Finite Group Databasebeta

← #10729219

Subgroups — #10729219

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×#947C211yesmaximal, characteristic, complemented
2C2×C3×#395C211yesmaximal, characteristic, complemented
3C2×#5231C211yesmaximal, characteristic, complemented
4C2×#4991C211yesmaximal, characteristic, complemented
5C2×#4988C212yesmaximal, complemented
6C2×#4990C211yesmaximal, characteristic, complemented
7C2×#4671C211yesmaximal, characteristic
8#71570C212yesmaximal, complemented
9#69426C212yesmaximal, complemented
10#69408C212yesmaximal, complemented
11Dic3×#95C211yesmaximal, characteristic, complemented
12#14928—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×D12C2211yescharacteristic
15C23×D12C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2212yes—
18C2×#947—28no—
19C2×#947—24no—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×C4×Dic3C2212yes—
30C22×C4×Dic3C2211yescharacteristic
31C3×#395—24no—
32C2×C3×#95C2212yes—
33C2×C3×#95C2211yescharacteristic
34#5231—24no—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40#4991—24no—
41#4990—24no—
42#4988—28no—
43#4671—24no—
44C22×#124—31no—
45C2×#395D311yescharacteristic, complemented
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×#95—31no—
55C24×D3C2312yes—
56C24×D3C2311yescharacteristic
57C22×C3×Q8—24no—
58C22×C3×Q8—22no—
59C22×C3×Q8—22no—
60C22×C3×Q8—22no—
61C22×C3×Q8—42no—
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×Dic3C2311yescharacteristic
68C23×Dic3C2311yescharacteristic
69C23×Dic3C2312yes—
70C23×Dic3C2311yescharacteristic
71C22×D12—24no—
72C22×D12—24no—
73C22×D12—24no—
74C22×D12—22no—
75C22×D12—24no—
76C22×D12—24no—
77C22×D12—22no—
78C22×D12—22no—
79C22×D12—24no—
80C22×D12—42no—
81C22×D12—42no—
82C22×D12—42no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—42no—
89#947—232no—
90C2×(C2×D3)⋊C4—24no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—22no—
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—22no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—42no—
113C2×(C2×D3)⋊C4—42no—
114C2×(C2×D3)⋊C4—42no—
115C2×(C2×D3)⋊C4D418yescomplemented
116C2×C4×Dic3—24no—
117C2×C4×Dic3—24no—
118C2×C4×Dic3—24no—
119C2×C4×Dic3—42no—
120C2×C4×Dic3D414yescomplemented
121C3×#95—24no—
122C3×#95D414yes—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95D414yescomplemented
128C23×Q8C2×D311yescharacteristic
129C23×D4—31no—
130C23×D4—32no—
131C2×#124—64no—
132C2×#124—68no—
133C22×C4⋊C4C2×D311yescharacteristic
134C22×C4⋊C4C2×D312yes—
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×C42—31no—
145C22×C42—32no—
146#395—24no—
147#394—64no—
148#393—64no—
149#392—64no—
150#390—68no—
151#388—64no—
152C2×#95—31no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—31no—
156C2×#95—31no—
157C2×#95C2×D312yes—
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—21no—
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—21no—
182C23×D3—22no—
183C23×D3—21no—
184C23×D3C2×D414yes—
185C23×D3#4112yes—
186C2×C3×Q8—28no—
187C2×C3×Q8—48no—
188C2×C3×Q8—48no—
189C2×C3×Q8—44no—
190C2×C3×Q8—44no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—22no—
214C22×C3×C4C2×D414yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D414yes—
218C22×C3×C4C2×D412yes—
219C22×C3×C4#4112yes—
220C22×C3×C4#4114yes—
221C22×C3×C4#4114yes—
222C22×Dic3—22no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—21no—
231C22×Dic3—22no—
232C22×Dic3—21no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3C2×D414yes—
241C22×Dic3C2×D412yes—
242C22×Dic3C2×D412yes—
243C22×Dic3C2×D414yes—
244C2×D12—28no—
245C2×D12—216no—
246C2×D12—48no—
247C2×D12—48no—
248C2×D12—48no—
249C2×D12—48no—
250C2×D12—48no—
251C2×D12—48no—
252C2×D12—44no—
253C2×D12—48no—
254C2×D12—48no—
255C2×D12—44no—
256C3×C4⋊C4—48no—
257C3×C4⋊C4—44no—
258(C2×D3)⋊C4—28no—
259(C2×D3)⋊C4—216no—
260(C2×D3)⋊C4—216no—
261(C2×D3)⋊C4—48no—
262(C2×D3)⋊C4—48no—
263(C2×D3)⋊C4—48no—
264(C2×D3)⋊C4—48no—
265(C2×D3)⋊C4—44no—
266(C2×D3)⋊C4—44no—
267C4×Dic3—28no—
268C4×Dic3—48no—
269C25—32no—
270C25—31no—
271C22×Q8—24no—
272C22×Q8—22no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—42no—
276C22×D4—64no—
277C22×D4—64no—
278C22×D4—64no—
279C22×D4—62no—
280C22×D4—62no—
281C22×D4—64no—
282C22×D4—64no—
283C22×D4—62no—
284C22×D4—64no—
285C22×D4—122no—
286C22×D4—122no—
287C22×D4—122no—
288C23×C4—31no—
289C23×C4—32no—
290C23×C4—31no—
291C23×C4—31no—
292C23×C4C22×D311yescharacteristic
293C23×C4C22×D312yes—
294C23×C4C22×D311yescharacteristic
295C23×C4C22×D311yescharacteristic
296C23×C4C22×D312yes—
297#124—632no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—42no—
304C2×C22⋊C4—38no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—62no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—62no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—62no—
313C2×C22⋊C4—62no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—122no—
328C2×C22⋊C4—122no—
329C2×C22⋊C4—122no—
330C2×C42—34no—
331C2×C42—64no—
332C2×C42—64no—
333C2×C42—64no—
334C2×C42—122no—
335#95—24no—
336#95—34no—
337#95—62no—
338#95—62no—
339#95—64no—
340#95—64no—
341#95#6714yes—
342C23×C3C22×D411yescharacteristic
343C23×C3C22×D412yes—
344C23×C3C22×D411yescharacteristic
345C23×C3C22×D411yescharacteristic
346C23×C3C2×#4112yes—
347C23×C3C2×#4111yescharacteristic
348C23×C3C2×#4112yes—
349C23×C3C2×#4111yescharacteristic
350C23×C3H(5,𝔽2)12yes—
351C23×C3H(5,𝔽2)11yescharacteristic
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—
411C3×Q8—416no—
412C2×C3×C4—22no—
413C2×C3×C4—24no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
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—22no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—41no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—41no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4#12418yescomplemented
442C2×C3×C4#12714yes—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—24no—
446C2×Dic3—24no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—42no—
464C2×Dic3#12014yes—
465D12—416no—
466D12—432no—
467C24—34no—
468C24—32no—
469C24—61no—
470C24—61no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—62no—
477C24—62no—
478C24—62no—
479C24—62no—
480C24—62no—
481C24—61no—
482C24—62no—
483C24—62no—
484C24—62no—
485C24—62no—
486C24—61no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—61no—
491C24—62no—
492C24—61no—
493C24C23×D311yescharacteristic
494C2×Q8—28no—
495C2×Q8—48no—
496C2×Q8—48no—
497C2×Q8—44no—
498C2×Q8—44no—
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—128no—
508C2×D4—124no—
509C2×D4—124no—
510C2×D4—128no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—32no—
535C22×C4—34no—
536C22×C4—34no—
537C22×C4—32no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—61no—
548C22×C4—62no—
549C22×C4—61no—
550C22×C4—62no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—61no—
556C22×C4D3×D414yes—
557C22×C4D3×D412yes—
558C22×C4D3×D412yes—
559C22×C4#23912yes—
560C22×C4#23914yes—
561C22×C4#23914yes—
562C22×C4C2×#6712yes—
563C22×C4C2×#6714yes—
564C4⋊C4—48no—
565C4⋊C4—44no—
566C22⋊C4—616no—
567C22⋊C4—616no—
568C22⋊C4—68no—
569C22⋊C4—128no—
570C22⋊C4—128no—
571C22⋊C4—124no—
572C22⋊C4—128no—
573C22⋊C4—124no—
574C22⋊C4—128no—
575C42—68no—
576C42—128no—
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#54611yescharacteristic
593C22×C3#54612yes—
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—28no—
628C3×C4—44no—
629C3×C4—42no—
630C3×C4—81no—
631Dic3—24no—
632Dic3—42no—
633Dic3—44no—
634Dic3—81no—
635C23—62no—
636C23—64no—
637C23—64no—
638C23—64no—
639C23—64no—
640C23—62no—
641C23—64no—
642C23—64no—
643C23—62no—
644C23—64no—
645C23—64no—
646C23—64no—
647C23—122no—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—121no—
654C23—122no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23—121no—
661C23—122no—
662C23—122no—
663C23—122no—
664C23—122no—
665C23—122no—
666C23—122no—
667C23—122no—
668C23—122no—
669C23—122no—
670C23—122no—
671C23—122no—
672C23—121no—
673C23—122no—
674C23—122no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—121no—
679C23—122no—
680C23—121no—
681C23—122no—
682C23—122no—
683C23—122no—
684C23—121no—
685C23—122no—
686C23—122no—
687C23—121no—
688C23—122no—
689C23—122no—
690C23—122no—
691C23—121no—
692C23—122no—
693C23C2×D3×D411yescharacteristic
694C23C2×D3×D411yescharacteristic
695C23C2×D3×D412yes—
696C23#100412yes—
697C23C2×#23912yes—
698C23C2×#23912yes—
699C23C2×#23911yescharacteristic
700C23#100711yescharacteristic
701C23D3×#4111yescharacteristic
702C23#100911yescharacteristic
703C23C22×#6711yescharacteristic
704Q8—416no—
705D4—1232no—
706D4—1216no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—34no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—62no—
738C2×C4—64no—
739C2×C4—62no—
740C2×C4—64no—
741C2×C4—62no—
742C2×C4—64no—
743C2×C4—62no—
744C2×C4—64no—
745C2×C4—62no—
746C2×C4—64no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—121no—
754C2×C4—122no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—122no—
758C2×C4#94014yes—
759C2×C4#94718yescomplemented
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—122no—
783C22—124no—
784C22—124no—
785C22—241no—
786C22—242no—
787C22—242no—
788C22—242no—
789C22—242no—
790C22—242no—
791C22—242no—
792C22—242no—
793C22—242no—
794C22—242no—
795C22—241no—
796C22—242no—
797C22—241no—
798C22—241no—
799C22D3×#12011yescharacteristic
800C22#559012yes—
801C22#559211yescharacteristic
802C22#562712yes—
803C22#562711yescharacteristic
804C22#562911yescharacteristic
805C22#563012yes—
806C22#563011yescharacteristic
807C22#563311yescharacteristic
808C22#563712yes—
809C22#564412yes—
810C22#572511yescharacteristic
811C22#572512yes—
812C22#572511yescharacteristic
813C22#572512yes—
814C22#572612yes—
815C22#573312yes—
816C22#573412yes—
817C22D4×#6712yes—
818C22C2×#94011yescharacteristic
819C22C2×#94712yes—
820C22#581711yescharacteristic
821C22#582911yescharacteristic
822C4—28no—
823C4—24no—
824C4—42no—
825C4—44no—
826C4—64no—
827C4—81no—
828C4—122no—
829C4—124no—
830C4—241no—
831C3#1492811yescharacteristic, complemented, Sylow
832C2—244no—
833C2—242no—
834C2#7716911yescharacteristic
835C2#7717612yes—
836C2#7718712yes—
837C2#7719911yescharacteristic
838C2#7720911yescharacteristic
839C2#7725011yescharacteristic
840C2#8258811yescharacteristic
841C2#8276912yes—
842C2#8277911yescharacteristic
843C2#8325111yescharacteristic
844C2#8325712yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#395C2
prime radicalC2×#4671C2
hypercenterC2×#395D3
hypocenterC3#14928
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#947C2semidirect
2. C2×C3×#395C2semidirect
3. C2×#5231C2semidirect
4. C2×#4991C2semidirect
5. C2×#4988C2semidirect
6. C2×#4990C2semidirect
8. #71570C2semidirect
9. #69426C2semidirect
10. #69408C2semidirect
11. Dic3×#95C2semidirect
45. C2×#395D3semidirect
115. C2×(C2×D3)⋊C4D4semidirect
120. C2×C4×Dic3D4semidirect
127. C3⋊#95D4semidirect
441. C2×C3×C4#124semidirect
759. C2×C4#947semidirect
831. C3#14928semidirect

Maximal subgroups

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

subgroupindex
C22×#9472
C2×C3×#3952
C2×#52312
C2×#49912
C2×#49882
C2×#49902
C2×#46712
#715702
#694262
#694082
Dic3×#952
#149283