Finite Group Databasebeta

← #33057325

Subgroups — #33057325

Order 18688.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619937C211yesmaximal, characteristic
2#22619029C211yesmaximal, characteristic, complemented
3#22618963C211yesmaximal, characteristic
4#22608824C211yesmaximal, characteristic, complemented
5#22608810C211yesmaximal, characteristic, complemented
6#22608787C211yesmaximal, characteristic, complemented
7#22608772C211yesmaximal, characteristic, complemented
8#22608765C211yesmaximal, characteristic, complemented
9#22608745C211yesmaximal, characteristic, complemented
10#22608728C211yesmaximal, characteristic, complemented
11#22608710C211yesmaximal, characteristic, complemented
12#22608402C211yesmaximal, characteristic, complemented
13#22608320C211yesmaximal, characteristic
14#22608232C211yesmaximal, characteristic, complemented
15C73×#1592C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×D4×D73C2211yescharacteristic
18#17988919C411yescharacteristic
19#17988916C411yescharacteristic
20#17988876C411yescharacteristic
21#17988875C411yescharacteristic
22#17988791C411yescharacteristic
23#17988790C411yescharacteristic
24#17988739C411yescharacteristic
25#17988736C411yescharacteristic
26#17988715—21no—
27#17988714C2211yescharacteristic, complemented
28Q8×#10596831C2211yescharacteristic, complemented
29C8×Dic146C2211yescharacteristic, complemented
30#17988711—21no—
31C4×#11924017C2211yescharacteristic
32C4×#11924015C2211yescharacteristic
33C4×#11924016C2211yescharacteristic
34#17988665C2211yescharacteristic
35#17988661—21no—
36#17988656—21no—
37C8×D292C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988649—21no—
40#17988647—21no—
41#17988643C2211yescharacteristic
42#17988639C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988638C2211yescharacteristic
45#17988638C2211yescharacteristic
46#17988550—21no—
47C22⋊C8×D73—21no—
48#17988340C2211yescharacteristic, complemented
49#17988337C2211yescharacteristic, complemented
50#17988337C2211yescharacteristic, complemented
51#17988319C2211yescharacteristic, complemented
52Q8⋊#10596831C2211yescharacteristic, complemented
53#17988317C2211yescharacteristic, complemented
54#17988316C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic, complemented
58#17988308C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60#446×C73C2211yescharacteristic, complemented
61C4×SD16×C73C2211yescharacteristic
62#436×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic, complemented
67C2×D4×D73C2×C411yescharacteristic
68C22×C4×D73—21no—
69C2×#11924017C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924015C2×C411yescharacteristic
72C2×#11924012—21no—
73C2×C8×D73—21no—
74C2×C8×D73—21no—
75#14556590C2×C411yescharacteristic
76#14556589C2×C411yescharacteristic
77#14556581—21no—
78#14556571C2×C411yescharacteristic
79#14556569—21no—
80#14556567C2×C411yescharacteristic
81C4×Dic146—21no—
82C4×Dic146C2311yescharacteristic
83C4×D292C2311yescharacteristic
84D4×Dic73C2×C411yescharacteristic
85#14556553C2×C411yescharacteristic
86C4×C22⋊D73—21no—
87#14556551—21no—
88#14556548—21no—
89C4⋊C4×D73C2×C411yescharacteristic
90C22⋊C4×D73—21no—
91C42×D73C2311yescharacteristic
92#14556523C2×C411yescharacteristic
93#14556522C2×C411yescharacteristic
94#14556522C2×C411yescharacteristic
95C4⋊#10596831—21no—
96C4⋊#10596831C2311yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98#14556520—21no—
99#14556520—21no—
100#14556520—21no—
101#14556520C2×C411yescharacteristic
102#14556520C2×C411yescharacteristic
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#14556503C2×C411yescharacteristic
118#14556503C2×C411yescharacteristic
119#14556503D411yescharacteristic
120#14556503D411yescharacteristic
121#14556501—21no—
122#14556501—21no—
123C4×#10596831—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×SD16×C73C2×C411yescharacteristic
130C2×M16×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
144C23×D73—21no—
145C2×Dic146—21no—
146C2×Dic146C22×C411yescharacteristic
147C2×D292C22×C411yescharacteristic
148C2×C22⋊D73—21no—
149D4×D73—22no—
150D4×D73—41no—
151C22×Dic73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—81no—
156C2×C4×D73—81no—
157C2×C4×D73C22×C411yescharacteristic
158C2×C4×D73C2×D411yescharacteristic
159C2×C4×D73#4111yescharacteristic
160#11924017—22no—
161#11924016—41no—
162#11924015—22no—
163#11924012—81no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831C22×C411yescharacteristic
168C2×#10596831C22×C411yescharacteristic
169C2×#10596831C2×D411yescharacteristic
170C2×#10596831C2×D411yescharacteristic
171C8×D73—81no—
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—
195M16×C73—81no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
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×D73—42no—
212C22×D73—42no—
213C22×D73—81no—
214C22×D73C4×D411yescharacteristic
215Q8×C73—21no—
216Q8×C73—21no—
217D4×C73—21no—
218D4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73C23×C411yescharacteristic
225C2×C4×C73C22×D411yescharacteristic
226C2×C4×C73C2×#4111yescharacteristic
227C22⋊D73—42no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—81no—
232C2×Dic73C4×D411yescharacteristic
233C2×Dic73C4×D411yescharacteristic
234C2×Dic73C4×D411yescharacteristic
235D292—21no—
236D292#13112yes—
237C4×D73—21no—
238C4×D73—21no—
239C4×D73—21no—
240C4×D73—21no—
241C4×D73—41no—
242C4×D73—41no—
243C4×D73—41no—
244C4×D73—81no—
245C4×D73—81no—
246Dic146—21no—
247Dic146—21no—
248Dic146—42no—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—21no—
252C8×C73—21no—
253C8×C73—41no—
254C8×C73—41no—
255C8×C73—41no—
256#10596831—21no—
257#10596831—21no—
258#10596831—21no—
259#10596831—21no—
260#10596831—41no—
261#10596831—41no—
262#10596831—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73C2×C4×D411yescharacteristic
267C2×D73—21no—
268C2×D73—22no—
269C2×D73—21no—
270C2×D73—21no—
271C2×D73—41no—
272C2×D73—41no—
273C2×D73—84no—
274C4×C73—21no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73C2×#13111yescharacteristic
279C4×C73#56811yescharacteristic
280C4×C73#57711yescharacteristic
281C4×C73#57711yescharacteristic
282Dic73—21no—
283Dic73—21no—
284Dic73—21no—
285Dic73—41no—
286Dic73—41no—
287Dic73—41no—
288#18028—731nomaximal, Sylow
289C2×C73—81no—
290C2×C73#293311yescharacteristic
291C2×C73#294911yescharacteristic
292C2×C73#295511yescharacteristic
293D73—41no—
294D73—42no—
295#3101—731no—
296#2986—731no—
297#2974—731no—
298#1592D7311yescharacteristic, complemented
299#1590—731no—
300#1588—731no—
301#1585—731no—
302#1583—731no—
303#1582—731no—
304SD16⋊C8—731no—
305C8×SD16—731no—
306#1572—731no—
307#1497—731no—
308#1478—731no—
309#1454—731no—
310C73#1802811yescharacteristic, complemented, Sylow
311#533—731no—
312C2×C4×D4—731no—
313#483—731no—
314#483—731no—
315#476—731no—
316#476—731no—
317#461—731no—
318#461—731no—
319#450—731no—
320#450—731no—
321#446—731no—
322#446—1461no—
323#446C2×D7311yescharacteristic, complemented
324C8×Q8—731no—
325C8×Q8—731no—
326C8×Q8—1461no—
327C4×SD16—731no—
328C4×SD16—731no—
329C4×SD16—731no—
330C4×SD16C2×D7311yescharacteristic
331#436—731no—
332#436C2×D7311yescharacteristic
333#435—1461no—
334#435—1461no—
335C8×D4—731no—
336C8×D4—731no—
337#433—1461no—
338#433—1461no—
339#432—731no—
340#431—731no—
341#431—731no—
342#431—731no—
343#431—731no—
344#407—1461no—
345C2×C22⋊C8—1461no—
346#335—731no—
347#335C2×D7311yescharacteristic, complemented
348#334—731no—
349#334—731no—
350Q8⋊C8—731no—
351Q8⋊C8—731no—
352Q8⋊C8—731no—
353Q8⋊C8C2×D7311yescharacteristic, complemented
354D4⋊C8—731no—
355D4⋊C8—731no—
356D4⋊C8—731no—
357D4⋊C8C2×D7311yescharacteristic
358#322—731no—
359#322—731no—
360#322C2×D7311yescharacteristic, complemented
361C82—731no—
362C22×D4—731no—
363C23×C4—1461no—
364C2×SD16—731no—
365C2×SD16—731no—
366C2×SD16—731no—
367C2×SD16C4×D7311yescharacteristic
368C2×M16—21no—
369C2×M16—1461no—
370C22×C8—1461no—
371C22×C8—1461no—
372C4⋊Q8—731no—
373C4⋊Q8—731no—
374#125—1461no—
375C22⋊Q8—731no—
376C22⋊Q8—731no—
377C22⋊Q8—1461no—
378C4×Q8—731no—
379C4×Q8—1461no—
380C4×Q8C22×D7311yescharacteristic
381C4×D4—731no—
382C4×D4—731no—
383C4×D4—731no—
384C4×D4—1461no—
385C4×D4—1461no—
386C4×D4C22×D7311yescharacteristic
387#117—1461no—
388C2×C4⋊C4—731no—
389C2×C22⋊C4—1461no—
390C2×C42—731no—
391#106—731no—
392#106—731no—
393#106—731no—
394#106C4×D7311yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—731no—
401C4⋊C8—731no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8—1461no—
405C4⋊C8—1461no—
406C4⋊C8C22×D7311yescharacteristic
407C4⋊C8C22×D7311yescharacteristic
408#103—731no—
409#103—731no—
410#103—731no—
411#103C4×D7311yescharacteristic
412#102—731no—
413#102—731no—
414#102—731no—
415#102C4×D7311yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—731no—
418C22⋊C8—731no—
419C22⋊C8—731no—
420C22⋊C8—731no—
421C22⋊C8—1461no—
422C22⋊C8—1461no—
423C22⋊C8—1461no—
424C22⋊C8—1461no—
425C22⋊C8—1461no—
426C22⋊C8—1461no—
427#97—21no—
428#97—1461no—
429#97—1461no—
430C4×C8—731no—
431C4×C8—731no—
432C4×C8—731no—
433C4×C8—1461no—
434C4×C8—1461no—
435C4×C8—1461no—
436C4×C8C22×D7311yescharacteristic
437C4×C8C22×D7311yescharacteristic
438C4×C8C22×D7311yescharacteristic
439C24—1461no—
440C2×Q8—731no—
441C2×Q8—1461no—
442C2×Q8C2×C4×D7311yescharacteristic
443C2×D4—2921no—
444C2×D4—731no—
445C2×D4—1461no—
446C2×D4—1462no—
447C2×D4C2×C4×D7311yescharacteristic
448C22×C4—21no—
449C22×C4—5841no—
450C22×C4—5841no—
451C22×C4—731no—
452C22×C4—731no—
453C22×C4—731no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1461no—
458SD16—41no—
459SD16—2921no—
460SD16—1462no—
461SD16—1462no—
462M16—81no—
463M16—5841no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—5841no—
468C2×C8—5841no—
469C2×C8—731no—
470C2×C8—731no—
471C2×C8—731no—
472C2×C8—731no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8C2×C4×D7311yescharacteristic
477C2×C8C2×C4×D7311yescharacteristic
478C2×C8D4×D7311yescharacteristic
479C2×C8D4×D7311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—731no—
482C4⋊C4—731no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4—1461no—
490C4⋊C4C2×C4×D7311yescharacteristic
491C4⋊C4C2×C4×D7311yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—1461no—
494C22⋊C4—1461no—
495C22⋊C4—1461no—
496C22⋊C4—1461no—
497C22⋊C4—1461no—
498C42—21no—
499C42—731no—
500C42—731no—
501C42—731no—
502C42—1461no—
503C42C23×D7311yescharacteristic
504C23—21no—
505C23—2922no—
506C23—2922no—
507C23—5841no—
508C23—731no—
509C23—1461no—
510Q8—21no—
511Q8—21no—
512Q8—2922no—
513Q8—1461no—
514Q8—1461no—
515D4—21no—
516D4—21no—
517D4—2922no—
518D4—732no—
519D4—1461no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—2921no—
526C2×C4—2921no—
527C2×C4—2921no—
528C2×C4—5841no—
529C2×C4—5841no—
530C2×C4—5841no—
531C2×C4—731no—
532C2×C4—731no—
533C2×C4—731no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1461no—
539C2×C4—1461no—
540C2×C4—1461no—
541C2×C4C22×C4×D7311yescharacteristic
542C2×C4C2×D4×D7311yescharacteristic
543C2×C4#41×D7311yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—2921no—
552C8—2921no—
553C8—2921no—
554C8—1461no—
555C8—1461no—
556C8—1461no—
557C8—1461no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—2921no—
562C22—2921no—
563C22—5844no—
564C22—1461no—
565C22—1462no—
566C22—1461no—
567C22—1461no—
568C22C4×D4×D7311yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—2921no—
574C4—2921no—
575C4—2921no—
576C4—1461no—
577C4—1461no—
578C4—1461no—
579C4#131×D7311yescharacteristic
580C4#1798935311yescharacteristic
581C4#1798939611yescharacteristic
582C4#1798939711yescharacteristic
583C2—81no—
584C2—2922no—
585C2—2921no—
586C2#2261866011yescharacteristic
587C2#2261878711yescharacteristic
588C2#2261883111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1592C2
socleC22×C73C2×C4×D4
prime radicalC2×D4×D73C2×C4
cosocleC42×C73C24
hypercenter#1592D73
hypocenterC73#18028
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
2. #22619029C2semidirect
4. #22608824C2semidirect
5. #22608810C2semidirect
6. #22608787C2semidirect
7. #22608772C2semidirect
8. #22608765C2semidirect
9. #22608745C2semidirect
10. #22608728C2semidirect
11. #22608710C2semidirect
12. #22608402C2semidirect
14. #22608232C2semidirect
15. C73×#1592C2semidirect
27. #17988714C22semidirect
28. Q8×#10596831C22semidirect
29. C8×Dic146C22semidirect
48. #17988340C22semidirect
49. #17988337C22semidirect
50. #17988337C22semidirect
51. #17988319C22semidirect
52. Q8⋊#10596831C22semidirect
53. #17988317C22semidirect
57. #17988309C22semidirect
58. #17988308C22semidirect
59. C8×#10596831C22semidirect
60. #446×C73C22semidirect
63. #335×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
66. #322×C73C22semidirect
298. #1592D73semidirect
310. C73#18028semidirect
323. #446C2×D73semidirect
347. #335C2×D73semidirect
353. Q8⋊C8C2×D73semidirect
360. #322C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199372
#226190292
#226189632
#226088242
#226088102
#226087872
#226087722
#226087652
#226087452
#226087282
#226087102
#226084022
#226083202
#226082322
C73×#15922
#1802873