Finite Group Databasebeta

← #11898258

Subgroups — #11898258

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic, complemented
3#10592772C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5#10591482C212yesmaximal, complemented
6#10591481C212yesmaximal, complemented
7#10591429C212yesmaximal, complemented
8#10591400C212yesmaximal, complemented
9#10590349C211yesmaximal, characteristic, complemented
10C4×#3713C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83582—31nomaximal
13#80324—31nomaximal
14C2×C3×#237—21no—
15C2×#3799—21no—
16C32×#127C2211yescharacteristic
17C2×#3753C2212yes—
18C2×#3753C2212yes—
19#64083C2211yescharacteristic
20C3×#940C2212yes—
21C3×#939—22no—
22C3×#938—21no—
23C3×D4×Dic3C2212yes—
24C2×C3×#213C2212yes—
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28#63911C2212yes—
29#63910—22no—
30#63909—21no—
31#63894C2212yes—
32C2×#3714C2212yes—
33C2×#3713C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#832C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63576C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5718D311yescharacteristic, complemented
45#5577—31no—
46#5553—31no—
47C3×#459—31no—
48#5151—32no—
49#5150—32no—
50#5073—31no—
51#5073—31no—
52#5073—32no—
53#5073—61no—
54#5072—32no—
55#5072D311yescharacteristic, complemented
56Q8×C3⋊C8—31no—
57#5015—32no—
58#5015—31no—
59C4×#213—31no—
60C4×#213—31no—
61C4×#213—32no—
62#4843—31no—
63#4830—31no—
64#4786—32no—
65#4756—32no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C3×#67—22no—
73C2×C3×#67—22no—
74C22×C3×Dic3—22no—
75C3×#237—44no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6D411yescharacteristic
81C2×#626—22no—
82C2×#626—22no—
83C2×#624—22no—
84#3799—44no—
85C32×C42C2311yescharacteristic
86#3753—24no—
87#3753—42no—
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C3×#217—22no—
91C3×#213—42no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3D411yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4D412yes—
98C3×C4×Dic3C2312yes—
99C2×C3×C3⋊C8C2312yes—
100#3722—22no—
101#3714—42no—
102#3713—22no—
103#3391—91noSylow
104C2×C3×#41—61no—
105C2×#239—61no—
106C2×#237—21no—
107C2×#235—61no—
108C2×C3×D8—32no—
109C3×#127—21no—
110C3×#127—32no—
111C3×#127C2×D311yescharacteristic
112C3×#127C2×D311yescharacteristic
113C3×#121—61no—
114C3×#121—62no—
115C3×C4×Q8—31no—
116C3×C4×D4—32no—
117C3×C4×D4—31no—
118C3×C4×D4—31no—
119#940—32no—
120#940C2×D312yes—
121#939—22no—
122#938—21no—
123D4×Dic3C2×D312yes—
124C2×#213—32no—
125C2×#213—32no—
126C2×#213—31no—
127C2×#213—31no—
128C2×#213—32no—
129C2×#213—32no—
130C2×#213—32no—
131C2×#213—62no—
132C2×#213—62no—
133C2×#213C2×D312yes—
134#930—61no—
135C2×D24—32no—
136#895—62no—
137#895—61no—
138#893—32no—
139#884—62no—
140#874—32no—
141#874—31no—
142#874—31no—
143#874—61no—
144C4×D12—32no—
145C4×D12C2×D311yescharacteristic
146C4×D12C2×D311yescharacteristic
147C4×Dic6C2×D311yescharacteristic
148C3×C4⋊C8—31no—
149C3×#102—32no—
150#832—31no—
151#832—31no—
152#832C2×D312yes—
153#821—32no—
154Dic3⋊C8—32no—
155C8×Dic3—32no—
156#809—31no—
157#809—31no—
158#809—32no—
159#807—31no—
160#807—31no—
161C4⋊(C3⋊C8)—32no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4×C3⋊C8—31no—
164C4×C3⋊C8—31no—
165C4×C3⋊C8—32no—
166C4×C3⋊C8—61no—
167C23×C32—22no—
168C22×C3⋊D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C32×D4—22no—
172C32×D4—22no—
173C32×D4—42no—
174C32×D4—81no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—42no—
181C4⋊(C3⋊D3)—81no—
182C3×#67—44no—
183C3×#67—82no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—44no—
187C2×C3×Dic3C2×D412yes—
188C2×C3×Dic3C2×D412yes—
189C3×D12—21no—
190C3×D12—21no—
191C3×D12—21no—
192C3×D12—21no—
193C3×C4×D3—42no—
194C3×C4×D3—42no—
195C3×Dic6D814yescomplemented
196#626—44no—
197#626—82no—
198#624—44no—
199C3⋊(C3⋊C8)—21no—
200C3⋊(C3⋊C8)#4112yescomplemented
201C3×C3⋊C8—22no—
202#550—31no—
203#550—91no—
204#493—92no—
205#493—91no—
206#459—31no—
207#459—92no—
208#459—91no—
209#459—92no—
210C8×Q8—91no—
211C4×D8—92no—
212C4×D8—91no—
213C3×#41—124no—
214C2×C3×Q8—31no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—22no—
220C2×C3×D4—31no—
221C2×C3×D4—31no—
222C2×C3×D4—41no—
223C2×C3×D4—41no—
224C2×C3×D4—62no—
225C2×C3×D4—62no—
226C2×C3×D4C22×D312yes—
227C2×C3×D4C22×D312yes—
228C22×C3×C4—62no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C2×#67—22no—
232C2×#67—22no—
233C2×#67—62no—
234C2×#67—62no—
235C22×Dic3—22no—
236#239—124no—
237#237—44no—
238#235—124no—
239C2×D12—32no—
240C2×D12—32no—
241C2×D12—62no—
242C2×D12—62no—
243C2×D12—61no—
244C2×D12—61no—
245C2×D12—62no—
246C2×D12—61no—
247C2×D12—61no—
248C2×D12—121no—
249C2×D12—121no—
250C2×D12C22×D311yescharacteristic
251C2×D12C22×D311yescharacteristic
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×Dic6#6711yescharacteristic
257C3×D8—122no—
258C2×C3×C8—32no—
259C3×C4⋊C4—32no—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—31no—
263C3×C22⋊C4—62no—
264C3×C22⋊C4—61no—
265C3×C22⋊C4—61no—
266C3×C42—21no—
267C3×C42—32no—
268C3×C42C22×D311yescharacteristic
269C3×C42C22×D311yescharacteristic
270#217—22no—
271#213—42no—
272#213—62no—
273#213—62no—
274#213—64no—
275#213—64no—
276#213—124no—
277#213—122no—
278#213—122no—
279#213—122no—
280#213—124no—
281(C2×D3)⋊C4—21no—
282(C2×D3)⋊C4—21no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285C4⋊Dic3#6711yescharacteristic
286C4⋊Dic3C22×D311yescharacteristic
287C4⋊Dic3C22×D311yescharacteristic
288Dic3⋊C4#6712yes—
289C4×Dic3C22×D312yes—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—61no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8C22×D312yes—
297D24—122no—
298C22×C32—42no—
299C22×C32—42no—
300C22×C32—42no—
301C22×C32C22×D411yescharacteristic
302C2×C3⋊D3—42no—
303C2×C3⋊D3—42no—
304C2×C3⋊D3—42no—
305C2×C3×D3—41no—
306C2×C3×D3—41no—
307C2×C3×D3—41no—
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3—41no—
311C32×C4—21no—
312C32×C4C2×D812yes—
313C32×C4C2×#4111yescharacteristic
314C32×C4H(5,𝔽2)11yescharacteristic
315C3×Dic3—22no—
316C3×Dic3—41no—
317C3×Dic3—41no—
318C3×Dic3C2×D814yes—
319C2×#41—61no—
320C2×#41—181no—
321C2×D8—32no—
322C2×D8—92no—
323C2×D8—91no—
324C2×D8—92no—
325C2×D8—92no—
326#127—32no—
327#127—92no—
328#127—91no—
329#127D3211yescharacteristic
330#121—61no—
331#121—62no—
332#121—182no—
333#121—181no—
334C4×Q8—31no—
335C4×D4—32no—
336C4×D4—31no—
337C4×D4—31no—
338C4×D4—92no—
339#107—91no—
340C4⋊C8—31no—
341C4⋊C8—92no—
342#102—32no—
343#102—92no—
344#102—91no—
345#102—91no—
346C4×C8—92no—
347C4×C8—91no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—42no—
351C23×C3—61no—
352C23×C3—61no—
353C22×D3—21no—
354C22×D3—21no—
355C22×D3—62no—
356C22×D3—62no—
357C22×D3—122no—
358C3×Q8—34no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—22no—
363C3×D4—42no—
364C3×D4—42no—
365C3×D4—42no—
366C3×D4—42no—
367C3×D4—61no—
368C3×D4—61no—
369C3×D4—61no—
370C3×D4—61no—
371C3×D4—82no—
372C3×D4—81no—
373C3×D4—81no—
374C3×D4—82no—
375C3×D4—124no—
376C3×D4—242no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—32no—
381C2×C3×C4—32no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—124no—
385C2×C3×C4—122no—
386C2×C3×C4—122no—
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393#67—44no—
394#67—82no—
395#67—124no—
396#67—242no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—44no—
400C2×Dic3C2×#6712yes—
401C2×Dic3C2×#6712yes—
402D12—21no—
403D12—21no—
404D12—21no—
405D12—21no—
406D12—62no—
407D12—62no—
408D12—62no—
409D12—62no—
410D12—122no—
411D12—122no—
412D12—124no—
413D12—122no—
414D12—122no—
415D12—242no—
416D12—241no—
417D12—241no—
418D12—242no—
419D12—242no—
420C4×D3—42no—
421C4×D3—42no—
422C4×D3—124no—
423C4×D3—124no—
424Dic6#21314yescomplemented
425C3×C8—62no—
426C3⋊C8—22no—
427C3⋊C8—32no—
428C3⋊C8—32no—
429C3⋊C8—62no—
430C3⋊C8—62no—
431C3⋊C8—61no—
432C3⋊C8—61no—
433C2×C32—82no—
434C2×C32#55011yescharacteristic
435C2×C32C22×D811yescharacteristic
436C2×C32#57611yescharacteristic
437C3⋊D3—82no—
438C3×D3—81no—
439C3×D3—81no—
440#41—124no—
441#41—364no—
442C2×Q8—31no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—31no—
446C2×D4—31no—
447C2×D4—62no—
448C2×D4—62no—
449C2×D4—92no—
450C2×D4—182no—
451C2×D4—182no—
452C2×D4—181no—
453C2×D4—181no—
454C2×D4C2×D3212yes—
455C22×C4—62no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—182no—
459D8—122no—
460D8—184no—
461D8—182no—
462D8—362no—
463D8—362no—
464C2×C8—32no—
465C2×C8—91no—
466C2×C8—91no—
467C4⋊C4—32no—
468C4⋊C4—31no—
469C4⋊C4—31no—
470C4⋊C4—31no—
471C22⋊C4—62no—
472C22⋊C4—61no—
473C22⋊C4—61no—
474C22⋊C4—182no—
475C42—32no—
476C42C2×D3211yescharacteristic
477C22×C3—21no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—82no—
485C22×C3—82no—
486C22×C3—82no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3—121no—
493C22×C3C2×D3×D411yescharacteristic
494C22×C3C22×#6711yescharacteristic
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—242no—
508C2×D3—242no—
509C2×D3—242no—
510C3×C4—22no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—22no—
516C3×C4—34no—
517C3×C4—62no—
518C3×C4—121no—
519C3×C4—121no—
520C3×C4D3×D812yes—
521C3×C4C2×#21312yes—
522C3×C4#100411yescharacteristic
523C3×C4D3×#4111yescharacteristic
524C3×C4D3×#4111yescharacteristic
525C3×C4#100911yescharacteristic
526Dic3—22no—
527Dic3—41no—
528Dic3—41no—
529Dic3C2×#21314yes—
530C32#339111yescharacteristic, complemented, Sylow
531C23—22no—
532C23—61no—
533C23—61no—
534C23—182no—
535Q8—34no—
536D4—22no—
537D4—22no—
538D4—42no—
539D4—61no—
540D4—61no—
541D4—61no—
542D4—61no—
543D4—81no—
544D4—124no—
545D4—182no—
546D4—182no—
547D4—242no—
548D4—364no—
549D4—362no—
550D4—721no—
551D4—722no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—124no—
557C2×C4—122no—
558C2×C4—122no—
559C2×C4—364no—
560C2×C4D3×#6711yescharacteristic
561C2×C4D3×#6711yescharacteristic
562C2×C4C22×D3211yescharacteristic
563C8—62no—
564C8—92no—
565C8—181no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—82no—
570C2×C3—82no—
571C2×C3—162no—
572C2×C3—241no—
573C2×C3—241no—
574C2×C3#559911yescharacteristic
575C2×C3C2×D3×D811yescharacteristic
576C2×C3#577411yescharacteristic
577C2×C3C22×#21311yescharacteristic
578C2×C3#583411yescharacteristic
579C2×C3#583511yescharacteristic
580D3—81no—
581D3—81no—
582D3—242no—
583D3—242no—
584D3—482no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—121no—
589C22—121no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22—121no—
594C22—362no—
595C22—362no—
596C22—362no—
597C22C2×D3×#6711yescharacteristic
598C4—21no—
599C4—34no—
600C4—62no—
601C4—121no—
602C4—121no—
603C4D3×#21312yes—
604C4#6431211yescharacteristic
605C4#6431411yescharacteristic
606C3—21no—
607C3#8032411yescharacteristic, complemented
608C3#8358211yescharacteristic, complemented
609C2—82no—
610C2—241no—
611C2—241no—
612C2—722no—
613C2C2×D3×#21311yescharacteristic
614C2#1059509711yescharacteristic
615C2#1059523611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3391
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5718C2semidirect
2. #10593902C2semidirect
3. #10592772C2semidirect
4. C3×#5072C2semidirect
5. #10591482C2semidirect
6. #10591481C2semidirect
7. #10591429C2semidirect
8. #10591400C2semidirect
9. #10590349C2semidirect
10. C4×#3713C2semidirect
11. #10590250C2semidirect
44. #5718D3semidirect
55. #5072D3semidirect
195. C3×Dic6D8semidirect
200. C3⋊(C3⋊C8)#41semidirect
424. Dic6#213semidirect
530. C32#3391semidirect
607. C3#80324semidirect
608. C3#83582semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105939022
#105927722
C3×#50722
#105914822
#105914812
#105914292
#105914002
#105903492
C4×#37132
#105902502
#835823
#803243