Finite Group Databasebeta

← #11856284

Subgroups — #11856284

Order 1152.

2321 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C2×#63976C211yesmaximal, characteristic
3C2×#63905C212yesmaximal, complemented
4#10592909C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6#10591718C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic, complemented
8#10591706C211yesmaximal, characteristic, complemented
9#10591381C212yesmaximal, complemented
10#10591294C212yesmaximal, complemented
11#10591278C212yesmaximal, complemented
12#84033—31nomaximal
13#74936—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×C4×D3—28no—
19C22×C3×C4×D3—24no—
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2212yes—
22C22×#625C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3750C2212yescomplemented
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2212yescomplemented
29#63976—24no—
30C2×Dic3⋊Dic3C2212yescomplemented
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yescomplemented
36#63905—28no—
37#63658C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39#63579C2212yescomplemented
40#63579C2212yescomplemented
41C24×C3×C4—31no—
42C23×C4×D3D311yescharacteristic, complemented
43C2×#953—31no—
44C2×#937—31no—
45C2×#929—32no—
46C2×#883—32no—
47C3×#386—31no—
48#5247—31no—
49#5220—31no—
50#5213—31no—
51#5213—32no—
52#5213D311yescharacteristic, complemented
53#5211—32no—
54#5210—31no—
55#5210—31no—
56#5210—31no—
57#5210—32no—
58#5210—61no—
59#4956—32no—
60#4955—31no—
61#4950—31no—
62#4668—32no—
63#4664—32no—
64C24×C32C2311yescharacteristic
65C23×C3×D3—22no—
66C23×C3×D3—22no—
67C23×C3×D3—24no—
68C23×C3×D3—24no—
69C23×C3×D3D414yes—
70C23×C3×D3C2311yescharacteristic
71C23×C3×D3C2311yescharacteristic
72C23×C3×D3C2311yescharacteristic
73C22×C32×C4—22no—
74C22×C32×C4—24no—
75C22×C32×C4C2312yes—
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C2×C3×#67—22no—
80C2×C3×#67—22no—
81C2×C3×#67—22no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—24no—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×C4×D3—232no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3D418yescomplemented
94C2×#625—24no—
95C2×#625—22no—
96C2×#625—22no—
97C2×#625—24no—
98#3757—22no—
99#3757—22no—
100#3750—24no—
101C3×#217—22no—
102C3×(C2×D3)⋊C4—24no—
103Dic3⋊Dic3—24no—
104(C2×D3)⋊Dic3—24no—
105(C2×D3)⋊Dic3—22no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—24no—
108(C2×D3)⋊Dic3—24no—
109#2849—91noSylow
110C25×C3—31no—
111C24×D3C2×D311yescharacteristic
112C22×C3×D4—31no—
113C23×C3×C4—21no—
114C23×C3×C4—32no—
115C23×C3×C4—31no—
116C23×C3×C4—32no—
117C23×C3×C4—68no—
118C23×C3×C4—64no—
119C23×C3×C4C2×D311yescharacteristic
120C23×C3×C4C2×D311yescharacteristic
121C22×#67—31no—
122C22×#67—31no—
123C22×#67—31no—
124C22×#67—31no—
125C22×#67C2×D311yescharacteristic
126C23×Dic3C2×D311yescharacteristic
127C22×C4×D3—24no—
128C22×C4×D3—28no—
129C22×C4×D3C2×D312yes—
130C22×C4×D3C2×D312yes—
131C2×C3×C22⋊C4—31no—
132C2×C3×C22⋊C4—32no—
133#953—64no—
134C2×#217—31no—
135C2×#217—31no—
136C2×#217—31no—
137C2×#217—31no—
138C2×#217—31no—
139C2×#217—32no—
140C2×#217—31no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—61no—
144C2×#217—61no—
145C2×#217C2×D311yescharacteristic
146#937—64no—
147#929—68no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4C2×D312yescomplemented
154C2×C4⋊Dic3—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—62no—
159#883—68no—
160C3×#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—32no—
164C3⋊#95—32no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C3⋊#95—62no—
168C3⋊#95C2×D312yescomplemented
169C23×C32—22no—
170C23×C32—22no—
171C23×C32C2×D412yes—
172C23×C32#4112yes—
173C23×C32#4112yes—
174C23×C32C2411yescharacteristic
175C22×C3×D3—216no—
176C22×C3×D3—216no—
177C22×C3×D3—28no—
178C22×C3×D3—22no—
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—21no—
183C22×C3×D3—22no—
184C22×C3×D3—28no—
185C22×C3×D3—28no—
186C22×C3×D3—22no—
187C22×C3×D3—21no—
188C22×C3×D3—22no—
189C22×C3×D3—21no—
190C22×C3×D3—21no—
191C22×C3×D3C2×D414yes—
192C22×C3×D3C2×D412yes—
193C22×C3×D3C2×D412yes—
194C22×C3×D3#4114yes—
195C2×C32×C4—28no—
196C2×C32×C4—22no—
197C2×C32×C4—22no—
198C2×C32×C4C2×D414yes—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—22no—
206C3×#67—44no—
207C2×C3×Dic3—28no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3C2×D414yes—
217C3×C4×D3—216no—
218C3×C4×D3—216no—
219#625—44no—
220#625—44no—
221C24×C4—31no—
222C2×#123—92no—
223C2×#120—91no—
224#386—31no—
225#386—92no—
226#386—91no—
227#385—92no—
228#385—91no—
229#385—91no—
230#381—92no—
231#379—91no—
232C24×C3—21no—
233C24×C3—31no—
234C24×C3—31no—
235C24×C3—34no—
236C24×C3—31no—
237C24×C3—64no—
238C24×C3—64no—
239C24×C3—62no—
240C24×C3—62no—
241C24×C3C22×D311yescharacteristic
242C24×C3C22×D311yescharacteristic
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—24no—
246C23×D3—24no—
247C23×D3#6714yes—
248C23×D3C22×D311yescharacteristic
249C23×D3C22×D311yescharacteristic
250C23×D3C22×D311yescharacteristic
251C2×C3×D4—62no—
252C2×C3×D4—62no—
253C2×C3×D4—62no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—24no—
257C22×C3×C4—24no—
258C22×C3×C4—22no—
259C22×C3×C4—32no—
260C22×C3×C4—38no—
261C22×C3×C4—31no—
262C22×C3×C4—32no—
263C22×C3×C4—44no—
264C22×C3×C4—42no—
265C22×C3×C4—64no—
266C22×C3×C4—64no—
267C22×C3×C4—64no—
268C22×C3×C4—64no—
269C22×C3×C4—632no—
270C22×C3×C4—64no—
271C22×C3×C4—62no—
272C22×C3×C4—64no—
273C22×C3×C4C22×D312yes—
274C22×C3×C4C22×D312yes—
275C2×#67—22no—
276C2×#67—22no—
277C2×#67—22no—
278C2×#67—64no—
279C2×#67—62no—
280C2×#67—62no—
281C2×#67—64no—
282C2×#67—64no—
283C2×#67—64no—
284C2×#67—62no—
285C2×#67—62no—
286C22×Dic3—22no—
287C22×Dic3—24no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—32no—
291C22×Dic3—32no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—62no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D312yes—
299C22×Dic3C22×D312yes—
300C2×C4×D3—232no—
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—24no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3#6718yescomplemented
307C3×C22⋊C4—62no—
308C3×C22⋊C4—64no—
309#217—22no—
310#217—64no—
311#217—64no—
312#217—62no—
313#217—62no—
314#217—64no—
315#217—62no—
316#217—62no—
317#217—62no—
318#217—62no—
319#217—64no—
320#217—122no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—64no—
323(C2×D3)⋊C4—64no—
324(C2×D3)⋊C4—64no—
325(C2×D3)⋊C4—62no—
326(C2×D3)⋊C4—62no—
327C4⋊Dic3—64no—
328Dic3⋊C4—64no—
329Dic3⋊C4—64no—
330Dic3⋊C4—64no—
331Dic3⋊C4—124no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—24no—
335C22×C32—24no—
336C22×C32#12314yescomplemented
337C22×C32C22×D411yescharacteristic
338C22×C32C22×D412yes—
339C22×C32C2×#4111yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C22×C32C2×#4112yes—
342C2×C3×D3—232no—
343C2×C3×D3—22no—
344C2×C3×D3—22no—
345C2×C3×D3—22no—
346C2×C3×D3—22no—
347C2×C3×D3—24no—
348C2×C3×D3—24no—
349C2×C3×D3—24no—
350C2×C3×D3—24no—
351C2×C3×D3—41no—
352C2×C3×D3—41no—
353C2×C3×D3—41no—
354C2×C3×D3—42no—
355C2×C3×D3—42no—
356C2×C3×D3#12014yes—
357C2×C3×D3#12314yescomplemented
358C32×C4—24no—
359C3⋊Dic3—42no—
360C3⋊Dic3—41no—
361C3⋊Dic3—41no—
362C3×Dic3—24no—
363C3×Dic3—41no—
364C3×Dic3—42no—
365C25—31no—
366C22×D4—31no—
367C22×D4—91no—
368C22×D4—91no—
369C23×C4—32no—
370C23×C4—31no—
371C23×C4—32no—
372C23×C4—68no—
373C23×C4—64no—
374C23×C4D3211yescharacteristic
375#123—188no—
376#120—184no—
377C2×C4⋊C4—92no—
378C2×C4⋊C4—92no—
379C2×C22⋊C4—31no—
380C2×C22⋊C4—32no—
381C2×C22⋊C4—91no—
382C2×C22⋊C4—91no—
383C2×C22⋊C4—92no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4—92no—
386C2×C22⋊C4—91no—
387C2×C22⋊C4—91no—
388#95—32no—
389#95—92no—
390#95—92no—
391#95—92no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—21no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—34no—
401C23×C3—32no—
402C23×C3—32no—
403C23×C3—34no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—68no—
407C23×C3—68no—
408C23×C3—616no—
409C23×C3—616no—
410C23×C3—68no—
411C23×C3—61no—
412C23×C3—61no—
413C23×C3—62no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—62no—
417C23×C3—62no—
418C23×C3—61no—
419C23×C3—61no—
420C23×C3—62no—
421C23×C3—61no—
422C23×C3#23512yes—
423C23×C3#23512yes—
424C23×C3#23512yes—
425C23×C3D3×D412yes—
426C23×C3#23712yes—
427C23×C3C2×#6712yes—
428C23×C3C23×D311yescharacteristic
429C23×C3C23×D311yescharacteristic
430C22×D3—216no—
431C22×D3—216no—
432C22×D3—28no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—28no—
440C22×D3—28no—
441C22×D3—21no—
442C22×D3—22no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—22no—
446C22×D3#23514yes—
447C22×D3C2×#6712yes—
448C22×D3C2×#6712yes—
449C22×D3C2×#6714yes—
450C3×D4—124no—
451C2×C3×C4—28no—
452C2×C3×C4—28no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—24no—
458C2×C3×C4—34no—
459C2×C3×C4—42no—
460C2×C3×C4—42no—
461C2×C3×C4—48no—
462C2×C3×C4—616no—
463C2×C3×C4—616no—
464C2×C3×C4—68no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—62no—
472C2×C3×C4—61no—
473C2×C3×C4D3×D414yes—
474C2×C3×C4C2×#6714yes—
475#67—44no—
476#67—124no—
477#67—124no—
478#67—124no—
479#67—124no—
480C2×Dic3—28no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—21no—
484C2×Dic3—22no—
485C2×Dic3—21no—
486C2×Dic3—22no—
487C2×Dic3—21no—
488C2×Dic3—22no—
489C2×Dic3—64no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—62no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—122no—
505C2×Dic3—122no—
506C2×Dic3—122no—
507C2×Dic3—121no—
508C2×Dic3—121no—
509C2×Dic3—122no—
510C2×Dic3C2×#6714yes—
511C4×D3—216no—
512C4×D3—216no—
513C2×C32—24no—
514C2×C32C2×#12011yescharacteristic
515C2×C32C2×#12311yescharacteristic
516C2×C32C2×#12311yescharacteristic
517C2×C32#52512yes—
518C2×C32#52512yes—
519C3×D3—24no—
520C3×D3—24no—
521C3×D3—81no—
522C24—31no—
523C24—31no—
524C24—34no—
525C24—31no—
526C24—64no—
527C24—64no—
528C24—62no—
529C24—62no—
530C24C2×D3211yescharacteristic
531C2×D4—62no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—182no—
535C2×D4—182no—
536C2×D4—184no—
537C2×D4—184no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—32no—
541C22×C4—38no—
542C22×C4—31no—
543C22×C4—32no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—632no—
549C22×C4—64no—
550C22×C4—62no—
551C22×C4—64no—
552C22×C4—91no—
553C22×C4—92no—
554C22×C4—91no—
555C22×C4C2×D3212yes—
556C4⋊C4—184no—
557C4⋊C4—184no—
558C22⋊C4—62no—
559C22⋊C4—64no—
560C22⋊C4—184no—
561C22⋊C4—182no—
562C22⋊C4—182no—
563C22⋊C4—184no—
564C22⋊C4—184no—
565C22⋊C4—182no—
566C22⋊C4—182no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—24no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—24no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—21no—
580C22×C3—24no—
581C22×C3—34no—
582C22×C3—34no—
583C22×C3—42no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—42no—
587C22×C3—632no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—62no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—62no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3—121no—
597C22×C3—121no—
598C22×C3—122no—
599C22×C3—122no—
600C22×C3—121no—
601C22×C3#88314yescomplemented
602C22×C3#92914yescomplemented
603C22×C3C2×#23511yescharacteristic
604C22×C3C2×#23511yescharacteristic
605C22×C3C2×#23511yescharacteristic
606C22×C3C2×#23512yes—
607C22×C3C2×D3×D411yescharacteristic
608C22×C3C2×D3×D412yes—
609C22×C3C2×#23711yescharacteristic
610C22×C3D3×#4112yes—
611C22×C3C22×#6711yescharacteristic
612C22×C3C22×#6712yes—
613C2×D3—232no—
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—22no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—22no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—42no—
625C2×D3—41no—
626C2×D3—42no—
627C2×D3#92914yescomplemented
628C2×D3#95314yes—
629C3×C4—24no—
630C3×C4—24no—
631C3×C4—44no—
632C3×C4—64no—
633C3×C4—121no—
634C3×C4—122no—
635Dic3—24no—
636Dic3—41no—
637Dic3—42no—
638Dic3—124no—
639Dic3—121no—
640Dic3—121no—
641Dic3—122no—
642Dic3—122no—
643Dic3—121no—
644Dic3—121no—
645Dic3—241no—
646Dic3—241no—
647C32#284911yescharacteristic, complemented, Sylow
648C23—22no—
649C23—22no—
650C23—34no—
651C23—34no—
652C23—32no—
653C23—32no—
654C23—68no—
655C23—68no—
656C23—616no—
657C23—616no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23—62no—
663C23—62no—
664C23—68no—
665C23—61no—
666C23—61no—
667C23—62no—
668C23—62no—
669C23—61no—
670C23#379512yes—
671C23#379812yes—
672C23D3×#6712yes—
673C23C22×D3211yescharacteristic
674D4—124no—
675D4—364no—
676D4—364no—
677C2×C4—28no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—34no—
681C2×C4—616no—
682C2×C4—616no—
683C2×C4—68no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—61no—
692C2×C4—182no—
693C2×C4—182no—
694C2×C4—182no—
695C2×C4—182no—
696C2×C4—181no—
697C2×C4—181no—
698C2×C4—182no—
699C2×C4D3×#6714yes—
700C2×C3—24no—
701C2×C3—24no—
702C2×C3—22no—
703C2×C3—21no—
704C2×C3—22no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—44no—
708C2×C3—64no—
709C2×C3—64no—
710C2×C3—241no—
711C2×C3C2×#88311yescharacteristic
712C2×C3#554712yes—
713C2×C3D3×#12011yescharacteristic
714C2×C3#560612yes—
715C2×C3D3×#12311yescharacteristic
716C2×C3C2×#92911yescharacteristic
717C2×C3C2×#92911yescharacteristic
718C2×C3#579112yes—
719C2×C3#579112yes—
720C2×C3C2×#95311yescharacteristic
721D3—24no—
722D3—24no—
723D3—81no—
724C22—24no—
725C22—24no—
726C22—22no—
727C22—22no—
728C22—34no—
729C22—34no—
730C22—632no—
731C22—64no—
732C22—64no—
733C22—62no—
734C22—62no—
735C22—64no—
736C22—64no—
737C22—62no—
738C22—62no—
739C22—122no—
740C22—121no—
741C22—122no—
742C22—121no—
743C22—121no—
744C22#6390514yescomplemented
745C22C2×#379511yescharacteristic
746C22C2×#379811yescharacteristic
747C22D3×#23512yes—
748C22C2×D3×#6712yes—
749C22C2×D3×#6711yescharacteristic
750C4—24no—
751C4—64no—
752C4—122no—
753C4—121no—
754C4—362no—
755C4—361no—
756C4—361no—
757C3—21no—
758C3#7493611yescharacteristic, complemented
759C3#8403311yescharacteristic, complemented
760C2—24no—
761C2—64no—
762C2—64no—
763C2—241no—
764C2#1059489212yes—
765C2C2×#6390511yescharacteristic
766C2#1059500212yes—
767C2D3×#92911yescharacteristic
768C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC2×#63976C2
hypercenterC23×C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
3. C2×#63905C2semidirect
4. #10592909C2semidirect
5. C3×#5213C2semidirect
6. #10591718C2semidirect
7. #10591710C2semidirect
8. #10591706C2semidirect
9. #10591381C2semidirect
10. #10591294C2semidirect
11. #10591278C2semidirect
26. C2×#3750C22semidirect
28. C2×C3×(C2×D3)⋊C4C22semidirect
30. C2×Dic3⋊Dic3C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
37. #63658C22semidirect
38. C3×C3⋊#95C22semidirect
39. #63579C22semidirect
40. #63579C22semidirect
42. C23×C4×D3D3semidirect
52. #5213D3semidirect
93. C2×C3×C4×D3D4semidirect
153. C2×(C2×D3)⋊C4C2×D3semidirect
168. C3⋊#95C2×D3semidirect
306. C2×C4×D3#67semidirect
336. C22×C32#123semidirect
357. C2×C3×D3#123semidirect
601. C22×C3#883semidirect
602. C22×C3#929semidirect
627. C2×D3#929semidirect
647. C32#2849semidirect
744. C22#63905semidirect
758. C3#74936semidirect
759. C3#84033semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C2×#639762
C2×#639052
#105929092
C3×#52132
#105917182
#105917102
#105917062
#105913812
#105912942
#105912782
#840333
#749363