Finite Group Databasebeta

← #13120646

Subgroups — #13120646

Order 1664.

668 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88150C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D13C211yesmaximal, characteristic
3C13×#396C211yesmaximal, characteristic, complemented
4#11718655C211yesmaximal, characteristic, complemented
5#11718655C211yesmaximal, characteristic, complemented
6#11718653C211yesmaximal, characteristic, complemented
7#11718650C211yesmaximal, characteristic, complemented
8#11718648C211yesmaximal, characteristic, complemented
9#11718616C211yesmaximal, characteristic
10#11718616C211yesmaximal, characteristic
11#11718610C211yesmaximal, characteristic, complemented
12#11718609C211yesmaximal, characteristic, complemented
13#11718608C211yesmaximal, characteristic, complemented
14#11718334C211yesmaximal, characteristic, complemented
15#11718329C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic, complemented
20C2×C13×C4⋊C4C2211yescharacteristic, complemented
21C2×C13×C4⋊C4C2211yescharacteristic, complemented
22C2×C13×C4⋊C4C2211yescharacteristic, complemented
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×C4⋊Dic13C2211yescharacteristic, complemented
40C2×C4⋊Dic13C2211yescharacteristic, complemented
41C2×#6101C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44C2×#6101C2211yescharacteristic, complemented
45#88150—24no—
46C22⋊C4×D13—24no—
47C13×#95C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53C24×C13C2311yescharacteristic
54C23×D13—22no—
55C23×D13—22no—
56C23×D13—41no—
57C23×D13—41no—
58C23×D13—41no—
59C23×D13—41no—
60C23×D13Q814yescomplemented
61C23×D13C2311yescharacteristic
62C23×D13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C2×C4×D13—22no—
76C2×C4×D13—41no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×C4×D13D414yes—
81C2×Dic26—22no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C22⋊C4—22no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C22⋊Dic13—22no—
91C22⋊Dic13—41no—
92C22⋊Dic13—41no—
93#6103—22no—
94#6103—22no—
95#6103—22no—
96#6103—22no—
97#6103—22no—
98#6103—22no—
99#6103—41no—
100#6103—41no—
101#6103—41no—
102#6103—41no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105#6101—22no—
106#6101—22no—
107#6101—41no—
108#6101—41no—
109#2626—131nomaximal, Sylow
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13C2×Q812yes—
117C23×C13C2411yescharacteristic
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—28no—
129C22×D13—44no—
130C22×D13—44no—
131C22×D13—44no—
132C22×D13—44no—
133C22×D13—44no—
134C22×D13—44no—
135C22×D13C2×D412yes—
136C22×D13C2×Q812yes—
137C22×D13C2×Q812yes—
138C22×D13#4112yes—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13C2×D412yes—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—21no—
169C2×Dic13—21no—
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13—21no—
173C2×Dic13—21no—
174C2×Dic13C2×D412yes—
175C4×D13—44no—
176C4×D13—44no—
177Dic26—44no—
178C2×C22⋊Q8—131no—
179C22×C22⋊C4—131no—
180#399—131no—
181#399—131no—
182#396—131no—
183#396—131no—
184#396—131no—
185#396D1311yescharacteristic, complemented
186#393—131no—
187#393—131no—
188#385—131no—
189#385—131no—
190#380—131no—
191#379—131no—
192#379—131no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—22no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13C22×D411yescharacteristic
201C22×C13C22×Q811yescharacteristic
202C22×C13C2×#4111yescharacteristic
203C22×C13H(5,𝔽2)11yescharacteristic
204C22×C13H(5,𝔽2)11yescharacteristic
205C22×C13H(5,𝔽2)11yescharacteristic
206C22×C13H(5,𝔽2)11yescharacteristic
207C2×D13—22no—
208C2×D13—22no—
209C2×D13—22no—
210C2×D13—22no—
211C2×D13—22no—
212C2×D13—22no—
213C2×D13—22no—
214C2×D13—22no—
215C2×D13—22no—
216C2×D13—416no—
217C2×D13—41no—
218C2×D13—41no—
219C2×D13—41no—
220C2×D13—41no—
221C2×D13C22⋊Q814yes—
222C4×C13—22no—
223C4×C13—41no—
224C4×C13—41no—
225C4×C13—41no—
226C4×C13—41no—
227C4×C13—41no—
228Dic13—22no—
229Dic13—41no—
230Dic13—41no—
231Dic13—41no—
232Dic13—41no—
233Dic13—41no—
234C25—131no—
235C22×Q8—131no—
236C23×C4—131no—
237C23×C4—131no—
238C22⋊Q8—264no—
239C2×C4⋊C4—131no—
240C2×C4⋊C4—131no—
241C2×C4⋊C4—131no—
242C2×C4⋊C4—131no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—131no—
245C2×C4⋊C4C2×D1311yescharacteristic, complemented
246C2×C4⋊C4C2×D1311yescharacteristic, complemented
247C2×C4⋊C4C2×D1311yescharacteristic, complemented
248C2×C22⋊C4—131no—
249C2×C22⋊C4—131no—
250C2×C22⋊C4—131no—
251C2×C22⋊C4—131no—
252C2×C22⋊C4—131no—
253C2×C22⋊C4—131no—
254C2×C22⋊C4—131no—
255C2×C22⋊C4—131no—
256C2×C22⋊C4—131no—
257C2×C22⋊C4—131no—
258C2×C22⋊C4—131no—
259C2×C22⋊C4—131no—
260C2×C22⋊C4—131no—
261C2×C22⋊C4—264no—
262C2×C22⋊C4C2×D1311yescharacteristic
263C2×C22⋊C4C2×D1311yescharacteristic
264C2×C22⋊C4C2×D1311yescharacteristic
265#95—131no—
266#95—131no—
267#95—131no—
268#95—131no—
269#95—131no—
270#95C2×D1311yescharacteristic, complemented
271C2×C13—42no—
272C2×C13C2×C22⋊Q811yescharacteristic
273C2×C13#53411yescharacteristic
274C2×C13#53511yescharacteristic
275C2×C13#53811yescharacteristic
276C2×C13#53811yescharacteristic
277C2×C13#54311yescharacteristic
278C2×C13#54311yescharacteristic
279D13—24no—
280D13—42no—
281C24—131no—
282C24—131no—
283C24—134no—
284C24—262no—
285C24—262no—
286C24—521no—
287C24—521no—
288C24—521no—
289C24—521no—
290C24C22×D1311yescharacteristic
291C2×Q8—262no—
292C2×Q8—521no—
293C2×Q8—521no—
294C22×C4—131no—
295C22×C4—134no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—131no—
299C22×C4—131no—
300C22×C4—131no—
301C22×C4—262no—
302C22×C4—521no—
303C22×C4—521no—
304C22×C4—521no—
305C22×C4—521no—
306C22×C4C22×D1311yescharacteristic
307C22×C4C22×D1311yescharacteristic
308C22×C4C22×D1311yescharacteristic
309C22×C4C22×D1311yescharacteristic
310C22×C4C22×D1311yescharacteristic
311C22×C4C22×D1311yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—262no—
316C4⋊C4—262no—
317C4⋊C4—521no—
318C4⋊C4—521no—
319C4⋊C4—521no—
320C4⋊C4—521no—
321C22⋊C4—22no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—262no—
325C22⋊C4—262no—
326C22⋊C4—262no—
327C22⋊C4—262no—
328C22⋊C4—262no—
329C22⋊C4—262no—
330C22⋊C4—262no—
331C22⋊C4—521no—
332C22⋊C4—521no—
333C22⋊C4—521no—
334C22⋊C4—521no—
335C22⋊C4—521no—
336C22⋊C4—521no—
337C13#262611yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—132no—
345C23—132no—
346C23—132no—
347C23—132no—
348C23—268no—
349C23—261no—
350C23—261no—
351C23—261no—
352C23—261no—
353C23—261no—
354C23—261no—
355C23—261no—
356C23—261no—
357C23—261no—
358C23—261no—
359C23—524no—
360C23—524no—
361C23—524no—
362C23—524no—
363C23—524no—
364C23—524no—
365C23Q8×D1312yes—
366C23C23×D1311yescharacteristic
367Q8—524no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—132no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—261no—
389C2×C4—261no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—261no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—261no—
399C2×C4—261no—
400C2×C4—261no—
401C2×C4—261no—
402C2×C4—261no—
403C2×C4—524no—
404C2×C4—524no—
405C2×C4D4×D1312yes—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—134no—
414C22—262no—
415C22—262no—
416C22—262no—
417C22—262no—
418C22—262no—
419C22—262no—
420C22—262no—
421C22—262no—
422C22—262no—
423C22—5216no—
424C22—521no—
425C22—521no—
426C22—521no—
427C22—521no—
428C22C2×D4×D1311yescharacteristic
429C22#8825111yescharacteristic
430C22#8825111yescharacteristic
431C22C2×Q8×D1311yescharacteristic
432C22#41×D1311yescharacteristic
433C22#8825611yescharacteristic
434C22#8825611yescharacteristic
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—262no—
442C4—521no—
443C4—521no—
444C4—521no—
445C4—521no—
446C4—521no—
447C2—42no—
448C2—264no—
449C2—522no—
450C2#1171931011yescharacteristic
451C2#1171931211yescharacteristic
452C2#1171931811yescharacteristic
453C2D13×C22⋊Q811yescharacteristic
454C2#1171933911yescharacteristic
455C2#1171933911yescharacteristic
456C2#1171940911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#396C2
prime radicalC24×D13C22
hypercenter#396D13
hypocenterC13#2626
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#88150C2semidirect
3. C13×#396C2semidirect
4. #11718655C2semidirect
5. #11718655C2semidirect
6. #11718653C2semidirect
7. #11718650C2semidirect
8. #11718648C2semidirect
11. #11718610C2semidirect
12. #11718609C2semidirect
13. #11718608C2semidirect
14. #11718334C2semidirect
15. #11718329C2semidirect
19. C22×Dic26C22semidirect
20. C2×C13×C4⋊C4C22semidirect
21. C2×C13×C4⋊C4C22semidirect
22. C2×C13×C4⋊C4C22semidirect
39. C2×C4⋊Dic13C22semidirect
40. C2×C4⋊Dic13C22semidirect
41. C2×#6101C22semidirect
42. C2×#6101C22semidirect
43. C2×#6101C22semidirect
44. C2×#6101C22semidirect
47. C13×#95C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
60. C23×D13Q8semidirect
185. #396D13semidirect
245. C2×C4⋊C4C2×D13semidirect
246. C2×C4⋊C4C2×D13semidirect
247. C2×C4⋊C4C2×D13semidirect
270. #95C2×D13semidirect
337. C13#2626semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×C22⋊C4×D132
C13×#3962
#117186552
#117186532
#117186502
#117186482
#117186162
#117186102
#117186092
#117186082
#117183342
#117183292
#262613