Finite Group Databasebeta

← #11870370

Subgroups — #11870370

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic
3#10592665C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5#10591139C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic, complemented
7#10591070C211yesmaximal, characteristic, complemented
8#10590428C212yesmaximal, complemented
9#10590426C212yesmaximal, complemented
10#10590425C212yesmaximal, complemented
11#10590423C212yesmaximal, complemented
12#82574—31nomaximal
13#79112—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×C4×#67—22no—
19C3×#926C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#893—21no—
23C3×#892C2212yes—
24C3×D3×C4⋊C4C2212yes—
25C3×#887—21no—
26#63978—22no—
27#63916—21no—
28#63909C2212yes—
29#63871—21no—
30#63857C2212yes—
31#63637C2212yes—
32#63636C2212yes—
33C3×#808C2212yes—
34C3×#808C2212yes—
35#63576C2212yes—
36#63574C2212yes—
37#63567C2211yescharacteristic
38#63567C2211yescharacteristic
39#63564C2211yescharacteristic
40#63564C2211yescharacteristic
41(C2×D3)⋊(C3⋊C8)C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×#520—31no—
44#5833—31no—
45#5510—31no—
46#5504D311yescharacteristic, complemented
47C2×C3×#106—31no—
48#5234—31no—
49#5113—31no—
50#5110—31no—
51#5003—32no—
52#5002—31no—
53#4996—32no—
54#4995—31no—
55#4971—32no—
56#4968—32no—
57#4966—31no—
58#4966—31no—
59#4966—61no—
60#4964—31no—
61C2×#808D311yescharacteristic, complemented
62#4868—32no—
63#4866—32no—
64#4863—32no—
65#4862—32no—
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69#3828—22no—
70#3828—22no—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×#634C2311yescharacteristic
74C2×C3×#67D412yes—
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⋊C4—21no—
84C32×C4⋊C4C2312yes—
85#3748—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—21no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—22no—
96C2×C3×C3⋊C8—22no—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
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
108C22×C3×C8—31no—
109C3×C4×Q8—61no—
110C3×C4×D4—61no—
111C3×C4×D4—62no—
112C3×#117—31no—
113C3×#117—32no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C4⋊C4C2×D311yescharacteristic
119#946—61no—
120#939—62no—
121#938—61no—
122#930—32no—
123#930—62no—
124C4×#67—22no—
125#926C2×D311yescharacteristic
126C2×C4⋊Dic3C2×D311yescharacteristic
127#924—32no—
128C2×#208—31no—
129C2×#208—31no—
130C2×#208—61no—
131C22×C3⋊C8C2×D311yescharacteristic
132#897—32no—
133#897—61no—
134#895—32no—
135#895—61no—
136#893—21no—
137#892C2×D312yes—
138D3×C4⋊C4C2×D312yes—
139#887—21no—
140C3×#106—32no—
141C3×#106—32no—
142#830—32no—
143#830—32no—
144#821—31no—
145#821—31no—
146(C2×D3)⋊C8—32no—
147(C2×D3)⋊C8—32no—
148#816—31no—
149#816—31no—
150#810—32no—
151#810—32no—
152#810—31no—
153#810—31no—
154#810—62no—
155#809—32no—
156#809—32no—
157#809—31no—
158#809—31no—
159#809—62no—
160#808—32no—
161#808—32no—
162#808C2×D312yes—
163#808C2×D312yes—
164#807—32no—
165#807—32no—
166C23×C32C2×D411yescharacteristic
167C22×C3⋊D3—21no—
168C22×C3×D3C2×D412yes—
169C2×C32×C4—22no—
170C2×C32×C4—81no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4#4112yes—
173C2×C32×C4#4112yes—
174C2×C32×C4C2411yescharacteristic
175#638—42no—
176C2×C3⋊Dic3—21no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)—21no—
179C4×C3⋊D3—42no—
180#634—21no—
181#634—21no—
182C3×#67—24no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—81no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—22no—
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×C4×D3—82no—
192C3×Dic6—22no—
193#626—82no—
194C3⋊(C3⋊C8)—22no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—21no—
197#537—91no—
198#520—31no—
199#485—92no—
200#483—92no—
201#482—92no—
202#481—92no—
203#428—91no—
204C2×#106—31no—
205#417—91no—
206#416—91no—
207#408—91no—
208C3×#41—62no—
209C3×#41—62no—
210C2×C3×Q8—31no—
211C2×C3×D4—32no—
212C2×C3×D4—31no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—41no—
218C22×C3×C4—62no—
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—
228#235—22no—
229#235—22no—
230#235—64no—
231#235—62no—
232#235—62no—
233#235—62no—
234#235—62no—
235#235—122no—
236C2×D12—31no—
237C2×D12—31no—
238C2×D12—61no—
239C2×D12—62no—
240C2×D12#6711yescharacteristic
241C2×C4×D3—22no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—121no—
245C2×C4×D3C22×D312yes—
246C2×Dic6—31no—
247C2×Dic6—31no—
248C2×Dic6—61no—
249C2×Dic6#6711yescharacteristic
250C2×C3×C8—31no—
251C2×C3×C8—31no—
252C2×C3×C8—62no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—41no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4C22×D312yes—
263C3×C4⋊C4C22×D312yes—
264C3×C22⋊C4—62no—
265C3×C22⋊C4—61no—
266C3×C42—62no—
267C3×C42—61no—
268#217—21no—
269#217—62no—
270(C2×D3)⋊C4—22no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—62no—
273(C2×D3)⋊C4—62no—
274C4⋊Dic3—21no—
275C4⋊Dic3—62no—
276C4⋊Dic3C22×D311yescharacteristic
277C4⋊Dic3C22×D312yes—
278C4⋊Dic3C22×D311yescharacteristic
279Dic3⋊C4—22no—
280Dic3⋊C4—62no—
281C4×Dic3—21no—
282C4×Dic3—22no—
283#208—62no—
284#208—62no—
285#208—122no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—32no—
288C2×C3⋊C8—32no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8C22×D311yescharacteristic
291C2×C3⋊C8C22×D311yescharacteristic
292C22×C32—21no—
293C22×C32—21no—
294C22×C32#12312yes—
295C22×C32C22×D411yescharacteristic
296C2×C3⋊D3—41no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—41no—
299C2×C3×D3—22no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C32×C4—42no—
303C32×C4#12312yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4C2×#4111yescharacteristic
306C3⋊Dic3—41no—
307C3×Dic3—22no—
308C3×Dic3—42no—
309C3×Dic3—41no—
310C3×Dic3—41no—
311C2×#41—31no—
312C2×#41—91no—
313C2×M16—91no—
314C22×C8—31no—
315C22⋊Q8—92no—
316C22⋊Q8—181no—
317#121—92no—
318#121—181no—
319#121—182no—
320C4×Q8—61no—
321C4×D4—61no—
322C4×D4—62no—
323#117—31no—
324#117—32no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—32no—
327C2×C4⋊C4D3211yescharacteristic
328#107—92no—
329#106—32no—
330#106—32no—
331#106—92no—
332#103—91no—
333#103—91no—
334#103—92no—
335#102—91no—
336#102—91no—
337#102—92no—
338C22⋊C8—92no—
339C22⋊C8—92no—
340C23×C3—21no—
341C23×C3—32no—
342C23×C3D3×D411yescharacteristic
343C23×C3C2×#6711yescharacteristic
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—121no—
347C22×D3C2×#6712yes—
348C3×Q8—62no—
349C3×D4—64no—
350C3×D4—62no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—32no—
358C2×C3×C4—42no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—81no—
365C2×C3×C4—81no—
366C2×C3×C4—82no—
367C2×C3×C4—242no—
368C2×C3×C4—241no—
369C2×C3×C4#23512yes—
370C2×C3×C4#23512yes—
371C2×C3×C4#23512yes—
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4#23912yes—
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377#67—24no—
378#67—124no—
379#67—122no—
380#67—122no—
381#67—242no—
382C2×Dic3—22no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—81no—
388C2×Dic3—121no—
389C2×Dic3C2×#6712yes—
390D12—22no—
391D12—62no—
392D12—61no—
393D12—61no—
394D12—61no—
395D12—61no—
396D12—121no—
397D12—242no—
398C4×D3—22no—
399C4×D3—22no—
400C4×D3—82no—
401C4×D3—124no—
402C4×D3—122no—
403C4×D3—122no—
404Dic6—22no—
405Dic6—62no—
406Dic6—61no—
407Dic6—61no—
408Dic6—61no—
409Dic6—61no—
410Dic6—121no—
411C3×C8—61no—
412C3×C8—61no—
413C3⋊C8—21no—
414C3⋊C8—21no—
415C3⋊C8—62no—
416C3⋊C8—62no—
417C3⋊C8—122no—
418C2×C32—22no—
419C2×C32C2×#12311yescharacteristic
420C2×C32#57711yescharacteristic
421C2×C32#57711yescharacteristic
422C3⋊D3—81no—
423C3×D3—42no—
424#41—62no—
425#41—62no—
426#41—182no—
427#41—182no—
428C2×Q8—31no—
429C2×Q8—91no—
430C2×D4—32no—
431C2×D4—31no—
432C2×D4—91no—
433C2×D4—182no—
434C2×D4—181no—
435C22×C4—21no—
436C22×C4—32no—
437C22×C4—62no—
438C22×C4—61no—
439C22×C4—181no—
440C22×C4C2×D3211yescharacteristic
441M16—182no—
442C2×C8—31no—
443C2×C8—31no—
444C2×C8—62no—
445C2×C8—92no—
446C4⋊C4—21no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—32no—
450C4⋊C4—62no—
451C4⋊C4—61no—
452C4⋊C4—182no—
453C4⋊C4C2×D3212yes—
454C22⋊C4—62no—
455C22⋊C4—61no—
456C22⋊C4—182no—
457C22⋊C4—182no—
458C42—62no—
459C42—61no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—62no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3#89412yes—
472C22×C3#92912yes—
473C22×C3C2×D3×D411yescharacteristic
474C22×C3C22×#6711yescharacteristic
475C2×D3—22no—
476C2×D3—22no—
477C2×D3—22no—
478C2×D3—122no—
479C2×D3—121no—
480C2×D3—121no—
481C2×D3—121no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—121no—
485C2×D3—241no—
486C2×D3—241no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—42no—
491C3×C4—42no—
492C3×C4—62no—
493C3×C4—82no—
494C3×C4—121no—
495C3×C4—121no—
496C3×C4—122no—
497C3×C4#89412yes—
498C3×C4#92912yes—
499C3×C4C2×#23511yescharacteristic
500C3×C4C2×#23511yescharacteristic
501C3×C4C2×#23511yescharacteristic
502C3×C4C2×#23911yescharacteristic
503Dic3—22no—
504Dic3—42no—
505Dic3—41no—
506Dic3—41no—
507Dic3—122no—
508Dic3—121no—
509Dic3—121no—
510C32#309911yescharacteristic, complemented, Sylow
511C23—32no—
512C23—181no—
513C23D3×#6711yescharacteristic
514Q8—62no—
515Q8—181no—
516Q8—181no—
517D4—64no—
518D4—62no—
519D4—181no—
520D4—181no—
521D4—362no—
522D4—722no—
523C2×C4—22no—
524C2×C4—32no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—81no—
531C2×C4—181no—
532C2×C4—242no—
533C2×C4—241no—
534C2×C4—362no—
535C2×C4#379812yes—
536C2×C4#379912yes—
537C2×C4D3×#6711yescharacteristic
538C2×C4C22×D3211yescharacteristic
539C8—61no—
540C8—61no—
541C8—182no—
542C2×C3—22no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—42no—
548C2×C3—122no—
549C2×C3C2×#89411yescharacteristic
550C2×C3#576211yescharacteristic
551C2×C3#576211yescharacteristic
552C2×C3C2×#92911yescharacteristic
553C2×C3#583611yescharacteristic
554C2×C3#583711yescharacteristic
555D3—42no—
556D3—242no—
557D3—241no—
558D3—241no—
559C22—21no—
560C22—21no—
561C22—62no—
562C22—62no—
563C22—62no—
564C22—361no—
565C22—361no—
566C22—361no—
567C22#6385012yes—
568C22C2×D3×#6711yescharacteristic
569C4—42no—
570C4—62no—
571C4—121no—
572C4—122no—
573C4—121no—
574C4—361no—
575C4#6385012yes—
576C4C2×#379811yescharacteristic
577C4C2×#379911yescharacteristic
578C3—21no—
579C3#7911211yescharacteristic, complemented
580C3#8257411yescharacteristic, complemented
581C2—22no—
582C2—122no—
583C2—721no—
584C2C2×#6385011yescharacteristic
585C2#1059510511yescharacteristic
586C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5504C2semidirect
3. #10592665C2semidirect
4. C2×C3×#808C2semidirect
5. #10591139C2semidirect
6. #10591105C2semidirect
7. #10591070C2semidirect
8. #10590428C2semidirect
9. #10590426C2semidirect
10. #10590425C2semidirect
11. #10590423C2semidirect
46. #5504D3semidirect
61. C2×#808D3semidirect
510. C32#3099semidirect
579. C3#79112semidirect
580. C3#82574semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
#105950432
#105926652
C2×C3×#8082
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