Finite Group Databasebeta

← #33057835

Subgroups — #33057835

Order 18688.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620524C211yesmaximal, characteristic
2#22618932C211yesmaximal, characteristic, complemented
3#22618676C211yesmaximal, characteristic, complemented
4#22608842C211yesmaximal, characteristic, complemented
5#22608819C211yesmaximal, characteristic, complemented
6#22608808C211yesmaximal, characteristic, complemented
7#22608796C211yesmaximal, characteristic, complemented
8#22608769C211yesmaximal, characteristic, complemented
9#22608740C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608682C211yesmaximal, characteristic, complemented
12#22608346C211yesmaximal, characteristic, complemented
13#22608341C211yesmaximal, characteristic, complemented
14#22608235C211yesmaximal, characteristic, complemented
15C73×#1581C211yesmaximal, characteristic, complemented
16C2×#14556599—21no—
17#17989134C2211yescharacteristic
18#17989119C2211yescharacteristic
19#17988995C411yescharacteristic
20#17988975C411yescharacteristic
21#17988950C411yescharacteristic
22#17988945C411yescharacteristic
23#17988839C411yescharacteristic
24#17988837C411yescharacteristic
25#17988834C411yescharacteristic
26#17988832C411yescharacteristic
27#17988717C2211yescharacteristic
28#17988711C2211yescharacteristic
29C4×#11924017C2211yescharacteristic
30C4×#11924016C2211yescharacteristic
31C4×#11924013C2211yescharacteristic
32#17988665C2211yescharacteristic
33#17988664C2211yescharacteristic
34#17988662—21no—
35#17988658—21no—
36#17988656—21no—
37#17988655—21no—
38C8×D292C2211yescharacteristic
39D4×#10596831C2211yescharacteristic
40#17988645—21no—
41#17988639C2211yescharacteristic
42C4⋊C8×D73C2211yescharacteristic
43#17988552—21no—
44#17988542—21no—
45C4×#11924011C2211yescharacteristic
46C4×#11924011C2211yescharacteristic
47C4×#11924011C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988338C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988317C2211yescharacteristic
53#17988316C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C4×D8×C73C2211yescharacteristic
61#436×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924017C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71#14556599—44no—
72C2×#11924012—21no—
73C2×#11924011—21no—
74C2×#11924011—21no—
75C2×#11924011C2×C411yescharacteristic
76C2×#11924011C2×C411yescharacteristic
77C2×#11924011D411yescharacteristic
78C2×#11924011D411yescharacteristic
79C22×#10596831—21no—
80C2×C8×D73—21no—
81C2×C8×D73—21no—
82#14556590C2×C411yescharacteristic
83#14556587C2×C411yescharacteristic
84#14556584—21no—
85#14556582C2×C411yescharacteristic
86#14556578C2×C411yescharacteristic
87#14556577—21no—
88#14556573—21no—
89#14556571C2×C411yescharacteristic
90#14556566C2×C411yescharacteristic
91#14556564—21no—
92#14556562C2×C411yescharacteristic
93#14556562C2×C411yescharacteristic
94C4×Dic146C2311yescharacteristic
95C4×D292C2311yescharacteristic
96C4×C22⋊D73—21no—
97C4×C22⋊D73—21no—
98#14556550—21no—
99C42×D73C2311yescharacteristic
100#14556524C2×C411yescharacteristic
101#14556523C2×C411yescharacteristic
102#14556522C2×C411yescharacteristic
103C4⋊#10596831C2311yescharacteristic
104C4⋊#10596831C2311yescharacteristic
105#14556520—21no—
106#14556520—21no—
107#14556520—21no—
108#14556516C2×C411yescharacteristic
109#14556514C2×C411yescharacteristic
110#14556513C2×C411yescharacteristic
111#14556512C2×C411yescharacteristic
112#14556512C2×C411yescharacteristic
113#14556511C2×C411yescharacteristic
114C22⋊#10596831—21no—
115C22⋊#10596831—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556501—21no—
120#14556501—21no—
121#14556501C2×C411yescharacteristic
122#14556501C2×C411yescharacteristic
123#14556501D411yescharacteristic
124#14556501D411yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C4×#10596831C2311yescharacteristic
128C8×Dic73—21no—
129C8×Dic73—21no—
130C2×D8×C73C2×C411yescharacteristic
131C2×M16×C73—21no—
132C22×C8×C73—21no—
133C4×D4×C73C2311yescharacteristic
134C4×D4×C73C2311yescharacteristic
135#107×C73C2×C411yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138#102×C73C2×C411yescharacteristic
139#102×C73C2×C411yescharacteristic
140C22⋊C8×C73—21no—
141C22⋊C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145#11924028—42no—
146#11924028—42no—
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×C22⋊D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73C22×C411yescharacteristic
157C2×C4×D73C2×D411yescharacteristic
158C2×C4×D73#4111yescharacteristic
159#11924017—41no—
160#11924016—22no—
161#11924013—22no—
162#11924012—42no—
163#11924011—22no—
164#11924011—22no—
165#11924011—41no—
166#11924011—41no—
167#11924011—42no—
168#11924011—42no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—42no—
173C2×#10596831C22×C411yescharacteristic
174C2×#10596831C22×C411yescharacteristic
175C2×#10596831C2×D411yescharacteristic
176C2×#10596831C2×D411yescharacteristic
177C8×D73—42no—
178C8×D73—42no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73C22×C411yescharacteristic
182C4⋊Dic73C22×C411yescharacteristic
183#11924007—21no—
184#11924007—21no—
185#11924007—21no—
186C22⋊Dic73—21no—
187C22⋊Dic73—21no—
188C22⋊Dic73—21no—
189C22⋊Dic73—21no—
190#11924005—21no—
191#11924005—21no—
192#11924005—21no—
193C4×Dic73—21no—
194C4×Dic73C22×C411yescharacteristic
195C4×Dic73C2×D411yescharacteristic
196C4×Dic73#4111yescharacteristic
197C2×D4×C73C22×C411yescharacteristic
198C2×D4×C73C22×C411yescharacteristic
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201D8×C73—41no—
202M16×C73—42no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—42no—
207C2×C8×C73C22×C411yescharacteristic
208C2×C8×C73C22×C411yescharacteristic
209C2×C8×C73C2×D411yescharacteristic
210C2×C8×C73C2×D411yescharacteristic
211C4⋊C4×C73C22×C411yescharacteristic
212C4⋊C4×C73C22×C411yescharacteristic
213C22⋊C4×C73—21no—
214C22⋊C4×C73—21no—
215C42×C73C2411yescharacteristic
216C23×C73—21no—
217C23×C73—21no—
218C22×D73—21no—
219C22×D73C4×D411yescharacteristic
220D4×C73—21no—
221D4×C73—21no—
222D4×C73—21no—
223D4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73C23×C411yescharacteristic
231C2×C4×C73C22×D411yescharacteristic
232C2×C4×C73C2×#4111yescharacteristic
233C22⋊D73—42no—
234C22⋊D73—42no—
235C22⋊D73—81no—
236C22⋊D73—81no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73C4×D411yescharacteristic
241C2×Dic73C4×D411yescharacteristic
242C2×Dic73C4×D411yescharacteristic
243D292—21no—
244D292—21no—
245D292—42no—
246C4×D73—21no—
247C4×D73—21no—
248C4×D73—21no—
249C4×D73—21no—
250C4×D73—41no—
251C4×D73—41no—
252C4×D73—41no—
253Dic146—21no—
254Dic146—21no—
255Dic146—42no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73—41no—
262C8×C73AGL(1,ℤ/8)12yes—
263#10596831—22no—
264#10596831—21no—
265#10596831—21no—
266#10596831—21no—
267#10596831—41no—
268#10596831—41no—
269#10596831#13112yescomplemented
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73C2×C4×D411yescharacteristic
277C2×D73—21no—
278C2×D73—21no—
279C2×D73—21no—
280C2×D73—41no—
281C2×D73—41no—
282C2×D73—41no—
283C4×C73—21no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73C2×#13111yescharacteristic
287C4×C73#56811yescharacteristic
288C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C73#57511yescharacteristic
290Dic73—21no—
291Dic73—21no—
292Dic73—21no—
293Dic73—41no—
294Dic73—41no—
295Dic73—41no—
296#18076—731nomaximal, Sylow
297C2×C73—81no—
298C2×C73—81no—
299C2×C73#293511yescharacteristic
300C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
301C2×C73#295611yescharacteristic
302D73—41no—
303D73—81no—
304#3171—731no—
305#2969—731no—
306#2935—731no—
307#1594—731no—
308#1590—731no—
309#1588—731no—
310#1586—731no—
311#1582—731no—
312#1581D7311yescharacteristic, complemented
313SD16⋊C8—731no—
314C8×D8—731no—
315#1565—731no—
316#1484—731no—
317#1483—731no—
318#1455—731no—
319C73#1807611yescharacteristic, complemented, Sylow
320C2×#131—1461no—
321#532—731no—
322#529—731no—
323#501—731no—
324#496—731no—
325#490—731no—
326#489—731no—
327#469—731no—
328#469—731no—
329#468—731no—
330#468—731no—
331#446—731no—
332C8×Q8—731no—
333C4×SD16—731no—
334C4×SD16—731no—
335C4×D8—731no—
336C4×D8C2×D7311yescharacteristic
337#436—731no—
338#436—731no—
339#436—1461no—
340#436C2×D7311yescharacteristic
341#435—1461no—
342#435—1461no—
343#435—1461no—
344C8×D4—731no—
345C8×D4—731no—
346C8×D4C2×D7311yescharacteristic
347#433—1461no—
348#431—731no—
349C2×C4⋊C8—731no—
350#408—1461no—
351#405—1461no—
352C4×M16—731no—
353C4×M16—731no—
354C4×M16—731no—
355#335—731no—
356#335C2×D7311yescharacteristic
357#334—731no—
358#334—731no—
359Q8⋊C8—731no—
360Q8⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8C2×D7311yescharacteristic
366D4⋊C8C2×D7311yescharacteristic
367#322—731no—
368#322—731no—
369#322C2×D7311yescharacteristic
370C82—731no—
371C2×#41—1461no—
372C2×SD16—731no—
373C2×SD16—731no—
374C2×D8—731no—
375C2×D8C4×D7311yescharacteristic
376#131—2924no—
377C2×M16—21no—
378C2×M16—731no—
379C2×M16—731no—
380C2×M16—731no—
381C2×M16—731no—
382C2×M16—1461no—
383C2×M16—1461no—
384C2×M16—1461no—
385C22×C8—21no—
386C22×C8—1461no—
387C22×C8—1461no—
388C22×C8—1461no—
389C4⋊Q8—731no—
390#127—731no—
391#126—1461no—
392#125—731no—
393#124—731no—
394#124—1461no—
395#123—1461no—
396C22⋊Q8—731no—
397#121—731no—
398#121—731no—
399#121—731no—
400#121—1461no—
401C4×Q8—731no—
402C4×D4—731no—
403C4×D4—1461no—
404C4×D4—1461no—
405C4×D4C22×D7311yescharacteristic
406C4×D4C22×D7311yescharacteristic
407#117—1461no—
408C2×C42—731no—
409#107—731no—
410#107C4×D7311yescharacteristic
411#106—731no—
412#106—731no—
413C4⋊C8—731no—
414C4⋊C8—731no—
415C4⋊C8—1461no—
416C4⋊C8—1461no—
417C4⋊C8—1461no—
418C4⋊C8C22×D7311yescharacteristic
419C4⋊C8C22×D7311yescharacteristic
420#103—731no—
421#103—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102—731no—
426#102C4×D7311yescharacteristic
427#102C4×D7311yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435#97—731no—
436#97—731no—
437#97—731no—
438#97—731no—
439#97—1461no—
440#97—1461no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
444C4×C8—1461no—
445C4×C8—1461no—
446C4×C8C22×D7311yescharacteristic
447C4×C8C22×D7311yescharacteristic
448C4×C8C22×D7311yescharacteristic
449#41—2922no—
450#41—2922no—
451C2×Q8—731no—
452C2×Q8—1461no—
453C2×D4—731no—
454C2×D4—1461no—
455C2×D4—1461no—
456C2×D4—1461no—
457C2×D4—1461no—
458C2×D4—1461no—
459C2×D4C2×C4×D7311yescharacteristic
460C2×D4C2×C4×D7311yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—731no—
466C22×C4—1461no—
467SD16—2921no—
468SD16—1462no—
469D8—41no—
470D8—1462no—
471M16—42no—
472M16—2921no—
473M16—2921no—
474M16—2922no—
475M16—2922no—
476M16—2922no—
477M16—1462no—
478M16—1462no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
483C2×C8—2922no—
484C2×C8—2922no—
485C2×C8—2922no—
486C2×C8—731no—
487C2×C8—731no—
488C2×C8—731no—
489C2×C8—731no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8C2×C4×D7311yescharacteristic
494C2×C8C2×C4×D7311yescharacteristic
495C2×C8D4×D7311yescharacteristic
496C2×C8D4×D7311yescharacteristic
497C4⋊C4—731no—
498C4⋊C4—731no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4—1461no—
503C4⋊C4—1461no—
504C4⋊C4C2×C4×D7311yescharacteristic
505C4⋊C4C2×C4×D7311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C22⋊C4—1461no—
511C22⋊C4—1461no—
512C22⋊C4—1461no—
513C22⋊C4—1461no—
514C22⋊C4—1461no—
515C42—731no—
516C42—731no—
517C42—731no—
518C42—1461no—
519C42C23×D7311yescharacteristic
520C23—21no—
521C23—21no—
522C23—731no—
523C23—1461no—
524Q8—2922no—
525Q8—1461no—
526Q8—1461no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—2922no—
532D4—2922no—
533D4—2922no—
534D4—5841no—
535D4—5841no—
536D4—1461no—
537D4—1461no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—731no—
548C2×C4—731no—
549C2×C4—731no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4—1461no—
557C2×C4C22×C4×D7311yescharacteristic
558C2×C4C2×D4×D7311yescharacteristic
559C2×C4#41×D7311yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—2921no—
567C8—2921no—
568C8—732no—
569C8—1462no—
570C8—1461no—
571C8—1461no—
572C8—1461no—
573C8#1455661512yes—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—2921no—
581C22—2921no—
582C22—2921no—
583C22—1461no—
584C22—1461no—
585C22—1461no—
586C22C4×D4×D7311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—2921no—
591C4—2921no—
592C4—2921no—
593C4—1461no—
594C4—1461no—
595C4—1461no—
596C4#131×D7311yescharacteristic
597C4#1798935311yescharacteristic
598C4C2×#1455661511yescharacteristic
599C4#1798938411yescharacteristic
600C2—81no—
601C2—81no—
602C2—2921no—
603C2—5841no—
604C2#2261867211yescharacteristic
605C2C4×#1455661511yescharacteristic
606C2#2261883911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1581C2
socleC22×C73C2×C4×D4
prime radical#22620524C2
cosocleC42×C73C24
hypercenter#1581D73
hypocenterC73#18076
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #22618932C2semidirect
3. #22618676C2semidirect
4. #22608842C2semidirect
5. #22608819C2semidirect
6. #22608808C2semidirect
7. #22608796C2semidirect
8. #22608769C2semidirect
9. #22608740C2semidirect
10. C8×#11924013C2semidirect
11. #22608682C2semidirect
12. #22608346C2semidirect
13. #22608341C2semidirect
14. #22608235C2semidirect
15. C73×#1581C2semidirect
269. #10596831#131semidirect
312. #1581D73semidirect
319. C73#18076semidirect

Maximal subgroups

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

subgroupindex
#226205242
#226189322
#226186762
#226088422
#226088192
#226088082
#226087962
#226087692
#226087402
C8×#119240132
#226086822
#226083462
#226083412
#226082352
C73×#15812
#1807673