Finite Group Databasebeta

← #11900898

Subgroups — #11900898

Order 1152.

2535 conjugacy classes of subgroups.

The subgroup lattice has 667 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×C3×C42×D3C211yesmaximal, characteristic, complemented
4#10595022C212yesmaximal, complemented
5#10594949C214yesmaximal, complemented
6Dic3×#235C212yesmaximal, complemented
7#10594892C214yesmaximal, complemented
8#10593974C214yesmaximal, complemented
9#10593921C214yesmaximal, complemented
10#10593897C212yesmaximal, complemented
11C4×#3795C214yesmaximal, complemented
12#10593859C212yesmaximal, complemented
13#86219—31nomaximal
14#85680—31nomaximal
15C2×C3×#235C2212yes—
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C2×#3795C2214yes—
19C2×C32×C42C2211yescharacteristic
20#64135C2212yes—
21#64133C2214yes—
22#64079C2212yescomplemented
23#64078C2212yescomplemented
24C4×#634C2214yescomplemented
25C3×#930C2214yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C3×#875C2212yescomplemented
29C3×#874C2211yescharacteristic, complemented
30C3×C4×D12C2214yescomplemented
31C3×C42×D3C2212yes—
32C3×C42×D3C2212yes—
33C3×C42×D3C2212yes—
34C3×C42×D3C2212yes—
35C3×#869C2211yescharacteristic, complemented
36#63976C2214yes—
37Dic3×#67C2218yes—
38#63961C2214yes—
39#63908C2214yes—
40#63908C2214yes—
41#63905C2218yes—
42C4×#625C2218yes—
43Dic3×D12C2214yescomplemented
44Dic3×D12C2214yescomplemented
45#63879C2218yes—
46#63877C2218yescomplemented
47C4×D3×Dic3C2214yescomplemented
48#63869C2214yescomplemented
49#63860C2214yescomplemented
50#63859C2218yescomplemented
51#63857C2214yes—
52#63856C2214yes—
53#63855C2214yescomplemented
54#63844C2214yescomplemented
55Dic3×Dic6C2214yescomplemented
56#63841C2214yes—
57C3×#532—31no—
58C22×C3×C42—31no—
59#5828—32no—
60Dic3×#41—32no—
61#5791—32no—
62#5791—34no—
63#5728—32no—
64#5716—32no—
65#5680—34no—
66#5606—34no—
67#5600—34no—
68#5557—34no—
69C4×#237—34no—
70#5479—34no—
71#5479—34no—
72#5479—34no—
73#5477—32no—
74#5477D311yescharacteristic, complemented
75C4×#235—32no—
76C4×#235—34no—
77C2×C42×D3D311yescharacteristic, complemented
78#5470—31no—
79#5470—31no—
80#5470—32no—
81#5470—61no—
82C23×C3×D3C2311yescharacteristic
83C22×C32×C4C2312yes—
84C22×C32×C4C2311yescharacteristic
85C2×#634C2314yes—
86C2×C3×#67C2314yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C3×#235—28no—
90C2×C3×D12C2314yes—
91C2×C3×D12C2312yes—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—28no—
94C2×C3×C4×D3C2312yes—
95C2×C3×C4×D3C2312yes—
96C2×C3×C4×D3C2312yes—
97C2×C3×C4×D3C2312yes—
98C2×C3×C4×D3C2312yes—
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2312yes—
101C2×C3×Dic6C2312yes—
102C2×#625C2318yes—
103C2×D3×Dic3C2318yes—
104#3795—216no—
105C32×C42C2312yes—
106C32×C42C2311yescharacteristic
107C32×C42C2311yescharacteristic
108#3757C2314yes—
109C4⋊(C3⋊Dic3)C2314yes—
110C4⋊(C3⋊Dic3)C2314yes—
111#3750C2318yes—
112C4×C3⋊Dic3C2314yes—
113C3×(C2×D3)⋊C4C2318yes—
114C3×C4⋊Dic3C2314yes—
115C3×C4×Dic3C2312yes—
116C3×C4×Dic3C2312yes—
117C3×C4×Dic3C2311yescharacteristic
118C3×C4×Dic3C2312yes—
119C3×C4×Dic3C2312yes—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2312yes—
122#3724C2318yes—
123Dic3⋊Dic3C2318yes—
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126(C2×D3)⋊Dic3C2318yes—
127Dic32C2318yes—
128#3444—91noSylow
129C2×C3×#41—32no—
130C23×C3×C4—32no—
131C23×C3×C4—31no—
132C2×#237—34no—
133C2×#235—34no—
134C2×#235C2×D312yes—
135C22×C4×D3C2×D311yescharacteristic
136C22×C4×D3C2×D312yes—
137C3×C4⋊Q8—31no—
138C3×#127—31no—
139C3×#124—32no—
140C3×#121—34no—
141C3×C4×D4—34no—
142C2×C3×C42—21no—
143C2×C3×C42—31no—
144C2×C3×C42—32no—
145C2×C3×C42—32no—
146C2×C3×C42—32no—
147C2×C3×C42—32no—
148C2×C3×C42—32no—
149C2×C3×C42C2×D311yescharacteristic
150C2×C3×C42C2×D311yescharacteristic
151#953—34no—
152#946—34no—
153Q8×Dic3—34no—
154#938—34no—
155#938—34no—
156#937—34no—
157#936—34no—
158#935—34no—
159D4×Dic3—38no—
160D4×Dic3—34no—
161D4×Dic3—34no—
162#930—34no—
163#930—34no—
164#930C2×D314yes—
165#929—34no—
166#929—38no—
167C4×#67—38no—
168C4×#67—38no—
169C4×#67—38no—
170C4×#67—38no—
171#926—32no—
172#926—32no—
173#926—34no—
174#926—34no—
175#926—62no—
176#924—34no—
177#924—34no—
178#924—34no—
179#924—34no—
180#924—64no—
181C2×C4×Dic3—34no—
182C2×C4×Dic3C2×D311yescharacteristic
183C2×C4×Dic3C2×D312yes—
184#897—34no—
185#892—34no—
186#890—34no—
187#887—34no—
188#883—38no—
189#67⋊C4—38no—
190#879—38no—
191#877—38no—
192#876—38no—
193#875—34no—
194#875C2×D312yescomplemented
195#874C2×D311yescharacteristic, complemented
196C4×D12—34no—
197C4×D12—34no—
198C4×D12C2×D314yescomplemented
199#872—34no—
200#872—38no—
201C42×D3—34no—
202C42×D3C2×D312yes—
203C42×D3C2×D312yes—
204C42×D3C2×D312yes—
205C42×D3C2×D312yes—
206#870—32no—
207#870—32no—
208#870—34no—
209#870—62no—
210#869—32no—
211#869—32no—
212#869—62no—
213#869C2×D311yescharacteristic, complemented
214C4×Dic6—34no—
215C4×Dic6—34no—
216C4×Dic6—34no—
217C4×Dic6—34no—
218C4×Dic6—64no—
219C23×C32C2411yescharacteristic
220C22×C3×D3—22no—
221C22×C3×D3—24no—
222C22×C3×D3C2414yes—
223C22×C3×D3C2412yes—
224C2×C32×C4—24no—
225C2×C32×C4#4114yescomplemented
226C2×C32×C4C2412yes—
227C2×C32×C4C2412yes—
228C2×C32×C4C2411yescharacteristic
229C2×C32×C4C2411yescharacteristic
230C2×C3⋊Dic3C2418yes—
231#634—28no—
232C3×#67—28no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—24no—
235C2×C3×Dic3C2414yes—
236C2×C3×Dic3C2412yes—
237C2×C3×Dic3C2412yes—
238C2×C3×Dic3C2412yes—
239C3×D12—28no—
240C3×D12—24no—
241C3×C4×D3—24no—
242C3×C4×D3—24no—
243C3×C4×D3—24no—
244C3×C4×D3—24no—
245C3×C4×D3—28no—
246C3×C4×D3—24no—
247C3×C4×D3#4118yescomplemented
248C3×Dic6—24no—
249#625—216no—
250D3×Dic3—216no—
251#533—92no—
252#533—91no—
253#532—31no—
254#532—92no—
255#529—94no—
256#529—94no—
257#529—94no—
258#525—94no—
259#525—92no—
260C4×#41—94no—
261C4×#41—92no—
262C22×C42—31no—
263C24×C3—31no—
264C23×D3C22×D311yescharacteristic
265C3×#41—68no—
266C2×C3×Q8—32no—
267C2×C3×D4—34no—
268C2×C3×D4—32no—
269C2×C3×D4—34no—
270C22×C3×C4—21no—
271C22×C3×C4—22no—
272C22×C3×C4—32no—
273C22×C3×C4—32no—
274C22×C3×C4—31no—
275C22×C3×C4—34no—
276C22×C3×C4—32no—
277C22×C3×C4—32no—
278C22×C3×C4—32no—
279C22×C3×C4—32no—
280C22×C3×C4—32no—
281C22×C3×C4—68no—
282C22×C3×C4—64no—
283C22×C3×C4C22×D312yes—
284C22×C3×C4C22×D312yes—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C2×#67—38no—
288C2×#67—38no—
289C2×#67C22×D314yes—
290C22×Dic3—38no—
291C22×Dic3C22×D312yes—
292C22×Dic3C22×D311yescharacteristic
293#237—616no—
294#235—28no—
295#235—616no—
296C2×D12C22×D312yes—
297C2×D12C22×D314yes—
298C2×C4×D3—24no—
299C2×C4×D3—28no—
300C2×C4×D3—38no—
301C2×C4×D3C22×D314yes—
302C2×C4×D3C22×D312yes—
303C2×C4×D3C22×D312yes—
304C2×C4×D3C22×D312yes—
305C2×C4×D3C22×D312yes—
306C2×C4×D3C22×D312yes—
307C2×C4×D3C22×D312yes—
308C2×Dic6—34no—
309C2×Dic6—34no—
310C2×Dic6—64no—
311C2×Dic6C22×D312yes—
312C3×C4⋊C4—34no—
313C3×C22⋊C4—38no—
314C3×C42—22no—
315C3×C42—21no—
316C3×C42—21no—
317C3×C42—32no—
318C3×C42—32no—
319C3×C42—32no—
320C3×C42—31no—
321C3×C42—32no—
322C3×C42—31no—
323C3×C42—32no—
324C3×C42C22×D312yes—
325C3×C42C22×D312yes—
326C3×C42C22×D311yescharacteristic
327C3×C42C22×D311yescharacteristic
328C3×C42C22×D311yescharacteristic
329C3×C42C22×D311yescharacteristic
330#217—34no—
331#217—34no—
332#217—38no—
333#217—38no—
334#217—38no—
335#217—64no—
336(C2×D3)⋊C4—38no—
337(C2×D3)⋊C4—38no—
338(C2×D3)⋊C4—38no—
339(C2×D3)⋊C4C22×D318yes—
340C4⋊Dic3—34no—
341C4⋊Dic3—34no—
342C4⋊Dic3—34no—
343C4⋊Dic3—34no—
344C4⋊Dic3—38no—
345C4⋊Dic3—64no—
346C4⋊Dic3—64no—
347C4⋊Dic3C22×D314yes—
348Dic3⋊C4—38no—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—38no—
352Dic3⋊C4—38no—
353Dic3⋊C4—68no—
354C4×Dic3—34no—
355C4×Dic3—34no—
356C4×Dic3—38no—
357C4×Dic3—38no—
358C4×Dic3—64no—
359C4×Dic3C22×D312yes—
360C4×Dic3C22×D312yes—
361C4×Dic3C22×D312yes—
362C4×Dic3C22×D312yes—
363C4×Dic3C22×D311yescharacteristic
364C4×Dic3C22×D311yescharacteristic
365C4×Dic3C22×D312yes—
366C22×C32—22no—
367C22×C32C2×#4112yes—
368C22×C32C2511yescharacteristic
369C2×C3×D3—28no—
370C2×C3×D3—22no—
371C2×C3×D3—22no—
372C2×C3×D3—28no—
373C2×C3×D3—24no—
374C2×C3×D3C2×#4114yes—
375C32×C4—22no—
376C32×C4C2×#4112yes—
377C32×C4C2×#4112yes—
378C32×C4C2×#4114yes—
379C3⋊Dic3—28no—
380C3×Dic3—24no—
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3C2×#4114yes—
384C2×#41—32no—
385C2×#41—94no—
386C23×C4—32no—
387C23×C4—31no—
388C4⋊Q8—31no—
389C4⋊Q8—92no—
390#127—31no—
391#126—98no—
392#125—94no—
393#125—92no—
394#124—32no—
395#124—94no—
396#123—98no—
397#123—94no—
398C22⋊Q8—94no—
399C22⋊Q8—94no—
400C22⋊Q8—94no—
401#121—34no—
402#121—94no—
403#121—94no—
404#120—94no—
405C4×Q8—94no—
406C4×Q8—94no—
407C4×Q8—94no—
408C4×D4—34no—
409C4×D4—94no—
410C4×D4—94no—
411C4×D4—98no—
412C4×D4—98no—
413C4×D4—98no—
414#117—98no—
415#117—94no—
416#117—94no—
417#117—92no—
418C2×C42—31no—
419C2×C42—32no—
420C2×C42—32no—
421C2×C42—32no—
422C2×C42—32no—
423C2×C42—32no—
424C2×C42—94no—
425C2×C42D3211yescharacteristic
426C23×C3—21no—
427C23×C3—32no—
428C23×C3—34no—
429C23×C3—64no—
430C23×C3—62no—
431C23×C3C23×D311yescharacteristic
432C23×C3C23×D311yescharacteristic
433C22×D3—22no—
434C22×D3—24no—
435C22×D3C23×D314yes—
436C22×D3C23×D312yes—
437C3×Q8—64no—
438C3×D4—68no—
439C3×D4—68no—
440C3×D4—64no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—24no—
448C2×C3×C4—32no—
449C2×C3×C4—38no—
450C2×C3×C4—34no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—44no—
454C2×C3×C4—64no—
455C2×C3×C4—64no—
456C2×C3×C4—64no—
457C2×C3×C4—62no—
458C2×C3×C4—68no—
459C2×C3×C4—64no—
460C2×C3×C4—64no—
461C2×C3×C4—64no—
462C2×C3×C4#23514yescomplemented
463C2×C3×C4#23714yescomplemented
464C2×C3×C4C23×D312yes—
465C2×C3×C4C23×D312yes—
466C2×C3×C4C23×D311yescharacteristic
467C2×C3×C4C23×D312yes—
468C2×C3×C4C23×D311yescharacteristic
469C2×C3×C4C23×D312yes—
470C2×C3×C4C23×D311yescharacteristic
471C2×C3×C4C23×D311yescharacteristic
472#67—28no—
473#67—616no—
474#67—616no—
475C2×Dic3—22no—
476C2×Dic3—24no—
477C2×Dic3—38no—
478C2×Dic3—38no—
479C2×Dic3—68no—
480C2×Dic3—616no—
481C2×Dic3C23×D314yes—
482C2×Dic3C23×D312yes—
483C2×Dic3C23×D312yes—
484C2×Dic3C23×D312yes—
485D12—24no—
486D12—28no—
487C4×D3—24no—
488C4×D3—24no—
489C4×D3—24no—
490C4×D3—24no—
491C4×D3—28no—
492C4×D3—24no—
493C4×D3—616no—
494C4×D3#23518yescomplemented
495Dic6—24no—
496Dic6—68no—
497Dic6—68no—
498Dic6—128no—
499C2×C32—22no—
500C2×C32C22×#4111yescharacteristic
501C2×C32C22×#4112yes—
502C3×D3—24no—
503C3×D3—44no—
504C24—31no—
505#41—68no—
506#41—1816no—
507C2×Q8—32no—
508C2×Q8—94no—
509C2×D4—34no—
510C2×D4—34no—
511C2×D4—32no—
512C2×D4—98no—
513C22×C4—32no—
514C22×C4—32no—
515C22×C4—31no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—34no—
522C22×C4—68no—
523C22×C4—64no—
524C22×C4—98no—
525C22×C4C2×D3212yes—
526C22×C4C2×D3211yescharacteristic
527C4⋊C4—34no—
528C4⋊C4—98no—
529C4⋊C4—98no—
530C4⋊C4—94no—
531C4⋊C4—94no—
532C4⋊C4—98no—
533C22⋊C4—38no—
534C22⋊C4—98no—
535C22⋊C4—98no—
536C22⋊C4—98no—
537C22⋊C4—94no—
538C42—32no—
539C42—32no—
540C42—32no—
541C42—32no—
542C42—32no—
543C42—31no—
544C42—31no—
545C42—98no—
546C42—94no—
547C42C2×D3211yescharacteristic
548C42C2×D3211yescharacteristic
549C42C2×D3212yes—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—22no—
553C22×C3—21no—
554C22×C3—34no—
555C22×C3—42no—
556C22×C3—68no—
557C22×C3—62no—
558C22×C3—62no—
559C22×C3—68no—
560C22×C3—64no—
561C22×C3C2×#23512yes—
562C22×C3C2×#23712yes—
563C22×C3C24×D311yescharacteristic
564C22×C3C24×D311yescharacteristic
565C2×D3—28no—
566C2×D3—22no—
567C2×D3—22no—
568C2×D3—24no—
569C2×D3—28no—
570C2×D3C2×#23514yes—
571C3×C4—22no—
572C3×C4—22no—
573C3×C4—22no—
574C3×C4—22no—
575C3×C4—24no—
576C3×C4—34no—
577C3×C4—42no—
578C3×C4—64no—
579C3×C4—62no—
580C3×C4—62no—
581C3×C4C2×#23512yes—
582C3×C4C2×#23512yes—
583C3×C4C2×#23514yes—
584C3×C4C2×#23712yes—
585C3×C4C2×#23712yes—
586C3×C4D3×#4114yes—
587Dic3—22no—
588Dic3—22no—
589Dic3—24no—
590Dic3—68no—
591Dic3—68no—
592Dic3—128no—
593Dic3C2×#23514yes—
594C32#344411yescharacteristic, complemented, Sylow
595C23—32no—
596C23—34no—
597C23—64no—
598C23—62no—
599C23C22×D3211yescharacteristic
600Q8—64no—
601Q8—188no—
602D4—68no—
603D4—64no—
604D4—68no—
605D4—1816no—
606C2×C4—24no—
607C2×C4—32no—
608C2×C4—38no—
609C2×C4—32no—
610C2×C4—32no—
611C2×C4—34no—
612C2×C4—64no—
613C2×C4—64no—
614C2×C4—64no—
615C2×C4—62no—
616C2×C4—64no—
617C2×C4—64no—
618C2×C4—68no—
619C2×C4—64no—
620C2×C4—98no—
621C2×C4—1816no—
622C2×C4#379514yescomplemented
623C2×C4C22×D3212yes—
624C2×C4C22×D3211yescharacteristic
625C2×C4C22×D3212yes—
626C2×C4C22×D3211yescharacteristic
627C2×C3—22no—
628C2×C3—22no—
629C2×C3—21no—
630C2×C3—22no—
631C2×C3—42no—
632C2×C3—64no—
633C2×C3—124no—
634C2×C3C22×#23511yescharacteristic
635C2×C3C22×#23512yes—
636C2×C3C22×#23711yescharacteristic
637C2×C3C2×D3×#4112yes—
638D3—24no—
639D3—44no—
640C22—22no—
641C22—34no—
642C22—68no—
643C22—62no—
644C22—62no—
645C22—64no—
646C22—68no—
647C22C2×#379512yes—
648C22C23×D3211yescharacteristic
649C4—22no—
650C4—34no—
651C4—62no—
652C4—64no—
653C4—62no—
654C4—188no—
655C4C2×#379512yes—
656C4C2×#379512yes—
657C4D3×#23514yes—
658C3—21no—
659C3#8568011yescharacteristic, complemented
660C3#8621911yescharacteristic, complemented
661C2—22no—
662C2—64no—
663C2—124no—
664C2C22×#379511yescharacteristic
665C2C2×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. #10595941C2semidirect
2. C3×#5477C2semidirect
3. C2×C3×C42×D3C2semidirect
4. #10595022C2semidirect
5. #10594949C2semidirect
6. Dic3×#235C2semidirect
7. #10594892C2semidirect
8. #10593974C2semidirect
9. #10593921C2semidirect
10. #10593897C2semidirect
11. C4×#3795C2semidirect
12. #10593859C2semidirect
22. #64079C22semidirect
23. #64078C22semidirect
24. C4×#634C22semidirect
28. C3×#875C22semidirect
29. C3×#874C22semidirect
30. C3×C4×D12C22semidirect
35. C3×#869C22semidirect
43. Dic3×D12C22semidirect
44. Dic3×D12C22semidirect
46. #63877C22semidirect
47. C4×D3×Dic3C22semidirect
48. #63869C22semidirect
49. #63860C22semidirect
50. #63859C22semidirect
53. #63855C22semidirect
54. #63844C22semidirect
55. Dic3×Dic6C22semidirect
74. #5477D3semidirect
77. C2×C42×D3D3semidirect
194. #875C2×D3semidirect
195. #874C2×D3semidirect
198. C4×D12C2×D3semidirect
213. #869C2×D3semidirect
225. C2×C32×C4#41semidirect
247. C3×C4×D3#41semidirect
462. C2×C3×C4#235semidirect
463. C2×C3×C4#237semidirect
494. C4×D3#235semidirect
594. C32#3444semidirect
622. C2×C4#3795semidirect
659. C3#85680semidirect
660. C3#86219semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×#54772
C2×C3×C42×D32
#105950222
#105949492
Dic3×#2352
#105948922
#105939742
#105939212
#105938972
C4×#37952
#105938592
#862193
#856803