Finite Group Databasebeta

← #33056835

Subgroups — #33056835

Order 18688.

584 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620487C211yesmaximal, characteristic
2#22619027C211yesmaximal, characteristic, complemented
3#22619005C211yesmaximal, characteristic
4#22608812C211yesmaximal, characteristic, complemented
5#22608806C211yesmaximal, characteristic, complemented
6#22608788C211yesmaximal, characteristic, complemented
7#22608786C211yesmaximal, characteristic, complemented
8#22608775C211yesmaximal, characteristic, complemented
9#22608773C211yesmaximal, characteristic, complemented
10#22608769C211yesmaximal, characteristic, complemented
11#22608691C211yesmaximal, characteristic, complemented
12#22608402C211yesmaximal, characteristic, complemented
13#22608398C211yesmaximal, characteristic
14#22608222C211yesmaximal, characteristic, complemented
15C73×#1582C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17#17989134C2211yescharacteristic
18#17988984C411yescharacteristic
19#17988958C411yescharacteristic
20#17988936C411yescharacteristic
21#17988932C411yescharacteristic
22#17988819C411yescharacteristic
23#17988817C411yescharacteristic
24#17988815C411yescharacteristic
25#17988813C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988715—21no—
28#17988714—21no—
29Q8×#10596831C2211yescharacteristic
30#17988711C2211yescharacteristic
31C4×#11924017C2211yescharacteristic
32C4×#11924015C2211yescharacteristic
33C4×#11924016C2211yescharacteristic
34#17988665C2211yescharacteristic
35#17988664C2211yescharacteristic
36#17988661—21no—
37#17988658—21no—
38C8×D292C2211yescharacteristic
39#17988649—21no—
40#17988647—21no—
41#17988643C2211yescharacteristic
42#17988643C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988638C2211yescharacteristic
45#17988553—21no—
46#17988552—21no—
47C4×C8×D73C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53#17988317C2211yescharacteristic
54#17988316C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988308C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924017C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924011—21no—
73C2×C8×D73—21no—
74C2×C8×D73C2×C411yescharacteristic
75C2×C8×D73C2×C411yescharacteristic
76#14556590C2×C411yescharacteristic
77#14556590C2×C411yescharacteristic
78#14556589C2×C411yescharacteristic
79#14556587C2×C411yescharacteristic
80#14556581—21no—
81#14556577—21no—
82#14556571C2×C411yescharacteristic
83#14556569—21no—
84#14556567C2×C411yescharacteristic
85#14556566C2×C411yescharacteristic
86#14556564—21no—
87#14556562C2×C411yescharacteristic
88C4×Dic146—21no—
89C4×Dic146C2311yescharacteristic
90C4×D292C2311yescharacteristic
91C4×C22⋊D73—21no—
92#14556548—21no—
93C42×D73C2311yescharacteristic
94#14556523C2×C411yescharacteristic
95#14556522C2×C411yescharacteristic
96#14556522C2×C411yescharacteristic
97C4⋊#10596831—21no—
98C4⋊#10596831C2311yescharacteristic
99C4⋊#10596831C2311yescharacteristic
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520D411yescharacteristic
104#14556520D411yescharacteristic
105#14556516C2×C411yescharacteristic
106#14556515C2×C411yescharacteristic
107#14556514C2×C411yescharacteristic
108#14556513C2×C411yescharacteristic
109#14556512C2×C411yescharacteristic
110#14556511C2×C411yescharacteristic
111C22⋊#10596831—21no—
112#14556503—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503D411yescharacteristic
118#14556503D411yescharacteristic
119#14556501—21no—
120#14556501—21no—
121#14556501—21no—
122C4×#10596831—21no—
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73C2×C411yescharacteristic
128C8×Dic73C2×C411yescharacteristic
129C2×SD16×C73C2×C411yescharacteristic
130C22×C8×C73—21no—
131C4×Q8×C73C2311yescharacteristic
132C4×D4×C73C2311yescharacteristic
133#106×C73C2×C411yescharacteristic
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140#97×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—81no—
145#11924028—81no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146C22×C411yescharacteristic
149C2×D292—21no—
150C2×D292C22×C411yescharacteristic
151C2×C22⋊D73—21no—
152C2×C22⋊D73—21no—
153C2×C22⋊D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73C22×C411yescharacteristic
156C2×C4×D73C2×D411yescharacteristic
157C2×C4×D73#4111yescharacteristic
158#11924017—41no—
159#11924016—41no—
160#11924015—41no—
161#11924012—81no—
162#11924011—81no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C22×C411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C2×#10596831C2×D411yescharacteristic
170C8×D73—41no—
171C8×D73—41no—
172C8×D73—81no—
173C4⋊Dic73—21no—
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182C22⋊Dic73—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187C4×Dic73—21no—
188C4×Dic73C22×C411yescharacteristic
189C4×Dic73C2×D411yescharacteristic
190C4×Dic73#4111yescharacteristic
191C2×Q8×C73C22×C411yescharacteristic
192C2×D4×C73C22×C411yescharacteristic
193C22×C4×C73—21no—
194SD16×C73—41no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—81no—
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C4⋊C4×C73—21no—
204C4⋊C4×C73C22×C411yescharacteristic
205C4⋊C4×C73C22×C411yescharacteristic
206C22⋊C4×C73—21no—
207C42×C73—21no—
208C42×C73C2411yescharacteristic
209C23×C73—21no—
210C22×D73—21no—
211C22×D73C4×D411yescharacteristic
212Q8×C73—21no—
213Q8×C73—21no—
214D4×C73—21no—
215D4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73C23×C411yescharacteristic
222C2×C4×C73C22×D411yescharacteristic
223C2×C4×C73C2×#4111yescharacteristic
224C22⋊D73—81no—
225C22⋊D73—81no—
226C22⋊D73—81no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73C4×D411yescharacteristic
231C2×Dic73C4×D411yescharacteristic
232C2×Dic73C4×D411yescharacteristic
233D292—21no—
234D292—21no—
235D292—81no—
236C4×D73—21no—
237C4×D73—21no—
238C4×D73—21no—
239C4×D73—21no—
240C4×D73—41no—
241C4×D73—41no—
242C4×D73—41no—
243Dic146—21no—
244Dic146—21no—
245Dic146—81no—
246Dic146—81no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254#10596831—21no—
255#10596831—21no—
256#10596831—21no—
257#10596831—21no—
258#10596831—41no—
259#10596831—41no—
260#10596831—41no—
261C22×C73—41no—
262C22×C73—41no—
263C22×C73—41no—
264C22×C73C2×C4×D411yescharacteristic
265C2×D73—21no—
266C2×D73—21no—
267C2×D73—21no—
268C2×D73—41no—
269C2×D73—41no—
270C2×D73—41no—
271C4×C73—21no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73#56811yescharacteristic
276C4×C73#56811yescharacteristic
277C4×C73#57711yescharacteristic
278C4×C73#57711yescharacteristic
279Dic73—21no—
280Dic73—21no—
281Dic73—21no—
282Dic73—41no—
283Dic73—41no—
284Dic73—41no—
285#17990—731nomaximal, Sylow
286C2×C73—81no—
287C2×C73#293211yescharacteristic
288C2×C73#294911yescharacteristic
289C2×C73#295711yescharacteristic
290D73—41no—
291D73—81no—
292#3167—731no—
293#2985—731no—
294#2981—731no—
295#1588—731no—
296#1588—731no—
297#1585—731no—
298#1585—731no—
299#1583—731no—
300#1583—731no—
301#1582—731no—
302#1582D7311yescharacteristic, complemented
303#1568—731no—
304#1497—731no—
305#1496—731no—
306#1452—731no—
307C73#1799011yescharacteristic, complemented, Sylow
308#533—731no—
309#532—731no—
310#498—731no—
311#492—731no—
312#487—731no—
313#486—731no—
314#465—731no—
315#465—731no—
316#465—731no—
317#465—731no—
318#446—731no—
319#446—1461no—
320#446—1461no—
321#446C2×D7311yescharacteristic
322C8×Q8—731no—
323C8×Q8—731no—
324C4×SD16—731no—
325C4×SD16—731no—
326C4×SD16—731no—
327C4×SD16C2×D7311yescharacteristic
328#436—731no—
329#436—731no—
330#435—1461no—
331#435—1461no—
332C8×D4—731no—
333C8×D4C2×D7311yescharacteristic
334#433—1461no—
335#433—1461no—
336#432—731no—
337#432—731no—
338#431—731no—
339#431—731no—
340#408—1461no—
341#408—1461no—
342C2×C4×C8—731no—
343#335—731no—
344#335—731no—
345#334—731no—
346#334C2×D7311yescharacteristic
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349Q8⋊C8—731no—
350Q8⋊C8C2×D7311yescharacteristic
351D4⋊C8—731no—
352D4⋊C8—731no—
353D4⋊C8—731no—
354D4⋊C8C2×D7311yescharacteristic
355#322—731no—
356#322—731no—
357#322—731no—
358#322C2×D7311yescharacteristic
359C2×#41—1461no—
360C2×SD16—731no—
361C2×SD16—731no—
362C2×SD16—731no—
363C2×SD16C4×D7311yescharacteristic
364C2×M16—1461no—
365C2×M16—1461no—
366C22×C8—21no—
367C22×C8—731no—
368C22×C8—731no—
369C22×C8—1461no—
370C4⋊Q8—731no—
371C4⋊Q8—731no—
372C4⋊Q8—731no—
373#127—731no—
374#125—1461no—
375#124—1461no—
376C22⋊Q8—731no—
377C22⋊Q8—731no—
378C22⋊Q8—1461no—
379#121—731no—
380#121—731no—
381#121—1461no—
382C4×Q8—731no—
383C4×Q8—1461no—
384C4×Q8C22×D7311yescharacteristic
385C4×D4—731no—
386C4×D4—1461no—
387C4×D4C22×D7311yescharacteristic
388#117—1461no—
389C2×C42—731no—
390#106—731no—
391#106—731no—
392#106—731no—
393#106C4×D7311yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8C22×D7311yescharacteristic
404C4⋊C8C22×D7311yescharacteristic
405#103—731no—
406#103—731no—
407#103—731no—
408#103C4×D7311yescharacteristic
409#102—731no—
410#102—731no—
411#102—731no—
412#102C4×D7311yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—731no—
415C22⋊C8—731no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422#97—21no—
423#97—1461no—
424#97—1461no—
425#97—1461no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—1461no—
432C4×C8—1461no—
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435C4×C8C22×D7311yescharacteristic
436#41—5841no—
437#41—5841no—
438C2×Q8—731no—
439C2×Q8—1461no—
440C2×Q8—1461no—
441C2×Q8C2×C4×D7311yescharacteristic
442C2×D4—731no—
443C2×D4—1461no—
444C2×D4—1461no—
445C2×D4—1461no—
446C2×D4—1461no—
447C2×D4C2×C4×D7311yescharacteristic
448C22×C4—21no—
449C22×C4—731no—
450C22×C4—731no—
451C22×C4—731no—
452C22×C4—1461no—
453SD16—41no—
454SD16—2921no—
455SD16—2921no—
456SD16—2921no—
457M16—5841no—
458M16—5841no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—81no—
463C2×C8—2921no—
464C2×C8—2921no—
465C2×C8—5841no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—731no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8C2×C4×D7311yescharacteristic
474C2×C8C2×C4×D7311yescharacteristic
475C2×C8D4×D7311yescharacteristic
476C2×C8D4×D7311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—731no—
479C4⋊C4—731no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4C2×C4×D7311yescharacteristic
488C4⋊C4C2×C4×D7311yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C22⋊C4—1461no—
494C22⋊C4—1461no—
495C42—21no—
496C42—731no—
497C42—731no—
498C42—731no—
499C42—1461no—
500C42C23×D7311yescharacteristic
501C23—21no—
502C23—731no—
503C23—1461no—
504Q8—21no—
505Q8—21no—
506Q8—5841no—
507Q8—5841no—
508Q8—1461no—
509Q8—1461no—
510D4—21no—
511D4—21no—
512D4—5841no—
513D4—5841no—
514D4—5841no—
515D4—5841no—
516D4—1461no—
517D4—1461no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—2921no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—731no—
527C2×C4—731no—
528C2×C4—731no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4C22×C4×D7311yescharacteristic
537C2×C4C2×D4×D7311yescharacteristic
538C2×C4#41×D7311yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—2921no—
547C8—2921no—
548C8—2921no—
549C8—1461no—
550C8—1461no—
551C8—1461no—
552C8—1461no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—2921no—
557C22—2921no—
558C22—2921no—
559C22—1461no—
560C22—1461no—
561C22—1461no—
562C22C4×D4×D7311yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—2921no—
568C4—2921no—
569C4—2921no—
570C4—1461no—
571C4—1461no—
572C4—1461no—
573C4#1798935211yescharacteristic
574C4#1798935311yescharacteristic
575C4#1798939311yescharacteristic
576C4#1798939411yescharacteristic
577C2—81no—
578C2—2921no—
579C2—5841no—
580C2#2261864511yescharacteristic
581C2#2261878511yescharacteristic
582C2#2261884511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1582C2
socleC22×C73C2×C4×D4
prime radical#17989134C22
cosocleC42×C73C24
hypercenter#1582D73
hypocenterC73#17990
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #22619027C2semidirect
4. #22608812C2semidirect
5. #22608806C2semidirect
6. #22608788C2semidirect
7. #22608786C2semidirect
8. #22608775C2semidirect
9. #22608773C2semidirect
10. #22608769C2semidirect
11. #22608691C2semidirect
12. #22608402C2semidirect
14. #22608222C2semidirect
15. C73×#1582C2semidirect
302. #1582D73semidirect
307. C73#17990semidirect

Maximal subgroups

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

subgroupindex
#226204872
#226190272
#226190052
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