Finite Group Databasebeta

← #11856286

Subgroups — #11856286

Order 1152.

2347 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×#63969C212yesmaximal, complemented
4#10592919C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6#10591721C212yesmaximal, complemented
7#10591719C211yesmaximal, characteristic, complemented
8#10591706C211yesmaximal, characteristic, complemented
9#10591693C211yesmaximal, characteristic, complemented
10#10591373C212yesmaximal, complemented
11#10591362C212yesmaximal, complemented
12#82602—31nomaximal
13#74936—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×D3×Dic3—28no—
21C22×D3×Dic3—24no—
22C22×D3×Dic3C2212yes—
23C22×D3×Dic3C2212yes—
24C2×#3757C2211yescharacteristic
25C2×#3757C2212yescomplemented
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2212yescomplemented
29C3×#937—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32#63969—28no—
33C2×#3724C2212yescomplemented
34C2×Dic3⋊Dic3C2212yescomplemented
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37#63658C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39#63579C2212yescomplemented
40#63579C2212yescomplemented
41C24×Dic3—31no—
42C23×C4×D3—31no—
43C2×C3×#120—31no—
44C2×#937D311yescharacteristic
45C2×#935—32no—
46C2×#883—32no—
47C3×#386—31no—
48#5247—31no—
49#5220—31no—
50#5220—31no—
51#5220—32no—
52#5220—61no—
53#5220D311yescharacteristic, complemented
54#5210—31no—
55#4956—32no—
56#4955—31no—
57#4950—31no—
58#4946—31no—
59#4946—31no—
60#4946—32no—
61#4943—32no—
62#4668—32no—
63#4664—32no—
64C24×C32C2311yescharacteristic
65C24×C32C2311yescharacteristic
66C23×C3×D3—22no—
67C23×C3×D3—22no—
68C23×C3×D3—24no—
69C23×C3×D3—24no—
70C23×C3×D3D414yes—
71C23×C3×D3C2311yescharacteristic
72C23×C3×D3C2311yescharacteristic
73C2×C32×D4—22no—
74C2×C32×D4—22no—
75C2×C32×D4—22no—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3—22no—
78C22×C3⋊Dic3—24no—
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2312yes—
81C2×C3×#67—22no—
82C2×C3×#67—22no—
83C2×C3×#67—24no—
84C2×C3×#67—24no—
85C22×C3×Dic3—22no—
86C22×C3×Dic3—24no—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C2×D3×Dic3—232no—
92C2×D3×Dic3—24no—
93C2×D3×Dic3—24no—
94C2×D3×Dic3—24no—
95C2×D3×Dic3—24no—
96C2×D3×Dic3—24no—
97C2×D3×Dic3D418yescomplemented
98#3757—22no—
99#3757—24no—
100C3×#217—22no—
101C3×#217—22no—
102C3×#217—24no—
103C3×(C2×D3)⋊C4—22no—
104C3×(C2×D3)⋊C4—22no—
105#3724—24no—
106Dic3⋊Dic3—24no—
107(C2×D3)⋊Dic3—24no—
108(C2×D3)⋊Dic3—24no—
109#2849—91noSylow
110C25×C3—31no—
111C24×D3C2×D311yescharacteristic
112C22×C3×D4—21no—
113C22×C3×D4—31no—
114C22×C3×D4—31no—
115C22×C3×D4C2×D311yescharacteristic
116C22×C3×D4C2×D311yescharacteristic
117C23×C3×C4—31no—
118C22×#67C2×D311yescharacteristic
119C22×#67C2×D311yescharacteristic
120C23×Dic3—32no—
121C23×Dic3—31no—
122C23×Dic3—31no—
123C23×Dic3—32no—
124C23×Dic3—61no—
125C23×Dic3—68no—
126C23×Dic3—64no—
127C23×Dic3C2×D311yescharacteristic
128C22×C4×D3—32no—
129C22×C4×D3—32no—
130C22×C4×D3—68no—
131C22×C4×D3—64no—
132C3×#120—64no—
133C2×C3×C22⋊C4—31no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×#217—31no—
139C2×#217—31no—
140C2×#217—32no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—61no—
145C2×#217—62no—
146C2×#217C2×D311yescharacteristic
147C2×#217C2×D311yescharacteristic
148C2×#217C2×D312yescomplemented
149#937—24no—
150#935—68no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4C2×D311yescharacteristic
154C2×(C2×D3)⋊C4C2×D311yescharacteristic
155C2×C4⋊Dic3—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
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—21no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32—21no—
174C23×C32—22no—
175C23×C32—21no—
176C23×C32C2×D412yes—
177C23×C32#4112yes—
178C23×C32#4112yes—
179C23×C32C2411yescharacteristic
180C22×C3×D3—216no—
181C22×C3×D3—216no—
182C22×C3×D3—28no—
183C22×C3×D3—22no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3—22no—
189C22×C3×D3—28no—
190C22×C3×D3—28no—
191C22×C3×D3C2×D414yes—
192C22×C3×D3C2×D412yes—
193C22×C3×D3C2×D412yes—
194C22×C3×D3#4114yes—
195C32×D4—44no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C3⋊Dic3—28no—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3C2×D414yes—
206C3×#67—44no—
207C3×#67—44no—
208C2×C3×Dic3—28no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3C2×D414yes—
219D3×Dic3—216no—
220D3×Dic3—216no—
221C24×C4—91no—
222C2×#123—92no—
223C2×#120—31no—
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—21no—
234C24×C3—31no—
235C24×C3—31no—
236C24×C3—34no—
237C24×C3—64no—
238C24×C3—64no—
239C24×C3—62no—
240C24×C3—62no—
241C24×C3C22×D311yescharacteristic
242C24×C3C22×D311yescharacteristic
243C24×C3C22×D311yescharacteristic
244C24×C3C22×D311yescharacteristic
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—24no—
248C23×D3—24no—
249C23×D3#6714yes—
250C23×D3C22×D311yescharacteristic
251C23×D3C22×D311yescharacteristic
252C2×C3×D4—24no—
253C2×C3×D4—22no—
254C2×C3×D4—22no—
255C2×C3×D4—22no—
256C2×C3×D4—22no—
257C2×C3×D4—22no—
258C2×C3×D4—22no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—64no—
262C2×C3×D4—62no—
263C2×C3×D4—62no—
264C2×C3×D4—64no—
265C22×C3×C4—21no—
266C22×C3×C4—32no—
267C22×C3×C4—31no—
268C22×C3×C4—32no—
269C22×C3×C4—31no—
270C22×C3×C4—64no—
271C22×C3×C4—62no—
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D311yescharacteristic
274C2×#67—24no—
275C2×#67—24no—
276C2×#67—22no—
277C2×#67—22no—
278C22×Dic3—22no—
279C22×Dic3—24no—
280C22×Dic3—32no—
281C22×Dic3—32no—
282C22×Dic3—38no—
283C22×Dic3—32no—
284C22×Dic3—32no—
285C22×Dic3—62no—
286C22×Dic3—62no—
287C22×Dic3—64no—
288C22×Dic3—64no—
289C22×Dic3—64no—
290C22×Dic3—64no—
291C22×Dic3—632no—
292C22×Dic3—64no—
293C22×Dic3—64no—
294C22×Dic3—62no—
295C22×Dic3—62no—
296C22×Dic3—64no—
297C22×Dic3—124no—
298C22×Dic3—122no—
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D312yes—
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D312yes—
303C2×C4×D3—38no—
304C2×C4×D3—64no—
305C2×C4×D3—64no—
306C2×C4×D3—632no—
307C2×C4×D3—64no—
308C2×C4×D3—64no—
309C2×C4×D3—64no—
310C3×C22⋊C4—62no—
311C3×C22⋊C4—62no—
312C3×C22⋊C4—64no—
313C3×C22⋊C4—62no—
314C3×C22⋊C4—62no—
315#217—22no—
316#217—22no—
317#217—24no—
318#217—64no—
319#217—64no—
320#217—64no—
321#217—64no—
322#217—62no—
323#217—62no—
324#217—124no—
325#217—122no—
326(C2×D3)⋊C4—22no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—64no—
329(C2×D3)⋊C4—64no—
330C4⋊Dic3—64no—
331Dic3⋊C4—64no—
332Dic3⋊C4—64no—
333Dic3⋊C4—64no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—24no—
337C22×C32—24no—
338C22×C32—41no—
339C22×C32—42no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32—42no—
343C22×C32#12314yescomplemented
344C22×C32C22×D412yes—
345C22×C32C22×D411yescharacteristic
346C22×C32C2×#4111yescharacteristic
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4112yes—
349C2×C3×D3—232no—
350C2×C3×D3—22no—
351C2×C3×D3—22no—
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—24no—
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—24no—
358C2×C3×D3#12014yes—
359C2×C3×D3#12314yescomplemented
360C32×C4—41no—
361C3⋊Dic3—24no—
362C3⋊Dic3—42no—
363C3×Dic3—24no—
364C3×Dic3—41no—
365C3×Dic3—41no—
366C3×Dic3—42no—
367C25—31no—
368C22×D4—31no—
369C22×D4—31no—
370C22×D4D3211yescharacteristic
371C23×C4—31no—
372C23×C4—92no—
373C23×C4—92no—
374C23×C4—91no—
375C23×C4—188no—
376C23×C4—184no—
377#123—188no—
378#120—64no—
379C2×C4⋊C4—92no—
380C2×C4⋊C4—92no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—92no—
387C2×C22⋊C4—92no—
388C2×C22⋊C4—92no—
389C2×C22⋊C4—91no—
390#95—32no—
391#95—92no—
392#95—92no—
393#95—92no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—21no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—34no—
414C23×C3—32no—
415C23×C3—32no—
416C23×C3—34no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—42no—
423C23×C3—68no—
424C23×C3—68no—
425C23×C3—616no—
426C23×C3—616no—
427C23×C3—68no—
428C23×C3—61no—
429C23×C3—61no—
430C23×C3—62no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3—62no—
434C23×C3#23512yes—
435C23×C3D3×D412yes—
436C23×C3#23712yes—
437C23×C3#23712yes—
438C23×C3#23712yes—
439C23×C3C2×#6712yes—
440C23×C3C23×D311yescharacteristic
441C23×C3C23×D311yescharacteristic
442C22×D3—216no—
443C22×D3—216no—
444C22×D3—28no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—21no—
451C22×D3—28no—
452C22×D3—28no—
453C22×D3D3×D414yes—
454C22×D3#23714yes—
455C22×D3C2×#6712yes—
456C22×D3C2×#6712yes—
457C3×D4—48no—
458C3×D4—44no—
459C3×D4—44no—
460C3×D4—124no—
461C3×D4—124no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—34no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—68no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—62no—
480C2×C3×C4—62no—
481C2×C3×C4—62no—
482#67—44no—
483#67—44no—
484C2×Dic3—28no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—34no—
495C2×Dic3—34no—
496C2×Dic3—64no—
497C2×Dic3—616no—
498C2×Dic3—616no—
499C2×Dic3—68no—
500C2×Dic3—68no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—122no—
512C2×Dic3—122no—
513C2×Dic3—128no—
514C2×Dic3—122no—
515C2×Dic3—122no—
516C2×Dic3—122no—
517C2×Dic3D3×D414yes—
518C4×D3—616no—
519C4×D3—616no—
520C2×C32—24no—
521C2×C32—81no—
522C2×C32C2×#12011yescharacteristic
523C2×C32C2×#12311yescharacteristic
524C2×C32C2×#12311yescharacteristic
525C2×C32#52512yes—
526C2×C32#52512yes—
527C3×D3—24no—
528C3×D3—24no—
529C24—31no—
530C24—31no—
531C24—34no—
532C24—64no—
533C24—64no—
534C24—62no—
535C24—62no—
536C24C2×D3211yescharacteristic
537C24C2×D3211yescharacteristic
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—62no—
542C2×D4—62no—
543C2×D4—64no—
544C2×D4—64no—
545C22×C4—32no—
546C22×C4—32no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—64no—
550C22×C4—62no—
551C22×C4—98no—
552C22×C4—92no—
553C22×C4—92no—
554C22×C4—184no—
555C22×C4—184no—
556C22×C4—184no—
557C22×C4—184no—
558C22×C4—184no—
559C22×C4—1832no—
560C22×C4—184no—
561C22×C4—182no—
562C22×C4C2×D3211yescharacteristic
563C4⋊C4—184no—
564C4⋊C4—184no—
565C22⋊C4—62no—
566C22⋊C4—62no—
567C22⋊C4—64no—
568C22⋊C4—62no—
569C22⋊C4—62no—
570C22⋊C4—184no—
571C22⋊C4—184no—
572C22⋊C4—184no—
573C22⋊C4—182no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—24no—
580C22×C3—22no—
581C22×C3—24no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—24no—
588C22×C3—34no—
589C22×C3—34no—
590C22×C3—42no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—44no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—41no—
605C22×C3—42no—
606C22×C3—632no—
607C22×C3—62no—
608C22×C3—62no—
609C22×C3—62no—
610C22×C3—64no—
611C22×C3—64no—
612C22×C3—62no—
613C22×C3—64no—
614C22×C3—64no—
615C22×C3—82no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3#88314yescomplemented
619C22×C3#93514yescomplemented
620C22×C3C2×#23511yescharacteristic
621C22×C3C2×D3×D412yes—
622C22×C3C2×D3×D412yes—
623C22×C3C2×D3×D411yescharacteristic
624C22×C3C2×#23712yes—
625C22×C3C2×#23711yescharacteristic
626C22×C3C2×#23711yescharacteristic
627C22×C3C2×#23711yescharacteristic
628C22×C3D3×#4112yes—
629C22×C3C22×#6711yescharacteristic
630C2×D3—232no—
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—24no—
636C2×D3—24no—
637C2×D3—24no—
638C2×D3—24no—
639C2×D3#93514yescomplemented
640C2×D3#93714yes—
641C3×C4—42no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—64no—
645C3×C4—121no—
646C3×C4—122no—
647C3×C4—121no—
648Dic3—24no—
649Dic3—41no—
650Dic3—41no—
651Dic3—42no—
652Dic3—64no—
653Dic3—64no—
654Dic3—124no—
655Dic3—122no—
656Dic3—122no—
657Dic3—242no—
658C32#284911yescharacteristic, complemented, Sylow
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—34no—
667C23—34no—
668C23—32no—
669C23—32no—
670C23—68no—
671C23—68no—
672C23—616no—
673C23—616no—
674C23—62no—
675C23—62no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—68no—
681C23#380412yes—
682C23#380512yes—
683C23D3×#6712yes—
684C23C22×D3211yescharacteristic
685D4—44no—
686D4—124no—
687D4—124no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—34no—
692C2×C4—68no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—94no—
703C2×C4—1816no—
704C2×C4—1816no—
705C2×C4—188no—
706C2×C4—182no—
707C2×C4—182no—
708C2×C4—182no—
709C2×C4—182no—
710C2×C4—182no—
711C2×C3—24no—
712C2×C3—24no—
713C2×C3—22no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—44no—
719C2×C3—64no—
720C2×C3—64no—
721C2×C3—82no—
722C2×C3—81no—
723C2×C3—81no—
724C2×C3C2×#88311yescharacteristic
725C2×C3#554712yes—
726C2×C3#558612yes—
727C2×C3#558612yes—
728C2×C3D3×#12011yescharacteristic
729C2×C3#560612yes—
730C2×C3D3×#12311yescharacteristic
731C2×C3C2×#93511yescharacteristic
732C2×C3C2×#93511yescharacteristic
733C2×C3C2×#93711yescharacteristic
734D3—24no—
735D3—24no—
736C22—24no—
737C22—24no—
738C22—22no—
739C22—22no—
740C22—34no—
741C22—34no—
742C22—42no—
743C22—42no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—632no—
748C22—64no—
749C22—64no—
750C22—64no—
751C22—64no—
752C22—62no—
753C22—62no—
754C22—62no—
755C22—62no—
756C22#6396914yescomplemented
757C22D32×D412yes—
758C22D3×#23712yes—
759C22C2×#380411yescharacteristic
760C22C2×#380511yescharacteristic
761C22C2×D3×#6711yescharacteristic
762C4—41no—
763C4—64no—
764C4—122no—
765C4—121no—
766C4—121no—
767C4—184no—
768C4—362no—
769C3—21no—
770C3#7493611yescharacteristic, complemented
771C3#8260211yescharacteristic, complemented
772C2—24no—
773C2—64no—
774C2—64no—
775C2—81no—
776C2#1059512912yes—
777C2#1059513012yes—
778C2D3×#93511yescharacteristic
779C2D3×#93711yescharacteristic
780C2C2×#6396911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×D3×Dic3C2semidirect
3. C2×#63969C2semidirect
4. #10592919C2semidirect
5. C3×#5220C2semidirect
6. #10591721C2semidirect
7. #10591719C2semidirect
8. #10591706C2semidirect
9. #10591693C2semidirect
10. #10591373C2semidirect
11. #10591362C2semidirect
25. C2×#3757C22semidirect
28. C2×C3×#217C22semidirect
33. C2×#3724C22semidirect
34. C2×Dic3⋊Dic3C22semidirect
37. #63658C22semidirect
38. C3×C3⋊#95C22semidirect
39. #63579C22semidirect
40. #63579C22semidirect
53. #5220D3semidirect
97. C2×D3×Dic3D4semidirect
148. C2×#217C2×D3semidirect
168. C3⋊#95C2×D3semidirect
343. C22×C32#123semidirect
359. C2×C3×D3#123semidirect
618. C22×C3#883semidirect
619. C22×C3#935semidirect
639. C2×D3#935semidirect
658. C32#2849semidirect
756. C22#63969semidirect
770. C3#74936semidirect
771. C3#82602semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C2×C3×#9372
C2×#639692
#105929192
C3×#52202
#105917212
#105917192
#105917062
#105916932
#105913732
#105913622
#826023
#749363