Finite Group Databasebeta

← #11898256

Subgroups — #11898256

Order 1152.

990 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic, complemented
4C3×#5073C211yesmaximal, characteristic, complemented
5#10591482C212yesmaximal, complemented
6#10591481C212yesmaximal, complemented
7#10591428C212yesmaximal, complemented
8Dic3×#213C212yesmaximal, complemented
9#10590347C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83582—31nomaximal
13#81778—31nomaximal
14C2×C3×#237—21no—
15C2×#3796—21no—
16C32×#127C2211yescharacteristic
17C2×#3753C2212yes—
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C3×#940C2212yes—
20C3×#939—22no—
21C3×#938—21no—
22C3×D4×Dic3C2212yes—
23C2×C3×#213C2212yes—
24C2×C3×#213C2212yes—
25C3×#874C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28#63916—21no—
29#63911C2212yes—
30Dic3×D12C2212yes—
31#63886—22no—
32C2×#3714C2211yescharacteristic
33C2×#3713C2212yes—
34#63659C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2211yescharacteristic
40#63563C2211yescharacteristic
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5718—31no—
45#5718D311yescharacteristic, complemented
46#5577—31no—
47C3×#493—31no—
48#5151—32no—
49#5150—32no—
50#5150—32no—
51Dic3×D8—32no—
52#5073—32no—
53#5073D311yescharacteristic, complemented
54#5072—31no—
55#5072—31no—
56#5072—32no—
57#5072—31no—
58#5072—61no—
59Q8×C3⋊C8—31no—
60#5015—32no—
61#5015—31no—
62C4×#213—32no—
63C4×#213—31no—
64C4×D24—31no—
65C8×Dic6—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C22×C3×Dic3—22no—
74C3×#237—44no—
75C2×C3×D12—21no—
76C2×C3×D12—21no—
77C2×C3×D12C2312yes—
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×Dic6D411yescharacteristic
81C2×#626—22no—
82C2×#626—22no—
83C2×D3×Dic3—22no—
84#3796—44no—
85C32×C42C2311yescharacteristic
86#3753—42no—
87#3752—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—22no—
91C3×#213—24no—
92C3×#213—42no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3D411yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4D412yes—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100(C2×D3)⋊Dic3—22no—
101#3714—22no—
102#3713—42no—
103#3391—91noSylow
104C2×C3×#41—61no—
105C2×#239—61no—
106C2×#237—21no—
107C2×#237—61no—
108C2×C3×D8—32no—
109C2×C3×D8—32no—
110C3×#127—21no—
111C3×#127—32no—
112C3×#127—31no—
113C3×#127C2×D311yescharacteristic
114C3×#127C2×D311yescharacteristic
115C3×#121—61no—
116C3×#121—62no—
117C3×C4×Q8—31no—
118C3×C4×D4—32no—
119C3×C4×D4—31no—
120#940—32no—
121#940C2×D312yes—
122#939—22no—
123#939—62no—
124#938—21no—
125#938—61no—
126D4×Dic3—32no—
127D4×Dic3C2×D312yes—
128C2×#213—32no—
129C2×#213—32no—
130C2×#213—32no—
131C2×#213—32no—
132C2×#213—31no—
133C2×#213—62no—
134C2×#213C2×D312yes—
135C2×#213C2×D312yes—
136C2×D24—31no—
137#895—62no—
138#895—61no—
139#874—32no—
140#874C2×D311yescharacteristic
141C4×D12—32no—
142C4×D12—31no—
143C4×D12—31no—
144C4×D12—61no—
145C4×D12C2×D311yescharacteristic
146C4×Dic6C2×D311yescharacteristic
147C3×C4×C8—31no—
148#832—32no—
149#832—32no—
150#832—32no—
151#832—31no—
152#832—62no—
153#821—31no—
154#821—31no—
155#818—31no—
156Dic3⋊C8—32no—
157C8×Dic3—32no—
158#809—32no—
159#809—31no—
160#807—31no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—32no—
164C4⋊(C3⋊C8)—61no—
165C4×C3⋊C8—32no—
166C4×C3⋊C8C2×D311yescharacteristic
167C23×C32—22no—
168C22×C3⋊D3—21no—
169C22×C3×D3—22no—
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
178C2×C3⋊Dic3—21no—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)—21no—
181C4×C3⋊D3—42no—
182C3×#67—44no—
183C3×#67—82no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—44no—
186C2×C3×Dic3C2×D412yes—
187C2×C3×Dic3C2×D412yes—
188C3×D12—21no—
189C3×D12—22no—
190C3×D12—21no—
191C3×D12—22no—
192C3×D12—42no—
193C3×D12—81no—
194C3×C4×D3—42no—
195C3×Dic6D814yescomplemented
196#626—44no—
197#626—82no—
198D3×Dic3—44no—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8#4112yescomplemented
202#550—31no—
203#550—91no—
204#493—31no—
205#493—92no—
206#459—91no—
207#459—92no—
208#459—92no—
209#459—91no—
210C8×Q8—91no—
211C4×D8—91no—
212C4×D8—92no—
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—32no—
222C2×C3×D4—41no—
223C2×C3×D4—41no—
224C2×C3×D4—62no—
225C2×C3×D4—62no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C2×C3×D4C22×D312yes—
229C2×C3×D4C22×D312yes—
230C22×C3×C4—62no—
231C22×C3×C4—61no—
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—62no—
235C2×#67—62no—
236C22×Dic3—22no—
237C22×Dic3—62no—
238#239—124no—
239#237—44no—
240#237—124no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—31no—
244C2×D12—31no—
245C2×D12—61no—
246C2×D12—62no—
247C2×D12—62no—
248C2×D12C22×D312yes—
249C2×D12C22×D311yescharacteristic
250C2×C4×D3—21no—
251C2×C4×D3—62no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—121no—
255C2×Dic6#6711yescharacteristic
256C3×D8—64no—
257C3×D8—122no—
258C2×C3×C8—31no—
259C2×C3×C8—31no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—31no—
263C3×C22⋊C4—62no—
264C3×C22⋊C4—61no—
265C3×C42—21no—
266C3×C42—32no—
267C3×C42C22×D311yescharacteristic
268C3×C42C22×D311yescharacteristic
269#217—22no—
270#217—62no—
271#213—24no—
272#213—42no—
273#213—62no—
274#213—122no—
275#213—122no—
276#213—122no—
277#213—122no—
278#213—124no—
279(C2×D3)⋊C4—21no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—121no—
284C4⋊Dic3—31no—
285C4⋊Dic3—31no—
286C4⋊Dic3—61no—
287C4⋊Dic3#6711yescharacteristic
288C4⋊Dic3C22×D311yescharacteristic
289Dic3⋊C4#6712yes—
290C4×Dic3C22×D312yes—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—32no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8C22×D311yescharacteristic
295C2×C3⋊C8C22×D311yescharacteristic
296D24—62no—
297C22×C32—42no—
298C22×C32—42no—
299C22×C32—42no—
300C22×C32C22×D411yescharacteristic
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3⋊D3—41no—
304C2×C3×D3—42no—
305C2×C3×D3—41no—
306C2×C3×D3—42no—
307C2×C3×D3—41no—
308C2×C3×D3—42no—
309C2×C3×D3—41no—
310C32×C4—21no—
311C32×C4C2×D812yes—
312C32×C4C2×#4111yescharacteristic
313C32×C4H(5,𝔽2)11yescharacteristic
314C3⋊Dic3—41no—
315C3×Dic3—22no—
316C3×Dic3—41no—
317C3×Dic3C2×D814yes—
318C2×#41—61no—
319C2×#41—181no—
320C2×D8—32no—
321C2×D8—32no—
322C2×D8—91no—
323C2×D8—92no—
324C2×D8—92no—
325#127—32no—
326#127—31no—
327#127—92no—
328#127D3211yescharacteristic
329#121—61no—
330#121—62no—
331#121—181no—
332#121—182no—
333C4×Q8—31no—
334C4×D4—32no—
335C4×D4—31no—
336C4×D4—92no—
337C4×D4—91no—
338#107—91no—
339C4⋊C8—92no—
340C4⋊C8—91no—
341#102—91no—
342#102—92no—
343#102—91no—
344#102—92no—
345C4×C8—31no—
346C4×C8—92no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—42no—
350C23×C3—61no—
351C23×C3—62no—
352C22×D3—22no—
353C22×D3—21no—
354C22×D3—61no—
355C22×D3—61no—
356C22×D3—121no—
357C3×Q8—34no—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—42no—
363C3×D4—42no—
364C3×D4—42no—
365C3×D4—42no—
366C3×D4—61no—
367C3×D4—61no—
368C3×D4—62no—
369C3×D4—62no—
370C3×D4—82no—
371C3×D4—81no—
372C3×D4—81no—
373C3×D4—82no—
374C3×D4—124no—
375C3×D4—122no—
376C3×D4—241no—
377C3×D4—242no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—32no—
382C2×C3×C4—32no—
383C2×C3×C4—61no—
384C2×C3×C4—124no—
385C2×C3×C4—122no—
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4C2×#6711yescharacteristic
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392#67—44no—
393#67—82no—
394#67—124no—
395#67—242no—
396C2×Dic3—21no—
397C2×Dic3—44no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—121no—
401C2×Dic3—124no—
402C2×Dic3C2×#6712yes—
403C2×Dic3C2×#6712yes—
404D12—22no—
405D12—22no—
406D12—21no—
407D12—21no—
408D12—42no—
409D12—62no—
410D12—61no—
411D12—61no—
412D12—61no—
413D12—61no—
414D12—81no—
415D12—121no—
416D12—124no—
417D12—242no—
418C4×D3—42no—
419C4×D3—124no—
420C4×D3—122no—
421C4×D3—122no—
422C4×D3—242no—
423Dic6#21314yescomplemented
424C3×C8—32no—
425C3×C8—61no—
426C3⋊C8—21no—
427C3⋊C8—62no—
428C3⋊C8—62no—
429C3⋊C8—122no—
430C3⋊C8#23712yescomplemented
431C2×C32—82no—
432C2×C32#55011yescharacteristic
433C2×C32C22×D811yescharacteristic
434C2×C32#57611yescharacteristic
435C3⋊D3—81no—
436C3×D3—82no—
437C3×D3—81no—
438#41—124no—
439#41—364no—
440C2×Q8—31no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—31no—
444C2×D4—32no—
445C2×D4—62no—
446C2×D4—62no—
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—91no—
450C2×D4—182no—
451C2×D4—182no—
452C2×D4C2×D3212yes—
453C22×C4—62no—
454C22×C4—61no—
455C22×C4—182no—
456C22×C4—181no—
457D8—64no—
458D8—122no—
459D8—182no—
460D8—362no—
461D8—362no—
462C2×C8—31no—
463C2×C8—31no—
464C2×C8—92no—
465C4⋊C4—32no—
466C4⋊C4—31no—
467C4⋊C4—31no—
468C4⋊C4—91no—
469C22⋊C4—62no—
470C22⋊C4—61no—
471C22⋊C4—182no—
472C22⋊C4—181no—
473C42—32no—
474C42C2×D3211yescharacteristic
475C22×C3—21no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—82no—
483C22×C3—82no—
484C22×C3—82no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—122no—
489C22×C3—122no—
490C22×C3—122no—
491C22×C3C2×D3×D411yescharacteristic
492C22×C3C22×#6711yescharacteristic
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—42no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—122no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—121no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—121no—
506C2×D3—241no—
507C2×D3—241no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—34no—
514C3×C4—41no—
515C3×C4—62no—
516C3×C4—121no—
517C3×C4D3×D812yes—
518C3×C4C2×#21312yes—
519C3×C4C2×#23711yescharacteristic
520C3×C4#100411yescharacteristic
521C3×C4D3×#4111yescharacteristic
522C3×C4#100911yescharacteristic
523Dic3—22no—
524Dic3—41no—
525Dic3—121no—
526Dic3—121no—
527Dic3—241no—
528Dic3C2×#21314yes—
529C32#339111yescharacteristic, complemented, Sylow
530C23—22no—
531C23—61no—
532C23—62no—
533C23—181no—
534Q8—34no—
535D4—22no—
536D4—22no—
537D4—42no—
538D4—62no—
539D4—61no—
540D4—62no—
541D4—61no—
542D4—81no—
543D4—124no—
544D4—122no—
545D4—181no—
546D4—181no—
547D4—241no—
548D4—242no—
549D4—364no—
550D4—722no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—61no—
554C2×C4—124no—
555C2×C4—122no—
556C2×C4—181no—
557C2×C4—364no—
558C2×C4—362no—
559C2×C4D3×#6711yescharacteristic
560C2×C4D3×#6711yescharacteristic
561C2×C4C22×D3211yescharacteristic
562C8—32no—
563C8—61no—
564C8—182no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—82no—
569C2×C3—82no—
570C2×C3—162no—
571C2×C3—241no—
572C2×C3—242no—
573C2×C3#571811yescharacteristic
574C2×C3C2×D3×D811yescharacteristic
575C2×C3#575711yescharacteristic
576C2×C3C22×#21311yescharacteristic
577C2×C3#583411yescharacteristic
578C2×C3#583511yescharacteristic
579D3—82no—
580D3—81no—
581D3—242no—
582D3—241no—
583D3—241no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—121no—
588C22—122no—
589C22—121no—
590C22—122no—
591C22—122no—
592C22—121no—
593C22—361no—
594C22—361no—
595C22—361no—
596C22C2×D3×#6711yescharacteristic
597C4—21no—
598C4—34no—
599C4—62no—
600C4—121no—
601C4—361no—
602C4D3×#21312yes—
603C4D3×#23711yescharacteristic
604C4#6431411yescharacteristic
605C3—21no—
606C3#8177811yescharacteristic, complemented
607C3#8358211yescharacteristic, complemented
608C2—82no—
609C2—241no—
610C2—242no—
611C2—721no—
612C2C2×D3×#21311yescharacteristic
613C2#1059509611yescharacteristic
614C2#1059515811yescharacteristic
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. #10593900C2semidirect
3. #10592771C2semidirect
4. C3×#5073C2semidirect
5. #10591482C2semidirect
6. #10591481C2semidirect
7. #10591428C2semidirect
8. Dic3×#213C2semidirect
9. #10590347C2semidirect
10. C4×#3714C2semidirect
11. C3⋊C8×Dic6C2semidirect
45. #5718D3semidirect
53. #5073D3semidirect
195. C3×Dic6D8semidirect
201. C3×C3⋊C8#41semidirect
423. Dic6#213semidirect
430. C3⋊C8#237semidirect
529. C32#3391semidirect
606. C3#81778semidirect
607. C3#83582semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105939002
#105927712
C3×#50732
#105914822
#105914812
#105914282
Dic3×#2132
#105903472
C4×#37142
C3⋊C8×Dic62
#835823
#817783