Finite Group Databasebeta

← #11887060

Subgroups — #11887060

Order 1152.

1047 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D122C211yesmaximal, characteristic, complemented
2#10593895C211yesmaximal, characteristic, complemented
3#10592393C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic, complemented
5C3×C8×D12C211yesmaximal, characteristic, complemented
6#10590944C212yesmaximal, complemented
7D3×#821C212yesmaximal, complemented
8#10590826C212yesmaximal, complemented
9#10590679C212yesmaximal, complemented
10#10590349C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#79608—31nomaximal
13#79438—31nomaximal
14C2×D3×D12—21no—
15C2×D3×D12C2212yes—
16C2×#3795—21no—
17#64083C2211yescharacteristic
18#64078C2211yescharacteristic, complemented
19C2×C3×D24C2211yescharacteristic
20C2×C3×D3×C8C2212yescomplemented
21C3×C4×D12C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic, complemented
24#63923—22no—
25#63909—21no—
26#63909C2212yes—
27#63908C2212yescomplemented
28#63891—22no—
29D3×C4⋊Dic3C2212yescomplemented
30#63857—21no—
31C2×#3714C2212yescomplemented
32C32×C4×C8C2211yescharacteristic, complemented
33#63648C2212yescomplemented
34#63648C2212yescomplemented
35C3×#821C2211yescharacteristic
36C3×#821C2211yescharacteristic, complemented
37C3×(C2×D3)⋊C8C2212yescomplemented
38C3×#818C2211yescharacteristic, complemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63575C2212yescomplemented
41#63564C2212yescomplemented
42#63563C2212yes—
43#5555—31no—
44#5551—31no—
45D4×D12—31no—
46D4×D12—31no—
47C3×C4×D8—31no—
48C3×C8×D4—31no—
49#5156—32no—
50#5115—32no—
51C2×#821—32no—
52#5015—31no—
53#5007—31no—
54#4882—32no—
55#4846—31no—
56#4843—31no—
57#4775—32no—
58D3×#102—32no—
59#4736—32no—
60#4732—32no—
61#4694—31no—
62#4694—31no—
63#4694—61no—
64C4×D24D311yescharacteristic, complemented
65C8×D12D311yescharacteristic, complemented
66C22×D32—22no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×#634—21no—
71C2×C3×D12D411yescharacteristic
72C2×C3×D12C2311yescharacteristic
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3C2312yes—
77C2×#626—22no—
78C2×#626—22no—
79C2×#625—22no—
80C2×D3×Dic3—22no—
81D3×D12—24no—
82D3×D12—42no—
83D3×D12—44no—
84#3795—44no—
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C42C2311yescharacteristic
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4D412yes—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97C3×D24—22no—
98C3×D3×C8—42no—
99Dic3⋊Dic3—22no—
100#3722—22no—
101(C2×D3)⋊Dic3—22no—
102#3714—42no—
103#3294—91noSylow
104C2×#237—61no—
105C2×D3×D4—32no—
106C2×D3×D4—61no—
107C2×#235—61no—
108C22×D12—32no—
109C22×D12—61no—
110C2×C3×D8—31no—
111C22×C3×C8—32no—
112C3×C4×D4—31no—
113C3×C4×D4—31no—
114C3×C4×D4—31no—
115#938—32no—
116C2×#213—32no—
117#930—32no—
118#930—32no—
119#930—61no—
120C2×C4⋊Dic3—32no—
121#924—61no—
122C2×D24—32no—
123C2×D24C2×D311yescharacteristic
124C2×D3×C8C2×D312yescomplemented
125#897—61no—
126#895—32no—
127#895—61no—
128D3×C4⋊C4—32no—
129#886—62no—
130#883—62no—
131#882—62no—
132#882—62no—
133#874—31no—
134#874—31no—
135#874—61no—
136C4×D12C2×D311yescharacteristic
137C4×D12C2×D311yescharacteristic
138C4×D12C2×D311yescharacteristic, complemented
139#869—31no—
140#869—31no—
141#869—61no—
142C3×#107—31no—
143C3×C4⋊C8—31no—
144C3×#102—31no—
145C3×#102—31no—
146C3×C22⋊C8—32no—
147C3×C4×C8—21no—
148C3×C4×C8C2×D311yescharacteristic, complemented
149C3×C4×C8C2×D311yescharacteristic, complemented
150#832—32no—
151#821—32no—
152#821—32no—
153#821—32no—
154#821—32no—
155#821—32no—
156#821—32no—
157#821—62no—
158#821—62no—
159#821C2×D311yescharacteristic
160#821C2×D311yescharacteristic, complemented
161(C2×D3)⋊C8C2×D312yescomplemented
162#818—32no—
163#818C2×D311yescharacteristic, complemented
164#809—32no—
165#807—32no—
166C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
167C22×C3⋊D3—22no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3C2×D412yes—
171C2×D32—44no—
172C2×D32—44no—
173C2×D32—82no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—22no—
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—42no—
181C4⋊(C3⋊D3)—81no—
182#634—42no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C3×D12—21no—
187C3×D12—21no—
188C3×D12—21no—
189C3×D12D814yescomplemented
190C3×D12#4112yescomplemented
191C3×C4×D3—22no—
192C3×C4×D3—22no—
193C3×C4×D3—42no—
194C3×C4×D3—42no—
195#626—44no—
196#626—44no—
197#625—44no—
198D3×Dic3—44no—
199C32×C8—21no—
200C32×C8—21no—
201C3×C3⋊C8—22no—
202#547—91no—
203D42—91no—
204#486—91no—
205#480—92no—
206#474—91no—
207#466—92no—
208#459—91no—
209#447—92no—
210C4×D8—31no—
211C8×D4—31no—
212C2×#102—92no—
213C23×D3—62no—
214C23×D3—62no—
215C2×C3×D4—31no—
216C2×C3×D4—31no—
217C2×C3×D4—31no—
218C22×C3×C4—32no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C2×#67—62no—
222C2×#67—62no—
223C2×#67—62no—
224C2×#67—62no—
225C22×Dic3—62no—
226#237—124no—
227D3×D4—64no—
228D3×D4—122no—
229D3×D4—124no—
230#235—124no—
231C2×D12—32no—
232C2×D12—32no—
233C2×D12—62no—
234C2×D12—64no—
235C2×D12—62no—
236C2×D12—62no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—61no—
240C2×D12—61no—
241C2×D12—121no—
242C2×D12—121no—
243C2×D12—122no—
244C2×D12—124no—
245C2×D12D1211yescharacteristic
246C2×D12C22×D311yescharacteristic
247C2×D12C22×D311yescharacteristic
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—62no—
251C2×C4×D3C22×D312yes—
252C2×Dic6—61no—
253C2×Dic6—61no—
254C2×Dic6—121no—
255C3×D8—62no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—32no—
259C2×C3×C8—122no—
260C2×C3×C8C22×D311yescharacteristic
261C2×C3×C8C22×D311yescharacteristic
262C2×C3×C8C22×D311yescharacteristic
263C2×C3×C8C22×D311yescharacteristic
264C3×C4⋊C4—31no—
265C3×C4⋊C4—31no—
266C3×C4⋊C4—31no—
267C3×C22⋊C4—32no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C42—21no—
271C3×C42C22×D311yescharacteristic
272C3×C42C22×D311yescharacteristic
273#217—62no—
274#213—122no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—21no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4D1212yes—
281C4⋊Dic3—32no—
282C4⋊Dic3—32no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—121no—
288C4⋊Dic3D1211yescharacteristic
289C4⋊Dic3C22×D311yescharacteristic
290C4⋊Dic3C22×D311yescharacteristic
291Dic3⋊C4—62no—
292C2×C3⋊C8C22×D312yes—
293D24—22no—
294D24—122no—
295D3×C8—42no—
296C22×C32C22×D411yescharacteristic
297C2×C3⋊D3—42no—
298C2×C3⋊D3—42no—
299C2×C3⋊D3—42no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—22no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C2×C3×D3—41no—
307C2×C3×D3—41no—
308C2×C3×D3C2×D814yes—
309D32—88no—
310C32×C4—21no—
311C32×C4C2×D812yes—
312C32×C4C2×#4111yescharacteristic
313C32×C4H(5,𝔽2)11yescharacteristic
314C3⋊Dic3—42no—
315C3×Dic3—22no—
316C3×Dic3—41no—
317C3×Dic3—41no—
318C2×#41—181no—
319C22×D4—92no—
320C22×D4—181no—
321C2×D8—31no—
322C2×D8—92no—
323C22×C8—32no—
324C4⋊Q8—91no—
325#127—91no—
326#123—182no—
327C22⋊Q8—181no—
328#121—92no—
329#121—92no—
330#121—181no—
331#120—182no—
332C4×D4—31no—
333C4×D4—31no—
334C4×D4—31no—
335C2×C4⋊C4—92no—
336#107—31no—
337#107—92no—
338C4⋊C8—31no—
339#102—31no—
340#102—31no—
341#102—92no—
342#102—92no—
343#102—92no—
344#102—92no—
345C22⋊C8—32no—
346C4×C8D3211yescharacteristic, complemented
347C23×C3—32no—
348C23×C3—61no—
349C23×C3—61no—
350C22×D3—21no—
351C22×D3—21no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—122no—
355C22×D3—124no—
356C22×D3—124no—
357C22×D3—124no—
358C22×D3—124no—
359C22×D3—242no—
360C22×D3—242no—
361C22×D3C2×D1212yes—
362C3×D4—34no—
363C3×D4—32no—
364C3×D4—61no—
365C3×D4—61no—
366C3×D4—61no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—32no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—122no—
376C2×C3×C4—122no—
377C2×C3×C4C2×D1211yescharacteristic
378C2×C3×C4C2×D1211yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383#67—124no—
384#67—124no—
385#67—124no—
386#67—124no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—122no—
392C2×Dic3—124no—
393C2×Dic3C2×D1212yes—
394D12—21no—
395D12—21no—
396D12—21no—
397D12—62no—
398D12—62no—
399D12—62no—
400D12—62no—
401D12—122no—
402D12—122no—
403D12—124no—
404D12—124no—
405D12—122no—
406D12—122no—
407D12—242no—
408D12—241no—
409D12—241no—
410D12—242no—
411D12D2414yescomplemented
412D12#23512yescomplemented
413C4×D3—22no—
414C4×D3—22no—
415C4×D3—42no—
416C4×D3—42no—
417C4×D3—124no—
418Dic6—122no—
419Dic6—122no—
420Dic6—242no—
421C3×C8—21no—
422C3×C8—21no—
423C3×C8—21no—
424C3×C8—21no—
425C3×C8—41no—
426C3×C8—41no—
427C3×C8—62no—
428C3⋊C8—22no—
429C2×C32#54611yescharacteristic
430C2×C32C22×D811yescharacteristic
431C2×C32#57711yescharacteristic
432C3⋊D3—82no—
433C3×D3—24no—
434C3×D3—42no—
435C3×D3—81no—
436C24—182no—
437#41—364no—
438C2×Q8—181no—
439C2×D4—31no—
440C2×D4—31no—
441C2×D4—31no—
442C2×D4—92no—
443C2×D4—182no—
444C2×D4—184no—
445C2×D4—182no—
446C2×D4—182no—
447C2×D4—181no—
448C2×D4—181no—
449C2×D4—362no—
450C2×D4—364no—
451C22×C4—32no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—182no—
455D8—62no—
456D8—362no—
457C2×C8—32no—
458C2×C8—122no—
459C2×C8C2×D3211yescharacteristic
460C2×C8C2×D3211yescharacteristic
461C4⋊C4—31no—
462C4⋊C4—31no—
463C4⋊C4—31no—
464C4⋊C4—92no—
465C4⋊C4—182no—
466C4⋊C4—181no—
467C22⋊C4—32no—
468C22⋊C4—61no—
469C22⋊C4—61no—
470C22⋊C4—182no—
471C22⋊C4—182no—
472C42C2×D3211yescharacteristic
473C22×C3—21no—
474C22×C3—34no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3—62no—
478C22×C3—121no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3C22×D1211yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—22no—
488C2×D3—41no—
489C2×D3—41no—
490C2×D3—41no—
491C2×D3—41no—
492C2×D3—41no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—242no—
500C2×D3—242no—
501C2×D3—242no—
502C2×D3—248no—
503C2×D3—248no—
504C2×D3C2×D2414yes—
505C3×C4—22no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—62no—
512C3×C4—121no—
513C3×C4—121no—
514C3×C4C2×D2412yes—
515C3×C4D3×D812yes—
516C3×C4C2×#23511yescharacteristic
517C3×C4#100411yescharacteristic
518C3×C4D3×#4111yescharacteristic
519C3×C4#100911yescharacteristic
520Dic3—22no—
521Dic3—41no—
522Dic3—41no—
523Dic3—122no—
524Dic3—122no—
525Dic3—242no—
526C32#329411yescharacteristic, complemented, Sylow
527C23—32no—
528C23—61no—
529C23—61no—
530C23—182no—
531C23—364no—
532C23—364no—
533C23—722no—
534Q8—362no—
535D4—34no—
536D4—32no—
537D4—61no—
538D4—61no—
539D4—61no—
540D4—182no—
541D4—182no—
542D4—364no—
543D4—364no—
544D4—364no—
545D4—362no—
546D4—721no—
547C2×C4—32no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—122no—
553C2×C4—122no—
554C2×C4—182no—
555C2×C4—364no—
556C2×C4D3×D1211yescharacteristic
557C2×C4D3×D1211yescharacteristic
558C2×C4C22×D3211yescharacteristic
559C8—21no—
560C8—21no—
561C8—62no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—64no—
566C2×C3—122no—
567C2×C3—241no—
568C2×C3#555011yescharacteristic
569C2×C3#555411yescharacteristic
570C2×C3C22×D2411yescharacteristic
571C2×C3#575111yescharacteristic
572C2×C3C2×D3×D811yescharacteristic
573C2×C3#577011yescharacteristic
574D3—24no—
575D3—42no—
576D3—81no—
577D3—242no—
578D3—242no—
579D3—482no—
580C22—34no—
581C22—62no—
582C22—62no—
583C22—62no—
584C22—121no—
585C22—121no—
586C22—121no—
587C22—121no—
588C22—121no—
589C22—362no—
590C22—362no—
591C22—362no—
592C22—728no—
593C22C2×D3×D1211yescharacteristic
594C4—21no—
595C4—62no—
596C4—121no—
597C4—121no—
598C4—362no—
599C4D3×D2412yes—
600C4D3×#23511yescharacteristic
601C4#6430711yescharacteristic
602C3—21no—
603C3#7943811yescharacteristic, complemented
604C3#7960811yescharacteristic, complemented
605C2—64no—
606C2—122no—
607C2—241no—
608C2—722no—
609C2#1059400311yescharacteristic
610C2C2×D3×D2411yescharacteristic
611C2#1059467911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. D122C2semidirect
2. #10593895C2semidirect
3. #10592393C2semidirect
4. C3×C4×D24C2semidirect
5. C3×C8×D12C2semidirect
6. #10590944C2semidirect
7. D3×#821C2semidirect
8. #10590826C2semidirect
9. #10590679C2semidirect
10. #10590349C2semidirect
11. #10590272C2semidirect
18. #64078C22semidirect
20. C2×C3×D3×C8C22semidirect
23. C3×C4×D12C22semidirect
27. #63908C22semidirect
29. D3×C4⋊Dic3C22semidirect
31. C2×#3714C22semidirect
32. C32×C4×C8C22semidirect
33. #63648C22semidirect
34. #63648C22semidirect
36. C3×#821C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. C3×#818C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63575C22semidirect
41. #63564C22semidirect
64. C4×D24D3semidirect
65. C8×D12D3semidirect
124. C2×D3×C8C2×D3semidirect
138. C4×D12C2×D3semidirect
148. C3×C4×C8C2×D3semidirect
149. C3×C4×C8C2×D3semidirect
160. #821C2×D3semidirect
161. (C2×D3)⋊C8C2×D3semidirect
163. #818C2×D3semidirect
166. C4⋊(C3⋊C8)C2×D3semidirect
189. C3×D12D8semidirect
190. C3×D12#41semidirect
346. C4×C8D32semidirect
411. D12D24semidirect
412. D12#235semidirect
526. C32#3294semidirect
603. C3#79438semidirect
604. C3#79608semidirect

Maximal subgroups

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

subgroupindex
D1222
#105938952
#105923932
C3×C4×D242
C3×C8×D122
#105909442
D3×#8212
#105908262
#105906792
#105903492
#105902722
#796083
#794383