Finite Group Databasebeta

← #11900896

Subgroups — #11900896

Order 1152.

2579 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C2×C3×C42×D3C211yesmaximal, characteristic, complemented
3C3×#5470C211yesmaximal, characteristic, complemented
4#10595023C212yesmaximal, complemented
5#10595005C214yesmaximal, complemented
6#10594955C214yesmaximal, complemented
7#10594954C212yesmaximal, complemented
8#10593976C214yesmaximal, complemented
9#10593970C212yesmaximal, complemented
10C4×#3799C214yesmaximal, complemented
11#10593870C214yesmaximal, complemented
12#10593859C212yesmaximal, complemented
13#86257—31nomaximal
14#85680—31nomaximal
15C2×#3828C2212yes—
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C2×#3799C2214yes—
19C2×C32×C42C2211yescharacteristic
20#64139C2214yes—
21#64084C2212yescomplemented
22#64083C2211yescharacteristic, complemented
23C4×C4⋊(C3⋊D3)C2214yescomplemented
24#64078C2211yescharacteristic, complemented
25C3×#926C2212yes—
26C3×#924C2214yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29C3×C42×D3C2212yes—
30C3×C42×D3C2212yes—
31C3×C42×D3C2212yes—
32C3×C42×D3C2212yes—
33C3×#870C2212yescomplemented
34C3×#869C2212yescomplemented
35C3×C4×Dic6C2214yescomplemented
36#63977C2214yes—
37#63966C2214yes—
38#63952C2218yes—
39#63909C2214yes—
40#63909C2214yes—
41#63904C2218yes—
42C4×#626C2218yes—
43#63894C2214yescomplemented
44#63894C2214yescomplemented
45C4×#624C2214yescomplemented
46#63874C2214yescomplemented
47#63869C2214yescomplemented
48#63868C2218yescomplemented
49#63864C2214yescomplemented
50#63857C2214yes—
51#63856C2214yes—
52#63850C2218yes—
53#63844C2214yescomplemented
54Dic3×Dic6C2214yescomplemented
55#63841C2214yes—
56#63836C2218yescomplemented
57C3×#533—31no—
58C22×C3×C42—31no—
59#5791—32no—
60#5791—34no—
61#5728—32no—
62#5725—32no—
63#5691—34no—
64#5627—34no—
65#5624—34no—
66#5580—34no—
67C4×#239—34no—
68#5524—32no—
69#5522—32no—
70#5479—34no—
71#5479—34no—
72#5479—34no—
73#5477—31no—
74#5477—31no—
75#5477—32no—
76#5477—61no—
77C4×#235—32no—
78C4×#235—34no—
79C2×C42×D3D311yescharacteristic, complemented
80#5470—32no—
81#5470D311yescharacteristic, complemented
82C23×C3×D3C2311yescharacteristic
83C22×C32×C4C2312yes—
84C22×C32×C4C2311yescharacteristic
85C2×#638C2314yes—
86#3828—28no—
87C2×C4⋊(C3⋊D3)C2314yes—
88C2×C4⋊(C3⋊D3)C2312yes—
89C2×C4×C3⋊D3C2314yes—
90C2×#634C2312yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3—28no—
95C2×C3×C4×D3C2312yes—
96C2×C3×C4×D3C2312yes—
97C2×C3×C4×D3C2312yes—
98C2×C3×C4×D3C2312yes—
99C2×C3×C4×D3C2312yes—
100C2×C3×C4×D3C2312yes—
101C2×C3×Dic6C2314yes—
102C2×#626C2318yes—
103C2×#624C2318yes—
104#3799—216no—
105C32×C42C2311yescharacteristic
106C32×C42C2312yes—
107C32×C42C2311yescharacteristic
108#3752C2318yes—
109C4⋊(C3⋊Dic3)C2314yes—
110C3×#217C2314yes—
111C3×C4⋊Dic3C2314yes—
112C3×C4⋊Dic3C2314yes—
113C3×Dic3⋊C4C2318yes—
114C3×C4×Dic3C2312yes—
115C3×C4×Dic3C2312yes—
116C3×C4×Dic3C2312yes—
117C3×C4×Dic3C2312yes—
118C3×C4×Dic3C2312yes—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2314yes—
122#3724C2318yes—
123Dic3⋊Dic3C2318yes—
124#3722C2318yes—
125#3722C2318yes—
126(C2×D3)⋊Dic3C2318yes—
127Dic32C2318yes—
128#3444—91noSylow
129C23×C3×C4—32no—
130C23×C3×C4—31no—
131C2×#239—34no—
132C2×#235—32no—
133C2×#235—32no—
134C2×#235—34no—
135C2×#235—62no—
136C22×C4×D3C2×D311yescharacteristic
137C22×C4×D3C2×D312yes—
138C3×C4⋊Q8—32no—
139C3×#125—32no—
140C3×C22⋊Q8—34no—
141C3×C4×Q8—34no—
142C3×#117—32no—
143C2×C3×C42—21no—
144C2×C3×C42—31no—
145C2×C3×C42—32no—
146C2×C3×C42—32no—
147C2×C3×C42—32no—
148C2×C3×C42—32no—
149C2×C3×C42—32no—
150C2×C3×C42C2×D311yescharacteristic
151C2×C3×C42C2×D311yescharacteristic
152#953—34no—
153#947—34no—
154#946—34no—
155Q8×Dic3—34no—
156#930—34no—
157#930—34no—
158#930—34no—
159#930—34no—
160#930—64no—
161#929—34no—
162#929—38no—
163C4×#67—38no—
164C4×#67—38no—
165C4×#67—38no—
166#926—34no—
167#926C2×D312yes—
168#924—34no—
169#924—34no—
170#924C2×D314yes—
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D312yes—
173#898—38no—
174#897—34no—
175#895—34no—
176#895—34no—
177#894—38no—
178#893—38no—
179#893—34no—
180#893—34no—
181#892—34no—
182#892—38no—
183#890—34no—
184#887—34no—
185#886—34no—
186#882—34no—
187#67⋊C4—38no—
188#876—38no—
189#875—34no—
190#875—32no—
191#875—32no—
192#875—62no—
193#874—31no—
194#874—31no—
195#874—61no—
196C4×D12—38no—
197C4×D12—34no—
198C4×D12—34no—
199C4×D12—34no—
200C4×D12—34no—
201C4×D12—64no—
202#872—38no—
203#872—34no—
204#872—34no—
205C42×D3—34no—
206C42×D3—34no—
207C42×D3C2×D312yes—
208C42×D3C2×D312yes—
209C42×D3C2×D312yes—
210C42×D3C2×D312yes—
211#870—34no—
212#870C2×D312yescomplemented
213#869—31no—
214#869—31no—
215#869—61no—
216#869C2×D312yescomplemented
217C4×Dic6—34no—
218C4×Dic6—34no—
219C4×Dic6C2×D314yescomplemented
220C23×C32C2411yescharacteristic
221C22×C3⋊D3C2414yes—
222C22×C3×D3—22no—
223C22×C3×D3—24no—
224C22×C3×D3C2412yes—
225C2×C32×C4—24no—
226C2×C32×C4#4114yescomplemented
227C2×C32×C4C2412yes—
228C2×C32×C4C2411yescharacteristic
229C2×C32×C4C2411yescharacteristic
230C2×C32×C4C2412yes—
231#638—28no—
232C2×C3⋊Dic3C2414yes—
233C4⋊(C3⋊D3)—28no—
234C4⋊(C3⋊D3)—24no—
235C4×C3⋊D3—28no—
236#634—24no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3C2418yes—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2412yes—
242C2×C3×Dic3C2412yes—
243C3×C4×D3—24no—
244C3×C4×D3—24no—
245C3×C4×D3—24no—
246C3×C4×D3—24no—
247C3×C4×D3—24no—
248C3×C4×D3#4118yescomplemented
249C3×Dic6—28no—
250#626—216no—
251#624—216no—
252#533—31no—
253#533—92no—
254#532—92no—
255#532—91no—
256#529—94no—
257#529—94no—
258#529—94no—
259#525—92no—
260#525—94no—
261C4×#41—92no—
262C4×#41—94no—
263C22×C42—31no—
264C24×C3—31no—
265C23×D3C22×D311yescharacteristic
266C2×C3×Q8—34no—
267C22×C3×C4—21no—
268C22×C3×C4—22no—
269C22×C3×C4—32no—
270C22×C3×C4—32no—
271C22×C3×C4—31no—
272C22×C3×C4—32no—
273C22×C3×C4—32no—
274C22×C3×C4—32no—
275C22×C3×C4—32no—
276C22×C3×C4—32no—
277C22×C3×C4—68no—
278C22×C3×C4—64no—
279C22×C3×C4C22×D312yes—
280C22×C3×C4C22×D312yes—
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C2×#67—34no—
284C2×#67—34no—
285C2×#67—38no—
286C2×#67—64no—
287C22×Dic3C22×D312yes—
288C22×Dic3C22×D311yescharacteristic
289#239—616no—
290#235—616no—
291#235—68no—
292#235—68no—
293#235—128no—
294C2×D12—38no—
295C2×D12—32no—
296C2×D12—34no—
297C2×D12—34no—
298C2×D12—32no—
299C2×D12—64no—
300C2×D12—62no—
301C2×C4×D3—24no—
302C2×C4×D3—28no—
303C2×C4×D3—34no—
304C2×C4×D3—34no—
305C2×C4×D3—38no—
306C2×C4×D3—38no—
307C2×C4×D3—64no—
308C2×C4×D3C22×D312yes—
309C2×C4×D3C22×D312yes—
310C2×C4×D3C22×D312yes—
311C2×C4×D3C22×D312yes—
312C2×C4×D3C22×D312yes—
313C2×C4×D3C22×D312yes—
314C2×Dic6—32no—
315C2×Dic6—32no—
316C2×Dic6—62no—
317C2×Dic6C22×D314yes—
318C3×C4⋊C4—34no—
319C3×C4⋊C4—34no—
320C3×C4⋊C4—38no—
321C3×C22⋊C4—34no—
322C3×C42—21no—
323C3×C42—22no—
324C3×C42—21no—
325C3×C42—32no—
326C3×C42—32no—
327C3×C42—32no—
328C3×C42—31no—
329C3×C42—34no—
330C3×C42—32no—
331C3×C42—31no—
332C3×C42—32no—
333C3×C42C22×D312yes—
334C3×C42C22×D311yescharacteristic
335C3×C42C22×D311yescharacteristic
336C3×C42C22×D311yescharacteristic
337C3×C42C22×D312yes—
338C3×C42C22×D311yescharacteristic
339#217—38no—
340#217C22×D314yes—
341(C2×D3)⋊C4—38no—
342(C2×D3)⋊C4—38no—
343(C2×D3)⋊C4—38no—
344(C2×D3)⋊C4—38no—
345(C2×D3)⋊C4—38no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4—38no—
348(C2×D3)⋊C4—68no—
349C4⋊Dic3—34no—
350C4⋊Dic3—34no—
351C4⋊Dic3—38no—
352C4⋊Dic3—64no—
353C4⋊Dic3C22×D314yes—
354C4⋊Dic3C22×D314yes—
355Dic3⋊C4—38no—
356Dic3⋊C4—38no—
357Dic3⋊C4—38no—
358Dic3⋊C4C22×D318yes—
359C4×Dic3—38no—
360C4×Dic3—38no—
361C4×Dic3C22×D314yes—
362C4×Dic3C22×D311yescharacteristic
363C4×Dic3C22×D311yescharacteristic
364C4×Dic3C22×D312yes—
365C4×Dic3C22×D312yes—
366C4×Dic3C22×D312yes—
367C4×Dic3C22×D312yes—
368C4×Dic3C22×D312yes—
369C22×C32—22no—
370C22×C32C2×#4112yes—
371C22×C32C2511yescharacteristic
372C2×C3⋊D3—28no—
373C2×C3⋊D3—24no—
374C2×C3×D3—28no—
375C2×C3×D3—22no—
376C2×C3×D3—22no—
377C2×C3×D3C2×#4114yes—
378C32×C4—22no—
379C32×C4C2×#4112yes—
380C32×C4C2×#4112yes—
381C32×C4C2×#4114yes—
382C3⋊Dic3—24no—
383C3×Dic3—28no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3C2×#4114yes—
387C2×#41—94no—
388C2×#41—92no—
389C23×C4—32no—
390C23×C4—31no—
391C4⋊Q8—32no—
392C4⋊Q8—91no—
393#127—91no—
394#126—98no—
395#125—32no—
396#125—94no—
397#124—94no—
398#124—92no—
399#123—94no—
400#123—98no—
401C22⋊Q8—34no—
402C22⋊Q8—94no—
403C22⋊Q8—94no—
404#121—94no—
405#121—94no—
406#121—94no—
407#120—94no—
408C4×Q8—34no—
409C4×Q8—94no—
410C4×Q8—94no—
411C4×D4—94no—
412C4×D4—94no—
413C4×D4—98no—
414C4×D4—98no—
415C4×D4—98no—
416C4×D4—94no—
417#117—32no—
418#117—94no—
419#117—98no—
420#117—94no—
421C2×C42—31no—
422C2×C42—32no—
423C2×C42—32no—
424C2×C42—32no—
425C2×C42—32no—
426C2×C42—32no—
427C2×C42—94no—
428C2×C42D3211yescharacteristic
429C23×C3—21no—
430C23×C3—32no—
431C23×C3—64no—
432C23×C3—62no—
433C23×C3C23×D311yescharacteristic
434C23×C3C23×D311yescharacteristic
435C22×D3—22no—
436C22×D3—24no—
437C22×D3—34no—
438C22×D3—34no—
439C22×D3—64no—
440C22×D3C23×D312yes—
441C3×Q8—68no—
442C2×C3×C4—24no—
443C2×C3×C4—24no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—21no—
448C2×C3×C4—24no—
449C2×C3×C4—32no—
450C2×C3×C4—38no—
451C2×C3×C4—38no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—44no—
455C2×C3×C4—64no—
456C2×C3×C4—64no—
457C2×C3×C4—64no—
458C2×C3×C4—62no—
459C2×C3×C4—64no—
460C2×C3×C4—64no—
461C2×C3×C4—64no—
462C2×C3×C4#23514yescomplemented
463C2×C3×C4#23914yescomplemented
464C2×C3×C4C23×D312yes—
465C2×C3×C4C23×D312yes—
466C2×C3×C4C23×D312yes—
467C2×C3×C4C23×D311yescharacteristic
468C2×C3×C4C23×D311yescharacteristic
469C2×C3×C4C23×D312yes—
470C2×C3×C4C23×D311yescharacteristic
471C2×C3×C4C23×D311yescharacteristic
472#67—616no—
473#67—68no—
474#67—68no—
475#67—128no—
476C2×Dic3—22no—
477C2×Dic3—24no—
478C2×Dic3—34no—
479C2×Dic3—34no—
480C2×Dic3—64no—
481C2×Dic3C23×D318yes—
482C2×Dic3C23×D312yes—
483C2×Dic3C23×D312yes—
484C2×Dic3C23×D312yes—
485D12—616no—
486D12—64no—
487D12—68no—
488D12—64no—
489D12—68no—
490D12—128no—
491D12—124no—
492C4×D3—24no—
493C4×D3—24no—
494C4×D3—24no—
495C4×D3—24no—
496C4×D3—24no—
497C4×D3—616no—
498C4×D3—68no—
499C4×D3—68no—
500C4×D3—616no—
501C4×D3—128no—
502C4×D3#23518yescomplemented
503Dic6—28no—
504Dic6—64no—
505Dic6—64no—
506Dic6—124no—
507C2×C32—22no—
508C2×C32C22×#4111yescharacteristic
509C2×C32C22×#4112yes—
510C3⋊D3—44no—
511C3×D3—24no—
512C24—31no—
513#41—1816no—
514#41—188no—
515C2×Q8—34no—
516C2×Q8—92no—
517C2×D4—98no—
518C2×D4—94no—
519C2×D4—92no—
520C2×D4—94no—
521C22×C4—32no—
522C22×C4—32no—
523C22×C4—31no—
524C22×C4—32no—
525C22×C4—32no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—32no—
529C22×C4—68no—
530C22×C4—64no—
531C22×C4—98no—
532C22×C4—94no—
533C22×C4C2×D3212yes—
534C22×C4C2×D3211yescharacteristic
535C4⋊C4—34no—
536C4⋊C4—34no—
537C4⋊C4—38no—
538C4⋊C4—98no—
539C4⋊C4—98no—
540C4⋊C4—94no—
541C22⋊C4—34no—
542C22⋊C4—98no—
543C22⋊C4—98no—
544C22⋊C4—98no—
545C22⋊C4—98no—
546C42—32no—
547C42—32no—
548C42—32no—
549C42—32no—
550C42—32no—
551C42—31no—
552C42—31no—
553C42—34no—
554C42—98no—
555C42C2×D3211yescharacteristic
556C42C2×D3211yescharacteristic
557C42C2×D3212yes—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—21no—
562C22×C3—34no—
563C22×C3—42no—
564C22×C3—68no—
565C22×C3—62no—
566C22×C3—62no—
567C22×C3C2×#23512yes—
568C22×C3C2×#23912yes—
569C22×C3C24×D311yescharacteristic
570C22×C3C24×D311yescharacteristic
571C2×D3—28no—
572C2×D3—22no—
573C2×D3—22no—
574C2×D3—68no—
575C2×D3—64no—
576C2×D3—64no—
577C2×D3—68no—
578C2×D3—124no—
579C2×D3—128no—
580C2×D3C2×#23514yes—
581C3×C4—22no—
582C3×C4—22no—
583C3×C4—22no—
584C3×C4—22no—
585C3×C4—24no—
586C3×C4—34no—
587C3×C4—42no—
588C3×C4—68no—
589C3×C4—62no—
590C3×C4—62no—
591C3×C4C2×#23512yes—
592C3×C4C2×#23512yes—
593C3×C4C2×#23514yes—
594C3×C4C2×#23912yes—
595C3×C4C2×#23912yes—
596C3×C4D3×#4114yes—
597Dic3—22no—
598Dic3—22no—
599Dic3—28no—
600Dic3—64no—
601Dic3—64no—
602Dic3—124no—
603Dic3C2×#23514yes—
604C32#344411yescharacteristic, complemented, Sylow
605C23—32no—
606C23—64no—
607C23—62no—
608C23—94no—
609C23C22×D3211yescharacteristic
610Q8—68no—
611Q8—184no—
612D4—1816no—
613D4—188no—
614D4—184no—
615D4—188no—
616C2×C4—24no—
617C2×C4—32no—
618C2×C4—38no—
619C2×C4—32no—
620C2×C4—32no—
621C2×C4—38no—
622C2×C4—64no—
623C2×C4—64no—
624C2×C4—64no—
625C2×C4—62no—
626C2×C4—64no—
627C2×C4—64no—
628C2×C4—64no—
629C2×C4—94no—
630C2×C4—1816no—
631C2×C4—188no—
632C2×C4#379914yescomplemented
633C2×C4C22×D3212yes—
634C2×C4C22×D3211yescharacteristic
635C2×C4C22×D3212yes—
636C2×C4C22×D3211yescharacteristic
637C2×C3—22no—
638C2×C3—22no—
639C2×C3—21no—
640C2×C3—22no—
641C2×C3—42no—
642C2×C3—64no—
643C2×C3C22×#23511yescharacteristic
644C2×C3C22×#23512yes—
645C2×C3C22×#23911yescharacteristic
646C2×C3C2×D3×#4112yes—
647D3—24no—
648D3—124no—
649D3—124no—
650D3—244no—
651C22—22no—
652C22—34no—
653C22—68no—
654C22—62no—
655C22—62no—
656C22—184no—
657C22—188no—
658C22C2×#379912yes—
659C22C23×D3211yescharacteristic
660C4—22no—
661C4—34no—
662C4—62no—
663C4—62no—
664C4—68no—
665C4—184no—
666C4C2×#379912yes—
667C4C2×#379912yes—
668C4D3×#23514yes—
669C3—21no—
670C3#8568011yescharacteristic, complemented
671C3#8625711yescharacteristic, complemented
672C2—22no—
673C2—64no—
674C2—364no—
675C2C22×#379911yescharacteristic
676C2C2×D3×#23512yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C2×C3×C42×D3C2semidirect
3. C3×#5470C2semidirect
4. #10595023C2semidirect
5. #10595005C2semidirect
6. #10594955C2semidirect
7. #10594954C2semidirect
8. #10593976C2semidirect
9. #10593970C2semidirect
10. C4×#3799C2semidirect
11. #10593870C2semidirect
12. #10593859C2semidirect
21. #64084C22semidirect
22. #64083C22semidirect
23. C4×C4⋊(C3⋊D3)C22semidirect
24. #64078C22semidirect
33. C3×#870C22semidirect
34. C3×#869C22semidirect
35. C3×C4×Dic6C22semidirect
43. #63894C22semidirect
44. #63894C22semidirect
45. C4×#624C22semidirect
46. #63874C22semidirect
47. #63869C22semidirect
48. #63868C22semidirect
49. #63864C22semidirect
53. #63844C22semidirect
54. Dic3×Dic6C22semidirect
56. #63836C22semidirect
79. C2×C42×D3D3semidirect
81. #5470D3semidirect
212. #870C2×D3semidirect
216. #869C2×D3semidirect
219. C4×Dic6C2×D3semidirect
226. C2×C32×C4#41semidirect
248. C3×C4×D3#41semidirect
462. C2×C3×C4#235semidirect
463. C2×C3×C4#239semidirect
502. C4×D3#235semidirect
604. C32#3444semidirect
632. C2×C4#3799semidirect
670. C3#85680semidirect
671. C3#86257semidirect

Maximal subgroups

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

subgroupindex
#105959482
C2×C3×C42×D32
C3×#54702
#105950232
#105950052
#105949552
#105949542
#105939762
#105939702
C4×#37992
#105938702
#105938592
#862573
#856803