Finite Group Databasebeta

← #33056802

Subgroups — #33056802

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#22620524C211yesmaximal, characteristic
2#22619081C211yesmaximal, characteristic, complemented
3#22619008C211yesmaximal, characteristic, complemented
4#22608811C211yesmaximal, characteristic, complemented
5#22608798C211yesmaximal, characteristic, complemented
6#22608785C211yesmaximal, characteristic, complemented
7#22608772C211yesmaximal, characteristic, complemented
8#22608766C211yesmaximal, characteristic, complemented
9#22608761C211yesmaximal, characteristic, complemented
10#22608760C211yesmaximal, characteristic, complemented
11#22608695C211yesmaximal, characteristic, complemented
12#22608388C211yesmaximal, characteristic, complemented
13#22608380C211yesmaximal, characteristic, complemented
14#22608217C211yesmaximal, characteristic, complemented
15C73×#1586C211yesmaximal, characteristic, complemented
16#17989134C2211yescharacteristic
17#17989119C2211yescharacteristic
18#17988995C411yescharacteristic
19#17988975C411yescharacteristic
20#17988950C411yescharacteristic
21#17988945C411yescharacteristic
22#17988839C411yescharacteristic
23#17988837C411yescharacteristic
24#17988834C411yescharacteristic
25#17988832C411yescharacteristic
26#17988714C2211yescharacteristic
27C8×Dic146C2211yescharacteristic
28C4×#11924017C2211yescharacteristic
29C4×#11924016C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988665C2211yescharacteristic
33#17988662—21no—
34#17988658—21no—
35#17988656—21no—
36#17988655—21no—
37D4×#10596831C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988645—21no—
40#17988643C2211yescharacteristic
41#17988638C2211yescharacteristic
42#17988613—21no—
43#17988609C2211yescharacteristic
44#17988555—21no—
45#17988552—21no—
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988317C2211yescharacteristic
53#17988316C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59#17988308C2211yescharacteristic
60C4×D8×C73C2211yescharacteristic
61#436×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924017C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924011—21no—
73C2×#11924011—21no—
74C2×#11924011C2×C411yescharacteristic
75C2×#11924011C2×C411yescharacteristic
76C22×#10596831—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79#14556590C2×C411yescharacteristic
80#14556587C2×C411yescharacteristic
81#14556584—21no—
82#14556582C2×C411yescharacteristic
83#14556578C2×C411yescharacteristic
84#14556577—21no—
85#14556573—21no—
86#14556571C2×C411yescharacteristic
87#14556566C2×C411yescharacteristic
88#14556564—21no—
89#14556562C2×C411yescharacteristic
90#14556562C2×C411yescharacteristic
91C4×Dic146C2311yescharacteristic
92C4×D292C2311yescharacteristic
93C4×C22⋊D73—21no—
94C4×C22⋊D73—21no—
95#14556550—21no—
96C42×D73C2311yescharacteristic
97#14556524C2×C411yescharacteristic
98#14556523C2×C411yescharacteristic
99#14556522C2×C411yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520D411yescharacteristic
106#14556520D411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556514C2×C411yescharacteristic
109#14556513C2×C411yescharacteristic
110#14556512C2×C411yescharacteristic
111#14556512C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113C22⋊#10596831—21no—
114C22⋊#10596831—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503D411yescharacteristic
119#14556503D411yescharacteristic
120#14556501—21no—
121#14556501—21no—
122#14556501C2×C411yescharacteristic
123#14556501C2×C411yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×D8×C73C2×C411yescharacteristic
130C2×M16×C73—21no—
131C22×C8×C73—21no—
132C4×D4×C73C2311yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#107×C73C2×C411yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#102×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
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×D292C22×C411yescharacteristic
150C2×C22⋊D73—21no—
151C2×C22⋊D73—21no—
152C2×C22⋊D73—21no—
153C2×C22⋊D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73C22×C411yescharacteristic
156C2×C4×D73C2×D411yescharacteristic
157C2×C4×D73#4111yescharacteristic
158#11924017—41no—
159#11924016—41no—
160#11924013—41no—
161#11924012—81no—
162#11924011—41no—
163#11924011—41no—
164#11924011—81no—
165#11924011—81no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—81no—
170C2×#10596831C22×C411yescharacteristic
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C2×D411yescharacteristic
173C2×#10596831C2×D411yescharacteristic
174C8×D73—42no—
175C8×D73—81no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73C22×C411yescharacteristic
179C4⋊Dic73C22×C411yescharacteristic
180#11924007—21no—
181#11924007—21no—
182#11924007—21no—
183C22⋊Dic73—21no—
184C22⋊Dic73—21no—
185C22⋊Dic73—21no—
186C22⋊Dic73—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190C4×Dic73—21no—
191C4×Dic73C22×C411yescharacteristic
192C4×Dic73C2×D411yescharacteristic
193C4×Dic73#4111yescharacteristic
194C2×D4×C73C22×C411yescharacteristic
195C2×D4×C73C22×C411yescharacteristic
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198D8×C73—41no—
199M16×C73—81no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—81no—
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C2×C8×C73C2×D411yescharacteristic
208C4⋊C4×C73C22×C411yescharacteristic
209C4⋊C4×C73C22×C411yescharacteristic
210C22⋊C4×C73—21no—
211C22⋊C4×C73—21no—
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—21no—
215C22×D73—21no—
216C22×D73C4×D411yescharacteristic
217D4×C73—21no—
218D4×C73—21no—
219D4×C73—21no—
220D4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73C23×C411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C22⋊D73—81no—
231C22⋊D73—81no—
232C22⋊D73—81no—
233C22⋊D73—81no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73C4×D411yescharacteristic
238C2×Dic73C4×D411yescharacteristic
239C2×Dic73C4×D411yescharacteristic
240D292—21no—
241D292—21no—
242D292—81no—
243C4×D73—21no—
244C4×D73—21no—
245C4×D73—21no—
246C4×D73—21no—
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—41no—
259C8×C73—41no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73C2×C4×D411yescharacteristic
274C2×D73—21no—
275C2×D73—21no—
276C2×D73—21no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C4×C73—21no—
281C4×C73—41no—
282C4×C73—41no—
283C4×C73#56811yescharacteristic
284C4×C73#56811yescharacteristic
285C4×C73#57611yescharacteristic
286C4×C73#57711yescharacteristic
287Dic73—21no—
288Dic73—21no—
289Dic73—21no—
290Dic73—41no—
291Dic73—41no—
292Dic73—41no—
293#17987—731nomaximal, Sylow
294C2×C73—81no—
295C2×C73—81no—
296C2×C73#293211yescharacteristic
297C2×C73#294611yescharacteristic
298C2×C73#295611yescharacteristic
299D73—41no—
300D73—81no—
301#3171—731no—
302#2993—731no—
303#2981—731no—
304#1588—731no—
305#1586—731no—
306#1586D7311yescharacteristic, complemented
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#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×D8C2×D7311yescharacteristic
333#436—731no—
334#436—731no—
335#436—1461no—
336#436C2×D7311yescharacteristic
337#435—1461no—
338#435—1461no—
339#435—1461no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4C2×D7311yescharacteristic
343#433—1461no—
344#432—731no—
345#431—731no—
346#424—1461no—
347#423—731no—
348#408—1461no—
349#408—1461no—
350C4×M16—731no—
351C2×C4×C8—731no—
352#335—731no—
353#335—731no—
354#334—731no—
355#334C2×D7311yescharacteristic
356Q8⋊C8—731no—
357Q8⋊C8—731no—
358D4⋊C8—731no—
359D4⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8C2×D7311yescharacteristic
363D4⋊C8C2×D7311yescharacteristic
364#322—731no—
365#322—731no—
366#322—731no—
367#322C2×D7311yescharacteristic
368C2×#41—1461no—
369C2×SD16—731no—
370C2×SD16—731no—
371C2×D8—731no—
372C2×D8C4×D7311yescharacteristic
373C2×M16—21no—
374C2×M16—731no—
375C2×M16—731no—
376C2×M16—1461no—
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—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—1461no—
398C4×D4—1461no—
399C4×D4C22×D7311yescharacteristic
400C4×D4C22×D7311yescharacteristic
401#117—1461no—
402C2×C42—731no—
403#107—731no—
404#107C4×D7311yescharacteristic
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⋊C8C22×D7311yescharacteristic
415C4⋊C8C22×D7311yescharacteristic
416#103—731no—
417#103—731no—
418#102—731no—
419#102—731no—
420#102—731no—
421#102—731no—
422#102C4×D7311yescharacteristic
423#102C4×D7311yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—731no—
427C22⋊C8—731no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433#97—731no—
434#97—731no—
435#97—1461no—
436#97—1461no—
437C4×C8—731no—
438C4×C8—731no—
439C4×C8—731no—
440C4×C8—1461no—
441C4×C8—1461no—
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—1461no—
451C2×D4—1461no—
452C2×D4—1461no—
453C2×D4—1461no—
454C2×D4—1461no—
455C2×D4C2×C4×D7311yescharacteristic
456C2×D4C2×C4×D7311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—731no—
460C22×C4—731no—
461C22×C4—731no—
462C22×C4—1461no—
463SD16—2921no—
464SD16—2921no—
465D8—41no—
466D8—2921no—
467M16—81no—
468M16—2921no—
469M16—2921no—
470M16—5841no—
471M16—5841no—
472M16—5841no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—2922no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—731no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8C2×C4×D7311yescharacteristic
488C2×C8C2×C4×D7311yescharacteristic
489C2×C8D4×D7311yescharacteristic
490C2×C8D4×D7311yescharacteristic
491C4⋊C4—731no—
492C4⋊C4—731no—
493C4⋊C4—1461no—
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—1461no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C42—731no—
510C42—731no—
511C42—731no—
512C42—1461no—
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—21no—
516C23—731no—
517C23—1461no—
518Q8—5841no—
519Q8—1461no—
520Q8—1461no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—5841no—
526D4—5841no—
527D4—5841no—
528D4—5841no—
529D4—5841no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—731no—
542C2×C4—731no—
543C2×C4—731no—
544C2×C4—1461no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4C22×C4×D7311yescharacteristic
552C2×C4C2×D4×D7311yescharacteristic
553C2×C4#41×D7311yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—2921no—
562C8—2921no—
563C8—2921no—
564C8—1461no—
565C8—1461no—
566C8—1461no—
567C8—1461no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—2921no—
575C22—2921no—
576C22—2921no—
577C22—1461no—
578C22—1461no—
579C22—1461no—
580C22C4×D4×D7311yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—2921no—
585C4—2921no—
586C4—2921no—
587C4—1461no—
588C4—1461no—
589C4—1461no—
590C4#1798935211yescharacteristic
591C4#1798935311yescharacteristic
592C4#1798939111yescharacteristic
593C4#1798939711yescharacteristic
594C2—81no—
595C2—81no—
596C2—2921no—
597C2—5841no—
598C2#2261864511yescharacteristic
599C2#2261876011yescharacteristic
600C2#2261883611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1586C2
socleC22×C73C2×C4×D4
prime radical#22620524C2
cosocleC42×C73C24
hypercenter#1586D73
hypocenterC73#17987
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #22619081C2semidirect
3. #22619008C2semidirect
4. #22608811C2semidirect
5. #22608798C2semidirect
6. #22608785C2semidirect
7. #22608772C2semidirect
8. #22608766C2semidirect
9. #22608761C2semidirect
10. #22608760C2semidirect
11. #22608695C2semidirect
12. #22608388C2semidirect
13. #22608380C2semidirect
14. #22608217C2semidirect
15. C73×#1586C2semidirect
306. #1586D73semidirect
316. C73#17987semidirect

Maximal subgroups

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

subgroupindex
#226205242
#226190812
#226190082
#226088112
#226087982
#226087852
#226087722
#226087662
#226087612
#226087602
#226086952
#226083882
#226083802
#226082172
C73×#15862
#1798773