Finite Group Databasebeta

← #33057157

Subgroups — #33057157

Order 18688.

640 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619989C211yesmaximal, characteristic
2#22619055C211yesmaximal, characteristic, complemented
3#22618996C211yesmaximal, characteristic, complemented
4#22608818C211yesmaximal, characteristic, complemented
5#22608794C211yesmaximal, characteristic, complemented
6#22608793C211yesmaximal, characteristic, complemented
7#22608789C211yesmaximal, characteristic, complemented
8#22608786C211yesmaximal, characteristic, complemented
9C8×D584C211yesmaximal, characteristic, complemented
10#22608723C211yesmaximal, characteristic, complemented
11#22608718C211yesmaximal, characteristic, complemented
12#22608380C211yesmaximal, characteristic, complemented
13#22608312C211yesmaximal, characteristic, complemented
14#22608213C211yesmaximal, characteristic, complemented
15C73×#1590C211yesmaximal, characteristic, complemented
16#17989134C2211yescharacteristic
17C4×#11924029C2211yescharacteristic
18#17988913C411yescharacteristic
19#17988909C411yescharacteristic
20#17988880C411yescharacteristic
21#17988876C411yescharacteristic
22#17988785C411yescharacteristic
23#17988781C411yescharacteristic
24#17988735C411yescharacteristic
25#17988731C411yescharacteristic
26#17988718C2211yescharacteristic
27C4×#11924015C2211yescharacteristic
28C4×D584C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30#17988664C2211yescharacteristic
31#17988663—21no—
32#17988660—21no—
33#17988657—21no—
34C8×D292C2211yescharacteristic
35C8×D292C2211yescharacteristic
36D4×#10596831C2211yescharacteristic
37#17988652C2211yescharacteristic
38#17988650—21no—
39#17988642—21no—
40#17988639C2211yescharacteristic
41#17988638C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988609C2211yescharacteristic
44C4⋊C8×D73—21no—
45#17988555—21no—
46#17988552—21no—
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51Q8⋊#10596831C2211yescharacteristic
52#17988316C2211yescharacteristic
53#17988316C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62#436×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#11924029C2×C411yescharacteristic
68C2×#11924028—21no—
69C2×#11924015C2×C411yescharacteristic
70C2×D584C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924011—21no—
73C2×#11924011—21no—
74C22×#10596831—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79#14556590C2×C411yescharacteristic
80#14556587C2×C411yescharacteristic
81#14556577—21no—
82#14556566C2×C411yescharacteristic
83#14556564—21no—
84#14556562C2×C411yescharacteristic
85Q8×Dic73C2×C411yescharacteristic
86C4×D292—21no—
87C4×D292C2311yescharacteristic
88C4×D292C2311yescharacteristic
89#14556553—21no—
90#14556553C2×C411yescharacteristic
91C4×C22⋊D73—21no—
92#14556549—21no—
93#14556549C2×C411yescharacteristic
94C42×D73—21no—
95C42×D73C2311yescharacteristic
96#14556525C2×C411yescharacteristic
97#14556524C2×C411yescharacteristic
98#14556522C2×C411yescharacteristic
99C4⋊#10596831—21no—
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102#14556520—21no—
103#14556520C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556520D411yescharacteristic
106#14556520D411yescharacteristic
107#14556515C2×C411yescharacteristic
108#14556513C2×C411yescharacteristic
109#14556513C2×C411yescharacteristic
110#14556512C2×C411yescharacteristic
111#14556511C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113C22⋊#10596831—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503C2×C411yescharacteristic
120#14556503C2×C411yescharacteristic
121#14556503D411yescharacteristic
122#14556503D411yescharacteristic
123#14556502—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×SD16×C73C2×C411yescharacteristic
130C2×M16×C73—21no—
131C4×Q8×C73C2311yescharacteristic
132C4×D4×C73C2311yescharacteristic
133#106×C73C2×C411yescharacteristic
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140#97×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924029—22no—
145#11924029—41no—
146#11924028—81no—
147#11924028—81no—
148C2×Dic146—21no—
149C2×D292—21no—
150C2×D292—21no—
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—
159C2×C4×D73—21no—
160C2×C4×D73C22×C411yescharacteristic
161C2×C4×D73C2×D411yescharacteristic
162C2×C4×D73#4111yescharacteristic
163#11924015—41no—
164D584—22no—
165#11924013—22no—
166#11924011—81no—
167#11924011—81no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—81no—
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C22×C411yescharacteristic
174C2×#10596831C2×D411yescharacteristic
175C2×#10596831C2×D411yescharacteristic
176C8×D73—24no—
177C8×D73—81no—
178C8×D73—81no—
179C8×D73—81no—
180C4⋊Dic73—21no—
181C4⋊Dic73C22×C411yescharacteristic
182C4⋊Dic73C22×C411yescharacteristic
183#11924007—21no—
184C22⋊Dic73—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73C22×C411yescharacteristic
193C4×Dic73C2×D411yescharacteristic
194C4×Dic73#4111yescharacteristic
195C2×Q8×C73C22×C411yescharacteristic
196C2×D4×C73C22×C411yescharacteristic
197C22×C4×C73—21no—
198SD16×C73—41no—
199M16×C73—81no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C2×C8×C73C2×D411yescharacteristic
207C4⋊C4×C73—21no—
208C4⋊C4×C73C22×C411yescharacteristic
209C4⋊C4×C73C22×C411yescharacteristic
210C22⋊C4×C73—21no—
211C42×C73—21no—
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73C4×D411yescharacteristic
217Q8×C73—21no—
218Q8×C73—21no—
219D4×C73—21no—
220D4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73C23×C411yescharacteristic
227C2×C4×C73C22×D411yescharacteristic
228C2×C4×C73C2×#4111yescharacteristic
229C22⋊D73—42no—
230C22⋊D73—81no—
231C22⋊D73—81no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73C4×D411yescharacteristic
235C2×Dic73C4×D411yescharacteristic
236C2×Dic73C4×D411yescharacteristic
237D292—21no—
238D292—21no—
239D292—21no—
240D292—42no—
241D292—81no—
242D292#13112yes—
243C4×D73—21no—
244C4×D73—21no—
245C4×D73—21no—
246C4×D73—21no—
247C4×D73—22no—
248C4×D73—42no—
249C4×D73—41no—
250C4×D73—41no—
251C4×D73—41no—
252C4×D73—41no—
253C4×D73—42no—
254Dic146—81no—
255C8×C73—22no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—21no—
260C8×C73—41no—
261C8×C73—41no—
262#10596831—22no—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
266#10596831—21no—
267#10596831—41no—
268#10596831—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73C2×C4×D411yescharacteristic
273C2×D73—21no—
274C2×D73—22no—
275C2×D73—21no—
276C2×D73—21no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—41no—
282C4×C73—21no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73C2×#13111yescharacteristic
287C4×C73#56811yescharacteristic
288C4×C73#57611yescharacteristic
289C4×C73#57711yescharacteristic
290Dic73—21no—
291Dic73—21no—
292Dic73—41no—
293Dic73—41no—
294Dic73#44312yes—
295#18015—731nomaximal, Sylow
296C2×C73—81no—
297C2×C73#293311yescharacteristic
298C2×C73#294611yescharacteristic
299C2×C73C2×#44311yescharacteristic
300D73—41no—
301D73—42no—
302D73—81no—
303#3106—731no—
304#2990—731no—
305#2979—731no—
306#1590—731no—
307#1590D7311yescharacteristic, complemented
308#1586—731no—
309#1586—731no—
310#1585—731no—
311#1585—731no—
312C8×D8—731no—
313C8×D8—731no—
314#1574—731no—
315#1492—731no—
316#1476—731no—
317#1450—731no—
318C73#1801511yescharacteristic, complemented, Sylow
319#532—731no—
320C4×#41—731no—
321#482—731no—
322#482—731no—
323#477—731no—
324#476—731no—
325#460—731no—
326#459—731no—
327#449—731no—
328#449—731no—
329#446—731no—
330#446C2×D7311yescharacteristic
331C4×SD16—731no—
332C4×SD16C2×D7311yescharacteristic
333C4×D8—731no—
334C4×D8—731no—
335#436—731no—
336#436—1461no—
337#436C2×D7311yescharacteristic
338#435—1461no—
339#435—1461no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4—731no—
343C8×D4—731no—
344C8×D4—1461no—
345#432—1461no—
346#431—731no—
347#431—731no—
348#431—731no—
349#423—731no—
350C2×C4⋊C8—1461no—
351#408—1461no—
352#408—1461no—
353C2×C4×C8—731no—
354#335—731no—
355#335—731no—
356#334—731no—
357#334C2×D7311yescharacteristic
358Q8⋊C8—731no—
359Q8⋊C8C2×D7311yescharacteristic
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8C2×D7311yescharacteristic
366#322—731no—
367#322—731no—
368C82—731no—
369C82C2×D7311yescharacteristic
370C2×#41—731no—
371C2×#41—1461no—
372C2×SD16—731no—
373C2×SD16C4×D7311yescharacteristic
374C2×D8—731no—
375C2×D8—731no—
376C2×M16—21no—
377C2×M16—1461no—
378C2×M16—1461no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383C22×C8—1461no—
384C4⋊Q8—731no—
385#127—731no—
386#124—1461no—
387#121—731no—
388#121—731no—
389#121—1461no—
390C4×Q8—731no—
391C4×Q8C22×D7311yescharacteristic
392C4×D4—731no—
393C4×D4—731no—
394C4×D4—731no—
395C4×D4—1461no—
396C4×D4—1461no—
397C4×D4—1461no—
398C4×D4C22×D7311yescharacteristic
399#117—731no—
400#117—1461no—
401C2×C42—731no—
402C2×C42—1461no—
403#107—731no—
404#107—731no—
405#106—731no—
406#106C4×D7311yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—731no—
413C4⋊C8—731no—
414C4⋊C8—1461no—
415C4⋊C8—1461no—
416C4⋊C8C22×D7311yescharacteristic
417C4⋊C8C22×D7311yescharacteristic
418#103—731no—
419#103C4×D7311yescharacteristic
420#102—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102C4×D7311yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—731no—
428C22⋊C8—731no—
429C22⋊C8—731no—
430C22⋊C8—731no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437#97—21no—
438#97—1461no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—1461no—
443C4×C8—1461no—
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446C4×C8C22×D7311yescharacteristic
447#41—2921no—
448#41—5841no—
449#41—5841no—
450#41—1462no—
451C2×Q8—1461no—
452C2×Q8C2×C4×D7311yescharacteristic
453C2×D4—731no—
454C2×D4—731no—
455C2×D4—1461no—
456C2×D4—1461no—
457C2×D4—1461no—
458C2×D4—1461no—
459C2×D4—1461no—
460C2×D4C2×C4×D7311yescharacteristic
461C22×C4—21no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—1461no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1461no—
469SD16—41no—
470SD16—2921no—
471D8—1462no—
472D8—1462no—
473M16—81no—
474M16—5841no—
475M16—5841no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—5841no—
480C2×C8—5841no—
481C2×C8—5841no—
482C2×C8—5841no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—731no—
487C2×C8—1464no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8C2×C4×D7311yescharacteristic
492C2×C8C2×C4×D7311yescharacteristic
493C2×C8D4×D7311yescharacteristic
494C2×C8D4×D7311yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—731no—
497C4⋊C4—731no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4C2×C4×D7311yescharacteristic
501C4⋊C4C2×C4×D7311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C42—21no—
510C42—731no—
511C42—731no—
512C42—731no—
513C42—1461no—
514C42—1461no—
515C42C23×D7311yescharacteristic
516C23—21no—
517C23—731no—
518C23—1461no—
519C23—1461no—
520Q8—21no—
521Q8—21no—
522Q8—5841no—
523D4—21no—
524D4—21no—
525D4—2922no—
526D4—2922no—
527D4—5841no—
528D4—5841no—
529D4—5841no—
530D4—732no—
531D4—1461no—
532D4—1461no—
533D4—1461no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—2922no—
540C2×C4—2922no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—731no—
546C2×C4—731no—
547C2×C4—731no—
548C2×C4—1462no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4C22×C4×D7311yescharacteristic
556C2×C4C2×D4×D7311yescharacteristic
557C2×C4#41×D7311yescharacteristic
558C8—22no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—2921no—
566C8—2921no—
567C8—1462no—
568C8—1461no—
569C8—1461no—
570C8—1461no—
571C8—1461no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—2921no—
576C22—2921no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22—1462no—
581C22—1461no—
582C22—1461no—
583C22—1461no—
584C22C4×D4×D7311yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—2921no—
590C4—2921no—
591C4—732no—
592C4—1461no—
593C4—1461no—
594C4#131×D7311yescharacteristic
595C4#1798935311yescharacteristic
596C4#1798938911yescharacteristic
597C4#1798939311yescharacteristic
598C2—81no—
599C2—2922no—
600C2—2921no—
601C2—5841no—
602C2#2261866011yescharacteristic
603C2#2261875811yescharacteristic
604C2#443×D7311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1590C2
socleC22×C73C2×C4×D4
prime radical#22619989C2
cosocleC42×C73C24
hypercenter#1590D73
hypocenterC73#18015
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #22619055C2semidirect
3. #22618996C2semidirect
4. #22608818C2semidirect
5. #22608794C2semidirect
6. #22608793C2semidirect
7. #22608789C2semidirect
8. #22608786C2semidirect
9. C8×D584C2semidirect
10. #22608723C2semidirect
11. #22608718C2semidirect
12. #22608380C2semidirect
13. #22608312C2semidirect
14. #22608213C2semidirect
15. C73×#1590C2semidirect
307. #1590D73semidirect
318. C73#18015semidirect

Maximal subgroups

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

subgroupindex
#226199892
#226190552
#226189962
#226088182
#226087942
#226087932
#226087892
#226087862
C8×D5842
#226087232
#226087182
#226083802
#226083122
#226082132
C73×#15902
#1801573