Finite Group Databasebeta

← #11898261

Subgroups — #11898261

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×#5015C211yesmaximal, characteristic, complemented
5#10591482C212yesmaximal, complemented
6#10591428C212yesmaximal, complemented
7#10590547C212yesmaximal, complemented
8#10590452C212yesmaximal, complemented
9#10590355C211yesmaximal, characteristic, complemented
10#10590352C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83582—31nomaximal
13#80324—31nomaximal
14C2×C3×#235—21no—
15C2×#3796—21no—
16C32×C4×D4C2211yescharacteristic
17C2×#3753C2211yescharacteristic
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C3×#940C2212yes—
20C2×C3×#213C2212yes—
21C3×#930—21no—
22C3×#893C2212yes—
23C3×#884—22no—
24C3×#874C2211yescharacteristic
25C3×#874C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63916—21no—
28#63911C2212yes—
29Dic3×D12C2212yes—
30#63886—22no—
31C2×#3714C2212yes—
32C2×#3713C2212yes—
33C2×#3713C2212yes—
34#63659C2211yescharacteristic
35#63636C2211yescharacteristic
36#63634C2211yescharacteristic
37C4×C3⋊(C3⋊C8)C2211yescharacteristic
38C3×#809C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41#63563C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5718—31no—
45#5577—31no—
46#5553D311yescharacteristic, complemented
47C3×#459—31no—
48#5151—32no—
49#5150—32no—
50#5073—32no—
51#5073—31no—
52#5073—31no—
53#5072—32no—
54#5072—31no—
55Q8×C3⋊C8—31no—
56#5015—32no—
57#5015D311yescharacteristic, complemented
58C4×#213—31no—
59C4×#213—31no—
60C4×#213—32no—
61C4×#213—61no—
62#4843—31no—
63#4830—31no—
64#4786—32no—
65#4756—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C3×#235—44no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12—21no—
77C2×C3×D12C2312yes—
78C2×C3×D12C2312yes—
79C2×C3×C4×D3—22no—
80C2×C3×Dic6D411yescharacteristic
81C2×#626—22no—
82C2×#626—22no—
83C2×D3×Dic3—22no—
84#3796—44no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3753—22no—
89#3752—21no—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93C3×#213—42no—
94C3×(C2×D3)⋊C4—22no—
95C3×C4⋊Dic3D411yescharacteristic
96C3×Dic3⋊C4D412yes—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8C2312yes—
99(C2×D3)⋊Dic3—22no—
100#3714—42no—
101#3713—24no—
102#3713—42no—
103#3391—91noSylow
104C2×C3×#41—61no—
105C2×#239—61no—
106C2×#237—61no—
107C2×#235—21no—
108C2×C3×D8—32no—
109C3×#127—32no—
110C3×#127—31no—
111C3×#127—31no—
112C3×#121—62no—
113C3×#121—61no—
114C3×C4×Q8—31no—
115C3×C4×D4—21no—
116C3×C4×D4—32no—
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C2×D311yescharacteristic
119#940—32no—
120#940C2×D312yes—
121#939—62no—
122#938—61no—
123D4×Dic3—32no—
124C2×#213—31no—
125C2×#213—31no—
126C2×#213—32no—
127C2×#213—32no—
128C2×#213—32no—
129C2×#213—32no—
130C2×#213—32no—
131C2×#213—61no—
132C2×#213C2×D312yes—
133#930—21no—
134C2×D24—32no—
135#895—62no—
136#895—61no—
137#893C2×D312yes—
138#884—22no—
139#874—32no—
140#874C2×D311yescharacteristic
141#874C2×D311yescharacteristic
142C4×D12—32no—
143C4×D12—31no—
144C4×D12—31no—
145C4×D12—61no—
146C4×Dic6C2×D311yescharacteristic
147C3×C4⋊C8—31no—
148C3×#102—32no—
149#832—31no—
150#832—31no—
151#832—32no—
152#832—61no—
153#821—32no—
154Dic3⋊C8—32no—
155C8×Dic3—32no—
156#809—31no—
157#809—31no—
158#809—61no—
159#809C2×D312yes—
160#807—31no—
161#807—31no—
162#807—61no—
163C4⋊(C3⋊C8)—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8—31no—
166C4×C3⋊C8—31no—
167C4×C3⋊C8—32no—
168C4×C3⋊C8—61no—
169C23×C32—21no—
170C22×C3⋊D3—21no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C32×D4—21no—
174C32×D4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—42no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C4⋊(C3⋊D3)—21no—
182C4⋊(C3⋊D3)—21no—
183C4×C3⋊D3—42no—
184C3×#67—44no—
185C3×#67—82no—
186C2×C3×Dic3C2×D412yes—
187C2×C3×Dic3C2×D412yes—
188C3×D12—22no—
189C3×D12—22no—
190C3×D12—22no—
191C3×D12—22no—
192C3×D12—42no—
193C3×D12—42no—
194C3×D12—81no—
195C3×D12—81no—
196C3×C4×D3—44no—
197C3×Dic6D814yescomplemented
198#626—44no—
199#626—82no—
200D3×Dic3—44no—
201C3⋊(C3⋊C8)—21no—
202C3⋊(C3⋊C8)#4112yescomplemented
203C3×C3⋊C8—22no—
204#550—31no—
205#550—91no—
206#493—91no—
207#493—92no—
208#459—31no—
209#459—92no—
210#459—91no—
211#459—92no—
212C8×Q8—91no—
213C4×D8—92no—
214C4×D8—91no—
215C3×#41—124no—
216C2×C3×Q8—31no—
217C2×C3×D4—21no—
218C2×C3×D4—32no—
219C2×C3×D4—32no—
220C2×C3×D4—62no—
221C2×C3×D4—62no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C2×C3×D4C22×D311yescharacteristic
227C2×C3×D4C22×D311yescharacteristic
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—41no—
231C22×C3×C4—62no—
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—62no—
235C2×#67—62no—
236C22×Dic3—62no—
237#239—124no—
238#237—124no—
239#235—44no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—31no—
245C2×D12—31no—
246C2×D12—61no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12C22×D312yes—
250C2×D12C22×D312yes—
251C2×C4×D3—22no—
252C2×C4×D3—62no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—121no—
256C2×Dic6#6711yescharacteristic
257C3×D8—122no—
258C2×C3×C8—32no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—62no—
268C3×C42—21no—
269C3×C42—32no—
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D311yescharacteristic
272#217—62no—
273#213—42no—
274#213—64no—
275#213—64no—
276#213—62no—
277#213—62no—
278#213—64no—
279#213—122no—
280#213—122no—
281#213—122no—
282(C2×D3)⋊C4—22no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—61no—
285(C2×D3)⋊C4—61no—
286(C2×D3)⋊C4—121no—
287C4⋊Dic3—31no—
288C4⋊Dic3—31no—
289C4⋊Dic3—61no—
290C4⋊Dic3#6711yescharacteristic
291Dic3⋊C4#6712yes—
292C4×Dic3C22×D312yes—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—31no—
296C2×C3⋊C8—31no—
297C2×C3⋊C8—61no—
298C2×C3⋊C8—61no—
299C2×C3⋊C8C22×D312yes—
300D24—122no—
301C22×C32—41no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32C22×D411yescharacteristic
305C2×C3⋊D3—41no—
306C2×C3⋊D3—41no—
307C2×C3⋊D3—41no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—42no—
313C2×C3×D3—42no—
314C32×C4—21no—
315C32×C4—41no—
316C32×C4C2×D812yes—
317C32×C4C2×#4111yescharacteristic
318C32×C4H(5,𝔽2)11yescharacteristic
319C3⋊Dic3—41no—
320C3×Dic3—22no—
321C3×Dic3C2×D814yes—
322C2×#41—61no—
323C2×#41—181no—
324C2×D8—32no—
325C2×D8—92no—
326C2×D8—92no—
327C2×D8—91no—
328C2×D8—92no—
329#127—32no—
330#127—31no—
331#127—31no—
332#127—92no—
333#121—62no—
334#121—61no—
335#121—181no—
336#121—182no—
337C4×Q8—31no—
338C4×D4—32no—
339C4×D4—92no—
340C4×D4—91no—
341C4×D4D3211yescharacteristic
342#107—91no—
343C4⋊C8—31no—
344C4⋊C8—92no—
345#102—32no—
346#102—92no—
347#102—91no—
348#102—91no—
349C4×C8—92no—
350C4×C8—91no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—41no—
354C23×C3—62no—
355C23×C3—62no—
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—61no—
359C22×D3—61no—
360C22×D3—121no—
361C3×Q8—34no—
362C3×D4—22no—
363C3×D4—21no—
364C3×D4—21no—
365C3×D4—21no—
366C3×D4—21no—
367C3×D4—41no—
368C3×D4—62no—
369C3×D4—62no—
370C3×D4—62no—
371C3×D4—62no—
372C3×D4—124no—
373C3×D4—122no—
374C3×D4—122no—
375C3×D4—241no—
376C3×D4—241no—
377C3×D4—242no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—32no—
384C2×C3×C4—32no—
385C2×C3×C4—41no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—82no—
389C2×C3×C4—124no—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396#67—44no—
397#67—82no—
398#67—124no—
399#67—242no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—121no—
403C2×Dic3—124no—
404C2×Dic3C2×#6712yes—
405C2×Dic3C2×#6712yes—
406D12—22no—
407D12—22no—
408D12—22no—
409D12—22no—
410D12—42no—
411D12—42no—
412D12—62no—
413D12—61no—
414D12—61no—
415D12—61no—
416D12—61no—
417D12—81no—
418D12—81no—
419D12—121no—
420D12—124no—
421D12—242no—
422C4×D3—44no—
423C4×D3—124no—
424C4×D3—122no—
425C4×D3—122no—
426C4×D3—242no—
427Dic6#21314yescomplemented
428C3×C8—62no—
429C3⋊C8—22no—
430C3⋊C8—32no—
431C3⋊C8—32no—
432C3⋊C8—62no—
433C3⋊C8—61no—
434C3⋊C8—61no—
435C3⋊C8—121no—
436C2×C32—81no—
437C2×C32#55011yescharacteristic
438C2×C32C22×D811yescharacteristic
439C2×C32#57611yescharacteristic
440C3⋊D3—81no—
441C3×D3—82no—
442C3×D3—82no—
443#41—124no—
444#41—364no—
445C2×Q8—31no—
446C2×D4—32no—
447C2×D4—32no—
448C2×D4—62no—
449C2×D4—62no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4—91no—
455C2×D4—182no—
456C2×D4—182no—
457C2×D4C2×D3211yescharacteristic
458C22×C4—21no—
459C22×C4—62no—
460C22×C4—182no—
461C22×C4—181no—
462D8—122no—
463D8—182no—
464D8—184no—
465D8—362no—
466D8—362no—
467C2×C8—32no—
468C2×C8—91no—
469C2×C8—91no—
470C4⋊C4—32no—
471C4⋊C4—31no—
472C4⋊C4—91no—
473C4⋊C4C2×D3211yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—62no—
476C22⋊C4—182no—
477C22⋊C4—181no—
478C42—32no—
479C42C2×D3211yescharacteristic
480C22×C3—21no—
481C22×C3—42no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—81no—
489C22×C3—81no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—122no—
494C22×C3—122no—
495C22×C3—122no—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C22×#6711yescharacteristic
498C2×D3—42no—
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—42no—
502C2×D3—42no—
503C2×D3—42no—
504C2×D3—122no—
505C2×D3—121no—
506C2×D3—121no—
507C2×D3—121no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—241no—
512C2×D3—241no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—22no—
518C3×C4—34no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—41no—
522C3×C4—62no—
523C3×C4—81no—
524C3×C4D3×D812yes—
525C3×C4C2×#21312yes—
526C3×C4#100411yescharacteristic
527C3×C4D3×#4111yescharacteristic
528C3×C4D3×#4111yescharacteristic
529C3×C4#100911yescharacteristic
530Dic3—22no—
531Dic3—121no—
532Dic3—121no—
533Dic3—241no—
534Dic3C2×#21314yes—
535C32#339111yescharacteristic, complemented, Sylow
536C23—21no—
537C23—62no—
538C23—62no—
539C23—181no—
540Q8—34no—
541D4—21no—
542D4—21no—
543D4—62no—
544D4—62no—
545D4—62no—
546D4—62no—
547D4—124no—
548D4—122no—
549D4—122no—
550D4—181no—
551D4—181no—
552D4—241no—
553D4—241no—
554D4—242no—
555D4—364no—
556D4—722no—
557C2×C4—21no—
558C2×C4—32no—
559C2×C4—32no—
560C2×C4—42no—
561C2×C4—124no—
562C2×C4—181no—
563C2×C4—364no—
564C2×C4—362no—
565C2×C4D3×#6711yescharacteristic
566C2×C4D3×#6711yescharacteristic
567C2×C4C22×D3211yescharacteristic
568C8—62no—
569C8—92no—
570C8—181no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—82no—
575C2×C3—81no—
576C2×C3—81no—
577C2×C3—242no—
578C2×C3—242no—
579C2×C3#559911yescharacteristic
580C2×C3C2×D3×D811yescharacteristic
581C2×C3#577411yescharacteristic
582C2×C3C22×#21311yescharacteristic
583C2×C3#583411yescharacteristic
584C2×C3#583511yescharacteristic
585D3—82no—
586D3—82no—
587D3—242no—
588D3—241no—
589D3—241no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—122no—
594C22—122no—
595C22—122no—
596C22—122no—
597C22—122no—
598C22—122no—
599C22—361no—
600C22—361no—
601C22—361no—
602C22C2×D3×#6711yescharacteristic
603C4—21no—
604C4—34no—
605C4—41no—
606C4—62no—
607C4—361no—
608C4D3×#21312yes—
609C4#6430611yescharacteristic
610C4#6430711yescharacteristic
611C3—21no—
612C3#8032411yescharacteristic, complemented
613C3#8358211yescharacteristic, complemented
614C2—81no—
615C2—242no—
616C2—242no—
617C2—721no—
618C2#1059500611yescharacteristic
619C2C2×D3×#21311yescharacteristic
620C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3391
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×#5553C2semidirect
2. #10593900C2semidirect
3. C4×#3753C2semidirect
4. C3×#5015C2semidirect
5. #10591482C2semidirect
6. #10591428C2semidirect
7. #10590547C2semidirect
8. #10590452C2semidirect
9. #10590355C2semidirect
10. #10590352C2semidirect
11. #10590250C2semidirect
46. #5553D3semidirect
57. #5015D3semidirect
197. C3×Dic6D8semidirect
202. C3⋊(C3⋊C8)#41semidirect
427. Dic6#213semidirect
535. C32#3391semidirect
612. C3#80324semidirect
613. C3#83582semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105939002
C4×#37532
C3×#50152
#105914822
#105914282
#105905472
#105904522
#105903552
#105903522
#105902502
#835823
#803243