Finite Group Databasebeta

← #33056799

Subgroups — #33056799

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#22620520C211yesmaximal, characteristic
2#22619082C211yesmaximal, characteristic, complemented
3#22608807C211yesmaximal, characteristic, complemented
4#22608795C211yesmaximal, characteristic, complemented
5#22608793C211yesmaximal, characteristic, complemented
6#22608788C211yesmaximal, characteristic, complemented
7#22608772C211yesmaximal, characteristic, complemented
8#22608767C211yesmaximal, characteristic, complemented
9#22608760C211yesmaximal, characteristic, complemented
10#22608758C211yesmaximal, characteristic, complemented
11#22608699C211yesmaximal, characteristic, complemented
12#22608389C211yesmaximal, characteristic, complemented
13#22608382C211yesmaximal, characteristic, complemented
14#22608221C211yesmaximal, characteristic, complemented
15C73×#2981C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988993C411yescharacteristic
18#17988974C411yescharacteristic
19#17988951C411yescharacteristic
20#17988949C411yescharacteristic
21#17988838C411yescharacteristic
22#17988838C411yescharacteristic
23#17988831C411yescharacteristic
24#17988831C411yescharacteristic
25#17988717C2211yescharacteristic
26C8×Dic146C2211yescharacteristic
27C4×#11924016C2211yescharacteristic
28C4×#11924016C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988662—21no—
33#17988661—21no—
34C8×D292C2211yescharacteristic
35#17988647—21no—
36#17988612—21no—
37#17988611C2211yescharacteristic
38C4×#11924012C2211yescharacteristic
39C2×C4×#10596831C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44#17988317C2211yescharacteristic
45#17988317C2211yescharacteristic
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48D4⋊#10596831C2211yescharacteristic
49D4⋊#10596831C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55#17988308C2211yescharacteristic
56#532×C73C2211yescharacteristic
57#436×C73C2211yescharacteristic
58#436×C73C2211yescharacteristic
59#435×C73—21no—
60#435×C73—21no—
61C8×D4×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#432×C73C2211yescharacteristic
64#431×C73C2211yescharacteristic
65#408×C73—21no—
66#408×C73—21no—
67C2×#11924016C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924013C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924012C2×C411yescharacteristic
73C2×#11924012C2×C411yescharacteristic
74C2×#11924011—21no—
75C22×#10596831—21no—
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⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556520—21no—
95#14556520—21no—
96#14556514C2×C411yescharacteristic
97#14556514C2×C411yescharacteristic
98#14556512C2×C411yescharacteristic
99#14556512C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102#14556511C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104#14556503—21no—
105#14556503—21no—
106#14556502C2×C411yescharacteristic
107#14556502C2×C411yescharacteristic
108#14556501—21no—
109C4×#10596831—21no—
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C8×Dic73—21no—
115C2×#41×C73—21no—
116C2×M16×C73—21no—
117C2×M16×C73—21no—
118C22×C8×C73—21no—
119C22×C8×C73—21no—
120C4⋊Q8×C73C2×C411yescharacteristic
121#127×C73C2×C411yescharacteristic
122#124×C73—21no—
123#121×C73—21no—
124#121×C73C2×C411yescharacteristic
125#121×C73C2×C411yescharacteristic
126C4×D4×C73—21no—
127C4×D4×C73C2311yescharacteristic
128C4×D4×C73C2311yescharacteristic
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73D411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139C22⋊C8×C73D411yescharacteristic
140C22⋊C8×C73D411yescharacteristic
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#11924016—41no—
149#11924016—41no—
150#11924013—41no—
151#11924013—41no—
152#11924012—41no—
153#11924012—41no—
154#11924012—81no—
155#11924011—81no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—42no—
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C8×D73—81no—
166C4⋊Dic73C22×C411yescharacteristic
167C4⋊Dic73C22×C411yescharacteristic
168#11924007—21no—
169#11924007—21no—
170#11924007—21no—
171#11924007—21no—
172C22⋊Dic73—21no—
173#11924005—21no—
174#11924005—21no—
175#11924005—21no—
176#11924005—21no—
177C4×Dic73—21no—
178#41×C73—81no—
179#41×C73—81no—
180C2×Q8×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73C22×C411yescharacteristic
186C2×D4×C73C22×C411yescharacteristic
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73#4111yescharacteristic
192M16×C73—81no—
193M16×C73—81no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—81no—
197C2×C8×C73—81no—
198C2×C8×C73C2×D411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C4⋊C4×C73—21no—
203C4⋊C4×C73C22×C411yescharacteristic
204C4⋊C4×C73C22×C411yescharacteristic
205C22⋊C4×C73—21no—
206C22⋊C4×C73—21no—
207C22⋊C4×C73—21no—
208C22⋊C4×C73—21no—
209C42×C73C22×C411yescharacteristic
210C42×C73C2×D411yescharacteristic
211C42×C73#4111yescharacteristic
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—21no—
215C23×C73C4×D411yescharacteristic
216C22×D73—21no—
217Q8×C73—81no—
218D4×C73—21no—
219D4×C73—21no—
220D4×C73—21no—
221D4×C73—21no—
222D4×C73—81no—
223D4×C73—81no—
224D4×C73—81no—
225D4×C73—81no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73C4×D411yescharacteristic
238C2×C4×C73C4×D411yescharacteristic
239C2×C4×C73C4×D411yescharacteristic
240C2×C4×C73C23×C411yescharacteristic
241C2×C4×C73C22×D411yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C22⋊D73—81no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247D292—21no—
248D292—21no—
249C4×D73—41no—
250C4×D73—41no—
251Dic146—21no—
252Dic146—21no—
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×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73C2×C4×D411yescharacteristic
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#56811yescharacteristic
287C4×C73#56811yescharacteristic
288C4×C73#57611yescharacteristic
289C4×C73#57711yescharacteristic
290Dic73—41no—
291Dic73—41no—
292Dic73—41no—
293#17987—731nomaximal, Sylow
294C2×C73—41no—
295C2×C73—81no—
296C2×C73—81no—
297C2×C73#293211yescharacteristic
298C2×C73#294611yescharacteristic
299C2×C73#295611yescharacteristic
300D73—81no—
301#3171—731no—
302#2993—731no—
303#2981D7311yescharacteristic, complemented
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#532C2×D7311yescharacteristic
318#529—731no—
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#446—731no—
328C8×Q8—731no—
329C4×SD16—731no—
330C4×SD16—731no—
331C4×D8—731no—
332C4×D8—731no—
333#436—731no—
334#436—1461no—
335#436C2×D7311yescharacteristic
336#436C2×D7311yescharacteristic
337#435—21no—
338#435—21no—
339#435—1461no—
340C8×D4—731no—
341C8×D4C2×D7311yescharacteristic
342C8×D4C2×D7311yescharacteristic
343#433—1461no—
344#432C2×D7311yescharacteristic
345#431C2×D7311yescharacteristic
346#424—1461no—
347#423—731no—
348#408—21no—
349#408—21no—
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—21no—
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—21no—
381C22×C8—1461no—
382C22×C8—1461no—
383C4⋊Q8C4×D7311yescharacteristic
384#127C4×D7311yescharacteristic
385#126—1461no—
386#125—731no—
387#124—21no—
388#124—731no—
389#123—1461no—
390C22⋊Q8—731no—
391#121—21no—
392#121—731no—
393#121C4×D7311yescharacteristic
394#121C4×D7311yescharacteristic
395C4×Q8—731no—
396C4×D4—21no—
397C4×D4—731no—
398C4×D4—1461no—
399C4×D4C22×D7311yescharacteristic
400C4×D4C22×D7311yescharacteristic
401#117—1461no—
402C2×C42C22×D7311yescharacteristic
403#107—731no—
404#107—731no—
405#106—731no—
406#106—731no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—1461no—
410C4⋊C8—1461no—
411C4⋊C8—1461no—
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—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
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—731no—
438C4×C8—731no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—1461no—
442C4×C8—1461no—
443C4×C8C22×D7311yescharacteristic
444C4×C8C22×D7311yescharacteristic
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—731no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—731no—
454C2×D4—1461no—
455C2×D4C2×C4×D7311yescharacteristic
456C2×D4C2×C4×D7311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
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—81no—
477C2×C8—2922no—
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—731no—
493C4⋊C4—731no—
494C4⋊C4—1461no—
495C4⋊C4—1461no—
496C4⋊C4—1461no—
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—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C42—1461no—
510C42C2×C4×D7311yescharacteristic
511C42C2×C22⋊D7311yescharacteristic
512C42#1192402811yescharacteristic
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—21no—
516C23—1461no—
517C23C4×C22⋊D7311yescharacteristic
518Q8—81no—
519Q8—1461no—
520Q8—1461no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—5841no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—1461no—
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—41no—
575C22—41no—
576C22—41no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22C2×C4×C22⋊D7311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—2921no—
588C4—2921no—
589C4—2921no—
590C4#1798935211yescharacteristic
591C4#1798935211yescharacteristic
592C4#1798939011yescharacteristic
593C4#1798939811yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—5841no—
598C2#2261864711yescharacteristic
599C2#2261876311yescharacteristic
600C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2981C2
socleC22×C73C2×C4×D4
prime radical#22620520C2
cosocleC42×C73C24
hypercenter#2981D73
hypocenterC73#17987
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #22619082C2semidirect
3. #22608807C2semidirect
4. #22608795C2semidirect
5. #22608793C2semidirect
6. #22608788C2semidirect
7. #22608772C2semidirect
8. #22608767C2semidirect
9. #22608760C2semidirect
10. #22608758C2semidirect
11. #22608699C2semidirect
12. #22608389C2semidirect
13. #22608382C2semidirect
14. #22608221C2semidirect
15. C73×#2981C2semidirect
303. #2981D73semidirect
316. C73#17987semidirect

Maximal subgroups

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

subgroupindex
#226205202
#226190822
#226088072
#226087952
#226087932
#226087882
#226087722
#226087672
#226087602
#226087582
#226086992
#226083892
#226083822
#226082212
C73×#29812
#1798773