Finite Group Databasebeta

← #33056208

Subgroups — #33056208

Order 18688.

604 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619949C211yesmaximal, characteristic
2#22618900C211yesmaximal, characteristic, complemented
3#22618898C211yesmaximal, characteristic, complemented
4#22608825C211yesmaximal, characteristic, complemented
5#22608824C211yesmaximal, characteristic, complemented
6#22608818C211yesmaximal, characteristic, complemented
7#22608813C211yesmaximal, characteristic, complemented
8#22608784C211yesmaximal, characteristic, complemented
9#22608777C211yesmaximal, characteristic, complemented
10#22608770C211yesmaximal, characteristic, complemented
11#22608763C211yesmaximal, characteristic, complemented
12#22608712C211yesmaximal, characteristic, complemented
13#22608340C211yesmaximal, characteristic, complemented
14#22608215C211yesmaximal, characteristic, complemented
15C73×#1488C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988928C411yescharacteristic
18#17988911C411yescharacteristic
19#17988894C411yescharacteristic
20#17988887C411yescharacteristic
21#17988809C411yescharacteristic
22#17988802C411yescharacteristic
23#17988749C411yescharacteristic
24#17988732C411yescharacteristic
25#17988718C2211yescharacteristic
26#17988718C2211yescharacteristic
27#17988714C2211yescharacteristic
28#17988711C2211yescharacteristic
29C4×#11924018C2211yescharacteristic
30C4×#11924015C2211yescharacteristic
31C4×#11924016C2211yescharacteristic
32C4×#11924013C2211yescharacteristic
33#17988665C2211yescharacteristic
34#17988665C2211yescharacteristic
35#17988664C2211yescharacteristic
36#17988659—21no—
37#17988659—21no—
38#17988655—21no—
39#17988652C2211yescharacteristic
40#17988650—21no—
41#17988649—21no—
42#17988640—21no—
43#17988640C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988544—21no—
46C4×#11924012—21no—
47C2×C4×#10596831C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C4×#41×C73C2211yescharacteristic
61#432×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924012—21no—
73C2×#11924011—21no—
74C22×#10596831D411yescharacteristic
75C22×#10596831D411yescharacteristic
76C2×C8×D73—21no—
77#14556585—21no—
78#14556583C2×C411yescharacteristic
79#14556579C2×C411yescharacteristic
80#14556574—21no—
81#14556570C2×C411yescharacteristic
82#14556565C2×C411yescharacteristic
83C4×Dic146C2311yescharacteristic
84C4×D292C2311yescharacteristic
85C4×C22⋊D73—21no—
86#14556548—21no—
87#14556524C2×C411yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91C4⋊#10596831—21no—
92C4⋊#10596831—21no—
93C4⋊#10596831C2×C411yescharacteristic
94C4⋊#10596831C2×C411yescharacteristic
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556520—21no—
98#14556520—21no—
99#14556515C2×C411yescharacteristic
100#14556515C2×C411yescharacteristic
101#14556514C2×C411yescharacteristic
102#14556514C2×C411yescharacteristic
103#14556512C2×C411yescharacteristic
104#14556512C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831—21no—
109C22⋊#10596831—21no—
110C22⋊#10596831C2×C411yescharacteristic
111C22⋊#10596831C2×C411yescharacteristic
112#14556503—21no—
113#14556503—21no—
114#14556502—21no—
115#14556502—21no—
116#14556501—21no—
117C4×#10596831—21no—
118C4×#10596831D411yescharacteristic
119C4×#10596831D411yescharacteristic
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C2×#41×C73C2×C411yescharacteristic
126C4×Q8×C73C2×C411yescharacteristic
127C4×Q8×C73C2311yescharacteristic
128C4×D4×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73C2×C411yescharacteristic
131C4×D4×C73C2311yescharacteristic
132#117×C73—21no—
133#117×C73C2×C411yescharacteristic
134C2×C42×C73—21no—
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73—21no—
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141#97×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146C22×C411yescharacteristic
145C2×D292C22×C411yescharacteristic
146C2×C22⋊D73—21no—
147C2×C4×D73—21no—
148#11924018—41no—
149#11924016—41no—
150#11924015—41no—
151#11924013—41no—
152#11924012—42no—
153#11924012—42no—
154#11924011—42no—
155C2×#10596831—22no—
156C2×#10596831—22no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C2×D411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C8×D73—42no—
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170#11924007—21no—
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174C22⋊Dic73—21no—
175#11924005—21no—
176#11924005—21no—
177#11924005—21no—
178#11924005—21no—
179C4×Dic73—21no—
180#41×C73—41no—
181#41×C73—41no—
182C2×Q8×C73C22×C411yescharacteristic
183C2×D4×C73—21no—
184C2×D4×C73C22×C411yescharacteristic
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73#4111yescharacteristic
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73C22×C411yescharacteristic
198C4⋊C4×C73C22×C411yescharacteristic
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—21no—
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73—21no—
210C23×C73C4×D411yescharacteristic
211C22×D73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214D4×C73—21no—
215D4×C73—21no—
216D4×C73—42no—
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—41no—
225C2×C4×C73—42no—
226C2×C4×C73—42no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C4×D411yescharacteristic
232C2×C4×C73C23×C411yescharacteristic
233C2×C4×C73C22×D411yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C22⋊D73—42no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239D292—21no—
240D292—21no—
241C4×D73—41no—
242C4×D73—41no—
243Dic146—21no—
244Dic146—21no—
245C8×C73—41no—
246C8×C73—41no—
247C8×C73—41no—
248C8×C73—41no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—21no—
254#10596831—21no—
255#10596831—41no—
256#10596831—41no—
257#10596831#13512yes—
258#10596831#13512yes—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73C2×C4×D411yescharacteristic
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C4×C73—21no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73#56811yescharacteristic
277C4×C73#56811yescharacteristic
278C4×C73C2×#13511yescharacteristic
279C4×C73C2×#13511yescharacteristic
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283#17932—731nomaximal, Sylow
284C2×C73—41no—
285C2×C73—81no—
286C2×C73#293011yescharacteristic
287C2×C73C4×#13511yescharacteristic
288C2×C73#295511yescharacteristic
289D73—81no—
290#3102—731no—
291#2966—731no—
292#2965—731no—
293#1591—731no—
294#1590—731no—
295#1590—731no—
296#1589—731no—
297#1584—731no—
298#1583—731no—
299#1582—731no—
300#1581—731no—
301#1572—731no—
302#1488D7311yescharacteristic, complemented
303#1482—731no—
304#1450—731no—
305C73#1793211yescharacteristic, complemented, Sylow
306#529—731no—
307C4×#41C2×D7311yescharacteristic
308#485—731no—
309#482—731no—
310#479—731no—
311#478—731no—
312#464—731no—
313#463—731no—
314#452—731no—
315#449—731no—
316#446—731no—
317#446—731no—
318#446—731no—
319C8×Q8—731no—
320C4×Q16—731no—
321C4×SD16—731no—
322C4×SD16—731no—
323C4×D8—731no—
324#436—731no—
325#436—731no—
326#436—731no—
327#435—1461no—
328#435—1461no—
329#435—1461no—
330C8×D4—731no—
331C8×D4—1461no—
332#433—1461no—
333#432C2×D7311yescharacteristic
334#431—731no—
335#431—731no—
336#431—1461no—
337#431C2×D7311yescharacteristic
338#405—1461no—
339C4×M16—1461no—
340C2×C4×C8—731no—
341#335—731no—
342#335—731no—
343#334—731no—
344#334—731no—
345Q8⋊C8—731no—
346Q8⋊C8—731no—
347Q8⋊C8C2×D7311yescharacteristic
348Q8⋊C8C2×D7311yescharacteristic
349D4⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8C2×D7311yescharacteristic
352D4⋊C8C2×D7311yescharacteristic
353#322—731no—
354#322—731no—
355C82—731no—
356C82—731no—
357C2×#41C4×D7311yescharacteristic
358C2×Q16—731no—
359C2×SD16—731no—
360C2×SD16—731no—
361C2×D8—731no—
362C2×M16—1461no—
363C2×M16—1461no—
364C2×M16—1461no—
365C22×C8—731no—
366C22×C8—731no—
367C22×C8—1461no—
368#126—1461no—
369#125—731no—
370#124—731no—
371#123—1461no—
372C22⋊Q8—731no—
373#121—731no—
374C4×Q8—731no—
375C4×Q8C4×D7311yescharacteristic
376C4×Q8C22×D7311yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—731no—
380C4×D4—1461no—
381C4×D4C4×D7311yescharacteristic
382C4×D4C22×D7311yescharacteristic
383#117—21no—
384#117—1461no—
385#117C4×D7311yescharacteristic
386C2×C42—21no—
387C2×C42C22×D7311yescharacteristic
388#107—731no—
389#107—731no—
390#106—731no—
391#106—731no—
392C4⋊C8—21no—
393C4⋊C8—731no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—1461no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8C22×D7311yescharacteristic
402C4⋊C8C22×D7311yescharacteristic
403#103—731no—
404#103—731no—
405#103—731no—
406#103—731no—
407#102—731no—
408#102—731no—
409#102—731no—
410#102—731no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—731no—
414C22⋊C8—731no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420#97—21no—
421#97—1461no—
422#97—1461no—
423#97—1461no—
424C4×C8—731no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434#41—41no—
435#41—41no—
436C2×Q8—731no—
437C2×Q8C2×C4×D7311yescharacteristic
438C2×D4—21no—
439C2×D4—731no—
440C2×D4—1461no—
441C2×D4C2×C4×D7311yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—1461no—
446C22×C4C2×C4×D7311yescharacteristic
447C22×C4D4×D7311yescharacteristic
448C22×C4#1192402711yescharacteristic
449Q16—2921no—
450SD16—2921no—
451SD16—2921no—
452D8—2921no—
453M16—2922no—
454M16—2922no—
455M16—2922no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—2922no—
461C2×C8—731no—
462C2×C8—731no—
463C2×C8—731no—
464C2×C8—731no—
465C2×C8—731no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1462no—
472C2×C8—1462no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—731no—
476C4⋊C4—731no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4C2×C4×D7311yescharacteristic
482C4⋊C4C2×C4×D7311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1461no—
487C22⋊C4—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—1461no—
495C42C2×C4×D7311yescharacteristic
496C42D4×D7311yescharacteristic
497C42#1192402711yescharacteristic
498C42C23×D7311yescharacteristic
499C23—21no—
500C23—1461no—
501C23#1455655111yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—1461no—
505Q8—1461no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—2922no—
510D4—1461no—
511D4—1461no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4#1455655111yescharacteristic
530C2×C4#1455655111yescharacteristic
531C2×C4#1455655111yescharacteristic
532C2×C4C22×C4×D7311yescharacteristic
533C2×C4C2×D4×D7311yescharacteristic
534C2×C4C2×#1192402711yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—2921no—
540C8—2921no—
541C8—732no—
542C8—732no—
543C8—1461no—
544C8—1461no—
545C8—1461no—
546C8—1461no—
547C8—1461no—
548C8—1461no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—2921no—
556C22—2921no—
557C22—2921no—
558C22C2×#1455655111yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—2921no—
567C4—2921no—
568C4—2921no—
569C4#1798935311yescharacteristic
570C4#1798935311yescharacteristic
571C4#135×D7311yescharacteristic
572C4#135×D7311yescharacteristic
573C2—41no—
574C2—81no—
575C2—5841no—
576C2#2261863011yescharacteristic
577C2#2261869911yescharacteristic
578C2#2261883011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1488C2
socleC22×C73C2×C4×D4
prime radical#17988732C4
cosocleC42×C73C24
hypercenter#1488D73
hypocenterC73#17932
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #22618900C2semidirect
3. #22618898C2semidirect
4. #22608825C2semidirect
5. #22608824C2semidirect
6. #22608818C2semidirect
7. #22608813C2semidirect
8. #22608784C2semidirect
9. #22608777C2semidirect
10. #22608770C2semidirect
11. #22608763C2semidirect
12. #22608712C2semidirect
13. #22608340C2semidirect
14. #22608215C2semidirect
15. C73×#1488C2semidirect
302. #1488D73semidirect
305. C73#17932semidirect

Maximal subgroups

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

subgroupindex
#226199492
#226189002
#226188982
#226088252
#226088242
#226088182
#226088132
#226087842
#226087772
#226087702
#226087632
#226087122
#226083402
#226082152
C73×#14882
#1793273