Finite Group Databasebeta

← #10728746

Subgroups — #10728746

Order 768.

2470 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#872C211yesmaximal, characteristic, complemented
2C2×#4939C211yesmaximal, characteristic, complemented
3C2×#4671C211yesmaximal, characteristic
4C2×#4665C212yesmaximal, complemented
5C2×#4672C211yesmaximal, characteristic, complemented
6C3×#1434C211yesmaximal, characteristic, complemented
7#69428C212yesmaximal, complemented
8#69427C211yesmaximal, characteristic, complemented
9#69426C212yesmaximal, complemented
10#69410C211yesmaximal, characteristic, complemented
11#69408C212yesmaximal, complemented
12#14886—31nomaximal, Sylow
13C23×D12C2212yes—
14C23×D12C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×C42C2211yescharacteristic
17C22×(C2×D3)⋊C4C2212yes—
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×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C2×#872—24no—
30C2×#872—24no—
31C2×#872—24no—
32C2×C3×#95C2212yes—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2212yes—
35C2×C3×#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4939—24no—
40#4672—24no—
41#4671—24no—
42#4665—28no—
43C22×#117—31no—
44C2×#394—31no—
45C2×#392—31no—
46C2×#390—31no—
47C2×#386—32no—
48#1441—31no—
49#1439—31no—
50#1439—32no—
51#1438—32no—
52#1437—32no—
53#1434D311yescharacteristic, complemented
54C24×D3C2312yes—
55C24×D3C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2312yes—
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C23×Dic3C2312yes—
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2311yescharacteristic
65C22×D12—24no—
66C22×D12—24no—
67C22×D12—24no—
68C22×D12—22no—
69C22×D12—24no—
70C22×D12—24no—
71C22×D12—24no—
72C22×D12—22no—
73C22×D12—22no—
74C22×D12—42no—
75C22×D12—42no—
76C22×D12—42no—
77C22×C4×D3—22no—
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3D414yescomplemented
84C2×C3×C42—22no—
85C2×C3×C42—22no—
86C2×C3×C42D414yescomplemented
87C2×(C2×D3)⋊C4—22no—
88C2×(C2×D3)⋊C4—22no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
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—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
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)⋊C4—42no—
110C2×(C2×D3)⋊C4D414yes—
111C2×C4⋊Dic3—22no—
112C2×C4⋊Dic3—42no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4D414yescomplemented
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3—22no—
122#872—232no—
123C3×#95—24no—
124C3×#95—22no—
125C3×#95—22no—
126C3×#95—24no—
127C3⋊#95—24no—
128C3⋊#95—42no—
129C3⋊#95—42no—
130C23×D4—31no—
131C23×D4—32no—
132C24×C4—31no—
133C2×#117—64no—
134C2×#117—64no—
135C2×#117—64no—
136C22×C4⋊C4—31no—
137C22×C4⋊C4—31no—
138C22×C4⋊C4—31no—
139C22×C22⋊C4—31no—
140C22×C22⋊C4—32no—
141C22×C22⋊C4—31no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C42—31no—
148C22×C42C2×D311yescharacteristic
149#394—64no—
150#392—64no—
151#390—64no—
152#386—68no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95C2×D311yescharacteristic
157C2×#95C2×D311yescharacteristic
158C2×#95C2×D312yes—
159C2×#95C2×D312yes—
160C24×C3C2411yescharacteristic
161C23×D3—21no—
162C23×D3—21no—
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×D3C2×D412yes—
184C23×D3C2×D412yes—
185C23×D3#4114yes—
186C23×D3#4112yes—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
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×D412yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4#4114yes—
217C22×C3×C4#4112yes—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3C2×D412yes—
238C22×Dic3C2×D412yes—
239C22×Dic3C2×D412yes—
240C22×Dic3C2×D412yes—
241C22×Dic3#4112yes—
242C2×D12—28no—
243C2×D12—216no—
244C2×D12—48no—
245C2×D12—48no—
246C2×D12—48no—
247C2×D12—48no—
248C2×D12—44no—
249C2×D12—48no—
250C2×D12—48no—
251C2×D12—48no—
252C2×D12—48no—
253C2×D12—44no—
254C2×C4×D3—28no—
255C2×C4×D3—28no—
256C2×C4×D3—28no—
257C2×C4×D3—28no—
258C2×C4×D3—28no—
259C2×C4×D3—28no—
260C2×C4×D3—28no—
261C3×C42—28no—
262(C2×D3)⋊C4—28no—
263(C2×D3)⋊C4—28no—
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—
269(C2×D3)⋊C4—48no—
270C4⋊Dic3—44no—
271Dic3⋊C4—28no—
272Dic3⋊C4—28no—
273C4×Dic3—28no—
274C25—31no—
275C25—32no—
276C22×D4—64no—
277C22×D4—64no—
278C22×D4—64no—
279C22×D4—64no—
280C22×D4—64no—
281C22×D4—62no—
282C22×D4—64no—
283C22×D4—62no—
284C22×D4—62no—
285C22×D4—122no—
286C22×D4—122no—
287C22×D4—122no—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—34no—
292C23×C4—32no—
293C23×C4—62no—
294C23×C4—62no—
295C23×C4—62no—
296C23×C4—62no—
297C23×C4—62no—
298C23×C4—62no—
299C23×C4C22×D312yes—
300C23×C4C22×D311yescharacteristic
301C23×C4C22×D312yes—
302C23×C4C22×D311yescharacteristic
303C23×C4C22×D311yescharacteristic
304#117—632no—
305C2×C4⋊C4—34no—
306C2×C4⋊C4—62no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—62no—
309C2×C4⋊C4—62no—
310C2×C4⋊C4—62no—
311C2×C4⋊C4—62no—
312C2×C4⋊C4—122no—
313C2×C22⋊C4—34no—
314C2×C22⋊C4—62no—
315C2×C22⋊C4—62no—
316C2×C22⋊C4—62no—
317C2×C22⋊C4—62no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
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—122no—
332C2×C22⋊C4—122no—
333C2×C22⋊C4—122no—
334C2×C22⋊C4—122no—
335C2×C22⋊C4—122no—
336C2×C22⋊C4—122no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—62no—
340C2×C42—62no—
341C2×C42—62no—
342C2×C42D1214yescomplemented
343#95—24no—
344#95—24no—
345#95—22no—
346#95—22no—
347#95—64no—
348#95—122no—
349#95—122no—
350C23×C3C22×D411yescharacteristic
351C23×C3C22×D411yescharacteristic
352C23×C3C22×D411yescharacteristic
353C23×C3C22×D411yescharacteristic
354C23×C3C2×#4112yes—
355C23×C3C2×#4111yescharacteristic
356C23×C3C2×#4111yescharacteristic
357C23×C3C2×#4111yescharacteristic
358C23×C3C2×#4112yes—
359C23×C3H(5,𝔽2)12yes—
360C23×C3H(5,𝔽2)12yes—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—24no—
368C22×D3—24no—
369C22×D3—24no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—24no—
375C22×D3—24no—
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—41no—
381C22×D3—42no—
382C22×D3—41no—
383C22×D3—41no—
384C22×D3—41no—
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—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C22×D3#12114yes—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—22no—
430C2×C3×C4—24no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
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—42no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4#12014yes—
449C2×C3×C4#12114yes—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—24no—
459C2×Dic3—24no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3#12114yes—
474D12—416no—
475D12—432no—
476C4×D3—232no—
477C24—32no—
478C24—32no—
479C24—32no—
480C24—34no—
481C24—61no—
482C24—62no—
483C24—61no—
484C24—61no—
485C24—61no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24—62no—
496C24—62no—
497C24—62no—
498C24—62no—
499C24—62no—
500C24—62no—
501C24—62no—
502C24—62no—
503C24C23×D311yescharacteristic
504C2×D4—68no—
505C2×D4—616no—
506C2×D4—128no—
507C2×D4—128no—
508C2×D4—128no—
509C2×D4—128no—
510C2×D4—124no—
511C2×D4—128no—
512C2×D4—128no—
513C2×D4—128no—
514C2×D4—128no—
515C2×D4—124no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—32no—
540C22×C4—32no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—32no—
544C22×C4—68no—
545C22×C4—68no—
546C22×C4—68no—
547C22×C4—68no—
548C22×C4—68no—
549C22×C4—68no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—68no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—62no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4C2×D1212yes—
571C22×C4C2×D1212yes—
572C22×C4C2×D1212yes—
573C22×C4#23514yes—
574C22×C4D3×D412yes—
575C22×C4D3×D412yes—
576C22×C4D3×D412yes—
577C22×C4#23912yes—
578C4⋊C4—68no—
579C4⋊C4—68no—
580C4⋊C4—124no—
581C22⋊C4—68no—
582C22⋊C4—68no—
583C22⋊C4—128no—
584C22⋊C4—128no—
585C22⋊C4—128no—
586C22⋊C4—128no—
587C22⋊C4—128no—
588C22⋊C4—128no—
589C42—28no—
590C42—68no—
591C22×C3C2×#12011yescharacteristic
592C22×C3C2×#12111yescharacteristic
593C22×C3C2×#12111yescharacteristic
594C22×C3C2×#12111yescharacteristic
595C22×C3#52511yescharacteristic
596C22×C3#52511yescharacteristic
597C22×C3#52512yes—
598C22×C3#52511yescharacteristic
599C22×C3#52511yescharacteristic
600C22×C3#52912yes—
601C22×C3#53211yescharacteristic
602C22×C3#53512yes—
603C22×C3#53511yescharacteristic
604C22×C3#53511yescharacteristic
605C22×C3#54012yes—
606C22×C3#54612yes—
607C22×C3#54612yes—
608C22×C3#54612yes—
609C22×C3#55012yes—
610C22×C3#55112yes—
611C22×C3#55112yes—
612C22×C3#55312yes—
613C22×C3#55512yes—
614C2×D3—24no—
615C2×D3—28no—
616C2×D3—42no—
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—44no—
622C2×D3—42no—
623C2×D3—44no—
624C2×D3—44no—
625C2×D3—44no—
626C2×D3—44no—
627C2×D3—44no—
628C2×D3—44no—
629C2×D3—44no—
630C2×D3—44no—
631C2×D3—44no—
632C2×D3—82no—
633C2×D3—82no—
634C2×D3—82no—
635C2×D3—82no—
636C2×D3—82no—
637C2×D3—82no—
638C2×D3—82no—
639C2×D3—82no—
640C3×C4—24no—
641C3×C4—24no—
642C3×C4—44no—
643C3×C4—42no—
644C3×C4—82no—
645Dic3—24no—
646Dic3—42no—
647Dic3—42no—
648Dic3—82no—
649C23—34no—
650C23—64no—
651C23—64no—
652C23—64no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—64no—
657C23—64no—
658C23—64no—
659C23—62no—
660C23—62no—
661C23—62no—
662C23—64no—
663C23—64no—
664C23—64no—
665C23—64no—
666C23—64no—
667C23—64no—
668C23—64no—
669C23—122no—
670C23—122no—
671C23—122no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—122no—
683C23—122no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23—122no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23—122no—
704C23—122no—
705C23—122no—
706C23—122no—
707C23C22×D1211yescharacteristic
708C23C2×#23512yes—
709C23C2×D3×D411yescharacteristic
710C23C2×D3×D411yescharacteristic
711C23C2×D3×D411yescharacteristic
712C23C2×#23911yescharacteristic
713C23D3×#4112yes—
714C23D3×#4111yescharacteristic
715C23D3×#4111yescharacteristic
716C23#100912yes—
717C23#100912yes—
718D4—1216no—
719D4—1232no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—34no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—632no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—64no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—64no—
761C2×C4—122no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—122no—
773C2×C4—122no—
774C2×C4#88214yes—
775C2×C4#89514yes—
776C2×C3#239211yescharacteristic
777C2×C3#240411yescharacteristic
778C2×C3#241112yes—
779C2×C3#241412yes—
780C2×C3#243111yescharacteristic
781C2×C3#247112yes—
782C2×C3#247612yes—
783C2×C3#259811yescharacteristic
784C2×C3#261011yescharacteristic
785C2×C3#261911yescharacteristic
786C2×C3#284711yescharacteristic
787D3—44no—
788D3—84no—
789C22—64no—
790C22—68no—
791C22—122no—
792C22—124no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—122no—
797C22—122no—
798C22—124no—
799C22—124no—
800C22—124no—
801C22—124no—
802C22—124no—
803C22—124no—
804C22—124no—
805C22—124no—
806C22—124no—
807C22—242no—
808C22—242no—
809C22—242no—
810C22—242no—
811C22—242no—
812C22—242no—
813C22—242no—
814C22—242no—
815C22#547711yescharacteristic
816C22C2×#88211yescharacteristic
817C22C2×#89511yescharacteristic
818C22#552411yescharacteristic
819C22#552411yescharacteristic
820C22#552511yescharacteristic
821C22#552511yescharacteristic
822C22#552712yes—
823C22#553212yes—
824C22#554712yes—
825C22#555012yes—
826C22#555312yes—
827C22#558012yes—
828C22D3×#12111yescharacteristic
829C22D3×#12111yescharacteristic
830C22#562711yescharacteristic
831C22#562711yescharacteristic
832C22#565412yes—
833C22#565412yes—
834C22#567412yes—
835C22#569712yes—
836C22#570512yes—
837C22#570912yes—
838C4—24no—
839C4—24no—
840C4—44no—
841C4—42no—
842C4—64no—
843C4—82no—
844C4—122no—
845C4—122no—
846C4—242no—
847C3#1488611yescharacteristic, complemented, Sylow
848C2—124no—
849C2—244no—
850C2#7342611yescharacteristic
851C2#7358611yescharacteristic
852C2#7377611yescharacteristic
853C2#7404811yescharacteristic
854C2#7412511yescharacteristic
855C2#7424411yescharacteristic
856C2#7430711yescharacteristic
857C2#7500712yes—
858C2#7501412yes—
859C2#7549512yes—
860C2#7584212yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1434C2
prime radicalC2×#4671C2
hypercenter#1434D3
hypocenterC3#14886
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C22×#872C2semidirect
2. C2×#4939C2semidirect
4. C2×#4665C2semidirect
5. C2×#4672C2semidirect
6. C3×#1434C2semidirect
7. #69428C2semidirect
8. #69427C2semidirect
9. #69426C2semidirect
10. #69410C2semidirect
11. #69408C2semidirect
53. #1434D3semidirect
83. C22×C4×D3D4semidirect
86. C2×C3×C42D4semidirect
118. C2×Dic3⋊C4D4semidirect
342. C2×C42D12semidirect
847. C3#14886semidirect

Maximal subgroups

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

subgroupindex
C22×#8722
C2×#49392
C2×#46712
C2×#46652
C2×#46722
C3×#14342
#694282
#694272
#694262
#694102
#694082
#148863