Finite Group Databasebeta

← #33056803

Subgroups — #33056803

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#22620526C211yesmaximal, characteristic
2#22619082C211yesmaximal, characteristic, complemented
3#22619006C211yesmaximal, characteristic, complemented
4#22608811C211yesmaximal, characteristic, complemented
5#22608797C211yesmaximal, characteristic, complemented
6#22608797C211yesmaximal, characteristic, complemented
7#22608790C211yesmaximal, characteristic, complemented
8#22608776C211yesmaximal, characteristic, complemented
9#22608769C211yesmaximal, characteristic, complemented
10#22608762C211yesmaximal, characteristic, complemented
11#22608762C211yesmaximal, characteristic, complemented
12#22608698C211yesmaximal, characteristic, complemented
13#22608392C211yesmaximal, characteristic, complemented
14#22608383C211yesmaximal, characteristic, complemented
15C73×#1451C211yesmaximal, characteristic, complemented
16#17989137C2211yescharacteristic
17#17989121C2211yescharacteristic
18#17988996C411yescharacteristic
19#17988976C411yescharacteristic
20#17988952C411yescharacteristic
21#17988947C411yescharacteristic
22#17988840C411yescharacteristic
23#17988840C411yescharacteristic
24#17988833C411yescharacteristic
25#17988833C411yescharacteristic
26#17988717C2211yescharacteristic
27C8×Dic146C2211yescharacteristic
28C4×#11924017C2211yescharacteristic
29C4×#11924017C2211yescharacteristic
30C4×D584C2211yescharacteristic
31C4×D584C2211yescharacteristic
32#17988666C2211yescharacteristic
33#17988666C2211yescharacteristic
34#17988666C2211yescharacteristic
35#17988662—21no—
36#17988661—21no—
37#17988657—21no—
38#17988657—21no—
39C8×D292C2211yescharacteristic
40C8×D292C2211yescharacteristic
41C8×D292C2211yescharacteristic
42#17988647—21no—
43#17988644C2211yescharacteristic
44#17988612—21no—
45#17988611C2211yescharacteristic
46#17988552—21no—
47#17988552—21no—
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988338C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988316C2211yescharacteristic
57#17988316C2211yescharacteristic
58#17988316C2211yescharacteristic
59#17988316C2211yescharacteristic
60#431×C73C2211yescharacteristic
61C4×M16×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic
64#322×C73C2211yescharacteristic
65#322×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924017C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×D584C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×#11924012—21no—
73C2×#11924011—21no—
74C2×#11924011—21no—
75C2×#11924011—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79#14556591C2×C411yescharacteristic
80#14556588C2×C411yescharacteristic
81#14556585—21no—
82#14556583C2×C411yescharacteristic
83#14556579—21no—
84#14556579C2×C411yescharacteristic
85#14556574—21no—
86#14556570C2×C411yescharacteristic
87#14556565—21no—
88#14556565C2×C411yescharacteristic
89#14556565C2×C411yescharacteristic
90#14556565C2×C411yescharacteristic
91C4×Dic146C2311yescharacteristic
92C4×D292—21no—
93C4×D292C2311yescharacteristic
94C4×D292C2311yescharacteristic
95C4×D292C2311yescharacteristic
96C4×C22⋊D73—21no—
97#14556548—21no—
98#14556525C2×C411yescharacteristic
99#14556525C2×C411yescharacteristic
100#14556523C2×C411yescharacteristic
101#14556523C2×C411yescharacteristic
102C4⋊#10596831—21no—
103C4⋊#10596831C2311yescharacteristic
104C4⋊#10596831C2311yescharacteristic
105C4⋊#10596831C2311yescharacteristic
106C4⋊#10596831C2311yescharacteristic
107#14556520—21no—
108#14556520—21no—
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114#14556513C2×C411yescharacteristic
115#14556513C2×C411yescharacteristic
116#14556513C2×C411yescharacteristic
117C22⋊#10596831—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556503—21no—
122#14556503—21no—
123#14556503—21no—
124#14556502—21no—
125#14556501—21no—
126C8×Dic73—21no—
127C2×M16×C73C2×C411yescharacteristic
128C2×M16×C73C2×C411yescharacteristic
129C22×C8×C73—21no—
130C2×C42×C73C2311yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73D411yescharacteristic
133C22⋊C8×C73D411yescharacteristic
134C22⋊C8×C73D411yescharacteristic
135#97×C73C2×C411yescharacteristic
136#97×C73C2×C411yescharacteristic
137C4×C8×C73—21no—
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—81no—
145#11924028—81no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148C2×D292—21no—
149C2×D292—21no—
150C2×D292C22×C411yescharacteristic
151C2×D292C22×C411yescharacteristic
152C2×D292C22×C411yescharacteristic
153C2×C22⋊D73—21no—
154C2×C22⋊D73—21no—
155C2×C22⋊D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159#11924017—41no—
160#11924017—41no—
161D584—41no—
162D584—41no—
163#11924012—81no—
164#11924011—81no—
165#11924011—81no—
166#11924011—81no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C8×D73—81no—
172C8×D73—81no—
173C8×D73—81no—
174C4⋊Dic73—21no—
175C4⋊Dic73C22×C411yescharacteristic
176C4⋊Dic73C22×C411yescharacteristic
177C4⋊Dic73C22×C411yescharacteristic
178C4⋊Dic73C22×C411yescharacteristic
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182#11924007—21no—
183C22⋊Dic73—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190#11924005—21no—
191#11924005—21no—
192C4×Dic73—21no—
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73#4111yescharacteristic
196M16×C73—41no—
197M16×C73—41no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—42no—
201C2×C8×C73C22×C411yescharacteristic
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C2×C8×C73C2×D411yescharacteristic
208C2×C8×C73C2×D411yescharacteristic
209C42×C73C22×C411yescharacteristic
210C42×C73C2×D411yescharacteristic
211C42×C73#4111yescharacteristic
212C42×C73C2411yescharacteristic
213C23×C73C4×D411yescharacteristic
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—41no—
222C2×C4×C73C4×D411yescharacteristic
223C2×C4×C73C4×D411yescharacteristic
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C23×C411yescharacteristic
226C2×C4×C73C22×D411yescharacteristic
227C2×C4×C73C2×#4111yescharacteristic
228C22⋊D73—81no—
229C22⋊D73—81no—
230C22⋊D73—81no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236D292—21no—
237D292—21no—
238D292—21no—
239D292—21no—
240D292—21no—
241D292—21no—
242D292—81no—
243D292—81no—
244C4×D73—41no—
245C4×D73—41no—
246C4×D73—41no—
247C4×D73—41no—
248C4×D73—41no—
249C4×D73—41no—
250Dic146—21no—
251Dic146—21no—
252Dic146—81no—
253C8×C73—22no—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—21no—
260C8×C73—21no—
261C8×C73—21no—
262C8×C73—41no—
263#10596831—41no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267C22×C73—21no—
268C22×C73—21no—
269C22×C73—21no—
270C22×C73C2×C4×D411yescharacteristic
271C2×D73—41no—
272C2×D73—41no—
273C2×D73—41no—
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#56811yescharacteristic
285C4×C73#56811yescharacteristic
286C4×C73#57611yescharacteristic
287C4×C73#57711yescharacteristic
288Dic73—41no—
289Dic73—41no—
290Dic73—41no—
291Dic73—41no—
292Dic73—41no—
293#17987—731nomaximal, Sylow
294C2×C73—41no—
295C2×C73#293211yescharacteristic
296C2×C73#294611yescharacteristic
297C2×C73#295611yescharacteristic
298D73—81no—
299D73—81no—
300D73—81no—
301#3171—731no—
302#2993—731no—
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#1451D7311yescharacteristic, complemented
316C73#1798711yescharacteristic, complemented, Sylow
317#532—731no—
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—731no—
335#436—731no—
336#436—1461no—
337#435—1461no—
338#435—1461no—
339#435—1461no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4—731no—
343#433—1461no—
344#432—731no—
345#431C2×D7311yescharacteristic
346#424—1461no—
347#423—731no—
348#408—1461no—
349#408—1461no—
350C4×M16C2×D7311yescharacteristic
351C2×C4×C8C2×D7311yescharacteristic
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#322C2×D7311yescharacteristic
365#322C2×D7311yescharacteristic
366#322C2×D7311yescharacteristic
367#322C2×D7311yescharacteristic
368C2×#41—1461no—
369C2×SD16—731no—
370C2×SD16—731no—
371C2×D8—731no—
372C2×D8—731no—
373C2×M16—1461no—
374C2×M16—1461no—
375C2×M16—1461no—
376C2×M16—1461no—
377C2×M16C4×D7311yescharacteristic
378C2×M16C4×D7311yescharacteristic
379C22×C8—21no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383C4⋊Q8—731no—
384#127—731no—
385#126—1461no—
386#125—731no—
387#124—731no—
388#124—1461no—
389#123—1461no—
390C22⋊Q8—731no—
391#121—731no—
392#121—731no—
393#121—731no—
394#121—1461no—
395C4×Q8—731no—
396C4×D4—731no—
397C4×D4—731no—
398C4×D4—731no—
399C4×D4—1461no—
400C4×D4—1461no—
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—731no—
410C4⋊C8—731no—
411C4⋊C8—1461no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8D29211yescharacteristic
415C4⋊C8D29211yescharacteristic
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—1461no—
425C22⋊C8—1461no—
426C22⋊C8—1461no—
427C22⋊C8—1461no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8D29211yescharacteristic
432C22⋊C8D29211yescharacteristic
433#97—1461no—
434#97—1461no—
435#97C4×D7311yescharacteristic
436#97C4×D7311yescharacteristic
437C4×C8—21no—
438C4×C8—1461no—
439C4×C8C22×D7311yescharacteristic
440C4×C8C22×D7311yescharacteristic
441C4×C8C22×D7311yescharacteristic
442C4×C8C22×D7311yescharacteristic
443C4×C8C22×D7311yescharacteristic
444C4×C8C22×D7311yescharacteristic
445#41—5841no—
446#41—5841no—
447C2×Q8—731no—
448C2×Q8—1461no—
449C2×D4—731no—
450C2×D4—731no—
451C2×D4—731no—
452C2×D4—1461no—
453C2×D4—1461no—
454C2×D4—1461no—
455C2×D4—1461no—
456C2×D4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4C2×C4×D7311yescharacteristic
461C22×C4C2×D29211yescharacteristic
462C22×C4#1192402811yescharacteristic
463SD16—2921no—
464SD16—2921no—
465D8—2921no—
466D8—2921no—
467M16—41no—
468M16—41no—
469M16—5841no—
470M16—5841no—
471M16—5841no—
472M16—5841no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—42no—
476C2×C8—5841no—
477C2×C8—5841no—
478C2×C8—5841no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8C2×C4×D7311yescharacteristic
484C2×C8C2×C4×D7311yescharacteristic
485C2×C8C2×C4×D7311yescharacteristic
486C2×C8C2×C4×D7311yescharacteristic
487C2×C8C2×D29211yescharacteristic
488C2×C8C2×D29211yescharacteristic
489C2×C8C2×D29211yescharacteristic
490C2×C8C2×D29211yescharacteristic
491C4⋊C4—731no—
492C4⋊C4—731no—
493C4⋊C4—731no—
494C4⋊C4—731no—
495C4⋊C4—1461no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C22⋊C4—1461no—
501C22⋊C4—1461no—
502C22⋊C4—1461no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C42—1461no—
510C42C2×C4×D7311yescharacteristic
511C42C2×D29211yescharacteristic
512C42#1192402811yescharacteristic
513C42C23×D7311yescharacteristic
514C23—1461no—
515C23—1461no—
516C23—1461no—
517C23C4×D29211yescharacteristic
518Q8—5841no—
519Q8—1461no—
520Q8—1461no—
521D4—5841no—
522D4—5841no—
523D4—5841no—
524D4—5841no—
525D4—5841no—
526D4—1461no—
527D4—1461no—
528D4—1461no—
529D4—1461no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—1461no—
544C2×C4—1461no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4C4×D29211yescharacteristic
549C2×C4C4×D29211yescharacteristic
550C2×C4C4×D29211yescharacteristic
551C2×C4C22×C4×D7311yescharacteristic
552C2×C4C22×D29211yescharacteristic
553C2×C4C2×#1192402811yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—2921no—
565C8—2921no—
566C8—2921no—
567C8—2921no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—2921no—
572C22—2921no—
573C22—2921no—
574C22—2921no—
575C22—2921no—
576C22—2921no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22C2×C4×D29211yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—2921no—
586C4—2921no—
587C4—2921no—
588C4—2921no—
589C4—2921no—
590C4#1798935311yescharacteristic
591C4#1798935311yescharacteristic
592C4#1798939211yescharacteristic
593C4#1798939911yescharacteristic
594C2—41no—
595C2—5841no—
596C2—5841no—
597C2—5841no—
598C2#2261865011yescharacteristic
599C2#2261876511yescharacteristic
600C2#2261884211yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1451C2
socleC22×C73C2×C4×D4
prime radical#22620526C2
cosocleC42×C73C24
hypercenter#1451D73
hypocenterC73#17987
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1451

Complements

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

NH ≅ G/Ntype
2. #22619082C2semidirect
3. #22619006C2semidirect
4. #22608811C2semidirect
5. #22608797C2semidirect
6. #22608797C2semidirect
7. #22608790C2semidirect
8. #22608776C2semidirect
9. #22608769C2semidirect
10. #22608762C2semidirect
11. #22608762C2semidirect
12. #22608698C2semidirect
13. #22608392C2semidirect
14. #22608383C2semidirect
15. C73×#1451C2semidirect
315. #1451D73semidirect
316. C73#17987semidirect

Maximal subgroups

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

subgroupindex
#226205262
#226190822
#226190062
#226088112
#226087972
#226087902
#226087762
#226087692
#226087622
#226086982
#226083922
#226083832
C73×#14512
#1798773