Finite Group Databasebeta

← #33057355

Subgroups — #33057355

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619960C211yesmaximal, characteristic
2#22619017C211yesmaximal, characteristic, complemented
3#22618996C211yesmaximal, characteristic
4#22608818C211yesmaximal, characteristic, complemented
5#22608808C211yesmaximal, characteristic, complemented
6#22608789C211yesmaximal, characteristic, complemented
7#22608772C211yesmaximal, characteristic, complemented
8#22608765C211yesmaximal, characteristic, complemented
9#22608745C211yesmaximal, characteristic, complemented
10#22608734C211yesmaximal, characteristic, complemented
11#22608710C211yesmaximal, characteristic, complemented
12#22608398C211yesmaximal, characteristic
13#22608324C211yesmaximal, characteristic, complemented
14#22608232C211yesmaximal, characteristic, complemented
15C73×#1592C211yesmaximal, characteristic, complemented
16#17989134C2211yescharacteristic
17C4×Q8×D73C2211yescharacteristic
18#17988907C411yescharacteristic
19#17988904C411yescharacteristic
20#17988871C411yescharacteristic
21#17988870C411yescharacteristic
22#17988786C411yescharacteristic
23#17988785C411yescharacteristic
24#17988727C411yescharacteristic
25#17988724C411yescharacteristic
26#17988718C2211yescharacteristic
27#17988716—21no—
28#17988715—21no—
29C8×Dic146C2211yescharacteristic
30#17988711C2211yescharacteristic
31C4×#11924017C2211yescharacteristic
32C4×#11924015C2211yescharacteristic
33C4×#11924016C2211yescharacteristic
34#17988664C2211yescharacteristic
35#17988663—21no—
36C8×D292C2211yescharacteristic
37D4×#10596831C2211yescharacteristic
38#17988650—21no—
39#17988643C2211yescharacteristic
40#17988642—21no—
41#17988639—21no—
42#17988639C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988638C2211yescharacteristic
45#17988638C2211yescharacteristic
46#17988555—21no—
47#17988552—21no—
48#17988340C2211yescharacteristic
49#17988337C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53#17988317C2211yescharacteristic
54#17988316C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62#436×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×Q8×D73C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924015C2×C411yescharacteristic
72C2×#11924011—21no—
73C22×#10596831—21no—
74C2×C8×D73—21no—
75#14556590C2×C411yescharacteristic
76#14556587C2×C411yescharacteristic
77#14556577—21no—
78#14556566C2×C411yescharacteristic
79#14556564—21no—
80#14556562C2×C411yescharacteristic
81Q8×Dic73C2×C411yescharacteristic
82C4×Dic146—21no—
83C4×Dic146C2311yescharacteristic
84#14556556—21no—
85#14556556C2×C411yescharacteristic
86C4×D292C2311yescharacteristic
87C4×C22⋊D73—21no—
88C4⋊C4×D73—21no—
89C4⋊C4×D73C2×C411yescharacteristic
90C42×D73—21no—
91C42×D73C2311yescharacteristic
92#14556523C2×C411yescharacteristic
93#14556522C2×C411yescharacteristic
94#14556522C2×C411yescharacteristic
95C4⋊#10596831—21no—
96C4⋊#10596831C2311yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98#14556520—21no—
99#14556520—21no—
100#14556520—21no—
101#14556520C2×C411yescharacteristic
102#14556520C2×C411yescharacteristic
103#14556520D411yescharacteristic
104#14556520D411yescharacteristic
105#14556516C2×C411yescharacteristic
106#14556515C2×C411yescharacteristic
107#14556514C2×C411yescharacteristic
108#14556513C2×C411yescharacteristic
109#14556512C2×C411yescharacteristic
110#14556511C2×C411yescharacteristic
111C22⋊#10596831—21no—
112#14556503—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503C2×C411yescharacteristic
118#14556503C2×C411yescharacteristic
119#14556503D411yescharacteristic
120#14556503D411yescharacteristic
121#14556502—21no—
122#14556501—21no—
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
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#11924028—81no—
145#11924028—81no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146C22×C411yescharacteristic
149Q8×D73—22no—
150Q8×D73—41no—
151C2×D292—21no—
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×D73C22×C411yescharacteristic
160C2×C4×D73C2×D411yescharacteristic
161C2×C4×D73#4111yescharacteristic
162#11924017—22no—
163#11924016—22no—
164#11924015—41no—
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—81no—
175C4⋊Dic73—21no—
176C4⋊Dic73C22×C411yescharacteristic
177C4⋊Dic73C22×C411yescharacteristic
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182C22⋊Dic73—21no—
183#11924005—21no—
184#11924005—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73C22×C411yescharacteristic
189C4×Dic73C2×D411yescharacteristic
190C4×Dic73#4111yescharacteristic
191C2×Q8×C73C22×C411yescharacteristic
192C2×D4×C73C22×C411yescharacteristic
193C22×C4×C73—21no—
194SD16×C73—41no—
195M16×C73—81no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C4⋊C4×C73—21no—
204C4⋊C4×C73C22×C411yescharacteristic
205C4⋊C4×C73C22×C411yescharacteristic
206C22⋊C4×C73—21no—
207C42×C73—21no—
208C42×C73C2411yescharacteristic
209C23×C73—21no—
210C22×D73—21no—
211C22×D73C4×D411yescharacteristic
212Q8×C73—21no—
213Q8×C73—21no—
214D4×C73—21no—
215D4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73C23×C411yescharacteristic
222C2×C4×C73C22×D411yescharacteristic
223C2×C4×C73C2×#4111yescharacteristic
224C22⋊D73—42no—
225C22⋊D73—81no—
226C22⋊D73—81no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73C4×D411yescharacteristic
231C2×Dic73C4×D411yescharacteristic
232C2×Dic73C4×D411yescharacteristic
233D292—21no—
234D292—21no—
235D292—81no—
236C4×D73—21no—
237C4×D73—21no—
238C4×D73—21no—
239C4×D73—21no—
240C4×D73—41no—
241C4×D73—42no—
242C4×D73—42no—
243C4×D73—41no—
244C4×D73—41no—
245Dic146—21no—
246Dic146—42no—
247Dic146—81no—
248Dic146#13112yes—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—21no—
252C8×C73—21no—
253C8×C73—41no—
254C8×C73—41no—
255C8×C73—41no—
256#10596831—21no—
257#10596831—21no—
258#10596831—21no—
259#10596831—21no—
260#10596831—41no—
261#10596831—41no—
262#10596831—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73C2×C4×D411yescharacteristic
267C2×D73—21no—
268C2×D73—21no—
269C2×D73—21no—
270C2×D73—41no—
271C2×D73—41no—
272C2×D73—41no—
273C4×C73—21no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73C2×#13111yescharacteristic
278C4×C73#56811yescharacteristic
279C4×C73#57711yescharacteristic
280C4×C73#57711yescharacteristic
281Dic73—22no—
282Dic73—21no—
283Dic73—21no—
284Dic73—21no—
285Dic73—41no—
286Dic73—41no—
287#18030—731nomaximal, Sylow
288C2×C73—81no—
289C2×C73#293311yescharacteristic
290C2×C73#294911yescharacteristic
291C2×C73#295511yescharacteristic
292D73—41no—
293D73—81no—
294#3103—731no—
295#2984—731no—
296#2979—731no—
297#1592D7311yescharacteristic, complemented
298#1590—731no—
299#1588—731no—
300#1585—731no—
301#1583—731no—
302#1582—731no—
303SD16⋊C8—731no—
304C8×SD16—731no—
305#1572—731no—
306#1496—731no—
307#1479—731no—
308#1454—731no—
309C73#1803011yescharacteristic, complemented, Sylow
310#532—731no—
311C2×C4×Q8—731no—
312#481—731no—
313#481—731no—
314#475—731no—
315#475—731no—
316#460—731no—
317#460—731no—
318#448—731no—
319#448—731no—
320#446—731no—
321#446—1461no—
322#446—1461no—
323#446C2×D7311yescharacteristic
324C8×Q8—731no—
325C8×Q8—731no—
326C4×SD16—731no—
327C4×SD16—731no—
328C4×SD16—731no—
329C4×SD16C2×D7311yescharacteristic
330#436—731no—
331#436—1461no—
332#436C2×D7311yescharacteristic
333C8×D4—731no—
334C8×D4—731no—
335C8×D4—1461no—
336#432—731no—
337#432—1461no—
338#431—731no—
339#431—731no—
340#431—731no—
341#431—731no—
342#431—1461no—
343#408—1461no—
344#408—1461no—
345#335—731no—
346#335C2×D7311yescharacteristic
347#334—731no—
348#334—731no—
349Q8⋊C8—731no—
350Q8⋊C8—731no—
351Q8⋊C8—731no—
352Q8⋊C8C2×D7311yescharacteristic
353D4⋊C8—731no—
354D4⋊C8—731no—
355D4⋊C8—731no—
356D4⋊C8C2×D7311yescharacteristic
357#322—731no—
358#322—731no—
359#322C2×D7311yescharacteristic
360C82—731no—
361C2×#41—1461no—
362C22×Q8—731no—
363C2×SD16—731no—
364C2×SD16—731no—
365C2×SD16—731no—
366C2×SD16C4×D7311yescharacteristic
367C2×M16—21no—
368C2×M16—1461no—
369C22×C8—1461no—
370C22×C8—1461no—
371C4⋊Q8—731no—
372#127—731no—
373#124—1461no—
374#121—731no—
375#121—731no—
376#121—1461no—
377C4×Q8—731no—
378C4×Q8—731no—
379C4×Q8—731no—
380C4×Q8—1461no—
381C4×Q8—1461no—
382C4×Q8C22×D7311yescharacteristic
383C4×D4—731no—
384C4×D4—1461no—
385C4×D4C22×D7311yescharacteristic
386C2×C4⋊C4—731no—
387C2×C4⋊C4—1461no—
388C2×C42—731no—
389C2×C42—1461no—
390#106—731no—
391#106—731no—
392#106—731no—
393#106C4×D7311yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—731no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8—1461no—
405C4⋊C8C22×D7311yescharacteristic
406C4⋊C8C22×D7311yescharacteristic
407#103—731no—
408#103—731no—
409#103—731no—
410#103C4×D7311yescharacteristic
411#102—731no—
412#102—731no—
413#102—731no—
414#102C4×D7311yescharacteristic
415C22⋊C8—21no—
416C22⋊C8—731no—
417C22⋊C8—731no—
418C22⋊C8—731no—
419C22⋊C8—731no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422C22⋊C8—1461no—
423C22⋊C8—1461no—
424C22⋊C8—1461no—
425C22⋊C8—1461no—
426#97—21no—
427#97—1461no—
428#97—1461no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—731no—
432C4×C8—1461no—
433C4×C8—1461no—
434C4×C8—1461no—
435C4×C8C22×D7311yescharacteristic
436C4×C8C22×D7311yescharacteristic
437C4×C8C22×D7311yescharacteristic
438#41—5841no—
439#41—5841no—
440C2×Q8—2921no—
441C2×Q8—731no—
442C2×Q8—1461no—
443C2×Q8—1461no—
444C2×Q8—1462no—
445C2×Q8C2×C4×D7311yescharacteristic
446C2×D4—731no—
447C2×D4—1461no—
448C2×D4—1461no—
449C2×D4—1461no—
450C2×D4—1461no—
451C2×D4C2×C4×D7311yescharacteristic
452C22×C4—21no—
453C22×C4—731no—
454C22×C4—731no—
455C22×C4—731no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459SD16—41no—
460SD16—2921no—
461SD16—1462no—
462SD16—1462no—
463M16—81no—
464M16—5841no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—5841no—
469C2×C8—5841no—
470C2×C8—731no—
471C2×C8—731no—
472C2×C8—731no—
473C2×C8—731no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8C2×C4×D7311yescharacteristic
478C2×C8C2×C4×D7311yescharacteristic
479C2×C8D4×D7311yescharacteristic
480C2×C8D4×D7311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—731no—
483C4⋊C4—731no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4C2×C4×D7311yescharacteristic
490C4⋊C4C2×C4×D7311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—1461no—
493C22⋊C4—1461no—
494C22⋊C4—1461no—
495C42—21no—
496C42—731no—
497C42—731no—
498C42—731no—
499C42—1461no—
500C42—1461no—
501C42—1461no—
502C42C23×D7311yescharacteristic
503C23—21no—
504C23—731no—
505C23—1461no—
506Q8—21no—
507Q8—21no—
508Q8—2922no—
509Q8—5841no—
510Q8—732no—
511Q8—1461no—
512D4—21no—
513D4—21no—
514D4—2922no—
515D4—5841no—
516D4—5841no—
517D4—5841no—
518D4—1461no—
519D4—1461no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—2921no—
526C2×C4—2922no—
527C2×C4—2922no—
528C2×C4—2921no—
529C2×C4—2921no—
530C2×C4—731no—
531C2×C4—731no—
532C2×C4—731no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1461no—
539C2×C4—1461no—
540C2×C4C22×C4×D7311yescharacteristic
541C2×C4C2×D4×D7311yescharacteristic
542C2×C4#41×D7311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—2921no—
551C8—2921no—
552C8—2921no—
553C8—1461no—
554C8—1461no—
555C8—1461no—
556C8—1461no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—2921no—
561C22—2921no—
562C22—2921no—
563C22—1461no—
564C22—1461no—
565C22—1461no—
566C22C4×D4×D7311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—2921no—
572C4—2921no—
573C4—1462no—
574C4—1461no—
575C4—1461no—
576C4—1461no—
577C4#131×D7311yescharacteristic
578C4#1798935311yescharacteristic
579C4#1798939611yescharacteristic
580C4#1798939711yescharacteristic
581C2—81no—
582C2—2921no—
583C2—5841no—
584C2#2261866011yescharacteristic
585C2#2261878711yescharacteristic
586C2#2261883111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1592C2
socleC22×C73C2×C4×D4
prime radical#17989134C22
cosocleC42×C73C24
hypercenter#1592D73
hypocenterC73#18030
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
2. #22619017C2semidirect
4. #22608818C2semidirect
5. #22608808C2semidirect
6. #22608789C2semidirect
7. #22608772C2semidirect
8. #22608765C2semidirect
9. #22608745C2semidirect
10. #22608734C2semidirect
11. #22608710C2semidirect
13. #22608324C2semidirect
14. #22608232C2semidirect
15. C73×#1592C2semidirect
297. #1592D73semidirect
309. C73#18030semidirect

Maximal subgroups

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

subgroupindex
#226199602
#226190172
#226189962
#226088182
#226088082
#226087892
#226087722
#226087652
#226087452
#226087342
#226087102
#226083982
#226083242
#226082322
C73×#15922
#1803073