Finite Group Databasebeta

← #11870524

Subgroups — #11870524

Order 1152.

950 conjugacy classes of subgroups.

The subgroup lattice has 629 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×D12C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic, complemented
5C3×#4833C211yesmaximal, characteristic, complemented
6#10590942C212yesmaximal
7#10590792C212yesmaximal, complemented
8Dic3×#204C212yesmaximal, complemented
9#10590675C212yesmaximal, complemented
10#10590379C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#80408—31nomaximal
13#79298—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×C4×D32—21no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic, complemented
18C2×C3×#204C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×#869C2211yescharacteristic, complemented
22D3×(C2×D3)⋊C4—21no—
23C4×#626—21no—
24#63894C2211yescharacteristic
25Dic3×D12C2211yescharacteristic
26D3×C4⋊Dic3C2211yescharacteristic
27#63880—21no—
28#63869—21no—
29#63857—21no—
30#63856C2212yes—
31#63844—21no—
32Dic3×Dic6C2212yescomplemented
33#63841—21no—
34C2×#3717C2212yes—
35C32×C4⋊C8C2211yescharacteristic, complemented
36#63648C2212yes—
37#63644C2212yescomplemented
38C3×(C2×D3)⋊C8C2212yes—
39C3×#816C2212yescomplemented
40C3×C8×Dic3C2212yescomplemented
41C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
42#63573C2212yescomplemented
43#63566C2212yescomplemented
44#63563C2212yes—
45#5728—31no—
46C4×D3×D4—31no—
47C2×C4×D12—31no—
48#5470—31no—
49C3×#461—31no—
50C3×#431—31no—
51#5169—32no—
52Dic3×SD16—32no—
53#5083—31no—
54#5008—31no—
55#4842—31no—
56#4842—31no—
57#4842—31no—
58#4842—61no—
59#4841—31no—
60#4841D311yescharacteristic, complemented
61#4833D311yescharacteristic, complemented
62#4805—32no—
63#4788—32no—
64#4731—32no—
65#4721—32no—
66C4×#204—32no—
67C4×#204—32no—
68C22×D32—21no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×#634—21no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6C2312yes—
78C2×#626—21no—
79C2×#624—21no—
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82D3×D12—22no—
83D3×D12—22no—
84C4×D32—44no—
85C2×C32×C8C2312yes—
86C32×C42C2311yescharacteristic
87#3752—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99C3×#204—24no—
100#3724—22no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—21no—
103#3722—21no—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—21no—
106Dic32—22no—
107#3717—24no—
108#3101—91noSylow
109C2×D3×D4—31no—
110C22×D12—31no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C2×C3×SD16—32no—
114C3×C4⋊Q8—31no—
115C3×C4×D4—31no—
116C2×C3×C42—31no—
117#946—32no—
118Q8×Dic3—32no—
119C2×#215—32no—
120D4×Dic3—31no—
121C4×#67—61no—
122C2×(C2×D3)⋊C4—61no—
123#926—61no—
124C2×C4⋊Dic3—31no—
125#924—32no—
126#924—61no—
127C2×#204—32no—
128C2×#204C2×D312yes—
129#897—61no—
130#893—31no—
131#892—61no—
132D3×C4⋊C4—31no—
133#890—61no—
134#887—61no—
135#67⋊C4—61no—
136D3×C22⋊C4—61no—
137C4×D12—31no—
138C4×D12—31no—
139C4×D12—31no—
140C4×D12—31no—
141C4×D12—61no—
142C4×D12—61no—
143C4×D12—61no—
144C4×D12C2×D311yescharacteristic
145C42×D3C2×D311yescharacteristic
146#870—61no—
147#869—31no—
148#869—31no—
149#869—61no—
150#869C2×D311yescharacteristic, complemented
151C4×Dic6—32no—
152C4×Dic6—61no—
153C3×C4⋊C8—21no—
154C3×C4⋊C8—31no—
155C3×C4⋊C8C2×D311yescharacteristic, complemented
156C3×C4⋊C8C2×D311yescharacteristic, complemented
157C3×#103—32no—
158C3×C22⋊C8—32no—
159C3×C4×C8—32no—
160#835—32no—
161#832—32no—
162#821—32no—
163#821—32no—
164#821—32no—
165#821—62no—
166(C2×D3)⋊C8C2×D312yes—
167#817—32no—
168#817—32no—
169#817—32no—
170#817—62no—
171#816—32no—
172#816C2×D312yescomplemented
173C8×Dic3C2×D312yescomplemented
174#808—32no—
175C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
176C22×C3⋊D3—21no—
177C22×C3×D3—21no—
178C22×C3×D3C2×D411yescharacteristic
179C2×D32—24no—
180C2×D32—42no—
181C2×D32—42no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—21no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)#4112yes—
189C4×C3⋊D3—42no—
190#634—42no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—21no—
197C3×D12#4112yes—
198C3×C4×D3—21no—
199C3×C4×D3—21no—
200C3×C4×D3—41no—
201C3×C4×D3—42no—
202C3×C4×D3SD1614yescomplemented
203C3×Dic6—22no—
204C3×Dic6—22no—
205#626—24no—
206#624—42no—
207D3×Dic3—42no—
208D3×Dic3—42no—
209C32×C8—22no—
210C3×C3⋊C8—22no—
211#533—91no—
212C2×C4×D4—91no—
213#483—92no—
214#476—91no—
215#476—91no—
216#461—31no—
217#461—91no—
218#450—92no—
219C4×SD16—92no—
220C4×SD16—92no—
221#431—31no—
222C23×D3—61no—
223C23×D3—61no—
224C2×C3×Q8—32no—
225C2×C3×D4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—61no—
230C2×#67—61no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233D3×D4—62no—
234D3×D4—62no—
235C2×D12—31no—
236C2×D12—31no—
237C2×D12—61no—
238C2×D12—62no—
239C2×D12—61no—
240C2×D12—62no—
241C2×D12C22×D311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—121no—
250C2×C4×D3—124no—
251C2×C4×D3—124no—
252C2×C4×D3D1211yescharacteristic
253C2×C4×D3D1211yescharacteristic
254C2×C4×D3C22×D311yescharacteristic
255C2×Dic6—61no—
256C2×Dic6—61no—
257C2×Dic6—121no—
258C2×Dic6C22×D312yes—
259C3×SD16—64no—
260C2×C3×C8—22no—
261C2×C3×C8—32no—
262C2×C3×C8C22×D312yes—
263C2×C3×C8C22×D312yes—
264C3×C4⋊C4—31no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C22⋊C4—61no—
268C3×C42—21no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—31no—
272C3×C42C22×D311yescharacteristic
273C3×C42C22×D311yescharacteristic
274#217—62no—
275#217—61no—
276#215—64no—
277(C2×D3)⋊C4—21no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—61no—
284(C2×D3)⋊C4—121no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—32no—
288C4⋊Dic3—31no—
289C4⋊Dic3—32no—
290C4⋊Dic3—31no—
291C4⋊Dic3—61no—
292C4⋊Dic3—62no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3—61no—
296C4⋊Dic3—62no—
297C4⋊Dic3—121no—
298C4⋊Dic3C22×D311yescharacteristic
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301Dic3⋊C4—61no—
302Dic3⋊C4—62no—
303C4×Dic3—62no—
304C4×Dic3—62no—
305C4×Dic3D1211yescharacteristic
306C4×Dic3D1211yescharacteristic
307C4×Dic3C22×D311yescharacteristic
308C2×C3⋊C8C22×D312yes—
309#204—24no—
310#204—64no—
311C22×C32C22×D411yescharacteristic
312C2×C3⋊D3—22no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—41no—
315C2×C3×D3—21no—
316C2×C3×D3—21no—
317C2×C3×D3—22no—
318C2×C3×D3—41no—
319C2×C3×D3—41no—
320C2×C3×D3C2×SD1612yes—
321D32—48no—
322C32×C4—21no—
323C32×C4C2×SD1612yes—
324C32×C4C2×#4111yescharacteristic
325C32×C4C2×#4111yescharacteristic
326C3⋊Dic3—41no—
327C3⋊Dic3—42no—
328C3×Dic3—21no—
329C3×Dic3—21no—
330C3×Dic3—42no—
331C3×Dic3—41no—
332C3×Dic3C2×SD1612yes—
333C22×D4—91no—
334C23×C4—181no—
335C2×SD16—32no—
336C2×SD16—92no—
337C4⋊Q8—31no—
338C4⋊Q8—91no—
339#125—181no—
340C22⋊Q8—92no—
341C22⋊Q8—181no—
342C4×Q8—92no—
343C4×Q8—181no—
344C4×D4—31no—
345C4×D4—91no—
346C4×D4—91no—
347C4×D4—91no—
348C4×D4—181no—
349C4×D4—181no—
350#117—181no—
351C2×C4⋊C4—91no—
352C2×C22⋊C4—181no—
353C2×C42—31no—
354#106—92no—
355#106—92no—
356C4⋊C8—31no—
357C4⋊C8D3211yescharacteristic, complemented
358#103—32no—
359#103—92no—
360#102—92no—
361#102—92no—
362C22⋊C8—32no—
363C4×C8—32no—
364C23×C3—31no—
365C23×C3—61no—
366C22×D3—21no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—61no—
370C22×D3—61no—
371C22×D3—121no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3C2×D1211yescharacteristic
377C3×Q8—62no—
378C3×Q8—62no—
379C3×D4—32no—
380C3×D4—61no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—31no—
385C2×C3×C4—34no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—61no—
389C2×C3×C4—61no—
390C2×C3×C4—62no—
391C2×C3×C4—61no—
392C2×C3×C4—121no—
393C2×C3×C4—122no—
394C2×C3×C4C2×D1211yescharacteristic
395C2×C3×C4C2×D1211yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400#67—64no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—62no—
404C2×Dic3—61no—
405C2×Dic3—62no—
406C2×Dic3—61no—
407C2×Dic3—122no—
408C2×Dic3—121no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3C2×D1211yescharacteristic
412C2×Dic3C2×D1211yescharacteristic
413C2×Dic3C2×D1211yescharacteristic
414D12—21no—
415D12—32no—
416D12—32no—
417D12—62no—
418D12—64no—
419D12—61no—
420D12—61no—
421D12—121no—
422D12#23712yes—
423C4×D3—21no—
424C4×D3—21no—
425C4×D3—41no—
426C4×D3—42no—
427C4×D3—122no—
428C4×D3—122no—
429C4×D3—122no—
430C4×D3—122no—
431C4×D3—122no—
432C4×D3—122no—
433C4×D3—242no—
434C4×D3#20414yescomplemented
435Dic6—22no—
436Dic6—22no—
437Dic6—122no—
438Dic6—122no—
439Dic6—242no—
440C3×C8—22no—
441C3×C8—22no—
442C3×C8—42no—
443C3×C8—62no—
444C3⋊C8—22no—
445C2×C32#52511yescharacteristic
446C2×C32C22×SD1611yescharacteristic
447C2×C32#57511yescharacteristic
448C3⋊D3—42no—
449C3×D3—22no—
450C3×D3—42no—
451C24—181no—
452C2×Q8—32no—
453C2×Q8—181no—
454C2×D4—31no—
455C2×D4—91no—
456C2×D4—181no—
457C2×D4—182no—
458C2×D4—182no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—61no—
463C22×C4—181no—
464C22×C4—181no—
465C22×C4—181no—
466C22×C4—181no—
467C22×C4—364no—
468SD16—64no—
469SD16—184no—
470C2×C8—32no—
471C2×C8C2×D3212yes—
472C4⋊C4—31no—
473C4⋊C4—61no—
474C4⋊C4—61no—
475C4⋊C4—92no—
476C4⋊C4—91no—
477C4⋊C4—181no—
478C4⋊C4—182no—
479C4⋊C4—182no—
480C4⋊C4—181no—
481C22⋊C4—61no—
482C22⋊C4—181no—
483C22⋊C4—181no—
484C22⋊C4—182no—
485C22⋊C4—181no—
486C42—31no—
487C42—31no—
488C42—31no—
489C42—182no—
490C42C2×D3211yescharacteristic
491C22×C3—21no—
492C22×C3—32no—
493C22×C3—61no—
494C22×C3—61no—
495C22×C3—62no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3C22×D1211yescharacteristic
499C22×C3C2×D3×D411yescharacteristic
500C2×D3—21no—
501C2×D3—21no—
502C2×D3—22no—
503C2×D3—41no—
504C2×D3—41no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—122no—
508C2×D3—128no—
509C2×D3—128no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—121no—
513C2×D3—121no—
514C2×D3—241no—
515C2×D3—241no—
516C2×D3C2×#20412yes—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—22no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—32no—
523C3×C4—41no—
524C3×C4—61no—
525C3×C4—61no—
526C3×C4—121no—
527C3×C4—122no—
528C3×C4C2×#20412yes—
529C3×C4D3×SD1612yes—
530C3×C4C2×#23711yescharacteristic
531C3×C4D3×#4111yescharacteristic
532C3×C4D3×#4111yescharacteristic
533C3×C4D3×#4111yescharacteristic
534Dic3—21no—
535Dic3—21no—
536Dic3—41no—
537Dic3—42no—
538Dic3—121no—
539Dic3—122no—
540Dic3—121no—
541Dic3—122no—
542Dic3—242no—
543Dic3—241no—
544Dic3C2×#20412yes—
545C32#310111yescharacteristic, complemented, Sylow
546C23—31no—
547C23—61no—
548C23—184no—
549C23—181no—
550C23—362no—
551C23—362no—
552Q8—62no—
553Q8—62no—
554Q8—362no—
555D4—32no—
556D4—61no—
557D4—92no—
558D4—184no—
559D4—181no—
560C2×C4—31no—
561C2×C4—34no—
562C2×C4—31no—
563C2×C4—31no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—62no—
567C2×C4—61no—
568C2×C4—121no—
569C2×C4—122no—
570C2×C4—182no—
571C2×C4—181no—
572C2×C4—362no—
573C2×C4—362no—
574C2×C4—362no—
575C2×C4—362no—
576C2×C4D3×D1211yescharacteristic
577C2×C4D3×D1211yescharacteristic
578C2×C4C22×D3211yescharacteristic
579C8—22no—
580C8—62no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—62no—
585C2×C3—122no—
586C2×C3#552411yescharacteristic
587C2×C3#560611yescharacteristic
588C2×C3C22×#20411yescharacteristic
589C2×C3#574811yescharacteristic
590C2×C3C2×D3×SD1611yescharacteristic
591C2×C3#577711yescharacteristic
592D3—22no—
593D3—42no—
594D3—122no—
595D3—122no—
596D3—242no—
597C22—32no—
598C22—61no—
599C22—61no—
600C22—62no—
601C22—121no—
602C22—121no—
603C22—182no—
604C22—368no—
605C22—361no—
606C22—361no—
607C22C2×D3×D1211yescharacteristic
608C4—21no—
609C4—32no—
610C4—61no—
611C4—61no—
612C4—122no—
613C4—121no—
614C4—361no—
615C4—362no—
616C4D3×#20412yes—
617C4D3×#23711yescharacteristic
618C4#6431911yescharacteristic
619C3—21no—
620C3#7929811yescharacteristic, complemented
621C3#8040811yescharacteristic, complemented
622C2—62no—
623C2—122no—
624C2—362no—
625C2#1059462611yescharacteristic
626C2C2×D3×#20411yescharacteristic
627C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4⋊C8D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593859C2semidirect
3. #10592541C2semidirect
4. C3×#4841C2semidirect
5. C3×#4833C2semidirect
7. #10590792C2semidirect
8. Dic3×#204C2semidirect
9. #10590675C2semidirect
10. #10590379C2semidirect
11. #10590268C2semidirect
17. #64078C22semidirect
21. C3×#869C22semidirect
32. Dic3×Dic6C22semidirect
35. C32×C4⋊C8C22semidirect
37. #63644C22semidirect
39. C3×#816C22semidirect
40. C3×C8×Dic3C22semidirect
41. C3×C4⋊(C3⋊C8)C22semidirect
42. #63573C22semidirect
43. #63566C22semidirect
60. #4841D3semidirect
61. #4833D3semidirect
150. #869C2×D3semidirect
155. C3×C4⋊C8C2×D3semidirect
156. C3×C4⋊C8C2×D3semidirect
172. #816C2×D3semidirect
173. C8×Dic3C2×D3semidirect
175. C4⋊(C3⋊C8)C2×D3semidirect
202. C3×C4×D3SD16semidirect
357. C4⋊C8D32semidirect
434. C4×D3#204semidirect
545. C32#3101semidirect
620. C3#79298semidirect
621. C3#80408semidirect

Maximal subgroups

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

subgroupindex
C4×D3×D122
#105938592
#105925412
C3×#48412
C3×#48332
#105909422
#105907922
Dic3×#2042
#105906752
#105903792
#105902682
#804083
#792983