Finite Group Databasebeta

← #13122212

Subgroups — #13122212

Order 1664.

520 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#386C211yesmaximal, characteristic, complemented
2#11718884C211yesmaximal, characteristic
3#11718881C211yesmaximal, characteristic, complemented
4#11718874C211yesmaximal, characteristic, complemented
5#11718872C211yesmaximal, characteristic, complemented
6#11718619C211yesmaximal, characteristic, complemented
7#11718617C211yesmaximal, characteristic, complemented
8#11718617C211yesmaximal, characteristic, complemented
9#11718608C211yesmaximal, characteristic, complemented
10#11718608C211yesmaximal, characteristic, complemented
11#11718604C211yesmaximal, characteristic, complemented
12#11718334C211yesmaximal, characteristic, complemented
13#11718325C211yesmaximal, characteristic, complemented
14C13⋊#401C211yesmaximal, characteristic, complemented
15C13⋊#401C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C22×Dic26C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C13×#95C2211yescharacteristic
36C13×#95C2211yescharacteristic
37#88071C2211yescharacteristic
38#88071C2211yescharacteristic
39#88071C2211yescharacteristic
40#88071C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C24×C13C2311yescharacteristic
53C23×D13C2311yescharacteristic
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13—41no—
57C22×C4×C13—22no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C2×C22⋊D13—22no—
66C2×C22⋊D13—22no—
67C2×C22⋊D13—22no—
68C2×C22⋊D13—22no—
69C2×C22⋊D13—41no—
70C2×C22⋊D13—41no—
71C22×Dic13—22no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C2×C4×D13—22no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×Dic26—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C22⋊Dic13—41no—
91C22⋊Dic13—41no—
92C22⋊Dic13—41no—
93C22⋊Dic13—41no—
94C22⋊Dic13—41no—
95#6103—41no—
96#6103—41no—
97#6103—41no—
98#6103—41no—
99#2760—131nomaximal, Sylow
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13#4112yes—
113C23×C13#4112yes—
114C23×C13C2411yescharacteristic
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—21no—
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—21no—
121C22×D13#4112yes—
122D4×C13—44no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
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—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—44no—
139C22⋊D13—44no—
140C22⋊D13—44no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—44no—
163C4×D13—44no—
164Dic26—44no—
165#401—131no—
166#401—131no—
167#393—131no—
168#393—131no—
169#393—131no—
170#392—131no—
171#386—131no—
172#386—131no—
173#386—131no—
174#386—131no—
175#386—131no—
176#386D1311yescharacteristic, complemented
177#381—131no—
178#381—131no—
179#381—131no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13C2×#4111yescharacteristic
195C22×C13C2×#4111yescharacteristic
196C22×C13C2×#4111yescharacteristic
197C22×C13H(5,𝔽2)11yescharacteristic
198C22×C13H(5,𝔽2)11yescharacteristic
199C22×C13H(5,𝔽2)11yescharacteristic
200C22×C13H(5,𝔽2)11yescharacteristic
201C2×D13—22no—
202C2×D13—22no—
203C2×D13—22no—
204C2×D13—41no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—41no—
212C4×C13—41no—
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216Dic13—41no—
217Dic13—41no—
218Dic13—41no—
219Dic13—41no—
220C22×Q8—131no—
221C22×D4—131no—
222C22×D4—131no—
223C22×D4C2×D1311yescharacteristic
224C23×C4—131no—
225C23×C4—131no—
226C23×C4C2×D1311yescharacteristic
227C2×C22⋊C4—131no—
228C2×C22⋊C4—131no—
229C2×C22⋊C4—131no—
230C2×C22⋊C4—131no—
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4—131no—
234C2×C22⋊C4—131no—
235C2×C22⋊C4—131no—
236C2×C22⋊C4C2×D1311yescharacteristic
237C2×C22⋊C4C2×D1311yescharacteristic
238C2×C22⋊C4C2×D1311yescharacteristic
239#95—131no—
240#95—131no—
241#95—131no—
242#95—131no—
243#95—131no—
244#95—131no—
245#95—131no—
246#95—131no—
247#95—131no—
248#95—131no—
249#95—131no—
250#95—131no—
251#95—131no—
252#95—131no—
253#95C2×D1311yescharacteristic
254#95C2×D1311yescharacteristic
255C2×C13—42no—
256C2×C13—42no—
257C2×C13#53811yescharacteristic
258C2×C13#53811yescharacteristic
259C2×C13#53811yescharacteristic
260C2×C13#55111yescharacteristic
261C2×C13#55111yescharacteristic
262C2×C13#55111yescharacteristic
263C2×C13#56011yescharacteristic
264D13—42no—
265C24—131no—
266C24C22×D1311yescharacteristic
267C24C22×D1311yescharacteristic
268C2×Q8—521no—
269C2×Q8—521no—
270C2×Q8—521no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—41no—
274C2×D4—262no—
275C2×D4—262no—
276C2×D4—262no—
277C2×D4—262no—
278C2×D4—521no—
279C2×D4—521no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—262no—
291C22×C4—262no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4C22×D1311yescharacteristic
297C22×C4C22×D1311yescharacteristic
298C22×C4C22×D1311yescharacteristic
299C22×C4C22×D1311yescharacteristic
300C22×C4C22×D1311yescharacteristic
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—521no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C22⋊C4—521no—
308C22⋊C4—521no—
309C22⋊C4—521no—
310C22⋊C4—521no—
311C22⋊C4—521no—
312C22⋊C4—521no—
313C13#276011yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—132no—
327C23—261no—
328C23—261no—
329C23—261no—
330C23—261no—
331C23—261no—
332C23—261no—
333C23#612712yes—
334C23#612912yes—
335C23C23×D1311yescharacteristic
336Q8—524no—
337D4—44no—
338D4—524no—
339D4—524no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—44no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—524no—
378C2×C4—524no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—262no—
394C22—262no—
395C22—262no—
396C22—521no—
397C22—521no—
398C22—521no—
399C22—521no—
400C22C2×#612711yescharacteristic
401C22C2×#612911yescharacteristic
402C22#8825111yescharacteristic
403C22#8825111yescharacteristic
404C22#8825111yescharacteristic
405C22#41×D1311yescharacteristic
406C22#8825611yescharacteristic
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—521no—
413C4—521no—
414C4—521no—
415C4—521no—
416C4—521no—
417C4—521no—
418C4—521no—
419C2—42no—
420C2—42no—
421C2—522no—
422C2#1171920011yescharacteristic
423C2#1171926111yescharacteristic
424C2#1171926511yescharacteristic
425C2#1171929811yescharacteristic
426C2#1171931811yescharacteristic
427C2#1171932511yescharacteristic
428C2#1171936311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radical#11718884C2
hypercenter#386D13
hypocenterC13#2760
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C13×#386C2semidirect
3. #11718881C2semidirect
4. #11718874C2semidirect
5. #11718872C2semidirect
6. #11718619C2semidirect
7. #11718617C2semidirect
8. #11718617C2semidirect
9. #11718608C2semidirect
10. #11718608C2semidirect
11. #11718604C2semidirect
12. #11718334C2semidirect
13. #11718325C2semidirect
14. C13⋊#401C2semidirect
15. C13⋊#401C2semidirect
176. #386D13semidirect
313. C13#2760semidirect

Maximal subgroups

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

subgroupindex
C13×#3862
#117188842
#117188812
#117188742
#117188722
#117186192
#117186172
#117186082
#117186042
#117183342
#117183252
C13⋊#4012
#276013