Finite Group Databasebeta

← #11870358

Subgroups — #11870358

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 611 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596304C211yesmaximal, characteristic
2C3×#5827C211yesmaximal, characteristic, complemented
3C3×#5234C211yesmaximal, characteristic, complemented
4#10591136C212yesmaximal, complemented
5#10591134C212yesmaximal, complemented
6#10591131C211yesmaximal, characteristic, complemented
7#10591125C212yesmaximal, complemented
8#10591124C212yesmaximal, complemented
9C2×#63573C211yesmaximal, characteristic, complemented
10#10591106C211yesmaximal, characteristic, complemented
11#10591105C211yesmaximal, characteristic, complemented
12#82574—31nomaximal
13#78654—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16#64155—21no—
17#64148—22no—
18#64147—21no—
19#64139C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64133C2212yes—
22C3×Q8×Dic3—21no—
23C3×D4×Dic3—21no—
24C3×D4×Dic3—22no—
25C3×#926C2211yescharacteristic
26C3×#926C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2212yes—
29C2×C3×#208C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31C3×#830C2212yes—
32C3×#830C2212yes—
33#63575C2212yes—
34#63573C2212yes—
35#63573C2212yes—
36#63573C2212yes—
37#63567C2211yescharacteristic
38#63567C2211yescharacteristic
39#63567C2212yes—
40#63564C2211yescharacteristic
41#63564C2211yescharacteristic
42#63564C2212yes—
43C3×#520—31no—
44#5833—31no—
45#5833—31no—
46#5833—61no—
47#5827D311yescharacteristic, complemented
48C3×#408—31no—
49#5234D311yescharacteristic, complemented
50#5133—31no—
51#5121—31no—
52#5113—31no—
53C2×#817—31no—
54#5003—32no—
55#5002—31no—
56#4996—32no—
57#4995—31no—
58#4971—32no—
59#4968—32no—
60#4966—31no—
61C2×#808—31no—
62#4737—32no—
63#4735—32no—
64#4723—32no—
65#4721—32no—
66C32×#41—22no—
67C32×#41—22no—
68C2×C32×Q8D411yescharacteristic
69C2×C32×D4D411yescharacteristic
70C2×C32×D4D412yes—
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C2×#638—21no—
74C2×#638—22no—
75C22×C3⋊Dic3—21no—
76#3828—22no—
77#3828—22no—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3—21no—
80C2×#634C2311yescharacteristic
81C22×C3×Dic3—22no—
82C22×C3×Dic3—21no—
83#3757—22no—
84#3752—22no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87#3750—22no—
88C3×#217—22no—
89C3×#217—21no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3—22no—
96C3×C4×Dic3—21no—
97C3×#208—22no—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102#3099—91noSylow
103C2×C3×#41—21no—
104C2×C3×#41C2×D311yescharacteristic
105C2×C3×#41C2×D311yescharacteristic
106C2×#235—31no—
107C2×#235—31no—
108C2×#235—61no—
109C2×C3×M16—31no—
110C22×C3×C8—31no—
111C3×C4×Q8—61no—
112C3×C4×D4—61no—
113C3×C4×D4—62no—
114C3×#117—31no—
115C3×#117—32no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—32no—
118#946—62no—
119#946—61no—
120#946—61no—
121Q8×Dic3—21no—
122#939—64no—
123#939—62no—
124#939—62no—
125#938—62no—
126#938—61no—
127#938—61no—
128D4×Dic3—21no—
129D4×Dic3—22no—
130#930—32no—
131#930—32no—
132#930—62no—
133#926C2×D311yescharacteristic
134#926C2×D312yes—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—61no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139C2×C4⋊Dic3C2×D312yes—
140#924—32no—
141#924—32no—
142#924—62no—
143C2×#208C2×D311yescharacteristic
144C22×C3⋊C8C2×D311yescharacteristic
145C3×C22⋊C8—32no—
146C3×C22⋊C8—32no—
147#830C2×D312yes—
148#830C2×D312yes—
149#821—32no—
150#821—31no—
151#821—31no—
152#818—32no—
153#817—32no—
154#817—32no—
155#817—32no—
156#816—32no—
157#816—31no—
158#816—31no—
159#810—32no—
160#810—31no—
161#810—31no—
162#809—32no—
163#809—31no—
164#809—31no—
165#808—32no—
166#808—32no—
167#808—32no—
168#807—32no—
169C23×C32C2×D412yes—
170C23×C32C2×D411yescharacteristic
171C22×C3⋊D3—21no—
172C32×Q8—22no—
173C32×D4—24no—
174C32×D4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4#4112yes—
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182#638—42no—
183#638—82no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—81no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)—21no—
189C4×C3⋊D3—42no—
190#634—21no—
191#634—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—81no—
196C2×C3×Dic3—82no—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199C3×C3⋊C8—22no—
200#537—91no—
201#520—31no—
202#485—92no—
203#483—92no—
204#482—92no—
205#481—92no—
206#428—91no—
207C2×#106—91no—
208#417—91no—
209#416—91no—
210#408—31no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—22no—
214C3×#41—22no—
215C3×#41—42no—
216C3×#41—42no—
217C2×C3×Q8—21no—
218C2×C3×Q8D1211yescharacteristic
219C2×C3×Q8#6711yescharacteristic
220C2×C3×D4—21no—
221C2×C3×D4—22no—
222C2×C3×D4D1211yescharacteristic
223C2×C3×D4D1212yes—
224C2×C3×D4#6711yescharacteristic
225C2×C3×D4#6712yes—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—62no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D312yes—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—62no—
235C2×#67—61no—
236C2×#67—61no—
237C2×#67—64no—
238C2×#67—62no—
239C2×#67—62no—
240C22×Dic3—22no—
241C22×Dic3—21no—
242C22×Dic3—62no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245#235—62no—
246#235—62no—
247#235—62no—
248#235—62no—
249#235—122no—
250#235—122no—
251C2×D12—31no—
252C2×D12—31no—
253C2×D12—61no—
254C2×C4×D3—62no—
255C2×C4×D3—61no—
256C2×C4×D3—61no—
257C2×Dic6—31no—
258C2×Dic6—31no—
259C2×Dic6—61no—
260C3×M16—62no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—32no—
264C2×C3×C8—62no—
265C3×C4⋊C4—31no—
266C3×C4⋊C4—32no—
267C3×C4⋊C4—31no—
268C3×C4⋊C4—62no—
269C3×C4⋊C4—61no—
270C3×C22⋊C4—62no—
271C3×C22⋊C4—61no—
272C3×C42—62no—
273C3×C42—61no—
274#217—22no—
275#217—21no—
276#217—64no—
277#217—62no—
278#217—62no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—62no—
282C4⋊Dic3—22no—
283C4⋊Dic3—21no—
284C4⋊Dic3—32no—
285C4⋊Dic3—32no—
286C4⋊Dic3—62no—
287C4⋊Dic3—62no—
288C4⋊Dic3—61no—
289C4⋊Dic3—61no—
290C4⋊Dic3C22×D312yes—
291C4⋊Dic3C22×D311yescharacteristic
292C4⋊Dic3C22×D311yescharacteristic
293Dic3⋊C4—64no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296C4×Dic3—22no—
297C4×Dic3—21no—
298#208—22no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8C22×D312yes—
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D311yescharacteristic
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—22no—
308C22×C32#12312yes—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—41no—
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C32×C4—22no—
314C32×C4#12312yes—
315C32×C4C2×#4111yescharacteristic
316C32×C4C2×#4111yescharacteristic
317C3⋊Dic3—41no—
318C3⋊Dic3—42no—
319C3×Dic3—41no—
320C3×Dic3—42no—
321C3×Dic3—41no—
322C2×#41—91no—
323C2×#41D3211yescharacteristic
324C2×M16—31no—
325C22×C8—31no—
326C22⋊Q8—92no—
327C22⋊Q8—181no—
328#121—92no—
329#121—181no—
330#121—182no—
331C4×Q8—61no—
332C4×D4—62no—
333C4×D4—61no—
334#117—31no—
335#117—32no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—32no—
338C2×C4⋊C4—91no—
339#107—92no—
340#106—92no—
341#106—92no—
342#106—92no—
343#103—91no—
344#103—91no—
345#103—92no—
346#102—91no—
347#102—91no—
348#102—92no—
349C22⋊C8—32no—
350C22⋊C8—32no—
351C23×C3—21no—
352C23×C3—22no—
353C23×C3C2×D1212yes—
354C23×C3C2×D1211yescharacteristic
355C23×C3C2×#6712yes—
356C23×C3C2×#6711yescharacteristic
357C22×D3—62no—
358C22×D3—61no—
359C22×D3—61no—
360C3×Q8—22no—
361C3×Q8—22no—
362C3×Q8—42no—
363C3×D4—24no—
364C3×D4—24no—
365C3×D4—22no—
366C3×D4—22no—
367C3×D4—42no—
368C3×D4—44no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—61no—
381C2×C3×C4—62no—
382C2×C3×C4—61no—
383C2×C3×C4—241no—
384C2×C3×C4—242no—
385C2×C3×C4C2×D1212yes—
386C2×C3×C4C2×D1211yescharacteristic
387C2×C3×C4#23512yes—
388C2×C3×C4#23512yes—
389C2×C3×C4#23712yes—
390C2×C3×C4#23712yes—
391C2×C3×C4C2×#6712yes—
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—124no—
396#67—122no—
397#67—122no—
398#67—242no—
399#67—242no—
400#67—244no—
401C2×Dic3—21no—
402C2×Dic3—22no—
403C2×Dic3—21no—
404C2×Dic3—62no—
405C2×Dic3—64no—
406C2×Dic3—61no—
407C2×Dic3—62no—
408C2×Dic3—61no—
409C2×Dic3—62no—
410C2×Dic3—81no—
411C2×Dic3—82no—
412C2×Dic3—241no—
413C2×Dic3—241no—
414C2×Dic3—242no—
415D12—61no—
416D12—61no—
417D12—61no—
418D12—61no—
419D12—121no—
420D12—121no—
421C4×D3—124no—
422C4×D3—122no—
423C4×D3—122no—
424Dic6—61no—
425Dic6—61no—
426Dic6—61no—
427Dic6—61no—
428Dic6—121no—
429Dic6—121no—
430C3×C8—61no—
431C3×C8—61no—
432C3×C8—62no—
433C3⋊C8—21no—
434C3⋊C8—21no—
435C3⋊C8—22no—
436C2×C32—22no—
437C2×C32—42no—
438C2×C32C2×#12311yescharacteristic
439C2×C32#57711yescharacteristic
440C2×C32#57711yescharacteristic
441C3⋊D3—81no—
442#41—22no—
443#41—22no—
444#41—182no—
445#41—182no—
446C2×Q8—91no—
447C2×Q8#62611yescharacteristic
448C2×D4—91no—
449C2×D4—181no—
450C2×D4—182no—
451C2×D4#62612yes—
452C2×D4#62611yescharacteristic
453C22×C4—62no—
454C22×C4—61no—
455C22×C4—181no—
456C22×C4—181no—
457C22×C4C2×D3212yes—
458C22×C4C2×D3211yescharacteristic
459M16—62no—
460C2×C8—31no—
461C2×C8—31no—
462C2×C8—32no—
463C2×C8—62no—
464C4⋊C4—31no—
465C4⋊C4—32no—
466C4⋊C4—31no—
467C4⋊C4—62no—
468C4⋊C4—61no—
469C4⋊C4—92no—
470C4⋊C4—181no—
471C4⋊C4—182no—
472C22⋊C4—62no—
473C22⋊C4—61no—
474C22⋊C4—182no—
475C22⋊C4—182no—
476C42—62no—
477C42—61no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—21no—
489C22×C3—22no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3#88612yes—
496C22×C3#92912yes—
497C22×C3C22×D1211yescharacteristic
498C22×C3C22×#6711yescharacteristic
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—121no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—121no—
506C2×D3—121no—
507C2×D3—121no—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—42no—
514C3×C4—122no—
515C3×C4—121no—
516C3×C4—121no—
517C3×C4#88612yes—
518C3×C4#92912yes—
519C3×C4C2×#23511yescharacteristic
520C3×C4C2×#23511yescharacteristic
521C3×C4C2×#23711yescharacteristic
522C3×C4C2×#23711yescharacteristic
523Dic3—42no—
524Dic3—41no—
525Dic3—41no—
526Dic3—122no—
527Dic3—124no—
528Dic3—121no—
529Dic3—122no—
530Dic3—121no—
531Dic3—122no—
532C32#309911yescharacteristic, complemented, Sylow
533C23—181no—
534C23C2×#62612yes—
535C23C2×#62611yescharacteristic
536Q8—22no—
537Q8—181no—
538Q8—181no—
539D4—24no—
540D4—22no—
541D4—181no—
542D4—181no—
543D4—362no—
544D4—722no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—61no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—182no—
551C2×C4—181no—
552C2×C4—241no—
553C2×C4—242no—
554C2×C4—362no—
555C2×C4—721no—
556C2×C4#380412yes—
557C2×C4#380412yes—
558C2×C4C2×#62612yes—
559C2×C4C2×#62611yescharacteristic
560C2×C4C22×D3211yescharacteristic
561C8—61no—
562C8—61no—
563C8—62no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—42no—
570C2×C3—42no—
571C2×C3—42no—
572C2×C3—82no—
573C2×C3C2×#88611yescharacteristic
574C2×C3#575111yescharacteristic
575C2×C3#575111yescharacteristic
576C2×C3C2×#92911yescharacteristic
577C2×C3#583611yescharacteristic
578C2×C3#583711yescharacteristic
579D3—242no—
580D3—241no—
581D3—241no—
582C22—21no—
583C22—21no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—361no—
588C22—361no—
589C22—361no—
590C22#6396612yes—
591C22C22×#62611yescharacteristic
592C4—22no—
593C4—122no—
594C4—121no—
595C4—121no—
596C4—362no—
597C4—361no—
598C4#6396612yes—
599C4C2×#380411yescharacteristic
600C4C2×#380411yescharacteristic
601C3—21no—
602C3#7865411yescharacteristic, complemented
603C3#8257411yescharacteristic, complemented
604C2—22no—
605C2—42no—
606C2—721no—
607C2#1059544711yescharacteristic
608C2#1059544811yescharacteristic
609C2C2×#6396611yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radical#10596304C2
hypercenterC2×#41D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5827C2semidirect
3. C3×#5234C2semidirect
4. #10591136C2semidirect
5. #10591134C2semidirect
6. #10591131C2semidirect
7. #10591125C2semidirect
8. #10591124C2semidirect
9. C2×#63573C2semidirect
10. #10591106C2semidirect
11. #10591105C2semidirect
47. #5827D3semidirect
49. #5234D3semidirect
532. C32#3099semidirect
602. C3#78654semidirect
603. C3#82574semidirect

Maximal subgroups

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

subgroupindex
#105963042
C3×#58272
C3×#52342
#105911362
#105911342
#105911312
#105911252
#105911242
C2×#635732
#105911062
#105911052
#825743
#786543