Finite Group Databasebeta

← #11865784

Subgroups — #11865784

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 675 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C2×#63829C212yesmaximal, complemented
4C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5#10591105C212yesmaximal, complemented
6#10590385C211yesmaximal, characteristic, complemented
7#10590368C212yesmaximal, complemented
8#10590367C211yesmaximal, characteristic, complemented
9#10590366C212yesmaximal, complemented
10#10590365C211yesmaximal, characteristic, complemented
11#10590349C211yesmaximal, characteristic, complemented
12#82525—31nomaximal
13#79021—31nomaximal
14C2×#3828C2212yes—
15C2×C3×#235C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17#64139—21no—
18#64139—21no—
19#64084C2212yes—
20#64083C2211yescharacteristic
21C4×C4⋊(C3⋊D3)—21no—
22C4×C4⋊(C3⋊D3)—21no—
23#64078C2211yescharacteristic
24C3×C4×#67—21no—
25C3×C4×#67—21no—
26C3×#926C2211yescharacteristic
27C22×C3×C3⋊C8C2212yes—
28C3×C4×D12C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×#872—21no—
31C3×C42×D3—21no—
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34C2×#3719C2212yes—
35C2×#3717C2212yes—
36#63829—28no—
37C2×#3716C2212yes—
38C2×#3714C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41C3×C4⋊(C3⋊C8)C2212yes—
42#63567C2212yes—
43#63567C2212yes—
44#63564C2212yes—
45#63564C2212yes—
46C3×C4×#41—31no—
47C2×#950—32no—
48C2×#904—32no—
49#5477—31no—
50#5477—31no—
51#5477—61no—
52C4×#235D311yescharacteristic, complemented
53C2×C3×C4⋊C8—31no—
54#5113—32no—
55#5031—31no—
56#5028—32no—
57#5027—31no—
58#5019—31no—
59#5016—32no—
60#5015—31no—
61#5002—32no—
62C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
63#4849—31no—
64#4848—31no—
65#4845—32no—
66#4844—32no—
67#4843—31no—
68#4841—31no—
69C22×C32×C4D411yescharacteristic
70C22×C32×C4D411yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×#638—22no—
73#3828—24no—
74#3828—24no—
75C2×C4⋊(C3⋊D3)—21no—
76C2×C4⋊(C3⋊D3)—21no—
77C2×C4⋊(C3⋊D3)C2312yes—
78C2×C4×C3⋊D3—22no—
79C2×#634C2312yes—
80C2×C3×#67—21no—
81C3×#235—22no—
82C3×#235D414yescomplemented
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3—21no—
86C2×C3×C4×D3—21no—
87C2×C3×Dic6C2311yescharacteristic
88C32×C42D411yescharacteristic
89C32×C42D411yescharacteristic
90C32×C42C2311yescharacteristic
91C32×C42C2311yescharacteristic
92#3752—22no—
93#3752—22no—
94C4⋊(C3⋊Dic3)—21no—
95C4⋊(C3⋊Dic3)—21no—
96C3×#217—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×(C2×D3)⋊C4—21no—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4⋊Dic3C2311yescharacteristic
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3—21no—
105C3×C4×Dic3—21no—
106C2×C3×C3⋊C8—24no—
107C2×C3×C3⋊C8C2312yes—
108C2×C3×C3⋊C8C2312yes—
109#3719—24no—
110#3717—24no—
111#3716—24no—
112#3714—24no—
113#3035—91noSylow
114C2×C3×#41—31no—
115C2×#235—32no—
116C2×#235—32no—
117C2×#235—62no—
118C2×#235C2×D311yescharacteristic
119C22×C3×C8—32no—
120C3×C4×Q8—31no—
121C3×C4×Q8—31no—
122C3×C4×D4—31no—
123C3×C4×D4—31no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C3×#117—31no—
127C3×#117—61no—
128C2×C3×C42—21no—
129C2×C3×C42—61no—
130C2×C3×C42C2×D311yescharacteristic
131C2×C3×C42C2×D311yescharacteristic
132#950—68no—
133C2×#216—32no—
134C2×#215—32no—
135C2×#214—32no—
136C2×#213—32no—
137#930—62no—
138#930—62no—
139#930—61no—
140#930—61no—
141#930—61no—
142#930—61no—
143C4×#67—21no—
144C4×#67—21no—
145#926C2×D311yescharacteristic
146C22×C3⋊C8C2×D312yes—
147C2×Dic12—32no—
148#904—68no—
149C2×D24—32no—
150C2×#204—32no—
151C2×#204—32no—
152#875—32no—
153#875—32no—
154#875—62no—
155#874—31no—
156#874—31no—
157#874—61no—
158C4×D12—62no—
159C4×D12—62no—
160C4×D12—61no—
161C4×D12—61no—
162C4×D12—61no—
163C4×D12—61no—
164C4×D12C2×D311yescharacteristic
165C4×D12C2×D311yescharacteristic
166#872—21no—
167C42×D3—21no—
168#869—31no—
169#869—31no—
170#869—61no—
171C4×Dic6C2×D311yescharacteristic
172C4×Dic6C2×D311yescharacteristic
173C3×C4⋊C8—31no—
174C3×C4⋊C8—31no—
175C3×C4⋊C8—32no—
176#821—32no—
177#821—32no—
178#816—32no—
179#816—32no—
180#810—32no—
181#810—32no—
182#809—32no—
183#809—32no—
184C4⋊(C3⋊C8)C2×D311yescharacteristic
185C4⋊(C3⋊C8)C2×D312yes—
186C4⋊(C3⋊C8)C2×D311yescharacteristic
187C23×C32C2×D411yescharacteristic
188C22×C3⋊D3—22no—
189C22×C3×D3—21no—
190C2×C32×C4—22no—
191C2×C32×C4—41no—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2×D411yescharacteristic
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4#4112yes—
199C2×C32×C4C2411yescharacteristic
200#638—44no—
201C2×C3⋊Dic3—22no—
202C4⋊(C3⋊D3)—22no—
203C4⋊(C3⋊D3)—22no—
204C4⋊(C3⋊D3)—42no—
205C4⋊(C3⋊D3)—42no—
206C4×C3⋊D3—44no—
207#634—22no—
208#634—22no—
209C3×#67—24no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C3×D12—21no—
214C3×D12C2×D412yes—
215C3×C4×D3—24no—
216C3×C4×D3—42no—
217C3×C4×D3—42no—
218C3×Dic6—21no—
219C3×Dic6C2×D412yes—
220C3×C3⋊C8—22no—
221C3×C3⋊C8—22no—
222C2×#135—92no—
223#532—91no—
224C4×#41—31no—
225#464—92no—
226#463—92no—
227#462—91no—
228#461—91no—
229#460—91no—
230#459—91no—
231C2×C4⋊C8—31no—
232#416—92no—
233C3×#41—34no—
234C3×#41—62no—
235C2×C3×Q8—31no—
236C2×C3×D4—31no—
237C2×C3×D4—61no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—61no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4D1211yescharacteristic
245C22×C3×C4D1211yescharacteristic
246C22×C3×C4#6711yescharacteristic
247C22×C3×C4#6711yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—21no—
251C2×#67—64no—
252C2×#67—62no—
253C2×#67—62no—
254#235—22no—
255#235—64no—
256#235—64no—
257#235—64no—
258#235—64no—
259#235—124no—
260#235—124no—
261#235D1214yescomplemented
262C2×D12—32no—
263C2×D12—32no—
264C2×D12—62no—
265C2×D12—62no—
266C2×D12—62no—
267C2×D12—61no—
268C2×D12—61no—
269C2×D12—61no—
270C2×D12—61no—
271C2×D12C22×D311yescharacteristic
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—64no—
276C2×C4×D3—62no—
277C2×C4×D3—62no—
278C2×Dic6—32no—
279C2×Dic6—32no—
280C2×Dic6—62no—
281C2×Dic6C22×D311yescharacteristic
282C2×C3×C8—32no—
283C2×C3×C8—32no—
284C2×C3×C8—64no—
285C3×C4⋊C4—31no—
286C3×C4⋊C4—31no—
287C3×C4⋊C4—61no—
288C3×C4⋊C4—61no—
289C3×C22⋊C4—61no—
290C3×C22⋊C4—61no—
291C3×C22⋊C4—61no—
292C3×C42—21no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42—21no—
296C3×C42—61no—
297C3×C42—61no—
298C3×C42—61no—
299C3×C42D1211yescharacteristic
300C3×C42D1211yescharacteristic
301C3×C42#6711yescharacteristic
302C3×C42#6711yescharacteristic
303C3×C42C22×D311yescharacteristic
304C3×C42C22×D311yescharacteristic
305C3×C42C22×D311yescharacteristic
306C3×C42C22×D311yescharacteristic
307#217—21no—
308#216—64no—
309#215—64no—
310#214—64no—
311#213—64no—
312(C2×D3)⋊C4—21no—
313(C2×D3)⋊C4—21no—
314(C2×D3)⋊C4—64no—
315(C2×D3)⋊C4—64no—
316(C2×D3)⋊C4—62no—
317(C2×D3)⋊C4—62no—
318(C2×D3)⋊C4—62no—
319(C2×D3)⋊C4—62no—
320C4⋊Dic3—62no—
321C4⋊Dic3—62no—
322C4⋊Dic3—61no—
323C4⋊Dic3—61no—
324C4⋊Dic3—61no—
325C4⋊Dic3—61no—
326C4⋊Dic3C22×D311yescharacteristic
327C4⋊Dic3C22×D311yescharacteristic
328Dic3⋊C4—21no—
329Dic3⋊C4—21no—
330C4×Dic3—21no—
331C4×Dic3—21no—
332C4×Dic3—21no—
333C2×C3⋊C8—24no—
334C2×C3⋊C8C22×D312yes—
335C2×C3⋊C8C22×D312yes—
336Dic12—64no—
337D24—64no—
338#204—64no—
339#204—64no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32#12112yes—
343C22×C32C22×D411yescharacteristic
344C2×C3⋊D3—42no—
345C2×C3⋊D3—42no—
346C2×C3⋊D3—42no—
347C2×C3×D3—22no—
348C2×C3×D3—41no—
349C2×C3×D3—41no—
350C32×C4—21no—
351C32×C4—21no—
352C32×C4—21no—
353C32×C4#12112yes—
354C32×C4#13512yescomplemented
355C32×C4C22×D411yescharacteristic
356C32×C4C2×#4111yescharacteristic
357C3⋊Dic3—42no—
358C3×Dic3—22no—
359C3×Dic3—41no—
360C3×Dic3—41no—
361C2×#41—31no—
362C2×#41—92no—
363#135—188no—
364C2×Q16—92no—
365C2×SD16—92no—
366C2×SD16—92no—
367C2×D8—92no—
368C22×C8—32no—
369C4⋊Q8—91no—
370#127—91no—
371#124—92no—
372#121—181no—
373#121—181no—
374C4×Q8—31no—
375C4×Q8—31no—
376C4×D4—31no—
377C4×D4—31no—
378C4×D4—61no—
379C4×D4—61no—
380C4×D4—181no—
381C4×D4—181no—
382#117—31no—
383#117—61no—
384C2×C42—61no—
385C2×C42D3211yescharacteristic
386C4⋊C8—31no—
387C4⋊C8—31no—
388C4⋊C8—32no—
389#103—92no—
390#103—92no—
391#102—92no—
392#102—92no—
393C23×C3—21no—
394C23×C3—61no—
395C23×C3C2×D1211yescharacteristic
396C23×C3C2×#6711yescharacteristic
397C22×D3—21no—
398C22×D3—64no—
399C22×D3—62no—
400C22×D3—62no—
401C3×Q8—32no—
402C3×Q8—61no—
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—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—42no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—42no—
420C2×C3×C4—61no—
421C2×C3×C4—64no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—122no—
425C2×C3×C4—122no—
426C2×C3×C4C2×D1212yes—
427C2×C3×C4C2×D1211yescharacteristic
428C2×C3×C4C2×D1211yescharacteristic
429C2×C3×C4C2×D1211yescharacteristic
430C2×C3×C4C2×D1211yescharacteristic
431C2×C3×C4C2×D1211yescharacteristic
432C2×C3×C4#23512yes—
433C2×C3×C4D3×D412yes—
434C2×C3×C4#23912yes—
435C2×C3×C4C2×#6711yescharacteristic
436C2×C3×C4C2×#6711yescharacteristic
437C2×C3×C4C2×#6711yescharacteristic
438C2×C3×C4C2×#6711yescharacteristic
439C2×C3×C4C2×#6711yescharacteristic
440C2×C3×C4C23×D311yescharacteristic
441C2×C3×C4C23×D311yescharacteristic
442#67—24no—
443#67—128no—
444#67—124no—
445#67—124no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—64no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452D12—21no—
453D12—62no—
454D12—62no—
455D12—62no—
456D12—62no—
457D12—122no—
458D12—122no—
459D12—124no—
460D12—122no—
461D12—122no—
462D12—124no—
463D12—122no—
464D12—122no—
465D12C2×D1212yes—
466C4×D3—24no—
467C4×D3—42no—
468C4×D3—42no—
469C4×D3—128no—
470C4×D3—124no—
471C4×D3—124no—
472Dic6—21no—
473Dic6—62no—
474Dic6—62no—
475Dic6—62no—
476Dic6—62no—
477Dic6—122no—
478Dic6—122no—
479Dic6C2×D1212yes—
480C3×C8—62no—
481C3×C8—62no—
482C3⋊C8—22no—
483C3⋊C8—22no—
484C2×C32—22no—
485C2×C32C2×#12111yescharacteristic
486C2×C32C2×#13511yescharacteristic
487C2×C32#57511yescharacteristic
488C3⋊D3—82no—
489C3×D3—42no—
490#41—34no—
491#41—62no—
492#41—184no—
493#41—184no—
494C2×Q8—31no—
495C2×Q8—92no—
496C2×D4—31no—
497C2×D4—61no—
498C2×D4—92no—
499C2×D4—182no—
500C2×D4—181no—
501C2×D4—181no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—182no—
506C22×C4#62611yescharacteristic
507C22×C4#62611yescharacteristic
508C22×C4C2×D3211yescharacteristic
509Q16—184no—
510SD16—184no—
511SD16—184no—
512D8—184no—
513C2×C8—32no—
514C2×C8—32no—
515C2×C8—64no—
516C4⋊C4—31no—
517C4⋊C4—31no—
518C4⋊C4—61no—
519C4⋊C4—61no—
520C4⋊C4—181no—
521C4⋊C4—181no—
522C22⋊C4—61no—
523C22⋊C4—61no—
524C22⋊C4—61no—
525C22⋊C4—182no—
526C22⋊C4—182no—
527C42—61no—
528C42—61no—
529C42—61no—
530C42#62611yescharacteristic
531C42#62611yescharacteristic
532C42C2×D3211yescharacteristic
533C42C2×D3211yescharacteristic
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—22no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—62no—
543C22×C3—121no—
544C22×C3—121no—
545C22×C3#89512yes—
546C22×C3#93012yes—
547C22×C3C22×D1211yescharacteristic
548C22×C3C22×#6711yescharacteristic
549C2×D3—22no—
550C2×D3—41no—
551C2×D3—41no—
552C2×D3—124no—
553C2×D3—124no—
554C2×D3—124no—
555C2×D3—122no—
556C2×D3—122no—
557C2×D3—122no—
558C2×D3—122no—
559C2×D3—122no—
560C2×D3—122no—
561C3×C4—22no—
562C3×C4—21no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—22no—
571C3×C4—22no—
572C3×C4—41no—
573C3×C4—41no—
574C3×C4—62no—
575C3×C4—121no—
576C3×C4—121no—
577C3×C4#89512yes—
578C3×C4#90412yescomplemented
579C3×C4#93012yes—
580C3×C4#95012yescomplemented
581C3×C4C22×D1211yescharacteristic
582C3×C4C2×#23511yescharacteristic
583C3×C4C2×D3×D411yescharacteristic
584C3×C4C2×#23911yescharacteristic
585Dic3—22no—
586Dic3—41no—
587Dic3—41no—
588Dic3—124no—
589Dic3—122no—
590Dic3—122no—
591C32#303511yescharacteristic, complemented, Sylow
592C23—61no—
593C23—182no—
594C23C2×#62611yescharacteristic
595Q8—32no—
596Q8—61no—
597Q8—182no—
598Q8—182no—
599D4—32no—
600D4—64no—
601D4—61no—
602D4—182no—
603D4—182no—
604D4—362no—
605D4—364no—
606D4—362no—
607C2×C4—22no—
608C2×C4—41no—
609C2×C4—61no—
610C2×C4—64no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—122no—
614C2×C4—122no—
615C2×C4—182no—
616C2×C4—364no—
617C2×C4#379912yes—
618C2×C4D3×D1212yes—
619C2×C4C2×#62611yescharacteristic
620C2×C4C2×#62611yescharacteristic
621C2×C4C2×#62611yescharacteristic
622C2×C4C2×#62611yescharacteristic
623C2×C4C2×#62611yescharacteristic
624C2×C4C22×D3211yescharacteristic
625C8—62no—
626C8—62no—
627C2×C3—22no—
628C2×C3—22no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—42no—
633C2×C3—122no—
634C2×C3C2×#89511yescharacteristic
635C2×C3C2×#90411yescharacteristic
636C2×C3#574811yescharacteristic
637C2×C3C2×#93011yescharacteristic
638C2×C3C2×#95011yescharacteristic
639C2×C3#582211yescharacteristic
640D3—42no—
641D3—244no—
642D3—242no—
643D3—242no—
644C22—21no—
645C22—21no—
646C22—62no—
647C22—121no—
648C22—121no—
649C22—362no—
650C22—362no—
651C22—362no—
652C22#6390912yes—
653C22C22×#62611yescharacteristic
654C4—21no—
655C4—21no—
656C4—21no—
657C4—62no—
658C4—121no—
659C4—121no—
660C4—362no—
661C4#6382912yescomplemented
662C4#6390912yes—
663C4C2×#379911yescharacteristic
664C4C2×D3×D1211yescharacteristic
665C3—21no—
666C3#7902111yescharacteristic, complemented
667C3#8252511yescharacteristic, complemented
668C2—22no—
669C2—122no—
670C2—722no—
671C2C2×#6382911yescharacteristic
672C2#1059479511yescharacteristic
673C2C2×#6390911yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C3×C4×#235C2semidirect
3. C2×#63829C2semidirect
4. C2×C3×C4⋊(C3⋊C8)C2semidirect
5. #10591105C2semidirect
6. #10590385C2semidirect
7. #10590368C2semidirect
8. #10590367C2semidirect
9. #10590366C2semidirect
10. #10590365C2semidirect
11. #10590349C2semidirect
52. C4×#235D3semidirect
62. C2×C4⋊(C3⋊C8)D3semidirect
82. C3×#235D4semidirect
261. #235D12semidirect
354. C32×C4#135semidirect
578. C3×C4#904semidirect
580. C3×C4#950semidirect
591. C32#3035semidirect
661. C4#63829semidirect
666. C3#79021semidirect
667. C3#82525semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×C4×#2352
C2×#638292
C2×C3×C4⋊(C3⋊C8)2
#105911052
#105903852
#105903682
#105903672
#105903662
#105903652
#105903492
#825253
#790213