Finite Group Databasebeta

← #33057348

Subgroups — #33057348

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619962C211yesmaximal, characteristic
2#22618997C211yesmaximal, characteristic
3#22608831C211yesmaximal, characteristic, complemented
4#22608821C211yesmaximal, characteristic, complemented
5#22608809C211yesmaximal, characteristic, complemented
6#22608786C211yesmaximal, characteristic, complemented
7#22608774C211yesmaximal, characteristic, complemented
8#22608765C211yesmaximal, characteristic, complemented
9#22608741C211yesmaximal, characteristic, complemented
10C8×#11924015C211yesmaximal, characteristic, complemented
11#22608712C211yesmaximal, characteristic, complemented
12#22608399C211yesmaximal, characteristic
13#22608326C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#2984C211yesmaximal, characteristic, complemented
16#17989137C2211yescharacteristic
17#17988905C411yescharacteristic
18#17988905C411yescharacteristic
19#17988872C411yescharacteristic
20#17988872C411yescharacteristic
21#17988787C411yescharacteristic
22#17988787C411yescharacteristic
23#17988726C411yescharacteristic
24#17988726C411yescharacteristic
25C4×#11924015C2211yescharacteristic
26C4×#11924015C2211yescharacteristic
27C4×#11924015C2211yescharacteristic
28C4×#11924015C2211yescharacteristic
29#17988666C2211yescharacteristic
30#17988666C2211yescharacteristic
31#17988664—21no—
32C8×D292C2211yescharacteristic
33C8×D292C2211yescharacteristic
34#17988652—21no—
35#17988640C2211yescharacteristic
36#17988640C2211yescharacteristic
37#17988640C2211yescharacteristic
38#17988552—21no—
39#17988552—21no—
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46Q8⋊#10596831C2211yescharacteristic
47Q8⋊#10596831C2211yescharacteristic
48#17988314C2211yescharacteristic
49#17988314C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55C8×#10596831C2211yescharacteristic
56C2×C4×Q8×C73C2211yescharacteristic
57#446×C73—21no—
58#446×C73—21no—
59#446×C73C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C8×Q8×C73C2211yescharacteristic
63#432×C73—21no—
64#432×C73C2211yescharacteristic
65#431×C73—21no—
66#431×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924015C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924015C2×C411yescharacteristic
72C2×#11924011—21no—
73C2×#11924011—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76#14556591C2×C411yescharacteristic
77#14556588C2×C411yescharacteristic
78#14556579—21no—
79#14556565—21no—
80#14556565C2×C411yescharacteristic
81#14556565C2×C411yescharacteristic
82C4×D292—21no—
83C4×D292C2311yescharacteristic
84C4×D292C2311yescharacteristic
85#14556522C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89C4⋊#10596831—21no—
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556515C2×C411yescharacteristic
95#14556515C2×C411yescharacteristic
96#14556515C2×C411yescharacteristic
97#14556515C2×C411yescharacteristic
98#14556511C2×C411yescharacteristic
99#14556511C2×C411yescharacteristic
100#14556511C2×C411yescharacteristic
101#14556511C2×C411yescharacteristic
102C22⋊#10596831—21no—
103C22⋊#10596831—21no—
104C22⋊#10596831C2×C411yescharacteristic
105C22⋊#10596831C2×C411yescharacteristic
106#14556503—21no—
107#14556503—21no—
108#14556503—21no—
109#14556503—21no—
110C4×#10596831—21no—
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C4×#10596831C2311yescharacteristic
115C22×Q8×C73C2×C411yescharacteristic
116C4×Q8×C73—21no—
117C4×Q8×C73—21no—
118C4×Q8×C73C2×C411yescharacteristic
119C4×Q8×C73C2×C411yescharacteristic
120C4×Q8×C73C2311yescharacteristic
121C4×Q8×C73C2311yescharacteristic
122C2×C4⋊C4×C73—21no—
123C2×C4⋊C4×C73C2×C411yescharacteristic
124C2×C42×C73—21no—
125C2×C42×C73C2311yescharacteristic
126C4⋊C8×C73—21no—
127C4⋊C8×C73—21no—
128C4⋊C8×C73—21no—
129C4⋊C8×C73—21no—
130C4⋊C8×C73D411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73D411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137#97×C73—21no—
138#97×C73—21no—
139#97×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73—21no—
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×C4×D73—21no—
154C2×C4×D73—21no—
155#11924015—22no—
156#11924015—22no—
157#11924015—41no—
158#11924015—41no—
159#11924011—81no—
160#11924011—81no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C22×C411yescharacteristic
168C2×#10596831C22×C411yescharacteristic
169C8×D73—81no—
170C8×D73—81no—
171C4⋊Dic73—21no—
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174#11924005—21no—
175#11924005—21no—
176#11924005—21no—
177#11924005—21no—
178C2×Q8×C73—21no—
179C2×Q8×C73—22no—
180C2×Q8×C73—41no—
181C2×Q8×C73C22×C411yescharacteristic
182C2×Q8×C73C22×C411yescharacteristic
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73#4111yescharacteristic
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73C2×D411yescharacteristic
191C2×C8×C73C2×D411yescharacteristic
192C2×C8×C73C2×D411yescharacteristic
193C2×C8×C73C2×D411yescharacteristic
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73C22×C411yescharacteristic
200C4⋊C4×C73C22×C411yescharacteristic
201C42×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—21no—
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73C4×D411yescharacteristic
210C22×D73—21no—
211C22×D73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215Q8×C73—42no—
216Q8×C73#13112yes—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—41no—
226C2×C4×C73—42no—
227C2×C4×C73—42no—
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C23×C411yescharacteristic
232C2×C4×C73C22×D411yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C22⋊D73—81no—
235C22⋊D73—81no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238D292—21no—
239D292—21no—
240D292—21no—
241D292—21no—
242D292—42no—
243D292—81no—
244C4×D73—41no—
245C4×D73—41no—
246C4×D73—41no—
247C4×D73—41no—
248Dic146—81no—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—21no—
252C8×C73—21no—
253C8×C73—41no—
254C8×C73—41no—
255#10596831—21no—
256#10596831—21no—
257#10596831—21no—
258#10596831—21no—
259#10596831—41no—
260#10596831—41no—
261#10596831—41no—
262#10596831—41no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—21no—
266C22×C73C2×C4×D411yescharacteristic
267C2×D73—41no—
268C2×D73—41no—
269C2×D73—41no—
270C2×D73—41no—
271C2×D73—41no—
272C2×D73—41no—
273C4×C73—21no—
274C4×C73—22no—
275C4×C73—21no—
276C4×C73—21no—
277C4×C73—21no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73C2×#13111yescharacteristic
282C4×C73#56811yescharacteristic
283C4×C73#57711yescharacteristic
284C4×C73#57711yescharacteristic
285Dic73—41no—
286Dic73—41no—
287#18030—731nomaximal, Sylow
288C2×C73—41no—
289C2×C73#293311yescharacteristic
290C2×C73#294911yescharacteristic
291C2×C73#295511yescharacteristic
292D73—81no—
293D73—81no—
294#3103—731no—
295#2984D7311yescharacteristic, complemented
296#2979—731no—
297#1592—731no—
298#1590—731no—
299#1588—731no—
300#1585—731no—
301#1583—731no—
302#1582—731no—
303SD16⋊C8—731no—
304C8×SD16—731no—
305#1572—731no—
306#1496—731no—
307#1479—731no—
308#1454—731no—
309C73#1803011yescharacteristic, complemented, Sylow
310#532—731no—
311C2×C4×Q8C2×D7311yescharacteristic
312#481—731no—
313#481—731no—
314#475—731no—
315#475—731no—
316#460—731no—
317#460—731no—
318#448—731no—
319#448—731no—
320#446—21no—
321#446—21no—
322#446C2×D7311yescharacteristic
323#446C2×D7311yescharacteristic
324C8×Q8C2×D7311yescharacteristic
325C8×Q8C2×D7311yescharacteristic
326C4×SD16—731no—
327C4×SD16—731no—
328C4×SD16—731no—
329C4×SD16—731no—
330#436—731no—
331#436—731no—
332#436—1461no—
333C8×D4—731no—
334C8×D4—731no—
335C8×D4—1461no—
336#432—21no—
337#432C2×D7311yescharacteristic
338#431—21no—
339#431—731no—
340#431—731no—
341#431—731no—
342#431C2×D7311yescharacteristic
343#408—1461no—
344#408—1461no—
345#335—731no—
346#335—731no—
347#334—731no—
348#334—731no—
349Q8⋊C8—731no—
350Q8⋊C8—731no—
351Q8⋊C8—731no—
352Q8⋊C8—731no—
353D4⋊C8—731no—
354D4⋊C8—731no—
355D4⋊C8—731no—
356D4⋊C8—731no—
357#322—731no—
358#322—731no—
359#322—731no—
360C82—731no—
361C2×#41—1461no—
362C22×Q8C4×D7311yescharacteristic
363C2×SD16—731no—
364C2×SD16—731no—
365C2×SD16—731no—
366C2×SD16—731no—
367C2×M16—1461no—
368C2×M16—1461no—
369C22×C8—1461no—
370C22×C8—1461no—
371C4⋊Q8—731no—
372#127—731no—
373#124—1461no—
374#121—731no—
375#121—731no—
376#121—1461no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C4×D7311yescharacteristic
380C4×Q8C4×D7311yescharacteristic
381C4×Q8C22×D7311yescharacteristic
382C4×Q8C22×D7311yescharacteristic
383C4×D4—731no—
384C4×D4—731no—
385C4×D4—1461no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4C4×D7311yescharacteristic
388C2×C42—21no—
389C2×C42C22×D7311yescharacteristic
390#106—731no—
391#106—731no—
392#106—731no—
393#106—731no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—731no—
401C4⋊C8—731no—
402C4⋊C8—1461no—
403C4⋊C8C22⋊D7311yescharacteristic
404C4⋊C8C22⋊D7311yescharacteristic
405C4⋊C8C22×D7311yescharacteristic
406C4⋊C8C22×D7311yescharacteristic
407#103—731no—
408#103—731no—
409#103—731no—
410#103—731no—
411#102—731no—
412#102—731no—
413#102—731no—
414#102—731no—
415C22⋊C8—21no—
416C22⋊C8—731no—
417C22⋊C8—731no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422C22⋊C8—1461no—
423C22⋊C8—1461no—
424C22⋊C8C22⋊D7311yescharacteristic
425C22⋊C8C22⋊D7311yescharacteristic
426#97—21no—
427#97—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8—731no—
432C4×C8—731no—
433C4×C8—731no—
434C4×C8—731no—
435C4×C8—1461no—
436C4×C8C22×D7311yescharacteristic
437C4×C8C22×D7311yescharacteristic
438#41—5841no—
439#41—5841no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8—1461no—
444C2×Q8C2×C4×D7311yescharacteristic
445C2×Q8C2×C4×D7311yescharacteristic
446C2×D4—731no—
447C2×D4—731no—
448C2×D4—1461no—
449C2×D4—1461no—
450C2×D4—1461no—
451C2×D4—1461no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4C2×C4×D7311yescharacteristic
457C22×C4C2×C22⋊D7311yescharacteristic
458C22×C4#1192402811yescharacteristic
459SD16—2921no—
460SD16—2921no—
461SD16—1462no—
462SD16—1462no—
463M16—5841no—
464M16—5841no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—5841no—
468C2×C8—5841no—
469C2×C8—731no—
470C2×C8—731no—
471C2×C8—731no—
472C2×C8—731no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8C2×C22⋊D7311yescharacteristic
478C2×C8C2×C22⋊D7311yescharacteristic
479C2×C8C2×C22⋊D7311yescharacteristic
480C2×C8C2×C22⋊D7311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—731no—
487C4⋊C4—731no—
488C4⋊C4—1461no—
489C4⋊C4C2×C4×D7311yescharacteristic
490C4⋊C4C2×C4×D7311yescharacteristic
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C22⋊C4—1461no—
494C22⋊C4—1461no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42C2×C4×D7311yescharacteristic
500C42C2×C22⋊D7311yescharacteristic
501C42#1192402811yescharacteristic
502C42C23×D7311yescharacteristic
503C23—1461no—
504C23—1461no—
505C23C4×C22⋊D7311yescharacteristic
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—42no—
510Q8—5841no—
511Q8#1455659912yes—
512D4—2922no—
513D4—5841no—
514D4—5841no—
515D4—5841no—
516D4—1461no—
517D4—1461no—
518D4—1461no—
519D4—1461no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—2921no—
534C2×C4—2921no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4C4×C22⋊D7311yescharacteristic
538C2×C4C4×C22⋊D7311yescharacteristic
539C2×C4C4×C22⋊D7311yescharacteristic
540C2×C4C22×C4×D7311yescharacteristic
541C2×C4C22×C22⋊D7311yescharacteristic
542C2×C4C2×#1192402811yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—2921no—
550C8—2921no—
551C8—2921no—
552C8—2921no—
553C8—1461no—
554C8—1461no—
555C8—1461no—
556C8—1461no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—2921no—
561C22—2921no—
562C22—2921no—
563C22—2921no—
564C22—2921no—
565C22—2921no—
566C22C2×C4×C22⋊D7311yescharacteristic
567C4—21no—
568C4—22no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—2921no—
576C4—2921no—
577C4C2×#1455659911yescharacteristic
578C4#1798935311yescharacteristic
579C4#1798939511yescharacteristic
580C4#1798939511yescharacteristic
581C2—41no—
582C2—5841no—
583C2—5841no—
584C2#2261865611yescharacteristic
585C2#2261879011yescharacteristic
586C2#2261883211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2984C2
socleC22×C73C2×C4×D4
prime radical#17989137C22
cosocleC42×C73C24
hypercenter#2984D73
hypocenterC73#18030
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #22608831C2semidirect
4. #22608821C2semidirect
5. #22608809C2semidirect
6. #22608786C2semidirect
7. #22608774C2semidirect
8. #22608765C2semidirect
9. #22608741C2semidirect
10. C8×#11924015C2semidirect
11. #22608712C2semidirect
13. #22608326C2semidirect
14. #22608231C2semidirect
15. C73×#2984C2semidirect
295. #2984D73semidirect
309. C73#18030semidirect

Maximal subgroups

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

subgroupindex
#226199622
#226189972
#226088312
#226088212
#226088092
#226087862
#226087742
#226087652
#226087412
C8×#119240152
#226087122
#226083992
#226083262
#226082312
C73×#29842
#1803073