Finite Group Databasebeta

← #13126962

Subgroups — #13126962

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×#550C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic, complemented
3#11718900C211yesmaximal, characteristic, complemented
4#11718900C211yesmaximal, characteristic, complemented
5#11718894C211yesmaximal, characteristic, complemented
6#11718893C211yesmaximal, characteristic, complemented
7#11718736C211yesmaximal, characteristic, complemented
8#11718732C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic, complemented
10#11718702C211yesmaximal, characteristic, complemented
11#11718696C211yesmaximal, characteristic, complemented
12#11718695C211yesmaximal, characteristic, complemented
13#11718691C211yesmaximal, characteristic, complemented
14#11718683C211yesmaximal, characteristic, complemented
15#11718672C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×#41C2211yescharacteristic
18C13×#127—21no—
19C13×#127C2211yescharacteristic
20C13×#121—21no—
21C13×#121—21no—
22C13×#121C2211yescharacteristic
23C13×#121C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13—21no—
26C4×D4×C13C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28#88189—21no—
29C2×#6105C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31#88180C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33#88178C2211yescharacteristic
34#88178C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C22×#1055C2211yescharacteristic
37#88143—21no—
38#88133—21no—
39#88131—21no—
40#88124C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88072C2211yescharacteristic
51C22⋊#1055C2211yescharacteristic
52C22⋊#1055C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C13×#41—22no—
60C13×#41—22no—
61C13×#41—41no—
62C13×#41—41no—
63C2×Q8×C13C2311yescharacteristic
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13D411yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C2×D4×C13C2311yescharacteristic
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13C2311yescharacteristic
76C22×C4×C13C2311yescharacteristic
77C22×Dic13—21no—
78C2×Dic26C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4D411yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C13×C22⋊C4—21no—
84C13×C22⋊C4D411yescharacteristic
85C13×C22⋊C4D411yescharacteristic
86C42×C13—21no—
87C42×C13C2311yescharacteristic
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91#6107—22no—
92#6105—41no—
93#6105—41no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105#6099—41no—
106C2×#1055—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3317—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C23×C13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13#4112yes—
118D4×C13—21no—
119D4×C13—21no—
120D4×C13—21no—
121D4×C13—21no—
122D4×C13—41no—
123D4×C13—42no—
124D4×C13—42no—
125D4×C13—42no—
126D4×C13—81no—
127D4×C13—81no—
128D4×C13—81no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2411yescharacteristic
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—42no—
147Dic26—21no—
148Dic26—21no—
149#1055—21no—
150#1055—21no—
151#1055—21no—
152#1055—21no—
153#552—131no—
154#550D1311yescharacteristic
155#490—131no—
156#482—131no—
157#481—131no—
158#479—131no—
159#468—131no—
160#465—131no—
161#460—131no—
162#452—131no—
163#452—131no—
164#441—131no—
165#435—131no—
166#417—131no—
167#416—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×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13C22×D411yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—41no—
187C4×C13C2×#4111yescharacteristic
188C4×C13H(5,𝔽2)11yescharacteristic
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193C2×#41C2×D1311yescharacteristic
194C2×#41C2×D1311yescharacteristic
195C2×Q16—131no—
196C2×SD16—131no—
197C2×SD16—131no—
198C2×M16—131no—
199C22×C8—131no—
200#127—21no—
201#127C2×D1311yescharacteristic
202#126—261no—
203#125—131no—
204#125—261no—
205#123—261no—
206C22⋊Q8—131no—
207C22⋊Q8—131no—
208#121—21no—
209#121—21no—
210#121C2×D1311yescharacteristic
211#121C2×D1311yescharacteristic
212C4×Q8—131no—
213C4×Q8C2×D1311yescharacteristic
214C4×D4—21no—
215C4×D4C2×D1311yescharacteristic
216#117—131no—
217#117—261no—
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#102—131no—
228#102—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233C22⋊C8—131no—
234C22⋊C8—131no—
235#97—131no—
236C2×C13—41no—
237C2×C13—41no—
238C2×C13—81no—
239C2×C13—81no—
240C2×C13#54611yescharacteristic
241C2×C13#57511yescharacteristic
242C2×C13#57711yescharacteristic
243#41—22no—
244#41—22no—
245#41—41no—
246#41—41no—
247C2×Q8—131no—
248C2×Q8C22×D1311yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4C22⋊D1311yescharacteristic
256C2×D4C22×D1311yescharacteristic
257C2×D4C22×D1311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—261no—
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263Q16—262no—
264SD16—521no—
265SD16—521no—
266M16—521no—
267C2×C8—131no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8—131no—
271C2×C8—521no—
272C4⋊C4—21no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4C22⋊D1311yescharacteristic
283C4⋊C4C22×D1311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4C22⋊D1311yescharacteristic
290C22⋊C4C22⋊D1311yescharacteristic
291C42—21no—
292C42—261no—
293C42—261no—
294C42C22×D1311yescharacteristic
295C13#331711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23C2×C22⋊D1311yescharacteristic
299C23C2×C22⋊D1311yescharacteristic
300Q8—21no—
301Q8—261no—
302Q8—261no—
303Q8#612912yes—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—42no—
310D4—42no—
311D4—42no—
312D4—81no—
313D4—81no—
314D4—81no—
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—261no—
327C2×C4—522no—
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—41no—
347C22—41no—
348C22—41no—
349C22C22×C22⋊D1311yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—521no—
357C4—521no—
358C4—521no—
359C4—521no—
360C4C2×#612911yescharacteristic
361C4#8825111yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—81no—
366C2#1171951111yescharacteristic
367C2#1171952711yescharacteristic
368C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#550C2
socleC22×C13C22×D4
hypercenter#550D13
hypocenterC13#3317
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
2. #11719246C2semidirect
3. #11718900C2semidirect
4. #11718900C2semidirect
5. #11718894C2semidirect
6. #11718893C2semidirect
7. #11718736C2semidirect
8. #11718732C2semidirect
9. #11718703C2semidirect
10. #11718702C2semidirect
11. #11718696C2semidirect
12. #11718695C2semidirect
13. #11718691C2semidirect
14. #11718683C2semidirect
15. #11718672C2semidirect
295. C13#3317semidirect

Maximal subgroups

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

subgroupindex
C13×#5502
#117192462
#117189002
#117188942
#117188932
#117187362
#117187322
#117187032
#117187022
#117186962
#117186952
#117186912
#117186832
#117186722
#331713