Finite Group Databasebeta

← #33056591

Subgroups — #33056591

Order 18688.

662 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620524C211yesmaximal, characteristic
2#22618903C211yesmaximal, characteristic, complemented
3#22618638C211yesmaximal, characteristic, complemented
4#22608824C211yesmaximal, characteristic, complemented
5#22608820C211yesmaximal, characteristic, complemented
6#22608816C211yesmaximal, characteristic, complemented
7#22608813C211yesmaximal, characteristic, complemented
8#22608753C211yesmaximal, characteristic, complemented
9#22608745C211yesmaximal, characteristic, complemented
10#22608743C211yesmaximal, characteristic, complemented
11#22608695C211yesmaximal, characteristic, complemented
12#22608398C211yesmaximal, characteristic, complemented
13#22608393C211yesmaximal, characteristic, complemented
14#22608210C211yesmaximal, characteristic, complemented
15C73×#1580C211yesmaximal, characteristic, complemented
16C2×#14556597—21no—
17#17989134C2211yescharacteristic
18#17989119C2211yescharacteristic
19#17988995C411yescharacteristic
20#17988975C411yescharacteristic
21#17988950C411yescharacteristic
22#17988945C411yescharacteristic
23#17988839C411yescharacteristic
24#17988837C411yescharacteristic
25#17988834C411yescharacteristic
26#17988832C411yescharacteristic
27#17988714C2211yescharacteristic
28C8×Dic146C2211yescharacteristic
29C4×#11924017C2211yescharacteristic
30C4×#11924016C2211yescharacteristic
31C4×#11924013C2211yescharacteristic
32#17988665C2211yescharacteristic
33#17988665C2211yescharacteristic
34#17988664C2211yescharacteristic
35#17988662—21no—
36#17988661—21no—
37C8×D292C2211yescharacteristic
38C8×C22⋊D73—21no—
39C8×C22⋊D73—21no—
40#17988645—21no—
41#17988643C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988609C2211yescharacteristic
44#17988552—21no—
45#17988542—21no—
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988317C2211yescharacteristic
53#17988316C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C4×D8×C73C2211yescharacteristic
61C8×D4×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924017C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71#14556597—44no—
72C2×#11924012—21no—
73C2×#11924012—21no—
74C2×#11924011—21no—
75C2×#11924011—21no—
76C2×#11924011C2×C411yescharacteristic
77C2×#11924011C2×C411yescharacteristic
78C2×C8×D73—21no—
79C2×C8×D73D411yescharacteristic
80C2×C8×D73D411yescharacteristic
81#14556590C2×C411yescharacteristic
82#14556587C2×C411yescharacteristic
83#14556584—21no—
84#14556582C2×C411yescharacteristic
85#14556578C2×C411yescharacteristic
86#14556577—21no—
87#14556573—21no—
88#14556571C2×C411yescharacteristic
89#14556566C2×C411yescharacteristic
90#14556564—21no—
91#14556562C2×C411yescharacteristic
92#14556562C2×C411yescharacteristic
93C4×Dic146C2311yescharacteristic
94C4×D292C2311yescharacteristic
95C4×C22⋊D73—21no—
96C4×C22⋊D73—21no—
97#14556550—21no—
98C42×D73C2311yescharacteristic
99#14556524C2×C411yescharacteristic
100#14556523C2×C411yescharacteristic
101#14556522C2×C411yescharacteristic
102C4⋊#10596831C2311yescharacteristic
103C4⋊#10596831C2311yescharacteristic
104#14556520—21no—
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#14556503—21no—
120#14556501—21no—
121#14556501—21no—
122#14556501C2×C411yescharacteristic
123#14556501C2×C411yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73—21no—
128C8×Dic73D411yescharacteristic
129C8×Dic73D411yescharacteristic
130C2×D8×C73C2×C411yescharacteristic
131C22×C8×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—22no—
160#11924016—22no—
161#11924013—22no—
162#11924012—42no—
163#11924012—42no—
164#11924011—22no—
165#11924011—22no—
166#11924011—42no—
167#11924011—42no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C2×D411yescharacteristic
174C2×#10596831C2×D411yescharacteristic
175C8×D73—22no—
176C8×D73—41no—
177C8×D73—42no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73C22×C411yescharacteristic
181C4⋊Dic73C22×C411yescharacteristic
182#11924007—21no—
183#11924007—21no—
184#11924007—21no—
185C22⋊Dic73—21no—
186C22⋊Dic73—21no—
187C22⋊Dic73—21no—
188C22⋊Dic73—21no—
189#11924005—21no—
190#11924005—21no—
191#11924005—21no—
192C4×Dic73—21no—
193C4×Dic73C22×C411yescharacteristic
194C4×Dic73C2×D411yescharacteristic
195C4×Dic73#4111yescharacteristic
196C2×D4×C73C22×C411yescharacteristic
197C2×D4×C73C22×C411yescharacteristic
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200D8×C73—22no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—42no—
205C2×C8×C73—42no—
206C2×C8×C73C22×C411yescharacteristic
207C2×C8×C73C22×C411yescharacteristic
208C2×C8×C73C2×D411yescharacteristic
209C2×C8×C73C2×D411yescharacteristic
210C4⋊C4×C73C22×C411yescharacteristic
211C4⋊C4×C73C22×C411yescharacteristic
212C22⋊C4×C73—21no—
213C22⋊C4×C73—21no—
214C42×C73C2411yescharacteristic
215C23×C73—21no—
216C23×C73—21no—
217C22×D73—21no—
218C22×D73C4×D411yescharacteristic
219D4×C73—21no—
220D4×C73—21no—
221D4×C73—21no—
222D4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73C23×C411yescharacteristic
230C2×C4×C73C22×D411yescharacteristic
231C2×C4×C73C2×#4111yescharacteristic
232C22⋊D73—42no—
233C22⋊D73—42no—
234C22⋊D73—42no—
235C22⋊D73—42no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73C4×D411yescharacteristic
240C2×Dic73C4×D411yescharacteristic
241C2×Dic73C4×D411yescharacteristic
242D292—21no—
243D292—21no—
244D292—42no—
245C4×D73—21no—
246C4×D73—21no—
247C4×D73—21no—
248C4×D73—21no—
249C4×D73—41no—
250C4×D73—41no—
251C4×D73—41no—
252Dic146—21no—
253Dic146—21no—
254Dic146—42no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—41no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73#13112yescomplemented
262#10596831—21no—
263#10596831—21no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267#10596831#13112yescomplemented
268#10596831AGL(1,ℤ/8)12yes—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73C2×C4×D411yescharacteristic
276C2×D73—21no—
277C2×D73—21no—
278C2×D73—21no—
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—41no—
282C4×C73—21no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73C2×#13111yescharacteristic
286C4×C73C2×#13111yescharacteristic
287C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C73#57511yescharacteristic
289Dic73—21no—
290Dic73—21no—
291Dic73—21no—
292Dic73—41no—
293Dic73—41no—
294Dic73—41no—
295#17966—731nomaximal, Sylow
296C2×C73—81no—
297C2×C73—81no—
298C2×C73#293111yescharacteristic
299C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
300C2×C73#295511yescharacteristic
301D73—41no—
302D73—81no—
303#3171—731no—
304#2966—731no—
305#2931—731no—
306#1590—731no—
307#1590—731no—
308#1589—731no—
309#1589—731no—
310#1580—731no—
311#1580D7311yescharacteristic, complemented
312SD16⋊C8—731no—
313SD16⋊C8—731no—
314#1569—731no—
315#1496—731no—
316#1495—731no—
317C8×M16—731no—
318C73#1796611yescharacteristic, complemented, Sylow
319C2×#131—1461no—
320#532—731no—
321#529—731no—
322#501—731no—
323#496—731no—
324#490—731no—
325#489—731no—
326#469—731no—
327#469—731no—
328#468—731no—
329#468—731no—
330#446—731no—
331C8×Q8—731no—
332C4×SD16—731no—
333C4×SD16—731no—
334C4×D8—731no—
335C4×D8C2×D7311yescharacteristic
336#436—731no—
337#436—731no—
338#436—731no—
339#436—1461no—
340#435—1461no—
341C8×D4—731no—
342C8×D4—1461no—
343C8×D4—1461no—
344C8×D4C2×D7311yescharacteristic
345C8×D4C2×D7311yescharacteristic
346#433—1461no—
347#432—731no—
348#431—731no—
349#423—731no—
350#408—1461no—
351#405—1461no—
352C4×M16—731no—
353C2×C4×C8—731no—
354#335—731no—
355#335—731no—
356#334—731no—
357#334C2×D7311yescharacteristic
358Q8⋊C8—731no—
359Q8⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8C2×D7311yescharacteristic
365D4⋊C8C2×D7311yescharacteristic
366#322—731no—
367#322C2×D7311yescharacteristic
368C82—731no—
369C82—731no—
370C2×#41—1461no—
371C2×SD16—731no—
372C2×SD16—731no—
373C2×D8—731no—
374C2×D8C4×D7311yescharacteristic
375#131—2924no—
376C2×M16—731no—
377C2×M16—731no—
378C2×M16—1461no—
379C2×M16—1461no—
380C2×M16—1461no—
381C2×M16—1461no—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—731no—
385C22×C8—731no—
386C22×C8—1461no—
387C4⋊Q8—731no—
388#127—731no—
389#126—1461no—
390#125—731no—
391#124—731no—
392#124—1461no—
393#123—1461no—
394C22⋊Q8—731no—
395#121—731no—
396#121—731no—
397#121—731no—
398#121—1461no—
399C4×Q8—731no—
400C4×D4—731no—
401C4×D4—1461no—
402C4×D4—1461no—
403C4×D4C22×D7311yescharacteristic
404C4×D4C22×D7311yescharacteristic
405#117—1461no—
406C2×C42—731no—
407#107—731no—
408#107C4×D7311yescharacteristic
409#106—731no—
410#106—731no—
411C4⋊C8—731no—
412C4⋊C8—731no—
413C4⋊C8—1461no—
414C4⋊C8—1461no—
415C4⋊C8—1461no—
416C4⋊C8—1461no—
417C4⋊C8C22×D7311yescharacteristic
418C4⋊C8C22×D7311yescharacteristic
419#103—731no—
420#103—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102C4×D7311yescharacteristic
426#102C4×D7311yescharacteristic
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435#97—731no—
436#97—731no—
437#97—1461no—
438#97—1461no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
444C4×C8—1461no—
445C4×C8C22×D7311yescharacteristic
446C4×C8C22×D7311yescharacteristic
447C4×C8C22×D7311yescharacteristic
448#41—2922no—
449#41—2922no—
450C2×Q8—731no—
451C2×Q8—1461no—
452C2×D4—731no—
453C2×D4—1461no—
454C2×D4—1461no—
455C2×D4—1461no—
456C2×D4—1461no—
457C2×D4—1461no—
458C2×D4C2×C4×D7311yescharacteristic
459C2×D4C2×C4×D7311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—1461no—
466SD16—1462no—
467SD16—1462no—
468D8—22no—
469D8—1462no—
470M16—2922no—
471M16—2922no—
472M16—2922no—
473M16—2922no—
474M16—1462no—
475M16—1462no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—42no—
481C2×C8—2922no—
482C2×C8—2921no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—731no—
487C2×C8—1462no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8C2×C4×D7311yescharacteristic
492C2×C8C2×C4×D7311yescharacteristic
493C2×C8D4×D7311yescharacteristic
494C2×C8D4×D7311yescharacteristic
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4C2×C4×D7311yescharacteristic
503C4⋊C4C2×C4×D7311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C22⋊C4—1461no—
511C22⋊C4—1461no—
512C22⋊C4—1461no—
513C42—731no—
514C42—731no—
515C42—731no—
516C42—1461no—
517C42C23×D7311yescharacteristic
518C23—21no—
519C23—21no—
520C23—731no—
521C23—1461no—
522Q8—2922no—
523Q8—1461no—
524Q8—1461no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—2922no—
530D4—2922no—
531D4—2922no—
532D4—2922no—
533D4—2922no—
534D4—1461no—
535D4—1461no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—731no—
546C2×C4—731no—
547C2×C4—731no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4C22×C4×D7311yescharacteristic
556C2×C4C2×D4×D7311yescharacteristic
557C2×C4#41×D7311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—2921no—
565C8—2921no—
566C8—2921no—
567C8—732no—
568C8—732no—
569C8—1461no—
570C8—1461no—
571C8#1455659712yescomplemented
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—2921no—
579C22—2921no—
580C22—2921no—
581C22—1461no—
582C22—1461no—
583C22—1461no—
584C22C4×D4×D7311yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—2921no—
589C4—2921no—
590C4—2921no—
591C4—1461no—
592C4—1461no—
593C4—1461no—
594C4#131×D7311yescharacteristic
595C4C2×#1455659711yescharacteristic
596C4AGL(1,ℤ/8)×D7311yescharacteristic
597C4#1798938311yescharacteristic
598C2—81no—
599C2—81no—
600C2—2921no—
601C2—5841no—
602C2#2261863811yescharacteristic
603C2#2261874211yescharacteristic
604C2#2261883111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1580C2
socleC22×C73C2×C4×D4
prime radical#22620524C2
cosocleC42×C73C24
hypercenter#1580D73
hypocenterC73#17966
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #22618903C2semidirect
3. #22618638C2semidirect
4. #22608824C2semidirect
5. #22608820C2semidirect
6. #22608816C2semidirect
7. #22608813C2semidirect
8. #22608753C2semidirect
9. #22608745C2semidirect
10. #22608743C2semidirect
11. #22608695C2semidirect
12. #22608398C2semidirect
13. #22608393C2semidirect
14. #22608210C2semidirect
15. C73×#1580C2semidirect
261. C8×C73#131semidirect
267. #10596831#131semidirect
311. #1580D73semidirect
318. C73#17966semidirect
571. C8#14556597semidirect

Maximal subgroups

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

subgroupindex
#226205242
#226189032
#226186382
#226088242
#226088202
#226088162
#226088132
#226087532
#226087452
#226087432
#226086952
#226083982
#226083932
#226082102
C73×#15802
#1796673