Finite Group Databasebeta

← #33055601

Subgroups — #33055601

Order 18688.

662 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#11924029C211yesmaximal, characteristic
2#446×D73C211yesmaximal, characteristic, complemented
3C4×#14556623C211yesmaximal, characteristic
4#22608802C211yesmaximal, characteristic, complemented
5#22608790C211yesmaximal, characteristic, complemented
6#22608786C211yesmaximal, characteristic, complemented
7#22608782C211yesmaximal, characteristic, complemented
8#22608778C211yesmaximal, characteristic, complemented
9#22608770C211yesmaximal, characteristic, complemented
10#22608766C211yesmaximal, characteristic, complemented
11#22608680C211yesmaximal, characteristic, complemented
12#22608324C211yesmaximal, characteristic, complemented
13#22608317C211yesmaximal, characteristic
14#22608219C211yesmaximal, characteristic, complemented
15C73×#1587C211yesmaximal, characteristic, complemented
16C2×#14556623C411yescharacteristic
17C4×#11924029C2211yescharacteristic
18C4×Q8×D73C2211yescharacteristic
19#17988718C2211yescharacteristic
20#17988717C2211yescharacteristic
21#17988716—21no—
22#17988715—21no—
23#17988714C2211yescharacteristic
24Q8×#10596831C2211yescharacteristic
25#17988694C411yescharacteristic
26#17988691C411yescharacteristic
27#17988690C411yescharacteristic
28#17988686C411yescharacteristic
29C4×#11924018C2211yescharacteristic
30C4×#11924017C2211yescharacteristic
31C4×#11924015C2211yescharacteristic
32C8×D292—21no—
33C8×D292C2211yescharacteristic
34#17988652—21no—
35#17988652C2211yescharacteristic
36#17988639—21no—
37#17988639C2211yescharacteristic
38#17988638C2211yescharacteristic
39#17988628C411yescharacteristic
40C4⋊C8×D73—21no—
41C4⋊C8×D73C2211yescharacteristic
42#17988594C411yescharacteristic
43#17988587C411yescharacteristic
44C4×#11924011C2211yescharacteristic
45#97×D73—21no—
46C4×C8×D73—21no—
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988309C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924029C2×C411yescharacteristic
68C2×Q8×D73C2×C411yescharacteristic
69#14556623—24no—
70C2×#11924018C2×C411yescharacteristic
71C2×#11924017C2×C411yescharacteristic
72C2×#11924015C2×C411yescharacteristic
73C2×#11924011C2×C411yescharacteristic
74C2×#11924011C2×C411yescharacteristic
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C2×C8×D73D411yescharacteristic
79C2×C8×D73D411yescharacteristic
80Q8×Dic73C2×C411yescharacteristic
81Q8×Dic73C2×C411yescharacteristic
82C4×Dic146—21no—
83C4×Dic146C2311yescharacteristic
84#14556556—21no—
85#14556556C2×C411yescharacteristic
86C4×D292—21no—
87C4×D292C2311yescharacteristic
88#14556553—21no—
89#14556553C2×C411yescharacteristic
90#14556549—21no—
91#14556549C2×C411yescharacteristic
92C4⋊C4×D73—21no—
93C4⋊C4×D73C2×C411yescharacteristic
94C42×D73—21no—
95C42×D73—21no—
96C42×D73C2311yescharacteristic
97#14556524C2×C411yescharacteristic
98#14556523C2×C411yescharacteristic
99#14556522C2×C411yescharacteristic
100C4⋊#10596831—21no—
101C4⋊#10596831—21no—
102C4⋊#10596831C2311yescharacteristic
103C4⋊#10596831C2311yescharacteristic
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556520—21no—
108#14556516C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556515C2×C411yescharacteristic
111#14556514C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556511C2×C411yescharacteristic
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556502—21no—
119#14556501—21no—
120#14556501—21no—
121#14556501C2×C411yescharacteristic
122#14556501C2×C411yescharacteristic
123C4×#10596831—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73—21no—
128C8×Dic73D411yescharacteristic
129C8×Dic73D411yescharacteristic
130C2×Q16×C73C2×C411yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132C4×Q8×C73C2311yescharacteristic
133#107×C73C2×C411yescharacteristic
134C4⋊C8×C73—21no—
135C4⋊C8×C73—21no—
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138#103×C73C2×C411yescharacteristic
139#103×C73C2×C411yescharacteristic
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145#11924029—22no—
146#11924029M1614yes—
147C2×Dic146—21no—
148C2×Dic146C22×C411yescharacteristic
149Q8×D73—22no—
150Q8×D73—22no—
151C2×D292—21no—
152C2×D292C22×C411yescharacteristic
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73C22×C411yescharacteristic
159C2×C4×D73C2×D411yescharacteristic
160C2×C4×D73#4111yescharacteristic
161#11924018—22no—
162#11924017—22no—
163#11924015—22no—
164#11924011—22no—
165#11924011—22no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831C22×C411yescharacteristic
171C2×#10596831C2×D411yescharacteristic
172C2×#10596831C2×D411yescharacteristic
173C8×D73—22no—
174C8×D73—41no—
175C8×D73—42no—
176C8×D73—42no—
177C8×D73—42no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73C22×C411yescharacteristic
181C4⋊Dic73C22×C411yescharacteristic
182#11924007—21no—
183#11924007—21no—
184#11924007—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73C22×C411yescharacteristic
194C4×Dic73C2×D411yescharacteristic
195C4×Dic73#4111yescharacteristic
196C2×Q8×C73C22×C411yescharacteristic
197C2×Q8×C73C22×C411yescharacteristic
198Q16×C73—22no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C2×D411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73C22×C411yescharacteristic
209C4⋊C4×C73C22×C411yescharacteristic
210C42×C73—21no—
211C42×C73—21no—
212C42×C73C2411yescharacteristic
213C22×D73—21no—
214C22×D73C4×D411yescharacteristic
215Q8×C73—21no—
216Q8×C73—21no—
217Q8×C73—21no—
218Q8×C73C2×M1612yes—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73C23×C411yescharacteristic
224C2×C4×C73C22×D411yescharacteristic
225C2×C4×C73C2×#4111yescharacteristic
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73C4×D411yescharacteristic
230C2×Dic73C4×D411yescharacteristic
231C2×Dic73C4×D411yescharacteristic
232D292—24no—
233D292—21no—
234D292C2×M1612yes—
235C4×D73—21no—
236C4×D73—21no—
237C4×D73—24no—
238C4×D73—41no—
239C4×D73—42no—
240C4×D73—42no—
241C4×D73—42no—
242C4×D73—41no—
243C4×D73—41no—
244C4×D73C2×M1612yes—
245C4×D73#13112yes—
246Dic146—21no—
247Dic146—21no—
248Dic146—42no—
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—41no—
260#10596831—41no—
261#10596831—41no—
262#10596831#13712yescomplemented
263C22×C73C2×C4×D411yescharacteristic
264C2×D73—21no—
265C2×D73—21no—
266C2×D73—22no—
267C2×D73—41no—
268C2×D73—41no—
269C2×D73#43512yes—
270C4×C73—22no—
271C4×C73—21no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73C22×M1611yescharacteristic
276C4×C73C2×#13111yescharacteristic
277C4×C73C2×#13711yescharacteristic
278C4×C73#57511yescharacteristic
279Dic73—21no—
280Dic73—21no—
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284Dic73#43512yes—
285#17872—731nomaximal, Sylow
286C2×C73C2×#43511yescharacteristic
287C2×C73C4×#13711yescharacteristic
288C2×C73#295511yescharacteristic
289D73—22no—
290D73—42no—
291C8×#41—731no—
292C2×#446—731no—
293C4×#137—731no—
294#1587—731no—
295#1587D7311yescharacteristic, complemented
296#1585—731no—
297#1585—731no—
298#1584—731no—
299#1584—731no—
300#1582—731no—
301#1582—731no—
302#1565—731no—
303#1479—731no—
304#1477—731no—
305#1451—731no—
306C73#1787211yescharacteristic, complemented, Sylow
307C2×#137—731no—
308C4×#41—731no—
309C2×C4×Q8—731no—
310#446—731no—
311#446—731no—
312#446—731no—
313#446—1461no—
314#446—1461no—
315#446C2×D7311yescharacteristic
316C8×Q8—731no—
317C8×Q8C2×D7311yescharacteristic
318#441—731no—
319#441—731no—
320#440—731no—
321#440—731no—
322C4×Q16—731no—
323C4×Q16C2×D7311yescharacteristic
324C4×SD16—731no—
325C4×SD16—731no—
326C8×D4—731no—
327C8×D4—731no—
328C8×D4—1461no—
329C8×D4—1461no—
330#431—731no—
331#431—731no—
332#431—1461no—
333#428—731no—
334C2×C4⋊C8—731no—
335C2×C4⋊C8—1461no—
336#419—731no—
337#417—731no—
338C4×M16—731no—
339C2×#97—1461no—
340C2×C4×C8—731no—
341C2×C4×C8—1461no—
342#335—731no—
343#335—731no—
344#334—731no—
345#334C2×D7311yescharacteristic
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349Q8⋊C8—731no—
350Q8⋊C8C2×D7311yescharacteristic
351Q8⋊C8C2×D7311yescharacteristic
352D4⋊C8—731no—
353D4⋊C8—731no—
354#322—731no—
355#322—731no—
356#322—731no—
357#322C2×D7311yescharacteristic
358C2×#41—731no—
359C22×Q8—731no—
360#137—1464no—
361C2×Q16—731no—
362C2×Q16C4×D7311yescharacteristic
363C2×SD16—731no—
364C2×SD16—731no—
365C2×M16—731no—
366C2×M16—731no—
367C22×C8—731no—
368C22×C8—731no—
369C22×C8—1461no—
370C22×C8—1461no—
371C22×C8—1461no—
372C4×Q8—731no—
373C4×Q8—731no—
374C4×Q8—731no—
375C4×Q8—731no—
376C4×Q8—1461no—
377C4×Q8—1461no—
378C4×Q8C22×D7311yescharacteristic
379C4×Q8C22×D7311yescharacteristic
380C4×D4—731no—
381C4×D4—731no—
382C4×D4—1461no—
383C4×D4—1461no—
384#117—731no—
385#117—1461no—
386C2×C4⋊C4—731no—
387C2×C4⋊C4—1461no—
388C2×C42—731no—
389C2×C42—1461no—
390C2×C42—1461no—
391#107—731no—
392#107C4×D7311yescharacteristic
393#106—731no—
394#106—731no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
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#103—731no—
411#103C4×D7311yescharacteristic
412#103C4×D7311yescharacteristic
413#102—731no—
414#102—731no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419#97—21no—
420#97—731no—
421#97—731no—
422#97—1461no—
423#97—1461no—
424#97—1461no—
425C4×C8—21no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—1461no—
432C4×C8—1461no—
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435C4×C8C22×D7311yescharacteristic
436#41—734no—
437#41—1462no—
438C2×Q8—731no—
439C2×Q8—1461no—
440C2×Q8—1462no—
441C2×Q8—1462no—
442C2×Q8C2×C4×D7311yescharacteristic
443C2×Q8C2×C4×D7311yescharacteristic
444C2×D4—731no—
445C2×D4—1461no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—731no—
449C22×C4—1461no—
450C22×C4—1461no—
451C22×C4—1461no—
452C22×C4—1461no—
453C22×C4—1461no—
454Q16—22no—
455Q16—1462no—
456SD16—1462no—
457SD16—1462no—
458M16—1462no—
459M16—1462no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—2922no—
464C2×C8—2921no—
465C2×C8—2922no—
466C2×C8—2922no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—731no—
470C2×C8—731no—
471C2×C8—1462no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8C2×C4×D7311yescharacteristic
476C2×C8C2×C4×D7311yescharacteristic
477C2×C8D4×D7311yescharacteristic
478C2×C8D4×D7311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—731no—
482C4⋊C4—731no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4C2×C4×D7311yescharacteristic
489C4⋊C4C2×C4×D7311yescharacteristic
490C22⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C42—21no—
494C42—21no—
495C42—731no—
496C42—731no—
497C42—731no—
498C42—1461no—
499C42—1461no—
500C42—1461no—
501C42—1461no—
502C42—1461no—
503C42C23×D7311yescharacteristic
504C23—731no—
505C23—1461no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—2922no—
510Q8—1461no—
511Q8—1461no—
512Q8M16×D7312yes—
513D4—732no—
514D4—1464no—
515D4—1461no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—2921no—
521C2×C4—2922no—
522C2×C4—2922no—
523C2×C4—2922no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—731no—
527C2×C4—732no—
528C2×C4—732no—
529C2×C4—731no—
530C2×C4—731no—
531C2×C4—1464no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4C22×C4×D7311yescharacteristic
538C2×C4C2×D4×D7311yescharacteristic
539C2×C4#41×D7311yescharacteristic
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—2921no—
548C8—2921no—
549C8—2921no—
550C8—732no—
551C8—1461no—
552C8—1461no—
553C8—1461no—
554C22—2921no—
555C22—2921no—
556C22—732no—
557C22—1462no—
558C22—1461no—
559C22—1461no—
560C22C4×D4×D7311yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—2921no—
567C4—2921no—
568C4—2921no—
569C4—732no—
570C4—1461no—
571C4—1461no—
572C4C2×M16×D7311yescharacteristic
573C4#131×D7311yescharacteristic
574C4#137×D7311yescharacteristic
575C4#1798938611yescharacteristic
576C2—2922no—
577C2—1462no—
578C2#435×D7311yescharacteristic
579C2#2261874711yescharacteristic
580C2#2261882911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1587C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924029C2×C4
cosocleC42×C73C24
hypercenter#1587D73
hypocenterC73#17872
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
2. #446×D73C2semidirect
4. #22608802C2semidirect
5. #22608790C2semidirect
6. #22608786C2semidirect
7. #22608782C2semidirect
8. #22608778C2semidirect
9. #22608770C2semidirect
10. #22608766C2semidirect
11. #22608680C2semidirect
12. #22608324C2semidirect
14. #22608219C2semidirect
15. C73×#1587C2semidirect
262. #10596831#137semidirect
295. #1587D73semidirect
306. C73#17872semidirect

Maximal subgroups

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

subgroupindex
C8×#119240292
#446×D732
C4×#145566232
#226088022
#226087902
#226087862
#226087822
#226087782
#226087702
#226087662
#226086802
#226083242
#226083172
#226082192
C73×#15872
#1787273