Finite Group Databasebeta

← #11903381

Subgroups — #11903381

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5584C212yesmaximal, complemented
3#10595429C212yesmaximal, complemented
4#10595413C212yesmaximal, complemented
5#10594656C214yesmaximal, complemented
6#10594602C212yesmaximal, complemented
7#10594581C212yesmaximal, complemented
8#10594472C214yesmaximal, complemented
9#10594009C212yesmaximal
10C4×#3802C211yesmaximal, characteristic
11#10593942C214yesmaximal, complemented
12#10593909C211yesmaximal, characteristic, complemented
13C4×#3797C212yesmaximal, complemented
14#10593863C212yesmaximal, complemented
15D3×#556—32nomaximal
16C2×Q8×C3⋊D3C2211yescharacteristic
17C2×#3802C2211yescharacteristic
18C2×C4×D32C2212yes—
19C2×#3797C2212yes—
20C32×C4×Q8C2211yescharacteristic, complemented
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C4⋊C4×C3⋊D3C2212yes—
24#64096C2211yescharacteristic, complemented
25#64096C2212yescomplemented
26C42×C3⋊D3C2212yes—
27C42×C3⋊D3C2211yescharacteristic
28C4×#634C2211yescharacteristic, complemented
29C4×#634C2212yescomplemented
30C3×#946C2214yescomplemented
31C3×#898C2218yescomplemented
32C3×#892C2214yescomplemented
33C3×#875C2214yes—
34C3×C4×D12C2212yes—
35C3×#869C2212yescomplemented
36C3×C4×Dic6C2214yescomplemented
37#63921C2214yes—
38#63921C2212yes—
39#63921C2214yes—
40#63919C2212yescomplemented
41#63919C2212yescomplemented
42C4×#627C2214yescomplemented
43#63915C2214yes—
44#63915C2214yes—
45#63902C2212yes—
46C4×#625C2212yes—
47#63900C2212yes—
48#63900C2212yes—
49#63900C2211yescharacteristic
50#63898C2212yes—
51#63896C2218yescomplemented
52#63883C2214yes—
53C4×#624C2214yes—
54#63877C2218yescomplemented
55#63873C2212yescomplemented
56#63863C2214yes—
57#63861C2218yescomplemented
58#63859C2218yescomplemented
59#63858C2218yescomplemented
60#63857C2214yescomplemented
61#63843C2214yescomplemented
62#63841C2214yescomplemented
63#63838C2214yescomplemented
64C3×#556—32no—
65#5732—32no—
66D3×C4⋊Q8—32no—
67D3×#126—38no—
68#5702—38no—
69D3×#124—34no—
70#5671—34no—
71#5641—34no—
72D3×C22⋊Q8—34no—
73#5584D312yescomplemented
74C4×D3×Q8—32no—
75C4×D3×Q8—34no—
76C4×D3×Q8—61no—
77#5568—34no—
78C4×D3×D4—32no—
79#5542—32no—
80#5533—34no—
81D3×#117—34no—
82C22×D32C2312yes—
83C2×C32×Q8C2311yescharacteristic
84Q8×C3⋊D3—24no—
85C2×C4×C3⋊D3C2312yes—
86C2×C4×C3⋊D3C2311yescharacteristic
87C2×C4×C3⋊D3C2312yes—
88C2×C4×C3⋊D3C2311yescharacteristic
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C2×#634C2312yes—
92C2×C3×D12C2312yes—
93C2×C3×C4×D3C2314yes—
94C2×C3×Dic6C2314yes—
95C2×#627C2314yes—
96C2×#625C2312yes—
97C2×#624C2314yes—
98C2×#624C2312yes—
99C2×D3×Dic3C2314yes—
100#3802—24no—
101C4×D32—28no—
102#3797—28no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2312yes—
105C32×C42C2312yes—
106C32×C42C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2312yes—
109#3750C2312yes—
110#3750C2312yes—
111#3750C2312yes—
112C4×C3⋊Dic3C2312yes—
113C4×C3⋊Dic3C2311yescharacteristic
114C4×C3⋊Dic3C2312yes—
115C4×C3⋊Dic3C2311yescharacteristic
116C4×C3⋊Dic3C2312yes—
117C4×C3⋊Dic3C2311yescharacteristic
118C3×(C2×D3)⋊C4C2318yes—
119C3×(C2×D3)⋊C4C2314yes—
120C3×(C2×D3)⋊C4C2318yes—
121C3×C4⋊Dic3C2314yes—
122C3×C4⋊Dic3C2314yes—
123C3×C4⋊Dic3C2312yes—
124C3×Dic3⋊C4C2318yes—
125C3×C4×Dic3C2318yes—
126#3724C2312yes—
127#3724C2314yes—
128#3724C2314yes—
129Dic3⋊Dic3C2318yes—
130(C2×D3)⋊Dic3C2318yes—
131(C2×D3)⋊Dic3C2318yes—
132(C2×D3)⋊Dic3C2314yes—
133Dic32C2318yes—
134C2×#556—91noSylow
135C2×D3×Q8—32no—
136C2×D3×Q8—34no—
137C2×D3×Q8—61no—
138C2×D3×D4—32no—
139C22×C4×D3—34no—
140C3×C4⋊Q8—32no—
141C3×#126—38no—
142C3×#124—34no—
143C3×C22⋊Q8—34no—
144C3×C4×Q8—21no—
145C3×C4×Q8—34no—
146C3×C4×Q8C2×D312yescomplemented
147C3×C4×D4—32no—
148C3×#117—34no—
149#947—34no—
150#946C2×D314yescomplemented
151Q8×Dic3—32no—
152Q8×Dic3—34no—
153Q8×Dic3—61no—
154#944—34no—
155#936—34no—
156D4×Dic3—32no—
157C4×#67—34no—
158#926—34no—
159#924—34no—
160#898—38no—
161#898—38no—
162#898C2×D318yescomplemented
163#897—34no—
164#896—38no—
165#893—32no—
166#892—34no—
167#892C2×D314yescomplemented
168D3×C4⋊C4—34no—
169D3×C4⋊C4—32no—
170D3×C4⋊C4—34no—
171D3×C4⋊C4—34no—
172D3×C4⋊C4—32no—
173D3×C4⋊C4—38no—
174D3×C4⋊C4—61no—
175D3×C4⋊C4—62no—
176#888—34no—
177#888—34no—
178#887—34no—
179#887—34no—
180#887—32no—
181#887—38no—
182#887—61no—
183#887—62no—
184#885—38no—
185#885—38no—
186#67⋊C4—34no—
187D3×C22⋊C4—38no—
188D3×C22⋊C4—38no—
189D3×C22⋊C4—34no—
190#879—38no—
191#879—38no—
192#879—38no—
193#878—38no—
194#877—38no—
195#876—38no—
196#875C2×D314yes—
197C4×D12C2×D312yes—
198#872—38no—
199C42×D3—34no—
200C42×D3—32no—
201C42×D3—38no—
202C42×D3—61no—
203C42×D3—62no—
204#869C2×D312yescomplemented
205C4×Dic6—34no—
206C4×Dic6—32no—
207C4×Dic6—38no—
208C4×Dic6—61no—
209C4×Dic6—62no—
210C4×Dic6C2×D314yescomplemented
211C22×C3⋊D3C2411yescharacteristic
212C22×C3×D3C2414yes—
213C2×D32—24no—
214C2×D32—24no—
215C2×D32—24no—
216C32×Q8—22no—
217C2×C32×C4C2412yes—
218C2×C32×C4C2412yes—
219C2×C32×C4C2411yescharacteristic
220C2×C32×C4C2411yescharacteristic
221C2×C32×C4C2411yescharacteristic
222C2×C3⋊Dic3C2412yes—
223C2×C3⋊Dic3C2412yes—
224C2×C3⋊Dic3C2411yescharacteristic
225C2×C3⋊Dic3C2411yescharacteristic
226C2×C3⋊Dic3C2411yescharacteristic
227C4×C3⋊D3—24no—
228C4×C3⋊D3—24no—
229C4×C3⋊D3—22no—
230C4×C3⋊D3#4114yes—
231C4×C3⋊D3#4114yes—
232#634—22no—
233#634—24no—
234C2×C3×Dic3C2414yes—
235C2×C3×Dic3C2418yes—
236C3×D12—24no—
237C3×C4×D3—28no—
238C3×Dic6—28no—
239#627—28no—
240#625—24no—
241#624—28no—
242#624—24no—
243D3×Dic3—28no—
244#556—32no—
245#556—92no—
246#556—92no—
247#556—94no—
248#556—92no—
249#556—94no—
250C2×C4⋊Q8—91no—
251C2×#126—94no—
252C2×#124—92no—
253C2×C22⋊Q8—92no—
254C2×C4×Q8—92no—
255C2×C4×Q8—91no—
256C2×C4×D4—91no—
257C2×#117—92no—
258C23×D3—34no—
259C2×C3×Q8—21no—
260C2×C3×Q8—34no—
261C2×C3×Q8C22×D312yes—
262C2×C3×D4—32no—
263C22×C3×C4—34no—
264C2×#67—34no—
265C22×Dic3—34no—
266D3×Q8—616no—
267D3×Q8—68no—
268D3×Q8—68no—
269D3×D4—68no—
270C2×D12C22×D312yes—
271C2×C4×D3—32no—
272C2×C4×D3—32no—
273C2×C4×D3—34no—
274C2×C4×D3—34no—
275C2×C4×D3—32no—
276C2×C4×D3—34no—
277C2×C4×D3—34no—
278C2×C4×D3—38no—
279C2×C4×D3—61no—
280C2×C4×D3—61no—
281C2×C4×D3—62no—
282C2×C4×D3—62no—
283C2×C4×D3—61no—
284C2×C4×D3—616no—
285C2×C4×D3C22×D314yes—
286C2×Dic6—34no—
287C2×Dic6—32no—
288C2×Dic6—38no—
289C2×Dic6—61no—
290C2×Dic6—62no—
291C2×Dic6C22×D314yes—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—32no—
295C3×C4⋊C4—38no—
296C3×C4⋊C4—34no—
297C3×C4⋊C4—34no—
298C3×C4⋊C4C22×D312yes—
299C3×C4⋊C4C22×D314yes—
300C3×C22⋊C4—38no—
301C3×C22⋊C4—38no—
302C3×C22⋊C4—34no—
303C3×C42—21no—
304C3×C42—22no—
305C3×C42—38no—
306C3×C42C22×D314yes—
307C3×C42C22×D312yes—
308#217—38no—
309#217—38no—
310#217—34no—
311(C2×D3)⋊C4—38no—
312(C2×D3)⋊C4—34no—
313(C2×D3)⋊C4—38no—
314(C2×D3)⋊C4C22×D318yes—
315(C2×D3)⋊C4C22×D314yes—
316(C2×D3)⋊C4C22×D318yes—
317C4⋊Dic3—34no—
318C4⋊Dic3—32no—
319C4⋊Dic3—38no—
320C4⋊Dic3—61no—
321C4⋊Dic3—62no—
322C4⋊Dic3C22×D312yes—
323C4⋊Dic3C22×D314yes—
324C4⋊Dic3C22×D314yes—
325Dic3⋊C4—34no—
326Dic3⋊C4—34no—
327Dic3⋊C4—34no—
328Dic3⋊C4—34no—
329Dic3⋊C4—38no—
330Dic3⋊C4—38no—
331Dic3⋊C4—38no—
332Dic3⋊C4—62no—
333Dic3⋊C4—62no—
334Dic3⋊C4—62no—
335Dic3⋊C4C22×D318yes—
336C4×Dic3—34no—
337C4×Dic3—34no—
338C4×Dic3—32no—
339C4×Dic3—32no—
340C4×Dic3—34no—
341C4×Dic3—32no—
342C4×Dic3—38no—
343C4×Dic3—38no—
344C4×Dic3—61no—
345C4×Dic3—62no—
346C4×Dic3—61no—
347C4×Dic3—62no—
348C4×Dic3—61no—
349C4×Dic3—62no—
350C4×Dic3C22×D318yes—
351C22×C32C2511yescharacteristic
352C2×C3⋊D3C2×#4112yes—
353C2×C3⋊D3C2×#4112yes—
354C2×C3⋊D32−1+412yes—
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—24no—
358D32—48no—
359C32×C4—22no—
360C32×C4—22no—
361C32×C4—21no—
362C32×C4C2×#4112yes—
363C32×C4C2×#4112yes—
364C3⋊Dic3—22no—
365C3⋊Dic3—22no—
366C3⋊Dic3—21no—
367C3⋊Dic3C2×#4112yes—
368C3⋊Dic3C2×#4112yes—
369C3×Dic3—24no—
370C3×Dic3—28no—
371C22×Q8—92no—
372C22×Q8—91no—
373C22×D4—91no—
374C23×C4—92no—
375C4⋊Q8—32no—
376C4⋊Q8—92no—
377C4⋊Q8—92no—
378C4⋊Q8—92no—
379#126—38no—
380#126—98no—
381#126—98no—
382#126—98no—
383#124—34no—
384#124—94no—
385#124—94no—
386#124—94no—
387C22⋊Q8—34no—
388C22⋊Q8—98no—
389C22⋊Q8—94no—
390C4×Q8—34no—
391C4×Q8—94no—
392C4×Q8—94no—
393C4×Q8—94no—
394C4×Q8—91no—
395C4×Q8—92no—
396C4×Q8—91no—
397C4×Q8—92no—
398C4×Q8—91no—
399C4×Q8D3211yescharacteristic, complemented
400C4×D4—32no—
401C4×D4—92no—
402C4×D4—92no—
403C4×D4—92no—
404#117—34no—
405#117—98no—
406#117—94no—
407C2×C4⋊C4—92no—
408C2×C4⋊C4—91no—
409C2×C4⋊C4—94no—
410C2×C4⋊C4—92no—
411C2×C4⋊C4—91no—
412C2×C4⋊C4—92no—
413C2×C22⋊C4—94no—
414C2×C22⋊C4—92no—
415C2×C22⋊C4—94no—
416C2×C42—94no—
417C2×C42—91no—
418C2×C42—92no—
419C23×C3—34no—
420C22×D3—32no—
421C22×D3—61no—
422C22×D3—68no—
423C22×D3—68no—
424C22×D3—68no—
425C22×D3C23×D314yes—
426C3×Q8—24no—
427C3×Q8—24no—
428C3×Q8—68no—
429C3×D4—64no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—34no—
436C2×C3×C4—38no—
437C2×C3×C4—68no—
438C2×C3×C4C23×D314yes—
439C2×C3×C4C23×D312yes—
440C2×C3×C4C23×D314yes—
441C2×C3×C4C23×D312yes—
442C2×C3×C4C23×D312yes—
443#67—68no—
444C2×Dic3—32no—
445C2×Dic3—32no—
446C2×Dic3—34no—
447C2×Dic3—32no—
448C2×Dic3—34no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—61no—
454C2×Dic3—68no—
455C2×Dic3C23×D314yes—
456C2×Dic3C23×D318yes—
457D12—24no—
458C4×D3—28no—
459C4×D3—38no—
460C4×D3—38no—
461C4×D3—64no—
462C4×D3—64no—
463C4×D3—68no—
464C4×D3—616no—
465C4×D3—68no—
466C4×D3—68no—
467C4×D3—64no—
468C4×D3—68no—
469C4×D3—68no—
470C4×D3—124no—
471C4×D3—122no—
472Dic6—28no—
473Dic6—616no—
474Dic6—68no—
475Dic6—68no—
476Dic6—64no—
477Dic6—64no—
478C2×C32C22×#4111yescharacteristic
479C2×C32C22×#4111yescharacteristic
480C2×C32C2×2−1+411yescharacteristic
481C3⋊D3#55614yescomplemented
482C3×D3—44no—
483C24—92no—
484C2×Q8—34no—
485C2×Q8—94no—
486C2×Q8—92no—
487C2×Q8—91no—
488C2×Q8—184no—
489C2×Q8—188no—
490C2×Q8C2×D3211yescharacteristic
491C2×D4—32no—
492C2×D4—92no—
493C2×D4—184no—
494C22×C4—34no—
495C22×C4—92no—
496C22×C4—94no—
497C22×C4—94no—
498C22×C4—91no—
499C22×C4—91no—
500C22×C4—92no—
501C22×C4—91no—
502C22×C4—92no—
503C22×C4—188no—
504C4⋊C4—34no—
505C4⋊C4—32no—
506C4⋊C4—38no—
507C4⋊C4—34no—
508C4⋊C4—94no—
509C4⋊C4—92no—
510C4⋊C4—98no—
511C4⋊C4—94no—
512C4⋊C4—92no—
513C4⋊C4—91no—
514C4⋊C4—92no—
515C4⋊C4—92no—
516C4⋊C4—92no—
517C4⋊C4C2×D3211yescharacteristic
518C4⋊C4C2×D3212yes—
519C22⋊C4—38no—
520C22⋊C4—34no—
521C22⋊C4—38no—
522C22⋊C4—98no—
523C22⋊C4—94no—
524C22⋊C4—98no—
525C42—38no—
526C42—98no—
527C42—91no—
528C42—91no—
529C42—91no—
530C42—92no—
531C42—92no—
532C42—92no—
533C42C2×D3211yescharacteristic
534C42C2×D3212yes—
535C22×C3—21no—
536C22×C3—64no—
537C22×C3—64no—
538C22×C3—64no—
539C22×C3C24×D312yes—
540C2×D3—24no—
541C2×D3—24no—
542C2×D3—24no—
543C2×D3—34no—
544C2×D3—34no—
545C2×D3—34no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—62no—
549C2×D3—1216no—
550C3×C4—24no—
551C3×C4—24no—
552C3×C4—24no—
553C3×C4—22no—
554C3×C4—22no—
555C3×C4—22no—
556C3×C4—42no—
557C3×C4—41no—
558C3×C4—68no—
559C3×C4—64no—
560C3×C4D3×#4114yes—
561C3×C4D3×#4114yes—
562Dic3—28no—
563Dic3—24no—
564Dic3—34no—
565Dic3—34no—
566Dic3—62no—
567Dic3—62no—
568Dic3—64no—
569Dic3—64no—
570Dic3—64no—
571Dic3—62no—
572Dic3—122no—
573Dic3—121no—
574C32C2×#55611yescharacteristic, complemented, Sylow
575C23—34no—
576C23—91no—
577C23—184no—
578C23—184no—
579C23—184no—
580Q8—22no—
581Q8—68no—
582Q8—184no—
583Q8—188no—
584Q8—182no—
585D4—64no—
586D4—184no—
587C2×C4—34no—
588C2×C4—38no—
589C2×C4—68no—
590C2×C4—91no—
591C2×C4—91no—
592C2×C4—94no—
593C2×C4—94no—
594C2×C4—92no—
595C2×C4—91no—
596C2×C4—92no—
597C2×C4—184no—
598C2×C4—184no—
599C2×C4—182no—
600C2×C4—184no—
601C2×C4—188no—
602C2×C4—188no—
603C2×C4C22×D3212yes—
604C2×C4C22×D3211yescharacteristic
605C2×C4C22×D3212yes—
606C2×C4C22×D3211yescharacteristic
607C2×C4C22×D3211yescharacteristic
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—124no—
612C2×C3C2×D3×#4112yes—
613C2×C3C2×D3×#4112yes—
614C2×C3D3×2−1+412yes—
615D3—38no—
616D3—44no—
617D3—64no—
618C22—64no—
619C22—64no—
620C22—64no—
621C22—92no—
622C22—92no—
623C22—92no—
624C22—368no—
625C22C23×D3211yescharacteristic
626C4—22no—
627C4—22no—
628C4—21no—
629C4—64no—
630C4—68no—
631C4—92no—
632C4—92no—
633C4—182no—
634C4—182no—
635C4—181no—
636C4#6430612yes—
637C4#6431912yes—
638C3—21no—
639C3D3×#55612yescomplemented
640C2—94no—
641C2—124no—
642C2C2×#6430611yescharacteristic
643C2C2×#6431911yescharacteristic
644C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3802C22
hypercenterC4×Q8D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×#5584C2semidirect
3. #10595429C2semidirect
4. #10595413C2semidirect
5. #10594656C2semidirect
6. #10594602C2semidirect
7. #10594581C2semidirect
8. #10594472C2semidirect
11. #10593942C2semidirect
12. #10593909C2semidirect
13. C4×#3797C2semidirect
14. #10593863C2semidirect
20. C32×C4×Q8C22semidirect
21. Q8×C3⋊Dic3C22semidirect
24. #64096C22semidirect
25. #64096C22semidirect
28. C4×#634C22semidirect
29. C4×#634C22semidirect
30. C3×#946C22semidirect
31. C3×#898C22semidirect
32. C3×#892C22semidirect
35. C3×#869C22semidirect
36. C3×C4×Dic6C22semidirect
40. #63919C22semidirect
41. #63919C22semidirect
42. C4×#627C22semidirect
51. #63896C22semidirect
54. #63877C22semidirect
55. #63873C22semidirect
57. #63861C22semidirect
58. #63859C22semidirect
59. #63858C22semidirect
60. #63857C22semidirect
61. #63843C22semidirect
62. #63841C22semidirect
63. #63838C22semidirect
73. #5584D3semidirect
146. C3×C4×Q8C2×D3semidirect
150. #946C2×D3semidirect
162. #898C2×D3semidirect
167. #892C2×D3semidirect
204. #869C2×D3semidirect
210. C4×Dic6C2×D3semidirect
399. C4×Q8D32semidirect
481. C3⋊D3#556semidirect
574. C32C2×#556semidirect
639. C3D3×#556semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#55842
#105954292
#105954132
#105946562
#105946022
#105945812
#105944722
#105940092
C4×#38022
#105939422
#105939092
C4×#37972
#105938632
D3×#5563