Finite Group Databasebeta

← #15830491

Subgroups — #15830491

Order 3328.

882 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128932C211yesmaximal, characteristic
2#13123925C211yesmaximal, characteristic, complemented
3#13113411C212yesmaximal
4#13113399C212yesmaximal, complemented
5#13113386C212yesmaximal, complemented
6#13113372C212yesmaximal
7#13113359C211yesmaximal, characteristic
8#13113347C211yesmaximal, characteristic, complemented
9#13113334C211yesmaximal, characteristic, complemented
10#13113320C211yesmaximal, characteristic
11C13×#2320C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C13C2211yescharacteristic
13Q8×C22⋊D13—21no—
14#11719289C412yescomplemented
15#11719289C411yescharacteristic, complemented
16#11719288—21no—
17#11719288—22no—
18Q8×D52C411yescharacteristic, complemented
19#11719277—21no—
20#11719275C411yescharacteristic, complemented
21#11719272C412yescomplemented
22#11719272C411yescharacteristic, complemented
23#11719218—22no—
24#11719218—21no—
25#11719184C2211yescharacteristic
26#11719184C2212yes—
27#11719175C2211yescharacteristic
28#11719175C2212yes—
29C13×#391—21no—
30C13×#389—21no—
31C13×#387—22no—
32C13×#383C2212yes—
33C13×#382C2212yes—
34C4×C13×C4⋊C4C2211yescharacteristic
35C13×#376C2211yescharacteristic
36#11718685—21no—
37#11718685—22no—
38Q8×#1055—21no—
39#11718587C2211yescharacteristic
40#11718587C2212yes—
41#11718586C2212yes—
42#11718586C2211yescharacteristic
43#11718044C2212yes—
44#11718044C2212yes—
45#11718044C2212yes—
46#11718044C2212yes—
47#11718044C2211yescharacteristic
48#11718044C2211yescharacteristic
49#11718044C2212yes—
50#11718043C2212yes—
51#11718043C2211yescharacteristic
52#11718043C2211yescharacteristic
53C22×Q8×C13D411yescharacteristic
54C2×Q8×D13—21no—
55C4×Q8×C13C2×C411yescharacteristic
56C4×Q8×C13C2×C412yes—
57C4×Q8×C13C2×C411yescharacteristic
58C4×Q8×C13D411yescharacteristic
59C4×Q8×C13D411yescharacteristic
60C4×Q8×C13D412yes—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4D412yes—
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C42×C13—21no—
66C2×C42×C13—21no—
67C2×C42×C13C2311yescharacteristic
68C2×C42×C13C2312yes—
69#88200—21no—
70#88200—22no—
71Q8×Dic13—21no—
72#88198—21no—
73#88198—22no—
74#88184C2311yescharacteristic
75#88183—21no—
76#88183—22no—
77C4×C22⋊D13—21no—
78C4×C22⋊D13—22no—
79#88180—21no—
80#88180—22no—
81#88178—21no—
82#88178—22no—
83#88178C2312yes—
84#88178C2311yescharacteristic
85#88152—22no—
86#88152—22no—
87#88152—22no—
88#88151—22no—
89#88151—21no—
90#88146—22no—
91#88146—21no—
92#88144—22no—
93#88144—21no—
94#88143—22no—
95#88143—22no—
96#88143—22no—
97#88141—22no—
98#88141—21no—
99#88130—22no—
100#88130—21no—
101#88129C2×C411yescharacteristic
102#88129C2×C412yes—
103C4×D52C2×C411yescharacteristic
104C4×D52C2×C412yes—
105#88126—21no—
106#88126—22no—
107#88124—22no—
108#88124—21no—
109#88124C2×C411yescharacteristic
110#88124C2×C412yes—
111#88123C2×C411yescharacteristic
112#88123C2×C412yes—
113#88123C2×C411yescharacteristic
114#88123C2×C412yes—
115C4×Dic26—21no—
116C4×Dic26—22no—
117C4×Dic26C2×C412yes—
118C4×Dic26C2×C412yes—
119C4×Dic26C2×C412yes—
120C4×Dic26C2×C411yescharacteristic
121C4×Dic26C2×C412yes—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—22no—
125C13×#95—21no—
126C13×#95C2312yes—
127C13×#95C2311yescharacteristic
128C13×#95C2311yescharacteristic
129C22⋊#1055C2311yescharacteristic
130C22⋊#1055C2312yes—
131C22⋊#1055C2311yescharacteristic
132C4⋊#1055—21no—
133C4⋊#1055—22no—
134C4⋊#1055—22no—
135C4⋊#1055—21no—
136#88043—22no—
137#88043—21no—
138C4×#1055—21no—
139C4×#1055—22no—
140#17601—131nomaximal, Sylow
141C2×Q8×C13—42no—
142C2×Q8×C13C22⋊C411yescharacteristic
143C2×Q8×C13C22⋊C411yescharacteristic
144C2×Q8×C13C22⋊C412yes—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2411yescharacteristic
153C2×C22⋊D13—21no—
154Q8×D13—44no—
155C2×D52C22×C411yescharacteristic
156C2×C4×D13—22no—
157C2×C4×D13—21no—
158C2×Dic26—22no—
159C2×Dic26—21no—
160C2×Dic26C22×C412yes—
161C2×Dic26C22×C411yescharacteristic
162C13×C4⋊C4—42no—
163C13×C4⋊C4—82no—
164C13×C4⋊C4C22⋊C412yes—
165C13×C4⋊C4C22⋊C411yescharacteristic
166C13×C4⋊C4C22⋊C412yes—
167C13×C4⋊C4C22⋊C412yes—
168C13×C4⋊C4C22⋊C412yes—
169C13×C4⋊C4C22⋊C412yes—
170C13×C4⋊C4C22⋊C411yescharacteristic
171C42×C13—42no—
172C42×C13—81no—
173C42×C13C22×C411yescharacteristic
174C42×C13C22×C412yes—
175C42×C13C22×C412yes—
176C42×C13C22×C411yescharacteristic
177C42×C13C2×D411yescharacteristic
178C42×C13C2×D412yes—
179C42×C13C2×D412yes—
180C42×C13C2×D411yescharacteristic
181C22⋊Dic13—22no—
182C22⋊Dic13—21no—
183#6103—21no—
184#6103—22no—
185#6103—22no—
186#6103—21no—
187#6103—21no—
188#6103—22no—
189#6103—21no—
190C4⋊Dic13—22no—
191C4⋊Dic13—21no—
192C4⋊Dic13—22no—
193C4⋊Dic13—21no—
194C4⋊Dic13—22no—
195C4⋊Dic13—21no—
196C4⋊Dic13C22×C411yescharacteristic
197C4⋊Dic13C22×C412yes—
198C4⋊Dic13C22×C411yescharacteristic
199#6101—22no—
200#6101—22no—
201#6101—22no—
202#6101—22no—
203#6101—21no—
204#6101—21no—
205#6101—22no—
206#6101—21no—
207#6101—22no—
208#6101—22no—
209#6101—21no—
210C4×Dic13—22no—
211C4×Dic13—22no—
212C4×Dic13—22no—
213C4×Dic13—22no—
214C4×Dic13—21no—
215C2×#1055—21no—
216C2×#1055—22no—
217C2×#1055—21no—
218#3523—131no—
219#2984—131no—
220#2320D1311yescharacteristic, complemented
221#1521—132no—
222#1518—132no—
223#1515—132no—
224#1512—132no—
225#1509—131no—
226#1506—131no—
227#1503—131no—
228#1500—131no—
229C23×C13C22×D411yescharacteristic
230C22×D13—21no—
231Q8×C13—22no—
232Q8×C13—22no—
233Q8×C13—42no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—42no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—42no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13C2×C22⋊C411yescharacteristic
251C2×C4×C13C2×C22⋊C412yes—
252C2×C4×C13C2×C22⋊C412yes—
253C2×C4×C13C2×C22⋊C411yescharacteristic
254C2×C4×C13C2×C22⋊C412yes—
255C2×C4×C13C2×C22⋊C412yes—
256C2×C4×C13C2×C22⋊C411yescharacteristic
257C2×C4×C13C2×C22⋊C411yescharacteristic
258C2×C4×C13C23×C411yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C22⋊D13—41no—
261C22⋊D13—41no—
262C2×Dic13—21no—
263C2×Dic13—22no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—22no—
267D52—41no—
268C4×D13—44no—
269C4×D13—42no—
270Dic26—44no—
271Dic26—42no—
272Dic26—42no—
273Dic26—41no—
274#1055—41no—
275#1055—42no—
276#1055—41no—
277#557—131no—
278#557—132no—
279#557—131no—
280#556—131no—
281#556—132no—
282#552—262no—
283#552—261no—
284D4×Q8—131no—
285D4×Q8—261no—
286#541—261no—
287#541—262no—
288#533—131no—
289#533—132no—
290#529—131no—
291#529—132no—
292#519—261no—
293C2×C4×Q8C2×D1311yescharacteristic
294#446—261no—
295#446—262no—
296C8×Q8—261no—
297#432—131no—
298#432—132no—
299#431—131no—
300#431—132no—
301#391—21no—
302#389—21no—
303#387—22no—
304#383C2×D1312yes—
305#382C2×D1312yes—
306C4×C4⋊C4C2×D1311yescharacteristic
307#376C2×D1311yescharacteristic
308#328—131no—
309#328—131no—
310#328—132no—
311#328—132no—
312#328—132no—
313#328—132no—
314#328—132no—
315#327—131no—
316#327—131no—
317#327—132no—
318C22×C13—21no—
319C22×C13—21no—
320C22×C13C22×C22⋊C411yescharacteristic
321C22×C13#57711yescharacteristic
322C22×C13#57811yescharacteristic
323C2×D13—41no—
324C2×D13—41no—
325C2×D13—41no—
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—22no—
331C4×C13—22no—
332C4×C13—22no—
333C4×C13—21no—
334C4×C13—22no—
335C4×C13—81no—
336C4×C13—82no—
337C4×C13—81no—
338C4×C13#42112yes—
339Dic13—42no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—42no—
344C22×Q8—261no—
345C22×Q8C22⋊D1311yescharacteristic
346C4⋊Q8—131no—
347C4⋊Q8—132no—
348C4⋊Q8—131no—
349C4⋊Q8—132no—
350C4⋊Q8—261no—
351C4⋊Q8—262no—
352#126—262no—
353#126—262no—
354#126—262no—
355#126—262no—
356#126—261no—
357#125—131no—
358#125—132no—
359#125—262no—
360#125—262no—
361#125—262no—
362#125—262no—
363#125—261no—
364#125—262no—
365#125—261no—
366#124—131no—
367#124—132no—
368#123—261no—
369#123—262no—
370C22⋊Q8—131no—
371C22⋊Q8—132no—
372C22⋊Q8—261no—
373C22⋊Q8—262no—
374C22⋊Q8—261no—
375C22⋊Q8—262no—
376C22⋊Q8—262no—
377C22⋊Q8—261no—
378#121—131no—
379C4×Q8—131no—
380C4×Q8—132no—
381C4×Q8—132no—
382C4×Q8—132no—
383C4×Q8—132no—
384C4×Q8—261no—
385C4×Q8—262no—
386C4×Q8—261no—
387C4×Q8—261no—
388C4×Q8—262no—
389C4×Q8C4×D1311yescharacteristic
390C4×Q8C4×D1311yescharacteristic
391C4×Q8C4×D1312yes—
392C4×Q8D5211yescharacteristic
393C4×Q8D5211yescharacteristic
394C4×Q8D5212yes—
395C4×D4—131no—
396C4×D4—132no—
397C4×D4—261no—
398C4×D4—262no—
399#117—261no—
400#117—262no—
401#117—262no—
402#117—261no—
403#117—261no—
404#117—262no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4C22⋊D1312yes—
408C2×C4⋊C4C22⋊D1311yescharacteristic
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C22×D1311yescharacteristic
412C2×C42C22×D1312yes—
413C4⋊C8—262no—
414C4⋊C8—261no—
415C4⋊C8—261no—
416C4⋊C8—262no—
417C22⋊C8—131no—
418C22⋊C8—131no—
419C22⋊C8—132no—
420#97—262no—
421#97—261no—
422C4×C8—261no—
423C4×C8—262no—
424#95—21no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95C22×D1311yescharacteristic
429#95C22×D1311yescharacteristic
430#95C22×D1312yes—
431C2×C13—21no—
432C2×C13—21no—
433C2×C13#288411yescharacteristic
434C2×C13#289811yescharacteristic
435C2×C13C2×#42111yescharacteristic
436D13—81no—
437C2×Q8—42no—
438C2×Q8—131no—
439C2×Q8—132no—
440C2×Q8—262no—
441C2×Q8—261no—
442C2×Q8—524no—
443C2×Q8#610311yescharacteristic
444C2×Q8#610311yescharacteristic
445C2×Q8#610312yes—
446C2×D4—131no—
447C2×D4—261no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—262no—
452C22×C4—261no—
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C2×C22⋊D1312yes—
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C2×C22⋊D1312yes—
457C22×C4C23×D1311yescharacteristic
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—262no—
461C4⋊C4—42no—
462C4⋊C4—82no—
463C4⋊C4—131no—
464C4⋊C4—132no—
465C4⋊C4—131no—
466C4⋊C4—262no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—262no—
470C4⋊C4—262no—
471C4⋊C4—261no—
472C4⋊C4—262no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—262no—
476C4⋊C4—262no—
477C4⋊C4—262no—
478C4⋊C4—262no—
479C4⋊C4—262no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—262no—
483C4⋊C4#610312yes—
484C4⋊C4#610311yescharacteristic
485C4⋊C4#610312yes—
486C4⋊C4#610311yescharacteristic
487C4⋊C4#610312yes—
488C4⋊C4#610312yes—
489C4⋊C4#610312yes—
490C22⋊C4—262no—
491C22⋊C4—261no—
492C22⋊C4—261no—
493C22⋊C4—262no—
494C22⋊C4—262no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C22⋊C4—262no—
498C22⋊C4—261no—
499C42—42no—
500C42—81no—
501C42—262no—
502C42—262no—
503C42—262no—
504C42—262no—
505C42—261no—
506C42C2×C4×D1312yes—
507C42C2×C4×D1311yescharacteristic
508C42C2×C4×D1311yescharacteristic
509C42C2×C4×D1312yes—
510C42C2×D5211yescharacteristic
511C42C2×D5212yes—
512C42C2×D5212yes—
513C42C2×D5211yescharacteristic
514C13#1760111yescharacteristic, complemented, Sylow
515C23—261no—
516C23C22×C22⋊D1311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—42no—
520Q8—521no—
521Q8—522no—
522Q8—524no—
523Q8—522no—
524D4—521no—
525D4—521no—
526D4—521no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—262no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—262no—
547C2×C4—261no—
548C2×C4—524no—
549C2×C4—522no—
550C2×C4C2×#610311yescharacteristic
551C2×C4C2×#610312yes—
552C2×C4C2×#610312yes—
553C2×C4C2×#610312yes—
554C2×C4C2×#610311yescharacteristic
555C2×C4C2×#610311yescharacteristic
556C2×C4C2×#610312yes—
557C2×C4C2×#610311yescharacteristic
558C2×C4C22×C4×D1311yescharacteristic
559C2×C4C22×D5211yescharacteristic
560C8—521no—
561C8—521no—
562C8—522no—
563C22—21no—
564C22—21no—
565C22—521no—
566C22—521no—
567C22—521no—
568C22C22×#610311yescharacteristic
569C22#1171954111yescharacteristic
570C22#1171954311yescharacteristic
571C4—21no—
572C4—21no—
573C4—22no—
574C4—22no—
575C4—21no—
576C4—22no—
577C4—22no—
578C4—21no—
579C4—21no—
580C4—81no—
581C4—82no—
582C4—81no—
583C4—521no—
584C4—522no—
585C4—521no—
586C4—522no—
587C4—521no—
588C4#1171866612yes—
589C2—21no—
590C2—21no—
591C2—1041no—
592C2#1312329911yescharacteristic
593C2#1312336611yescharacteristic
594C2C2×#1171866611yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2320C2
socleC22×C13C22×C22⋊C4
prime radical#88184C23
cosocleC22×C4×C13C24
hypercenter#2320D13
hypocenterC13#17601
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #13123925C2semidirect
4. #13113399C2semidirect
5. #13113386C2semidirect
8. #13113347C2semidirect
9. #13113334C2semidirect
11. C13×#2320C2semidirect
14. #11719289C4semidirect
15. #11719289C4semidirect
18. Q8×D52C4semidirect
20. #11719275C4semidirect
21. #11719272C4semidirect
22. #11719272C4semidirect
220. #2320D13semidirect
514. C13#17601semidirect

Maximal subgroups

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

subgroupindex
#131289322
#131239252
#131134112
#131133992
#131133862
#131133722
#131133592
#131133472
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