Finite Group Databasebeta

← #11858075

Subgroups — #11858075

Order 1152.

1533 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×#64298C211yesmaximal, characteristic
2C3×#5504C211yesmaximal, characteristic, complemented
3C2×#63815C211yesmaximal, characteristic, complemented
4C2×#63637C211yesmaximal, characteristic, complemented
5C3×#4966C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590608C212yesmaximal, complemented
9#10590607C212yesmaximal, complemented
10#10590600C212yesmaximal, complemented
11D3×#810C212yesmaximal, complemented
12#82570—31nomaximal
13#78883—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C2×#3805—22no—
18#64298—24no—
19#64298C418yescomplemented
20C2×#3795—21no—
21C2×#3795C2212yes—
22C2×D3×Dic6—21no—
23C2×D3×Dic6C2212yes—
24C2×C32×C4⋊C4C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×#67—22no—
27C3×#926C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C3×#893—21no—
30C3×#892C2212yes—
31C3×D3×C4⋊C4C2212yes—
32C3×#887—21no—
33C2×#3711C2212yes—
34#63815—24no—
35C2×D3×C3⋊C8C2212yes—
36#63637C2212yes—
37#63637C2212yes—
38C3×#810C2212yes—
39C3×#809C2212yes—
40#63567C2212yes—
41#63567C2212yes—
42#63565C2211yescharacteristic
43#63565C2211yescharacteristic
44#63562C2211yescharacteristic
45#63562C2211yescharacteristic
46C2×#1010—31no—
47C2×#1010—31no—
48C3×#520—31no—
49C2×#948—31no—
50C2×#907—31no—
51#5504D311yescharacteristic, complemented
52C3×#417—31no—
53#5233—31no—
54#5120—31no—
55#5004—31no—
56#5004—32no—
57#5002—31no—
58#5002—32no—
59C2×#810—31no—
60C2×#810—31no—
61C2×#810—32no—
62C2×#810—61no—
63#4966—32no—
64#4966D311yescharacteristic, complemented
65#4802—32no—
66D3×#103—32no—
67#4772—32no—
68#4771—32no—
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C2×#634—21no—
73C2×#634—22no—
74C2×#634C2×C414yescomplemented
75C2×#634C2312yes—
76C2×C3×#67—21no—
77C2×C3×#67D412yes—
78C3×#235—22no—
79C3×#235C2×C414yes—
80C3×#235C2×C414yescomplemented
81C3×#235D414yes—
82C2×C3×D12D411yescharacteristic
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3C2312yes—
87C2×C3×Dic6D411yescharacteristic
88C2×C3×Dic6C2311yescharacteristic
89C2×#627—22no—
90C2×#625—22no—
91#3805—216no—
92C2×D3×Dic3—22no—
93C2×D3×Dic3—22no—
94#3795—28no—
95#3795—24no—
96#3795C2×C418yescomplemented
97D3×Dic6—24no—
98D3×Dic6—28no—
99D3×Dic6C2×C418yescomplemented
100C32×C4⋊C4—21no—
101C32×C4⋊C4C2312yes—
102C2×C3⋊(C3⋊C8)—22no—
103C2×C3⋊(C3⋊C8)C2311yescharacteristic
104C2×C3⋊(C3⋊C8)C2311yescharacteristic
105C3×#217—21no—
106C3×(C2×D3)⋊C4—22no—
107C3×C4⋊Dic3C2311yescharacteristic
108C3×C4⋊Dic3C2311yescharacteristic
109C3×Dic3⋊C4—22no—
110C3×C4×Dic3—21no—
111C3×C4×Dic3—22no—
112C3×#208—22no—
113C2×C3×C3⋊C8C2312yes—
114#3711—24no—
115D3×C3⋊C8—24no—
116#2898—91noSylow
117C2×C3×#41—31no—
118C2×C3×#41—31no—
119#1010—38no—
120#1010—38no—
121#1010—64no—
122#1010—64no—
123C2×D3×Q8—32no—
124C2×D3×Q8—61no—
125C2×#237—32no—
126C2×#237—61no—
127C2×#237—62no—
128C2×#237—62no—
129C2×#235—32no—
130C2×#235—61no—
131C2×#235C2×D311yescharacteristic
132C2×#235C2×D311yescharacteristic
133C22×Dic6—31no—
134C22×Dic6—31no—
135C22×Dic6—32no—
136C22×Dic6—61no—
137C22×Dic6—61no—
138C2×C3×M16—31no—
139C3×C4×Q8—61no—
140C3×C4×D4—61no—
141C3×C4×D4—62no—
142C3×#117—31no—
143C3×#117—32no—
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4C2×D311yescharacteristic
147C2×C3×C4⋊C4C2×D311yescharacteristic
148#948—64no—
149C4×#67—22no—
150#926C2×D311yescharacteristic
151C2×#208—32no—
152C2×#208C2×D311yescharacteristic
153C22×C3⋊C8—31no—
154C22×C3⋊C8—31no—
155C22×C3⋊C8—32no—
156C22×C3⋊C8—61no—
157#907—64no—
158C2×ΓL(1,𝔽25)—32no—
159C2×D3×C8—32no—
160#893—21no—
161#892C2×D312yes—
162D3×C4⋊C4C2×D312yes—
163#887—21no—
164C3×#103—32no—
165C3×#102—32no—
166#835—31no—
167#835—31no—
168#832—31no—
169#832—31no—
170#816—32no—
171#816—32no—
172#810—31no—
173#810—31no—
174#810—32no—
175#810—32no—
176#810—32no—
177#810—32no—
178#810—32no—
179#810—32no—
180#810—62no—
181#810—62no—
182#810C2×D312yes—
183#809—31no—
184#809—31no—
185#809C2×D312yes—
186C23×C32C2×D411yescharacteristic
187C22×C3×D3—21no—
188C22×C3×D3C2×D412yes—
189C2×C32×C4—22no—
190C2×C32×C4—81no—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2411yescharacteristic
195C2×C3⋊Dic3—24no—
196C2×C3⋊Dic3—22no—
197#634—24no—
198#634—22no—
199#634C22×C414yes—
200C3×#67—24no—
201C3×#67C22⋊C418yes—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3C2×D412yes—
206C3×D12—21no—
207C3×D12C22⋊C414yes—
208C3×D12C22×C412yes—
209C3×C4×D3—24no—
210C3×C4×D3—82no—
211C3×C4×D3C22×C414yes—
212C3×C4×D3C2×D414yes—
213C3×Dic6—21no—
214C3×Dic6C22⋊C414yes—
215C3×Dic6C22×C412yes—
216#627—28no—
217#625—28no—
218D3×Dic3—28no—
219D3×Dic3—28no—
220C3⋊(C3⋊C8)—21no—
221C3⋊(C3⋊C8)—21no—
222C3×C3⋊C8—22no—
223C2×2−1+4—91no—
224C2×#131—91no—
225#520—31no—
226#419—92no—
227#419—91no—
228#417—31no—
229#417—92no—
230#416—92no—
231#416—91no—
232C2×#103—92no—
233C2×#103—91no—
234C3×#41—34no—
235C3×#41—34no—
236C3×#41—34no—
237C3×#41—62no—
238C2×C3×Q8—31no—
239C2×C3×Q8—31no—
240C2×C3×D4—32no—
241C2×C3×D4—31no—
242C2×C3×D4—31no—
243C2×C3×D4—61no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—32no—
248C22×C3×C4—41no—
249C22×C3×C4—62no—
250C22×C3×C4—61no—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C2×#67—21no—
254C2×#67—62no—
255C2×#67—62no—
256C2×#67#6712yes—
257C22×Dic3—62no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—62no—
261C22×Dic3—121no—
262D3×Q8—38no—
263D3×Q8—68no—
264D3×Q8—64no—
265#237—38no—
266#237—68no—
267#237—616no—
268#237—616no—
269#237—64no—
270#235—22no—
271#235—38no—
272#235—64no—
273#235—68no—
274#235C4×D314yes—
275#235C4×D314yescomplemented
276#235D1214yes—
277C2×D12#6711yescharacteristic
278C2×D12C22×D311yescharacteristic
279C2×C4×D3—21no—
280C2×C4×D3—22no—
281C2×C4×D3—62no—
282C2×C4×D3—62no—
283C2×C4×D3C22×D312yes—
284C2×Dic6—34no—
285C2×Dic6—34no—
286C2×Dic6—32no—
287C2×Dic6—32no—
288C2×Dic6—38no—
289C2×Dic6—62no—
290C2×Dic6—64no—
291C2×Dic6—64no—
292C2×Dic6—62no—
293C2×Dic6—62no—
294C2×Dic6—61no—
295C2×Dic6—62no—
296C2×Dic6—61no—
297C2×Dic6—62no—
298C2×Dic6—68no—
299C2×Dic6—122no—
300C2×Dic6—121no—
301C2×Dic6#6711yescharacteristic
302C2×Dic6C22×D311yescharacteristic
303C3×M16—62no—
304C2×C3×C8—32no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—22no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—41no—
311C3×C4⋊C4—62no—
312C3×C4⋊C4C22×D312yes—
313C3×C4⋊C4C22×D312yes—
314C3×C22⋊C4—62no—
315C3×C22⋊C4—61no—
316C3×C42—62no—
317C3×C42—61no—
318#217—21no—
319(C2×D3)⋊C4—22no—
320C4⋊Dic3C22×D311yescharacteristic
321C4⋊Dic3C22×D311yescharacteristic
322Dic3⋊C4—22no—
323C4×Dic3—21no—
324C4×Dic3—22no—
325#208—22no—
326#208—64no—
327C2×C3⋊C8—31no—
328C2×C3⋊C8—31no—
329C2×C3⋊C8—31no—
330C2×C3⋊C8—31no—
331C2×C3⋊C8—61no—
332C2×C3⋊C8—61no—
333C2×C3⋊C8—64no—
334C2×C3⋊C8—62no—
335C2×C3⋊C8—62no—
336C2×C3⋊C8—122no—
337C2×C3⋊C8C22×D312yes—
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—42no—
351C32×C4C2×C22⋊C412yes—
352C32×C4C23×C411yescharacteristic
353C32×C4C22×D411yescharacteristic
354C3⋊Dic3—24no—
355C3×Dic3—22no—
356C3×Dic3—41no—
357C3×Dic3—41no—
358C3×Dic3C2×C22⋊C414yes—
3592−1+4—98no—
3602−1+4—184no—
361C2×#41—31no—
362C2×#41—31no—
363C2×#41—92no—
364C2×#41—181no—
365C2×#41—182no—
366C22×Q8—92no—
367C22×Q8—91no—
368C22×Q8—181no—
369#131—184no—
370C2×M16—31no—
371C2×M16—92no—
372C22×C8—92no—
373C22×C8—91no—
374C4×Q8—61no—
375C4×D4—61no—
376C4×D4—62no—
377#117—31no—
378#117—32no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4D3211yescharacteristic
381#103—32no—
382#103—92no—
383#103—92no—
384#103—91no—
385#103—91no—
386#103—92no—
387#103—92no—
388#102—32no—
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—34no—
399C3×Q8—32no—
400C3×Q8—61no—
401C3×D4—38no—
402C3×D4—34no—
403C3×D4—32no—
404C3×D4—64no—
405C3×D4—61no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—32no—
413C2×C3×C4—34no—
414C2×C3×C4—34no—
415C2×C3×C4—42no—
416C2×C3×C4—61no—
417C2×C3×C4—64no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—81no—
421C2×C3×C4—81no—
422C2×C3×C4—82no—
423C2×C3×C4—242no—
424C2×C3×C4C2×C4×D312yes—
425C2×C3×C4C2×C4×D312yes—
426C2×C3×C4C2×D1212yes—
427C2×C3×C4D3×D412yes—
428C2×C3×C4D3×D411yescharacteristic
429C2×C3×C4C2×#6711yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431C2×C3×C4C23×D311yescharacteristic
432#67—24no—
433#67—68no—
434#67—68no—
435#67(C2×D3)⋊C418yes—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—68no—
440C2×Dic3—64no—
441C2×Dic3—64no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—68no—
445C2×Dic3—122no—
446C2×Dic3—124no—
447C2×Dic3C2×#6712yes—
448D12—21no—
449D12(C2×D3)⋊C414yes—
450D12C2×C4×D312yes—
451C4×D3—24no—
452C4×D3—68no—
453C4×D3—68no—
454C4×D3—82no—
455C4×D3C2×C4×D314yes—
456C4×D3C2×D1214yes—
457Dic6—21no—
458Dic6—34no—
459Dic6—34no—
460Dic6—64no—
461Dic6—68no—
462Dic6—64no—
463Dic6—64no—
464Dic6—62no—
465Dic6—62no—
466Dic6—68no—
467Dic6—122no—
468Dic6—124no—
469Dic6(C2×D3)⋊C414yes—
470Dic6C2×C4×D312yes—
471C3×C8—62no—
472C3⋊C8—22no—
473C3⋊C8—61no—
474C3⋊C8—61no—
475C3⋊C8—61no—
476C3⋊C8—61no—
477C3⋊C8—121no—
478C3⋊C8—121no—
479C2×C32—22no—
480C2×C32C22×C22⋊C411yescharacteristic
481C2×C32#57711yescharacteristic
482C2×C32#57811yescharacteristic
483C3×D3—24no—
484C3×D3—42no—
485#41—34no—
486#41—34no—
487#41—34no—
488#41—62no—
489#41—98no—
490#41—184no—
491#41—188no—
492#41—1816no—
493C2×Q8—31no—
494C2×Q8—31no—
495C2×Q8—98no—
496C2×Q8—92no—
497C2×Q8—94no—
498C2×Q8—182no—
499C2×Q8—184no—
500C2×Q8—188no—
501C2×Q8—182no—
502C2×Q8—181no—
503C2×D4—32no—
504C2×D4—31no—
505C2×D4—31no—
506C2×D4—61no—
507C2×D4—182no—
508C22×C4—21no—
509C22×C4—32no—
510C22×C4—62no—
511C22×C4—61no—
512C22×C4—182no—
513C22×C4—182no—
514C22×C4—181no—
515C22×C4C2×D3211yescharacteristic
516M16—62no—
517M16—184no—
518C2×C8—32no—
519C2×C8—91no—
520C2×C8—91no—
521C2×C8—184no—
522C2×C8—182no—
523C4⋊C4—21no—
524C4⋊C4—31no—
525C4⋊C4—31no—
526C4⋊C4—62no—
527C4⋊C4C2×D3212yes—
528C22⋊C4—62no—
529C22⋊C4—61no—
530C42—62no—
531C42—61no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—22no—
540C22×C3—34no—
541C22×C3—62no—
542C22×C3—62no—
543C22×C3—62no—
544C22×C3—121no—
545C22×C3—121no—
546C22×C3D3×C22⋊C412yes—
547C22×C3C2×(C2×D3)⋊C412yes—
548C22×C3C2×D3×D411yescharacteristic
549C22×C3C22×#6711yescharacteristic
550C2×D3—22no—
551C2×D3—22no—
552C2×D3—22no—
553C2×D3—41no—
554C2×D3—41no—
555C2×D3C2×(C2×D3)⋊C414yes—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—22no—
559C3×C4—34no—
560C3×C4—42no—
561C3×C4—42no—
562C3×C4—62no—
563C3×C4—82no—
564C3×C4—121no—
565C3×C4—121no—
566C3×C4D3×C22⋊C412yes—
567C3×C4C2×(C2×D3)⋊C412yes—
568C3×C4C22×C4×D311yescharacteristic
569C3×C4C22×C4×D311yescharacteristic
570C3×C4C22×D1211yescharacteristic
571C3×C4C2×D3×D411yescharacteristic
572Dic3—22no—
573Dic3—41no—
574Dic3—41no—
575Dic3—64no—
576Dic3—64no—
577Dic3—124no—
578Dic3C2×(C2×D3)⋊C414yes—
579C32#289811yescharacteristic, complemented, Sylow
580C23—32no—
581C23—61no—
582C23D3×#6711yescharacteristic
583Q8—34no—
584Q8—32no—
585Q8—61no—
586Q8—94no—
587Q8—188no—
588Q8—182no—
589Q8—184no—
590D4—38no—
591D4—32no—
592D4—34no—
593D4—64no—
594D4—61no—
595D4—188no—
596C2×C4—22no—
597C2×C4—32no—
598C2×C4—34no—
599C2×C4—34no—
600C2×C4—61no—
601C2×C4—64no—
602C2×C4—61no—
603C2×C4—61no—
604C2×C4—81no—
605C2×C4—188no—
606C2×C4—188no—
607C2×C4—182no—
608C2×C4—184no—
609C2×C4—242no—
610C2×C4C4×D3212yes—
611C2×C4D3×D1212yes—
612C2×C4D3×#6711yescharacteristic
613C2×C4C22×D3211yescharacteristic
614C8—62no—
615C8—181no—
616C8—181no—
617C2×C3—24no—
618C2×C3—22no—
619C2×C3—22no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—64no—
624C2×C3—122no—
625C2×C3C2×D3×C22⋊C411yescharacteristic
626C2×C3#577511yescharacteristic
627C2×C3#577911yescharacteristic
628C2×C3C22×(C2×D3)⋊C411yescharacteristic
629C2×C3#583611yescharacteristic
630C2×C3#583811yescharacteristic
631D3—24no—
632D3—42no—
633C22—21no—
634C22—21no—
635C22—34no—
636C22—62no—
637C22—62no—
638C22—62no—
639C22—121no—
640C22—121no—
641C22D3×(C2×D3)⋊C412yes—
642C22C2×D3×#6711yescharacteristic
643C4—34no—
644C4—42no—
645C4—62no—
646C4—121no—
647C4—121no—
648C4—184no—
649C4D3×(C2×D3)⋊C412yes—
650C4C2×C4×D3211yescharacteristic
651C4C2×D3×D1211yescharacteristic
652C3—21no—
653C3#7888311yescharacteristic, complemented
654C3#8257011yescharacteristic, complemented
655C2—22no—
656C2—64no—
657C2—122no—
658C2C2×D3×(C2×D3)⋊C411yescharacteristic
659C2#1059510611yescharacteristic
660C2#1059532811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×#64298C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2898
LCSG ▷ 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
2. C3×#5504C2semidirect
3. C2×#63815C2semidirect
4. C2×#63637C2semidirect
5. C3×#4966C2semidirect
6. #10591107C2semidirect
7. #10591083C2semidirect
8. #10590608C2semidirect
9. #10590607C2semidirect
10. #10590600C2semidirect
11. D3×#810C2semidirect
19. #64298C4semidirect
51. #5504D3semidirect
64. #4966D3semidirect
74. C2×#634C2×C4semidirect
80. C3×#235C2×C4semidirect
96. #3795C2×C4semidirect
99. D3×Dic6C2×C4semidirect
275. #235C4×D3semidirect
579. C32#2898semidirect
653. C3#78883semidirect
654. C3#82570semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C3×#55042
C2×#638152
C2×#636372
C3×#49662
#105911072
#105910832
#105906082
#105906072
#105906002
D3×#8102
#825703
#788833