Finite Group Databasebeta

← #10782799

Subgroups — #10782799

Order 768.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2994C211yesmaximal, characteristic
2#83155C211yesmaximal, characteristic
3#83154C211yesmaximal, characteristic
4#79272C211yesmaximal, characteristic, complemented
5#70966C211yesmaximal, characteristic, complemented
6#70964C211yesmaximal, characteristic, complemented
7#70946C211yesmaximal, characteristic, complemented
8#70944C211yesmaximal, characteristic, complemented
9#70875C211yesmaximal, characteristic, complemented
10#70873C211yesmaximal, characteristic, complemented
11#70854C211yesmaximal, characteristic, complemented
12#70852C211yesmaximal, characteristic, complemented
13#70752C211yesmaximal, characteristic, complemented
14#70439C211yesmaximal, characteristic, complemented
15C2×#4486C211yesmaximal, characteristic, complemented
16#19590—31nomaximal, Sylow
17C3×#529C2211yescharacteristic
18#5470C2211yescharacteristic
19C2×#869C2211yescharacteristic
20C3×#446C2211yescharacteristic
21C3×C8×Q8C2211yescharacteristic
22C3×#436C2211yescharacteristic
23C3×#435—21no—
24C3×C8×D4—21no—
25C3×C8×D4C2211yescharacteristic
26C3×#433—21no—
27C3×#431C2211yescharacteristic
28C3×#424—21no—
29C2×C3×C4⋊C8C2211yescharacteristic
30#5069—21no—
31#5063—21no—
32#5060—21no—
33#5054—21no—
34#5051—21no—
35#5050—21no—
36#5041—21no—
37#5040—21no—
38#5031C2211yescharacteristic
39#5031C2211yescharacteristic
40#5031C2211yescharacteristic
41#5020C2211yescharacteristic
42#5019C2211yescharacteristic
43#5019C2211yescharacteristic
44#5019C2211yescharacteristic
45#5007C2211yescharacteristic
46#4926C2211yescharacteristic
47C2×C4⋊(C3⋊C8)C2211yescharacteristic
48#4850—21no—
49#4850—21no—
50#4722—21no—
51#4722—21no—
52#4682C2211yescharacteristic
53#4682C2211yescharacteristic
54#4681C2211yescharacteristic
55#4681C2211yescharacteristic
56#4486C2211yescharacteristic
57#4486C2211yescharacteristic
58#4486C2211yescharacteristic
59#4486C2211yescharacteristic
60#4486C2211yescharacteristic
61#4486C2211yescharacteristic
62#4482C2211yescharacteristic
63#4482C2211yescharacteristic
64#4458C2211yescharacteristic
65#4458C2211yescharacteristic
66#4457C2211yescharacteristic
67#4457C2211yescharacteristic
68#3248—31no—
69#3230—31no—
70#3218—31no—
71#2994D311yescharacteristic
72#1700—31no—
73#1699—31no—
74#1694—31no—
75#1693—31no—
76#1680—31no—
77#1679—31no—
78#1674—31no—
79#1673—31no—
80#1573—31no—
81#1552—31no—
82C2×#332—31no—
83C22×Dic6—21no—
84C2×C3×M16—21no—
85C22×C3×C8—21no—
86C22×C3×C8—21no—
87C3×#126—21no—
88C3×#125D411yescharacteristic
89C3×#124D411yescharacteristic
90C3×#123—21no—
91C3×C22⋊Q8D411yescharacteristic
92C3×#121D411yescharacteristic
93C3×C4×Q8C2311yescharacteristic
94C3×C4×D4—21no—
95C3×C4×D4C2311yescharacteristic
96C3×#117—21no—
97C2×C3×C42C2311yescharacteristic
98C2×#216—21no—
99C2×#216—21no—
100C2×#216—21no—
101C2×#214—21no—
102C2×#214—21no—
103C2×#214—21no—
104#926—21no—
105C2×C4⋊Dic3—21no—
106C2×C4⋊Dic3—21no—
107#924—21no—
108#924—21no—
109C22×C3⋊C8—21no—
110#870—21no—
111#869—21no—
112#869—21no—
113#869—21no—
114#869C2311yescharacteristic
115#869C2311yescharacteristic
116#869C2311yescharacteristic
117#869C2311yescharacteristic
118C4×Dic6—21no—
119C4×Dic6—21no—
120C3×C4⋊C8—21no—
121C3×C4⋊C8—21no—
122C3×C4⋊C8—21no—
123C3×C4⋊C8D411yescharacteristic
124C3×C4⋊C8D411yescharacteristic
125C3×C4⋊C8C2311yescharacteristic
126C3×C4⋊C8C2311yescharacteristic
127C3×C22⋊C8—21no—
128C3×C22⋊C8—21no—
129C3×C22⋊C8D411yescharacteristic
130C3×C22⋊C8D411yescharacteristic
131C3×#97—21no—
132C3×C4×C8—21no—
133C3×C4×C8C2311yescharacteristic
134C3×C4×C8C2311yescharacteristic
135#835—21no—
136#832—21no—
137#830—21no—
138#818—21no—
139#818—21no—
140#818—21no—
141#818—21no—
142#816—21no—
143#816—21no—
144#816—21no—
145#816—21no—
146#810—21no—
147#810—21no—
148#810—21no—
149#810—21no—
150#810—21no—
151#810—21no—
152#808—21no—
153#807—21no—
154C4⋊(C3⋊C8)—21no—
155C4⋊(C3⋊C8)C2311yescharacteristic
156C4⋊(C3⋊C8)C2311yescharacteristic
157C4⋊(C3⋊C8)C2311yescharacteristic
158C4⋊(C3⋊C8)C2311yescharacteristic
159#803—21no—
160#533—31no—
161C2×C4⋊Q8—31no—
162#529C2×D311yescharacteristic
163#500—31no—
164#500—31no—
165#497—61no—
166#491—61no—
167#487—31no—
168#487—31no—
169#484—61no—
170#484—61no—
171#479—61no—
172#477—61no—
173#477—61no—
174#475—31no—
175#474—31no—
176#467—61no—
177#465—61no—
178#464—61no—
179#462—31no—
180#462—31no—
181#462—31no—
182#461—31no—
183#461—31no—
184#461—31no—
185#451—61no—
186#448—61no—
187#446C2×D311yescharacteristic
188C8×Q8C2×D311yescharacteristic
189#436C2×D311yescharacteristic
190#435—21no—
191C8×D4—21no—
192C8×D4C2×D311yescharacteristic
193#433—21no—
194#432—31no—
195#431C2×D311yescharacteristic
196#424—21no—
197C2×C4⋊C8—31no—
198C2×C4⋊C8C2×D311yescharacteristic
199#335—31no—
200#335—31no—
201#334—31no—
202#334—31no—
203#332—31no—
204#332—31no—
205#332—31no—
206#332—31no—
207#332—31no—
208#332—31no—
209#332—31no—
210#332—31no—
211C2×C3×Q8C2×D411yescharacteristic
212C2×C3×D4—21no—
213C2×C3×D4C2×D411yescharacteristic
214C22×C3×C4—21no—
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4#4111yescharacteristic
218C22×Dic3—41no—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6—41no—
224C2×Dic6—81no—
225C2×Dic6—81no—
226C3×M16—81no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—81no—
230C2×C3×C8—81no—
231C2×C3×C8C2×D411yescharacteristic
232C2×C3×C8C2×D411yescharacteristic
233C2×C3×C8C2×D411yescharacteristic
234C2×C3×C8C2×D411yescharacteristic
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4C2×D411yescharacteristic
240C3×C4⋊C4C2×D411yescharacteristic
241C3×C22⋊C4—21no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C42—21no—
247C3×C42C2×D411yescharacteristic
248C3×C42C2×D411yescharacteristic
249C3×C42#4111yescharacteristic
250C3×C42C2411yescharacteristic
251#217—41no—
252#216—81no—
253#216—81no—
254#216—81no—
255#214—81no—
256#214—81no—
257#214—81no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—21no—
265C4⋊Dic3—21no—
266C4⋊Dic3—41no—
267C4⋊Dic3—41no—
268Dic3⋊C4—41no—
269Dic3⋊C4—41no—
270C4×Dic3—41no—
271C2×C3⋊C8—21no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—21no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—81no—
276C22×Q8—61no—
277C2×Q16—61no—
278C2×Q16—61no—
279C2×Q16—61no—
280C2×SD16—61no—
281C2×SD16—61no—
282C2×SD16—61no—
283C2×M16—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—61no—
287C4⋊Q8—31no—
288C4⋊Q8—31no—
289C4⋊Q8—31no—
290C4⋊Q8—31no—
291C4⋊Q8—61no—
292C4⋊Q8—61no—
293C4⋊Q8—61no—
294#126—21no—
295#125—61no—
296#125D1211yescharacteristic
297#124D1211yescharacteristic
298#123—21no—
299C22⋊Q8—61no—
300C22⋊Q8—61no—
301C22⋊Q8D1211yescharacteristic
302#121D1211yescharacteristic
303C4×Q8—61no—
304C4×Q8—61no—
305C4×Q8C22×D311yescharacteristic
306C4×D4—21no—
307C4×D4C22×D311yescharacteristic
308#117—21no—
309#117—61no—
310C2×C4⋊C4—61no—
311C2×C4⋊C4—61no—
312C2×C42C22×D311yescharacteristic
313#107—61no—
314#107—61no—
315#107—61no—
316#107—61no—
317#107—61no—
318#106—61no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8—31no—
323C4⋊C8—31no—
324C4⋊C8—31no—
325C4⋊C8—31no—
326C4⋊C8—61no—
327C4⋊C8#6711yescharacteristic
328C4⋊C8#6711yescharacteristic
329C4⋊C8C22×D311yescharacteristic
330C4⋊C8C22×D311yescharacteristic
331#103—61no—
332#103—61no—
333#103—61no—
334#103—61no—
335#103—61no—
336#103—61no—
337#103—61no—
338#103—61no—
339#103—61no—
340#103—61no—
341#103—61no—
342#102—61no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—61no—
346C22⋊C8#6711yescharacteristic
347C22⋊C8#6711yescharacteristic
348#97—21no—
349#97—61no—
350C4×C8—21no—
351C4×C8C22×D311yescharacteristic
352C4×C8C22×D311yescharacteristic
353C23×C3—21no—
354C23×C3#12111yescharacteristic
355C3×Q8—21no—
356C3×Q8—21no—
357C3×D4—21no—
358C3×D4—21no—
359C3×D4—42no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4#12111yescharacteristic
371C2×C3×C4#12111yescharacteristic
372C2×C3×C4#12111yescharacteristic
373C2×C3×C4C22×D411yescharacteristic
374C2×C3×C4C22×D411yescharacteristic
375C2×C3×C4C2×#4111yescharacteristic
376C2×Dic3—41no—
377C2×Dic3—41no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3—82no—
381Dic6—41no—
382Dic6—41no—
383Dic6—41no—
384Dic6—41no—
385Dic6—41no—
386Dic6—41no—
387Dic6—41no—
388Dic6—41no—
389Dic6—82no—
390C3×C8—21no—
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—41no—
395C3×C8—41no—
396C3⋊C8—41no—
397C3⋊C8—41no—
398C3⋊C8—41no—
399C3⋊C8—41no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8—121no—
405C2×Q8—241no—
406C2×Q8—241no—
407C2×Q8C2×D1211yescharacteristic
408C2×D4—21no—
409C2×D4C2×D1211yescharacteristic
410C22×C4—21no—
411C22×C4—121no—
412C22×C4C2×D1211yescharacteristic
413C22×C4#23511yescharacteristic
414C22×C4C2×#6711yescharacteristic
415Q16—241no—
416Q16—241no—
417Q16—241no—
418SD16—241no—
419SD16—241no—
420SD16—241no—
421M16—81no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—61no—
425C2×C8—61no—
426C2×C8—61no—
427C2×C8—61no—
428C2×C8—81no—
429C2×C8—81no—
430C2×C8—241no—
431C2×C8C2×#6711yescharacteristic
432C2×C8C2×#6711yescharacteristic
433C2×C8C2×#6711yescharacteristic
434C2×C8C2×#6711yescharacteristic
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—61no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—61no—
445C4⋊C4—61no—
446C4⋊C4—61no—
447C4⋊C4—121no—
448C4⋊C4—121no—
449C4⋊C4—121no—
450C4⋊C4—121no—
451C4⋊C4C2×D1211yescharacteristic
452C4⋊C4C2×D1211yescharacteristic
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—21no—
458C22⋊C4—121no—
459C42—21no—
460C42—121no—
461C42C2×D1211yescharacteristic
462C42#23511yescharacteristic
463C42C2×#6711yescharacteristic
464C42C23×D311yescharacteristic
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3#47312yes—
471C22×C3C2×#12111yescharacteristic
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4—41no—
479C3×C4#57611yescharacteristic
480C3×C4#57711yescharacteristic
481C3×C4#57711yescharacteristic
482C3×C4#57811yescharacteristic
483Dic3—81no—
484Dic3—81no—
485Dic3—81no—
486Dic3—81no—
487C23—21no—
488C23#93011yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—121no—
492Q8—121no—
493Q8—121no—
494Q8—121no—
495Q8—121no—
496Q8—121no—
497Q8—121no—
498Q8—121no—
499Q8—242no—
500D4—21no—
501D4—21no—
502D4—42no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—121no—
514C2×C4—121no—
515C2×C4—121no—
516C2×C4—121no—
517C2×C4—242no—
518C2×C4#93011yescharacteristic
519C2×C4#93011yescharacteristic
520C2×C4#93011yescharacteristic
521C2×C4C22×D1211yescharacteristic
522C2×C4C2×#23511yescharacteristic
523C2×C4C22×#6711yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—121no—
531C8—121no—
532C8—121no—
533C8—121no—
534C2×C3—22no—
535C2×C3—81no—
536C2×C3#304611yescharacteristic
537C2×C3#306211yescharacteristic
538C2×C3C2×#47311yescharacteristic
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22#514312yes—
545C22C2×#93011yescharacteristic
546C4—21no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—241no—
554C4—241no—
555C4—241no—
556C4—241no—
557C4#575111yescharacteristic
558C4#575211yescharacteristic
559C4#583611yescharacteristic
560C4#583811yescharacteristic
561C3#1959011yescharacteristic, complemented, Sylow
562C2—22no—
563C2—81no—
564C2#8257211yescharacteristic
565C2#8380211yescharacteristic
566C2C2×#514311yescharacteristic
subgroupG/H
centerC22C2×#930
commutator, cosocleC3×C42C24
FrattiniC42C23×D3
FittingC3×#2994C2
socleC22×C3C2×#121
prime radicalC3×#121D4
hypercenter#2994D3
hypocenterC3#19590
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2994

Complements

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

NH ≅ G/Ntype
4. #79272C2semidirect
5. #70966C2semidirect
6. #70964C2semidirect
7. #70946C2semidirect
8. #70944C2semidirect
9. #70875C2semidirect
10. #70873C2semidirect
11. #70854C2semidirect
12. #70852C2semidirect
13. #70752C2semidirect
14. #70439C2semidirect
15. C2×#4486C2semidirect
561. C3#19590semidirect

Maximal subgroups

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

subgroupindex
C3×#29942
#831552
#831542
#792722
#709662
#709642
#709462
#709442
#708752
#708732
#708542
#708522
#707522
#704392
C2×#44862
#195903