Finite Group Databasebeta

← #11858080

Subgroups — #11858080

Order 1152.

1527 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic, complemented
3C2×#63814C211yesmaximal, characteristic, complemented
4#10592924C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591557C212yesmaximal, complemented
7#10591556C212yesmaximal, complemented
8#10591550C212yesmaximal, complemented
9D3×#835C212yesmaximal, complemented
10#10591087C211yesmaximal, characteristic, complemented
11#10591084C211yesmaximal, characteristic, complemented
12#84111—31nomaximal
13#78790—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C3×#1007—24no—
16C3×#1007C418yescomplemented
17C2×C3×#239—21no—
18C2×C3×#239C2212yes—
19C2×C3×D3×Q8—21no—
20C2×C3×D3×Q8C2212yes—
21C2×C3×#235—22no—
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2211yescharacteristic
24#64135C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28Dic3×#67—22no—
29#63898—21no—
30D3×C4⋊Dic3C2212yes—
31#63843—21no—
32#63841C2212yes—
33C2×#3711C2212yes—
34#63814—24no—
35C2×D3×C3⋊C8C2212yes—
36#63662C2212yes—
37#63662C2212yes—
38C3×#835C2212yes—
39C3×#835C2212yes—
40#63566C2211yescharacteristic
41#63566C2211yescharacteristic
42#63565C2212yes—
43#63563C2211yescharacteristic
44#63563C2211yescharacteristic
45#63562C2212yes—
46C2×C3×2−1+4—31no—
47C2×#1007D311yescharacteristic
48#5827—31no—
49C2×#948—31no—
50C2×#901—31no—
51#5504—31no—
52C2×C3×#103—31no—
53#5233—31no—
54#5233—32no—
55#5232—31no—
56#5232—32no—
57#5225—31no—
58#5225—31no—
59#5225—32no—
60#5225—61no—
61C2×#835—32no—
62C2×#835D311yescharacteristic, complemented
63#5113—31no—
64#4966—31no—
65#4804—32no—
66#4803—32no—
67#4802—32no—
68D3×#103—32no—
69C2×C32×Q8—21no—
70C2×C32×Q8—22no—
71C2×C32×Q8C2×C414yescomplemented
72C2×C32×Q8C2312yes—
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×C3×#67—21no—
76C2×C3×#67D412yes—
77C22×C3×Dic3—21no—
78C3×#239—28no—
79C3×#239—24no—
80C3×#239C2×C418yescomplemented
81C3×D3×Q8—24no—
82C3×D3×Q8—28no—
83C3×D3×Q8C2×C418yescomplemented
84C3×#235—22no—
85C3×#235—216no—
86C3×#235C2×C414yes—
87C3×#235C2×C414yescomplemented
88C3×#235D414yes—
89C2×C3×D12—22no—
90C2×C3×D12D411yescharacteristic
91C2×C3×D12C2311yescharacteristic
92C2×C3×C4×D3—22no—
93C2×C3×C4×D3—21no—
94C2×C3×C4×D3—22no—
95C2×C3×C4×D3C2312yes—
96C2×C3×Dic6—22no—
97C2×C3×Dic6D411yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×D3×Dic3—22no—
100#3757—21no—
101C4⋊(C3⋊Dic3)C2311yescharacteristic
102C4⋊(C3⋊Dic3)C2311yescharacteristic
103C4×C3⋊Dic3—21no—
104#3748—22no—
105C2×C3⋊(C3⋊C8)C2312yes—
106C3×C4⋊Dic3—21no—
107C3×C4⋊Dic3C2312yes—
108C2×C3×C3⋊C8—22no—
109C2×C3×C3⋊C8C2311yescharacteristic
110C2×C3×C3⋊C8C2311yescharacteristic
111Dic3⋊Dic3—22no—
112(C2×D3)⋊Dic3—22no—
113Dic32—22no—
114#3711—24no—
115D3×C3⋊C8—24no—
116#2898—91noSylow
117C3×2−1+4—38no—
118C3×2−1+4—64no—
119C2×C3×#41—31no—
120C2×C3×#41—32no—
121C2×C3×#41—31no—
122C2×C3×#41—62no—
123C2×C3×#41—61no—
124C22×C3×Q8—21no—
125C22×C3×Q8—32no—
126C22×C3×Q8—61no—
127C22×C3×Q8C2×D311yescharacteristic
128C22×C3×Q8C2×D311yescharacteristic
129#1007—24no—
130#1007Dic318yescomplemented
131C2×#239—21no—
132C2×#239C2×D312yes—
133C2×D3×Q8—21no—
134C2×D3×Q8C2×D312yes—
135C2×#235—22no—
136C2×#235C2×D311yescharacteristic
137C2×#235C2×D311yescharacteristic
138C22×C3×C8—31no—
139C2×C3×C4⋊C4—31no—
140#948—64no—
141Q8×Dic3—61no—
142D4×Dic3—61no—
143D4×Dic3—62no—
144C4×#67—62no—
145#926—31no—
146#926—31no—
147#926—32no—
148#926—61no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×#208—31no—
152C2×#208—31no—
153C2×#208—32no—
154C2×#208—61no—
155C22×C3⋊C8—32no—
156C22×C3⋊C8C2×D311yescharacteristic
157#901—64no—
158C2×ΓL(1,𝔽25)—32no—
159C2×D3×C8—32no—
160#893—61no—
161#892—32no—
162D3×C4⋊C4—32no—
163#887—61no—
164C3×#103—32no—
165C3×#103—32no—
166#835—32no—
167#835—32no—
168#835—32no—
169#835—32no—
170#835—32no—
171#835—31no—
172#835—31no—
173#835—62no—
174#835—62no—
175#835C2×D312yes—
176#835C2×D312yes—
177#832—32no—
178#832—31no—
179#832—31no—
180#821—31no—
181#821—31no—
182#816—31no—
183#816—31no—
184#810—32no—
185#809—32no—
186C23×C32C2×D411yescharacteristic
187C22×C3×D3—21no—
188C22×C3×D3C2×D412yes—
189C32×Q8—24no—
190C32×Q8—22no—
191C32×Q8C22×C414yes—
192C2×C32×C4—24no—
193C2×C32×C4—22no—
194C2×C32×C4C22×C412yes—
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2×D412yes—
197C2×C32×C4C2411yescharacteristic
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C3×#67—24no—
201C3×#67C22⋊C418yes—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—81no—
205C2×C3×Dic3C2×D412yes—
206C3×D12—28no—
207C3×D12—21no—
208C3×D12C22⋊C414yes—
209C3×D12C22×C412yes—
210C3×C4×D3—28no—
211C3×C4×D3—24no—
212C3×C4×D3—28no—
213C3×C4×D3C22×C414yes—
214C3×C4×D3C2×D414yes—
215C3×Dic6—21no—
216C3×Dic6—28no—
217C3×Dic6C22⋊C414yes—
218C3×Dic6C22×C412yes—
219D3×Dic3—82no—
220C3⋊(C3⋊C8)—22no—
221C3×C3⋊C8—21no—
222C3×C3⋊C8—21no—
223C2×2−1+4—31no—
224C2×#131—91no—
225#520—91no—
226#419—92no—
227#419—91no—
228#417—92no—
229#417—91no—
230#416—92no—
231#416—91no—
232C2×#103—31no—
233C2×#103—92no—
234C3×#41—34no—
235C3×#41—34no—
236C3×#41—38no—
237C3×#41—34no—
238C3×#41—616no—
239C3×#41—64no—
240C3×#41—68no—
241C3×#41—62no—
242C2×C3×Q8—21no—
243C2×C3×Q8—22no—
244C2×C3×Q8—21no—
245C2×C3×Q8—22no—
246C2×C3×Q8—24no—
247C2×C3×Q8—22no—
248C2×C3×Q8—31no—
249C2×C3×Q8—38no—
250C2×C3×Q8—31no—
251C2×C3×Q8—41no—
252C2×C3×Q8—42no—
253C2×C3×Q8—62no—
254C2×C3×Q8—64no—
255C2×C3×Q8—68no—
256C2×C3×Q8C4×D314yescomplemented
257C2×C3×Q8C2×Dic314yescomplemented
258C2×C3×Q8C22×D312yes—
259C2×C3×Q8C22×D312yes—
260C2×C3×D4—32no—
261C2×C3×D4—31no—
262C2×C3×D4—31no—
263C2×C3×D4—62no—
264C2×C3×D4—61no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—32no—
269C22×C3×C4—41no—
270C22×C3×C4—62no—
271C22×C3×C4—62no—
272C22×C3×C4—61no—
273C22×C3×C4—61no—
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D311yescharacteristic
276C2×#67—21no—
277C2×#67#6712yes—
278C22×Dic3—21no—
279C22×Dic3—62no—
280#239—28no—
281#239—24no—
282#239C2×Dic318yescomplemented
283D3×Q8—24no—
284D3×Q8—28no—
285D3×Q8C2×Dic318yescomplemented
286#235—22no—
287#235—216no—
288#235C2×Dic314yes—
289#235C2×Dic314yescomplemented
290#235#6714yes—
291C2×D12—22no—
292C2×D12#6711yescharacteristic
293C2×D12C22×D311yescharacteristic
294C2×C4×D3—22no—
295C2×C4×D3—21no—
296C2×C4×D3—22no—
297C2×C4×D3—62no—
298C2×C4×D3C22×D312yes—
299C2×Dic6—22no—
300C2×Dic6#6711yescharacteristic
301C2×Dic6C22×D311yescharacteristic
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C2×C3×C8—62no—
305C3×C4⋊C4—32no—
306C3×C4⋊C4—61no—
307#217—62no—
308#217—61no—
309#217—61no—
310#217—121no—
311(C2×D3)⋊C4—62no—
312C4⋊Dic3—21no—
313C4⋊Dic3—31no—
314C4⋊Dic3—31no—
315C4⋊Dic3—31no—
316C4⋊Dic3—31no—
317C4⋊Dic3—61no—
318C4⋊Dic3—61no—
319C4⋊Dic3—62no—
320C4⋊Dic3C22×D312yes—
321Dic3⋊C4—62no—
322C4×Dic3—62no—
323C4×Dic3—61no—
324C4×Dic3—61no—
325C4×Dic3—62no—
326C4×Dic3—121no—
327#208—64no—
328#208—62no—
329#208—62no—
330#208—122no—
331C2×C3⋊C8—22no—
332C2×C3⋊C8—32no—
333C2×C3⋊C8—32no—
334C2×C3⋊C8—62no—
335C2×C3⋊C8—64no—
336C2×C3⋊C8C22×D311yescharacteristic
337C2×C3⋊C8C22×D311yescharacteristic
338ΓL(1,𝔽25)—64no—
339D3×C8—64no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32C2×C22⋊C412yes—
343C22×C32C22×D411yescharacteristic
344C2×C3×D3—22no—
345C2×C3×D3—22no—
346C2×C3×D3—22no—
347C2×C3×D3—41no—
348C2×C3×D3—41no—
349C2×C3×D3C2×C22⋊C414yes—
350C32×C4—24no—
351C32×C4C2×C22⋊C412yes—
352C32×C4C23×C411yescharacteristic
353C32×C4C22×D411yescharacteristic
354C3⋊Dic3—41no—
355C3⋊Dic3—41no—
356C3×Dic3—22no—
357C3×Dic3—42no—
358C3×Dic3C2×C22⋊C414yes—
3592−1+4—38no—
3602−1+4—64no—
361C2×#41—31no—
362C2×#41—32no—
363C2×#41—31no—
364C2×#41—62no—
365C2×#41—61no—
366C22×Q8—32no—
367C22×Q8—61no—
368C22×Q8D3211yescharacteristic
369#131—184no—
370C2×M16—92no—
371C2×M16—91no—
372C22×C8—31no—
373C22×C8—92no—
374C4×Q8—181no—
375C4×D4—181no—
376C4×D4—182no—
377#117—92no—
378#117—91no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—92no—
381#103—32no—
382#103—32no—
383#103—92no—
384#103—91no—
385#103—91no—
386#103—92no—
387#103—92no—
388#102—92no—
389#102—91no—
390#102—91no—
391C23×C3—21no—
392C23×C3—32no—
393C23×C3—61no—
394C23×C3D3×D411yescharacteristic
395C23×C3C2×#6711yescharacteristic
396C22×D3—21no—
397C22×D3C2×#6712yes—
398C3×Q8—24no—
399C3×Q8—24no—
400C3×Q8—22no—
401C3×Q8—22no—
402C3×Q8—24no—
403C3×Q8—34no—
404C3×Q8—32no—
405C3×Q8—42no—
406C3×Q8—44no—
407C3×Q8—68no—
408C3×Q8—61no—
409C3×Q8C2×C4×D314yes—
410C3×Q8C22×Dic314yes—
411C3×D4—38no—
412C3×D4—34no—
413C3×D4—32no—
414C3×D4—68no—
415C3×D4—64no—
416C3×D4—61no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—21no—
425C2×C3×C4—32no—
426C2×C3×C4—34no—
427C2×C3×C4—34no—
428C2×C3×C4—42no—
429C2×C3×C4—44no—
430C2×C3×C4—68no—
431C2×C3×C4—68no—
432C2×C3×C4—61no—
433C2×C3×C4—64no—
434C2×C3×C4—62no—
435C2×C3×C4—241no—
436C2×C3×C4C2×C4×D312yes—
437C2×C3×C4D3×D411yescharacteristic
438C2×C3×C4D3×D412yes—
439C2×C3×C4C22×Dic312yes—
440C2×C3×C4C2×#6711yescharacteristic
441C2×C3×C4C2×#6712yes—
442C2×C3×C4C23×D311yescharacteristic
443C2×C3×C4C23×D311yescharacteristic
444#67—24no—
445#67#21718yes—
446C2×Dic3—21no—
447C2×Dic3—22no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452C2×Dic3—81no—
453C2×Dic3—121no—
454C2×Dic3—121no—
455C2×Dic3—242no—
456C2×Dic3C2×#6712yes—
457D12—28no—
458D12—21no—
459D12#21714yes—
460D12C22×Dic312yes—
461C4×D3—28no—
462C4×D3—24no—
463C4×D3—28no—
464C4×D3—242no—
465C4×D3C22×Dic314yes—
466C4×D3C2×#6714yes—
467Dic6—21no—
468Dic6—28no—
469Dic6#21714yes—
470Dic6C22×Dic312yes—
471C3×C8—61no—
472C3×C8—61no—
473C3⋊C8—21no—
474C3⋊C8—21no—
475C3⋊C8—62no—
476C3⋊C8—62no—
477C3⋊C8—122no—
478C2×C32—22no—
479C2×C32C22×C22⋊C411yescharacteristic
480C2×C32#57711yescharacteristic
481C2×C32#57811yescharacteristic
482C3×D3—24no—
483C3×D3—42no—
484#41—34no—
485#41—34no—
486#41—38no—
487#41—34no—
488#41—616no—
489#41—64no—
490#41—68no—
491#41—62no—
492C2×Q8—21no—
493C2×Q8—22no—
494C2×Q8—31no—
495C2×Q8—38no—
496C2×Q8—31no—
497C2×Q8—62no—
498C2×Q8—64no—
499C2×Q8—68no—
500C2×Q8D3×Dic314yescomplemented
501C2×Q8C2×D3212yes—
502C2×D4—32no—
503C2×D4—31no—
504C2×D4—31no—
505C2×D4—62no—
506C2×D4—61no—
507C22×C4—21no—
508C22×C4—32no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—182no—
514C22×C4C2×D3211yescharacteristic
515M16—184no—
516M16—182no—
517C2×C8—31no—
518C2×C8—31no—
519C2×C8—62no—
520C2×C8—92no—
521C2×C8—184no—
522C4⋊C4—32no—
523C4⋊C4—61no—
524C4⋊C4—91no—
525C4⋊C4—91no—
526C4⋊C4—182no—
527C22⋊C4—182no—
528C22⋊C4—181no—
529C42—182no—
530C42—181no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—22no—
537C22×C3—34no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—62no—
541C22×C3—62no—
542C22×C3—62no—
543C22×C3—121no—
544C22×C3—121no—
545C22×C3D3×C22⋊C412yes—
546C22×C3C2×#21712yes—
547C22×C3C2×D3×D411yescharacteristic
548C22×C3C22×#6711yescharacteristic
549C2×D3—22no—
550C2×D3—22no—
551C2×D3—22no—
552C2×D3—41no—
553C2×D3—41no—
554C2×D3C2×#21714yes—
555C3×C4—24no—
556C3×C4—24no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—22no—
560C3×C4—34no—
561C3×C4—44no—
562C3×C4—62no—
563C3×C4—122no—
564C3×C4D3×C22⋊C412yes—
565C3×C4C2×#21712yes—
566C3×C4C22×C4×D311yescharacteristic
567C3×C4C2×D3×D411yescharacteristic
568C3×C4C23×Dic311yescharacteristic
569C3×C4C22×#6711yescharacteristic
570Dic3—22no—
571Dic3—42no—
572Dic3—121no—
573Dic3—121no—
574Dic3—121no—
575Dic3—121no—
576Dic3—241no—
577Dic3—241no—
578Dic3C2×#21714yes—
579C32#289811yescharacteristic, complemented, Sylow
580C23—32no—
581C23—61no—
582C23D3×#6711yescharacteristic
583Q8—22no—
584Q8—24no—
585Q8—34no—
586Q8—32no—
587Q8—68no—
588Q8—61no—
589Q8C2×D3×Dic314yes—
590D4—38no—
591D4—32no—
592D4—34no—
593D4—68no—
594D4—64no—
595D4—61no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—32no—
599C2×C4—34no—
600C2×C4—34no—
601C2×C4—68no—
602C2×C4—68no—
603C2×C4—61no—
604C2×C4—64no—
605C2×C4—62no—
606C2×C4—181no—
607C2×C4—181no—
608C2×C4—241no—
609C2×C4—722no—
610C2×C4C2×D3×Dic312yes—
611C2×C4D3×#6712yes—
612C2×C4D3×#6711yescharacteristic
613C2×C4C22×D3211yescharacteristic
614C8—61no—
615C8—61no—
616C8—182no—
617C2×C3—22no—
618C2×C3—22no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—42no—
623C2×C3—64no—
624C2×C3—122no—
625C2×C3C2×D3×C22⋊C411yescharacteristic
626C2×C3#576211yescharacteristic
627C2×C3#576611yescharacteristic
628C2×C3#583711yescharacteristic
629C2×C3#583811yescharacteristic
630C2×C3C22×#21711yescharacteristic
631D3—24no—
632D3—42no—
633C22—21no—
634C22—21no—
635C22—34no—
636C22—62no—
637C22—62no—
638C22—62no—
639C22—121no—
640C22—121no—
641C22D3×#21712yes—
642C22C2×D3×#6711yescharacteristic
643C4—24no—
644C4—34no—
645C4—62no—
646C4—122no—
647C4—361no—
648C4—361no—
649C4D3×#21712yes—
650C4C22×D3×Dic311yescharacteristic
651C4C2×D3×#6711yescharacteristic
652C3—21no—
653C3#7879011yescharacteristic, complemented
654C3#8411111yescharacteristic, complemented
655C2—22no—
656C2—64no—
657C2—122no—
658C2#1059531811yescharacteristic
659C2#1059532711yescharacteristic
660C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#1007C2
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32#2898
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #10594986C2semidirect
3. C2×#63814C2semidirect
4. #10592924C2semidirect
5. C2×C3×#835C2semidirect
6. #10591557C2semidirect
7. #10591556C2semidirect
8. #10591550C2semidirect
9. D3×#835C2semidirect
10. #10591087C2semidirect
11. #10591084C2semidirect
16. C3×#1007C4semidirect
62. C2×#835D3semidirect
71. C2×C32×Q8C2×C4semidirect
80. C3×#239C2×C4semidirect
83. C3×D3×Q8C2×C4semidirect
87. C3×#235C2×C4semidirect
130. #1007Dic3semidirect
256. C2×C3×Q8C4×D3semidirect
257. C2×C3×Q8C2×Dic3semidirect
282. #239C2×Dic3semidirect
285. D3×Q8C2×Dic3semidirect
289. #235C2×Dic3semidirect
500. C2×Q8D3×Dic3semidirect
579. C32#2898semidirect
653. C3#78790semidirect
654. C3#84111semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
#105949862
C2×#638142
#105929242
C2×C3×#8352
#105915572
#105915562
#105915502
D3×#8352
#105910872
#105910842
#841113
#787903