Finite Group Databasebeta

← #11887033

Subgroups — #11887033

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5555C211yesmaximal, characteristic, complemented
2C3×D4×D12C211yesmaximal, characteristic, complemented
3D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10591166C212yesmaximal, complemented
5#10591160C212yesmaximal, complemented
6#10591089C212yesmaximal, complemented
7C2×#63562C212yesmaximal, complemented
8#10590347C211yesmaximal, characteristic, complemented
9C4×#3713C211yesmaximal, characteristic, complemented
10#10590277C211yesmaximal, characteristic, complemented
11#10590269C211yesmaximal, characteristic, complemented
12#83525—31nomaximal
13#83482—31nomaximal
14C2×C3×#237—21no—
15C2×C3×D3×D4—21no—
16C22×C3×D12C2212yes—
17C32×C4×D4C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2212yescomplemented
19C3×#930C2212yes—
20C3×#930C2212yescomplemented
21C2×C3×C4⋊Dic3C2212yescomplemented
22C3×#897—21no—
23C3×#895—21no—
24C3×#886—22no—
25C3×#882—22no—
26C3×#874C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic, complemented
29C3×#869C2211yescharacteristic, complemented
30C2×#3713C2211yescharacteristic
31C2×#3713C2212yescomplemented
32#63657C2212yescomplemented
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
34C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
35#63576C2212yescomplemented
36#63576C2211yescharacteristic, complemented
37#63562C2212yes—
38#63562C2211yescharacteristic
39#63562C2212yescomplemented
40#63562C2212yescomplemented
41#63562C2212yescomplemented
42#63562C2211yescharacteristic, complemented
43C3×#547—31no—
44C3×D42—31no—
45#5555D311yescharacteristic, complemented
46D4×D12D311yescharacteristic, complemented
47#5217—32no—
48C2×#832—32no—
49#5088—31no—
50#5087—31no—
51#5072—31no—
52#5070—31no—
53#5038—32no—
54#5038—32no—
55#5036—32no—
56#5033—32no—
57#5015—31no—
58C4×#213—31no—
59C4×#213—31no—
60D4×C3⋊C8—31no—
61D4×C3⋊C8—31no—
62D4×C3⋊C8—61no—
63#5007—31no—
64#4967—32no—
65C2×#809—32no—
66C23×C3×D3—22no—
67C2×C32×D4D411yescharacteristic
68C22×C32×C4C2312yes—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C22×C3×Dic3—22no—
72C3×#237—44no—
73C3×D3×D4—44no—
74C2×C3×D12—24no—
75C2×C3×D12—22no—
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12—42no—
79C2×C3×D12C2312yes—
80C2×C3×D12C2311yescharacteristic
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—21no—
84C2×C3×Dic6—21no—
85C32×C4⋊C4D411yescharacteristic
86C32×C22⋊C4D412yes—
87C32×C42C2311yescharacteristic
88C2×C3⋊(C3⋊C8)—42no—
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2312yes—
91C2×C3⋊(C3⋊C8)C2311yescharacteristic
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—22no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—22no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2312yes—
100C3×C4⋊Dic3C2311yescharacteristic
101#3713—22no—
102#3713—42no—
103#3294—91noSylow
104C2×C3×#41—61no—
105C22×C3×D4—32no—
106C22×C3×D4—61no—
107C2×#237—21no—
108C2×D3×D4—21no—
109C22×D12C2×D312yes—
110C3×C4⋊Q8—31no—
111C3×#127—31no—
112C3×#123—62no—
113C3×C22⋊Q8—61no—
114C3×#121—32no—
115C3×#121—32no—
116C3×#121—61no—
117C3×#120—62no—
118C3×C4×D4—21no—
119C3×C4×D4—31no—
120C3×C4×D4—31no—
121C3×C4×D4C2×D311yescharacteristic
122C3×C4×D4C2×D311yescharacteristic
123C2×C3×C4⋊C4—32no—
124C2×#213—31no—
125C2×#213—31no—
126C2×#213—32no—
127C2×#213—32no—
128#930C2×D312yes—
129#930C2×D312yescomplemented
130C2×C4⋊Dic3C2×D312yescomplemented
131C22×C3⋊C8—32no—
132C22×C3⋊C8—32no—
133C22×C3⋊C8—62no—
134#897—21no—
135#895—21no—
136#886—22no—
137#882—22no—
138#874C2×D311yescharacteristic
139C4×D12C2×D311yescharacteristic
140C4×D12C2×D311yescharacteristic, complemented
141#869C2×D311yescharacteristic, complemented
142#832—31no—
143#832—32no—
144#832—32no—
145#832—32no—
146#832—32no—
147#832—31no—
148#830—32no—
149#830—32no—
150#830—62no—
151#809—31no—
152#809—32no—
153#809—32no—
154#809—32no—
155#809—32no—
156#809—31no—
157#807—31no—
158#807—32no—
159#807—32no—
160#807—31no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—61no—
164C4×C3⋊C8—31no—
165C4×C3⋊C8—31no—
166C4×C3⋊C8—61no—
167C23×C32C2×D412yes—
168C22×C3×D3—21no—
169C22×C3×D3—22no—
170C22×C3×D3—21no—
171C22×C3×D3—44no—
172C22×C3×D3—44no—
173C22×C3×D3—82no—
174C32×D4D814yescomplemented
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C3×#67—44no—
182C3×#67—44no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—44no—
187C3×D12—21no—
188C3×D12—22no—
189C3×D12—21no—
190C3×D12—21no—
191C3×D12—22no—
192C3×D12—44no—
193C3×D12—42no—
194C3×D12—81no—
195C3×D12#4112yescomplemented
196C3×C4×D3—42no—
197C3×C4×D3—42no—
198C3×Dic6—42no—
199C3⋊(C3⋊C8)—21no—
200C3⋊(C3⋊C8)—21no—
201C3⋊(C3⋊C8)—22no—
202#547—31no—
203D42—31no—
204#486—91no—
205#480—92no—
206#474—91no—
207#466—92no—
208#459—91no—
209#447—92no—
210C4×D8—91no—
211C8×D4—91no—
212C2×#102—92no—
213C24×C3—62no—
214C23×D3—22no—
215C3×#41—124no—
216C2×C3×Q8—61no—
217C2×C3×D4—21no—
218C2×C3×D4—31no—
219C2×C3×D4—32no—
220C2×C3×D4—31no—
221C2×C3×D4—64no—
222C2×C3×D4—62no—
223C2×C3×D4—62no—
224C2×C3×D4—62no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C2×C3×D4—122no—
228C2×C3×D4—124no—
229C2×C3×D4#6711yescharacteristic
230C2×C3×D4#6711yescharacteristic
231C22×C3×C4—22no—
232C22×C3×C4—62no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4C22×D312yes—
236C22×C3×C4C22×D312yes—
237C2×#67—22no—
238C2×#67—22no—
239C22×Dic3—22no—
240#237—44no—
241D3×D4—44no—
242C2×D12—24no—
243C2×D12—21no—
244C2×D12—22no—
245C2×D12—21no—
246C2×D12—42no—
247C2×D12C22×D312yes—
248C2×D12C22×D311yescharacteristic
249C2×D12C22×D311yescharacteristic
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×Dic6—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—62no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4#6711yescharacteristic
260C3×C4⋊C4#6711yescharacteristic
261C3×C22⋊C4—22no—
262C3×C22⋊C4—61no—
263C3×C22⋊C4—61no—
264C3×C22⋊C4—62no—
265C3×C22⋊C4—62no—
266C3×C22⋊C4#6712yes—
267C3×C22⋊C4#6712yes—
268C3×C42—21no—
269C3×C42C22×D311yescharacteristic
270C3×C42C22×D311yescharacteristic
271#213—62no—
272#213—62no—
273#213—122no—
274#213—122no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—21no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—22no—
279C4⋊Dic3—21no—
280C4⋊Dic3—22no—
281C4⋊Dic3C22×D311yescharacteristic
282C4⋊Dic3C22×D312yes—
283C4⋊Dic3C22×D311yescharacteristic
284C2×C3⋊C8—31no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—32no—
289C2×C3⋊C8—32no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—122no—
294C2×C3⋊C8—122no—
295C2×C3⋊C8—124no—
296C22×C32—22no—
297C22×C32—22no—
298C22×C32C2×D814yes—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C2×C3×D3—42no—
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C2×C3×D3—42no—
307C2×C3×D3—42no—
308C2×C3×D3—41no—
309C2×C3×D3—88no—
310C32×C4—22no—
311C32×C4—21no—
312C32×C4C2×D812yes—
313C32×C4C2×#4111yescharacteristic
314C32×C4H(5,𝔽2)11yescharacteristic
315C3×Dic3—42no—
316C3×Dic3—41no—
317C3×Dic3—41no—
318C2×#41—61no—
319C22×D4—32no—
320C22×D4—61no—
321C2×D8—91no—
322C2×D8—92no—
323C22×C8—92no—
324C4⋊Q8—31no—
325#127—31no—
326#123—62no—
327C22⋊Q8—61no—
328#121—32no—
329#121—32no—
330#121—61no—
331#120—62no—
332C4×D4—31no—
333C4×D4—31no—
334C4×D4D3211yescharacteristic
335C2×C4⋊C4—32no—
336#107—91no—
337#107—92no—
338C4⋊C8—91no—
339#102—91no—
340#102—92no—
341#102—92no—
342#102—92no—
343#102—91no—
344#102—92no—
345C22⋊C8—92no—
346C4×C8—91no—
347C23×C3—22no—
348C23×C3—61no—
349C23×C3—61no—
350C23×C3—62no—
351C23×C3—124no—
352C23×C3—124no—
353C23×C3—242no—
354C23×C3C2×#6712yes—
355C23×C3C2×#6712yes—
356C22×D3—21no—
357C22×D3—21no—
358C22×D3—22no—
359C22×D3—44no—
360C22×D3—44no—
361C22×D3—82no—
362C3×Q8—122no—
363C3×D4—24no—
364C3×D4—32no—
365C3×D4—61no—
366C3×D4—61no—
367C3×D4—62no—
368C3×D4—61no—
369C3×D4—62no—
370C3×D4—124no—
371C3×D4—124no—
372C3×D4—124no—
373C3×D4—122no—
374C3×D4—241no—
375C3×D4#21314yescomplemented
376C3×D4#21314yescomplemented
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—62no—
390C2×C3×C4—124no—
391C2×C3×C4—122no—
392C2×C3×C4—122no—
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C2×#6712yes—
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C2×#6712yes—
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—44no—
402#67—44no—
403C2×Dic3—22no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—44no—
407D12—22no—
408D12—21no—
409D12—22no—
410D12—21no—
411D12—21no—
412D12—44no—
413D12—42no—
414D12—81no—
415D12#23712yescomplemented
416C4×D3—42no—
417C4×D3—42no—
418Dic6—42no—
419C3⋊C8—62no—
420C3⋊C8—61no—
421C3⋊C8—61no—
422C3⋊C8—62no—
423C3⋊C8—61no—
424C3⋊C8—61no—
425C3⋊C8—62no—
426C3⋊C8—121no—
427C3⋊C8—122no—
428C2×C32—24no—
429C2×C32#54611yescharacteristic
430C2×C32C22×D811yescharacteristic
431C2×C32#57711yescharacteristic
432C3×D3—42no—
433C3×D3—81no—
434C3×D3—82no—
435C24—62no—
436#41—124no—
437C2×Q8—61no—
438C2×D4—31no—
439C2×D4—32no—
440C2×D4—31no—
441C2×D4—64no—
442C2×D4—62no—
443C2×D4—62no—
444C2×D4—62no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—122no—
448C2×D4—124no—
449C2×D4#62511yescharacteristic
450C22×C4—62no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4C2×D3212yes—
454D8—182no—
455D8—362no—
456C2×C8—91no—
457C2×C8—91no—
458C2×C8—92no—
459C2×C8—362no—
460C4⋊C4—31no—
461C4⋊C4—32no—
462C4⋊C4—31no—
463C4⋊C4—62no—
464C4⋊C4—61no—
465C4⋊C4#62511yescharacteristic
466C22⋊C4—61no—
467C22⋊C4—61no—
468C22⋊C4—62no—
469C22⋊C4—62no—
470C22⋊C4#62512yes—
471C42C2×D3211yescharacteristic
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—21no—
477C22×C3—24no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—62no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3—121no—
484C22×C3—122no—
485C22×C3—121no—
486C22×C3—122no—
487C22×C3—121no—
488C22×C3—122no—
489C22×C3—248no—
490C22×C3C2×#21314yes—
491C22×C3C2×#21314yes—
492C22×C3C22×#6711yescharacteristic
493C22×C3C22×#6711yescharacteristic
494C2×D3—22no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—42no—
499C2×D3—42no—
500C2×D3—41no—
501C2×D3—42no—
502C2×D3—41no—
503C2×D3—88no—
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—42no—
512C3×C4—41no—
513C3×C4—121no—
514C3×C4—121no—
515C3×C4—122no—
516C3×C4C2×#21312yes—
517C3×C4C2×#21312yes—
518C3×C4C2×#23711yescharacteristic
519C3×C4#100411yescharacteristic
520C3×C4D3×#4111yescharacteristic
521C3×C4#100911yescharacteristic
522Dic3—42no—
523Dic3—41no—
524Dic3—41no—
525C32#329411yescharacteristic, complemented, Sylow
526C23—61no—
527C23—61no—
528C23—62no—
529C23—124no—
530C23—124no—
531C23—242no—
532C23C2×#62512yes—
533Q8—122no—
534D4—32no—
535D4—61no—
536D4—62no—
537D4—61no—
538D4—61no—
539D4—62no—
540D4—124no—
541D4—124no—
542D4—124no—
543D4—122no—
544D4—241no—
545D4#371314yescomplemented
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—62no—
551C2×C4—124no—
552C2×C4—122no—
553C2×C4—122no—
554C2×C4C2×#62511yescharacteristic
555C2×C4C2×#62512yes—
556C2×C4C2×#62511yescharacteristic
557C2×C4C22×D3211yescharacteristic
558C8—181no—
559C8—181no—
560C8—182no—
561C2×C3—24no—
562C2×C3—24no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—44no—
567C2×C3—122no—
568C2×C3—241no—
569C2×C3—242no—
570C2×C3C22×#21311yescharacteristic
571C2×C3C22×#21311yescharacteristic
572C2×C3#580611yescharacteristic
573C2×C3#582911yescharacteristic
574C2×C3#583611yescharacteristic
575C2×C3#583711yescharacteristic
576D3—42no—
577D3—82no—
578D3—81no—
579C22—22no—
580C22—22no—
581C22—62no—
582C22—121no—
583C22—121no—
584C22—122no—
585C22—121no—
586C22—122no—
587C22—121no—
588C22—121no—
589C22—122no—
590C22—248no—
591C22C2×#371314yes—
592C22C22×#62511yescharacteristic
593C4—21no—
594C4—22no—
595C4—121no—
596C4—121no—
597C4—122no—
598C4C2×#371312yes—
599C4D3×#23711yescharacteristic
600C4#6431411yescharacteristic
601C3—21no—
602C3#8348211yescharacteristic, complemented
603C3#8352511yescharacteristic, complemented
604C2—24no—
605C2—122no—
606C2—242no—
607C2—241no—
608C2C22×#371311yescharacteristic
609C2#1059524411yescharacteristic
610C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
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 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5555C2semidirect
2. C3×D4×D12C2semidirect
3. D4×C3⋊(C3⋊C8)C2semidirect
4. #10591166C2semidirect
5. #10591160C2semidirect
6. #10591089C2semidirect
7. C2×#63562C2semidirect
8. #10590347C2semidirect
9. C4×#3713C2semidirect
10. #10590277C2semidirect
11. #10590269C2semidirect
18. C22×C3⋊(C3⋊C8)C22semidirect
20. C3×#930C22semidirect
21. C2×C3×C4⋊Dic3C22semidirect
28. C3×C4×D12C22semidirect
29. C3×#869C22semidirect
31. C2×#3713C22semidirect
32. #63657C22semidirect
33. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. C4×C3⋊(C3⋊C8)C22semidirect
35. #63576C22semidirect
36. #63576C22semidirect
39. #63562C22semidirect
40. #63562C22semidirect
41. #63562C22semidirect
42. #63562C22semidirect
45. #5555D3semidirect
46. D4×D12D3semidirect
129. #930C2×D3semidirect
130. C2×C4⋊Dic3C2×D3semidirect
140. C4×D12C2×D3semidirect
141. #869C2×D3semidirect
174. C32×D4D8semidirect
195. C3×D12#41semidirect
375. C3×D4#213semidirect
376. C3×D4#213semidirect
415. D12#237semidirect
525. C32#3294semidirect
545. D4#3713semidirect
602. C3#83482semidirect
603. C3#83525semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C3×D4×D122
D4×C3⋊(C3⋊C8)2
#105911662
#105911602
#105910892
C2×#635622
#105903472
C4×#37132
#105902772
#105902692
#835253
#834823