Finite Group Databasebeta

← #15759403

Subgroups — #15759403

Order 3328.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123892C211yesmaximal, characteristic, complemented
2#13113340C211yesmaximal, characteristic, complemented
3C2×#11718129C211yesmaximal, characteristic, complemented
4#13113196C211yesmaximal, characteristic, complemented
5#13112724C211yesmaximal, characteristic, complemented
6#13112678C211yesmaximal, characteristic, complemented
7C13×#3188C211yesmaximal, characteristic
8C13×#525C2211yescharacteristic
9C2×C13×#121C2211yescharacteristic
10C13×#484C411yescharacteristic, complemented
11C13×#482—21no—
12C13×#481C411yescharacteristic, complemented
13C13×#466—21no—
14C13×#465—21no—
15C13×#450C411yescharacteristic, complemented
16C13×#449—21no—
17C13×#447C411yescharacteristic, complemented
18C2×C13×C22⋊C8C2211yescharacteristic
19#11718895—21no—
20C2×#88071C2211yescharacteristic
21#11718868C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23C2×C22⋊#1055C2211yescharacteristic
24#11718672—21no—
25#11718672—21no—
26D4×#1055—21no—
27D4×#1055—21no—
28#11718661—21no—
29#11718130—21no—
30#11718129—21no—
31#11718129—21no—
32#11718129—21no—
33#11718117—21no—
34#11718117—21no—
35C2×C13×#41D411yescharacteristic
36C22×D4×C13—21no—
37C22×D4×C13C2×C411yescharacteristic
38C23×C4×C13C2311yescharacteristic
39C23×Dic13—21no—
40C2×C13×SD16—21no—
41C2×C13×D8—21no—
42C22×C8×C13—21no—
43C13×#123—21no—
44C13×C22⋊Q8C2×C411yescharacteristic
45C13×C22⋊Q8D411yescharacteristic
46C13×#121—21no—
47C13×#121—21no—
48C13×#121—21no—
49C13×#121—21no—
50C13×#121C2×C411yescharacteristic
51C13×#121D411yescharacteristic
52C13×#120—21no—
53C4×D4×C13—21no—
54C4×D4×C13—21no—
55C13×#117D411yescharacteristic
56C2×C13×C4⋊C4C2×C411yescharacteristic
57C2×C13×C22⋊C4—21no—
58C2×#6099—21no—
59C2×#6099—21no—
60C22×#1055—21no—
61C22×#1055—21no—
62C22×#1055—21no—
63C13×#107—21no—
64C13×#106—21no—
65C13×#103—21no—
66C13×#102—21no—
67C13×#102—21no—
68C13×#102—21no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8C2×C411yescharacteristic
71C13×C22⋊C8C2×C411yescharacteristic
72#88071—21no—
73#88071—21no—
74C22⋊#1055—21no—
75C22⋊#1055—21no—
76C22⋊#1055—21no—
77C22⋊#1055—21no—
78C22⋊#1055—21no—
79C22⋊#1055—21no—
80C22⋊#1055D411yescharacteristic
81C22⋊#1055D411yescharacteristic
82C22⋊#1055D411yescharacteristic
83C22⋊#1055D411yescharacteristic
84C4⋊#1055—21no—
85C4⋊#1055—21no—
86#88043—21no—
87C4×#1055—21no—
88#9264—131nomaximal, Sylow
89C24×C13—21no—
90C24×C13#4111yescharacteristic
91C13×#41—81no—
92C2×Q8×C13C22⋊C411yescharacteristic
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—21no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—81no—
101C2×D4×C13—81no—
102C2×D4×C13—81no—
103C2×D4×C13C22⋊C411yescharacteristic
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—81no—
107C22×C4×C13C22×C411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13#4111yescharacteristic
113C22×Dic13—22no—
114C22×Dic13—41no—
115C22×Dic13—41no—
116C22×Dic13—81no—
117C22×Dic13—81no—
118C13×SD16—81no—
119C13×D8—81no—
120C2×C8×C13—21no—
121C2×C8×C13—21no—
122C2×C8×C13—81no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4C22⋊C411yescharacteristic
128C13×C4⋊C4C22⋊C411yescharacteristic
129C13×C22⋊C4—21no—
130C13×C22⋊C4—21no—
131C13×C22⋊C4—21no—
132C13×C22⋊C4—21no—
133C13×C22⋊C4—21no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C42×C13—21no—
137#6099—81no—
138#6099—81no—
139C2×#1055—21no—
140C2×#1055—21no—
141C2×#1055—21no—
142C2×#1055—21no—
143C2×#1055—41no—
144C2×#1055—81no—
145C2×#1055—81no—
146C2×#1055—81no—
147#3188D1311yescharacteristic
148#2977—131no—
149#1504—131no—
150C2×#327—131no—
151#1471—131no—
152#1298—131no—
153#1280—131no—
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—21no—
157C23×C13—21no—
158C23×C13—21no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—81no—
164C23×C13—81no—
165C23×C13C4×D411yescharacteristic
166C23×C13#12111yescharacteristic
167C23×C13#12311yescharacteristic
168Q8×C13—41no—
169D4×C13—41no—
170D4×C13—41no—
171D4×C13—41no—
172D4×C13—41no—
173D4×C13—41no—
174D4×C13—41no—
175D4×C13—41no—
176D4×C13—81no—
177D4×C13—81no—
178D4×C13—82no—
179D4×C13—81no—
180D4×C13—81no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—81no—
194C2×C4×C13C2×C22⋊C411yescharacteristic
195C2×C4×C13C4×D411yescharacteristic
196C2×C4×C13#12011yescharacteristic
197C2×C4×C13#12111yescharacteristic
198C2×Dic13—42no—
199C2×Dic13—81no—
200C2×Dic13—82no—
201C2×Dic13—81no—
202C2×Dic13—82no—
203C8×C13—41no—
204C8×C13—41no—
205#1055—41no—
206#1055—41no—
207#1055—41no—
208#1055—41no—
209#1055—81no—
210#525C2×D1311yescharacteristic
211C2×#121C2×D1311yescharacteristic
212#484Dic1311yescharacteristic, complemented
213#482—21no—
214#481Dic1311yescharacteristic, complemented
215#466—21no—
216#465—21no—
217#450Dic1311yescharacteristic, complemented
218#449—21no—
219#447Dic1311yescharacteristic, complemented
220#435—261no—
221#435—261no—
222C8×D4—261no—
223C8×D4—261no—
224#433—261no—
225#408—261no—
226#407—131no—
227C2×C22⋊C8—131no—
228C2×C22⋊C8—131no—
229C2×C22⋊C8C2×D1311yescharacteristic
230C2×#95—131no—
231#328—261no—
232#327—261no—
233#327—261no—
234#327—261no—
235#323—261no—
236#323—261no—
237C22×C13—21no—
238C22×C13—21no—
239C22×C13—21no—
240C22×C13—21no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—21no—
244C22×C13—41no—
245C22×C13—41no—
246C22×C13—41no—
247C22×C13—41no—
248C22×C13—41no—
249C22×C13—41no—
250C22×C13—41no—
251C22×C13—81no—
252C22×C13—81no—
253C22×C13—81no—
254C22×C13—161no—
255C22×C13—161no—
256C22×C13#38611yescharacteristic
257C22×C13#44311yescharacteristic
258C22×C13#44411yescharacteristic
259C22×C13#47111yescharacteristic
260C22×C13#47211yescharacteristic
261C4×C13—21no—
262C4×C13—21no—
263C4×C13—21no—
264C4×C13—21no—
265C4×C13—41no—
266C4×C13—41no—
267C4×C13—41no—
268C4×C13—81no—
269Dic13—82no—
270C2×#41C22⋊D1311yescharacteristic
271C22×D4—21no—
272C22×D4C2×Dic1311yescharacteristic
273C23×C4—261no—
274C23×C4C22×D1311yescharacteristic
275C2×SD16—21no—
276C2×D8—21no—
277C2×M16—261no—
278C2×M16—261no—
279C22×C8—21no—
280C22×C8—261no—
281C22×C8—261no—
282C22×C8—261no—
283#123—21no—
284C22⋊Q8C2×Dic1311yescharacteristic
285C22⋊Q8C22⋊D1311yescharacteristic
286#121—21no—
287#121—21no—
288#121—21no—
289#121—21no—
290#121C2×Dic1311yescharacteristic
291#121C22⋊D1311yescharacteristic
292#120—21no—
293C4×D4—21no—
294C4×D4—21no—
295#117C22⋊D1311yescharacteristic
296C2×C4⋊C4C2×Dic1311yescharacteristic
297C2×C22⋊C4—21no—
298#107—21no—
299#106—21no—
300C4⋊C8—261no—
301C4⋊C8—261no—
302#103—21no—
303#102—21no—
304#102—21no—
305#102—21no—
306C22⋊C8—21no—
307C22⋊C8—131no—
308C22⋊C8—131no—
309C22⋊C8—131no—
310C22⋊C8—131no—
311C22⋊C8—261no—
312C22⋊C8—261no—
313C22⋊C8—261no—
314C22⋊C8—261no—
315C22⋊C8—261no—
316C22⋊C8—261no—
317C22⋊C8C2×Dic1311yescharacteristic
318C22⋊C8C2×Dic1311yescharacteristic
319#97—261no—
320C4×C8—261no—
321#95—261no—
322#95—261no—
323C2×C13—21no—
324C2×C13—21no—
325C2×C13—21no—
326C2×C13—21no—
327C2×C13—41no—
328C2×C13—81no—
329C2×C13—161no—
330C2×C13#187611yescharacteristic
331C2×C13#190711yescharacteristic
332C2×C13#191311yescharacteristic
333C24—21no—
334C24#612911yescharacteristic
335#41—81no—
336C2×Q8C22⋊Dic1311yescharacteristic
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—81no—
345C2×D4—81no—
346C2×D4—81no—
347C2×D4C22⋊Dic1311yescharacteristic
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—81no—
351C22×C4—262no—
352C22×C4—521no—
353C22×C4—521no—
354C22×C4—1041no—
355C22×C4—1041no—
356C22×C4D4×D1311yescharacteristic
357C22×C4D4×D1311yescharacteristic
358C22×C4#612911yescharacteristic
359C22×C4C22×Dic1311yescharacteristic
360C22×C4C2×C22⋊D1311yescharacteristic
361C22×C4C2×C22⋊D1311yescharacteristic
362SD16—81no—
363D8—81no—
364M16—1041no—
365M16—1041no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—81no—
369C2×C8—261no—
370C2×C8—261no—
371C2×C8—261no—
372C2×C8—261no—
373C2×C8—521no—
374C2×C8—1041no—
375C2×C8—1041no—
376C2×C8—1041no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4C22⋊Dic1311yescharacteristic
382C4⋊C4C22⋊Dic1311yescharacteristic
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C42—21no—
391C13#926411yescharacteristic, complemented, Sylow
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23D4×Dic1311yescharacteristic
404C23#8818911yescharacteristic
405C23#8819311yescharacteristic
406Q8—41no—
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—81no—
415D4—81no—
416D4—82no—
417D4—81no—
418D4—81no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—81no—
432C2×C4—522no—
433C2×C4—1041no—
434C2×C4—1042no—
435C2×C4—1041no—
436C2×C4—1042no—
437C2×C4D4×Dic1311yescharacteristic
438C2×C4#8819111yescharacteristic
439C2×C4#8819311yescharacteristic
440C2×C4C2×C22⋊Dic1311yescharacteristic
441C8—41no—
442C8—41no—
443C8—521no—
444C8—521no—
445C8—521no—
446C8—521no—
447C8—1041no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—161no—
466C22—161no—
467C22#1171885711yescharacteristic
468C22#1171885811yescharacteristic
469C22#1171886011yescharacteristic
470C22#1171886111yescharacteristic
471C22#1171888111yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—81no—
480C4—1042no—
481C2—21no—
482C2—21no—
483C2—21no—
484C2—21no—
485C2—41no—
486C2—81no—
487C2—161no—
488C2#1311516511yescharacteristic
489C2#1311534611yescharacteristic
490C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#3188C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenter#3188D13
hypocenterC13#9264
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3188

Complements

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

NH ≅ G/Ntype
1. #13123892C2semidirect
2. #13113340C2semidirect
3. C2×#11718129C2semidirect
4. #13113196C2semidirect
5. #13112724C2semidirect
6. #13112678C2semidirect
10. C13×#484C4semidirect
12. C13×#481C4semidirect
15. C13×#450C4semidirect
17. C13×#447C4semidirect
212. #484Dic13semidirect
214. #481Dic13semidirect
217. #450Dic13semidirect
219. #447Dic13semidirect
391. C13#9264semidirect

Maximal subgroups

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

subgroupindex
#131238922
#131133402
C2×#117181292
#131131962
#131127242
#131126782
C13×#31882
#926413