Finite Group Databasebeta

← #11887157

Subgroups — #11887157

Order 1152.

1038 conjugacy classes of subgroups.

The subgroup lattice has 605 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596050C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic
3C3×#5027C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591652C212yesmaximal, complemented
6#10591591C212yesmaximal, complemented
7#10590593C212yesmaximal, complemented
8#10590511C212yesmaximal, complemented
9#10590327C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#80395—31nomaximal
13#79676—31nomaximal
14C2×#3802C2212yes—
15C2×D3×D12—21no—
16C32×C4×Q8C2211yescharacteristic, complemented
17#64155C2212yescomplemented
18#64105—22no—
19C4⋊C4×C3⋊D3C2212yescomplemented
20C4×C4⋊(C3⋊D3)—21no—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22#64079—21no—
23#64078C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C2×C3×#215C2212yescomplemented
26C3×#874C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28#63922—22no—
29#63916C2212yes—
30#63908—21no—
31C2×#3710C2212yescomplemented
32C3×#835C2211yescharacteristic, complemented
33C3×#809C2211yescharacteristic
34C3×#809C2212yescomplemented
35C3×#808C2211yescharacteristic, complemented
36C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63573C2212yescomplemented
39#63563C2212yes—
40#63563C2212yescomplemented
41#63563C2212yescomplemented
42#63557C2212yescomplemented
43#5717—31no—
44#5579—31no—
45#5579—31no—
46#5579—61no—
47D4×D12—31no—
48C3×#460—31no—
49C3×C4×SD16—31no—
50#5171—32no—
51#5169—32no—
52#5169—32no—
53#5070—31no—
54#5027D311yescharacteristic, complemented
55C4×#215D311yescharacteristic, complemented
56#5008—31no—
57#4863—32no—
58#4842—31no—
59#4834—31no—
60#4807—32no—
61#4777—32no—
62D3×#102—32no—
63D3×#102—32no—
64#4694—31no—
65C8×D12—31no—
66C22×D32—22no—
67C2×C32×Q8C2311yescharacteristic
68C2×C4⋊(C3⋊D3)D411yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3C2312yes—
71C2×#634—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×#626—22no—
78C2×#625—22no—
79#3802—24no—
80#3802—42no—
81D3×D12—44no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C42—21no—
85C32×C42C2311yescharacteristic
86#3752—22no—
87#3752D412yes—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)D411yescharacteristic
90C4⋊(C3⋊Dic3)C2312yes—
91#3750—22no—
92#3750—22no—
93C3×#215—22no—
94C3×#215—42no—
95C3×(C2×D3)⋊C4—21no—
96C3×C4⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99C2×C3×C3⋊C8C2311yescharacteristic
100(C2×D3)⋊Dic3—22no—
101#3710—42no—
102#3295—91noSylow
103C2×D3×D4—32no—
104C2×D3×D4—32no—
105C2×D3×D4—61no—
106C22×D12—61no—
107C2×C3×SD16—31no—
108C2×C3×SD16—32no—
109C3×#127—31no—
110C3×C4×Q8—21no—
111C3×C4×Q8C2×D311yescharacteristic, complemented
112C3×C4×Q8C2×D311yescharacteristic, complemented
113C3×C4×D4—31no—
114#946—32no—
115#946—32no—
116#946—62no—
117C2×#215C2×D311yescharacteristic
118C2×#215C2×D312yescomplemented
119#938—32no—
120#938—61no—
121#937—62no—
122#930—61no—
123C2×D3×C8—32no—
124C2×D3×C8—32no—
125#896—62no—
126#896—62no—
127#896—64no—
128#895—32no—
129D3×C4⋊C4—32no—
130D3×C4⋊C4—32no—
131D3×C4⋊C4—62no—
132#882—62no—
133#874C2×D311yescharacteristic
134C4×D12—31no—
135C4×D12—31no—
136C4×D12—61no—
137C4×D12—61no—
138C4×D12—61no—
139C4×D12—62no—
140C4×D12C2×D311yescharacteristic
141#870—61no—
142#870—61no—
143#870—62no—
144#869—31no—
145#869—31no—
146#869—61no—
147C3×#106—31no—
148C3×C4⋊C8—31no—
149C3×#103—31no—
150C3×#102—31no—
151C3×#102—32no—
152C3×C4×C8—31no—
153#835C2×D311yescharacteristic, complemented
154#832—32no—
155#832—32no—
156#832—32no—
157#821—32no—
158#821—32no—
159#821—32no—
160(C2×D3)⋊C8—32no—
161(C2×D3)⋊C8—32no—
162#817—32no—
163#809C2×D311yescharacteristic
164#809C2×D312yescomplemented
165#808—32no—
166#808C2×D311yescharacteristic, complemented
167C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
168C4×C3⋊C8C2×D311yescharacteristic, complemented
169C22×C3⋊D3C2×D412yes—
170C22×C3×D3—21no—
171C22×C3×D3—22no—
172C2×D32—44no—
173C2×D32—44no—
174C2×D32—82no—
175C32×Q8—21no—
176C32×Q8—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3C2×D412yes—
184C4⋊(C3⋊D3)SD1614yescomplemented
185C4×C3⋊D3—22no—
186C4×C3⋊D3—22no—
187C4×C3⋊D3—82no—
188#634—81no—
189C2×C3×Dic3—21no—
190C3×D12—22no—
191C3×D12—21no—
192C3×D12—22no—
193C3×D12—42no—
194C3×D12—81no—
195C3×D12#4112yes—
196C3×C4×D3—42no—
197#626—44no—
198#625—44no—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—22no—
202#554—91no—
203D42—91no—
204#486—91no—
205#481—92no—
206#476—91no—
207#465—92no—
208#460—31no—
209#450—92no—
210C4×SD16—31no—
211C8×D4—91no—
212C2×#102—92no—
213C23×D3—62no—
214C23×D3—62no—
215C2×C3×Q8—21no—
216C2×C3×Q8C22×D311yescharacteristic
217C2×C3×Q8C22×D311yescharacteristic
218C2×C3×D4—31no—
219C2×C3×D4—32no—
220C2×C3×D4—61no—
221C2×C3×D4—61no—
222C22×C3×C4—61no—
223C2×#67—62no—
224C2×#67—62no—
225C2×#67—62no—
226D3×D4—64no—
227D3×D4—64no—
228D3×D4—124no—
229D3×D4—122no—
230D3×D4—122no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—31no—
234C2×D12—31no—
235C2×D12—61no—
236C2×D12—62no—
237C2×D12—124no—
238C2×D12C22×D312yes—
239C2×D12C22×D311yescharacteristic
240C2×C4×D3—21no—
241C2×C4×D3—32no—
242C2×C4×D3—32no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—64no—
247C2×Dic6—62no—
248C2×Dic6—61no—
249C2×Dic6—61no—
250C3×SD16—62no—
251C3×SD16—122no—
252C2×C3×C8—32no—
253C2×C3×C8—31no—
254C2×C3×C8—31no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C22⋊C4—61no—
263C3×C42—22no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42C22×D311yescharacteristic
268C3×C42C22×D311yescharacteristic
269#217—62no—
270#215—22no—
271#215—42no—
272(C2×D3)⋊C4—21no—
273(C2×D3)⋊C4—32no—
274(C2×D3)⋊C4—32no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—64no—
280C4⋊Dic3—31no—
281C4⋊Dic3—31no—
282C4⋊Dic3—32no—
283C4⋊Dic3—32no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—62no—
291Dic3⋊C4—62no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294Dic3⋊C4—64no—
295Dic3⋊C4—64no—
296C2×C3⋊C8C22×D311yescharacteristic
297C2×C3⋊C8C22×D311yescharacteristic
298C2×C3⋊C8C22×D312yes—
299D3×C8—122no—
300D3×C8—122no—
301C22×C32C22×D411yescharacteristic
302C2×C3⋊D3—22no—
303C2×C3⋊D3—22no—
304C2×C3⋊D3C2×SD1614yes—
305C2×C3×D3—22no—
306C2×C3×D3—41no—
307C2×C3×D3—41no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C2×C3×D3—42no—
311D32—88no—
312C32×C4—21no—
313C32×C4—41no—
314C32×C4—41no—
315C32×C4C2×SD1612yes—
316C32×C4C2×#4111yescharacteristic
317C32×C4H(5,𝔽2)11yescharacteristic
318C3⋊Dic3—22no—
319C3⋊Dic3—42no—
320C3×Dic3—41no—
321C22×D4—92no—
322C22×D4—181no—
323C2×SD16—31no—
324C2×SD16—32no—
325C22×C8—92no—
326C4⋊Q8—91no—
327#127—31no—
328#125—181no—
329C22⋊Q8—92no—
330C22⋊Q8—182no—
331#121—92no—
332#121—181no—
333#120—182no—
334C4×Q8D3211yescharacteristic, complemented
335C4×D4—31no—
336C4×D4—91no—
337C4×D4—181no—
338C2×C4⋊C4—92no—
339#106—31no—
340#106—92no—
341C4⋊C8—31no—
342#103—31no—
343#102—31no—
344#102—32no—
345#102—92no—
346#102—92no—
347#102—92no—
348C22⋊C8—92no—
349C4×C8—31no—
350C23×C3—61no—
351C23×C3—62no—
352C22×D3—21no—
353C22×D3—22no—
354C22×D3—32no—
355C22×D3—32no—
356C22×D3—62no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3—124no—
360C22×D3—124no—
361C22×D3—242no—
362C22×D3—242no—
363C3×Q8—21no—
364C3×Q8—21no—
365C3×Q8—21no—
366C3×Q8—21no—
367C3×Q8—41no—
368C3×Q8—41no—
369C3×D4—32no—
370C3×D4—62no—
371C3×D4—61no—
372C3×D4—62no—
373C3×D4—122no—
374C3×D4—241no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—61no—
385C2×C3×C4—122no—
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392#67—124no—
393#67—124no—
394#67—124no—
395C2×Dic3—21no—
396C2×Dic3—32no—
397C2×Dic3—32no—
398C2×Dic3—62no—
399C2×Dic3—64no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402D12—22no—
403D12—22no—
404D12—21no—
405D12—34no—
406D12—34no—
407D12—42no—
408D12—64no—
409D12—81no—
410D12—124no—
411D12#23512yes—
412C4×D3—42no—
413C4×D3—62no—
414C4×D3—62no—
415C4×D3—62no—
416C4×D3—62no—
417C4×D3—122no—
418C4×D3—122no—
419C4×D3—242no—
420C4×D3—242no—
421C4×D3—244no—
422Dic6—241no—
423Dic6—241no—
424Dic6—242no—
425C3×C8—61no—
426C3×C8—61no—
427C3×C8—62no—
428C3⋊C8—21no—
429C3⋊C8—22no—
430C3⋊C8—21no—
431C2×C32#54611yescharacteristic
432C2×C32C22×SD1611yescharacteristic
433C2×C32#57611yescharacteristic
434C3⋊D3—24no—
435C3×D3—42no—
436C3×D3—82no—
437C24—182no—
438C2×Q8—181no—
439C2×Q8C2×D3211yescharacteristic
440C2×D4—31no—
441C2×D4—32no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—91no—
445C2×D4—182no—
446C2×D4—182no—
447C2×D4—184no—
448C2×D4—364no—
449C2×D4—362no—
450C22×C4—61no—
451C22×C4—92no—
452C22×C4—182no—
453SD16—62no—
454SD16—122no—
455C2×C8—31no—
456C2×C8—31no—
457C2×C8—32no—
458C2×C8—362no—
459C4⋊C4—21no—
460C4⋊C4—31no—
461C4⋊C4—91no—
462C4⋊C4—92no—
463C4⋊C4—182no—
464C4⋊C4—182no—
465C4⋊C4—181no—
466C4⋊C4C2×D3211yescharacteristic
467C22⋊C4—61no—
468C22⋊C4—92no—
469C22⋊C4—182no—
470C22⋊C4—182no—
471C42—21no—
472C42C2×D3211yescharacteristic
473C22×C3—21no—
474C22×C3—62no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C2×D3×D411yescharacteristic
482C2×D3—22no—
483C2×D3—34no—
484C2×D3—34no—
485C2×D3—41no—
486C2×D3—41no—
487C2×D3—42no—
488C2×D3—42no—
489C2×D3—42no—
490C2×D3—64no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—248no—
498C2×D3—248no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—22no—
504C3×C4—41no—
505C3×C4—42no—
506C3×C4—42no—
507C3×C4—41no—
508C3×C4—41no—
509C3×C4—41no—
510C3×C4—41no—
511C3×C4—121no—
512C3×C4D3×SD1612yes—
513C3×C4D3×SD1612yes—
514C3×C4C2×#23511yescharacteristic
515C3×C4#100411yescharacteristic
516C3×C4D3×#4111yescharacteristic
517C3×C4#100911yescharacteristic
518Dic3—41no—
519Dic3—62no—
520Dic3—62no—
521Dic3—122no—
522Dic3—124no—
523Dic3—122no—
524Dic3—122no—
525C32#329511yescharacteristic, complemented, Sylow
526C23—61no—
527C23—62no—
528C23—92no—
529C23—364no—
530C23—364no—
531C23—722no—
532Q8—21no—
533Q8—21no—
534Q8—721no—
535D4—32no—
536D4—62no—
537D4—61no—
538D4—62no—
539D4—94no—
540D4—122no—
541D4—241no—
542D4—364no—
543D4—364no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—61no—
547C2×C4—92no—
548C2×C4—122no—
549C2×C4—182no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4—722no—
553C2×C4#381111yescharacteristic
554C2×C4#381111yescharacteristic
555C2×C4C22×D3211yescharacteristic
556C8—61no—
557C8—61no—
558C8—62no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—122no—
563C2×C3—242no—
564C2×C3#555011yescharacteristic
565C2×C3#561211yescharacteristic
566C2×C3C2×D3×SD1611yescharacteristic
567C2×C3C2×D3×SD1611yescharacteristic
568C2×C3#576911yescharacteristic
569C2×C3#577411yescharacteristic
570D3—42no—
571D3—64no—
572D3—64no—
573D3—82no—
574D3—124no—
575C22—62no—
576C22—94no—
577C22—121no—
578C22—121no—
579C22—122no—
580C22—122no—
581C22—122no—
582C22—182no—
583C22—182no—
584C22—728no—
585C22C2×#381111yescharacteristic
586C4—21no—
587C4—41no—
588C4—41no—
589C4—121no—
590C4—182no—
591C4—362no—
592C4#6394012yes—
593C4D3×#23511yescharacteristic
594C4#6430711yescharacteristic
595C3—21no—
596C3#7967611yescharacteristic, complemented
597C3#8039511yescharacteristic, complemented
598C2—122no—
599C2—184no—
600C2—242no—
601C2#1059507811yescharacteristic
602C2C2×#6394011yescharacteristic
603C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594004C2
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. #10596050C2semidirect
3. C3×#5027C2semidirect
4. C3×C4×#215C2semidirect
5. #10591652C2semidirect
6. #10591591C2semidirect
7. #10590593C2semidirect
8. #10590511C2semidirect
9. #10590327C2semidirect
10. #10590273C2semidirect
11. #10590268C2semidirect
16. C32×C4×Q8C22semidirect
17. #64155C22semidirect
19. C4⋊C4×C3⋊D3C22semidirect
23. #64078C22semidirect
25. C2×C3×#215C22semidirect
31. C2×#3710C22semidirect
32. C3×#835C22semidirect
34. C3×#809C22semidirect
35. C3×#808C22semidirect
36. C3×C4⋊(C3⋊C8)C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63573C22semidirect
40. #63563C22semidirect
41. #63563C22semidirect
42. #63557C22semidirect
54. #5027D3semidirect
55. C4×#215D3semidirect
111. C3×C4×Q8C2×D3semidirect
112. C3×C4×Q8C2×D3semidirect
118. C2×#215C2×D3semidirect
153. #835C2×D3semidirect
164. #809C2×D3semidirect
166. #808C2×D3semidirect
167. C4⋊(C3⋊C8)C2×D3semidirect
168. C4×C3⋊C8C2×D3semidirect
184. C4⋊(C3⋊D3)SD16semidirect
334. C4×Q8D32semidirect
525. C32#3295semidirect
596. C3#79676semidirect
597. C3#80395semidirect

Maximal subgroups

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

subgroupindex
#105960502
#105940042
C3×#50272
C3×C4×#2152
#105916522
#105915912
#105905932
#105905112
#105903272
#105902732
#105902682
#803953
#796763