Finite Group Databasebeta

← #10720098

Subgroups — #10720098

Order 768.

4046 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×D3×C22⋊C4C211yesmaximal, characteristic
3C2×C3×#385C211yesmaximal, characteristic, complemented
4C2×#5210C211yesmaximal, characteristic, complemented
5C2×#4989C212yesmaximal, complemented
6C2×#4955C211yesmaximal, characteristic
7#71570C212yesmaximal, complemented
8#71544C211yesmaximal, characteristic, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69428C212yesmaximal, complemented
11(C2×D3)⋊#95C212yesmaximal, complemented
12#14127—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C23×C4×D3C2211yescharacteristic
18C22×C3×C4⋊C4C2212yescomplemented
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×(C2×D3)⋊C4—24no—
24C22×(C2×D3)⋊C4—28no—
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×(C2×D3)⋊C4C2212yes—
31C22×Dic3⋊C4C2212yescomplemented
32C2×D3×C22⋊C4—24no—
33C2×D3×C22⋊C4—24no—
34C2×D3×C22⋊C4—24no—
35C3×#385—24no—
36C2×C3×#95C2212yescomplemented
37#5210—24no—
38C2×C3⋊#95C2212yescomplemented
39C2×C3⋊#95C2212yescomplemented
40C2×C3⋊#95C2212yescomplemented
41C2×C3⋊#95C2212yescomplemented
42C2×C3⋊#95C2212yescomplemented
43#4989—28no—
44#4955C418yescomplemented
45C23×C22⋊C4—31no—
46C23×C22⋊C4—31no—
47C2×#385—31no—
48C2×#385—32no—
49C2×#385D311yescharacteristic, complemented
50C2×#379—31no—
51#1439—32no—
52#1439—32no—
53C22⋊#95—32no—
54C22⋊#95—31no—
55C22⋊#95—31no—
56C25×C3C2311yescharacteristic
57C24×D3—22no—
58C24×D3—22no—
59C24×D3—22no—
60C24×D3—22no—
61C24×D3—24no—
62C24×D3—24no—
63C24×D3—42no—
64C24×D3—42no—
65C24×D3C2×C414yes—
66C24×D3D414yes—
67C24×D3Q814yes—
68C24×D3C2311yescharacteristic
69C24×D3C2311yescharacteristic
70C23×C3×C4—22no—
71C23×C3×C4—24no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—42no—
75C23×C3×C4C2312yes—
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C23×Dic3—22no—
80C23×Dic3—24no—
81C23×Dic3—22no—
82C23×Dic3—22no—
83C23×Dic3—42no—
84C23×Dic3C2312yes—
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2312yes—
88C22×C4×D3—22no—
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—24no—
95C22×C4×D3—24no—
96C22×C4×D3—42no—
97C22×C4×D3—42no—
98C2×C3×C4⋊C4—24no—
99C2×C3×C4⋊C4—24no—
100C2×C3×C4⋊C4—42no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4C2×C414yescomplemented
106C2×C3×C22⋊C4D414yes—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217C2×C414yescomplemented
112C2×#217D414yes—
113C2×(C2×D3)⋊C4—232no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—24no—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—24no—
127C2×(C2×D3)⋊C4—42no—
128C2×(C2×D3)⋊C4—42no—
129C2×(C2×D3)⋊C4C2×C418yescomplemented
130C2×(C2×D3)⋊C4C2×C418yescomplemented
131C2×(C2×D3)⋊C4D418yes—
132C2×Dic3⋊C4—24no—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—42no—
135D3×C22⋊C4—232no—
136C3×#95—24no—
137C3⋊#95—24no—
138C3⋊#95—24no—
139C3⋊#95—24no—
140C3⋊#95—42no—
141C3⋊#95—42no—
142C26—31no—
143C24×C4—31no—
144C24×C4—31no—
145C24×C4—31no—
146C24×C4C2×D311yescharacteristic
147C22×C4⋊C4—32no—
148C22×C4⋊C4C2×D312yescomplemented
149C22×C22⋊C4—31no—
150C22×C22⋊C4—31no—
151C22×C22⋊C4—32no—
152C22×C22⋊C4—32no—
153C22×C22⋊C4—32no—
154C22×C22⋊C4—32no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—64no—
158C22×C22⋊C4—64no—
159C22×C22⋊C4—68no—
160C22×C22⋊C4—64no—
161C22×C22⋊C4—64no—
162C22×C22⋊C4C2×D311yescharacteristic
163C22×C22⋊C4C2×D311yescharacteristic
164#385—24no—
165#385—68no—
166#385—64no—
167#379—38no—
168C2×#95—32no—
169C2×#95—32no—
170C2×#95—32no—
171C2×#95—32no—
172C2×#95—32no—
173C2×#95C2×D312yescomplemented
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3C22×C412yes—
179C24×C3C2×D412yes—
180C24×C3C2×D412yes—
181C24×C3C2×D412yes—
182C24×C3C2×Q812yes—
183C24×C3#4112yes—
184C24×C3#4112yes—
185C24×C3C2411yescharacteristic
186C23×D3—21no—
187C23×D3—21no—
188C23×D3—21no—
189C23×D3—21no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—28no—
193C23×D3—28no—
194C23×D3—28no—
195C23×D3—28no—
196C23×D3—28no—
197C23×D3—28no—
198C23×D3—22no—
199C23×D3—21no—
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—22no—
204C23×D3—22no—
205C23×D3—22no—
206C23×D3—216no—
207C23×D3—28no—
208C23×D3—216no—
209C23×D3—28no—
210C23×D3—48no—
211C23×D3—44no—
212C23×D3—44no—
213C23×D3—48no—
214C23×D3—48no—
215C23×D3—48no—
216C23×D3—48no—
217C23×D3—48no—
218C23×D3—48no—
219C23×D3—48no—
220C23×D3—48no—
221C23×D3—48no—
222C23×D3C4⋊C4116yescomplemented
223C23×D3C22×C412yes—
224C23×D3C22×C412yes—
225C23×D3C2×D412yes—
226C23×D3C2×D412yes—
227C23×D3C2×D414yes—
228C23×D3C2×Q812yes—
229C23×D3C2×Q812yes—
230C23×D3#4114yes—
231C22×C3×C4—28no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—48no—
253C22×C3×C4—48no—
254C22×C3×C4—44no—
255C22×C3×C4—44no—
256C22×C3×C4C22×C414yes—
257C22×C3×C4C2×D414yes—
258C22×C3×C4C2×D412yes—
259C22×C3×C4C2×D412yes—
260C22×Dic3—28no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—48no—
282C22×Dic3—48no—
283C22×Dic3—44no—
284C22×Dic3—44no—
285C22×Dic3C22×C414yes—
286C22×Dic3C2×D414yes—
287C22×Dic3C2×D412yes—
288C22×Dic3C2×D412yes—
289C2×C4×D3—28no—
290C2×C4×D3—28no—
291C2×C4×D3—48no—
292C2×C4×D3—48no—
293C2×C4×D3—48no—
294C2×C4×D3—48no—
295C2×C4×D3—44no—
296C2×C4×D3—44no—
297C2×C4×D3—44no—
298C2×C4×D3—44no—
299C3×C4⋊C4—48no—
300C3×C22⋊C4—28no—
301C3×C22⋊C4—28no—
302#217—28no—
303#217—28no—
304(C2×D3)⋊C4—28no—
305(C2×D3)⋊C4—28no—
306(C2×D3)⋊C4—216no—
307(C2×D3)⋊C4—216no—
308(C2×D3)⋊C4—216no—
309(C2×D3)⋊C4—48no—
310Dic3⋊C4—48no—
311C25—31no—
312C25—31no—
313C25—34no—
314C25—34no—
315C25—34no—
316C25—64no—
317C25—64no—
318C25—62no—
319C25—62no—
320C25—62no—
321C25—62no—
322C25—122no—
323C25—122no—
324C25C22×D311yescharacteristic
325C23×C4—22no—
326C23×C4—24no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—32no—
330C23×C4—31no—
331C23×C4—32no—
332C23×C4—31no—
333C23×C4—42no—
334C23×C4—62no—
335C23×C4—62no—
336C23×C4—62no—
337C23×C4—62no—
338C23×C4—64no—
339C23×C4—64no—
340C23×C4—64no—
341C23×C4—62no—
342C23×C4—62no—
343C23×C4—62no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—122no—
347C23×C4—122no—
348C23×C4—122no—
349C23×C4C22×D312yes—
350C23×C4C22×D312yes—
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—64no—
357C2×C4⋊C4—64no—
358C2×C4⋊C4—122no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—34no—
364C2×C22⋊C4—34no—
365C2×C22⋊C4—38no—
366C2×C22⋊C4—38no—
367C2×C22⋊C4—38no—
368C2×C22⋊C4—632no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—64no—
372C2×C22⋊C4—64no—
373C2×C22⋊C4—64no—
374C2×C22⋊C4—62no—
375C2×C22⋊C4—62no—
376C2×C22⋊C4—64no—
377C2×C22⋊C4—64no—
378C2×C22⋊C4—64no—
379C2×C22⋊C4—632no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—62no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—122no—
388C2×C22⋊C4—122no—
389C2×C22⋊C4C4×D314yescomplemented
390C2×C22⋊C4#6714yes—
391#95—24no—
392#95—64no—
393#95—64no—
394#95—64no—
395#95—122no—
396#95—122no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—22no—
400C23×C3—24no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—24no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3C2×C4⋊C414yes—
414C23×C3C4×D414yes—
415C23×C3C4×D414yes—
416C23×C3#12014yes—
417C23×C3C22⋊Q814yes—
418C23×C3C22⋊Q814yes—
419C23×C3#12314yes—
420C23×C3C23×C411yescharacteristic
421C23×C3C22×D411yescharacteristic
422C23×C3C22×D412yes—
423C23×C3C22×D411yescharacteristic
424C23×C3C22×D411yescharacteristic
425C23×C3C22×Q811yescharacteristic
426C23×C3C2×#4111yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4112yes—
429C23×C3H(5,𝔽2)12yes—
430C23×C3H(5,𝔽2)12yes—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—24no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—24no—
441C22×D3—24no—
442C22×D3—24no—
443C22×D3—24no—
444C22×D3—24no—
445C22×D3—24no—
446C22×D3—24no—
447C22×D3—24no—
448C22×D3—24no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—24no—
452C22×D3—24no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—24no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—24no—
463C22×D3—232no—
464C22×D3—232no—
465C22×D3—416no—
466C22×D3—432no—
467C22×D3—432no—
468C22×D3—416no—
469C22×D3—416no—
470C22×D3—416no—
471C22×D3—432no—
472C22×D3—432no—
473C22×D3—416no—
474C22×D3—42no—
475C22×D3—42no—
476C22×D3—42no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—42no—
482C22×D3C2×C4⋊C414yes—
483C22×D3C2×C4⋊C414yes—
484C22×D3C4×D418yes—
485C22×D3#12014yes—
486C22×D3C22⋊Q818yes—
487C22×D3#12314yes—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—24no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—416no—
499C2×C3×C4—41no—
500C2×C3×C4—42no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—42no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—42no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4—42no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3—24no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—24no—
520C2×Dic3—24no—
521C2×Dic3—24no—
522C2×Dic3—24no—
523C2×Dic3—416no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—42no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—42no—
530C2×Dic3—42no—
531C2×Dic3—42no—
532C2×Dic3—42no—
533C2×Dic3—42no—
534C2×Dic3—42no—
535C2×Dic3—42no—
536C2×Dic3—42no—
537C2×Dic3—42no—
538C4×D3—416no—
539C4×D3—416no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—32no—
545C24—34no—
546C24—32no—
547C24—32no—
548C24—34no—
549C24—32no—
550C24—32no—
551C24—32no—
552C24—316no—
553C24—68no—
554C24—68no—
555C24—616no—
556C24—616no—
557C24—61no—
558C24—61no—
559C24—62no—
560C24—61no—
561C24—62no—
562C24—61no—
563C24—68no—
564C24—68no—
565C24—68no—
566C24—68no—
567C24—68no—
568C24—68no—
569C24—61no—
570C24—61no—
571C24—62no—
572C24—62no—
573C24—61no—
574C24—62no—
575C24—62no—
576C24—61no—
577C24—128no—
578C24—124no—
579C24—128no—
580C24—124no—
581C24—128no—
582C24—128no—
583C24—128no—
584C24—128no—
585C24—128no—
586C24—128no—
587C24—128no—
588C24—128no—
589C24C2×C4×D312yes—
590C24#23512yes—
591C24D3×D412yes—
592C24D3×D412yes—
593C24D3×Q812yes—
594C24#23912yes—
595C24C2×#6712yes—
596C24C23×D311yescharacteristic
597C22×C4—28no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—34no—
619C22×C4—32no—
620C22×C4—34no—
621C22×C4—32no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—68no—
627C22×C4—68no—
628C22×C4—68no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—62no—
646C22×C4—62no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—128no—
650C22×C4—128no—
651C22×C4—128no—
652C22×C4—128no—
653C22×C4—124no—
654C22×C4—124no—
655C22×C4—124no—
656C22×C4—124no—
657C22×C4—128no—
658C22×C4—128no—
659C22×C4—124no—
660C22×C4—124no—
661C22×C4C2×C4×D314yes—
662C22×C4D3×D414yes—
663C22×C4C2×#6712yes—
664C22×C4C2×#6712yes—
665C4⋊C4—48no—
666C4⋊C4—128no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—616no—
670C22⋊C4—616no—
671C22⋊C4—68no—
672C22⋊C4—68no—
673C22⋊C4—616no—
674C22⋊C4—68no—
675C22⋊C4—68no—
676C22⋊C4—128no—
677C22×C3—24no—
678C22×C3—28no—
679C22×C3—28no—
680C22×C3—24no—
681C22×C3—24no—
682C22×C3—24no—
683C22×C3—28no—
684C22×C3—28no—
685C22×C3—24no—
686C22×C3—24no—
687C22×C3#38518yescomplemented
688C22×C3C22×C4⋊C411yescharacteristic
689C22×C3C2×C4×D411yescharacteristic
690C22×C3C2×C4×D411yescharacteristic
691C22×C3C2×C4×D412yes—
692C22×C3#51812yes—
693C22×C3C2×#12011yescharacteristic
694C22×C3C2×#12011yescharacteristic
695C22×C3C2×C22⋊Q811yescharacteristic
696C22×C3C2×C22⋊Q811yescharacteristic
697C22×C3C2×C22⋊Q812yes—
698C22×C3C2×#12311yescharacteristic
699C22×C3C2×#12311yescharacteristic
700C22×C3#53411yescharacteristic
701C22×C3#53411yescharacteristic
702C22×C3#54312yes—
703C22×C3D4212yes—
704C22×C3D4212yes—
705C22×C3#54612yes—
706C22×C3#54612yes—
707C22×C3#54612yes—
708C22×C3#54612yes—
709C22×C3#55112yes—
710C22×C3#55112yes—
711C2×D3—24no—
712C2×D3—28no—
713C2×D3—28no—
714C2×D3—24no—
715C2×D3—24no—
716C2×D3—24no—
717C2×D3—28no—
718C2×D3—28no—
719C2×D3—24no—
720C2×D3—24no—
721C2×D3—24no—
722C2×D3—24no—
723C2×D3—24no—
724C2×D3—464no—
725C2×D3—44no—
726C2×D3—44no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—44no—
731C2×D3—44no—
732C2×D3—42no—
733C2×D3#38518yescomplemented
734C3×C4—44no—
735C3×C4—42no—
736C3×C4—44no—
737C3×C4—42no—
738Dic3—44no—
739Dic3—42no—
740Dic3—42no—
741Dic3—44no—
742C23—24no—
743C23—24no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—22no—
754C23—22no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—34no—
759C23—34no—
760C23—38no—
761C23—34no—
762C23—38no—
763C23—34no—
764C23—632no—
765C23—64no—
766C23—64no—
767C23—62no—
768C23—64no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—64no—
775C23—64no—
776C23—64no—
777C23—64no—
778C23—62no—
779C23—64no—
780C23—62no—
781C23—64no—
782C23—64no—
783C23—64no—
784C23—62no—
785C23—62no—
786C23—632no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—64no—
793C23—64no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—64no—
798C23—1216no—
799C23—1232no—
800C23—1216no—
801C23—1232no—
802C23—1232no—
803C23—1216no—
804C23—1216no—
805C23—1216no—
806C23—1232no—
807C23—122no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—122no—
812C23—122no—
813C23—122no—
814C23—122no—
815C23D3×C4⋊C414yes—
816C23#89314yes—
817C23#89414yes—
818C23#89614yes—
819C23C4×#6714yes—
820C23#93714yes—
821C23#94614yes—
822C23C22×C4×D311yescharacteristic
823C23C2×#23511yescharacteristic
824C23C2×D3×D411yescharacteristic
825C23C2×D3×D411yescharacteristic
826C23C2×D3×D412yes—
827C23#100412yes—
828C23C2×D3×Q811yescharacteristic
829C23C2×#23911yescharacteristic
830C23D3×#4112yes—
831C23#100912yes—
832C23C22×#6711yescharacteristic
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—416no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—64no—
859C2×C4—64no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—64no—
863C2×C4—64no—
864C2×C4—64no—
865C2×C4—64no—
866C2×C4—64no—
867C2×C4—64no—
868C2×C4—1216no—
869C2×C4—1216no—
870C2×C4—1216no—
871C2×C4—122no—
872C2×C4—121no—
873C2×C4—122no—
874C2×C4—121no—
875C2×C4—122no—
876C2×C4—122no—
877C2×C4—122no—
878C2×C4—122no—
879C2×C4—122no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—122no—
883C2×C4—122no—
884C2×C4—122no—
885C2×C3—28no—
886C2×C3C2×#38511yescharacteristic
887C2×C3C2×#38511yescharacteristic
888C2×C3#231511yescharacteristic
889C2×C3#235812yes—
890C2×C3#235812yes—
891C2×C3#240311yescharacteristic
892C2×C3#240511yescharacteristic
893C2×C3#240511yescharacteristic
894C2×C3#243712yes—
895C2×C3#243712yes—
896C2×C3#248311yescharacteristic
897D3—28no—
898D3—44no—
899C22—24no—
900C22—24no—
901C22—28no—
902C22—24no—
903C22—28no—
904C22—28no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—28no—
909C22—38no—
910C22—64no—
911C22—64no—
912C22—68no—
913C22—64no—
914C22—68no—
915C22—68no—
916C22—64no—
917C22—64no—
918C22—64no—
919C22—68no—
920C22—64no—
921C22—64no—
922C22—64no—
923C22—1264no—
924C22—124no—
925C22—122no—
926C22—124no—
927C22—124no—
928C22—122no—
929C22—122no—
930C22—122no—
931C22—124no—
932C22#498918yescomplemented
933C22C2×D3×C4⋊C411yescharacteristic
934C22C2×#89311yescharacteristic
935C22C2×#89411yescharacteristic
936C22C2×#89611yescharacteristic
937C22C4×D3×D412yes—
938C22#554512yes—
939C22#555012yes—
940C22#555612yes—
941C22D3×#12011yescharacteristic
942C22#558911yescharacteristic
943C22#559012yes—
944C22D3×C22⋊Q812yes—
945C22#563012yes—
946C22#563412yes—
947C22#563712yes—
948C22D3×#12311yescharacteristic
949C22#565311yescharacteristic
950C22#565412yes—
951C22C2×C4×#6711yescharacteristic
952C22C2×#93711yescharacteristic
953C22D4×#6712yes—
954C22C2×#94611yescharacteristic
955C22#582912yes—
956C4—44no—
957C4—42no—
958C4—42no—
959C4—44no—
960C4—124no—
961C4—124no—
962C4—122no—
963C4—122no—
964C3#1412711yescharacteristic, complemented, Sylow
965C2—28no—
966C2—68no—
967C2—124no—
968C2#7445511yescharacteristic
969C2D3×#38511yescharacteristic
970C2#7459111yescharacteristic
971C2#7459612yes—
972C2#7459911yescharacteristic
973C2#7460712yes—
974C2C2×#498911yescharacteristic
975C2#8239812yes—
976C2#8260411yescharacteristic
977C2#8281612yes—
978C2#8289311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#385C2
socle, cosocleC24×C3C24
prime radicalC25×D3C22
hypercenterC2×#385D3
hypocenterC3#14127
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×C3×#385C2semidirect
4. C2×#5210C2semidirect
5. C2×#4989C2semidirect
7. #71570C2semidirect
8. #71544C2semidirect
9. #71544C2semidirect
10. #69428C2semidirect
11. (C2×D3)⋊#95C2semidirect
18. C22×C3×C4⋊C4C22semidirect
31. C22×Dic3⋊C4C22semidirect
36. C2×C3×#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
41. C2×C3⋊#95C22semidirect
42. C2×C3⋊#95C22semidirect
44. #4955C4semidirect
49. C2×#385D3semidirect
105. C2×C3×C22⋊C4C2×C4semidirect
111. C2×#217C2×C4semidirect
129. C2×(C2×D3)⋊C4C2×C4semidirect
130. C2×(C2×D3)⋊C4C2×C4semidirect
148. C22×C4⋊C4C2×D3semidirect
173. C2×#95C2×D3semidirect
222. C23×D3C4⋊C4semidirect
389. C2×C22⋊C4C4×D3semidirect
687. C22×C3#385semidirect
733. C2×D3#385semidirect
932. C22#4989semidirect
964. C3#14127semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D3)⋊C42
C22×D3×C22⋊C42
C2×C3×#3852
C2×#52102
C2×#49892
C2×#49552
#715702
#715442
#694282
(C2×D3)⋊#952
#141273