finite Group Databasebeta

← #13127089

Subgroups — #13127089

Order 1664.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#548C211yesmaximal, characteristic, complemented
2#11719270C211yesmaximal, characteristic, complemented
3#11718899C211yesmaximal, characteristic, complemented
4#11718893C211yesmaximal, characteristic, complemented
5#11718888C211yesmaximal, characteristic, complemented
6#11718886C211yesmaximal, characteristic, complemented
7#11718718C211yesmaximal, characteristic, complemented
8#11718717C211yesmaximal, characteristic, complemented
9#11718710C211yesmaximal, characteristic, complemented
10#11718704C211yesmaximal, characteristic, complemented
11#11718700C211yesmaximal, characteristic, complemented
12#11718696C211yesmaximal, characteristic, complemented
13C4×#6106C211yesmaximal, characteristic, complemented
14#11718683C211yesmaximal, characteristic, complemented
15#11718673C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C13×#124—21no—
19C13×#124C2211yescharacteristic
20C13×C22⋊Q8—21no—
21C13×C22⋊Q8C2211yescharacteristic
22C13×#121—21no—
23C13×#121C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13—21no—
26C4×D4×C13C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29#88193—21no—
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88184C2211yescharacteristic
33#88180C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C2×#6099C2211yescharacteristic
37#88152—21no—
38#88137—21no—
39#88135—21no—
40C4×D52C2211yescharacteristic
41#88124C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88072C2211yescharacteristic
51C22⋊#1055C2211yescharacteristic
52C22⋊#1055C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C13×#41—22no—
60C13×#41—41no—
61C2×Q8×C13—21no—
62C2×Q8×C13—22no—
63C2×Q8×C13—41no—
64C2×Q8×C13C2311yescharacteristic
65C2×Q8×C13C2311yescharacteristic
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13D411yescharacteristic
69C2×D4×C13C2311yescharacteristic
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C2×C22⋊D13—21no—
75C2×C22⋊D13—21no—
76C22×Dic13—21no—
77C2×D52C2311yescharacteristic
78C2×C4×D13—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4D411yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C13×C22⋊C4—21no—
87C13×C22⋊C4D411yescharacteristic
88C13×C22⋊C4D411yescharacteristic
89C42×C13—21no—
90C42×C13C2311yescharacteristic
91C22⋊Dic13—21no—
92#6106—22no—
93#6106—41no—
94#6104—41no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105#6099—41no—
106#6099—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3326—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C23×C13C2×D411yescharacteristic
115C22×D13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119Q8×C13—42no—
120Q8×C13#4112yes—
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—41no—
124D4×C13—42no—
125D4×C13—42no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2411yescharacteristic
140C22⋊D13—42no—
141C22⋊D13—81no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—81no—
146D52—21no—
147D52—21no—
148C4×D13—81no—
149#1055—21no—
150#1055—21no—
151#1055—21no—
152#1055—21no—
153#553—131no—
154#548D1311yescharacteristic, complemented
155#488—131no—
156#483—131no—
157#482—131no—
158#479—131no—
159#469—131no—
160#468—131no—
161#463—131no—
162#449—131no—
163#448—131no—
164C4×SD16—131no—
165#436—131no—
166#419—131no—
167#417—131no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13C22×D411yescharacteristic
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13C2×#4111yescharacteristic
189C4×C13H(5,𝔽2)11yescharacteristic
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193C2×#41C2×D1311yescharacteristic
194C22×Q8C2×D1311yescharacteristic
195C2×SD16—131no—
196C2×SD16—131no—
197C2×D8—131no—
198C2×M16—131no—
199C2×M16—131no—
200#126—261no—
201#125—131no—
202#124—21no—
203#124C2×D1311yescharacteristic
204#123—261no—
205C22⋊Q8—21no—
206C22⋊Q8C2×D1311yescharacteristic
207#121—21no—
208#121—131no—
209#121—131no—
210#121—261no—
211#121C2×D1311yescharacteristic
212C4×Q8C2×D1311yescharacteristic
213C4×D4—21no—
214C4×D4—131no—
215C4×D4—261no—
216C4×D4C2×D1311yescharacteristic
217#117—131no—
218C2×C4⋊C4—131no—
219#107—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#103—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233C22⋊C8—131no—
234C22⋊C8—131no—
235C4×C8—131no—
236C2×C13—41no—
237C2×C13—41no—
238C2×C13—81no—
239C2×C13#54611yescharacteristic
240C2×C13#57511yescharacteristic
241C2×C13#57711yescharacteristic
242D13—81no—
243#41—22no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8C22×D1311yescharacteristic
249C2×Q8C22×D1311yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—131no—
253C2×D4—261no—
254C2×D4—261no—
255C2×D4C22⋊D1311yescharacteristic
256C2×D4C22×D1311yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263SD16—262no—
264SD16—521no—
265D8—521no—
266M16—521no—
267M16—521no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8—131no—
271C2×C8—131no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—131no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4C22⋊D1311yescharacteristic
281C4⋊C4C22×D1311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4C22⋊D1311yescharacteristic
291C22⋊C4C22⋊D1311yescharacteristic
292C42—21no—
293C42—261no—
294C42C22×D1311yescharacteristic
295C13#332611yescharacteristic, complemented, Sylow
296C23—21no—
297C23—261no—
298C23C2×C22⋊D1311yescharacteristic
299C23C2×C22⋊D1311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#612912yes—
305D4—21no—
306D4—21no—
307D4—41no—
308D4—42no—
309D4—42no—
310D4—261no—
311D4—261no—
312D4—522no—
313D4—1041no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—1041no—
327C2×C4—1041no—
328C2×C4C2×C22⋊D1311yescharacteristic
329C2×C4C2×C22⋊D1311yescharacteristic
330C2×C4C2×C22⋊D1311yescharacteristic
331C2×C4C2×C22⋊D1311yescharacteristic
332C2×C4C23×D1311yescharacteristic
333C8—261no—
334C8—261no—
335C8—261no—
336C8—261no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—521no—
347C22—521no—
348C22—521no—
349C22C22×C22⋊D1311yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—521no—
358C4—521no—
359C4—521no—
360C4C2×#612911yescharacteristic
361C4#8825111yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—1041no—
366C2#1171951111yescharacteristic
367C2#1171952711yescharacteristic
368C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#548C2
socleC22×C13C22×D4
hypercenter#548D13
hypocenterC13#3326
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C13×#548C2semidirect
2. #11719270C2semidirect
3. #11718899C2semidirect
4. #11718893C2semidirect
5. #11718888C2semidirect
6. #11718886C2semidirect
7. #11718718C2semidirect
8. #11718717C2semidirect
9. #11718710C2semidirect
10. #11718704C2semidirect
11. #11718700C2semidirect
12. #11718696C2semidirect
13. C4×#6106C2semidirect
14. #11718683C2semidirect
15. #11718673C2semidirect
154. #548D13semidirect
295. C13#3326semidirect

Maximal subgroups

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

subgroupindex
C13×#5482
#117192702
#117188992
#117188932
#117188882
#117188862
#117187182
#117187172
#117187102
#117187042
#117187002
#117186962
C4×#61062
#117186832
#117186732
#332613