Finite Group Databasebeta

← #33056929

Subgroups — #33056929

Order 18688.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619951C211yesmaximal, characteristic
2#22618948C211yesmaximal, characteristic, complemented
3#22618929C211yesmaximal, characteristic, complemented
4#22608820C211yesmaximal, characteristic, complemented
5#22608815C211yesmaximal, characteristic, complemented
6#22608780C211yesmaximal, characteristic, complemented
7#22608773C211yesmaximal, characteristic, complemented
8#22608773C211yesmaximal, characteristic, complemented
9#22608759C211yesmaximal, characteristic, complemented
10#22608737C211yesmaximal, characteristic, complemented
11#22608730C211yesmaximal, characteristic, complemented
12#22608389C211yesmaximal, characteristic, complemented
13#22608311C211yesmaximal, characteristic, complemented
14#22608212C211yesmaximal, characteristic, complemented
15C73×#1572C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17C4×#11924028C2211yescharacteristic
18#17988929C411yescharacteristic
19#17988912C411yescharacteristic
20#17988895C411yescharacteristic
21#17988888C411yescharacteristic
22#17988810C411yescharacteristic
23#17988803C411yescharacteristic
24#17988751C411yescharacteristic
25#17988734C411yescharacteristic
26#17988714C2211yescharacteristic
27#17988711C2211yescharacteristic
28#17988711C2211yescharacteristic
29#17988711C2211yescharacteristic
30C4×Dic292C2211yescharacteristic
31C4×#11924017C2211yescharacteristic
32C4×#11924017C2211yescharacteristic
33C4×D584C2211yescharacteristic
34#17988664C2211yescharacteristic
35#17988664C2211yescharacteristic
36#17988664C2211yescharacteristic
37#17988662—21no—
38#17988662—21no—
39#17988662—21no—
40#17988661—21no—
41#17988652C2211yescharacteristic
42#17988646—21no—
43#17988642—21no—
44#17988541—21no—
45C4×#11924012C2211yescharacteristic
46#17988539—21no—
47C2×C4×#10596831C2211yescharacteristic
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50#17988317C2211yescharacteristic
51#17988317C2211yescharacteristic
52#17988314C2211yescharacteristic
53#17988314C2211yescharacteristic
54#17988314C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#432×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64#335×C73C2211yescharacteristic
65#334×C73C2211yescharacteristic
66#334×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×#11924012D411yescharacteristic
73C2×#11924012D411yescharacteristic
74C2×#11924011—21no—
75C2×#11924011—21no—
76C2×#11924011—21no—
77C22×#10596831—21no—
78C2×C8×D73—21no—
79#14556585—21no—
80#14556583C2×C411yescharacteristic
81#14556579C2×C411yescharacteristic
82#14556574—21no—
83#14556570C2×C411yescharacteristic
84#14556565C2×C411yescharacteristic
85C4×Dic146C2×C411yescharacteristic
86C4×Dic146C2311yescharacteristic
87C4×Dic146C2311yescharacteristic
88C4×D292C2×C411yescharacteristic
89C4×D292C2311yescharacteristic
90C4×D292C2311yescharacteristic
91C4×C22⋊D73—21no—
92C4×C22⋊D73—21no—
93C4×C22⋊D73—21no—
94#14556550C2×C411yescharacteristic
95#14556548—21no—
96#14556548—21no—
97C42×D73—21no—
98#14556525C2×C411yescharacteristic
99#14556525C2×C411yescharacteristic
100#14556523C2×C411yescharacteristic
101#14556523C2×C411yescharacteristic
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556516C2×C411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556516C2×C411yescharacteristic
110#14556513C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556502D411yescharacteristic
119#14556502D411yescharacteristic
120#14556501—21no—
121C4×#10596831—21no—
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73C2×C411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73C2×C411yescharacteristic
139C22⋊C8×C73C2×C411yescharacteristic
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—41no—
146C2×Dic146C22×C411yescharacteristic
147C2×Dic146C22×C411yescharacteristic
148C2×D292C22×C411yescharacteristic
149C2×D292C22×C411yescharacteristic
150C2×C22⋊D73—21no—
151C2×C22⋊D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156Dic292—22no—
157#11924017—22no—
158#11924017—41no—
159D584—41no—
160#11924012—22no—
161#11924012—22no—
162#11924011—42no—
163#11924011—42no—
164#11924011—42no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—42no—
168C2×#10596831C2×D411yescharacteristic
169C2×#10596831C2×D411yescharacteristic
170C2×#10596831C2×D411yescharacteristic
171C2×#10596831C2×D411yescharacteristic
172C8×D73—42no—
173C4⋊Dic73C22×C411yescharacteristic
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176C4⋊Dic73C22×C411yescharacteristic
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182#11924007—21no—
183C22⋊Dic73—21no—
184C22⋊Dic73—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190#11924005—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73#4111yescharacteristic
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C42×C73C22×C411yescharacteristic
207C42×C73C2×D411yescharacteristic
208C42×C73#4111yescharacteristic
209C42×C73C2411yescharacteristic
210C23×C73C4×D411yescharacteristic
211C22×D73—21no—
212C22×D73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—41no—
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×D411yescharacteristic
220C2×C4×C73C4×D411yescharacteristic
221C2×C4×C73C23×C411yescharacteristic
222C2×C4×C73C22×D411yescharacteristic
223C2×C4×C73C2×#4111yescharacteristic
224C22⋊D73—42no—
225C22⋊D73—81no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232D292—21no—
233D292—21no—
234D292—21no—
235D292—21no—
236C4×D73—42no—
237C4×D73—41no—
238C4×D73—41no—
239C4×D73—41no—
240C4×D73—41no—
241C4×D73—81no—
242Dic146—21no—
243Dic146—21no—
244Dic146—21no—
245Dic146#13112yes—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254#10596831—22no—
255#10596831—21no—
256#10596831—21no—
257#10596831—41no—
258#10596831#13512yes—
259#10596831#13512yes—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73C2×C4×D411yescharacteristic
264C2×D73—41no—
265C2×D73—41no—
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C2×D73—41no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73C2×#13111yescharacteristic
275C4×C73#56811yescharacteristic
276C4×C73C2×#13511yescharacteristic
277C4×C73C2×#13511yescharacteristic
278Dic73—22no—
279Dic73—41no—
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284#17999—731nomaximal, Sylow
285C2×C73—41no—
286C2×C73#293311yescharacteristic
287C2×C73C4×#13511yescharacteristic
288C2×C73#295611yescharacteristic
289D73—81no—
290D73—81no—
291#3102—731no—
292#2971—731no—
293#2969—731no—
294#1590—731no—
295#1589—731no—
296#1584—731no—
297#1583—731no—
298#1583—731no—
299#1581—731no—
300C8×Q16—731no—
301C8×SD16—731no—
302#1572D7311yescharacteristic, complemented
303#1494—731no—
304#1476—731no—
305C8×M16—731no—
306C73#1799911yescharacteristic, complemented, Sylow
307#529—731no—
308C4×#41—731no—
309#485—731no—
310#482—731no—
311#479—731no—
312#478—731no—
313#464—731no—
314#463—731no—
315#452—731no—
316#449—731no—
317#446—731no—
318C8×Q8—731no—
319C8×Q8—731no—
320C8×Q8—731no—
321C4×Q16—731no—
322C4×SD16—731no—
323C4×SD16—731no—
324C4×D8—731no—
325#436—731no—
326#436—731no—
327#436—731no—
328#436—1461no—
329#436—1461no—
330#436—1461no—
331#435—1461no—
332C8×D4—731no—
333#433—1461no—
334#432—1461no—
335#432C2×D7311yescharacteristic
336#431C2×D7311yescharacteristic
337#431C2×D7311yescharacteristic
338#405—1461no—
339C4×M16—731no—
340C4×M16—1461no—
341C2×C4×C8—731no—
342#335C2×D7311yescharacteristic
343#335C2×D7311yescharacteristic
344#334C2×D7311yescharacteristic
345#334C2×D7311yescharacteristic
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349Q8⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8—731no—
353D4⋊C8—731no—
354#322—731no—
355#322—731no—
356C82—731no—
357C82—731no—
358C2×#41—731no—
359C2×Q16—731no—
360C2×SD16—731no—
361C2×SD16—731no—
362C2×D8—731no—
363C2×M16—731no—
364C2×M16—731no—
365C2×M16—1461no—
366C2×M16—1461no—
367C2×M16—1461no—
368C22×C8—1461no—
369C22×C8—1461no—
370#126—1461no—
371#125—731no—
372#124—731no—
373#123—1461no—
374C22⋊Q8—731no—
375#121—731no—
376C4×Q8—731no—
377C4×Q8—731no—
378C4×Q8—731no—
379C4×D4—731no—
380C4×D4—731no—
381C4×D4—731no—
382C4×D4—1461no—
383C4×D4—1461no—
384C4×D4—1461no—
385#117—731no—
386#117—1461no—
387#117—1461no—
388C2×C42—1461no—
389C2×C42C22×D7311yescharacteristic
390#107—731no—
391#107—731no—
392#106—731no—
393#106—731no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8—1461no—
398C4⋊C8C4×D7311yescharacteristic
399C4⋊C8C4×D7311yescharacteristic
400C4⋊C8C22×D7311yescharacteristic
401C4⋊C8C22×D7311yescharacteristic
402C4⋊C8C22×D7311yescharacteristic
403C4⋊C8C22×D7311yescharacteristic
404#103—731no—
405#103—731no—
406#103—731no—
407#103—731no—
408#102—731no—
409#102—731no—
410#102—731no—
411#102—731no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—1461no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8C4×D7311yescharacteristic
419C22⋊C8C4×D7311yescharacteristic
420#97—21no—
421#97—731no—
422#97—731no—
423#97—1461no—
424C4×C8—21no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—1461no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8—1461no—
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435#41—2921no—
436#41—1462no—
437C2×Q8—731no—
438C2×Q8—731no—
439C2×D4—731no—
440C2×D4—731no—
441C2×D4—1461no—
442C2×D4—1461no—
443C22×C4—1461no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4C2×C4×D7311yescharacteristic
448C22×C4D4×D7311yescharacteristic
449C22×C4#1192402911yescharacteristic
450Q16—1462no—
451SD16—2921no—
452SD16—1462no—
453D8—2921no—
454M16—2922no—
455M16—2922no—
456M16—2922no—
457M16—1462no—
458M16—1462no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—2922no—
464C2×C8—2922no—
465C2×C8—731no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8C2×C4×D7311yescharacteristic
472C2×C8C2×C4×D7311yescharacteristic
473C2×C8C2×C4×D7311yescharacteristic
474C2×C8C2×C4×D7311yescharacteristic
475C4⋊C4—731no—
476C4⋊C4—731no—
477C4⋊C4—731no—
478C4⋊C4—731no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C22⋊C4—1461no—
486C22⋊C4—1461no—
487C22⋊C4—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C42—1461no—
494C42—1461no—
495C42—1461no—
496C42—1461no—
497C42C2×C4×D7311yescharacteristic
498C42D4×D7311yescharacteristic
499C42#1192402911yescharacteristic
500C42C23×D7311yescharacteristic
501C23—1461no—
502C23—1461no—
503C23#1455655311yescharacteristic
504Q8—732no—
505Q8—1461no—
506Q8—1461no—
507Q8—1461no—
508D4—2922no—
509D4—5841no—
510D4—1461no—
511D4—1461no—
512D4—1461no—
513D4—1461no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—2922no—
520C2×C4—2921no—
521C2×C4—2921no—
522C2×C4—2921no—
523C2×C4—2921no—
524C2×C4—5841no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4#1455655311yescharacteristic
532C2×C4#1455655311yescharacteristic
533C2×C4#1455655311yescharacteristic
534C2×C4C22×C4×D7311yescharacteristic
535C2×C4C2×D4×D7311yescharacteristic
536C2×C4C2×#1192402911yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—2921no—
546C8—732no—
547C8—732no—
548C8—1462no—
549C8—1461no—
550C8—1461no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—2921no—
555C22—2921no—
556C22—2921no—
557C22—2921no—
558C22—2921no—
559C22—2921no—
560C22C2×#1455655311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—2921no—
566C4—2921no—
567C4—2921no—
568C4—2921no—
569C4—2921no—
570C4—1462no—
571C4#131×D7311yescharacteristic
572C4#1798935211yescharacteristic
573C4#135×D7311yescharacteristic
574C4#135×D7311yescharacteristic
575C2—41no—
576C2—5841no—
577C2—5841no—
578C2#2261865511yescharacteristic
579C2#2261870211yescharacteristic
580C2#2261884011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1572C2
socleC22×C73C2×C4×D4
prime radical#17988734C4
cosocleC42×C73C24
hypercenter#1572D73
hypocenterC73#17999
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #22618948C2semidirect
3. #22618929C2semidirect
4. #22608820C2semidirect
5. #22608815C2semidirect
6. #22608780C2semidirect
7. #22608773C2semidirect
8. #22608773C2semidirect
9. #22608759C2semidirect
10. #22608737C2semidirect
11. #22608730C2semidirect
12. #22608389C2semidirect
13. #22608311C2semidirect
14. #22608212C2semidirect
15. C73×#1572C2semidirect
302. #1572D73semidirect
306. C73#17999semidirect

Maximal subgroups

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

subgroupindex
#226199512
#226189482
#226189292
#226088202
#226088152
#226087802
#226087732
#226087592
#226087372
#226087302
#226083892
#226083112
#226082122
C73×#15722
#1799973