Finite Group Databasebeta

← #11870361

Subgroups — #11870361

Order 1152.

875 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic
3#10592701C211yesmaximal, characteristic, complemented
4C3×#4995C211yesmaximal, characteristic, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6#10591106C211yesmaximal, characteristic, complemented
7#10591071C211yesmaximal, characteristic, complemented
8#10590429C212yesmaximal, complemented
9#10590426C212yesmaximal, complemented
10#10590424C212yesmaximal, complemented
11#10590423C212yesmaximal, complemented
12#82574—31nomaximal
13#79222—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#892C2212yes—
22C3×D3×C4⋊C4C2212yes—
23C3×#67⋊C4—22no—
24C3×C4×D12—21no—
25C3×C4×Dic6—21no—
26#63978—22no—
27#63916—21no—
28#63909C2212yes—
29#63871—21no—
30#63857C2212yes—
31#63637C2211yescharacteristic
32#63637C2211yescharacteristic
33#63636C2211yescharacteristic
34#63636C2211yescharacteristic
35C3×#808C2212yes—
36C3×#807C2212yes—
37#63574C2212yes—
38#63574C2212yes—
39#63567C2212yes—
40#63564C2212yes—
41(C2×D3)⋊(C3⋊C8)C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×#520—31no—
44#5833—31no—
45#5523D311yescharacteristic, complemented
46#5510—31no—
47C3×#428—31no—
48#5234—31no—
49#5133—31no—
50#5129—31no—
51#5003—32no—
52#5002—31no—
53#5002—31no—
54#5002—61no—
55#4996—32no—
56#4995D311yescharacteristic, complemented
57#4971—32no—
58#4968—32no—
59#4966—31no—
60C2×#808—31no—
61C2×#808—31no—
62#4888—32no—
63#4885—32no—
64#4863—32no—
65#4862—32no—
66C22×C32×C4C2311yescharacteristic
67C2×#638—21no—
68#3828—22no—
69#3828—22no—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×#634C2311yescharacteristic
73C2×C3×#67D412yes—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12D411yescharacteristic
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3C2312yes—
81C2×C3×Dic6D411yescharacteristic
82C2×#626—22no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86C32×C42—21no—
87C2×C3⋊(C3⋊C8)—22no—
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—22no—
97C3×#208—22no—
98C2×C3×C3⋊C8C2312yes—
99Dic3⋊Dic3—22no—
100#3722—22no—
101(C2×D3)⋊Dic3—22no—
102#3099—91noSylow
103C2×C3×#41—31no—
104C2×#235—31no—
105C2×#235—31no—
106C2×#235—61no—
107C2×#235C2×D311yescharacteristic
108C2×C3×M16—31no—
109C3×C4×Q8—61no—
110C3×C4×D4—61no—
111C3×C4×D4—62no—
112C3×#117—21no—
113C3×#117—32no—
114C3×#117C2×D311yescharacteristic
115C3×#117C2×D311yescharacteristic
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—32no—
119#946—61no—
120#939—62no—
121#938—61no—
122#930—32no—
123#930—62no—
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×C4⋊Dic3C2×D311yescharacteristic
126#924—32no—
127C2×#208C2×D311yescharacteristic
128C22×C3⋊C8—31no—
129C22×C3⋊C8—31no—
130C22×C3⋊C8—61no—
131#897—32no—
132#897—61no—
133#895—32no—
134#895—61no—
135#892C2×D312yes—
136D3×C4⋊C4C2×D312yes—
137#67⋊C4—22no—
138C4×D12—21no—
139C4×Dic6—21no—
140C3×#107—32no—
141C3×#106—32no—
142#830—32no—
143#830—32no—
144#821—32no—
145(C2×D3)⋊C8—32no—
146(C2×D3)⋊C8—32no—
147#816—32no—
148#810—31no—
149#810—31no—
150#810—31no—
151#810—31no—
152#810—32no—
153#810—61no—
154#810—61no—
155#809—31no—
156#809—31no—
157#809—31no—
158#809—31no—
159#809—32no—
160#809—61no—
161#809—61no—
162#808—32no—
163#808—32no—
164#808—32no—
165#808—32no—
166#808C2×D312yes—
167#807C2×D312yes—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3×D3C2×D412yes—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4#4112yes—
175C2×C32×C4#4112yes—
176C2×C32×C4C2411yescharacteristic
177#638—42no—
178C2×C3⋊Dic3—21no—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)—21no—
181C4×C3⋊D3—42no—
182#634—21no—
183#634—21no—
184C3×#67—24no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—81no—
188C2×C3×Dic3—81no—
189C2×C3×Dic3C2×D412yes—
190C3×D12—22no—
191C3×C4×D3—22no—
192C3×C4×D3—22no—
193C3×C4×D3—82no—
194C3×Dic6—22no—
195#626—82no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198C3×C3⋊C8—22no—
199#537—91no—
200#520—31no—
201#485—92no—
202#483—92no—
203#482—92no—
204#481—92no—
205#428—31no—
206C2×#106—91no—
207#417—91no—
208#416—91no—
209#408—91no—
210C3×#41—62no—
211C3×#41—62no—
212C2×C3×Q8—31no—
213C2×C3×D4—32no—
214C2×C3×D4—31no—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—62no—
218C22×C3×C4—61no—
219C22×C3×C4—61no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C2×#67—62no—
223C2×#67—61no—
224C2×#67—61no—
225C2×#67—121no—
226C2×#67#6712yes—
227C22×Dic3—21no—
228C22×Dic3—21no—
229#235—22no—
230#235—22no—
231#235—64no—
232#235—62no—
233#235—62no—
234#235—62no—
235#235—62no—
236#235—122no—
237C2×D12—31no—
238C2×D12—31no—
239C2×D12—61no—
240C2×D12—62no—
241C2×D12#6711yescharacteristic
242C2×C4×D3—22no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—121no—
246C2×C4×D3C22×D312yes—
247C2×Dic6—31no—
248C2×Dic6—31no—
249C2×Dic6—61no—
250C2×Dic6#6711yescharacteristic
251C3×M16—62no—
252C2×C3×C8—32no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—62no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
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—21no—
270C3×C42—41no—
271C3×C42—62no—
272#217—62no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3—62no—
280C4⋊Dic3C22×D312yes—
281C4⋊Dic3C22×D312yes—
282Dic3⋊C4—22no—
283Dic3⋊C4—62no—
284C4×Dic3—22no—
285#208—22no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8—122no—
295C2×C3⋊C8C22×D312yes—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32#12312yes—
299C22×C32C22×D411yescharacteristic
300C2×C3⋊D3—41no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3×D3—22no—
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C32×C4—41no—
307C32×C4—41no—
308C32×C4#12312yes—
309C32×C4C2×#4111yescharacteristic
310C32×C4C2×#4111yescharacteristic
311C3⋊Dic3—41no—
312C3×Dic3—22no—
313C3×Dic3—42no—
314C3×Dic3—42no—
315C2×#41—31no—
316C2×#41—91no—
317C2×M16—31no—
318C22×C8—91no—
319C22⋊Q8—92no—
320C22⋊Q8—181no—
321#121—92no—
322#121—181no—
323#121—182no—
324C4×Q8—61no—
325C4×D4—61no—
326C4×D4—62no—
327#117—32no—
328#117D3211yescharacteristic
329C2×C4⋊C4—31no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—32no—
332#107—32no—
333#106—32no—
334#106—92no—
335#106—92no—
336#103—92no—
337#103—91no—
338#103—91no—
339#102—92no—
340#102—91no—
341#102—91no—
342C22⋊C8—92no—
343C22⋊C8—92no—
344C23×C3—21no—
345C23×C3—32no—
346C23×C3D3×D411yescharacteristic
347C23×C3C2×#6711yescharacteristic
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—121no—
351C22×D3C2×#6712yes—
352C3×Q8—62no—
353C3×D4—64no—
354C3×D4—62no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—32no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—242no—
371C2×C3×C4—241no—
372C2×C3×C4—241no—
373C2×C3×C4#23512yes—
374C2×C3×C4#23512yes—
375C2×C3×C4#23512yes—
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4#23912yes—
378C2×C3×C4C2×#6711yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381#67—24no—
382#67—124no—
383#67—122no—
384#67—122no—
385#67—242no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—81no—
391C2×Dic3—81no—
392C2×Dic3—121no—
393C2×Dic3C2×#6712yes—
394D12—22no—
395D12—62no—
396D12—61no—
397D12—61no—
398D12—61no—
399D12—61no—
400D12—121no—
401D12—242no—
402C4×D3—22no—
403C4×D3—22no—
404C4×D3—82no—
405C4×D3—124no—
406C4×D3—122no—
407C4×D3—122no—
408Dic6—22no—
409Dic6—62no—
410Dic6—61no—
411Dic6—61no—
412Dic6—61no—
413Dic6—61no—
414Dic6—121no—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—61no—
418C3⋊C8—61no—
419C3⋊C8—61no—
420C3⋊C8—61no—
421C3⋊C8—121no—
422C3⋊C8—121no—
423C2×C32—22no—
424C2×C32C2×#12311yescharacteristic
425C2×C32#57711yescharacteristic
426C2×C32#57711yescharacteristic
427C3⋊D3—81no—
428C3×D3—42no—
429#41—62no—
430#41—62no—
431#41—182no—
432#41—182no—
433C2×Q8—31no—
434C2×Q8—91no—
435C2×D4—32no—
436C2×D4—31no—
437C2×D4—91no—
438C2×D4—182no—
439C2×D4—181no—
440C22×C4—32no—
441C22×C4—62no—
442C22×C4—61no—
443C22×C4—61no—
444C22×C4—181no—
445C22×C4C2×D3211yescharacteristic
446M16—62no—
447C2×C8—32no—
448C2×C8—91no—
449C2×C8—91no—
450C2×C8—182no—
451C4⋊C4—32no—
452C4⋊C4—32no—
453C4⋊C4—62no—
454C4⋊C4—61no—
455C4⋊C4—61no—
456C4⋊C4—182no—
457C4⋊C4C2×D3211yescharacteristic
458C4⋊C4C2×D3211yescharacteristic
459C22⋊C4—21no—
460C22⋊C4—62no—
461C22⋊C4—182no—
462C22⋊C4—182no—
463C42—21no—
464C42—62no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—22no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—62no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3#89412yes—
477C22×C3#92912yes—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C22×#6711yescharacteristic
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—122no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C2×D3—121no—
488C2×D3—121no—
489C2×D3—121no—
490C2×D3—241no—
491C2×D3—241no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—41no—
499C3×C4—62no—
500C3×C4—81no—
501C3×C4—81no—
502C3×C4—122no—
503C3×C4—122no—
504C3×C4#89412yes—
505C3×C4#92912yes—
506C3×C4C2×#23511yescharacteristic
507C3×C4C2×#23511yescharacteristic
508C3×C4C2×#23511yescharacteristic
509C3×C4C2×#23911yescharacteristic
510Dic3—22no—
511Dic3—42no—
512Dic3—42no—
513Dic3—122no—
514Dic3—121no—
515Dic3—121no—
516C32#309911yescharacteristic, complemented, Sylow
517C23—32no—
518C23—181no—
519C23D3×#6711yescharacteristic
520Q8—62no—
521Q8—181no—
522Q8—181no—
523D4—64no—
524D4—62no—
525D4—181no—
526D4—181no—
527D4—362no—
528D4—722no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—32no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—181no—
537C2×C4—242no—
538C2×C4—241no—
539C2×C4—241no—
540C2×C4—362no—
541C2×C4#379812yes—
542C2×C4#379912yes—
543C2×C4D3×#6711yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—62no—
546C8—181no—
547C8—181no—
548C2×C3—22no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—42no—
554C2×C3—122no—
555C2×C3C2×#89411yescharacteristic
556C2×C3#577511yescharacteristic
557C2×C3#577811yescharacteristic
558C2×C3C2×#92911yescharacteristic
559C2×C3#583611yescharacteristic
560C2×C3#583711yescharacteristic
561D3—42no—
562D3—242no—
563D3—241no—
564D3—241no—
565C22—21no—
566C22—21no—
567C22—62no—
568C22—62no—
569C22—62no—
570C22—361no—
571C22—361no—
572C22—361no—
573C22#6385012yes—
574C22C2×D3×#6711yescharacteristic
575C4—41no—
576C4—41no—
577C4—62no—
578C4—122no—
579C4—122no—
580C4—361no—
581C4#6385012yes—
582C4C2×#379811yescharacteristic
583C4C2×#379911yescharacteristic
584C3—21no—
585C3#7922211yescharacteristic, complemented
586C3#8257411yescharacteristic, complemented
587C2—22no—
588C2—122no—
589C2—721no—
590C2C2×#6385011yescharacteristic
591C2#1059545511yescharacteristic
592C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenter#117D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5523C2semidirect
3. #10592701C2semidirect
4. C3×#4995C2semidirect
5. C2×#63574C2semidirect
6. #10591106C2semidirect
7. #10591071C2semidirect
8. #10590429C2semidirect
9. #10590426C2semidirect
10. #10590424C2semidirect
11. #10590423C2semidirect
45. #5523D3semidirect
56. #4995D3semidirect
516. C32#3099semidirect
585. C3#79222semidirect
586. C3#82574semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
#105950432
#105927012
C3×#49952
C2×#635742
#105911062
#105910712
#105904292
#105904262
#105904242
#105904232
#825743
#792223