Finite Group Databasebeta

← #11887028

Subgroups — #11887028

Order 1152.

1042 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
1C3×D4×D12C211yesmaximal, characteristic, complemented
2#10593895C211yesmaximal, characteristic, complemented
3#10592706C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591447C212yesmaximal, complemented
6D3×#832C212yesmaximal, complemented
7#10590499C212yesmaximal, complemented
8#10590438C212yesmaximal, complemented
9#10590347C211yesmaximal, characteristic, complemented
10C3⋊C8×D12C211yesmaximal, characteristic, complemented
11#10590273C211yesmaximal, characteristic, complemented
12#83482—31nomaximal
13#79608—31nomaximal
14C2×C3×D3×D4C2212yes—
15C22×C3×D12—21no—
16C2×#3795—21no—
17C32×C4×D4C2211yescharacteristic
18#64078C2211yescharacteristic, complemented
19C2×C3×#213C2211yescharacteristic
20C3×#930—21no—
21C3×#895C2212yes—
22C3×#882—22no—
23C3×#874C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic, complemented
26#63908C2212yescomplemented
27#63891—22no—
28D3×C4⋊Dic3C2212yescomplemented
29#63857—21no—
30C2×#3713C2212yescomplemented
31C2×D3×C3⋊C8C2212yescomplemented
32#63659C2212yes—
33#63634C2212yescomplemented
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
35C3×#832C2211yescharacteristic
36C3×#809C2211yescharacteristic, complemented
37C3×#807C2211yescharacteristic, complemented
38C3×C4×C3⋊C8C2211yescharacteristic, complemented
39#63563C2212yescomplemented
40#63563C2212yescomplemented
41#63562C2212yescomplemented
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43C3×D42—31no—
44#5555—31no—
45#5551—31no—
46D4×D12D311yescharacteristic, complemented
47C3×C4×D8—31no—
48#5217—32no—
49C2×#832—32no—
50#5156—32no—
51#5072—31no—
52#5070—31no—
53#5038—32no—
54#5033—32no—
55#5015—31no—
56C4×#213D311yescharacteristic, complemented
57D4×C3⋊C8—31no—
58#5007—31no—
59#5007—31no—
60#5007—61no—
61#4882—32no—
62#4775—32no—
63D3×#102—32no—
64#4694—31no—
65C8×D12—31no—
66C23×C3×D3—22no—
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×#634—21no—
70C2×C3×#67—22no—
71C3×D3×D4—24no—
72C3×D3×D4—42no—
73C2×C3×D12—22no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12—44no—
77C2×C3×D12D411yescharacteristic
78C2×C3×D12C2312yes—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3C2312yes—
82C2×#625—22no—
83C2×D3×Dic3—22no—
84#3795—44no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×#213—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4D412yes—
95C3×C4⋊Dic3D411yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99Dic3⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101#3713—42no—
102D3×C3⋊C8—42no—
103#3294—91noSylow
104C22×C3×D4—32no—
105C22×C3×D4—61no—
106C2×#237—61no—
107C2×D3×D4C2×D312yes—
108C2×#235—61no—
109C22×D12—21no—
110C2×C3×D8—31no—
111C3×#127—31no—
112C3×#121—32no—
113C3×#121—61no—
114C3×#120—62no—
115C3×C4×D4—21no—
116C3×C4×D4—31no—
117C3×C4×D4—31no—
118C3×C4×D4C2×D311yescharacteristic
119C3×C4×D4C2×D311yescharacteristic
120#938—32no—
121C2×#213—32no—
122C2×#213—32no—
123C2×#213C2×D311yescharacteristic
124#930—21no—
125#930—32no—
126C2×C4⋊Dic3—32no—
127#924—61no—
128C22×C3⋊C8—32no—
129C2×D3×C8—32no—
130#897—61no—
131#895C2×D312yes—
132D3×C4⋊C4—32no—
133#886—62no—
134#883—62no—
135#882—22no—
136#874C2×D311yescharacteristic
137C4×D12C2×D311yescharacteristic
138C4×D12C2×D311yescharacteristic, complemented
139#869—31no—
140#869—31no—
141#869—61no—
142C3×#107—31no—
143C3×#102—31no—
144C3×#102—31no—
145C3×C4×C8—31no—
146#832—32no—
147#832—32no—
148#832—32no—
149#832—32no—
150#832—32no—
151#832—62no—
152#832C2×D311yescharacteristic
153#830—32no—
154#821—32no—
155#821—32no—
156(C2×D3)⋊C8—32no—
157#809—32no—
158#809C2×D311yescharacteristic, complemented
159#807—32no—
160#807—32no—
161#807—62no—
162#807C2×D311yescharacteristic, complemented
163C4⋊(C3⋊C8)—31no—
164C4⋊(C3⋊C8)—31no—
165C4⋊(C3⋊C8)—61no—
166C4×C3⋊C8C2×D311yescharacteristic, complemented
167C23×C32—21no—
168C22×C3×D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3—44no—
171C22×C3×D3—44no—
172C22×C3×D3—82no—
173C22×C3×D3C2×D412yes—
174C32×D4—21no—
175C32×D4#4112yescomplemented
176C2×C32×C4—21no—
177C2×C32×C4—42no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—22no—
182#634—42no—
183C3×#67—44no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C3×D12—21no—
187C3×D12—22no—
188C3×D12—21no—
189C3×D12—22no—
190C3×D12—44no—
191C3×D12—42no—
192C3×D12—81no—
193C3×D12D814yescomplemented
194C3×C4×D3—22no—
195C3×C4×D3—22no—
196C3×C4×D3—42no—
197#625—44no—
198D3×Dic3—44no—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—21no—
202#547—91no—
203D42—31no—
204#486—91no—
205#480—92no—
206#474—91no—
207#466—92no—
208#459—91no—
209#447—92no—
210C4×D8—31no—
211C8×D4—91no—
212C2×#102—92no—
213C24×C3—62no—
214C23×D3—22no—
215C2×C3×D4—21no—
216C2×C3×D4—31no—
217C2×C3×D4—32no—
218C2×C3×D4—31no—
219C2×C3×D4—62no—
220C2×C3×D4—62no—
221C2×C3×D4—64no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C2×C3×D4—124no—
225C2×C3×D4—122no—
226C2×C3×D4C22×D311yescharacteristic
227C2×C3×D4C22×D311yescharacteristic
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—32no—
231C22×C3×C4—41no—
232C22×C3×C4—61no—
233C2×#67—22no—
234C2×#67—62no—
235C2×#67—62no—
236C22×Dic3—62no—
237#237—124no—
238D3×D4—24no—
239D3×D4—42no—
240#235—124no—
241C2×D12—22no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—44no—
245C2×D12#6711yescharacteristic
246C2×D12C22×D312yes—
247C2×D12C22×D311yescharacteristic
248C2×C4×D3—21no—
249C2×C4×D3—62no—
250C2×C4×D3C22×D312yes—
251C2×Dic6—61no—
252C2×Dic6—61no—
253C2×Dic6—121no—
254C3×D8—62no—
255C2×C3×C8—31no—
256C2×C3×C8—31no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C22⋊C4—21no—
263C3×C22⋊C4—21no—
264C3×C22⋊C4—32no—
265C3×C22⋊C4—41no—
266C3×C22⋊C4—62no—
267C3×C22⋊C4—61no—
268C3×C42—21no—
269C3×C42C22×D311yescharacteristic
270C3×C42C22×D311yescharacteristic
271#217—62no—
272#213—22no—
273#213—122no—
274#213—122no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4#6712yes—
279C4⋊Dic3—32no—
280C4⋊Dic3—32no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—121no—
286C4⋊Dic3#6711yescharacteristic
287C4⋊Dic3C22×D311yescharacteristic
288Dic3⋊C4—62no—
289C2×C3⋊C8—32no—
290C2×C3⋊C8—32no—
291C2×C3⋊C8—62no—
292C2×C3⋊C8—122no—
293C2×C3⋊C8C22×D311yescharacteristic
294C2×C3⋊C8C22×D311yescharacteristic
295D3×C8—122no—
296C22×C32—22no—
297C22×C32—41no—
298C22×C32—41no—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—42no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3—42no—
306C2×C3×D3—42no—
307C2×C3×D3—41no—
308C2×C3×D3—88no—
309C2×C3×D3C2×D814yes—
310C32×C4—21no—
311C32×C4—41no—
312C32×C4C2×D812yes—
313C32×C4C2×#4111yescharacteristic
314C32×C4H(5,𝔽2)11yescharacteristic
315C3⋊Dic3—42no—
316C3×Dic3—22no—
317C3×Dic3—41no—
318C2×#41—181no—
319C22×D4—32no—
320C22×D4—61no—
321C2×D8—31no—
322C2×D8—92no—
323C22×C8—92no—
324C4⋊Q8—91no—
325#127—31no—
326#123—182no—
327C22⋊Q8—181no—
328#121—32no—
329#121—61no—
330#121—92no—
331#120—62no—
332C4×D4—31no—
333C4×D4—31no—
334C4×D4D3211yescharacteristic
335C2×C4⋊C4—92no—
336#107—31no—
337#107—92no—
338C4⋊C8—91no—
339#102—31no—
340#102—31no—
341#102—92no—
342#102—92no—
343#102—92no—
344#102—92no—
345C22⋊C8—92no—
346C4×C8—31no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—32no—
350C23×C3—41no—
351C23×C3—62no—
352C23×C3—61no—
353C23×C3—124no—
354C23×C3—124no—
355C23×C3—242no—
356C22×D3—21no—
357C22×D3—22no—
358C22×D3—44no—
359C22×D3—44no—
360C22×D3—82no—
361C22×D3C2×#6712yes—
362C3×D4—21no—
363C3×D4—21no—
364C3×D4—22no—
365C3×D4—34no—
366C3×D4—41no—
367C3×D4—62no—
368C3×D4—61no—
369C3×D4—61no—
370C3×D4—62no—
371C3×D4—124no—
372C3×D4—124no—
373C3×D4—122no—
374C3×D4—241no—
375C3×D4#23512yescomplemented
376C3×D4#23712yescomplemented
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—32no—
383C2×C3×C4—41no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—61no—
389C2×C3×C4—82no—
390C2×C3×C4—122no—
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397#67—44no—
398#67—124no—
399#67—124no—
400C2×Dic3—21no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—122no—
404C2×Dic3—124no—
405C2×Dic3C2×#6712yes—
406D12—21no—
407D12—22no—
408D12—22no—
409D12—21no—
410D12—44no—
411D12—42no—
412D12—81no—
413D12#21314yescomplemented
414C4×D3—22no—
415C4×D3—22no—
416C4×D3—42no—
417C4×D3—124no—
418Dic6—122no—
419Dic6—122no—
420Dic6—242no—
421C3×C8—61no—
422C3×C8—61no—
423C3⋊C8—21no—
424C3⋊C8—21no—
425C3⋊C8—62no—
426C3⋊C8—62no—
427C3⋊C8—122no—
428C2×C32—42no—
429C2×C32#54611yescharacteristic
430C2×C32C22×D811yescharacteristic
431C2×C32#57711yescharacteristic
432C3×D3—24no—
433C3×D3—81no—
434C3×D3—82no—
435C24—62no—
436#41—364no—
437C2×Q8—181no—
438C2×D4—31no—
439C2×D4—32no—
440C2×D4—31no—
441C2×D4—62no—
442C2×D4—62no—
443C2×D4—64no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—124no—
447C2×D4—122no—
448C2×D4—182no—
449C2×D4C2×D3211yescharacteristic
450C22×C4—21no—
451C22×C4—32no—
452C22×C4—61no—
453C22×C4—182no—
454D8—62no—
455D8—362no—
456C2×C8—31no—
457C2×C8—31no—
458C2×C8—92no—
459C2×C8—362no—
460C4⋊C4—31no—
461C4⋊C4—31no—
462C4⋊C4—92no—
463C4⋊C4—182no—
464C4⋊C4—181no—
465C4⋊C4C2×D3211yescharacteristic
466C22⋊C4—21no—
467C22⋊C4—32no—
468C22⋊C4—62no—
469C22⋊C4—61no—
470C22⋊C4—182no—
471C42C2×D3211yescharacteristic
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—21no—
475C22×C3—34no—
476C22×C3—42no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—62no—
482C22×C3—62no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—121no—
488C22×C3—122no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3—248no—
492C22×C3C2×D3×D411yescharacteristic
493C22×C3C22×#6711yescharacteristic
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—42no—
499C2×D3—41no—
500C2×D3—42no—
501C2×D3—42no—
502C2×D3—88no—
503C2×D3C2×#21314yes—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—41no—
510C3×C4—41no—
511C3×C4—41no—
512C3×C4—62no—
513C3×C4—81no—
514C3×C4—121no—
515C3×C4D3×D812yes—
516C3×C4C2×#21312yes—
517C3×C4C2×#23511yescharacteristic
518C3×C4C2×#23711yescharacteristic
519C3×C4#100411yescharacteristic
520C3×C4#100911yescharacteristic
521Dic3—22no—
522Dic3—41no—
523Dic3—122no—
524Dic3—122no—
525Dic3—242no—
526C32#329411yescharacteristic, complemented, Sylow
527C23—21no—
528C23—32no—
529C23—61no—
530C23—62no—
531C23—124no—
532C23—124no—
533C23—242no—
534Q8—362no—
535D4—21no—
536D4—34no—
537D4—61no—
538D4—62no—
539D4—61no—
540D4—62no—
541D4—124no—
542D4—124no—
543D4—122no—
544D4—241no—
545D4—364no—
546D4#379512yescomplemented
547C2×C4—21no—
548C2×C4—32no—
549C2×C4—42no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—61no—
553C2×C4—122no—
554C2×C4—182no—
555C2×C4—364no—
556C2×C4D3×#6711yescharacteristic
557C2×C4D3×#6711yescharacteristic
558C2×C4C22×D3211yescharacteristic
559C8—61no—
560C8—61no—
561C8—182no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—42no—
566C2×C3—42no—
567C2×C3—64no—
568C2×C3—82no—
569C2×C3—241no—
570C2×C3—242no—
571C2×C3#555011yescharacteristic
572C2×C3C2×D3×D811yescharacteristic
573C2×C3#577011yescharacteristic
574C2×C3C22×#21311yescharacteristic
575C2×C3#580611yescharacteristic
576C2×C3#583611yescharacteristic
577D3—24no—
578D3—82no—
579D3—81no—
580C22—22no—
581C22—34no—
582C22—41no—
583C22—41no—
584C22—62no—
585C22—62no—
586C22—121no—
587C22—122no—
588C22—122no—
589C22—121no—
590C22—122no—
591C22—121no—
592C22—248no—
593C22C2×D3×#6711yescharacteristic
594C4—21no—
595C4—41no—
596C4—62no—
597C4—121no—
598C4—362no—
599C4D3×#21312yes—
600C4C2×#379511yescharacteristic
601C4#6430711yescharacteristic
602C3—21no—
603C3#7960811yescharacteristic, complemented
604C3#8348211yescharacteristic, complemented
605C2—42no—
606C2—64no—
607C2—242no—
608C2—241no—
609C2#1059488611yescharacteristic
610C2C2×D3×#21311yescharacteristic
611C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×D12C2semidirect
2. #10593895C2semidirect
3. #10592706C2semidirect
4. C3×C4×#213C2semidirect
5. #10591447C2semidirect
6. D3×#832C2semidirect
7. #10590499C2semidirect
8. #10590438C2semidirect
9. #10590347C2semidirect
10. C3⋊C8×D12C2semidirect
11. #10590273C2semidirect
18. #64078C22semidirect
25. C3×C4×D12C22semidirect
26. #63908C22semidirect
28. D3×C4⋊Dic3C22semidirect
30. C2×#3713C22semidirect
31. C2×D3×C3⋊C8C22semidirect
33. #63634C22semidirect
34. C4⋊(C3⋊(C3⋊C8))C22semidirect
36. C3×#809C22semidirect
37. C3×#807C22semidirect
38. C3×C4×C3⋊C8C22semidirect
39. #63563C22semidirect
40. #63563C22semidirect
41. #63562C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
46. D4×D12D3semidirect
56. C4×#213D3semidirect
138. C4×D12C2×D3semidirect
158. #809C2×D3semidirect
162. #807C2×D3semidirect
166. C4×C3⋊C8C2×D3semidirect
175. C32×D4#41semidirect
193. C3×D12D8semidirect
375. C3×D4#235semidirect
376. C3×D4#237semidirect
413. D12#213semidirect
526. C32#3294semidirect
546. D4#3795semidirect
603. C3#79608semidirect
604. C3#83482semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D122
#105938952
#105927062
C3×C4×#2132
#105914472
D3×#8322
#105904992
#105904382
#105903472
C3⋊C8×D122
#105902732
#834823
#796083