Finite Group Databasebeta

← #33055699

Subgroups — #33055699

Order 18688.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619047C211yesmaximal, characteristic, complemented
2#22619041C211yesmaximal, characteristic, complemented
3C4×#14556614C211yesmaximal, characteristic
4#22608803C211yesmaximal, characteristic, complemented
5#22608797C211yesmaximal, characteristic, complemented
6#22608794C211yesmaximal, characteristic, complemented
7#22608774C211yesmaximal, characteristic, complemented
8#22608771C211yesmaximal, characteristic, complemented
9#22608770C211yesmaximal, characteristic, complemented
10#22608765C211yesmaximal, characteristic, complemented
11#334×D73C211yesmaximal, characteristic, complemented
12#22608317C211yesmaximal, characteristic, complemented
13#22608317C211yesmaximal, characteristic, complemented
14#22608222C211yesmaximal, characteristic, complemented
15C73×#1587C211yesmaximal, characteristic, complemented
16C2×#14556614C411yescharacteristic
17C4×#11924029C2211yescharacteristic
18C4×#11924029C2211yescharacteristic
19#17988718C2211yescharacteristic
20Q8×#10596831C2211yescharacteristic
21Q16×Dic73C411yescharacteristic
22C4×#11924015C2211yescharacteristic
23C4×#11924015C2211yescharacteristic
24#17988672C411yescharacteristic
25#17988672C411yescharacteristic
26C4×D584C2211yescharacteristic
27#17988669C411yescharacteristic
28#17988666C2211yescharacteristic
29#17988664C2211yescharacteristic
30#17988660—21no—
31#17988657—21no—
32C8×D292—21no—
33C8×D292C2211yescharacteristic
34#17988652—21no—
35#17988652C2211yescharacteristic
36#17988642—21no—
37#17988638—21no—
38#17988638C2211yescharacteristic
39#17988638C2211yescharacteristic
40#17988624C411yescharacteristic
41#17988609—21no—
42C4⋊C8×D73—21no—
43C4⋊C8×D73C2211yescharacteristic
44C4⋊C8×D73C2211yescharacteristic
45#17988582C411yescharacteristic
46#17988582C411yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988338C2211yescharacteristic
49#17988337C2211yescharacteristic
50#17988337C2211yescharacteristic
51Q8⋊#10596831C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53#17988316C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988308C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924029C2×C411yescharacteristic
68C2×#11924029C2×C411yescharacteristic
69#14556614—24no—
70C2×#11924015C2×C411yescharacteristic
71C2×#11924015C2×C411yescharacteristic
72C2×D584C2×C411yescharacteristic
73C2×#11924011—21no—
74C2×#11924011—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79C2×C8×D73C2×C411yescharacteristic
80C2×C8×D73C2×C411yescharacteristic
81Q8×Dic73C2×C411yescharacteristic
82Q8×Dic73C2×C411yescharacteristic
83C4×D292—21no—
84C4×D292—21no—
85C4×D292C2311yescharacteristic
86C4×D292C2311yescharacteristic
87#14556553—21no—
88#14556553—21no—
89#14556553C2×C411yescharacteristic
90#14556553C2×C411yescharacteristic
91#14556549—21no—
92#14556549—21no—
93#14556549C2×C411yescharacteristic
94#14556549C2×C411yescharacteristic
95C42×D73—21no—
96C42×D73—21no—
97C42×D73C2311yescharacteristic
98#14556525C2×C411yescharacteristic
99#14556522C2×C411yescharacteristic
100#14556522C2×C411yescharacteristic
101C4⋊#10596831—21no—
102C4⋊#10596831—21no—
103C4⋊#10596831C2311yescharacteristic
104C4⋊#10596831C2311yescharacteristic
105#14556520—21no—
106#14556520—21no—
107#14556520—21no—
108#14556520D411yescharacteristic
109#14556520D411yescharacteristic
110#14556515C2×C411yescharacteristic
111#14556515C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114#14556511C2×C411yescharacteristic
115#14556511C2×C411yescharacteristic
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556503D411yescharacteristic
122#14556503D411yescharacteristic
123#14556502—21no—
124C4×#10596831—21no—
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C4×#10596831C2311yescharacteristic
128C8×Dic73C2×C411yescharacteristic
129C8×Dic73C2×C411yescharacteristic
130C2×Q16×C73C2×C411yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132C4×Q8×C73C2311yescharacteristic
133#107×C73C2×C411yescharacteristic
134C4⋊C8×C73—21no—
135C4⋊C8×C73—21no—
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138#103×C73C2×C411yescharacteristic
139#103×C73C2×C411yescharacteristic
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145#11924029—22no—
146#11924029—22no—
147#11924029—22no—
148#11924029M1614yescomplemented
149C2×D292—21no—
150C2×D292—21no—
151C2×D292C22×C411yescharacteristic
152C2×D292C22×C411yescharacteristic
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73C22×C411yescharacteristic
160C2×C4×D73C2×D411yescharacteristic
161C2×C4×D73#4111yescharacteristic
162#11924015—22no—
163#11924015—22no—
164D584—22no—
165#11924011—81no—
166#11924011—81no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831C22×C411yescharacteristic
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C2×D411yescharacteristic
173C2×#10596831C2×D411yescharacteristic
174C8×D73—22no—
175C8×D73—22no—
176C8×D73—81no—
177C8×D73—81no—
178C8×D73—81no—
179C8×D73—81no—
180C4⋊Dic73—21no—
181C4⋊Dic73—21no—
182C4⋊Dic73C22×C411yescharacteristic
183C4⋊Dic73C22×C411yescharacteristic
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73C22×C411yescharacteristic
195C4×Dic73C2×D411yescharacteristic
196C4×Dic73#4111yescharacteristic
197C2×Q8×C73C22×C411yescharacteristic
198C2×Q8×C73C22×C411yescharacteristic
199Q16×C73—22no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73C22×C411yescharacteristic
210C4⋊C4×C73C22×C411yescharacteristic
211C42×C73—21no—
212C42×C73—21no—
213C42×C73C2411yescharacteristic
214C22×D73—21no—
215C22×D73—21no—
216C22×D73C4×D411yescharacteristic
217Q8×C73—21no—
218Q8×C73—21no—
219Q8×C73—21no—
220Q8×C73C2×M1612yes—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73C23×C411yescharacteristic
226C2×C4×C73C22×D411yescharacteristic
227C2×C4×C73C2×#4111yescharacteristic
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73C4×D411yescharacteristic
231C2×Dic73C4×D411yescharacteristic
232C2×Dic73C4×D411yescharacteristic
233D292—24no—
234D292—21no—
235D292—21no—
236D292—21no—
237D292—42no—
238D292C2×M1612yes—
239C4×D73—21no—
240C4×D73—21no—
241C4×D73—24no—
242C4×D73—41no—
243C4×D73—41no—
244C4×D73—41no—
245C4×D73—41no—
246C4×D73—41no—
247C4×D73—42no—
248C4×D73—81no—
249C4×D73—81no—
250C4×D73C2×M1612yes—
251C4×D73#13112yes—
252C8×C73—21no—
253C8×C73—21no—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—41no—
257C8×C73—41no—
258C8×C73—41no—
259#10596831—21no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—41no—
264#10596831—41no—
265#10596831—41no—
266C22×C73C2×C4×D411yescharacteristic
267C2×D73—21no—
268C2×D73—21no—
269C2×D73—22no—
270C2×D73—41no—
271C2×D73—41no—
272C2×D73—41no—
273C2×D73—41no—
274C2×D73—41no—
275C2×D73#43512yes—
276C4×C73—22no—
277C4×C73—21no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73C22×M1611yescharacteristic
282C4×C73C2×#13111yescharacteristic
283C4×C73#57711yescharacteristic
284C4×C73#57711yescharacteristic
285Dic73—21no—
286Dic73—21no—
287Dic73—41no—
288Dic73—41no—
289Dic73#43512yes—
290#17882—731nomaximal, Sylow
291C2×C73C2×#43511yescharacteristic
292C2×C73#295211yescharacteristic
293C2×C73#295711yescharacteristic
294D73—22no—
295D73—42no—
296D73—81no—
297#2989—731no—
298#2988—731no—
299C4×#135—731no—
300#1587—731no—
301#1587D7311yescharacteristic, complemented
302#1586—731no—
303#1586—731no—
304#1583—731no—
305#1583—731no—
306#1582—731no—
307#1582—731no—
308C2×#334—731no—
309#1477—731no—
310#1477—731no—
311#1452—731no—
312C73#1788211yescharacteristic, complemented, Sylow
313C2×#135—731no—
314C4×#41—731no—
315C4×#41—731no—
316#446—731no—
317#446C2×D7311yescharacteristic
318C8×Q8—731no—
319C8×Q8C2×D7311yescharacteristic
320C4×Q16—731no—
321C4×Q16C2×D7311yescharacteristic
322C4×SD16—731no—
323C4×SD16—731no—
324C4×SD16—731no—
325C4×SD16—731no—
326C4×D8—731no—
327C4×D8—731no—
328#436—731no—
329#436—731no—
330#435—1461no—
331#435—1461no—
332C8×D4—731no—
333C8×D4—731no—
334C8×D4—1461no—
335C8×D4—1461no—
336#432—1461no—
337#431—731no—
338#431—731no—
339#431—1461no—
340#427—731no—
341#423—1461no—
342C2×C4⋊C8—731no—
343C2×C4⋊C8—731no—
344C2×C4⋊C8—1461no—
345#416—731no—
346#416—731no—
347C2×C4×C8—731no—
348#334—731no—
349#334—731no—
350#334—731no—
351#334C2×D7311yescharacteristic
352Q8⋊C8—731no—
353Q8⋊C8—731no—
354Q8⋊C8C2×D7311yescharacteristic
355Q8⋊C8C2×D7311yescharacteristic
356D4⋊C8—731no—
357D4⋊C8—731no—
358D4⋊C8—731no—
359D4⋊C8—731no—
360#322—731no—
361#322—731no—
362#322—731no—
363#322C2×D7311yescharacteristic
364C2×#41—731no—
365C2×#41—731no—
366#135—1464no—
367C2×Q16C4×D7311yescharacteristic
368C2×SD16—731no—
369C2×SD16—731no—
370C2×D8—731no—
371C2×M16—1461no—
372C2×M16—1461no—
373C22×C8—731no—
374C22×C8—731no—
375C22×C8—1461no—
376C22×C8—1461no—
377C22×C8—1461no—
378C22×C8—1461no—
379C4×Q8—731no—
380C4×Q8—731no—
381C4×Q8C22×D7311yescharacteristic
382C4×Q8C22×D7311yescharacteristic
383C4×D4—731no—
384C4×D4—731no—
385C4×D4—731no—
386C4×D4—731no—
387C4×D4—1461no—
388C4×D4—1461no—
389C4×D4—1461no—
390C4×D4—1461no—
391#117—731no—
392#117—731no—
393#117—1461no—
394#117—1461no—
395C2×C42—731no—
396C2×C42—1461no—
397C2×C42—1461no—
398#107—731no—
399#107C4×D7311yescharacteristic
400#106—731no—
401#106—731no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—731no—
405C4⋊C8—731no—
406C4⋊C8—731no—
407C4⋊C8—731no—
408C4⋊C8—1461no—
409C4⋊C8—1461no—
410C4⋊C8—1461no—
411C4⋊C8—1461no—
412C4⋊C8—1461no—
413C4⋊C8C22×D7311yescharacteristic
414C4⋊C8C22×D7311yescharacteristic
415#103—731no—
416#103—731no—
417#103C4×D7311yescharacteristic
418#103C4×D7311yescharacteristic
419#102—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423C22⋊C8—731no—
424C22⋊C8—731no—
425C22⋊C8—1461no—
426C22⋊C8—1461no—
427C22⋊C8—1461no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430#97—21no—
431#97—1461no—
432C4×C8—21no—
433C4×C8—731no—
434C4×C8—731no—
435C4×C8—731no—
436C4×C8—731no—
437C4×C8—731no—
438C4×C8—1461no—
439C4×C8C22×D7311yescharacteristic
440C4×C8C22×D7311yescharacteristic
441C4×C8C22×D7311yescharacteristic
442#41—734no—
443#41—1462no—
444#41—1462no—
445#41—1462no—
446C2×Q8C2×C4×D7311yescharacteristic
447C2×Q8C2×C4×D7311yescharacteristic
448C2×D4—731no—
449C2×D4—731no—
450C2×D4—1461no—
451C2×D4—1461no—
452C22×C4—731no—
453C22×C4—731no—
454C22×C4—731no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4—1461no—
461Q16—22no—
462SD16—1462no—
463SD16—1462no—
464D8—1462no—
465M16—5841no—
466M16—5841no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—5841no—
471C2×C8—5841no—
472C2×C8—5841no—
473C2×C8—5841no—
474C2×C8—731no—
475C2×C8—731no—
476C2×C8—731no—
477C2×C8—731no—
478C2×C8—1462no—
479C2×C8—1462no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8C2×C4×D7311yescharacteristic
484C2×C8C2×C4×D7311yescharacteristic
485C2×C8D4×D7311yescharacteristic
486C2×C8D4×D7311yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—731no—
490C4⋊C4—731no—
491C4⋊C4—1461no—
492C4⋊C4—1461no—
493C4⋊C4C2×C4×D7311yescharacteristic
494C4⋊C4C2×C4×D7311yescharacteristic
495C22⋊C4—1461no—
496C22⋊C4—1461no—
497C22⋊C4—1461no—
498C22⋊C4—1461no—
499C22⋊C4—1461no—
500C22⋊C4—1461no—
501C42—21no—
502C42—21no—
503C42—731no—
504C42—731no—
505C42—731no—
506C42—1461no—
507C42—1461no—
508C42—1461no—
509C42—1461no—
510C42C23×D7311yescharacteristic
511C23—731no—
512C23—1461no—
513C23—1461no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8M16×D7312yes—
518D4—2922no—
519D4—732no—
520D4—1464no—
521D4—1461no—
522D4—1461no—
523D4—1461no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—2921no—
529C2×C4—2922no—
530C2×C4—2921no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—2921no—
534C2×C4—5841no—
535C2×C4—5841no—
536C2×C4—731no—
537C2×C4—732no—
538C2×C4—732no—
539C2×C4—731no—
540C2×C4—731no—
541C2×C4—1464no—
542C2×C4—1461no—
543C2×C4—1461no—
544C2×C4—1461no—
545C2×C4—1461no—
546C2×C4C22×C4×D7311yescharacteristic
547C2×C4C2×D4×D7311yescharacteristic
548C2×C4#41×D7311yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—2921no—
557C8—2921no—
558C8—2921no—
559C8—1461no—
560C8—1461no—
561C8—1461no—
562C8—1461no—
563C22—2921no—
564C22—2921no—
565C22—2921no—
566C22—2921no—
567C22—2921no—
568C22—732no—
569C22—1462no—
570C22—1461no—
571C22—1461no—
572C22C4×D4×D7311yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—2921no—
579C4—2921no—
580C4—732no—
581C4—1461no—
582C4—1461no—
583C4C2×M16×D7311yescharacteristic
584C4#131×D7311yescharacteristic
585C4#1798939611yescharacteristic
586C4#1798939611yescharacteristic
587C2—2922no—
588C2—5841no—
589C2—1462no—
590C2#435×D7311yescharacteristic
591C2#2261881111yescharacteristic
592C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1587C2
socleC22×C73C2×C4×D4
prime radicalC2×#14556614C4
cosocleC42×C73C24
hypercenter#1587D73
hypocenterC73#17882
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
1. #22619047C2semidirect
2. #22619041C2semidirect
4. #22608803C2semidirect
5. #22608797C2semidirect
6. #22608794C2semidirect
7. #22608774C2semidirect
8. #22608771C2semidirect
9. #22608770C2semidirect
10. #22608765C2semidirect
11. #334×D73C2semidirect
12. #22608317C2semidirect
13. #22608317C2semidirect
14. #22608222C2semidirect
15. C73×#1587C2semidirect
148. #11924029M16semidirect
301. #1587D73semidirect
312. C73#17882semidirect

Maximal subgroups

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

subgroupindex
#226190472
#226190412
C4×#145566142
#226088032
#226087972
#226087942
#226087742
#226087712
#226087702
#226087652
#334×D732
#226083172
#226082222
C73×#15872
#1788273