Finite Group Databasebeta

← #10750396

Subgroups — #10750396

Order 768.

2266 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#875C211yesmaximal, characteristic, complemented
2C2×#4991C212yesmaximal, complemented
3C2×#4940C211yesmaximal, characteristic, complemented
4C2×#4673C211yesmaximal, characteristic, complemented
5C2×#4671C211yesmaximal, characteristic
6C3×C4⋊#95C211yesmaximal, characteristic, complemented
7#71570C212yesmaximal, complemented
8#69428C212yesmaximal, complemented
9#69426C211yesmaximal, characteristic, complemented
10#69426C212yesmaximal, complemented
11#69424C211yesmaximal, characteristic, complemented
12#16504—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C23×D12C2212yes—
15C23×Dic6C2211yescharacteristic
16C22×C3×C4⋊C4C2212yes—
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2212yes—
27C22×Dic3⋊C4C2211yescharacteristic
28C2×#875—24no—
29C2×#875—28no—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38#4991—28no—
39#4940—24no—
40#4673—24no—
41#4671—24no—
42C22×#124—31no—
43C2×#394—32no—
44C2×#393—31no—
45C2×#392—31no—
46C2×#388—31no—
47#1446—31no—
48#1439—32no—
49#1439—32no—
50#1438—32no—
51#1438—31no—
52C4⋊#95D311yescharacteristic, complemented
53C24×D3C2311yescharacteristic
54C24×D3C2312yes—
55C23×C3×C4C2312yes—
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×Dic3C2311yescharacteristic
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2312yes—
63C23×Dic3C2311yescharacteristic
64C22×D12—24no—
65C22×D12—22no—
66C22×D12—24no—
67C22×D12—24no—
68C22×D12—22no—
69C22×D12—24no—
70C22×D12—22no—
71C22×D12—42no—
72C22×D12—42no—
73C22×D12—42no—
74C22×D12—42no—
75C22×D12—42no—
76C22×Dic6—22no—
77C22×Dic6—24no—
78C22×Dic6—22no—
79C22×Dic6—22no—
80C22×Dic6—42no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—42no—
84C2×C3×C42—24no—
85C2×C3×C42D414yescomplemented
86C2×(C2×D3)⋊C4—24no—
87C2×(C2×D3)⋊C4—22no—
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—24no—
90C2×(C2×D3)⋊C4—24no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—42no—
102C2×(C2×D3)⋊C4—42no—
103C2×(C2×D3)⋊C4—42no—
104C2×(C2×D3)⋊C4—42no—
105C2×(C2×D3)⋊C4—42no—
106C2×(C2×D3)⋊C4—42no—
107C2×(C2×D3)⋊C4—42no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4D414yes—
110C2×(C2×D3)⋊C4D418yescomplemented
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—42no—
113#875—232no—
114C3×#95—22no—
115C3×#95—22no—
116C3×#95—42no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—42no—
122C23×Q8—31no—
123C23×D4—31no—
124C23×D4—32no—
125C2×#124—68no—
126C2×#124—64no—
127C22×C4⋊C4—31no—
128C22×C4⋊C4C2×D312yes—
129C22×C22⋊C4—31no—
130C22×C22⋊C4—32no—
131C22×C22⋊C4—31no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—31no—
137C22×C22⋊C4—32no—
138C22×C42C2×D311yescharacteristic
139#394—68no—
140#393—64no—
141#392—64no—
142#388—64no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95—31no—
146C2×#95—31no—
147C2×#95—32no—
148C2×#95C2×D311yescharacteristic
149C2×#95C2×D311yescharacteristic
150C2×#95C2×D312yes—
151C24×C3C2411yescharacteristic
152C23×D3—21no—
153C23×D3—22no—
154C23×D3—22no—
155C23×D3—22no—
156C23×D3—22no—
157C23×D3—22no—
158C23×D3—21no—
159C23×D3—22no—
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—21no—
170C23×D3—21no—
171C23×D3—22no—
172C23×D3—21no—
173C23×D3—21no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3C2×D412yes—
177C23×D3C2×D414yes—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×D414yes—
204C22×C3×C4C2×D412yes—
205C22×C3×C4#4114yes—
206C22×C3×C4#4112yes—
207C22×Dic3—21no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—21no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3C2×D412yes—
228C22×Dic3C2×D414yes—
229C2×D12—28no—
230C2×D12—48no—
231C2×D12—48no—
232C2×D12—48no—
233C2×D12—48no—
234C2×D12—44no—
235C2×D12—48no—
236C2×D12—48no—
237C2×D12—48no—
238C2×D12—48no—
239C2×D12—48no—
240C2×D12—44no—
241C2×Dic6—28no—
242C2×Dic6—48no—
243C2×Dic6—48no—
244C2×Dic6—44no—
245C2×Dic6—44no—
246C3×C4⋊C4—48no—
247C3×C42—28no—
248(C2×D3)⋊C4—216no—
249(C2×D3)⋊C4—216no—
250(C2×D3)⋊C4—28no—
251(C2×D3)⋊C4—48no—
252(C2×D3)⋊C4—48no—
253(C2×D3)⋊C4—44no—
254(C2×D3)⋊C4—48no—
255(C2×D3)⋊C4—48no—
256(C2×D3)⋊C4—44no—
257Dic3⋊C4—44no—
258C25—31no—
259C25—32no—
260C22×Q8—64no—
261C22×Q8—62no—
262C22×Q8—62no—
263C22×Q8—62no—
264C22×Q8—122no—
265C22×D4—64no—
266C22×D4—64no—
267C22×D4—64no—
268C22×D4—62no—
269C22×D4—64no—
270C22×D4—62no—
271C22×D4—62no—
272C22×D4—122no—
273C22×D4—122no—
274C22×D4—122no—
275C22×D4—122no—
276C22×D4—122no—
277C23×C4—31no—
278C23×C4—32no—
279C23×C4—31no—
280C23×C4—31no—
281C23×C4C22×D312yes—
282C23×C4C22×D311yescharacteristic
283C23×C4C22×D312yes—
284C23×C4C22×D311yescharacteristic
285C23×C4C22×D311yescharacteristic
286#124—632no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—62no—
291C2×C4⋊C4—122no—
292C2×C22⋊C4—38no—
293C2×C22⋊C4—34no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—62no—
299C2×C22⋊C4—64no—
300C2×C22⋊C4—62no—
301C2×C22⋊C4—64no—
302C2×C22⋊C4—64no—
303C2×C22⋊C4—64no—
304C2×C22⋊C4—64no—
305C2×C22⋊C4—62no—
306C2×C22⋊C4—62no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—122no—
310C2×C22⋊C4—122no—
311C2×C22⋊C4—122no—
312C2×C22⋊C4—122no—
313C2×C22⋊C4—122no—
314C2×C22⋊C4—122no—
315C2×C22⋊C4—122no—
316C2×C22⋊C4—122no—
317C2×C42—24no—
318C2×C42D1214yescomplemented
319#95—22no—
320#95—22no—
321#95—42no—
322#95—64no—
323#95—64no—
324#95—62no—
325#95—62no—
326#95—122no—
327C23×C3C22×D411yescharacteristic
328C23×C3C22×D412yes—
329C23×C3C22×D411yescharacteristic
330C23×C3C2×#4112yes—
331C23×C3C2×#4111yescharacteristic
332C23×C3H(5,𝔽2)11yescharacteristic
333C23×C3H(5,𝔽2)11yescharacteristic
334C23×C3H(5,𝔽2)12yes—
335C23×C3H(5,𝔽2)12yes—
336C23×C32−1+411yescharacteristic
337C23×C32−1+411yescharacteristic
338C22×D3—24no—
339C22×D3—22no—
340C22×D3—24no—
341C22×D3—22no—
342C22×D3—22no—
343C22×D3—24no—
344C22×D3—24no—
345C22×D3—24no—
346C22×D3—24no—
347C22×D3—24no—
348C22×D3—24no—
349C22×D3—24no—
350C22×D3—41no—
351C22×D3—42no—
352C22×D3—42no—
353C22×D3—41no—
354C22×D3—41no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3—41no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—41no—
364C22×D3—41no—
365C22×D3—42no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—42no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—42no—
374C22×D3—42no—
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—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—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4#12014yes—
424C2×C3×C4#12114yes—
425C2×Dic3—24no—
426C2×Dic3—22no—
427C2×Dic3—24no—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—42no—
431C2×Dic3—41no—
432C2×Dic3—41no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—42no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447D12—416no—
448D12—432no—
449Dic6—416no—
450C24—32no—
451C24—34no—
452C24—61no—
453C24—62no—
454C24—62no—
455C24—62no—
456C24—62no—
457C24—62no—
458C24—62no—
459C24—62no—
460C24—62no—
461C24—62no—
462C24—61no—
463C24—61no—
464C24—61no—
465C24—62no—
466C24—61no—
467C24—61no—
468C24—62no—
469C24—62no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24C23×D311yescharacteristic
477C2×Q8—68no—
478C2×Q8—128no—
479C2×Q8—128no—
480C2×Q8—124no—
481C2×Q8—124no—
482C2×D4—68no—
483C2×D4—128no—
484C2×D4—128no—
485C2×D4—128no—
486C2×D4—128no—
487C2×D4—124no—
488C2×D4—128no—
489C2×D4—128no—
490C2×D4—128no—
491C2×D4—128no—
492C2×D4—128no—
493C2×D4—124no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—32no—
517C22×C4—34no—
518C22×C4—61no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4C2×D1212yes—
539C22×C4C2×D1212yes—
540C22×C4C2×D1212yes—
541C22×C4#23514yes—
542C22×C4D3×D414yes—
543C22×C4D3×D412yes—
544C22×C4#23912yes—
545C4⋊C4—48no—
546C4⋊C4—124no—
547C22⋊C4—616no—
548C22⋊C4—616no—
549C22⋊C4—68no—
550C22⋊C4—128no—
551C22⋊C4—124no—
552C22⋊C4—128no—
553C22⋊C4—128no—
554C22⋊C4—128no—
555C22⋊C4—124no—
556C42—28no—
557C22×C3C2×#12011yescharacteristic
558C22×C3C2×#12111yescharacteristic
559C22×C3#53211yescharacteristic
560C22×C3#53511yescharacteristic
561C22×C3#53511yescharacteristic
562C22×C3#53511yescharacteristic
563C22×C3#53512yes—
564C22×C3#53611yescharacteristic
565C22×C3#53711yescharacteristic
566C22×C3#53711yescharacteristic
567C22×C3#53712yes—
568C22×C3#53812yes—
569C22×C3#54211yescharacteristic
570C22×C3#54211yescharacteristic
571C22×C3#54212yes—
572C22×C3D4212yes—
573C22×C3#54612yes—
574C22×C3#54612yes—
575C22×C3#54612yes—
576C22×C3#54712yes—
577C22×C3#55912yes—
578C22×C3H(3,𝔽4)12yes—
579C22×C3#56212yes—
580C2×D3—44no—
581C2×D3—42no—
582C2×D3—44no—
583C2×D3—42no—
584C2×D3—44no—
585C2×D3—44no—
586C2×D3—44no—
587C2×D3—44no—
588C2×D3—44no—
589C2×D3—44no—
590C2×D3—44no—
591C2×D3—42no—
592C2×D3—81no—
593C2×D3—82no—
594C2×D3—81no—
595C2×D3—82no—
596C2×D3—82no—
597C2×D3—81no—
598C2×D3—82no—
599C2×D3—82no—
600C2×D3—81no—
601C2×D3—82no—
602C2×D3—82no—
603C2×D3—82no—
604C2×D3—82no—
605C2×D3—82no—
606C3×C4—24no—
607C3×C4—24no—
608C3×C4—42no—
609C3×C4—44no—
610C3×C4—82no—
611Dic3—44no—
612Dic3—42no—
613Dic3—81no—
614Dic3—81no—
615C23—62no—
616C23—62no—
617C23—64no—
618C23—64no—
619C23—62no—
620C23—64no—
621C23—64no—
622C23—64no—
623C23—64no—
624C23—64no—
625C23—64no—
626C23—64no—
627C23—122no—
628C23—122no—
629C23—122no—
630C23—122no—
631C23—122no—
632C23—122no—
633C23—122no—
634C23—122no—
635C23—121no—
636C23—122no—
637C23—122no—
638C23—121no—
639C23—121no—
640C23—122no—
641C23—121no—
642C23—122no—
643C23—122no—
644C23—122no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23—121no—
649C23—121no—
650C23—122no—
651C23—121no—
652C23—122no—
653C23—121no—
654C23—122no—
655C23—122no—
656C23—122no—
657C23—122no—
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—
673C23C22×D1211yescharacteristic
674C23C2×#23512yes—
675C23C2×D3×D411yescharacteristic
676C23C2×D3×D412yes—
677C23#100411yescharacteristic
678C23#100411yescharacteristic
679C23C2×#23911yescharacteristic
680C23#100711yescharacteristic
681C23#100711yescharacteristic
682C23#100912yes—
683C23#100912yes—
684Q8—1216no—
685D4—1216no—
686D4—1232no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—64no—
715C2×C4—62no—
716C2×C4—64no—
717C2×C4—64no—
718C2×C4—64no—
719C2×C4—121no—
720C2×C4—122no—
721C2×C4—121no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4#88214yes—
737C2×C4#89514yes—
738C2×C3#240811yescharacteristic
739C2×C3#243011yescharacteristic
740C2×C3#254411yescharacteristic
741C2×C3#261511yescharacteristic
742C2×C3#262011yescharacteristic
743C2×C3#266211yescharacteristic
744C2×C3#267012yes—
745C2×C3#267212yes—
746C2×C3#271012yes—
747C2×C3#271212yes—
748C2×C3#281911yescharacteristic
749D3—84no—
750D3—82no—
751C22—124no—
752C22—122no—
753C22—124no—
754C22—122no—
755C22—124no—
756C22—122no—
757C22—124no—
758C22—124no—
759C22—124no—
760C22—124no—
761C22—124no—
762C22—124no—
763C22—242no—
764C22—241no—
765C22—241no—
766C22—242no—
767C22—242no—
768C22—241no—
769C22—242no—
770C22—242no—
771C22—242no—
772C22—241no—
773C22—242no—
774C22—242no—
775C22—242no—
776C22—242no—
777C22#547711yescharacteristic
778C22C2×#88211yescharacteristic
779C22#549012yes—
780C22C2×#89511yescharacteristic
781C22#550712yes—
782C22#551011yescharacteristic
783C22#551011yescharacteristic
784C22#552511yescharacteristic
785C22#552511yescharacteristic
786C22#555012yes—
787C22#556012yes—
788C22#558212yes—
789C22#558512yes—
790C22#560712yes—
791C22#560912yes—
792C22#562912yes—
793C22#563012yes—
794C22#568312yes—
795C22#570012yes—
796C22#571511yescharacteristic
797C22#572411yescharacteristic
798C22#573311yescharacteristic
799C22#573311yescharacteristic
800C4—24no—
801C4—24no—
802C4—42no—
803C4—44no—
804C4—82no—
805C4—124no—
806C4—122no—
807C4—241no—
808C4—241no—
809C3#1650411yescharacteristic, complemented, Sylow
810C2—244no—
811C2—242no—
812C2#7337611yescharacteristic
813C2#7380111yescharacteristic
814C2#7381611yescharacteristic
815C2#7401611yescharacteristic
816C2#7403011yescharacteristic
817C2#7425411yescharacteristic
818C2#7437011yescharacteristic
819C2#7625712yes—
820C2#7626812yes—
821C2#7646112yes—
822C2#7665212yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C4⋊#95C2
prime radicalC2×#4671C2
hypercenterC4⋊#95D3
hypocenterC3#16504
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×#4991C2semidirect
3. C2×#4940C2semidirect
4. C2×#4673C2semidirect
6. C3×C4⋊#95C2semidirect
7. #71570C2semidirect
8. #69428C2semidirect
9. #69426C2semidirect
10. #69426C2semidirect
11. #69424C2semidirect
52. C4⋊#95D3semidirect
85. C2×C3×C42D4semidirect
110. C2×(C2×D3)⋊C4D4semidirect
318. C2×C42D12semidirect
809. C3#16504semidirect

Maximal subgroups

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

subgroupindex
C22×#8752
C2×#49912
C2×#49402
C2×#46732
C2×#46712
C3×C4⋊#952
#715702
#694282
#694262
#694242
#165043