Finite Group Databasebeta

← #33056079

Subgroups — #33056079

Order 18688.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619989C211yesmaximal, characteristic
2#22619041C211yesmaximal, characteristic, complemented
3#22619005C211yesmaximal, characteristic, complemented
4#22608810C211yesmaximal, characteristic, complemented
5#22608794C211yesmaximal, characteristic, complemented
6#22608771C211yesmaximal, characteristic, complemented
7#22608763C211yesmaximal, characteristic, complemented
8#22608753C211yesmaximal, characteristic, complemented
9#22608741C211yesmaximal, characteristic, complemented
10C8×D584C211yesmaximal, characteristic, complemented
11#22608713C211yesmaximal, characteristic, complemented
12#22608364C211yesmaximal, characteristic, complemented
13#22608328C211yesmaximal, characteristic, complemented
14#22608230C211yesmaximal, characteristic, complemented
15C8×SD16×C73C211yesmaximal, characteristic, complemented
16#17989134C2211yescharacteristic
17C4×#11924029C2211yescharacteristic
18#17988913C411yescharacteristic
19#17988909C411yescharacteristic
20#17988880C411yescharacteristic
21#17988876C411yescharacteristic
22#17988785C411yescharacteristic
23#17988781C411yescharacteristic
24#17988735C411yescharacteristic
25#17988731C411yescharacteristic
26Q8×#10596831C2211yescharacteristic
27C4×#11924015C2211yescharacteristic
28C4×D584C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30#17988665C2211yescharacteristic
31#17988664C2211yescharacteristic
32#17988661—21no—
33#17988658—21no—
34C8×D292—21no—
35C8×D292C2211yescharacteristic
36C8×D292C2211yescharacteristic
37#17988652—21no—
38#17988652C2211yescharacteristic
39#17988643C2211yescharacteristic
40#17988638—21no—
41#17988638C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988638C2211yescharacteristic
44C4⋊C8×D73—21no—
45C4⋊C8×D73C2211yescharacteristic
46#17988553—21no—
47#17988552—21no—
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51Q8⋊#10596831C2211yescharacteristic
52#17988316C2211yescharacteristic
53#17988316C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988309C2211yescharacteristic
60C8×Q8×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62C8×D4×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×#11924012—21no—
73C2×#11924011—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78#14556590C2×C411yescharacteristic
79#14556587C2×C411yescharacteristic
80#14556577—21no—
81#14556566C2×C411yescharacteristic
82#14556564—21no—
83#14556562C2×C411yescharacteristic
84Q8×Dic73C2×C411yescharacteristic
85C4×D292—21no—
86C4×D292C2311yescharacteristic
87C4×D292C2311yescharacteristic
88#14556553—21no—
89#14556553C2×C411yescharacteristic
90C4×C22⋊D73—21no—
91#14556549—21no—
92#14556549C2×C411yescharacteristic
93C42×D73—21no—
94C42×D73C2311yescharacteristic
95#14556525C2×C411yescharacteristic
96#14556524C2×C411yescharacteristic
97#14556522C2×C411yescharacteristic
98C4⋊#10596831—21no—
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101#14556520—21no—
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#14556503—21no—
120#14556503C2×C411yescharacteristic
121#14556503C2×C411yescharacteristic
122#14556503D411yescharacteristic
123#14556503D411yescharacteristic
124#14556501—21no—
125C4×#10596831—21no—
126C4×#10596831C2311yescharacteristic
127C4×#10596831C2311yescharacteristic
128C4×#10596831C2311yescharacteristic
129C2×SD16×C73C2×C411yescharacteristic
130C22×C8×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—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924029—22no—
145#11924029—22no—
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—22no—
164D584—22no—
165#11924013—22no—
166#11924012—81no—
167#11924011—81no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C2×D411yescharacteristic
174C2×#10596831C2×D411yescharacteristic
175C8×D73—81no—
176C8×D73—81no—
177C8×D73—81no—
178C8×D73—81no—
179C4⋊Dic73—21no—
180C4⋊Dic73C22×C411yescharacteristic
181C4⋊Dic73C22×C411yescharacteristic
182#11924007—21no—
183C22⋊Dic73—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73C22×C411yescharacteristic
192C4×Dic73C2×D411yescharacteristic
193C4×Dic73#4111yescharacteristic
194C2×Q8×C73C22×C411yescharacteristic
195C2×D4×C73C22×C411yescharacteristic
196C22×C4×C73—21no—
197SD16×C73—22no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—81no—
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C2×D411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C4⋊C4×C73—21no—
207C4⋊C4×C73C22×C411yescharacteristic
208C4⋊C4×C73C22×C411yescharacteristic
209C22⋊C4×C73—21no—
210C42×C73—21no—
211C42×C73C2411yescharacteristic
212C23×C73—21no—
213C22×D73—21no—
214C22×D73—21no—
215C22×D73C4×D411yescharacteristic
216Q8×C73—21no—
217Q8×C73#13112yes—
218D4×C73—21no—
219D4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
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×Dic73C4×D411yescharacteristic
234C2×Dic73C4×D411yescharacteristic
235C2×Dic73C4×D411yescharacteristic
236D292—24no—
237D292—21no—
238D292—21no—
239D292—21no—
240D292—81no—
241D292#13112yes—
242C4×D73—24no—
243C4×D73—21no—
244C4×D73—21no—
245C4×D73—21no—
246C4×D73—21no—
247C4×D73—41no—
248C4×D73—41no—
249C4×D73—41no—
250C4×D73—41no—
251C4×D73—41no—
252C4×D73—81no—
253Dic146—81no—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—41no—
259C8×C73—41no—
260C8×C73—41no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—21no—
265#10596831—41no—
266#10596831—41no—
267#10596831—41no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73C2×C4×D411yescharacteristic
272C2×D73—21no—
273C2×D73—22no—
274C2×D73—21no—
275C2×D73—21no—
276C2×D73—41no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C4×C73—22no—
282C4×C73—21no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73C2×#13111yescharacteristic
286C4×C73C2×#13111yescharacteristic
287C4×C73#57611yescharacteristic
288C4×C73#57711yescharacteristic
289Dic73—21no—
290Dic73—21no—
291Dic73—21no—
292Dic73—41no—
293Dic73—41no—
294#17920—731nomaximal, Sylow
295C2×C73—81no—
296C2×C73#292911yescharacteristic
297C2×C73#294611yescharacteristic
298C2×C73#295711yescharacteristic
299D73—41no—
300D73—42no—
301D73—81no—
302#3106—731no—
303#2988—731no—
304#2981—731no—
305#1588—731no—
306#1586—731no—
307#1583—731no—
308#1581—731no—
309#1580—731no—
310SD16⋊C8—731no—
311C8×SD16D7311yescharacteristic, complemented
312C8×D8—731no—
313#1573—731no—
314#1488—731no—
315#1480—731no—
316#1454—731no—
317C73#1792011yescharacteristic, complemented, Sylow
318#532—731no—
319C4×#41—731no—
320#482—731no—
321#482—731no—
322#477—731no—
323#476—731no—
324#460—731no—
325#459—731no—
326#449—731no—
327#449—731no—
328C8×Q8—731no—
329C8×Q8C2×D7311yescharacteristic
330C4×SD16—731no—
331C4×SD16C2×D7311yescharacteristic
332C4×D8—731no—
333C4×D8—731no—
334#436—731no—
335#436—731no—
336#435—1461no—
337#435—1461no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—731no—
341C8×D4—1461no—
342C8×D4—1461no—
343C8×D4C2×D7311yescharacteristic
344#432—731no—
345#431—731no—
346#431—731no—
347#431—731no—
348#431—1461no—
349C2×C4⋊C8—731no—
350C2×C4⋊C8—1461no—
351#408—1461no—
352#408—1461no—
353#335—731no—
354#335—731no—
355#334—731no—
356#334C2×D7311yescharacteristic
357Q8⋊C8—731no—
358Q8⋊C8C2×D7311yescharacteristic
359D4⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8C2×D7311yescharacteristic
365#322—731no—
366#322—731no—
367#322—731no—
368C82C2×D7311yescharacteristic
369C2×#41—731no—
370C2×#41—1461no—
371C2×SD16—731no—
372C2×SD16C4×D7311yescharacteristic
373C2×D8—731no—
374C2×D8—731no—
375C2×M16—1461no—
376C2×M16—1461no—
377C22×C8—21no—
378C22×C8—1461no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C4⋊Q8—731no—
383#127—731no—
384#124—1461no—
385#121—731no—
386#121—731no—
387#121—1461no—
388C4×Q8—731no—
389C4×Q8C22×D7311yescharacteristic
390C4×D4—731no—
391C4×D4—731no—
392C4×D4—731no—
393C4×D4—1461no—
394C4×D4—1461no—
395C4×D4—1461no—
396C4×D4C22×D7311yescharacteristic
397#117—731no—
398#117—1461no—
399C2×C42—731no—
400C2×C42—1461no—
401#107—731no—
402#107—731no—
403#106—731no—
404#106C4×D7311yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—731no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8—1461no—
415C4⋊C8C22×D7311yescharacteristic
416C4⋊C8C22×D7311yescharacteristic
417#103—731no—
418#103C4×D7311yescharacteristic
419#102—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102C4×D7311yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—731no—
427C22⋊C8—731no—
428C22⋊C8—731no—
429C22⋊C8—731no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437#97—1461no—
438C4×C8—21no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—1461no—
443C4×C8C22×D7311yescharacteristic
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446#41—5841no—
447#41—5841no—
448#41—1462no—
449#41—1462no—
450C2×Q8—1461no—
451C2×Q8C2×C4×D7311yescharacteristic
452C2×D4—731no—
453C2×D4—731no—
454C2×D4—1461no—
455C2×D4—1461no—
456C2×D4—1461no—
457C2×D4—1461no—
458C2×D4—1461no—
459C2×D4C2×C4×D7311yescharacteristic
460C22×C4—21no—
461C22×C4—731no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—1461no—
465C22×C4—1461no—
466C22×C4—1461no—
467C22×C4—1461no—
468SD16—22no—
469SD16—1462no—
470D8—1462no—
471D8—1462no—
472M16—5841no—
473M16—5841no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—81no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—5841no—
481C2×C8—5841no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8C2×C4×D7311yescharacteristic
490C2×C8C2×C4×D7311yescharacteristic
491C2×C8D4×D7311yescharacteristic
492C2×C8D4×D7311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—731no—
495C4⋊C4—731no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4C2×C4×D7311yescharacteristic
499C4⋊C4C2×C4×D7311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—1461no—
502C22⋊C4—1461no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C42—21no—
508C42—731no—
509C42—731no—
510C42—731no—
511C42—1461no—
512C42—1461no—
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—731no—
516C23—1461no—
517C23—1461no—
518Q8—21no—
519Q8—5841no—
520Q8#1455659712yes—
521D4—21no—
522D4—21no—
523D4—5841no—
524D4—5841no—
525D4—5841no—
526D4—5841no—
527D4—732no—
528D4—1464no—
529D4—1461no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—5841no—
543C2×C4—731no—
544C2×C4—731no—
545C2×C4—731no—
546C2×C4—1464no—
547C2×C4—1461no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4C22×C4×D7311yescharacteristic
554C2×C4C2×D4×D7311yescharacteristic
555C2×C4#41×D7311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—2921no—
564C8—2921no—
565C8—2921no—
566C8—1461no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—2921no—
574C22—2921no—
575C22—2921no—
576C22—2921no—
577C22—2921no—
578C22—1461no—
579C22—1461no—
580C22—1462no—
581C22—1461no—
582C22C4×D4×D7311yescharacteristic
583C4—21no—
584C4—22no—
585C4—41no—
586C4—41no—
587C4—2921no—
588C4—2921no—
589C4—1461no—
590C4—1461no—
591C4—1461no—
592C4#131×D7311yescharacteristic
593C4C2×#1455659711yescharacteristic
594C4#1798938911yescharacteristic
595C4#1798939311yescharacteristic
596C2—81no—
597C2—2922no—
598C2—2921no—
599C2—5841no—
600C2#2261862011yescharacteristic
601C2#2261875811yescharacteristic
602C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC8×SD16×C73C2
socleC22×C73C2×C4×D4
prime radical#22619989C2
cosocleC42×C73C24
hypercenterC8×SD16D73
hypocenterC73#17920
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
2. #22619041C2semidirect
3. #22619005C2semidirect
4. #22608810C2semidirect
5. #22608794C2semidirect
6. #22608771C2semidirect
7. #22608763C2semidirect
8. #22608753C2semidirect
9. #22608741C2semidirect
10. C8×D584C2semidirect
11. #22608713C2semidirect
12. #22608364C2semidirect
13. #22608328C2semidirect
14. #22608230C2semidirect
15. C8×SD16×C73C2semidirect
311. C8×SD16D73semidirect
317. C73#17920semidirect

Maximal subgroups

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

subgroupindex
#226199892
#226190412
#226190052
#226088102
#226087942
#226087712
#226087632
#226087532
#226087412
C8×D5842
#226087132
#226083642
#226083282
#226082302
C8×SD16×C732
#1792073