Finite Group Databasebeta

← #10726575

Subgroups — #10726575

Order 768.

3654 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#946C211yesmaximal, characteristic, complemented
2C22×D3×C22⋊C4C211yesmaximal, characteristic
3C2×C3×#393C211yesmaximal, characteristic, complemented
4C2×#5231C211yesmaximal, characteristic, complemented
5C2×#4955C212yesmaximal
6#71547C212yesmaximal, complemented
7#71546C211yesmaximal, characteristic, complemented
8#69428C212yesmaximal, complemented
9#69427C211yesmaximal, characteristic, complemented
10(C2×D3)⋊#95C212yesmaximal, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#14717—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C23×C3×Q8C2211yescharacteristic, complemented
15C23×C4×D3C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2211yescharacteristic
20C22×#217C2212yes—
21C2×#946—24no—
22C2×#946—28no—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic, complemented
30C22×Dic3⋊C4C2212yescomplemented
31C2×D3×C22⋊C4—24no—
32C2×D3×C22⋊C4—24no—
33C2×D3×C22⋊C4—24no—
34C3×#393—24no—
35C2×C3×#95C2211yescharacteristic, complemented
36C2×C3×#95C2212yescomplemented
37#5231—24no—
38C2×C3⋊#95C2211yescharacteristic, complemented
39C2×C3⋊#95C2212yescomplemented
40C2×C3⋊#95C2212yescomplemented
41C2×C3⋊#95C2212yescomplemented
42C2×C3⋊#95C2212yescomplemented
43#4955—28no—
44C22×C22⋊Q8—31no—
45C23×C22⋊C4—31no—
46C2×#393—31no—
47C2×#393D311yescharacteristic, complemented
48C2×#379—32no—
49#1439—31no—
50#1439—32no—
51#1439—31no—
52#1439—32no—
53C22⋊#95—32no—
54C22⋊#95—31no—
55C25×C3C2311yescharacteristic
56C24×D3—22no—
57C24×D3—22no—
58C24×D3—22no—
59C24×D3—22no—
60C24×D3—22no—
61C24×D3—22no—
62C24×D3—24no—
63C24×D3—24no—
64C24×D3—42no—
65C24×D3—42no—
66C24×D3Q814yescomplemented
67C24×D3C2311yescharacteristic
68C24×D3C2311yescharacteristic
69C22×C3×Q8—24no—
70C22×C3×Q8—22no—
71C22×C3×Q8—22no—
72C22×C3×Q8—22no—
73C22×C3×Q8—42no—
74C23×C3×C4C2312yes—
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2312yes—
77C23×C3×C4C2311yescharacteristic
78C23×Dic3C2312yes—
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2312yes—
82C22×C4×D3—22no—
83C22×C4×D3—24no—
84C22×C4×D3—22no—
85C22×C4×D3—22no—
86C22×C4×D3—22no—
87C22×C4×D3—22no—
88C22×C4×D3—24no—
89C22×C4×D3—42no—
90C22×C4×D3—42no—
91C22×C4×D3D414yes—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C22⋊C4D414yes—
98C2×#217—22no—
99C2×#217—22no—
100C2×#217—22no—
101C2×#217—24no—
102C2×#217—24no—
103C2×#217—42no—
104#946—232no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—24no—
119C2×(C2×D3)⋊C4—42no—
120C2×(C2×D3)⋊C4—42no—
121C2×(C2×D3)⋊C4D418yes—
122C2×(C2×D3)⋊C4D414yes—
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—24no—
125C2×Dic3⋊C4—24no—
126C2×Dic3⋊C4—24no—
127C2×Dic3⋊C4—24no—
128D3×C22⋊C4—232no—
129C3×#95—24no—
130C3×#95—22no—
131C3⋊#95—22no—
132C3⋊#95—24no—
133C3⋊#95—42no—
134C3⋊#95—42no—
135C3⋊#95—42no—
136C26—31no—
137C23×Q8C2×D311yescharacteristic, complemented
138C24×C4—31no—
139C24×C4—31no—
140C2×C22⋊Q8—68no—
141C2×C22⋊Q8—64no—
142C22×C4⋊C4—32no—
143C22×C4⋊C4—31no—
144C22×C22⋊C4—31no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—31no—
147C22×C22⋊C4—31no—
148C22×C22⋊C4—32no—
149C22×C22⋊C4—32no—
150C22×C22⋊C4—32no—
151C22×C22⋊C4—32no—
152C22×C22⋊C4—64no—
153C22×C22⋊C4—64no—
154C22×C22⋊C4—64no—
155C22×C22⋊C4C2×D312yes—
156C22×C22⋊C4C2×D311yescharacteristic
157#393—24no—
158#393—64no—
159#379—68no—
160C2×#95—32no—
161C2×#95—31no—
162C2×#95—32no—
163C2×#95—32no—
164C2×#95—32no—
165C2×#95C2×D311yescharacteristic, complemented
166C2×#95C2×D312yescomplemented
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3C2×D412yes—
176C24×C3C2×Q812yes—
177C24×C3#4112yes—
178C24×C3C2411yescharacteristic
179C23×D3—21no—
180C23×D3—21no—
181C23×D3—21no—
182C23×D3—21no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—28no—
186C23×D3—28no—
187C23×D3—28no—
188C23×D3—28no—
189C23×D3—28no—
190C23×D3—21no—
191C23×D3—22no—
192C23×D3—21no—
193C23×D3—21no—
194C23×D3—21no—
195C23×D3—22no—
196C23×D3—22no—
197C23×D3—22no—
198C23×D3—28no—
199C23×D3—28no—
200C23×D3—216no—
201C23×D3—48no—
202C23×D3—48no—
203C23×D3—48no—
204C23×D3—48no—
205C23×D3—48no—
206C23×D3—48no—
207C23×D3—48no—
208C23×D3—48no—
209C23×D3—48no—
210C23×D3—44no—
211C23×D3—44no—
212C23×D3—48no—
213C23×D3—44no—
214C23×D3—48no—
215C23×D3—44no—
216C23×D3C2×D412yes—
217C23×D3C2×D414yes—
218C23×D3C2×D412yes—
219C23×D3C2×Q812yes—
220C23×D3C2×Q812yes—
221C23×D3#4112yes—
222C23×D3#4112yes—
223C23×D3#4114yes—
224C2×C3×Q8—28no—
225C2×C3×Q8—48no—
226C2×C3×Q8—48no—
227C2×C3×Q8—44no—
228C2×C3×Q8—44no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4C2×D414yes—
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3C2×D412yes—
275C22×Dic3C2×D412yes—
276C22×Dic3C2×D414yes—
277C2×C4×D3—28no—
278C2×C4×D3—28no—
279C2×C4×D3—28no—
280C2×C4×D3—44no—
281C2×C4×D3—48no—
282C2×C4×D3—48no—
283C2×C4×D3—48no—
284C2×C4×D3—48no—
285C2×C4×D3—44no—
286C2×C4×D3—44no—
287C3×C22⋊C4—28no—
288C3×C22⋊C4—48no—
289#217—28no—
290#217—48no—
291(C2×D3)⋊C4—28no—
292(C2×D3)⋊C4—216no—
293(C2×D3)⋊C4—28no—
294(C2×D3)⋊C4—48no—
295(C2×D3)⋊C4—48no—
296(C2×D3)⋊C4—48no—
297C4⋊Dic3—28no—
298Dic3⋊C4—216no—
299C25—31no—
300C25—31no—
301C25—34no—
302C25—62no—
303C25—62no—
304C25—62no—
305C25—62no—
306C25—64no—
307C25—64no—
308C25—62no—
309C25—62no—
310C25—122no—
311C25—122no—
312C25C22×D311yescharacteristic
313C22×Q8—24no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—42no—
318C23×C4—32no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—34no—
322C23×C4—32no—
323C23×C4—62no—
324C23×C4—62no—
325C23×C4—64no—
326C23×C4—64no—
327C23×C4—62no—
328C23×C4—62no—
329C23×C4—62no—
330C23×C4—122no—
331C23×C4—122no—
332C23×C4C22×D312yes—
333C23×C4C22×D312yes—
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C22⋊Q8—632no—
337C2×C4⋊C4—64no—
338C2×C4⋊C4—64no—
339C2×C4⋊C4—64no—
340C2×C4⋊C4—64no—
341C2×C4⋊C4—62no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—34no—
347C2×C22⋊C4—38no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—632no—
350C2×C22⋊C4—62no—
351C2×C22⋊C4—62no—
352C2×C22⋊C4—64no—
353C2×C22⋊C4—64no—
354C2×C22⋊C4—62no—
355C2×C22⋊C4—62no—
356C2×C22⋊C4—62no—
357C2×C22⋊C4—62no—
358C2×C22⋊C4—62no—
359C2×C22⋊C4—62no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—64no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—64no—
367C2×C22⋊C4—64no—
368C2×C22⋊C4—64no—
369C2×C22⋊C4—122no—
370C2×C22⋊C4—122no—
371C2×C22⋊C4—122no—
372C2×C22⋊C4#6714yes—
373#95—24no—
374#95—22no—
375#95—64no—
376#95—62no—
377#95—122no—
378#95—122no—
379#95—122no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—24no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—42no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3C22⋊Q814yescomplemented
403C23×C3C22×D411yescharacteristic
404C23×C3C22×D411yescharacteristic
405C23×C3C22×D412yes—
406C23×C3C22×D411yescharacteristic
407C23×C3C22×Q811yescharacteristic
408C23×C3C2×#4111yescharacteristic
409C23×C3C2×#4111yescharacteristic
410C23×C3C2×#4111yescharacteristic
411C23×C3C2×#4112yes—
412C23×C3H(5,𝔽2)12yes—
413C23×C3H(5,𝔽2)12yes—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—24no—
423C22×D3—24no—
424C22×D3—24no—
425C22×D3—24no—
426C22×D3—24no—
427C22×D3—24no—
428C22×D3—24no—
429C22×D3—24no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—232no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—24no—
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—432no—
446C22×D3—432no—
447C22×D3—416no—
448C22×D3—416no—
449C22×D3—416no—
450C22×D3—416no—
451C22×D3—416no—
452C22×D3—432no—
453C22×D3—432no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—42no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—42no—
460C22×D3—42no—
461C22×D3—42no—
462C22×D3—42no—
463C22×D3—42no—
464C22×D3—416no—
465C22×D3#12014yes—
466C22×D3C22⋊Q814yes—
467C22×D3C22⋊Q818yes—
468C22×D3C22⋊Q814yescomplemented
469C22×D3#12418yes—
470C22×D3#12414yes—
471C3×Q8—416no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—42no—
482C2×C3×C4—41no—
483C2×C3×C4—42no—
484C2×C3×C4—41no—
485C2×C3×C4—42no—
486C2×C3×C4—42no—
487C2×C3×C4—42no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4#12014yes—
496C2×Dic3—22no—
497C2×Dic3—24no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—24no—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—42no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—42no—
508C2×Dic3—42no—
509C2×Dic3—42no—
510C2×Dic3—42no—
511C2×Dic3—42no—
512C2×Dic3—42no—
513C2×Dic3—42no—
514C2×Dic3—42no—
515C2×Dic3—42no—
516C2×Dic3—42no—
517C2×Dic3—42no—
518C2×Dic3—42no—
519C2×Dic3—42no—
520C4×D3—416no—
521C4×D3—416no—
522C24—21no—
523C24—21no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—21no—
528C24—21no—
529C24—22no—
530C24—34no—
531C24—32no—
532C24—32no—
533C24—32no—
534C24—34no—
535C24—32no—
536C24—32no—
537C24—32no—
538C24—68no—
539C24—68no—
540C24—616no—
541C24—68no—
542C24—68no—
543C24—68no—
544C24—68no—
545C24—61no—
546C24—62no—
547C24—61no—
548C24—61no—
549C24—62no—
550C24—61no—
551C24—68no—
552C24—62no—
553C24—61no—
554C24—62no—
555C24—61no—
556C24—62no—
557C24—61no—
558C24—62no—
559C24—61no—
560C24—128no—
561C24—128no—
562C24—128no—
563C24—128no—
564C24—128no—
565C24—128no—
566C24—124no—
567C24—124no—
568C24—128no—
569C24—128no—
570C24—128no—
571C24—128no—
572C24—124no—
573C24—128no—
574C24—124no—
575C24D3×Q812yes—
576C24#23912yes—
577C24C2×#6712yes—
578C24C23×D311yescharacteristic
579C2×Q8—28no—
580C2×Q8—48no—
581C2×Q8—48no—
582C2×Q8—44no—
583C2×Q8—44no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—32no—
604C22×C4—34no—
605C22×C4—32no—
606C22×C4—68no—
607C22×C4—68no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—68no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—124no—
631C22×C4—128no—
632C22×C4—128no—
633C22×C4—128no—
634C22×C4—128no—
635C22×C4—124no—
636C22×C4—124no—
637C22×C4D3×D414yes—
638C22×C4D3×D412yes—
639C22×C4D3×D412yes—
640C22×C4C2×#6712yes—
641C22×C4C2×#6712yes—
642C4⋊C4—616no—
643C4⋊C4—68no—
644C22⋊C4—28no—
645C22⋊C4—48no—
646C22⋊C4—616no—
647C22⋊C4—68no—
648C22⋊C4—68no—
649C22⋊C4—68no—
650C22⋊C4—128no—
651C22⋊C4—128no—
652C22⋊C4—128no—
653C22⋊C4—128no—
654C22×C3—24no—
655C22×C3—28no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3C2×#12011yescharacteristic
666C22×C3C2×#12011yescharacteristic
667C22×C3C2×C22⋊Q811yescharacteristic
668C22×C3C2×C22⋊Q811yescharacteristic
669C22×C3C2×C22⋊Q811yescharacteristic
670C22×C3C2×C22⋊Q812yes—
671C22×C3#52511yescharacteristic
672C22×C3#52511yescharacteristic
673C22×C3#52511yescharacteristic
674C22×C3C2×#12411yescharacteristic
675C22×C3C2×#12412yes—
676C22×C3#53411yescharacteristic
677C22×C3#53511yescharacteristic
678C22×C3#53812yes—
679C22×C3#54312yes—
680C22×C3D4212yes—
681C22×C3D4212yes—
682C22×C3#54612yes—
683C22×C3#54612yes—
684C22×C3#54612yes—
685C22×C3#54612yes—
686C22×C3#55112yes—
687C22×C3#55112yes—
688C2×D3—24no—
689C2×D3—24no—
690C2×D3—24no—
691C2×D3—24no—
692C2×D3—24no—
693C2×D3—24no—
694C2×D3—28no—
695C2×D3—28no—
696C2×D3—28no—
697C2×D3—28no—
698C2×D3—24no—
699C2×D3—28no—
700C2×D3—464no—
701C2×D3—42no—
702C2×D3—42no—
703C2×D3—42no—
704C2×D3—42no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—44no—
708C2×D3—44no—
709C2×D3—44no—
710C2×D3#39318yescomplemented
711C3×C4—24no—
712C3×C4—44no—
713C3×C4—42no—
714C3×C4—82no—
715Dic3—42no—
716Dic3—44no—
717Dic3—42no—
718Dic3—82no—
719C23—24no—
720C23—24no—
721C23—22no—
722C23—24no—
723C23—22no—
724C23—24no—
725C23—24no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—38no—
732C23—34no—
733C23—34no—
734C23—38no—
735C23—34no—
736C23—34no—
737C23—41no—
738C23—42no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—632no—
748C23—64no—
749C23—64no—
750C23—62no—
751C23—64no—
752C23—64no—
753C23—64no—
754C23—64no—
755C23—62no—
756C23—64no—
757C23—62no—
758C23—62no—
759C23—64no—
760C23—62no—
761C23—64no—
762C23—62no—
763C23—62no—
764C23—62no—
765C23—64no—
766C23—64no—
767C23—64no—
768C23—64no—
769C23—64no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—64no—
774C23—64no—
775C23—62no—
776C23—62no—
777C23—62no—
778C23—1232no—
779C23—1216no—
780C23—1232no—
781C23—1216no—
782C23—1232no—
783C23—1216no—
784C23—1216no—
785C23—1216no—
786C23—1216no—
787C23—1232no—
788C23—122no—
789C23—121no—
790C23—122no—
791C23—121no—
792C23—122no—
793C23—122no—
794C23—122no—
795C23—121no—
796C23—121no—
797C23—122no—
798C23#94614yescomplemented
799C23C2×D3×D411yescharacteristic
800C23C2×D3×D412yes—
801C23C2×D3×D411yescharacteristic
802C23#100412yes—
803C23C2×D3×Q811yescharacteristic
804C23C2×#23911yescharacteristic
805C23D3×#4112yes—
806C23D3×#4111yescharacteristic
807C23D3×#4111yescharacteristic
808C23#100912yes—
809C23C22×#6711yescharacteristic
810Q8—416no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—64no—
835C2×C4—64no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—64no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—64no—
842C2×C4—1216no—
843C2×C4—1216no—
844C2×C4—121no—
845C2×C4—121no—
846C2×C4—122no—
847C2×C4—122no—
848C2×C4—122no—
849C2×C4—122no—
850C2×C4—122no—
851C2×C4—122no—
852C2×C4—122no—
853C2×C4—122no—
854C2×C4—122no—
855C2×C4—122no—
856C2×C4—122no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4—122no—
860C2×C4#93714yes—
861C2×C3—44no—
862C2×C3C2×#39311yescharacteristic
863C2×C3#240311yescharacteristic
864C2×C3#240411yescharacteristic
865C2×C3#243511yescharacteristic
866C2×C3#243712yes—
867C2×C3#243712yes—
868C2×C3#247212yes—
869C2×C3#247212yes—
870C2×C3#256111yescharacteristic
871C2×C3#262611yescharacteristic
872C2×C3#284811yescharacteristic
873D3—28no—
874D3—44no—
875C22—28no—
876C22—24no—
877C22—38no—
878C22—42no—
879C22—44no—
880C22—42no—
881C22—42no—
882C22—44no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—44no—
887C22—64no—
888C22—68no—
889C22—64no—
890C22—68no—
891C22—64no—
892C22—64no—
893C22—68no—
894C22—64no—
895C22—64no—
896C22—68no—
897C22—68no—
898C22—64no—
899C22—1264no—
900C22—122no—
901C22—124no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—124no—
907C22—122no—
908C22—124no—
909C22D3×#12011yescharacteristic
910C22#558911yescharacteristic
911C22#559012yes—
912C22D3×C22⋊Q812yes—
913C22D3×C22⋊Q811yescharacteristic
914C22D3×C22⋊Q811yescharacteristic
915C22#562711yescharacteristic
916C22#562711yescharacteristic
917C22#563012yes—
918C22#563412yes—
919C22#563712yes—
920C22D3×#12411yescharacteristic
921C22D3×#12412yes—
922C22#567411yescharacteristic
923C22#567612yes—
924C22#567612yes—
925C22#567812yes—
926C22#567912yes—
927C22C2×#93711yescharacteristic
928C22D4×#6712yes—
929C22C2×#94611yescharacteristic
930C22#582811yescharacteristic
931C22#582912yes—
932C4—24no—
933C4—42no—
934C4—44no—
935C4—82no—
936C4—122no—
937C4—124no—
938C4—122no—
939C4—242no—
940C3#1471711yescharacteristic, complemented, Sylow
941C2—44no—
942C2—68no—
943C2—124no—
944C2#7679012yes—
945C2D3×#39311yescharacteristic
946C2#7686311yescharacteristic
947C2#7686512yes—
948C2#7686811yescharacteristic
949C2#7687111yescharacteristic
950C2#8260411yescharacteristic
951C2#8281612yes—
952C2#8283411yescharacteristic
953C2#8296011yescharacteristic
954C2#8296512yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#393C2
prime radicalC25×D3C22
hypercenterC2×#393D3
hypocenterC3#14717
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#946C2semidirect
3. C2×C3×#393C2semidirect
4. C2×#5231C2semidirect
6. #71547C2semidirect
7. #71546C2semidirect
8. #69428C2semidirect
9. #69427C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. (C2×D3)⋊#95C2semidirect
14. C23×C3×Q8C22semidirect
29. C22×C4⋊Dic3C22semidirect
30. C22×Dic3⋊C4C22semidirect
35. C2×C3×#95C22semidirect
36. C2×C3×#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
41. C2×C3⋊#95C22semidirect
42. C2×C3⋊#95C22semidirect
47. C2×#393D3semidirect
66. C24×D3Q8semidirect
137. C23×Q8C2×D3semidirect
165. C2×#95C2×D3semidirect
166. C2×#95C2×D3semidirect
402. C23×C3C22⋊Q8semidirect
468. C22×D3C22⋊Q8semidirect
710. C2×D3#393semidirect
798. C23#946semidirect
940. C3#14717semidirect

Maximal subgroups

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

subgroupindex
C22×#9462
C22×D3×C22⋊C42
C2×C3×#3932
C2×#52312
C2×#49552
#715472
#715462
#694282
#694272
(C2×D3)⋊#952
#147173