Finite Group Databasebeta

← #33056795

Subgroups — #33056795

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620527C211yesmaximal, characteristic
2#22619006C211yesmaximal, characteristic, complemented
3#22608809C211yesmaximal, characteristic, complemented
4#22608795C211yesmaximal, characteristic, complemented
5#22608793C211yesmaximal, characteristic, complemented
6#22608786C211yesmaximal, characteristic, complemented
7#22608774C211yesmaximal, characteristic, complemented
8#22608765C211yesmaximal, characteristic, complemented
9#22608760C211yesmaximal, characteristic, complemented
10#22608758C211yesmaximal, characteristic, complemented
11#22608696C211yesmaximal, characteristic, complemented
12#22608391C211yesmaximal, characteristic, complemented
13#22608381C211yesmaximal, characteristic, complemented
14#22608221C211yesmaximal, characteristic, complemented
15C73×#2993C211yesmaximal, characteristic, complemented
16#17989137C2211yescharacteristic
17#17988997C411yescharacteristic
18#17988977C411yescharacteristic
19#17988953C411yescharacteristic
20#17988946C411yescharacteristic
21#17988838C411yescharacteristic
22#17988838C411yescharacteristic
23#17988835C411yescharacteristic
24#17988835C411yescharacteristic
25C4×#11924015C2211yescharacteristic
26C4×#11924015C2211yescharacteristic
27C4×#11924013C2211yescharacteristic
28C4×#11924013C2211yescharacteristic
29#17988666C2211yescharacteristic
30#17988666C2211yescharacteristic
31#17988657—21no—
32#17988657—21no—
33C8×D292C2211yescharacteristic
34C8×D292C2211yescharacteristic
35#17988644C2211yescharacteristic
36#17988552—21no—
37#17988552—21no—
38C4×#11924012C2211yescharacteristic
39C2×C4×#10596831C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48#17988314C2211yescharacteristic
49#17988314C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55#17988308C2211yescharacteristic
56#529×C73C2211yescharacteristic
57#446×C73C2211yescharacteristic
58C8×Q8×C73C2211yescharacteristic
59#436×C73—21no—
60#436×C73C2211yescharacteristic
61#435×C73—21no—
62C8×D4×C73C2211yescharacteristic
63#433×C73—21no—
64#431×C73C2211yescharacteristic
65#424×C73—21no—
66#423×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924015C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924012C2×C411yescharacteristic
73C2×#11924012C2×C411yescharacteristic
74C2×#11924011—21no—
75C2×#11924011—21no—
76C22×#10596831—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79#14556591C2×C411yescharacteristic
80#14556588C2×C411yescharacteristic
81#14556579—21no—
82#14556565—21no—
83#14556565C2×C411yescharacteristic
84#14556565C2×C411yescharacteristic
85C4×D292—21no—
86C4×D292C2311yescharacteristic
87C4×D292C2311yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556524C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91#14556522C2×C411yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556515C2×C411yescharacteristic
95#14556515C2×C411yescharacteristic
96#14556512C2×C411yescharacteristic
97#14556512C2×C411yescharacteristic
98#14556511C2×C411yescharacteristic
99#14556511C2×C411yescharacteristic
100#14556511C2×C411yescharacteristic
101#14556511C2×C411yescharacteristic
102C22⋊#10596831—21no—
103#14556503—21no—
104#14556503—21no—
105#14556503—21no—
106#14556503—21no—
107#14556502—21no—
108#14556502C2×C411yescharacteristic
109#14556502C2×C411yescharacteristic
110C4×#10596831—21no—
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C4×#10596831C2311yescharacteristic
115C2×M16×C73—21no—
116C2×M16×C73—21no—
117C22×C8×C73—21no—
118#126×C73—21no—
119#125×C73C2×C411yescharacteristic
120#124×C73C2×C411yescharacteristic
121#123×C73—21no—
122C22⋊Q8×C73C2×C411yescharacteristic
123#121×C73C2×C411yescharacteristic
124C4×Q8×C73C2311yescharacteristic
125C4×D4×C73—21no—
126C4×D4×C73C2311yescharacteristic
127#117×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73—21no—
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73D411yescharacteristic
133C4⋊C8×C73D411yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73D411yescharacteristic
139C22⋊C8×C73D411yescharacteristic
140#97×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—41no—
156#11924015—41no—
157#11924013—41no—
158#11924013—41no—
159#11924012—41no—
160#11924012—41no—
161#11924011—81no—
162#11924011—81no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—42no—
168C2×#10596831C22×C411yescharacteristic
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831C22×C411yescharacteristic
171C2×#10596831C22×C411yescharacteristic
172C8×D73—81no—
173C8×D73—81no—
174C4⋊Dic73—21no—
175C4⋊Dic73C22×C411yescharacteristic
176C4⋊Dic73C22×C411yescharacteristic
177#11924005—21no—
178#11924005—21no—
179#11924005—21no—
180#11924005—21no—
181C2×Q8×C73C22×C411yescharacteristic
182C2×D4×C73—21no—
183C2×D4×C73C22×C411yescharacteristic
184C22×C4×C73—21no—
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73#4111yescharacteristic
188M16×C73—81no—
189M16×C73—81no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—81no—
193C2×C8×C73C2×D411yescharacteristic
194C2×C8×C73C2×D411yescharacteristic
195C2×C8×C73C2×D411yescharacteristic
196C2×C8×C73C2×D411yescharacteristic
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73C22×C411yescharacteristic
202C4⋊C4×C73C22×C411yescharacteristic
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C22⋊C4×C73—21no—
206C22⋊C4×C73—21no—
207C22⋊C4×C73—21no—
208C42×C73—21no—
209C42×C73C22×C411yescharacteristic
210C42×C73C2×D411yescharacteristic
211C42×C73#4111yescharacteristic
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73C4×D411yescharacteristic
215C22×D73—21no—
216C22×D73—21no—
217Q8×C73—21no—
218Q8×C73—21no—
219D4×C73—21no—
220D4×C73—21no—
221D4×C73—81no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73C4×D411yescharacteristic
233C2×C4×C73C4×D411yescharacteristic
234C2×C4×C73C4×D411yescharacteristic
235C2×C4×C73C23×C411yescharacteristic
236C2×C4×C73C22×D411yescharacteristic
237C2×C4×C73C2×#4111yescharacteristic
238C22⋊D73—81no—
239C22⋊D73—81no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242D292—21no—
243D292—21no—
244D292—21no—
245D292—21no—
246D292—81no—
247D292—81no—
248C4×D73—41no—
249C4×D73—41no—
250C4×D73—41no—
251C4×D73—41no—
252Dic146—81no—
253C8×C73—21no—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—41no—
258C8×C73—41no—
259#10596831—22no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267C22×C73—21no—
268C22×C73—21no—
269C22×C73—21no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73C2×C4×D411yescharacteristic
274C2×D73—41no—
275C2×D73—41no—
276C2×D73—41no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C4×C73—21no—
281C4×C73—21no—
282C4×C73—21no—
283C4×C73—21no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73—41no—
287C4×C73#56811yescharacteristic
288C4×C73#56811yescharacteristic
289C4×C73#57611yescharacteristic
290C4×C73#57711yescharacteristic
291Dic73—41no—
292Dic73—41no—
293#17987—731nomaximal, Sylow
294C2×C73—41no—
295C2×C73—81no—
296C2×C73#293211yescharacteristic
297C2×C73#294611yescharacteristic
298C2×C73#295611yescharacteristic
299D73—81no—
300D73—81no—
301#3171—731no—
302#2993D7311yescharacteristic, complemented
303#2981—731no—
304#1588—731no—
305#1586—731no—
306#1586—731no—
307#1585—731no—
308#1583—731no—
309#1582—731no—
310#1581—731no—
311#1581—731no—
312#1569—731no—
313#1494—731no—
314#1492—731no—
315#1451—731no—
316C73#1798711yescharacteristic, complemented, Sylow
317#532—731no—
318#529C2×D7311yescharacteristic
319#501—731no—
320#496—731no—
321#490—731no—
322#489—731no—
323#469—731no—
324#469—731no—
325#468—731no—
326#468—731no—
327#446C2×D7311yescharacteristic
328C8×Q8C2×D7311yescharacteristic
329C4×SD16—731no—
330C4×SD16—731no—
331C4×D8—731no—
332C4×D8—731no—
333#436—21no—
334#436—731no—
335#436—731no—
336#436C2×D7311yescharacteristic
337#435—21no—
338#435—1461no—
339#435—1461no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4C2×D7311yescharacteristic
343#433—21no—
344#432—731no—
345#431C2×D7311yescharacteristic
346#424—21no—
347#423C2×D7311yescharacteristic
348#408—1461no—
349#408—1461no—
350C4×M16—731no—
351C2×C4×C8—731no—
352#335—731no—
353#335—731no—
354#334—731no—
355#334—731no—
356Q8⋊C8—731no—
357Q8⋊C8—731no—
358D4⋊C8—731no—
359D4⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364#322—731no—
365#322—731no—
366#322—731no—
367#322—731no—
368C2×#41—1461no—
369C2×SD16—731no—
370C2×SD16—731no—
371C2×D8—731no—
372C2×D8—731no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—731no—
376C2×M16—731no—
377C2×M16—1461no—
378C2×M16—1461no—
379C22×C8—21no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383C4⋊Q8—731no—
384#127—731no—
385#126—21no—
386#125C4×D7311yescharacteristic
387#124—1461no—
388#124C4×D7311yescharacteristic
389#123—21no—
390C22⋊Q8C4×D7311yescharacteristic
391#121—731no—
392#121—731no—
393#121—1461no—
394#121C4×D7311yescharacteristic
395C4×Q8C22×D7311yescharacteristic
396C4×D4—21no—
397C4×D4—731no—
398C4×D4—731no—
399C4×D4—1461no—
400C4×D4C22×D7311yescharacteristic
401#117—21no—
402C2×C42C22×D7311yescharacteristic
403#107—731no—
404#107—731no—
405#106—731no—
406#106—731no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8C22⋊D7311yescharacteristic
413C4⋊C8C22⋊D7311yescharacteristic
414C4⋊C8C22×D7311yescharacteristic
415C4⋊C8C22×D7311yescharacteristic
416#103—731no—
417#103—731no—
418#102—731no—
419#102—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—1461no—
427C22⋊C8—1461no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8C22⋊D7311yescharacteristic
432C22⋊C8C22⋊D7311yescharacteristic
433#97—21no—
434#97—731no—
435#97—731no—
436#97—1461no—
437C4×C8—21no—
438C4×C8—731no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—1461no—
443C4×C8C22×D7311yescharacteristic
444C4×C8C22×D7311yescharacteristic
445#41—5841no—
446#41—5841no—
447C2×Q8—1461no—
448C2×Q8C2×C4×D7311yescharacteristic
449C2×D4—21no—
450C2×D4—731no—
451C2×D4—731no—
452C2×D4—1461no—
453C2×D4—1461no—
454C2×D4—1461no—
455C2×D4—1461no—
456C2×D4C2×C4×D7311yescharacteristic
457C22×C4—21no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4C2×C4×D7311yescharacteristic
461C22×C4C2×C22⋊D7311yescharacteristic
462C22×C4#1192402811yescharacteristic
463SD16—2921no—
464SD16—2921no—
465D8—2921no—
466D8—2921no—
467M16—81no—
468M16—81no—
469M16—2921no—
470M16—2921no—
471M16—5841no—
472M16—5841no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—2922no—
477C2×C8—5841no—
478C2×C8—5841no—
479C2×C8—731no—
480C2×C8—731no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8C2×C22⋊D7311yescharacteristic
488C2×C8C2×C22⋊D7311yescharacteristic
489C2×C8C2×C22⋊D7311yescharacteristic
490C2×C8C2×C22⋊D7311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—1461no—
498C4⋊C4C2×C4×D7311yescharacteristic
499C4⋊C4C2×C4×D7311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C42—21no—
510C42C2×C4×D7311yescharacteristic
511C42C2×C22⋊D7311yescharacteristic
512C42#1192402811yescharacteristic
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—1461no—
516C23—1461no—
517C23C4×C22⋊D7311yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—5841no—
521D4—21no—
522D4—21no—
523D4—81no—
524D4—5841no—
525D4—5841no—
526D4—5841no—
527D4—5841no—
528D4—1461no—
529D4—1461no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4C4×C22⋊D7311yescharacteristic
549C2×C4C4×C22⋊D7311yescharacteristic
550C2×C4C4×C22⋊D7311yescharacteristic
551C2×C4C22×C4×D7311yescharacteristic
552C2×C4C22×C22⋊D7311yescharacteristic
553C2×C4C2×#1192402811yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—2921no—
561C8—2921no—
562C8—2921no—
563C8—1462no—
564C8—1461no—
565C8—1461no—
566C8—1461no—
567C8—1461no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—2921no—
575C22—2921no—
576C22—2921no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22C2×C4×C22⋊D7311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—2921no—
589C4—2921no—
590C4#1798935211yescharacteristic
591C4#1798935211yescharacteristic
592C4#1798939011yescharacteristic
593C4#1798939511yescharacteristic
594C2—41no—
595C2—81no—
596C2—5841no—
597C2—5841no—
598C2#2261864711yescharacteristic
599C2#2261875911yescharacteristic
600C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2993C2
socleC22×C73C2×C4×D4
prime radical#22620527C2
cosocleC42×C73C24
hypercenter#2993D73
hypocenterC73#17987
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #22619006C2semidirect
3. #22608809C2semidirect
4. #22608795C2semidirect
5. #22608793C2semidirect
6. #22608786C2semidirect
7. #22608774C2semidirect
8. #22608765C2semidirect
9. #22608760C2semidirect
10. #22608758C2semidirect
11. #22608696C2semidirect
12. #22608391C2semidirect
13. #22608381C2semidirect
14. #22608221C2semidirect
15. C73×#2993C2semidirect
302. #2993D73semidirect
316. C73#17987semidirect

Maximal subgroups

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

subgroupindex
#226205272
#226190062
#226088092
#226087952
#226087932
#226087862
#226087742
#226087652
#226087602
#226087582
#226086962
#226083912
#226083812
#226082212
C73×#29932
#1798773