Finite Group Databasebeta

← #33068402

Subgroups — #33068402

Order 18688.

672 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620486C211yesmaximal, characteristic, complemented
2#22619719C211yesmaximal, characteristic, complemented
3#41×#10596831C211yesmaximal, characteristic, complemented
4#22609363C211yesmaximal, characteristic, complemented
5#22609356C211yesmaximal, characteristic, complemented
6#22609345C211yesmaximal, characteristic, complemented
7#22609338C211yesmaximal, characteristic, complemented
8#22609311C211yesmaximal, characteristic, complemented
9#22609304C211yesmaximal, characteristic, complemented
10#22609277C211yesmaximal, characteristic, complemented
11#22609270C211yesmaximal, characteristic, complemented
12C2×#17988337C211yesmaximal, characteristic, complemented
13#22608589C211yesmaximal, characteristic, complemented
14#22608580C211yesmaximal, characteristic, complemented
15C73×#3035C211yesmaximal, characteristic
16#17989144C2211yescharacteristic
17#17988983C2211yescharacteristic
18#17988959C2211yescharacteristic
19#17988939C2211yescharacteristic
20#17988933C2211yescharacteristic
21#17988894—21no—
22#17988887—21no—
23#17988882C2211yescharacteristic
24#17988877C2211yescharacteristic
25#17988872C2211yescharacteristic
26#17988867C2211yescharacteristic
27#17988814—21no—
28#17988814—21no—
29Q8×#10596831C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31C4×#11924016—21no—
32C4×#11924016—21no—
33D4×#10596831—21no—
34D4×#10596831—21no—
35D4×#10596831C2211yescharacteristic
36D4×#10596831C2211yescharacteristic
37#17988640—21no—
38#17988640C2211yescharacteristic
39#17988623—21no—
40C2×C4⋊#10596831C2211yescharacteristic
41#17988583—21no—
42C2×C4×#10596831—21no—
43C2×C4×#10596831C2211yescharacteristic
44#17988337C2211yescharacteristic
45#17988337C2211yescharacteristic
46#17988337C2211yescharacteristic
47#17988337C2211yescharacteristic
48#17988335C2211yescharacteristic
49#17988335C2211yescharacteristic
50#17988333C2211yescharacteristic
51#17988333C2211yescharacteristic
52#17988332C2211yescharacteristic
53#17988332C2211yescharacteristic
54#17988331C2211yescharacteristic
55#17988331C2211yescharacteristic
56C2×#135×C73—21no—
57#532×C73C2211yescharacteristic
58C4×#41×C73C2211yescharacteristic
59#464×C73—21no—
60#463×C73—21no—
61#462×C73C2211yescharacteristic
62#461×C73C2211yescharacteristic
63#460×C73C2211yescharacteristic
64#459×C73C2211yescharacteristic
65C2×C4⋊C8×C73C2211yescharacteristic
66#416×C73—21no—
67C2×#11924016—21no—
68C2×#11924016—21no—
69C22×#10596831—21no—
70C22×#10596831—21no—
71C22×#10596831—21no—
72C22×#10596831D411yescharacteristic
73C22×#10596831D411yescharacteristic
74#14556591C2311yescharacteristic
75#14556591C2311yescharacteristic
76#14556583—21no—
77#14556570—21no—
78#14556570—21no—
79C4×Dic146—21no—
80C4×Dic146—21no—
81#14556550—21no—
82#14556524—21no—
83#14556524—21no—
84#14556522—21no—
85#14556522—21no—
86#14556522—21no—
87#14556522—21no—
88C4⋊#10596831—21no—
89C4⋊#10596831—21no—
90C4⋊#10596831—21no—
91C4⋊#10596831C2311yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94C4⋊#10596831C2311yescharacteristic
95#14556515—21no—
96#14556515—21no—
97#14556514—21no—
98#14556514—21no—
99#14556512—21no—
100#14556512—21no—
101#14556512—21no—
102#14556512—21no—
103C22⋊#10596831—21no—
104C22⋊#10596831—21no—
105C22⋊#10596831—21no—
106C4×#10596831—21no—
107C4×#10596831—21no—
108C4×#10596831—21no—
109C4×#10596831D411yescharacteristic
110C4×#10596831D411yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C2×#41×C73—21no—
114C2×#41×C73D411yescharacteristic
115#135×C73—44no—
116C2×Q16×C73—21no—
117C2×SD16×C73—21no—
118C2×SD16×C73—21no—
119C2×D8×C73—21no—
120C22×C8×C73—21no—
121C4⋊Q8×C73C2311yescharacteristic
122#127×C73C2311yescharacteristic
123#124×C73—21no—
124#121×C73—21no—
125#121×C73—21no—
126C4×Q8×C73D411yescharacteristic
127C4×Q8×C73C2311yescharacteristic
128C4×D4×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73—21no—
131C4×D4×C73—21no—
132C4×D4×C73D411yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#117×C73—21no—
135#117×C73D411yescharacteristic
136C2×C42×C73—21no—
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—21no—
139C4⋊C8×C73C2311yescharacteristic
140C4⋊C8×C73C2311yescharacteristic
141#103×C73—21no—
142#103×C73—21no—
143#102×C73—21no—
144#102×C73—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147#11924016—42no—
148#11924016—42no—
149C2×#10596831—22no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—41no—
155C2×#10596831—42no—
156C2×#10596831—42no—
157C2×#10596831—42no—
158C2×#10596831C2×D411yescharacteristic
159C2×#10596831C2×D411yescharacteristic
160C2×#10596831C2×D411yescharacteristic
161C2×#10596831C2×D411yescharacteristic
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166#11924007—41no—
167#11924007—41no—
168C22⋊Dic73—41no—
169C4×Dic73—41no—
170#41×C73—22no—
171#41×C73—42no—
172#41×C73—42no—
173#41×C73SD1614yescomplemented
174C2×Q8×C73—21no—
175C2×Q8×C73C2×D411yescharacteristic
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—41no—
181C2×D4×C73C2×D411yescharacteristic
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—41no—
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73#4111yescharacteristic
189Q16×C73—42no—
190SD16×C73—42no—
191SD16×C73—42no—
192D8×C73—42no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—42no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73C2×D411yescharacteristic
201C4⋊C4×C73C2×D411yescharacteristic
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C22⋊C4×C73—41no—
206C22⋊C4×C73—41no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73—21no—
210C42×C73C2×D411yescharacteristic
211C42×C73C2×D411yescharacteristic
212C42×C73#4111yescharacteristic
213C42×C73C2411yescharacteristic
214C23×C73—21no—
215C23×C73—41no—
216C23×C73#12111yescharacteristic
217Q8×C73—21no—
218Q8×C73—41no—
219Q8×C73—41no—
220Q8×C73C2×SD1612yes—
221D4×C73—24no—
222D4×C73—21no—
223D4×C73—41no—
224D4×C73—41no—
225D4×C73—41no—
226D4×C73—41no—
227D4×C73—81no—
228D4×C73—82no—
229D4×C73C2×SD1612yes—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—24no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—41no—
237C2×C4×C73—42no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—82no—
242C2×C4×C73#12111yescharacteristic
243C2×C4×C73#12111yescharacteristic
244C2×C4×C73#12111yescharacteristic
245C2×C4×C73C2×SD1612yes—
246C2×C4×C73#13512yes—
247C2×C4×C73C22×D411yescharacteristic
248C2×C4×C73C22×D411yescharacteristic
249C2×C4×C73C2×#4111yescharacteristic
250C2×Dic73—41no—
251C2×Dic73—41no—
252Dic146—41no—
253Dic146—41no—
254Dic146—81no—
255C8×C73—41no—
256C8×C73—41no—
257#10596831—21no—
258#10596831—21no—
259#10596831—21no—
260#10596831—41no—
261#10596831—41no—
262#10596831—41no—
263#10596831—41no—
264#10596831#13512yescomplemented
265C22×C73—21no—
266C22×C73—21no—
267C22×C73—22no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73—81no—
271C22×C73—81no—
272C22×C73—81no—
273C22×C73#46512yes—
274C22×C73C2×#12111yescharacteristic
275C4×C73—21no—
276C4×C73—22no—
277C4×C73—21no—
278C4×C73—21no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—81no—
282C4×C73#46512yes—
283C4×C73C22×SD1611yescharacteristic
284C4×C73C2×#13511yescharacteristic
285C4×C73C2×#13511yescharacteristic
286C4×C73#57511yescharacteristic
287Dic73—81no—
288Dic73—81no—
289#19124—731nomaximal, Sylow
290C2×C73—22no—
291C2×C73—42no—
292C2×C73—161no—
293C2×C73#303511yescharacteristic
294C2×C73C2×#46511yescharacteristic
295C2×C73#306711yescharacteristic
296#3167—731no—
297#3076—731no—
298#3035D7311yescharacteristic
299C8×#41—731no—
300#1680—731no—
301#1679—731no—
302#1678—731no—
303#1677—731no—
304#1672—731no—
305#1671—731no—
306#1666—731no—
307#1665—731no—
308C2×#334—731no—
309#1542—731no—
310#1540—731no—
311C73#1912411yescharacteristic, complemented, Sylow
312C2×#135—21no—
313#533—731no—
314#532C2×D7311yescharacteristic
315C4×#41C2×D7311yescharacteristic
316#498—731no—
317#492—731no—
318#487—731no—
319#486—731no—
320#479—1461no—
321#478—1461no—
322#477—731no—
323#476—731no—
324#475—731no—
325#474—731no—
326#465—1461no—
327#465—1461no—
328#464—21no—
329#463—21no—
330#462C2×D7311yescharacteristic
331#461C2×D7311yescharacteristic
332#460C2×D7311yescharacteristic
333#459C2×D7311yescharacteristic
334C8×Q8—731no—
335C8×Q8—731no—
336C4×SD16—1461no—
337C4×SD16—1461no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—1461no—
341C8×D4—1461no—
342#431—731no—
343#431—1461no—
344#427—1461no—
345C2×C4⋊C8—731no—
346C2×C4⋊C8C2×D7311yescharacteristic
347#416—21no—
348#416—1461no—
349C2×C4×C8—731no—
350C2×C4×C8—1461no—
351#334—731no—
352#334—731no—
353#334—731no—
354#334—731no—
355#333—731no—
356#333—731no—
357#332—731no—
358#332—731no—
359#332—731no—
360#332—731no—
361#331—731no—
362#331—731no—
363C2×#41—21no—
364C2×#41C22⋊D7311yescharacteristic
365#135—44no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—1461no—
370C2×SD16—1461no—
371C2×D8—21no—
372C22×C8—21no—
373C22×C8—731no—
374C22×C8—731no—
375C22×C8—1461no—
376C22×C8—1461no—
377C22×C8—1461no—
378C4⋊Q8—731no—
379C4⋊Q8—731no—
380C4⋊Q8C22×D7311yescharacteristic
381#127C22×D7311yescharacteristic
382#125—1461no—
383#124—21no—
384C22⋊Q8—1461no—
385C22⋊Q8—1461no—
386#121—21no—
387#121—21no—
388C4×Q8—1461no—
389C4×Q8—1461no—
390C4×Q8C22⋊D7311yescharacteristic
391C4×Q8C22×D7311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C22⋊D7311yescharacteristic
397C4×D4C22×D7311yescharacteristic
398#117—21no—
399#117—1461no—
400#117C22⋊D7311yescharacteristic
401C2×C42—21no—
402C2×C42C22×D7311yescharacteristic
403#107—1461no—
404#107—1461no—
405#106—1461no—
406#106—1461no—
407#106—1461no—
408#106—1461no—
409C4⋊C8—21no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—731no—
413C4⋊C8—731no—
414C4⋊C8—1461no—
415C4⋊C8—1461no—
416C4⋊C8—1461no—
417C4⋊C8C22×D7311yescharacteristic
418C4⋊C8C22×D7311yescharacteristic
419#103—21no—
420#103—21no—
421#103—1461no—
422#103—1461no—
423#103—1461no—
424#103—1461no—
425#102—21no—
426#102—21no—
427#102—1461no—
428#102—1461no—
429#102—1461no—
430#102—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C4×C8—731no—
435C4×C8—731no—
436C4×C8—731no—
437C4×C8—731no—
438C4×C8—1461no—
439C4×C8—1461no—
440C4×C8—1461no—
441#41—22no—
442#41—42no—
443#41—42no—
444#41#1192401614yescomplemented
445C2×Q8—21no—
446C2×Q8—1461no—
447C2×Q8—1461no—
448C2×Q8C2×C22⋊D7311yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4C2×C22⋊D7311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4D4×D7311yescharacteristic
460C22×C4C2×C22⋊D7311yescharacteristic
461C22×C4#1192402711yescharacteristic
462Q16—42no—
463SD16—42no—
464SD16—42no—
465SD16—2922no—
466SD16—2922no—
467D8—42no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—42no—
471C2×C8—2922no—
472C2×C8—2922no—
473C2×C8—2922no—
474C2×C8—2921no—
475C2×C8—731no—
476C2×C8—731no—
477C2×C8—731no—
478C2×C8—731no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1462no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—2921no—
489C4⋊C4—2921no—
490C4⋊C4—1461no—
491C4⋊C4—1461no—
492C4⋊C4—1461no—
493C4⋊C4—1461no—
494C4⋊C4C2×C22⋊D7311yescharacteristic
495C4⋊C4C2×C22⋊D7311yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—2921no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—2921no—
506C42D4×D7311yescharacteristic
507C42C2×C22⋊D7311yescharacteristic
508C42#1192402711yescharacteristic
509C42C23×D7311yescharacteristic
510C23—21no—
511C23—41no—
512C23#1455656311yescharacteristic
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—2921no—
517Q8—2921no—
518Q8—5841no—
519Q8C2×#1192401612yes—
520D4—24no—
521D4—21no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—81no—
527D4—82no—
528D4C2×#1192401612yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—24no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4#1455656311yescharacteristic
544C2×C4#1455656311yescharacteristic
545C2×C4#1455656311yescharacteristic
546C2×C4C2×#1192401612yes—
547C2×C4#1455661112yes—
548C2×C4C2×D4×D7311yescharacteristic
549C2×C4C22×C22⋊D7311yescharacteristic
550C2×C4C2×#1192402711yescharacteristic
551C8—41no—
552C8—41no—
553C8—2921no—
554C8—2921no—
555C8—2921no—
556C8—2921no—
557C8—732no—
558C8—1461no—
559C8—1461no—
560C8—1461no—
561C22—21no—
562C22—21no—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1798881412yes—
570C22C2×#1455656311yescharacteristic
571C4—21no—
572C4—21no—
573C4—22no—
574C4—21no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—5841no—
579C4—5841no—
580C4#1798881412yes—
581C4C22×#1192401611yescharacteristic
582C4#135×D7311yescharacteristic
583C4C2×#1455661111yescharacteristic
584C4#1798938411yescharacteristic
585C2—22no—
586C2—42no—
587C2—161no—
588C2#2261938211yescharacteristic
589C2C2×#1798881411yescharacteristic
590C2#2261964811yescharacteristic
subgroupG/H
centerC2×C4#14556563
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
Fitting, prime radicalC73×#3035C2
socleC22×C73C2×#121
hypercenter#3035D73
hypocenterC73#19124
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #22620486C2semidirect
2. #22619719C2semidirect
3. #41×#10596831C2semidirect
4. #22609363C2semidirect
5. #22609356C2semidirect
6. #22609345C2semidirect
7. #22609338C2semidirect
8. #22609311C2semidirect
9. #22609304C2semidirect
10. #22609277C2semidirect
11. #22609270C2semidirect
12. C2×#17988337C2semidirect
13. #22608589C2semidirect
14. #22608580C2semidirect
173. #41×C73SD16semidirect
264. #10596831#135semidirect
311. C73#19124semidirect
444. #41#11924016semidirect

Maximal subgroups

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

subgroupindex
#226204862
#226197192
#41×#105968312
#226093632
#226093562
#226093452
#226093382
#226093112
#226093042
#226092772
#226092702
C2×#179883372
#226085892
#226085802
C73×#30352
#1912473