Finite Group Databasebeta

← #10735671

Subgroups — #10735671

Order 768.

2506 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic, complemented
2C2×#4988C211yesmaximal, characteristic, complemented
3C2×#4673C212yesmaximal, complemented
4C2×#4671C211yesmaximal, characteristic
5C2×#4665C212yesmaximal, complemented
6C2×#4672C211yesmaximal, characteristic, complemented
7C3×#1445C211yesmaximal, characteristic, complemented
8#69428C212yesmaximal, complemented
9#69426C212yesmaximal, complemented
10#69408C211yesmaximal, characteristic, complemented
11#69405C211yesmaximal, characteristic, complemented
12#15453—31nomaximal, Sylow
13C23×D12C2212yes—
14C23×D12C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C23×Dic6C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C2×#896—24no—
30C2×#896—24no—
31C2×#896—24no—
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2212yes—
35C2×C3×#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4988—24no—
40#4673—28no—
41#4672—24no—
42#4671—24no—
43#4665—28no—
44C22×C22⋊Q8—31no—
45C2×#394—31no—
46C2×#393—32no—
47C2×#392—31no—
48C2×#390—31no—
49C2×#386—32no—
50#1445D311yescharacteristic, complemented
51#1439—32no—
52#1438—32no—
53#1437—31no—
54#1436—31no—
55C24×D3C2312yes—
56C24×D3C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2312yes—
61C23×C3×C4C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2312yes—
64C23×Dic3C2311yescharacteristic
65C23×Dic3C2311yescharacteristic
66C22×D12—24no—
67C22×D12—24no—
68C22×D12—24no—
69C22×D12—24no—
70C22×D12—22no—
71C22×D12—24no—
72C22×D12—24no—
73C22×D12—22no—
74C22×D12—22no—
75C22×D12—42no—
76C22×D12—42no—
77C22×D12—42no—
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—24no—
82C22×C4×D3—42no—
83C22×Dic6—22no—
84C22×Dic6—22no—
85C22×Dic6—22no—
86C22×Dic6—24no—
87C22×Dic6—42no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4D414yescomplemented
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—22no—
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—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4—42no—
111C2×(C2×D3)⋊C4—42no—
112C2×(C2×D3)⋊C4—42no—
113C2×(C2×D3)⋊C4—42no—
114C2×(C2×D3)⋊C4D414yes—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4D414yescomplemented
121C2×C4×Dic3—22no—
122C2×C4×Dic3—42no—
123#896—232no—
124C3×#95—24no—
125C3×#95—22no—
126C3×#95—22no—
127C3×#95—24no—
128C3⋊#95—24no—
129C3⋊#95—42no—
130C3⋊#95D418yescomplemented
131C23×Q8—31no—
132C23×D4—31no—
133C23×D4—32no—
134C24×C4—31no—
135C2×C22⋊Q8—64no—
136C2×C22⋊Q8—64no—
137C2×C22⋊Q8—64no—
138C22×C4⋊C4—31no—
139C22×C4⋊C4—31no—
140C22×C4⋊C4C2×D311yescharacteristic
141C22×C22⋊C4—31no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—31no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4—32no—
149C22×C42—31no—
150#394—64no—
151#393—68no—
152#392—64no—
153#390—64no—
154#386—68no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95C2×D311yescharacteristic
159C2×#95C2×D312yes—
160C2×#95C2×D311yescharacteristic
161C2×#95C2×D312yes—
162C24×C3C2411yescharacteristic
163C23×D3—21no—
164C23×D3—21no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—22no—
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—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3C2×D412yes—
185C23×D3#4114yes—
186C23×D3#4114yes—
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—21no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D414yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D412yes—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3C2×D414yes—
234C22×Dic3C2×D412yes—
235C22×Dic3C2×D412yes—
236C22×Dic3C2×D414yes—
237C22×Dic3C2×D412yes—
238C2×D12—28no—
239C2×D12—216no—
240C2×D12—48no—
241C2×D12—48no—
242C2×D12—48no—
243C2×D12—48no—
244C2×D12—44no—
245C2×D12—48no—
246C2×D12—48no—
247C2×D12—48no—
248C2×D12—48no—
249C2×D12—44no—
250C2×C4×D3—28no—
251C2×C4×D3—48no—
252C2×C4×D3—48no—
253C2×C4×D3—44no—
254C2×C4×D3—44no—
255C2×Dic6—28no—
256C2×Dic6—48no—
257C2×Dic6—48no—
258C2×Dic6—44no—
259C2×Dic6—44no—
260C3×C4⋊C4—28no—
261(C2×D3)⋊C4—28no—
262(C2×D3)⋊C4—28no—
263(C2×D3)⋊C4—48no—
264(C2×D3)⋊C4—48no—
265(C2×D3)⋊C4—48no—
266(C2×D3)⋊C4—48no—
267(C2×D3)⋊C4—48no—
268(C2×D3)⋊C4—48no—
269Dic3⋊C4—28no—
270Dic3⋊C4—28no—
271C4×Dic3—44no—
272C25—31no—
273C25—32no—
274C22×Q8—62no—
275C22×Q8—62no—
276C22×Q8—64no—
277C22×Q8—62no—
278C22×Q8—122no—
279C22×D4—64no—
280C22×D4—64no—
281C22×D4—64no—
282C22×D4—64no—
283C22×D4—64no—
284C22×D4—62no—
285C22×D4—64no—
286C22×D4—62no—
287C22×D4—62no—
288C22×D4—122no—
289C22×D4—122no—
290C22×D4—122no—
291C23×C4—31no—
292C23×C4—31no—
293C23×C4—31no—
294C23×C4—32no—
295C23×C4—62no—
296C23×C4—64no—
297C23×C4—62no—
298C23×C4—62no—
299C23×C4—122no—
300C23×C4C22×D312yes—
301C23×C4C22×D311yescharacteristic
302C23×C4C22×D311yescharacteristic
303C23×C4C22×D312yes—
304C23×C4C22×D311yescharacteristic
305C22⋊Q8—632no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—34no—
309C2×C4⋊C4—62no—
310C2×C4⋊C4—62no—
311C2×C4⋊C4—62no—
312C2×C4⋊C4—62no—
313C2×C4⋊C4—62no—
314C2×C4⋊C4D1214yescomplemented
315C2×C22⋊C4—34no—
316C2×C22⋊C4—62no—
317C2×C22⋊C4—62no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—62no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—122no—
335C2×C22⋊C4—122no—
336C2×C22⋊C4—122no—
337C2×C22⋊C4—122no—
338C2×C22⋊C4—122no—
339C2×C42—62no—
340C2×C42—122no—
341#95—24no—
342#95—22no—
343#95—24no—
344#95—22no—
345#95—38no—
346#95—64no—
347#95—122no—
348C23×C3C22×D411yescharacteristic
349C23×C3C22×D411yescharacteristic
350C23×C3C22×D411yescharacteristic
351C23×C3C22×D412yes—
352C23×C3C2×#4112yes—
353C23×C3C2×#4112yes—
354C23×C3H(5,𝔽2)12yes—
355C23×C3H(5,𝔽2)12yes—
356C23×C32−1+412yes—
357C22×D3—22no—
358C22×D3—24no—
359C22×D3—22no—
360C22×D3—24no—
361C22×D3—24no—
362C22×D3—24no—
363C22×D3—24no—
364C22×D3—24no—
365C22×D3—24no—
366C22×D3—24no—
367C22×D3—24no—
368C22×D3—24no—
369C22×D3—24no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—41no—
375C22×D3—41no—
376C22×D3—41no—
377C22×D3—41no—
378C22×D3—42no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—42no—
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—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—42no—
405C22×D3—42no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3#12414yes—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—42no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
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—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4#12014yes—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—24no—
445C2×Dic3—24no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—24no—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—42no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3#12714yes—
464D12—416no—
465D12—432no—
466C4×D3—416no—
467Dic6—416no—
468C24—32no—
469C24—34no—
470C24—34no—
471C24—61no—
472C24—61no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—62no—
477C24—62no—
478C24—62no—
479C24—62no—
480C24—62no—
481C24—62no—
482C24—62no—
483C24—62no—
484C24—62no—
485C24—62no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24C23×D311yescharacteristic
493C2×Q8—68no—
494C2×Q8—128no—
495C2×Q8—124no—
496C2×Q8—128no—
497C2×Q8—124no—
498C2×D4—68no—
499C2×D4—616no—
500C2×D4—128no—
501C2×D4—128no—
502C2×D4—128no—
503C2×D4—128no—
504C2×D4—124no—
505C2×D4—128no—
506C2×D4—128no—
507C2×D4—128no—
508C2×D4—128no—
509C2×D4—124no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—34no—
534C22×C4—32no—
535C22×C4—34no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—68no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—62no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—128no—
557C22×C4—124no—
558C22×C4—128no—
559C22×C4—124no—
560C22×C4C2×D1212yes—
561C22×C4C2×D1212yes—
562C22×C4C2×D1212yes—
563C22×C4D3×D414yes—
564C22×C4D3×D412yes—
565C22×C4D3×D412yes—
566C4⋊C4—28no—
567C4⋊C4—68no—
568C4⋊C4—68no—
569C22⋊C4—68no—
570C22⋊C4—68no—
571C22⋊C4—128no—
572C22⋊C4—128no—
573C22⋊C4—128no—
574C22⋊C4—128no—
575C22⋊C4—128no—
576C22⋊C4—128no—
577C42—124no—
578C22×C3C2×#12011yescharacteristic
579C22×C3#52512yes—
580C22×C3#52511yescharacteristic
581C22×C3C2×#12411yescharacteristic
582C22×C3C2×#12711yescharacteristic
583C22×C3#53511yescharacteristic
584C22×C3#53511yescharacteristic
585C22×C3#53611yescharacteristic
586C22×C3#53712yes—
587C22×C3#53812yes—
588C22×C3#53912yes—
589C22×C3D4212yes—
590C22×C3D4212yes—
591C22×C3#54612yes—
592C22×C3#54612yes—
593C22×C3#54612yes—
594C22×C3#54812yes—
595C22×C3#54812yes—
596C22×C3#54812yes—
597C22×C3#55112yes—
598C22×C3#56212yes—
599C2×D3—24no—
600C2×D3—28no—
601C2×D3—42no—
602C2×D3—44no—
603C2×D3—44no—
604C2×D3—42no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C2×D3—44no—
610C2×D3—44no—
611C2×D3—44no—
612C2×D3—44no—
613C2×D3—44no—
614C2×D3—44no—
615C2×D3—82no—
616C2×D3—82no—
617C2×D3—82no—
618C2×D3—82no—
619C2×D3—82no—
620C2×D3—82no—
621C2×D3—82no—
622C2×D3—82no—
623C3×C4—24no—
624C3×C4—42no—
625C3×C4—42no—
626C3×C4—44no—
627C3×C4—82no—
628Dic3—24no—
629Dic3—42no—
630Dic3—44no—
631Dic3—42no—
632C23—34no—
633C23—64no—
634C23—64no—
635C23—64no—
636C23—64no—
637C23—64no—
638C23—64no—
639C23—62no—
640C23—62no—
641C23—64no—
642C23—64no—
643C23—64no—
644C23—64no—
645C23—64no—
646C23—64no—
647C23—64no—
648C23—64no—
649C23—64no—
650C23—122no—
651C23—122no—
652C23—121no—
653C23—122no—
654C23—122no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—122no—
659C23—122no—
660C23—122no—
661C23—122no—
662C23—122no—
663C23—122no—
664C23—122no—
665C23—122no—
666C23—122no—
667C23—122no—
668C23—122no—
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—122no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23C22×D1211yescharacteristic
689C23C2×D3×D411yescharacteristic
690C23C2×D3×D412yes—
691C23C2×D3×D411yescharacteristic
692C23#100712yes—
693C23D3×#4112yes—
694C23D3×#4112yes—
695C23#100912yes—
696C23#100912yes—
697Q8—1216no—
698D4—1216no—
699D4—1232no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—34no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—64no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—64no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—64no—
738C2×C4—64no—
739C2×C4—64no—
740C2×C4—1216no—
741C2×C4—122no—
742C2×C4—121no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—122no—
748C2×C4—121no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4#88214yes—
752C2×C3#240411yescharacteristic
753C2×C3#243311yescharacteristic
754C2×C3#243611yescharacteristic
755C2×C3#246312yes—
756C2×C3#247212yes—
757C2×C3#254012yes—
758C2×C3#267612yes—
759C2×C3#268112yes—
760C2×C3#269612yes—
761D3—44no—
762D3—84no—
763C22—68no—
764C22—64no—
765C22—122no—
766C22—124no—
767C22—124no—
768C22—122no—
769C22—124no—
770C22—124no—
771C22—124no—
772C22—124no—
773C22—124no—
774C22—124no—
775C22—124no—
776C22—124no—
777C22—124no—
778C22—124no—
779C22—242no—
780C22—242no—
781C22—242no—
782C22—242no—
783C22—242no—
784C22—242no—
785C22—242no—
786C22—242no—
787C22C2×#88211yescharacteristic
788C22#552411yescharacteristic
789C22#552511yescharacteristic
790C22D4×D1212yes—
791C22#557612yes—
792C22#560912yes—
793C22#562912yes—
794C22#563312yes—
795C22#563312yes—
796C22#565412yes—
797C22#565412yes—
798C22#565412yes—
799C22#565612yes—
800C22D3×#12411yescharacteristic
801C22#567411yescharacteristic
802C22#569212yes—
803C22#570012yes—
804C22#570412yes—
805C22#570512yes—
806C22D3×#12711yescharacteristic
807C22#572411yescharacteristic
808C4—24no—
809C4—42no—
810C4—42no—
811C4—44no—
812C4—64no—
813C4—82no—
814C4—122no—
815C4—124no—
816C4—122no—
817C3#1545311yescharacteristic, complemented, Sylow
818C2—124no—
819C2—244no—
820C2#7412511yescharacteristic
821C2#7532712yes—
822C2#7538912yes—
823C2#7631411yescharacteristic
824C2#7650011yescharacteristic
825C2#7747412yes—
826C2#7797012yes—
827C2#7803612yes—
828C2#7824012yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1445C2
prime radicalC2×#4671C2
hypercenter#1445D3
hypocenterC3#15453
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
1. C22×#896C2semidirect
2. C2×#4988C2semidirect
3. C2×#4673C2semidirect
5. C2×#4665C2semidirect
6. C2×#4672C2semidirect
7. C3×#1445C2semidirect
8. #69428C2semidirect
9. #69426C2semidirect
10. #69408C2semidirect
11. #69405C2semidirect
50. #1445D3semidirect
90. C2×C3×C4⋊C4D4semidirect
120. C2×Dic3⋊C4D4semidirect
130. C3⋊#95D4semidirect
314. C2×C4⋊C4D12semidirect
817. C3#15453semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C2×#49882
C2×#46732
C2×#46712
C2×#46652
C2×#46722
C3×#14452
#694282
#694262
#694082
#694052
#154533