Finite Group Databasebeta

← #11887158

Subgroups — #11887158

Order 1152.

988 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic, complemented
2D122C211yesmaximal, characteristic
3#10592726C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591651C212yesmaximal, complemented
6#10591585C212yesmaximal, complemented
7D3×#809C212yesmaximal, complemented
8#10590423C212yesmaximal, complemented
9C3⋊C8×D12C211yesmaximal, characteristic, complemented
10#10590281C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#83634—31nomaximal
13#79676—31nomaximal
14C2×D3×D12—21no—
15C2×D3×D12C2212yes—
16C32×C4×Q8C2211yescharacteristic, complemented
17C2×#3755C2212yescomplemented
18#64083C2211yescharacteristic
19C3×#946C2212yescomplemented
20C2×C3×#215C2211yescharacteristic
21C3×#896—22no—
22C3×D3×C4⋊C4C2212yescomplemented
23C3×C4×D12—21no—
24C3×C4×D12C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×#870—21no—
27C3×#869C2211yescharacteristic, complemented
28#63923—22no—
29#63909—21no—
30#63909C2212yes—
31C2×D3×C3⋊C8C2212yescomplemented
32#63636C2212yescomplemented
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
34C3×#835C2211yescharacteristic, complemented
35C3×#809C2211yescharacteristic
36C3×#808C2211yescharacteristic, complemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63574C2212yescomplemented
39#63564C2212yescomplemented
40#63564C2212yescomplemented
41#63562C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43C3×#554—31no—
44#5579D311yescharacteristic, complemented
45D4×D12—31no—
46D4×D12—31no—
47C3×C4×SD16—31no—
48#5169—32no—
49#5088—31no—
50#5084—31no—
51#5048—32no—
52#5046—32no—
53#5027—31no—
54#5027—31no—
55#5027—61no—
56C4×#215D311yescharacteristic, complemented
57D4×C3⋊C8—31no—
58#5008—31no—
59#4968—32no—
60C2×#809—32no—
61#4863—32no—
62#4807—32no—
63D3×#102—32no—
64#4694—31no—
65C8×D12—31no—
66C22×D32—22no—
67C2×C32×Q8C2311yescharacteristic
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C3×D12D411yescharacteristic
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6—21no—
77C2×#626—22no—
78C2×#626—22no—
79D3×D12—24no—
80D3×D12—42no—
81D3×D12—44no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C42—21no—
85C32×C42C2311yescharacteristic
86#3755—42no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#215—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4D412yes—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—22no—
97C3×Dic3⋊C4—22no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100#3722—22no—
101D3×C3⋊C8—42no—
102#3295—91noSylow
103C2×D3×D4—32no—
104C2×D3×D4—61no—
105C22×D12—32no—
106C22×D12—61no—
107C2×C3×SD16—31no—
108C3×C4⋊Q8—31no—
109C3×#125—61no—
110C3×C22⋊Q8—32no—
111C3×C22⋊Q8—62no—
112C3×C4×Q8—21no—
113C3×C4×Q8C2×D311yescharacteristic, complemented
114C3×C4×Q8C2×D311yescharacteristic, complemented
115C3×C4×D4—31no—
116C3×C4×D4—31no—
117C3×C4×D4—61no—
118C2×C3×C4⋊C4—32no—
119#946C2×D312yescomplemented
120C2×#215—32no—
121C2×#215—32no—
122C2×#215—62no—
123C2×#215C2×D311yescharacteristic
124#930—32no—
125#930—61no—
126C22×C3⋊C8—32no—
127C2×D3×C8—32no—
128#896—22no—
129#895—32no—
130#895—61no—
131D3×C4⋊C4C2×D312yescomplemented
132#882—62no—
133#882—62no—
134#874—31no—
135#874—31no—
136#874—61no—
137C4×D12—21no—
138C4×D12C2×D311yescharacteristic
139C4×D12C2×D311yescharacteristic
140#870—21no—
141#869C2×D311yescharacteristic, complemented
142C3×#106—31no—
143C3×#103—31no—
144C3×#102—31no—
145C3×C4×C8—31no—
146#835C2×D311yescharacteristic, complemented
147#832—32no—
148#830—32no—
149#821—32no—
150#821—32no—
151(C2×D3)⋊C8—32no—
152#809—32no—
153#809—32no—
154#809—32no—
155#809—32no—
156#809—32no—
157#809—62no—
158#809C2×D311yescharacteristic
159#808—32no—
160#808—32no—
161#808C2×D311yescharacteristic, complemented
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—31no—
164C4⋊(C3⋊C8)—61no—
165C4×C3⋊C8C2×D311yescharacteristic, complemented
166C22×C3⋊D3—22no—
167C22×C3×D3—21no—
168C22×C3×D3C2×D412yes—
169C2×D32—44no—
170C2×D32—44no—
171C2×D32—82no—
172C32×Q8—21no—
173C32×Q8—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)—42no—
182C4⋊(C3⋊D3)—81no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C2×D412yes—
186C3×D12—21no—
187C3×D12SD1614yescomplemented
188C3×D12#4112yes—
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×C4×D3—42no—
192C3×C4×D3—82no—
193C3×Dic6—81no—
194#626—44no—
195#626—44no—
196C3⋊(C3⋊C8)—22no—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199#554—31no—
200D42—91no—
201#486—91no—
202#481—92no—
203#476—91no—
204#465—92no—
205#460—91no—
206#450—92no—
207C4×SD16—31no—
208C8×D4—91no—
209C2×#102—92no—
210C23×D3—62no—
211C23×D3—62no—
212C2×C3×Q8—21no—
213C2×C3×Q8—61no—
214C2×C3×Q8C22×D311yescharacteristic
215C2×C3×Q8C22×D311yescharacteristic
216C2×C3×D4—31no—
217C2×C3×D4—31no—
218C22×C3×C4—32no—
219C22×C3×C4—62no—
220C22×C3×C4—61no—
221C2×#67—62no—
222C2×#67—62no—
223D3×D4—64no—
224D3×D4—122no—
225D3×D4—124no—
226C2×D12—32no—
227C2×D12—32no—
228C2×D12—62no—
229C2×D12—64no—
230C2×D12—62no—
231C2×D12—62no—
232C2×D12—61no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12—61no—
236C2×D12—121no—
237C2×D12—121no—
238C2×D12—122no—
239C2×D12—124no—
240C2×D12#6711yescharacteristic
241C2×D12C22×D311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—22no—
244C2×C4×D3C22×D312yes—
245C2×Dic6—21no—
246C3×SD16—62no—
247C2×C3×C8—31no—
248C2×C3×C8—31no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—41no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—62no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4C22×D311yescharacteristic
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C22⋊C4—32no—
262C3×C22⋊C4—62no—
263C3×C22⋊C4—61no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42—41no—
268C3×C42C22×D311yescharacteristic
269C3×C42C22×D311yescharacteristic
270#215—22no—
271#215—122no—
272#215—122no—
273#215—124no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4#6712yes—
279C4⋊Dic3—21no—
280C4⋊Dic3#6711yescharacteristic
281C4⋊Dic3C22×D311yescharacteristic
282C4⋊Dic3C22×D312yes—
283Dic3⋊C4—22no—
284Dic3⋊C4—22no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—32no—
287C2×C3⋊C8—62no—
288C2×C3⋊C8—122no—
289C2×C3⋊C8C22×D311yescharacteristic
290C2×C3⋊C8C22×D311yescharacteristic
291D3×C8—122no—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—42no—
294C2×C3⋊D3—42no—
295C2×C3⋊D3—42no—
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—41no—
300C2×C3×D3—41no—
301C2×C3×D3C2×SD1614yes—
302D32—88no—
303C32×C4—21no—
304C32×C4—41no—
305C32×C4—41no—
306C32×C4C2×SD1612yes—
307C32×C4C2×#4111yescharacteristic
308C32×C4H(5,𝔽2)11yescharacteristic
309C3×Dic3—22no—
310C3×Dic3—41no—
311C3×Dic3—42no—
312C22×D4—92no—
313C22×D4—181no—
314C2×SD16—31no—
315C2×SD16—92no—
316C22×C8—92no—
317C4⋊Q8—31no—
318#127—91no—
319#125—61no—
320C22⋊Q8—32no—
321C22⋊Q8—62no—
322#121—92no—
323#121—181no—
324#120—182no—
325C4×Q8D3211yescharacteristic, complemented
326C4×D4—31no—
327C4×D4—31no—
328C4×D4—61no—
329C2×C4⋊C4—32no—
330#106—31no—
331#106—92no—
332C4⋊C8—91no—
333#103—31no—
334#102—31no—
335#102—92no—
336#102—92no—
337#102—92no—
338#102—92no—
339C22⋊C8—92no—
340C4×C8—31no—
341C23×C3—32no—
342C23×C3—61no—
343C22×D3—21no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—122no—
347C22×D3—124no—
348C22×D3—124no—
349C22×D3—124no—
350C22×D3—124no—
351C22×D3—242no—
352C22×D3—242no—
353C22×D3C2×#6712yes—
354C3×Q8—22no—
355C3×Q8—21no—
356C3×Q8—21no—
357C3×Q8—21no—
358C3×Q8—21no—
359C3×Q8—41no—
360C3×Q8—241no—
361C3×D4—34no—
362C3×D4—32no—
363C3×D4—61no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—32no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—61no—
378C2×C3×C4—122no—
379C2×C3×C4—242no—
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C2×#6711yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386#67—124no—
387#67—124no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3C2×#6712yes—
391D12—21no—
392D12—62no—
393D12—62no—
394D12—62no—
395D12—62no—
396D12—122no—
397D12—122no—
398D12—124no—
399D12—124no—
400D12—122no—
401D12—122no—
402D12—242no—
403D12—241no—
404D12—241no—
405D12—242no—
406D12#21514yescomplemented
407D12#23512yes—
408C4×D3—22no—
409C4×D3—22no—
410C4×D3—42no—
411C4×D3—82no—
412Dic6—81no—
413C3×C8—61no—
414C3×C8—61no—
415C3⋊C8—21no—
416C3⋊C8—21no—
417C3⋊C8—62no—
418C3⋊C8—62no—
419C3⋊C8—122no—
420C2×C32#54611yescharacteristic
421C2×C32C22×SD1611yescharacteristic
422C2×C32#57611yescharacteristic
423C3⋊D3—82no—
424C3×D3—24no—
425C3×D3—42no—
426C24—182no—
427C2×Q8—61no—
428C2×Q8C2×D3211yescharacteristic
429C2×D4—31no—
430C2×D4—31no—
431C2×D4—92no—
432C2×D4—182no—
433C2×D4—184no—
434C2×D4—182no—
435C2×D4—181no—
436C2×D4—181no—
437C2×D4—362no—
438C2×D4—364no—
439C22×C4—32no—
440C22×C4—62no—
441C22×C4—61no—
442SD16—62no—
443SD16—362no—
444C2×C8—31no—
445C2×C8—31no—
446C2×C8—92no—
447C2×C8—362no—
448C4⋊C4—21no—
449C4⋊C4—31no—
450C4⋊C4—32no—
451C4⋊C4—31no—
452C4⋊C4—62no—
453C4⋊C4—62no—
454C4⋊C4—61no—
455C4⋊C4C2×D3211yescharacteristic
456C22⋊C4—32no—
457C22⋊C4—62no—
458C22⋊C4—61no—
459C22⋊C4—182no—
460C42—21no—
461C42C2×D3211yescharacteristic
462C22×C3—21no—
463C22×C3—34no—
464C22×C3—62no—
465C22×C3—62no—
466C22×C3—62no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3C2×D3×D411yescharacteristic
470C22×C3C22×#6711yescharacteristic
471C2×D3—22no—
472C2×D3—22no—
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—122no—
481C2×D3—122no—
482C2×D3—242no—
483C2×D3—242no—
484C2×D3—242no—
485C2×D3—248no—
486C2×D3—248no—
487C2×D3C2×#21514yes—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—22no—
493C3×C4—41no—
494C3×C4—42no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—41no—
499C3×C4—62no—
500C3×C4—81no—
501C3×C4—122no—
502C3×C4—121no—
503C3×C4D3×SD1612yes—
504C3×C4C2×#21512yes—
505C3×C4C2×#23511yescharacteristic
506C3×C4D3×#4111yescharacteristic
507C3×C4#100911yescharacteristic
508C3×C4#100911yescharacteristic
509Dic3—22no—
510Dic3—41no—
511Dic3—42no—
512C32#329511yescharacteristic, complemented, Sylow
513C23—32no—
514C23—61no—
515C23—182no—
516C23—364no—
517C23—364no—
518C23—722no—
519Q8—21no—
520Q8—21no—
521Q8—241no—
522D4—32no—
523D4—34no—
524D4—61no—
525D4—182no—
526D4—182no—
527D4—364no—
528D4—364no—
529D4—362no—
530D4—721no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—32no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—122no—
539C2×C4—242no—
540C2×C4D3×#6711yescharacteristic
541C2×C4D3×#6711yescharacteristic
542C2×C4C22×D3211yescharacteristic
543C8—61no—
544C8—61no—
545C8—182no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—64no—
550C2×C3—122no—
551C2×C3#555011yescharacteristic
552C2×C3C2×D3×SD1611yescharacteristic
553C2×C3#576911yescharacteristic
554C2×C3C22×#21511yescharacteristic
555C2×C3#582911yescharacteristic
556C2×C3#583511yescharacteristic
557D3—24no—
558D3—42no—
559D3—242no—
560D3—242no—
561D3—482no—
562C22—34no—
563C22—62no—
564C22—62no—
565C22—62no—
566C22—121no—
567C22—121no—
568C22—362no—
569C22—362no—
570C22—362no—
571C22—728no—
572C22C2×D3×#6711yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—62no—
577C4—122no—
578C4—121no—
579C4D3×#21512yes—
580C4D3×#23511yescharacteristic
581C4#6430811yescharacteristic
582C3—21no—
583C3#7967611yescharacteristic, complemented
584C3#8363411yescharacteristic, complemented
585C2—64no—
586C2—122no—
587C2—722no—
588C2#1059506711yescharacteristic
589C2C2×D3×#21511yescharacteristic
590C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalD122C2
hypercenterC4×Q8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5579C2semidirect
3. #10592726C2semidirect
4. C3×C4×#215C2semidirect
5. #10591651C2semidirect
6. #10591585C2semidirect
7. D3×#809C2semidirect
8. #10590423C2semidirect
9. C3⋊C8×D12C2semidirect
10. #10590281C2semidirect
11. #10590266C2semidirect
16. C32×C4×Q8C22semidirect
17. C2×#3755C22semidirect
19. C3×#946C22semidirect
22. C3×D3×C4⋊C4C22semidirect
27. C3×#869C22semidirect
31. C2×D3×C3⋊C8C22semidirect
32. #63636C22semidirect
33. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. C3×#835C22semidirect
36. C3×#808C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63574C22semidirect
39. #63564C22semidirect
40. #63564C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
44. #5579D3semidirect
56. C4×#215D3semidirect
113. C3×C4×Q8C2×D3semidirect
114. C3×C4×Q8C2×D3semidirect
119. #946C2×D3semidirect
131. D3×C4⋊C4C2×D3semidirect
141. #869C2×D3semidirect
146. #835C2×D3semidirect
161. #808C2×D3semidirect
165. C4×C3⋊C8C2×D3semidirect
187. C3×D12SD16semidirect
325. C4×Q8D32semidirect
406. D12#215semidirect
512. C32#3295semidirect
583. C3#79676semidirect
584. C3#83634semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
D1222
#105927262
C3×C4×#2152
#105916512
#105915852
D3×#8092
#105904232
C3⋊C8×D122
#105902812
#105902662
#836343
#796763