Finite Group Databasebeta

← #33056824

Subgroups — #33056824

Order 18688.

624 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620507C211yesmaximal, characteristic
2#22619008C211yesmaximal, characteristic, complemented
3#22619005C211yesmaximal, characteristic, complemented
4#22608797C211yesmaximal, characteristic, complemented
5#22608796C211yesmaximal, characteristic, complemented
6#22608794C211yesmaximal, characteristic, complemented
7#22608763C211yesmaximal, characteristic, complemented
8#22608760C211yesmaximal, characteristic, complemented
9#22608758C211yesmaximal, characteristic, complemented
10#22608757C211yesmaximal, characteristic, complemented
11#22608691C211yesmaximal, characteristic, complemented
12#22608398C211yesmaximal, characteristic, complemented
13#22608398C211yesmaximal, characteristic, complemented
14#22608222C211yesmaximal, characteristic, complemented
15C73×#1586C211yesmaximal, characteristic, complemented
16#17989134C2211yescharacteristic
17#17989134C2211yescharacteristic
18#17988991C411yescharacteristic
19#17988962C411yescharacteristic
20#17988932C411yescharacteristic
21#17988932C411yescharacteristic
22#17988824C411yescharacteristic
23#17988822C411yescharacteristic
24#17988822C411yescharacteristic
25#17988820C411yescharacteristic
26C4×D584C2211yescharacteristic
27C4×#11924013C2211yescharacteristic
28C4×#11924013C2211yescharacteristic
29#17988666C2211yescharacteristic
30#17988665C2211yescharacteristic
31#17988664C2211yescharacteristic
32#17988661—21no—
33#17988658—21no—
34#17988656—21no—
35#17988655—21no—
36C8×D292C2211yescharacteristic
37D4×#10596831C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988643C2211yescharacteristic
40#17988643C2211yescharacteristic
41#17988638C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988555—21no—
44#17988553—21no—
45#17988552—21no—
46#17988552—21no—
47C4×C8×D73C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988316C2211yescharacteristic
52#17988316C2211yescharacteristic
53D4⋊#10596831C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988308C2211yescharacteristic
60C4×D8×C73C2211yescharacteristic
61#436×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924028—21no—
69C2×D584C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924012—21no—
73C2×#11924011—21no—
74C2×#11924011—21no—
75C22×#10596831—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C2×C8×D73C2×C411yescharacteristic
79C2×C8×D73C2×C411yescharacteristic
80#14556590C2×C411yescharacteristic
81#14556590C2×C411yescharacteristic
82#14556587C2×C411yescharacteristic
83#14556587C2×C411yescharacteristic
84#14556577—21no—
85#14556577—21no—
86#14556566C2×C411yescharacteristic
87#14556566C2×C411yescharacteristic
88#14556564—21no—
89#14556564—21no—
90#14556562C2×C411yescharacteristic
91#14556562C2×C411yescharacteristic
92C4×D292C2311yescharacteristic
93C4×D292C2311yescharacteristic
94C4×C22⋊D73—21no—
95C4×C22⋊D73—21no—
96C42×D73C2311yescharacteristic
97#14556525C2×C411yescharacteristic
98#14556524C2×C411yescharacteristic
99#14556524C2×C411yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102#14556520—21no—
103#14556520D411yescharacteristic
104#14556520D411yescharacteristic
105#14556513C2×C411yescharacteristic
106#14556513C2×C411yescharacteristic
107#14556512C2×C411yescharacteristic
108#14556512C2×C411yescharacteristic
109#14556511C2×C411yescharacteristic
110#14556511C2×C411yescharacteristic
111C22⋊#10596831—21no—
112C22⋊#10596831—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503D411yescharacteristic
121#14556503D411yescharacteristic
122#14556501—21no—
123#14556501—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73C2×C411yescharacteristic
128C8×Dic73C2×C411yescharacteristic
129C2×D8×C73C2×C411yescharacteristic
130C2×M16×C73—21no—
131C22×C8×C73—21no—
132C4×D4×C73C2311yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#107×C73C2×C411yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#102×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—81no—
145#11924028—81no—
146#11924028—81no—
147#11924028—81no—
148C2×Dic146—21no—
149C2×Dic146—21no—
150C2×D292—21no—
151C2×D292—21no—
152C2×D292C22×C411yescharacteristic
153C2×D292C22×C411yescharacteristic
154C2×C22⋊D73—21no—
155C2×C22⋊D73—21no—
156C2×C22⋊D73—21no—
157C2×C22⋊D73—21no—
158C2×C22⋊D73—21no—
159C2×C22⋊D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—21no—
162C2×C4×D73C22×C411yescharacteristic
163C2×C4×D73C2×D411yescharacteristic
164C2×C4×D73#4111yescharacteristic
165D584—41no—
166#11924013—41no—
167#11924013—41no—
168#11924012—81no—
169#11924011—81no—
170#11924011—81no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—81no—
175C2×#10596831C22×C411yescharacteristic
176C2×#10596831C22×C411yescharacteristic
177C2×#10596831C2×D411yescharacteristic
178C2×#10596831C2×D411yescharacteristic
179C8×D73—41no—
180C8×D73—41no—
181C8×D73—81no—
182C8×D73—81no—
183C4⋊Dic73C22×C411yescharacteristic
184C4⋊Dic73C22×C411yescharacteristic
185#11924007—21no—
186#11924007—21no—
187C22⋊Dic73—21no—
188C22⋊Dic73—21no—
189#11924005—21no—
190#11924005—21no—
191#11924005—21no—
192#11924005—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—41no—
201M16×C73—81no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—81no—
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×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—81no—
234C22⋊D73—81no—
235C22⋊D73—81no—
236C22⋊D73—81no—
237C22⋊D73—81no—
238C22⋊D73—81no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73C4×D411yescharacteristic
242C2×Dic73C4×D411yescharacteristic
243C2×Dic73C4×D411yescharacteristic
244D292—21no—
245D292—21no—
246D292—21no—
247D292—21no—
248D292—81no—
249D292—81no—
250C4×D73—21no—
251C4×D73—21no—
252C4×D73—21no—
253C4×D73—21no—
254C4×D73—41no—
255C4×D73—41no—
256C4×D73—41no—
257C4×D73—41no—
258C4×D73—41no—
259Dic146—81no—
260Dic146—81no—
261C8×C73—21no—
262C8×C73—21no—
263C8×C73—21no—
264C8×C73—21no—
265C8×C73—41no—
266C8×C73—41no—
267C8×C73—41no—
268#10596831—21no—
269#10596831—21no—
270#10596831—21no—
271#10596831—21no—
272#10596831—41no—
273#10596831—41no—
274#10596831—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73C2×C4×D411yescharacteristic
282C2×D73—21no—
283C2×D73—21no—
284C2×D73—21no—
285C2×D73—41no—
286C2×D73—41no—
287C2×D73—41no—
288C2×D73—41no—
289C2×D73—41no—
290C2×D73—41no—
291C4×C73—21no—
292C4×C73—41no—
293C4×C73—41no—
294C4×C73#56811yescharacteristic
295C4×C73#56811yescharacteristic
296C4×C73#57611yescharacteristic
297C4×C73#57611yescharacteristic
298Dic73—21no—
299Dic73—21no—
300Dic73—21no—
301Dic73—41no—
302Dic73—41no—
303#17989—731nomaximal, Sylow
304C2×C73—81no—
305C2×C73—81no—
306C2×C73#293211yescharacteristic
307C2×C73#294811yescharacteristic
308C2×C73#295711yescharacteristic
309D73—41no—
310D73—81no—
311D73—81no—
312#3169—731no—
313#2981—731no—
314#2981—731no—
315#1586—731no—
316#1586—731no—
317#1586—731no—
318#1586D7311yescharacteristic, complemented
319#1581—731no—
320#1581—731no—
321#1581—731no—
322#1581—731no—
323#1568—731no—
324#1496—731no—
325#1496—731no—
326#1452—731no—
327C73#1798911yescharacteristic, complemented, Sylow
328#532—731no—
329#532—731no—
330#500—731no—
331#493—731no—
332#486—731no—
333#486—731no—
334#466—731no—
335#466—731no—
336#466—731no—
337#466—731no—
338C4×D8—731no—
339C4×D8—731no—
340C4×D8—731no—
341C4×D8C2×D7311yescharacteristic
342#436—731no—
343#436—731no—
344#436—731no—
345#436C2×D7311yescharacteristic
346#435—1461no—
347#435—1461no—
348#435—1461no—
349#435—1461no—
350C8×D4—731no—
351C8×D4—731no—
352C8×D4—731no—
353C8×D4C2×D7311yescharacteristic
354#432—731no—
355#432—731no—
356#431—731no—
357#431—731no—
358#408—1461no—
359#408—1461no—
360#408—1461no—
361#408—1461no—
362C2×C4×C8—731no—
363#335—731no—
364#335—731no—
365#334—731no—
366#334C2×D7311yescharacteristic
367D4⋊C8—731no—
368D4⋊C8—731no—
369D4⋊C8—731no—
370D4⋊C8—731no—
371D4⋊C8—731no—
372D4⋊C8—731no—
373D4⋊C8C2×D7311yescharacteristic
374D4⋊C8C2×D7311yescharacteristic
375#322—731no—
376#322—731no—
377#322—731no—
378#322C2×D7311yescharacteristic
379C2×#41—1461no—
380C2×#41—1461no—
381C2×D8—731no—
382C2×D8—731no—
383C2×D8—731no—
384C2×D8C4×D7311yescharacteristic
385C2×M16—21no—
386C2×M16—1461no—
387C2×M16—1461no—
388C2×M16—1461no—
389C22×C8—21no—
390C22×C8—731no—
391C22×C8—731no—
392C22×C8—1461no—
393C22×C8—1461no—
394C22×C8—1461no—
395C4⋊Q8—731no—
396C4⋊Q8—731no—
397#127—731no—
398#127—731no—
399#124—1461no—
400#124—1461no—
401#121—731no—
402#121—731no—
403#121—731no—
404#121—731no—
405#121—1461no—
406#121—1461no—
407C4×D4—731no—
408C4×D4—731no—
409C4×D4—1461no—
410C4×D4—1461no—
411C4×D4C22×D7311yescharacteristic
412C4×D4C22×D7311yescharacteristic
413C2×C42—731no—
414#107—731no—
415#107—731no—
416#107—731no—
417#107C4×D7311yescharacteristic
418C4⋊C8—731no—
419C4⋊C8—731no—
420C4⋊C8—731no—
421C4⋊C8—731no—
422C4⋊C8—1461no—
423C4⋊C8C22×D7311yescharacteristic
424C4⋊C8C22×D7311yescharacteristic
425#102—731no—
426#102—731no—
427#102—731no—
428#102—731no—
429#102—731no—
430#102—731no—
431#102C4×D7311yescharacteristic
432#102C4×D7311yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—731no—
436C22⋊C8—731no—
437C22⋊C8—1461no—
438C22⋊C8—1461no—
439C22⋊C8—1461no—
440C22⋊C8—1461no—
441C22⋊C8—1461no—
442C22⋊C8—1461no—
443C22⋊C8—1461no—
444C22⋊C8—1461no—
445C22⋊C8—1461no—
446#97—1461no—
447#97—1461no—
448C4×C8—731no—
449C4×C8—731no—
450C4×C8—731no—
451C4×C8—731no—
452C4×C8—731no—
453C4×C8C22×D7311yescharacteristic
454C4×C8C22×D7311yescharacteristic
455C4×C8C22×D7311yescharacteristic
456#41—5841no—
457#41—5841no—
458#41—5841no—
459#41—5841no—
460C2×Q8—1461no—
461C2×Q8—1461no—
462C2×D4—731no—
463C2×D4—731no—
464C2×D4—1461no—
465C2×D4—1461no—
466C2×D4—1461no—
467C2×D4—1461no—
468C2×D4—1461no—
469C2×D4—1461no—
470C2×D4—1461no—
471C2×D4—1461no—
472C2×D4C2×C4×D7311yescharacteristic
473C2×D4C2×C4×D7311yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—731no—
477C22×C4—731no—
478C22×C4—731no—
479C22×C4—1461no—
480C22×C4—1461no—
481D8—41no—
482D8—2921no—
483D8—2921no—
484D8—2921no—
485M16—81no—
486M16—5841no—
487M16—5841no—
488M16—5841no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—81no—
493C2×C8—2921no—
494C2×C8—2921no—
495C2×C8—5841no—
496C2×C8—5841no—
497C2×C8—5841no—
498C2×C8—731no—
499C2×C8—731no—
500C2×C8—731no—
501C2×C8—731no—
502C2×C8—1461no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8C2×C4×D7311yescharacteristic
506C2×C8C2×C4×D7311yescharacteristic
507C2×C8D4×D7311yescharacteristic
508C2×C8D4×D7311yescharacteristic
509C4⋊C4—731no—
510C4⋊C4—731no—
511C4⋊C4—1461no—
512C4⋊C4—1461no—
513C4⋊C4C2×C4×D7311yescharacteristic
514C4⋊C4C2×C4×D7311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—1461no—
518C22⋊C4—1461no—
519C22⋊C4—1461no—
520C22⋊C4—1461no—
521C22⋊C4—1461no—
522C22⋊C4—1461no—
523C42—731no—
524C42—731no—
525C42—731no—
526C42C23×D7311yescharacteristic
527C23—21no—
528C23—21no—
529C23—731no—
530C23—1461no—
531C23—1461no—
532Q8—5841no—
533Q8—5841no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—5841no—
539D4—5841no—
540D4—5841no—
541D4—5841no—
542D4—5841no—
543D4—5841no—
544D4—5841no—
545D4—5841no—
546D4—1461no—
547D4—1461no—
548D4—1461no—
549D4—1461no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—2921no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—731no—
562C2×C4—731no—
563C2×C4—731no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4C22×C4×D7311yescharacteristic
571C2×C4C2×D4×D7311yescharacteristic
572C2×C4#41×D7311yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—2921no—
581C8—2921no—
582C8—2921no—
583C8—1461no—
584C8—1461no—
585C8—1461no—
586C8—1461no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—2921no—
594C22—2921no—
595C22—2921no—
596C22—2921no—
597C22—2921no—
598C22—2921no—
599C22—1461no—
600C22—1461no—
601C22—1461no—
602C22C4×D4×D7311yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—2921no—
607C4—2921no—
608C4—1461no—
609C4—1461no—
610C4—1461no—
611C4#1798935211yescharacteristic
612C4#1798935311yescharacteristic
613C4#1798939111yescharacteristic
614C4#1798939111yescharacteristic
615C2—81no—
616C2—81no—
617C2—2921no—
618C2—5841no—
619C2—5841no—
620C2#2261864511yescharacteristic
621C2#2261878011yescharacteristic
622C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1586C2
socleC22×C73C2×C4×D4
prime radical#22620507C2
cosocleC42×C73C24
hypercenter#1586D73
hypocenterC73#17989
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #22619008C2semidirect
3. #22619005C2semidirect
4. #22608797C2semidirect
5. #22608796C2semidirect
6. #22608794C2semidirect
7. #22608763C2semidirect
8. #22608760C2semidirect
9. #22608758C2semidirect
10. #22608757C2semidirect
11. #22608691C2semidirect
12. #22608398C2semidirect
13. #22608398C2semidirect
14. #22608222C2semidirect
15. C73×#1586C2semidirect
318. #1586D73semidirect
327. C73#17989semidirect

Maximal subgroups

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

subgroupindex
#226205072
#226190082
#226190052
#226087972
#226087962
#226087942
#226087632
#226087602
#226087582
#226087572
#226086912
#226083982
#226082222
C73×#15862
#1798973