Finite Group Databasebeta

← #10729217

Subgroups — #10729217

Order 768.

2430 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#875C211yesmaximal, characteristic, complemented
2C2×#4939C212yesmaximal, complemented
3C2×#4940C211yesmaximal, characteristic, complemented
4C2×#4673C211yesmaximal, characteristic, complemented
5C2×#4671C211yesmaximal, characteristic
6C2×#4656C211yesmaximal, characteristic, complemented
7C2×#4672C211yesmaximal, characteristic, complemented
8C3×C4×#95C211yesmaximal, characteristic, complemented
9#71537C212yesmaximal, complemented
10#69427C212yesmaximal, complemented
11#69426C212yesmaximal, complemented
12#14928—31nomaximal, Sylow
13C23×D12C2212yes—
14C23×D12C2211yescharacteristic
15C23×Dic6C2211yescharacteristic
16C22×C3×C42C2212yes—
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×C4⋊Dic3C2212yes—
28C22×Dic3⋊C4C2211yescharacteristic
29C2×#875—24no—
30C2×#875—28no—
31C2×C3×#95C2212yes—
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38#4940—24no—
39#4939—28no—
40#4673—24no—
41#4672—24no—
42#4671—24no—
43#4656—24no—
44C22×#124—31no—
45C2×#395—31no—
46C2×#394—31no—
47C2×#393—31no—
48C2×#392—31no—
49C2×#390—32no—
50C2×#388—31no—
51#1439—32no—
52#1438—32no—
53#1437—32no—
54C4×#95D311yescharacteristic, complemented
55C24×D3C2312yes—
56C24×D3C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2312yes—
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2312yes—
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2312yes—
65C23×Dic3C2311yescharacteristic
66C22×D12—24no—
67C22×D12—24no—
68C22×D12—24no—
69C22×D12—22no—
70C22×D12—24no—
71C22×D12—24no—
72C22×D12—22no—
73C22×D12—22no—
74C22×D12—24no—
75C22×D12—42no—
76C22×D12—42no—
77C22×D12—42no—
78C22×Dic6—22no—
79C22×Dic6—24no—
80C22×Dic6—22no—
81C22×Dic6—22no—
82C22×Dic6—42no—
83C2×C3×C42—24no—
84C2×C3×C42—24no—
85C2×C3×C42—24no—
86C2×C3×C42—42no—
87C2×C3×C42D414yescomplemented
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—24no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—42no—
111C2×(C2×D3)⋊C4—42no—
112C2×(C2×D3)⋊C4—42no—
113C2×(C2×D3)⋊C4D418yescomplemented
114C2×C4⋊Dic3—24no—
115C2×C4⋊Dic3—24no—
116C2×C4⋊Dic3—42no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4—22no—
120#875—232no—
121C3×#95—24no—
122C3×#95D414yes—
123C3×#95D414yescomplemented
124C3⋊#95—24no—
125C3⋊#95—24no—
126C3⋊#95—22no—
127C3⋊#95—22no—
128C23×Q8—31no—
129C23×D4—31no—
130C23×D4—32no—
131C2×#124—68no—
132C2×#124—64no—
133C22×C4⋊C4—31no—
134C22×C4⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—31no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—32no—
139C22×C22⋊C4—31no—
140C22×C22⋊C4—31no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C42C2×D312yes—
145C22×C42C2×D311yescharacteristic
146#395—64no—
147#394—64no—
148#393—64no—
149#392—64no—
150#390—68no—
151#388—64no—
152C2×#95—32no—
153C2×#95—32no—
154C2×#95—31no—
155C2×#95—31no—
156C2×#95C2×D312yes—
157C2×#95C2×D311yescharacteristic
158C2×#95C2×D311yescharacteristic
159C24×C3C2411yescharacteristic
160C23×D3—21no—
161C23×D3—21no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—21no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—21no—
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3—21no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—21no—
184C23×D3C2×D414yes—
185C23×D3#4112yes—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4C2×D414yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D414yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2×D414yes—
213C22×C3×C4#4114yes—
214C22×C3×C4#4114yes—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—22no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—22no—
233C22×Dic3—21no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3C2×D414yes—
238C22×Dic3#4112yes—
239C2×D12—28no—
240C2×D12—216no—
241C2×D12—48no—
242C2×D12—48no—
243C2×D12—48no—
244C2×D12—48no—
245C2×D12—48no—
246C2×D12—48no—
247C2×D12—44no—
248C2×D12—48no—
249C2×D12—48no—
250C2×D12—44no—
251C2×Dic6—28no—
252C2×Dic6—48no—
253C2×Dic6—48no—
254C2×Dic6—44no—
255C2×Dic6—44no—
256C3×C42—28no—
257C3×C42—48no—
258(C2×D3)⋊C4—216no—
259(C2×D3)⋊C4—28no—
260(C2×D3)⋊C4—216no—
261(C2×D3)⋊C4—48no—
262(C2×D3)⋊C4—48no—
263(C2×D3)⋊C4—48no—
264(C2×D3)⋊C4—44no—
265(C2×D3)⋊C4—48no—
266(C2×D3)⋊C4—44no—
267C4⋊Dic3—48no—
268Dic3⋊C4—44no—
269C25—32no—
270C25—31no—
271C22×Q8—64no—
272C22×Q8—62no—
273C22×Q8—62no—
274C22×Q8—62no—
275C22×Q8—122no—
276C22×D4—64no—
277C22×D4—64no—
278C22×D4—64no—
279C22×D4—62no—
280C22×D4—62no—
281C22×D4—64no—
282C22×D4—62no—
283C22×D4—64no—
284C22×D4—64no—
285C22×D4—122no—
286C22×D4—122no—
287C22×D4—122no—
288C23×C4—32no—
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—31no—
292C23×C4C22×D311yescharacteristic
293C23×C4C22×D312yes—
294C23×C4C22×D311yescharacteristic
295C23×C4C22×D312yes—
296C23×C4C22×D311yescharacteristic
297#124—632no—
298C2×C4⋊C4—64no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—62no—
302C2×C4⋊C4—64no—
303C2×C4⋊C4—122no—
304C2×C22⋊C4—38no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—62no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—62no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—62no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—62no—
317C2×C22⋊C4—62no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—122no—
328C2×C22⋊C4—122no—
329C2×C22⋊C4—122no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—42no—
334C2×C42D1214yescomplemented
335#95—24no—
336#95—62no—
337#95—62no—
338#95—64no—
339#95—64no—
340#95D1214yes—
341#95D1214yescomplemented
342C23×C3C22×D411yescharacteristic
343C23×C3C22×D411yescharacteristic
344C23×C3C22×D411yescharacteristic
345C23×C3C22×D412yes—
346C23×C3C2×#4112yes—
347C23×C3C2×#4112yes—
348C23×C3C2×#4111yescharacteristic
349C23×C3C2×#4111yescharacteristic
350C23×C3H(5,𝔽2)11yescharacteristic
351C23×C3H(5,𝔽2)12yes—
352C23×C32−1+411yescharacteristic
353C22×D3—24no—
354C22×D3—22no—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—22no—
361C22×D3—24no—
362C22×D3—24no—
363C22×D3—22no—
364C22×D3—24no—
365C22×D3—41no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—42no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—41no—
372C22×D3—42no—
373C22×D3—41no—
374C22×D3—41no—
375C22×D3—42no—
376C22×D3—42no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—41no—
384C22×D3—42no—
385C22×D3—41no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—41no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—41no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C2×C3×C4—22no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4#12014yes—
438C2×C3×C4#12418yescomplemented
439C2×C3×C4#12714yes—
440C2×Dic3—24no—
441C2×Dic3—22no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—41no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—41no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—42no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—42no—
461C2×Dic3—41no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464D12—416no—
465D12—432no—
466Dic6—416no—
467C24—34no—
468C24—32no—
469C24—61no—
470C24—61no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—61no—
475C24—62no—
476C24—62no—
477C24—62no—
478C24—62no—
479C24—62no—
480C24—62no—
481C24—62no—
482C24—62no—
483C24—62no—
484C24—61no—
485C24—62no—
486C24—61no—
487C24—61no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24C23×D311yescharacteristic
494C2×Q8—68no—
495C2×Q8—128no—
496C2×Q8—128no—
497C2×Q8—124no—
498C2×Q8—124no—
499C2×D4—68no—
500C2×D4—616no—
501C2×D4—128no—
502C2×D4—128no—
503C2×D4—128no—
504C2×D4—128no—
505C2×D4—128no—
506C2×D4—128no—
507C2×D4—124no—
508C2×D4—128no—
509C2×D4—124no—
510C2×D4—128no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—34no—
531C22×C4—32no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—61no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4C2×D1214yes—
555C22×C4C2×D1212yes—
556C22×C4C2×D1212yes—
557C22×C4C2×D1212yes—
558C22×C4C2×D1212yes—
559C22×C4C2×D1214yes—
560C22×C4C2×D1212yes—
561C22×C4#23514yes—
562C22×C4#23514yes—
563C22×C4D3×D414yes—
564C4⋊C4—128no—
565C4⋊C4—124no—
566C22⋊C4—616no—
567C22⋊C4—68no—
568C22⋊C4—616no—
569C22⋊C4—128no—
570C22⋊C4—128no—
571C22⋊C4—128no—
572C22⋊C4—124no—
573C22⋊C4—128no—
574C22⋊C4—124no—
575C42—28no—
576C42—48no—
577C22×C3C2×#12011yescharacteristic
578C22×C3#52511yescharacteristic
579C22×C3#52512yes—
580C22×C3C2×#12412yes—
581C22×C3C2×#12711yescharacteristic
582C22×C3#53211yescharacteristic
583C22×C3#53211yescharacteristic
584C22×C3#53212yes—
585C22×C3#53212yes—
586C22×C3#53511yescharacteristic
587C22×C3#53711yescharacteristic
588C22×C3#53812yes—
589C22×C3#54212yes—
590C22×C3D4212yes—
591C22×C3D4212yes—
592C22×C3#54612yes—
593C22×C3#54611yescharacteristic
594C22×C3#54611yescharacteristic
595C22×C3#54712yes—
596C22×C3#54811yescharacteristic
597C22×C3#54811yescharacteristic
598C22×C3#55112yes—
599C22×C3#55512yes—
600C2×D3—42no—
601C2×D3—44no—
602C2×D3—42no—
603C2×D3—44no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C2×D3—44no—
610C2×D3—42no—
611C2×D3—44no—
612C2×D3—82no—
613C2×D3—81no—
614C2×D3—82no—
615C2×D3—82no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—82no—
620C2×D3—82no—
621C2×D3—82no—
622C2×D3—82no—
623C2×D3—82no—
624C2×D3—82no—
625C2×D3—82no—
626C3×C4—24no—
627C3×C4—24no—
628C3×C4—28no—
629C3×C4—42no—
630C3×C4—44no—
631Dic3—44no—
632Dic3—42no—
633Dic3—81no—
634Dic3—81no—
635C23—64no—
636C23—64no—
637C23—64no—
638C23—62no—
639C23—64no—
640C23—64no—
641C23—64no—
642C23—64no—
643C23—64no—
644C23—64no—
645C23—62no—
646C23—62no—
647C23—121no—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—122no—
654C23—121no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—121no—
659C23—121no—
660C23—122no—
661C23—122no—
662C23—122no—
663C23—122no—
664C23—121no—
665C23—122no—
666C23—122no—
667C23—122no—
668C23—121no—
669C23—122no—
670C23—122no—
671C23—122no—
672C23—122no—
673C23—122no—
674C23—122no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—122no—
683C23—121no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23—122no—
689C23—121no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23C22×D1211yescharacteristic
694C23C22×D1211yescharacteristic
695C23C22×D1211yescharacteristic
696C23C2×#23512yes—
697C23C2×#23512yes—
698C23C2×D3×D412yes—
699C23#100411yescharacteristic
700C23#100711yescharacteristic
701C23D3×#4111yescharacteristic
702C23D3×#4111yescharacteristic
703C23#100912yes—
704Q8—1216no—
705D4—1216no—
706D4—1232no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—64no—
734C2×C4—62no—
735C2×C4—64no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—121no—
740C2×C4—122no—
741C2×C4—121no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4#87414yes—
758C2×C4#87518yescomplemented
759C2×C4#88214yes—
760C2×C3#238811yescharacteristic
761C2×C3#243011yescharacteristic
762C2×C3#243311yescharacteristic
763C2×C3#246112yes—
764C2×C3#247212yes—
765C2×C3#249112yes—
766C2×C3#254011yescharacteristic
767C2×C3#255512yes—
768C2×C3#261011yescharacteristic
769C2×C3#266211yescharacteristic
770C2×C3#285811yescharacteristic
771D3—82no—
772D3—84no—
773C22—124no—
774C22—124no—
775C22—124no—
776C22—122no—
777C22—124no—
778C22—122no—
779C22—124no—
780C22—124no—
781C22—124no—
782C22—124no—
783C22—124no—
784C22—122no—
785C22—242no—
786C22—242no—
787C22—242no—
788C22—242no—
789C22—242no—
790C22—241no—
791C22—241no—
792C22—242no—
793C22—241no—
794C22—242no—
795C22—242no—
796C22—242no—
797C22—241no—
798C22—242no—
799C22C2×#87411yescharacteristic
800C22C2×#87512yes—
801C22#547712yes—
802C22#547711yescharacteristic
803C22#547711yescharacteristic
804C22C2×#88211yescharacteristic
805C22#549012yes—
806C22#550712yes—
807C22#551011yescharacteristic
808C22#552411yescharacteristic
809C22#552511yescharacteristic
810C22#552712yes—
811C22#553212yes—
812C22#554712yes—
813C22#554812yes—
814C22D4×D1212yes—
815C22D4×D1212yes—
816C22#555411yescharacteristic
817C22#555411yescharacteristic
818C22#556012yes—
819C22#557611yescharacteristic
820C22#557611yescharacteristic
821C22#558212yes—
822C4—24no—
823C4—28no—
824C4—24no—
825C4—42no—
826C4—44no—
827C4—122no—
828C4—124no—
829C4—241no—
830C4—241no—
831C3#1492811yescharacteristic, complemented, Sylow
832C2—242no—
833C2—244no—
834C2#7331311yescharacteristic
835C2#7337611yescharacteristic
836C2#7342611yescharacteristic
837C2#7358011yescharacteristic
838C2#7358711yescharacteristic
839C2#7359412yes—
840C2#7360012yes—
841C2#7378212yes—
842C2#7378812yes—
843C2#7379811yescharacteristic
844C2#7381611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C4×#95C2
prime radicalC2×#4671C2
hypercenterC4×#95D3
hypocenterC3#14928
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
1. C22×#875C2semidirect
2. C2×#4939C2semidirect
3. C2×#4940C2semidirect
4. C2×#4673C2semidirect
6. C2×#4656C2semidirect
7. C2×#4672C2semidirect
8. C3×C4×#95C2semidirect
9. #71537C2semidirect
10. #69427C2semidirect
11. #69426C2semidirect
54. C4×#95D3semidirect
87. C2×C3×C42D4semidirect
113. C2×(C2×D3)⋊C4D4semidirect
123. C3×#95D4semidirect
334. C2×C42D12semidirect
341. #95D12semidirect
438. C2×C3×C4#124semidirect
758. C2×C4#875semidirect
831. C3#14928semidirect

Maximal subgroups

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

subgroupindex
C22×#8752
C2×#49392
C2×#49402
C2×#46732
C2×#46712
C2×#46562
C2×#46722
C3×C4×#952
#715372
#694272
#694262
#149283