Finite Group Databasebeta

← #10718598

Subgroups — #10718598

Order 768.

2538 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic3⋊C4C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic
3C2×#4958C211yesmaximal, characteristic
4C2×#4958C211yesmaximal, characteristic
5C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#4669C212yesmaximal, complemented
7C3×C22⋊#95C211yesmaximal, characteristic, complemented
8#71544C211yesmaximal, characteristic, complemented
9#69428C212yesmaximal, complemented
10#69414C212yesmaximal, complemented
11#69406C212yesmaximal, complemented
12#14019—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×Dic3⋊C4—24no—
25C22×Dic3⋊C4—28no—
26C22×Dic3⋊C4C2212yes—
27C22×Dic3⋊C4C2212yes—
28C22×C4×Dic3C2212yes—
29C2×C3×#95C2212yes—
30C2×C3×#95C2212yes—
31#5213—24no—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4958—24no—
40#4958C418yescomplemented
41Dic3×C22⋊C4—24no—
42#4669—28no—
43C23×C4⋊C4—31no—
44C2×#388—32no—
45C2×#386—31no—
46C2×#386—31no—
47C2×#386—31no—
48C2×C4×C22⋊C4—31no—
49#1442—32no—
50#1439—32no—
51#1436—32no—
52C22⋊#95—31no—
53C22⋊#95D311yescharacteristic, complemented
54C25×C3C2311yescharacteristic
55C24×D3C2311yescharacteristic
56C23×C3×C4—22no—
57C23×C3×C4—24no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—42no—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2312yes—
64C23×C3×C4C2312yes—
65C22×#67—22no—
66C22×#67—22no—
67C22×#67—22no—
68C22×#67—22no—
69C22×#67—22no—
70C22×#67—22no—
71C22×#67C2×C414yes—
72C23×Dic3—22no—
73C23×Dic3—22no—
74C23×Dic3—24no—
75C23×Dic3—24no—
76C23×Dic3—22no—
77C23×Dic3—22no—
78C23×Dic3—24no—
79C23×Dic3—42no—
80C23×Dic3C2×C414yes—
81C23×Dic3D414yes—
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2312yes—
85C23×Dic3C2312yes—
86C23×Dic3C2311yescharacteristic
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4C2×C414yes—
93C2×#217—22no—
94C2×#217—22no—
95C2×#217D414yes—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—42no—
104C2×(C2×D3)⋊C4—42no—
105C2×(C2×D3)⋊C4C2×C418yescomplemented
106C2×Dic3⋊C4—232no—
107C2×Dic3⋊C4—24no—
108C2×Dic3⋊C4—24no—
109C2×Dic3⋊C4—24no—
110C2×Dic3⋊C4—24no—
111C2×Dic3⋊C4—24no—
112C2×Dic3⋊C4D418yescomplemented
113C2×C4×Dic3—24no—
114C2×C4×Dic3—24no—
115C2×C4×Dic3—42no—
116C3×#95—24no—
117C3×#95—42no—
118C3⋊#95—24no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—22no—
122C3⋊#95—22no—
123C3⋊#95—24no—
124C3⋊#95C2×C418yescomplemented
125C23×D4—31no—
126C24×C4—31no—
127C24×C4—31no—
128C24×C4C2×D311yescharacteristic
129C22×C4⋊C4—32no—
130C22×C4⋊C4—32no—
131C22×C4⋊C4—68no—
132C22×C4⋊C4—64no—
133C22×C22⋊C4—31no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—31no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—31no—
138C22×C22⋊C4C2×D311yescharacteristic
139C22×C22⋊C4C2×D311yescharacteristic
140C22×C42—32no—
141#388—68no—
142#386—38no—
143#386—64no—
144#386—64no—
145C4×C22⋊C4—64no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—31no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95—31no—
153C2×#95C2×D312yes—
154C2×#95C2×D312yes—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3C22×C412yes—
160C24×C3C2×D412yes—
161C24×C3C2×D412yes—
162C24×C3#4112yes—
163C24×C3#4112yes—
164C24×C3#4112yes—
165C24×C3#4112yes—
166C24×C3C2411yescharacteristic
167C23×D3—22no—
168C23×D3—21no—
169C23×D3—21no—
170C23×D3—22no—
171C23×D3—21no—
172C23×D3—21no—
173C23×D3—21no—
174C23×D3—21no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3C22×C412yes—
178C22×C3×C4—28no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—48no—
202C22×C3×C4—48no—
203C22×C3×C4—44no—
204C22×C3×C4—44no—
205C22×C3×C4C22×C414yes—
206C22×C3×C4C2×D414yes—
207C2×#67—28no—
208C2×#67—28no—
209C2×#67—28no—
210C2×#67—44no—
211C2×#67—44no—
212C2×#67—44no—
213C2×#67—44no—
214C22×Dic3—28no—
215C22×Dic3—216no—
216C22×Dic3—28no—
217C22×Dic3—28no—
218C22×Dic3—21no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—216no—
226C22×Dic3—28no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—28no—
244C22×Dic3—44no—
245C22×Dic3—48no—
246C22×Dic3—48no—
247C22×Dic3C22×C412yes—
248C22×Dic3C22×C414yes—
249C22×Dic3C2×D414yes—
250C22×Dic3C2×D412yes—
251C22×Dic3C2×D414yes—
252C22×Dic3C2×D412yes—
253C22×Dic3C2×D414yes—
254C22×Dic3#4114yes—
255C3×C22⋊C4—28no—
256C3×C22⋊C4—44no—
257#217—28no—
258(C2×D3)⋊C4—216no—
259(C2×D3)⋊C4—48no—
260(C2×D3)⋊C4—44no—
261(C2×D3)⋊C4—44no—
262Dic3⋊C4—216no—
263Dic3⋊C4—216no—
264C4×Dic3—48no—
265C25—31no—
266C25C22×D311yescharacteristic
267C22×D4—34no—
268C22×D4—62no—
269C22×D4—62no—
270C22×D4—62no—
271C22×D4—62no—
272C22×D4—62no—
273C22×D4—62no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—32no—
279C23×C4—31no—
280C23×C4—34no—
281C23×C4—32no—
282C23×C4—31no—
283C23×C4—31no—
284C23×C4—34no—
285C23×C4—42no—
286C23×C4—64no—
287C23×C4—64no—
288C23×C4—64no—
289C23×C4—62no—
290C23×C4—62no—
291C23×C4—62no—
292C23×C4—62no—
293C23×C4—122no—
294C23×C4C22×D311yescharacteristic
295C23×C4C22×D311yescharacteristic
296C23×C4C22×D312yes—
297C23×C4C22×D312yes—
298C2×C4⋊C4—38no—
299C2×C4⋊C4—64no—
300C2×C4⋊C4—64no—
301C2×C4⋊C4—64no—
302C2×C4⋊C4—64no—
303C2×C4⋊C4—632no—
304C2×C4⋊C4—64no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—34no—
311C2×C22⋊C4—38no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—62no—
315C2×C22⋊C4—62no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—62no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—122no—
322C2×C22⋊C4—122no—
323C2×C22⋊C4C4×D314yes—
324C2×C42—64no—
325C2×C42—64no—
326C2×C42—122no—
327#95—24no—
328#95—38no—
329#95—42no—
330#95—64no—
331#95—64no—
332#95—64no—
333#95—62no—
334#95—62no—
335#95—64no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—24no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3#11714yes—
353C23×C3C4×D414yes—
354C23×C3C4×D414yes—
355C23×C3#12114yes—
356C23×C3#12314yes—
357C23×C3#12414yes—
358C23×C3#12614yes—
359C23×C3C23×C411yescharacteristic
360C23×C3C22×D411yescharacteristic
361C23×C3C22×D412yes—
362C23×C3C22×D411yescharacteristic
363C23×C3C2×#4111yescharacteristic
364C23×C3C2×#4111yescharacteristic
365C23×C3C2×#4111yescharacteristic
366C23×C3C2×#4111yescharacteristic
367C23×C3C2×#4112yes—
368C23×C3H(5,𝔽2)12yes—
369C23×C32−1+412yes—
370C22×D3—22no—
371C22×D3—24no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—24no—
375C22×D3—41no—
376C22×D3—41no—
377C22×D3—41no—
378C22×D3—41no—
379C22×D3—42no—
380C22×D3—41no—
381C22×D3—41no—
382C22×D3—41no—
383C22×D3—41no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—416no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418#67—416no—
419C2×Dic3—232no—
420C2×Dic3—24no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—22no—
424C2×Dic3—24no—
425C2×Dic3—24no—
426C2×Dic3—24no—
427C2×Dic3—22no—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—24no—
436C2×Dic3—22no—
437C2×Dic3—24no—
438C2×Dic3—24no—
439C2×Dic3—416no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—42no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3C4×D418yes—
451C2×Dic3#12014yes—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—32no—
457C24—61no—
458C24—61no—
459C24—62no—
460C24—61no—
461C24—61no—
462C24—61no—
463C24—62no—
464C24—61no—
465C24—62no—
466C24—62no—
467C24C2×C4×D312yes—
468C24#23512yes—
469C24#23512yes—
470C24D3×D412yes—
471C24D3×D412yes—
472C24#23712yes—
473C24#23912yes—
474C24C23×D311yescharacteristic
475C2×D4—68no—
476C2×D4—68no—
477C2×D4—68no—
478C2×D4—124no—
479C2×D4—124no—
480C2×D4—124no—
481C2×D4—124no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—34no—
506C22×C4—34no—
507C22×C4—32no—
508C22×C4—34no—
509C22×C4—34no—
510C22×C4—32no—
511C22×C4—34no—
512C22×C4—32no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—616no—
518C22×C4—68no—
519C22×C4—68no—
520C22×C4—68no—
521C22×C4—616no—
522C22×C4—68no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—68no—
531C22×C4—62no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—61no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—61no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—124no—
548C22×C4—128no—
549C22×C4—128no—
550C22×C4C2×C4×D314yes—
551C22×C4D3×D414yes—
552C4⋊C4—616no—
553C4⋊C4—616no—
554C22⋊C4—28no—
555C22⋊C4—44no—
556C22⋊C4—616no—
557C22⋊C4—68no—
558C22⋊C4—128no—
559C22⋊C4—124no—
560C22⋊C4—124no—
561C42—128no—
562C22×C3—24no—
563C22×C3—24no—
564C22×C3—28no—
565C22×C3—28no—
566C22×C3—24no—
567C22×C3—24no—
568C22×C3—24no—
569C22×C3—28no—
570C22×C3—28no—
571C22×C3—24no—
572C22×C3#38818yescomplemented
573C22×C3C2×#11711yescharacteristic
574C22×C3C2×C4×D411yescharacteristic
575C22×C3C2×C4×D411yescharacteristic
576C22×C3C2×C4×D412yes—
577C22×C3#52012yes—
578C22×C3C2×#12011yescharacteristic
579C22×C3C2×#12111yescharacteristic
580C22×C3C2×#12311yescharacteristic
581C22×C3#52511yescharacteristic
582C22×C3#52512yes—
583C22×C3C2×#12411yescharacteristic
584C22×C3C2×#12611yescharacteristic
585C22×C3#53411yescharacteristic
586C22×C3#53611yescharacteristic
587C22×C3#53912yes—
588C22×C3D4212yes—
589C22×C3#54612yes—
590C22×C3#54712yes—
591C22×C3#54812yes—
592C22×C3#54812yes—
593C22×C3#55212yes—
594C22×C3#55312yes—
595C22×C3#55312yes—
596C2×D3—42no—
597C2×D3—44no—
598C2×D3—44no—
599C2×D3—42no—
600C2×D3—42no—
601C2×D3—81no—
602C2×D3—81no—
603C2×D3—81no—
604C2×D3—81no—
605C2×D3—82no—
606C2×D3—82no—
607C3×C4—44no—
608C3×C4—44no—
609C3×C4—81no—
610C3×C4—81no—
611Dic3—24no—
612Dic3—28no—
613Dic3—42no—
614Dic3—44no—
615Dic3—42no—
616C23—24no—
617C23—22no—
618C23—24no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—64no—
636C23—64no—
637C23—122no—
638C23—121no—
639C23—122no—
640C23—121no—
641C23—121no—
642C23—122no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23—122no—
647C23—122no—
648C23—122no—
649C23—121no—
650C23—121no—
651C23—122no—
652C23—122no—
653C23—122no—
654C23—122no—
655C23#87214yes—
656C23#67⋊C414yes—
657C23#88414yes—
658C23#88514yes—
659C23#89314yes—
660C23#89414yes—
661C23#89814yes—
662C23C22×C4×D311yescharacteristic
663C23C2×#23511yescharacteristic
664C23C2×#23511yescharacteristic
665C23C2×D3×D411yescharacteristic
666C23C2×D3×D411yescharacteristic
667C23C2×D3×D412yes—
668C23C2×#23711yescharacteristic
669C23#100412yes—
670C23C2×#23911yescharacteristic
671C23D3×#4112yes—
672C23#101012yes—
673D4—1216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—38no—
681C2×C4—34no—
682C2×C4—416no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—632no—
702C2×C4—64no—
703C2×C4—62no—
704C2×C4—64no—
705C2×C4—64no—
706C2×C4—64no—
707C2×C4—64no—
708C2×C4—62no—
709C2×C4—64no—
710C2×C4—64no—
711C2×C4—64no—
712C2×C4—64no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—64no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—64no—
721C2×C4—1216no—
722C2×C4—122no—
723C2×C4—121no—
724C2×C4—122no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C3—28no—
733C2×C3C2×#38811yescharacteristic
734C2×C3C4×#12011yescharacteristic
735C2×C3#232211yescharacteristic
736C2×C3#235212yes—
737C2×C3#236112yes—
738C2×C3#241011yescharacteristic
739C2×C3#241311yescharacteristic
740C2×C3#243611yescharacteristic
741C2×C3#244312yes—
742C2×C3#248112yes—
743C2×C3#259111yescharacteristic
744D3—82no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—24no—
754C22—28no—
755C22—122no—
756C22—122no—
757C22—122no—
758C22—124no—
759C22—124no—
760C22—241no—
761C22—241no—
762C22—241no—
763C22—242no—
764C22—242no—
765C22—241no—
766C22#466918yescomplemented
767C22C2×#87211yescharacteristic
768C22C2×#67⋊C411yescharacteristic
769C22C2×#88411yescharacteristic
770C22#549012yes—
771C22C2×#88511yescharacteristic
772C22C2×#89311yescharacteristic
773C22C2×#89411yescharacteristic
774C22C2×#89811yescharacteristic
775C22#553112yes—
776C22#554012yes—
777C22C4×D3×D412yes—
778C22#554612yes—
779C22#555212yes—
780C22D3×#12011yescharacteristic
781C22#558911yescharacteristic
782C22#559012yes—
783C22#559812yes—
784C22#560112yes—
785C22#562712yes—
786C22#564512yes—
787C22#564811yescharacteristic
788C22#565512yes—
789C22#565611yescharacteristic
790C4—44no—
791C4—44no—
792C4—64no—
793C4—68no—
794C4—81no—
795C4—81no—
796C4—122no—
797C4—122no—
798C4—124no—
799C3#1401911yescharacteristic, complemented, Sylow
800C2—28no—
801C2—242no—
802C2C2×#466911yescharacteristic
803C2#7346112yes—
804C2#7385411yescharacteristic
805C2#7391012yes—
806C2#7406411yescharacteristic
807C2#7437911yescharacteristic
808C2#7438411yescharacteristic
809C2#7441812yes—
810C2#7467612yes—
811C2#7470111yescharacteristic
812C2#7477211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C22⋊#95C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#14019
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C23×Dic3⋊C4C2semidirect
5. C2×Dic3×C22⋊C4C2semidirect
6. C2×#4669C2semidirect
7. C3×C22⋊#95C2semidirect
8. #71544C2semidirect
9. #69428C2semidirect
10. #69414C2semidirect
11. #69406C2semidirect
40. #4958C4semidirect
53. C22⋊#95D3semidirect
105. C2×(C2×D3)⋊C4C2×C4semidirect
112. C2×Dic3⋊C4D4semidirect
124. C3⋊#95C2×C4semidirect
572. C22×C3#388semidirect
766. C22#4669semidirect
799. C3#14019semidirect

Maximal subgroups

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

subgroupindex
C23×Dic3⋊C42
C2×#52132
C2×#49582
C2×Dic3×C22⋊C42
C2×#46692
C3×C22⋊#952
#715442
#694282
#694142
#694062
#140193