Finite Group Databasebeta

← #33056800

Subgroups — #33056800

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620522C211yesmaximal, characteristic
2#22619083C211yesmaximal, characteristic, complemented
3#22619005C211yesmaximal, characteristic, complemented
4#22608806C211yesmaximal, characteristic, complemented
5#22608798C211yesmaximal, characteristic, complemented
6#22608797C211yesmaximal, characteristic, complemented
7#22608775C211yesmaximal, characteristic, complemented
8#22608765C211yesmaximal, characteristic, complemented
9#22608760C211yesmaximal, characteristic, complemented
10#22608759C211yesmaximal, characteristic, complemented
11#22608697C211yesmaximal, characteristic, complemented
12#22608390C211yesmaximal, characteristic, complemented
13#22608380C211yesmaximal, characteristic, complemented
14#22608217C211yesmaximal, characteristic, complemented
15C73×#1585C211yesmaximal, characteristic, complemented
16#17989134C2211yescharacteristic
17#17989124C2211yescharacteristic
18#17988994C411yescharacteristic
19#17988973C411yescharacteristic
20#17988950C411yescharacteristic
21#17988948C411yescharacteristic
22#17988841C411yescharacteristic
23#17988839C411yescharacteristic
24#17988836C411yescharacteristic
25#17988830C411yescharacteristic
26Q8×#10596831C2211yescharacteristic
27C4×#11924015C2211yescharacteristic
28C4×D584C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30#17988666C2211yescharacteristic
31#17988665C2211yescharacteristic
32#17988664—21no—
33#17988664C2211yescharacteristic
34#17988661—21no—
35#17988660—21no—
36#17988658—21no—
37C8×D292C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988649—21no—
40#17988643C2211yescharacteristic
41#17988638C2211yescharacteristic
42#17988612—21no—
43#17988609C2211yescharacteristic
44#17988553—21no—
45#17988552—21no—
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988338C2211yescharacteristic
50#17988337C2211yescharacteristic
51Q8⋊#10596831C2211yescharacteristic
52#17988316C2211yescharacteristic
53#17988316C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59#17988308C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924015C2×C411yescharacteristic
69C2×D584C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924011—21no—
73C2×#11924011—21no—
74C2×#11924011—21no—
75C2×#11924011C2×C411yescharacteristic
76C2×#11924011C2×C411yescharacteristic
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79C2×C8×D73—21no—
80#14556590C2×C411yescharacteristic
81#14556587C2×C411yescharacteristic
82#14556586—21no—
83#14556582C2×C411yescharacteristic
84#14556580C2×C411yescharacteristic
85#14556577—21no—
86#14556576—21no—
87#14556567C2×C411yescharacteristic
88#14556566C2×C411yescharacteristic
89#14556566C2×C411yescharacteristic
90#14556564—21no—
91#14556562C2×C411yescharacteristic
92C4×D292—21no—
93C4×D292C2311yescharacteristic
94C4×D292C2311yescharacteristic
95C4×C22⋊D73—21no—
96#14556548—21no—
97C42×D73C2311yescharacteristic
98#14556525C2×C411yescharacteristic
99#14556524C2×C411yescharacteristic
100#14556522C2×C411yescharacteristic
101C4⋊#10596831—21no—
102C4⋊#10596831C2311yescharacteristic
103C4⋊#10596831C2311yescharacteristic
104#14556520—21no—
105#14556520D411yescharacteristic
106#14556520D411yescharacteristic
107#14556515C2×C411yescharacteristic
108#14556513C2×C411yescharacteristic
109#14556513C2×C411yescharacteristic
110#14556512C2×C411yescharacteristic
111#14556511C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113C22⋊#10596831—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503D411yescharacteristic
120#14556503D411yescharacteristic
121#14556501—21no—
122#14556501C2×C411yescharacteristic
123#14556501C2×C411yescharacteristic
124C4×#10596831—21no—
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C4×#10596831C2311yescharacteristic
128C8×Dic73—21no—
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×D292—21no—
148C2×D292—21no—
149C2×D292C22×C411yescharacteristic
150C2×D292C22×C411yescharacteristic
151C2×C22⋊D73—21no—
152C2×C22⋊D73—21no—
153C2×C22⋊D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73C22×C411yescharacteristic
157C2×C4×D73C2×D411yescharacteristic
158C2×C4×D73#4111yescharacteristic
159#11924015—41no—
160D584—41no—
161#11924013—41no—
162#11924012—81no—
163#11924011—41no—
164#11924011—41no—
165#11924011—81no—
166#11924011—81no—
167#11924011—81no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C2×D411yescharacteristic
174C2×#10596831C2×D411yescharacteristic
175C8×D73—42no—
176C8×D73—81no—
177C8×D73—81no—
178C4⋊Dic73—21no—
179C4⋊Dic73C22×C411yescharacteristic
180C4⋊Dic73C22×C411yescharacteristic
181#11924007—21no—
182#11924007—21no—
183#11924007—21no—
184C22⋊Dic73—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190#11924005—21no—
191#11924005—21no—
192C4×Dic73C22×C411yescharacteristic
193C4×Dic73C2×D411yescharacteristic
194C4×Dic73#4111yescharacteristic
195C2×Q8×C73C22×C411yescharacteristic
196C2×D4×C73C22×C411yescharacteristic
197C22×C4×C73—21no—
198SD16×C73—41no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—81no—
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C4⋊C4×C73—21no—
208C4⋊C4×C73C22×C411yescharacteristic
209C4⋊C4×C73C22×C411yescharacteristic
210C22⋊C4×C73—21no—
211C42×C73—21no—
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73C4×D411yescharacteristic
217Q8×C73—21no—
218Q8×C73—21no—
219D4×C73—21no—
220D4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73C23×C411yescharacteristic
227C2×C4×C73C22×D411yescharacteristic
228C2×C4×C73C2×#4111yescharacteristic
229C22⋊D73—81no—
230C22⋊D73—81no—
231C22⋊D73—81no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73C4×D411yescharacteristic
235C2×Dic73C4×D411yescharacteristic
236C2×Dic73C4×D411yescharacteristic
237D292—21no—
238D292—21no—
239D292—21no—
240D292—21no—
241D292—81no—
242D292—81no—
243C4×D73—21no—
244C4×D73—21no—
245C4×D73—21no—
246C4×D73—21no—
247C4×D73—41no—
248C4×D73—41no—
249C4×D73—41no—
250C4×D73—41no—
251C4×D73—41no—
252Dic146—81no—
253C8×C73—22no—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—41no—
259C8×C73—41no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73C2×C4×D411yescharacteristic
271C2×D73—21no—
272C2×D73—21no—
273C2×D73—21no—
274C2×D73—41no—
275C2×D73—41no—
276C2×D73—41no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C4×C73—21no—
281C4×C73—41no—
282C4×C73—41no—
283C4×C73—41no—
284C4×C73#56811yescharacteristic
285C4×C73#56811yescharacteristic
286C4×C73#57611yescharacteristic
287C4×C73#57711yescharacteristic
288Dic73—21no—
289Dic73—21no—
290Dic73—21no—
291Dic73—41no—
292Dic73—41no—
293#17987—731nomaximal, Sylow
294C2×C73—81no—
295C2×C73#293211yescharacteristic
296C2×C73#294611yescharacteristic
297C2×C73#295611yescharacteristic
298D73—41no—
299D73—81no—
300D73—81no—
301#3171—731no—
302#2993—731no—
303#2981—731no—
304#1588—731no—
305#1586—731no—
306#1586—731no—
307#1585D7311yescharacteristic, complemented
308#1583—731no—
309#1582—731no—
310#1581—731no—
311#1581—731no—
312#1569—731no—
313#1494—731no—
314#1492—731no—
315#1451—731no—
316C73#1798711yescharacteristic, complemented, Sylow
317#532—731no—
318#529—731no—
319#501—731no—
320#496—731no—
321#490—731no—
322#489—731no—
323#469—731no—
324#469—731no—
325#468—731no—
326#468—731no—
327#446C2×D7311yescharacteristic
328C8×Q8—731no—
329C4×SD16—731no—
330C4×SD16C2×D7311yescharacteristic
331C4×D8—731no—
332C4×D8—731no—
333#436—731no—
334#436—731no—
335#436—731no—
336#436—1461no—
337#435—1461no—
338#435—1461no—
339#435—1461no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4C2×D7311yescharacteristic
343#433—1461no—
344#432—731no—
345#431—731no—
346#424—1461no—
347#423—731no—
348#408—1461no—
349#408—1461no—
350C4×M16—731no—
351C2×C4×C8—731no—
352#335—731no—
353#335C2×D7311yescharacteristic
354#334—731no—
355#334—731no—
356Q8⋊C8—731no—
357Q8⋊C8C2×D7311yescharacteristic
358D4⋊C8—731no—
359D4⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8C2×D7311yescharacteristic
364#322—731no—
365#322—731no—
366#322—731no—
367#322C2×D7311yescharacteristic
368C2×#41—1461no—
369C2×SD16—731no—
370C2×SD16C4×D7311yescharacteristic
371C2×D8—731no—
372C2×D8—731no—
373C2×M16—731no—
374C2×M16—731no—
375C2×M16—1461no—
376C2×M16—1461no—
377C2×M16—1461no—
378C2×M16—1461no—
379C22×C8—21no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383C4⋊Q8—731no—
384#127—731no—
385#126—1461no—
386#125—731no—
387#124—731no—
388#124—1461no—
389#123—1461no—
390C22⋊Q8—731no—
391#121—731no—
392#121—731no—
393#121—731no—
394#121—1461no—
395C4×Q8C22×D7311yescharacteristic
396C4×D4—731no—
397C4×D4—731no—
398C4×D4—1461no—
399C4×D4—1461no—
400C4×D4C22×D7311yescharacteristic
401#117—1461no—
402C2×C42—731no—
403#107—731no—
404#107—731no—
405#106—731no—
406#106C4×D7311yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8C22×D7311yescharacteristic
415C4⋊C8C22×D7311yescharacteristic
416#103—731no—
417#103C4×D7311yescharacteristic
418#102—731no—
419#102—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423#102C4×D7311yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—731no—
426C22⋊C8—731no—
427C22⋊C8—1461no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433#97—21no—
434#97—731no—
435#97—731no—
436#97—1461no—
437C4×C8—731no—
438C4×C8—731no—
439C4×C8—731no—
440C4×C8—1461no—
441C4×C8—1461no—
442C4×C8C22×D7311yescharacteristic
443C4×C8C22×D7311yescharacteristic
444C4×C8C22×D7311yescharacteristic
445#41—5841no—
446#41—5841no—
447C2×Q8—1461no—
448C2×Q8C2×C4×D7311yescharacteristic
449C2×D4—731no—
450C2×D4—731no—
451C2×D4—1461no—
452C2×D4—1461no—
453C2×D4—1461no—
454C2×D4—1461no—
455C2×D4—1461no—
456C2×D4C2×C4×D7311yescharacteristic
457C22×C4—21no—
458C22×C4—731no—
459C22×C4—731no—
460C22×C4—731no—
461C22×C4—1461no—
462C22×C4—1461no—
463SD16—41no—
464SD16—2921no—
465D8—2921no—
466D8—2921no—
467M16—2921no—
468M16—2921no—
469M16—5841no—
470M16—5841no—
471M16—5841no—
472M16—5841no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—2922no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—731no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8C2×C4×D7311yescharacteristic
488C2×C8C2×C4×D7311yescharacteristic
489C2×C8D4×D7311yescharacteristic
490C2×C8D4×D7311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—731no—
493C4⋊C4—731no—
494C4⋊C4—1461no—
495C4⋊C4—1461no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4C2×C4×D7311yescharacteristic
499C4⋊C4C2×C4×D7311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—1461no—
502C22⋊C4—1461no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C42—21no—
510C42—731no—
511C42—731no—
512C42—731no—
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—731no—
516C23—1461no—
517C23—1461no—
518Q8—21no—
519Q8—21no—
520Q8—5841no—
521D4—21no—
522D4—21no—
523D4—5841no—
524D4—5841no—
525D4—5841no—
526D4—5841no—
527D4—5841no—
528D4—1461no—
529D4—1461no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—731no—
543C2×C4—731no—
544C2×C4—731no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4C22×C4×D7311yescharacteristic
552C2×C4C2×D4×D7311yescharacteristic
553C2×C4#41×D7311yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—2921no—
562C8—2921no—
563C8—2921no—
564C8—1461no—
565C8—1461no—
566C8—1461no—
567C8—1461no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—2921no—
572C22—2921no—
573C22—2921no—
574C22—2921no—
575C22—2921no—
576C22—2921no—
577C22—1461no—
578C22—1461no—
579C22—1461no—
580C22C4×D4×D7311yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—2921no—
586C4—2921no—
587C4—1461no—
588C4—1461no—
589C4—1461no—
590C4#1798935211yescharacteristic
591C4#1798935311yescharacteristic
592C4#1798939111yescharacteristic
593C4#1798939611yescharacteristic
594C2—81no—
595C2—2921no—
596C2—5841no—
597C2—5841no—
598C2#2261864511yescharacteristic
599C2#2261876211yescharacteristic
600C2#2261883611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1585C2
socleC22×C73C2×C4×D4
prime radical#22620522C2
cosocleC42×C73C24
hypercenter#1585D73
hypocenterC73#17987
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
2. #22619083C2semidirect
3. #22619005C2semidirect
4. #22608806C2semidirect
5. #22608798C2semidirect
6. #22608797C2semidirect
7. #22608775C2semidirect
8. #22608765C2semidirect
9. #22608760C2semidirect
10. #22608759C2semidirect
11. #22608697C2semidirect
12. #22608390C2semidirect
13. #22608380C2semidirect
14. #22608217C2semidirect
15. C73×#1585C2semidirect
307. #1585D73semidirect
316. C73#17987semidirect

Maximal subgroups

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

subgroupindex
#226205222
#226190832
#226190052
#226088062
#226087982
#226087972
#226087752
#226087652
#226087602
#226087592
#226086972
#226083902
#226083802
#226082172
C73×#15852
#1798773