Finite Group Databasebeta

← #11802005

Subgroups — #11802005

Order 1152.

2565 conjugacy classes of subgroups.

The subgroup lattice has 762 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×Dic3×#67C211yesmaximal, characteristic, complemented
4C2×#63879C212yesmaximal, complemented
5#10592909C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8Dic3×#217C211yesmaximal, characteristic, complemented
9#10591381C212yesmaximal, complemented
10#10591278C212yesmaximal, complemented
11#10591237C212yesmaximal, complemented
12C4×#953—31nomaximal
13#74659—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×C4×D3—24no—
19C22×C3×C4×D3—28no—
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2212yes—
22C22×#625C2212yes—
23C22×D3×Dic3C2211yescharacteristic, complemented
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3750C2212yescomplemented
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2212yescomplemented
29#63976C418yescomplemented
30Dic3×#67—24no—
31C2×Dic3⋊Dic3C2211yescharacteristic, complemented
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
36C2×Dic32C2211yescharacteristic, complemented
37C2×Dic32C2212yescomplemented
38#63879—28no—
39#63658C2212yescomplemented
40C3×C3⋊#95C2212yescomplemented
41#63579C2212yescomplemented
42C24×C3×C4—31no—
43C23×C4×D3D311yescharacteristic, complemented
44C2×#953—31no—
45C2×#937—31no—
46C2×D4×Dic3—31no—
47C2×C4×#67—31no—
48C2×C4×#67—32no—
49C2×#67⋊C4—32no—
50C3×#386—31no—
51#5247—31no—
52#5213—32no—
53#5213D311yescharacteristic, complemented
54#5210—31no—
55#5210—31no—
56#5210—32no—
57#5210—61no—
58C4×#217—31no—
59C4×#217—32no—
60#4956—32no—
61#4955—31no—
62Dic3×C22⋊C4—31no—
63#4668—32no—
64#4666—32no—
65C24×C32C2311yescharacteristic
66C23×C3×D3—22no—
67C23×C3×D3—22no—
68C23×C3×D3—24no—
69C23×C3×D3—24no—
70C23×C3×D3C2×C414yescomplemented
71C23×C3×D3C2311yescharacteristic
72C23×C3×D3C2312yes—
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×#67C2×C414yescomplemented
82C22×C3×Dic3—24no—
83C22×C3×Dic3D414yescomplemented
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C2×C3×C4×D3—232no—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3D418yescomplemented
95C2×#625—24no—
96C2×#625—24no—
97C2×#625C2×C418yescomplemented
98C2×D3×Dic3—24no—
99C2×D3×Dic3—22no—
100#3757—22no—
101#3757C2×C414yescomplemented
102#3750—24no—
103C3×#217—22no—
104C3×(C2×D3)⋊C4—24no—
105Dic3⋊Dic3—22no—
106(C2×D3)⋊Dic3—24no—
107(C2×D3)⋊Dic3—24no—
108(C2×D3)⋊Dic3—22no—
109(C2×D3)⋊Dic3C2×C418yescomplemented
110Dic32—24no—
111Dic32—22no—
112C4×#120—91noSylow
113C25×C3—31no—
114C24×D3C2×D311yescharacteristic
115C22×C3×D4—31no—
116C23×C3×C4—21no—
117C23×C3×C4—31no—
118C23×C3×C4—32no—
119C23×C3×C4—32no—
120C23×C3×C4—64no—
121C23×C3×C4—68no—
122C23×C3×C4C2×D311yescharacteristic
123C23×C3×C4C2×D311yescharacteristic
124C22×#67—32no—
125C22×#67—32no—
126C22×#67C2×D311yescharacteristic
127C23×Dic3—31no—
128C23×Dic3C2×D311yescharacteristic
129C22×C4×D3—24no—
130C22×C4×D3—28no—
131C22×C4×D3—31no—
132C22×C4×D3C2×D312yes—
133C22×C4×D3C2×D312yes—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—32no—
136#953—38no—
137C2×#217—31no—
138C2×#217—31no—
139C2×#217—32no—
140C2×#217—31no—
141C2×#217—31no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—31no—
145C2×#217—61no—
146C2×#217—61no—
147C2×#217C2×D311yescharacteristic
148#937—38no—
149D4×Dic3—64no—
150C4×#67—68no—
151C4×#67—64no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4C2×D312yescomplemented
157C2×C4⋊Dic3—31no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—62no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—32no—
164C2×C4×Dic3—32no—
165C2×C4×Dic3—31no—
166#67⋊C4—68no—
167C3×#95—32no—
168C3⋊#95—32no—
169C3⋊#95—32no—
170C3⋊#95—32no—
171C3⋊#95—32no—
172C3⋊#95—62no—
173C3⋊#95C2×D312yescomplemented
174C23×C32—22no—
175C23×C32—22no—
176C23×C32C22×C412yes—
177C23×C32C2×D412yes—
178C23×C32#4112yes—
179C23×C32C2411yescharacteristic
180C22×C3×D3—216no—
181C22×C3×D3—28no—
182C22×C3×D3—28no—
183C22×C3×D3—28no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—216no—
189C22×C3×D3—21no—
190C22×C3×D3—22no—
191C22×C3×D3—22no—
192C22×C3×D3—21no—
193C22×C3×D3C22×C414yes—
194C22×C3×D3C22×C412yescomplemented
195C22×C3×D3C2×D414yes—
196C22×C3×D3#4114yes—
197C2×C32×C4—28no—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200C2×C32×C4C2×D414yes—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—22no—
207C2×C3⋊Dic3C22×C414yescomplemented
208C3×#67—28no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—28no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—22no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3C22×C412yescomplemented
217C2×C3×Dic3C2×D412yes—
218C2×C3×Dic3C2×D412yes—
219C2×C3×Dic3C2×D414yes—
220C3×C4×D3—216no—
221C3×C4×D3—216no—
222#625—216no—
223D3×Dic3—44no—
224C24×C4—31no—
225C2×#120—91no—
226C2×C4×D4—92no—
227C2×C4×D4—91no—
228#386—31no—
229#386—92no—
230#385—92no—
231#385—91no—
232#379—91no—
233C4×C22⋊C4—92no—
234C4×C22⋊C4—91no—
235C24×C3—21no—
236C24×C3—32no—
237C24×C3—34no—
238C24×C3—31no—
239C24×C3—64no—
240C24×C3—64no—
241C24×C3—62no—
242C24×C3—62no—
243C24×C3C22×D311yescharacteristic
244C24×C3C22×D311yescharacteristic
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—24no—
248C23×D3—24no—
249C23×D3C4×D314yescomplemented
250C23×D3C22×D311yescharacteristic
251C23×D3C22×D312yes—
252C2×C3×D4—34no—
253C2×C3×D4—62no—
254C2×C3×D4—62no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—24no—
258C22×C3×C4—24no—
259C22×C3×C4—22no—
260C22×C3×C4—31no—
261C22×C3×C4—34no—
262C22×C3×C4—31no—
263C22×C3×C4—31no—
264C22×C3×C4—38no—
265C22×C3×C4—32no—
266C22×C3×C4—44no—
267C22×C3×C4—42no—
268C22×C3×C4—64no—
269C22×C3×C4—64no—
270C22×C3×C4—64no—
271C22×C3×C4—64no—
272C22×C3×C4—632no—
273C22×C3×C4—64no—
274C22×C3×C4—64no—
275C22×C3×C4C22×D312yes—
276C22×C3×C4C22×D312yes—
277C2×#67—22no—
278C2×#67—22no—
279C2×#67—38no—
280C2×#67—38no—
281C2×#67—64no—
282C2×#67—64no—
283C2×#67—64no—
284C2×#67—64no—
285C2×#67C4×D314yescomplemented
286C22×Dic3—24no—
287C22×Dic3—32no—
288C22×Dic3—32no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—62no—
294C22×Dic3—61no—
295C22×Dic3—61no—
296C22×Dic3—64no—
297C22×Dic3—62no—
298C22×Dic3#6714yescomplemented
299C22×Dic3C22×D312yes—
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D311yescharacteristic
303C2×C4×D3—232no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—64no—
310C2×C4×D3—62no—
311C2×C4×D3#6718yescomplemented
312C3×C22⋊C4—62no—
313C3×C22⋊C4—64no—
314#217—22no—
315#217—34no—
316#217—34no—
317#217—38no—
318#217—64no—
319#217—64no—
320#217—64no—
321#217—62no—
322#217—62no—
323#217—62no—
324#217—122no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—38no—
327(C2×D3)⋊C4—62no—
328(C2×D3)⋊C4—64no—
329(C2×D3)⋊C4—64no—
330C4⋊Dic3—62no—
331Dic3⋊C4—62no—
332Dic3⋊C4—64no—
333Dic3⋊C4—64no—
334Dic3⋊C4—124no—
335C4×Dic3—62no—
336C4×Dic3—64no—
337C4×Dic3—64no—
338C4×Dic3—62no—
339C22×C32—24no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—24no—
343C22×C32C4×D414yescomplemented
344C22×C32C23×C411yescharacteristic
345C22×C32C22×D412yes—
346C22×C32C22×D411yescharacteristic
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4112yes—
349C2×C3×D3—232no—
350C2×C3×D3—24no—
351C2×C3×D3—24no—
352C2×C3×D3—24no—
353C2×C3×D3—24no—
354C2×C3×D3—24no—
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—22no—
358C2×C3×D3—41no—
359C2×C3×D3—41no—
360C2×C3×D3—42no—
361C2×C3×D3C4×D418yescomplemented
362C32×C4—24no—
363C3⋊Dic3—24no—
364C3⋊Dic3—41no—
365C3⋊Dic3—41no—
366C3×Dic3—22no—
367C3×Dic3—22no—
368C3×Dic3—42no—
369C3×Dic3#12014yescomplemented
370C25—31no—
371C22×D4—31no—
372C22×D4—92no—
373C23×C4—31no—
374C23×C4—32no—
375C23×C4—32no—
376C23×C4—64no—
377C23×C4—68no—
378C23×C4—91no—
379C23×C4D3211yescharacteristic
380#120—98no—
381C4×D4—188no—
382C4×D4—184no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—92no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—32no—
387C2×C22⋊C4—92no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—92no—
390C2×C22⋊C4—91no—
391C2×C22⋊C4—92no—
392C2×C22⋊C4—91no—
393C2×C42—91no—
394C2×C42—92no—
395#95—32no—
396#95—92no—
397#95—92no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—34no—
407C23×C3—34no—
408C23×C3—34no—
409C23×C3—32no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—616no—
413C23×C3—68no—
414C23×C3—68no—
415C23×C3—616no—
416C23×C3—68no—
417C23×C3—62no—
418C23×C3—62no—
419C23×C3—62no—
420C23×C3—62no—
421C23×C3—62no—
422C23×C3—61no—
423C23×C3—61no—
424C23×C3—62no—
425C23×C3C2×C4×D312yes—
426C23×C3C2×C4×D312yes—
427C23×C3#23512yes—
428C23×C3D3×D412yes—
429C23×C3#23712yes—
430C23×C3C2×#6712yes—
431C23×C3C23×D311yescharacteristic
432C23×C3C23×D311yescharacteristic
433C22×D3—28no—
434C22×D3—28no—
435C22×D3—216no—
436C22×D3—28no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—216no—
442C22×D3—22no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—22no—
446C22×D3C2×C4×D314yes—
447C22×D3C2×C4×D312yescomplemented
448C22×D3#23514yes—
449C22×D3C2×#6714yes—
450C3×D4—68no—
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—32no—
459C2×C3×C4—34no—
460C2×C3×C4—32no—
461C2×C3×C4—32no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—48no—
465C2×C3×C4—616no—
466C2×C3×C4—616no—
467C2×C3×C4—68no—
468C2×C3×C4—61no—
469C2×C3×C4—62no—
470C2×C3×C4—61no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4D3×D414yes—
475C2×C3×C4C2×#6714yes—
476#67—28no—
477#67—616no—
478#67—616no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—28no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—34no—
487C2×Dic3—34no—
488C2×Dic3—64no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—62no—
497C2×Dic3—62no—
498C2×Dic3—61no—
499C2×Dic3—62no—
500C2×Dic3—61no—
501C2×Dic3—122no—
502C2×Dic3—122no—
503C2×Dic3—122no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3—122no—
507C2×Dic3—124no—
508C2×Dic3C2×C4×D312yescomplemented
509C2×Dic3C2×#6712yes—
510C2×Dic3C2×#6712yes—
511C2×Dic3C2×#6714yes—
512C4×D3—216no—
513C4×D3—216no—
514C4×D3—124no—
515C2×C32—24no—
516C2×C32C2×C4×D411yescharacteristic
517C2×C32C2×C4×D412yes—
518C2×C32C2×#12011yescharacteristic
519C2×C32#52511yescharacteristic
520C2×C32#52512yes—
521C3×D3—28no—
522C3×D3—42no—
523C24—32no—
524C24—31no—
525C24—34no—
526C24—64no—
527C24—64no—
528C24—62no—
529C24—62no—
530C24C2×D3211yescharacteristic
531C2×D4—34no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—98no—
535C2×D4—184no—
536C2×D4—184no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—34no—
543C22×C4—38no—
544C22×C4—32no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—64no—
549C22×C4—632no—
550C22×C4—64no—
551C22×C4—64no—
552C22×C4—92no—
553C22×C4—91no—
554C22×C4—91no—
555C22×C4—184no—
556C22×C4—182no—
557C22×C4C2×D3212yes—
558C4⋊C4—182no—
559C4⋊C4—184no—
560C22⋊C4—62no—
561C22⋊C4—64no—
562C22⋊C4—98no—
563C22⋊C4—94no—
564C22⋊C4—182no—
565C22⋊C4—184no—
566C22⋊C4—184no—
567C22⋊C4—182no—
568C42—182no—
569C42—184no—
570C22×C3—22no—
571C22×C3—24no—
572C22×C3—24no—
573C22×C3—22no—
574C22×C3—24no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—24no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—21no—
583C22×C3—24no—
584C22×C3—38no—
585C22×C3—42no—
586C22×C3—44no—
587C22×C3—42no—
588C22×C3—44no—
589C22×C3—632no—
590C22×C3—64no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—64no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3—64no—
597C22×C3—62no—
598C22×C3—122no—
599C22×C3—121no—
600C22×C3—121no—
601C22×C3#67⋊C414yescomplemented
602C22×C3C4×#6714yescomplemented
603C22×C3C22×C4×D311yescharacteristic
604C22×C3C22×C4×D311yescharacteristic
605C22×C3C2×#23511yescharacteristic
606C22×C3C2×#23512yes—
607C22×C3C2×D3×D411yescharacteristic
608C22×C3C2×D3×D412yes—
609C22×C3C2×#23711yescharacteristic
610C22×C3D3×#4112yes—
611C22×C3C22×#6712yes—
612C22×C3C22×#6711yescharacteristic
613C2×D3—232no—
614C2×D3—24no—
615C2×D3—24no—
616C2×D3—24no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—22no—
621C2×D3—24no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—42no—
625C2×D3C4×#6718yescomplemented
626C3×C4—24no—
627C3×C4—24no—
628C3×C4—34no—
629C3×C4—44no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4—122no—
633Dic3—22no—
634Dic3—22no—
635Dic3—42no—
636Dic3—64no—
637Dic3—64no—
638Dic3—124no—
639Dic3—121no—
640Dic3—121no—
641Dic3—121no—
642Dic3—121no—
643Dic3—241no—
644Dic3—241no—
645Dic3#95314yescomplemented
646C32C4×#12011yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—34no—
650C23—34no—
651C23—34no—
652C23—32no—
653C23—616no—
654C23—68no—
655C23—616no—
656C23—68no—
657C23—62no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—68no—
662C23—61no—
663C23—62no—
664C23—62no—
665C23—61no—
666C23#379512yes—
667C23C4×D3212yes—
668C23D3×#6712yes—
669C23C22×D3211yescharacteristic
670D4—68no—
671D4—1816no—
672C2×C4—28no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—32no—
676C2×C4—34no—
677C2×C4—32no—
678C2×C4—32no—
679C2×C4—616no—
680C2×C4—616no—
681C2×C4—68no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—94no—
689C2×C4—182no—
690C2×C4—182no—
691C2×C4—182no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—182no—
695C2×C4—364no—
696C2×C4D3×#6714yes—
697C2×C3—24no—
698C2×C3—24no—
699C2×C3—21no—
700C2×C3—22no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—22no—
704C2×C3—44no—
705C2×C3—68no—
706C2×C3—122no—
707C2×C3C2×#67⋊C411yescharacteristic
708C2×C3C4×D3×D412yes—
709C2×C3D3×#12011yescharacteristic
710C2×C3#560612yes—
711C2×C3#565611yescharacteristic
712C2×C3C2×C4×#6711yescharacteristic
713C2×C3C2×C4×#6712yes—
714C2×C3#579112yes—
715C2×C3#579111yescharacteristic
716C2×C3C2×#95311yescharacteristic
717D3—28no—
718D3—42no—
719C22—24no—
720C22—22no—
721C22—22no—
722C22—24no—
723C22—38no—
724C22—632no—
725C22—64no—
726C22—64no—
727C22—64no—
728C22—64no—
729C22—64no—
730C22—64no—
731C22—62no—
732C22—64no—
733C22—122no—
734C22—121no—
735C22—121no—
736C22#6387914yescomplemented
737C22C2×#379511yescharacteristic
738C22C2×C4×D3211yescharacteristic
739C22D3×#23512yes—
740C22C2×D3×#6711yescharacteristic
741C22C2×D3×#6712yes—
742C4—24no—
743C4—34no—
744C4—62no—
745C4—62no—
746C4—122no—
747C4—184no—
748C4—361no—
749C4—361no—
750C3—21no—
751C3#7465911yescharacteristic, complemented
752C3C4×#95311yescharacteristic, complemented
753C2—24no—
754C2—68no—
755C2—122no—
756C2C2×#6387911yescharacteristic
757C2#1059489212yes—
758C2#1059489611yescharacteristic
759C2C4×D3×#6712yes—
760C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63976C2
hypercenterC23×C4D32
hypocenterC32C4×#120
LCSG ▷ C22×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×Dic3×#67C2semidirect
4. C2×#63879C2semidirect
5. #10592909C2semidirect
6. C3×#5213C2semidirect
7. #10591706C2semidirect
8. Dic3×#217C2semidirect
9. #10591381C2semidirect
10. #10591278C2semidirect
11. #10591237C2semidirect
23. C22×D3×Dic3C22semidirect
26. C2×#3750C22semidirect
28. C2×C3×(C2×D3)⋊C4C22semidirect
29. #63976C4semidirect
31. C2×Dic3⋊Dic3C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. C2×Dic32C22semidirect
37. C2×Dic32C22semidirect
39. #63658C22semidirect
40. C3×C3⋊#95C22semidirect
41. #63579C22semidirect
43. C23×C4×D3D3semidirect
53. #5213D3semidirect
70. C23×C3×D3C2×C4semidirect
81. C2×C3×#67C2×C4semidirect
83. C22×C3×Dic3D4semidirect
94. C2×C3×C4×D3D4semidirect
97. C2×#625C2×C4semidirect
101. #3757C2×C4semidirect
109. (C2×D3)⋊Dic3C2×C4semidirect
156. C2×(C2×D3)⋊C4C2×D3semidirect
173. C3⋊#95C2×D3semidirect
194. C22×C3×D3C22×C4semidirect
207. C2×C3⋊Dic3C22×C4semidirect
216. C2×C3×Dic3C22×C4semidirect
249. C23×D3C4×D3semidirect
285. C2×#67C4×D3semidirect
298. C22×Dic3#67semidirect
311. C2×C4×D3#67semidirect
343. C22×C32C4×D4semidirect
361. C2×C3×D3C4×D4semidirect
369. C3×Dic3#120semidirect
447. C22×D3C2×C4×D3semidirect
508. C2×Dic3C2×C4×D3semidirect
601. C22×C3#67⋊C4semidirect
602. C22×C3C4×#67semidirect
625. C2×D3C4×#67semidirect
645. Dic3#953semidirect
646. C32C4×#120semidirect
736. C22#63879semidirect
751. C3#74659semidirect
752. C3C4×#953semidirect

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×Dic3×#672
C2×#638792
#105929092
C3×#52132
#105917062
Dic3×#2172
#105913812
#105912782
#105912372
C4×#9533
#746593