Finite Group Databasebeta

← #33056900

Subgroups — #33056900

Order 18688.

618 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619943C211yesmaximal, characteristic
2#22618943C211yesmaximal, characteristic, complemented
3#22618936C211yesmaximal, characteristic, complemented
4#22608825C211yesmaximal, characteristic, complemented
5#22608824C211yesmaximal, characteristic, complemented
6#22608778C211yesmaximal, characteristic, complemented
7#22608770C211yesmaximal, characteristic, complemented
8#22608764C211yesmaximal, characteristic, complemented
9#22608763C211yesmaximal, characteristic, complemented
10#22608728C211yesmaximal, characteristic, complemented
11#22608723C211yesmaximal, characteristic, complemented
12#22608712C211yesmaximal, characteristic, complemented
13#22608314C211yesmaximal, characteristic, complemented
14C8×#11924012C211yesmaximal, characteristic, complemented
15C73×#1494C211yesmaximal, characteristic, complemented
16C4×#11924028C2211yescharacteristic
17#17988925C411yescharacteristic
18#17988908C411yescharacteristic
19#17988891C411yescharacteristic
20#17988884C411yescharacteristic
21#17988806C411yescharacteristic
22#17988799C411yescharacteristic
23#17988747C411yescharacteristic
24#17988730C411yescharacteristic
25#17988718C2211yescharacteristic
26#17988714C2211yescharacteristic
27#17988714C2211yescharacteristic
28Q8×#10596831C2211yescharacteristic
29C4×#11924018C2211yescharacteristic
30C4×#11924015C2211yescharacteristic
31C4×#11924016C2211yescharacteristic
32C4×#11924013C2211yescharacteristic
33#17988665—21no—
34#17988665C2211yescharacteristic
35#17988661—21no—
36#17988661—21no—
37#17988659—21no—
38D4×#10596831C2211yescharacteristic
39#17988652C2211yescharacteristic
40#17988652C2211yescharacteristic
41#17988648—21no—
42#17988642—21no—
43#17988640C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988543—21no—
46C4×#11924012C2211yescharacteristic
47#97×D73—21no—
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#529×C73C2211yescharacteristic
61#432×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924012—21no—
73C2×#11924012D411yescharacteristic
74C2×#11924012D411yescharacteristic
75C22×#10596831—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C4×Dic146C2×C411yescharacteristic
79C4×Dic146C2311yescharacteristic
80C4×D292C2×C411yescharacteristic
81C4×D292C2311yescharacteristic
82C4×C22⋊D73—21no—
83C4×C22⋊D73—21no—
84#14556550C2×C411yescharacteristic
85#14556548—21no—
86C42×D73—21no—
87#14556524C2×C411yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91C4⋊#10596831—21no—
92C4⋊#10596831—21no—
93C4⋊#10596831C2×C411yescharacteristic
94C4⋊#10596831C2×C411yescharacteristic
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556520—21no—
98#14556520—21no—
99#14556515C2×C411yescharacteristic
100#14556515C2×C411yescharacteristic
101#14556514C2×C411yescharacteristic
102#14556514C2×C411yescharacteristic
103#14556512C2×C411yescharacteristic
104#14556512C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831—21no—
109C22⋊#10596831—21no—
110C22⋊#10596831C2×C411yescharacteristic
111C22⋊#10596831C2×C411yescharacteristic
112#14556503—21no—
113#14556503—21no—
114#14556502—21no—
115#14556502D411yescharacteristic
116#14556502D411yescharacteristic
117#14556501—21no—
118#14556501—21no—
119C4×#10596831—21no—
120C4×#10596831—21no—
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C22×C8×C73—21no—
126#126×C73—21no—
127#125×C73C2×C411yescharacteristic
128#124×C73C2×C411yescharacteristic
129#123×C73—21no—
130C22⋊Q8×C73C2×C411yescharacteristic
131#121×C73C2×C411yescharacteristic
132C4×Q8×C73C2311yescharacteristic
133C4×D4×C73—21no—
134C4×D4×C73C2311yescharacteristic
135#117×C73—21no—
136C2×C42×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—41no—
146C2×Dic146C22×C411yescharacteristic
147C2×D292C22×C411yescharacteristic
148C2×C22⋊D73—21no—
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152#11924018—41no—
153#11924016—41no—
154#11924015—22no—
155#11924013—22no—
156#11924012—22no—
157#11924012—22no—
158#11924012—42no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—42no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C2×#10596831C2×D411yescharacteristic
170C8×D73—42no—
171C8×D73—42no—
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174#11924007—21no—
175#11924007—21no—
176C22⋊Dic73—21no—
177#11924005—21no—
178#11924005—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C2×Q8×C73C22×C411yescharacteristic
183C2×D4×C73—21no—
184C2×D4×C73C22×C411yescharacteristic
185C22×C4×C73—21no—
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73#4111yescharacteristic
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—42no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73C22×C411yescharacteristic
199C4⋊C4×C73C22×C411yescharacteristic
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C42×C73—21no—
206C42×C73C22×C411yescharacteristic
207C42×C73C2×D411yescharacteristic
208C42×C73#4111yescharacteristic
209C42×C73C2411yescharacteristic
210C23×C73—21no—
211C23×C73C4×D411yescharacteristic
212C22×D73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215D4×C73—21no—
216D4×C73—21no—
217D4×C73—81no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C23×C411yescharacteristic
232C2×C4×C73C22×D411yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C22⋊D73—42no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238D292—21no—
239D292#13112yes—
240C4×D73—42no—
241C4×D73—41no—
242C4×D73—41no—
243C4×D73—81no—
244Dic146—21no—
245Dic146—21no—
246C8×C73—22no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—21no—
254#10596831—21no—
255#10596831—21no—
256#10596831—41no—
257#10596831—41no—
258#10596831#13512yes—
259#10596831#13512yes—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73C2×C4×D411yescharacteristic
267C2×D73—22no—
268C2×D73—41no—
269C2×D73—41no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73C2×#13111yescharacteristic
278C4×C73#56811yescharacteristic
279C4×C73C2×#13511yescharacteristic
280C4×C73C2×#13511yescharacteristic
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284#17996—731nomaximal, Sylow
285C2×C73—41no—
286C2×C73—81no—
287C2×C73#293311yescharacteristic
288C2×C73C4×#13511yescharacteristic
289C2×C73#295611yescharacteristic
290D73—42no—
291#3102—731no—
292#2970—731no—
293#2969—731no—
294#1591—731no—
295#1590—731no—
296#1584—731no—
297#1582—731no—
298#1582—731no—
299#1581—731no—
300C8×SD16—731no—
301C8×D8—731no—
302#1572—731no—
303#1494D7311yescharacteristic, complemented
304#1476—731no—
305C8×M16—731no—
306C73#1799611yescharacteristic, complemented, Sylow
307#529C2×D7311yescharacteristic
308C4×#41—731no—
309#485—731no—
310#482—731no—
311#479—731no—
312#478—731no—
313#464—731no—
314#463—731no—
315#452—731no—
316#449—731no—
317#446—731no—
318#446—731no—
319#446—731no—
320C8×Q8—731no—
321C4×Q16—731no—
322C4×SD16—731no—
323C4×SD16—731no—
324C4×D8—731no—
325#436—731no—
326#436—1461no—
327#435—1461no—
328#435—1461no—
329#435—1461no—
330C8×D4—731no—
331C8×D4—731no—
332C8×D4—731no—
333#433—1461no—
334#432—1461no—
335#432C2×D7311yescharacteristic
336#431—731no—
337#431—731no—
338#405—1461no—
339C4×M16—731no—
340C2×#97—1461no—
341C2×C4×C8C2×D7311yescharacteristic
342#335—731no—
343#335—731no—
344#334—731no—
345#334—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8C2×D7311yescharacteristic
349Q8⋊C8C2×D7311yescharacteristic
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8C2×D7311yescharacteristic
353D4⋊C8C2×D7311yescharacteristic
354#322—731no—
355#322—731no—
356C82—731no—
357C82—731no—
358C2×#41—731no—
359C2×Q16—731no—
360C2×SD16—731no—
361C2×SD16—731no—
362C2×D8—731no—
363C2×M16—731no—
364C2×M16—731no—
365C2×M16—1461no—
366C22×C8—21no—
367C22×C8—1461no—
368C22×C8—1461no—
369C22×C8—1461no—
370#126—21no—
371#125C4×D7311yescharacteristic
372#124C4×D7311yescharacteristic
373#123—21no—
374C22⋊Q8C4×D7311yescharacteristic
375#121C4×D7311yescharacteristic
376C4×Q8—731no—
377C4×Q8—731no—
378C4×Q8C22×D7311yescharacteristic
379C4×D4—21no—
380C4×D4—731no—
381C4×D4—731no—
382C4×D4—1461no—
383C4×D4—1461no—
384C4×D4C22×D7311yescharacteristic
385#117—21no—
386#117—731no—
387#117—1461no—
388C2×C42—1461no—
389C2×C42C22×D7311yescharacteristic
390#107—731no—
391#107—731no—
392#106—731no—
393#106—731no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8C22×D7311yescharacteristic
403C4⋊C8C22×D7311yescharacteristic
404#103—731no—
405#103—731no—
406#103—731no—
407#103—731no—
408#102—731no—
409#102—731no—
410#102—731no—
411#102—731no—
412C22⋊C8—21no—
413C22⋊C8—731no—
414C22⋊C8—731no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420#97—21no—
421#97—731no—
422#97—731no—
423#97—1461no—
424#97—1461no—
425#97—1461no—
426C4×C8—21no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—1461no—
432C4×C8—1461no—
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435#41—2921no—
436#41—1462no—
437C2×Q8—731no—
438C2×Q8C2×C4×D7311yescharacteristic
439C2×D4—21no—
440C2×D4—731no—
441C2×D4—1461no—
442C2×D4C2×C4×D7311yescharacteristic
443C22×C4—21no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4C2×C4×D7311yescharacteristic
448C22×C4D4×D7311yescharacteristic
449C22×C4#1192402711yescharacteristic
450Q16—2921no—
451SD16—2921no—
452SD16—1462no—
453D8—1462no—
454M16—2922no—
455M16—1462no—
456M16—1462no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—42no—
462C2×C8—2922no—
463C2×C8—2922no—
464C2×C8—2922no—
465C2×C8—731no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—731no—
470C2×C8—731no—
471C2×C8—731no—
472C2×C8—731no—
473C2×C8—1461no—
474C2×C8—1461no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—731no—
480C4⋊C4—731no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4C2×C4×D7311yescharacteristic
484C4⋊C4C2×C4×D7311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C42—21no—
494C42—1461no—
495C42—1461no—
496C42—1461no—
497C42C2×C4×D7311yescharacteristic
498C42D4×D7311yescharacteristic
499C42#1192402711yescharacteristic
500C42C23×D7311yescharacteristic
501C23—21no—
502C23—1461no—
503C23#1455655111yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—1461no—
507Q8—1461no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—2922no—
512D4—732no—
513D4—1461no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—2922no—
525C2×C4—2921no—
526C2×C4—2921no—
527C2×C4—5841no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4#1455655111yescharacteristic
532C2×C4#1455655111yescharacteristic
533C2×C4#1455655111yescharacteristic
534C2×C4C22×C4×D7311yescharacteristic
535C2×C4C2×D4×D7311yescharacteristic
536C2×C4C2×#1192402711yescharacteristic
537C8—22no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—2921no—
542C8—2921no—
543C8—732no—
544C8—732no—
545C8—1461no—
546C8—1461no—
547C8—1461no—
548C8—1461no—
549C8—1461no—
550C8—1461no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—2921no—
558C22—2921no—
559C22—1462no—
560C22C2×#1455655111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—2921no—
569C4—2921no—
570C4—2921no—
571C4#131×D7311yescharacteristic
572C4#1798935211yescharacteristic
573C4#135×D7311yescharacteristic
574C4#135×D7311yescharacteristic
575C2—41no—
576C2—81no—
577C2—2922no—
578C2#2261866111yescharacteristic
579C2#2261869911yescharacteristic
580C2#2261883711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1494C2
socleC22×C73C2×C4×D4
prime radical#17988730C4
cosocleC42×C73C24
hypercenter#1494D73
hypocenterC73#17996
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #22618943C2semidirect
3. #22618936C2semidirect
4. #22608825C2semidirect
5. #22608824C2semidirect
6. #22608778C2semidirect
7. #22608770C2semidirect
8. #22608764C2semidirect
9. #22608763C2semidirect
10. #22608728C2semidirect
11. #22608723C2semidirect
12. #22608712C2semidirect
13. #22608314C2semidirect
14. C8×#11924012C2semidirect
15. C73×#1494C2semidirect
303. #1494D73semidirect
306. C73#17996semidirect

Maximal subgroups

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

subgroupindex
#226199432
#226189432
#226189362
#226088252
#226088242
#226087782
#226087702
#226087642
#226087632
#226087282
#226087232
#226087122
#226083142
C8×#119240122
C73×#14942
#1799673