Finite Group Databasebeta

← #10731738

Subgroups — #10731738

Order 768.

2038 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#888C211yesmaximal, characteristic, complemented
2C2×C3×#380C211yesmaximal, characteristic
3C2×#5212C211yesmaximal, characteristic
4C2×C4×#217C211yesmaximal, characteristic
5C2×#4947C212yesmaximal
6#71563C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71563C211yesmaximal, characteristic, complemented
9#71547C212yesmaximal
10#69424C212yesmaximal, complemented
11#69414C212yesmaximal, complemented
12#15125—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×Dic6C2212yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×#217C2212yes—
19C22×#217C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×Dic3⋊C4C2212yes—
24C22×C4×Dic3C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C2×#888—24no—
27C2×#888—24no—
28C2×#888—24no—
29C3×#380—24no—
30C2×C3×#95C2212yes—
31#5212—24no—
32C4×#217—24no—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42#4947—28no—
43C22×C4⋊Q8—31no—
44C2×#393—32no—
45C2×#380—31no—
46C2×#380D311yescharacteristic
47C2×C4×C22⋊C4—31no—
48#1446—32no—
49#1442—32no—
50#1439—32no—
51C4⋊#95—31no—
52C4⋊#95—31no—
53C4⋊#95—31no—
54C25×C3C2311yescharacteristic
55C23×C3×C4—22no—
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—22no—
61C23×C3×C4Q814yescomplemented
62C23×C3×C4C2312yes—
63C23×C3×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×Dic3C2312yes—
67C23×Dic3C2312yes—
68C23×Dic3C2311yescharacteristic
69C23×Dic3C2311yescharacteristic
70C23×Dic3C2311yescharacteristic
71C23×Dic3C2311yescharacteristic
72C22×Dic6—24no—
73C22×Dic6—24no—
74C22×Dic6—24no—
75C22×Dic6—24no—
76C22×Dic6—24no—
77C22×Dic6—42no—
78C22×Dic6—42no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4D414yes—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—42no—
88C2×#217—22no—
89C2×#217—22no—
90C2×#217—22no—
91C2×#217—22no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—42no—
95C2×#217D414yes—
96C2×#217Q814yescomplemented
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3D414yes—
103C2×Dic3⋊C4—24no—
104C2×Dic3⋊C4—24no—
105C2×Dic3⋊C4—24no—
106C2×C4×Dic3—22no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3D414yes—
112#888—232no—
113C3×#95—24no—
114C3⋊#95—24no—
115C3⋊#95—24no—
116C3⋊#95—24no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—42no—
122C3⋊#95—42no—
123C23×Q8—32no—
124C24×C4C2×D311yescharacteristic
125C2×C4⋊Q8—64no—
126C2×C4⋊Q8—64no—
127C2×C4⋊Q8—64no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4—32no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4C2×D311yescharacteristic
132C22×C4⋊C4C2×D311yescharacteristic
133C22×C22⋊C4—31no—
134C22×C22⋊C4—31no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4C2×D312yes—
137C22×C42—31no—
138C22×C42—31no—
139#393—68no—
140#380—24no—
141#380—64no—
142C4×C22⋊C4—64no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—31no—
148C2×#95—32no—
149C2×#95—31no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95C2×D312yes—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—21no—
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3C2×D412yes—
166C24×C3C2×Q812yes—
167C24×C3C2×Q812yes—
168C24×C3C2411yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—22no—
172C22×C3×C4—21no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—28no—
182C22×C3×C4—28no—
183C22×C3×C4—28no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—44no—
192C22×C3×C4—44no—
193C22×C3×C4—44no—
194C22×C3×C4—44no—
195C22×C3×C4C2×D412yes—
196C22×C3×C4C2×D412yes—
197C22×C3×C4C2×D414yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4C2×Q812yes—
200C22×C3×C4C2×Q812yes—
201C22×C3×C4#4112yes—
202C22×C3×C4#4112yes—
203C22×C3×C4#4112yes—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—21no—
229C22×Dic3—21no—
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×D414yes—
239C22×Dic3C2×D412yes—
240C22×Dic3C2×D412yes—
241C22×Dic3C2×D412yes—
242C22×Dic3C2×Q812yes—
243C22×Dic3C2×Q812yes—
244C22×Dic3#4112yes—
245C22×Dic3#4112yes—
246C2×Dic6—216no—
247C2×Dic6—48no—
248C2×Dic6—48no—
249C2×Dic6—48no—
250C2×Dic6—48no—
251C2×Dic6—48no—
252C2×Dic6—48no—
253C3×C4⋊C4—28no—
254C3×C4⋊C4—44no—
255C3×C22⋊C4—48no—
256#217—28no—
257#217—28no—
258#217—48no—
259C4⋊Dic3—28no—
260C4⋊Dic3—44no—
261Dic3⋊C4—216no—
262C4×Dic3—28no—
263C4×Dic3—44no—
264C25C22×D311yescharacteristic
265C22×Q8—64no—
266C22×Q8—64no—
267C22×Q8—64no—
268C22×Q8—64no—
269C22×Q8—64no—
270C22×Q8—122no—
271C22×Q8—122no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—31no—
279C23×C4—31no—
280C23×C4—32no—
281C23×C4—31no—
282C23×C4—31no—
283C23×C4—32no—
284C23×C4Dic614yescomplemented
285C23×C4C22×D312yes—
286C23×C4C22×D311yescharacteristic
287C23×C4C22×D312yes—
288C23×C4C22×D311yescharacteristic
289C4⋊Q8—632no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—34no—
296C2×C4⋊C4—64no—
297C2×C4⋊C4—64no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—64no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—62no—
302C2×C4⋊C4—62no—
303C2×C4⋊C4—62no—
304C2×C4⋊C4#6714yes—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—34no—
308C2×C22⋊C4—34no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—62no—
311C2×C22⋊C4—62no—
312C2×C22⋊C4—62no—
313C2×C22⋊C4—62no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—122no—
317C2×C42—34no—
318C2×C42—62no—
319C2×C42—62no—
320C2×C42—62no—
321C2×C42—62no—
322C2×C42—62no—
323#95—24no—
324#95—64no—
325#95—62no—
326#95—62no—
327#95—64no—
328#95—64no—
329#95—64no—
330#95—64no—
331#95—122no—
332#95—122no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3C4⋊Q814yescomplemented
368C23×C3C22×D411yescharacteristic
369C23×C3C22×D411yescharacteristic
370C23×C3C22×D411yescharacteristic
371C23×C3C22×D411yescharacteristic
372C23×C3C22×Q811yescharacteristic
373C23×C3C22×Q811yescharacteristic
374C23×C3C2×#4111yescharacteristic
375C23×C3C2×#4111yescharacteristic
376C23×C3C2×#4111yescharacteristic
377C23×C3C2×#4111yescharacteristic
378C23×C3C2×#4111yescharacteristic
379C23×C3H(5,𝔽2)11yescharacteristic
380C23×C3H(5,𝔽2)11yescharacteristic
381C23×C32−1+411yescharacteristic
382C23×C32−1+411yescharacteristic
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—41no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—416no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4#12014yes—
406C2×C3×C4C22⋊Q814yes—
407C2×C3×C4C22⋊Q814yes—
408C2×C3×C4C22⋊Q814yes—
409C2×C3×C4#12414yes—
410C2×C3×C4#12414yes—
411C2×C3×C4#12414yes—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—24no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—24no—
428C2×Dic3—24no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—42no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—42no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3#12114yes—
453C2×Dic3C22⋊Q814yes—
454Dic6—432no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24C2×Dic612yes—
468C24D3×D412yes—
469C24D3×Q812yes—
470C24C23×D311yescharacteristic
471C2×Q8—616no—
472C2×Q8—128no—
473C2×Q8—128no—
474C2×Q8—128no—
475C2×Q8—128no—
476C2×Q8—128no—
477C2×Q8—128no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—32no—
501C22×C4—32no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—32no—
507C22×C4—34no—
508C22×C4—32no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—61no—
536C22×C4—62no—
537C22×C4—61no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4C2×Dic612yes—
547C22×C4C2×Dic612yes—
548C22×C4#23512yes—
549C22×C4D3×D412yes—
550C22×C4D3×D412yes—
551C22×C4#23712yes—
552C22×C4#23712yes—
553C22×C4C2×#6714yes—
554C22×C4C2×#6712yes—
555C4⋊C4—28no—
556C4⋊C4—44no—
557C4⋊C4—616no—
558C4⋊C4—68no—
559C4⋊C4—124no—
560C22⋊C4—48no—
561C22⋊C4—68no—
562C22⋊C4—68no—
563C22⋊C4—128no—
564C42—68no—
565C42—124no—
566C22×C3—24no—
567C22×C3—24no—
568C22×C3—24no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3C2×#12011yescharacteristic
582C22×C3C2×#12111yescharacteristic
583C22×C3C2×C22⋊Q811yescharacteristic
584C22×C3C2×C22⋊Q811yescharacteristic
585C22×C3C2×C22⋊Q811yescharacteristic
586C22×C3C2×C22⋊Q811yescharacteristic
587C22×C3C2×#12411yescharacteristic
588C22×C3C2×#12411yescharacteristic
589C22×C3C2×#12411yescharacteristic
590C22×C3C2×C4⋊Q811yescharacteristic
591C22×C3#53211yescharacteristic
592C22×C3#53311yescharacteristic
593C22×C3#53311yescharacteristic
594C22×C3#53511yescharacteristic
595C22×C3#53611yescharacteristic
596C22×C3#54211yescharacteristic
597C22×C3#54211yescharacteristic
598C22×C3#54411yescharacteristic
599C22×C3#54411yescharacteristic
600C22×C3D4211yescharacteristic
601C22×C3D4211yescharacteristic
602C22×C3#54611yescharacteristic
603C22×C3#54611yescharacteristic
604C22×C3#54711yescharacteristic
605C22×C3#54711yescharacteristic
606C22×C3#54811yescharacteristic
607C22×C3#54811yescharacteristic
608C22×C3D4×Q811yescharacteristic
609C22×C3D4×Q811yescharacteristic
610C22×C3#55411yescharacteristic
611C22×C3#55411yescharacteristic
612C22×C3#55511yescharacteristic
613C22×C3#55511yescharacteristic
614C22×C3#55611yescharacteristic
615C22×C3#55611yescharacteristic
616C3×C4—42no—
617C3×C4—44no—
618C3×C4—82no—
619C3×C4#39318yescomplemented
620Dic3—24no—
621Dic3—24no—
622Dic3—42no—
623Dic3—44no—
624Dic3—42no—
625Dic3—82no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23#88814yescomplemented
661C23C22×Dic611yescharacteristic
662C23C2×#23511yescharacteristic
663C23C2×D3×D411yescharacteristic
664C23C2×D3×D411yescharacteristic
665C23C2×D3×D411yescharacteristic
666C23C2×#23711yescharacteristic
667C23C2×#23711yescharacteristic
668C23#100411yescharacteristic
669C23C2×D3×Q811yescharacteristic
670C23#100711yescharacteristic
671C23D3×#4111yescharacteristic
672C23D3×#4111yescharacteristic
673C23#100911yescharacteristic
674C23#101011yescharacteristic
675C23C22×#6711yescharacteristic
676Q8—1232no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—34no—
684C2×C4—34no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—416no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—64no—
717C2×C4—62no—
718C2×C4—64no—
719C2×C4—62no—
720C2×C4—64no—
721C2×C4—62no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4#87814yes—
742C2×C4#87814yes—
743C2×C4#88514yes—
744C2×C4#88514yes—
745C2×C4#92414yes—
746C2×C4#93614yes—
747C2×C4#93714yes—
748C2×C3—44no—
749C2×C3C2×#39311yescharacteristic
750C2×C3#240811yescharacteristic
751C2×C3#240911yescharacteristic
752C2×C3#243911yescharacteristic
753C2×C3#243911yescharacteristic
754C2×C3#244011yescharacteristic
755C2×C3#244011yescharacteristic
756C2×C3#249111yescharacteristic
757C2×C3#249111yescharacteristic
758C2×C3#249211yescharacteristic
759C2×C3#249211yescharacteristic
760C2×C3#254711yescharacteristic
761C2×C3#256311yescharacteristic
762C2×C3#262811yescharacteristic
763C2×C3#285711yescharacteristic
764C22—24no—
765C22—24no—
766C22—24no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22C2×#87811yescharacteristic
780C22C2×#87811yescharacteristic
781C22C2×#88511yescharacteristic
782C22C2×#88511yescharacteristic
783C22C2×#88811yescharacteristic
784C22#550011yescharacteristic
785C22#550711yescharacteristic
786C22#551111yescharacteristic
787C22#551711yescharacteristic
788C22#551911yescharacteristic
789C22#553211yescharacteristic
790C22#553311yescharacteristic
791C22#559611yescharacteristic
792C22#560311yescharacteristic
793C22D3×#12111yescharacteristic
794C22#560711yescharacteristic
795C22#560911yescharacteristic
796C22#561111yescharacteristic
797C22#561211yescharacteristic
798C22#561611yescharacteristic
799C22#562211yescharacteristic
800C22D3×C22⋊Q811yescharacteristic
801C22#562811yescharacteristic
802C22#563211yescharacteristic
803C22#563311yescharacteristic
804C22#563511yescharacteristic
805C22#564111yescharacteristic
806C22#564311yescharacteristic
807C22C2×#92411yescharacteristic
808C22C2×#93611yescharacteristic
809C22C2×#93711yescharacteristic
810C22D4×#6711yescharacteristic
811C22Q8×#6711yescharacteristic
812C22#582911yescharacteristic
813C22#583111yescharacteristic
814C4—42no—
815C4—44no—
816C4—64no—
817C4—64no—
818C4—82no—
819C4—124no—
820C4—122no—
821C4—122no—
822C4—242no—
823C4#494718yescomplemented
824C3#1512511yescharacteristic, complemented, Sylow
825C2—44no—
826C2#7389811yescharacteristic
827C2#7389911yescharacteristic
828C2#7391511yescharacteristic
829C2#7391611yescharacteristic
830C2#7393711yescharacteristic
831C2#7394211yescharacteristic
832C2#7395411yescharacteristic
833C2#7400111yescharacteristic
834C2C2×#494711yescharacteristic
835C2#8217111yescharacteristic
836C2#8224811yescharacteristic
837C2#8264011yescharacteristic
838C2#8266211yescharacteristic
839C2#8275111yescharacteristic
840C2#8277311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
prime radicalC25×C3C23
hypercenterC2×#380D3
hypocenterC3#15125
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#888C2semidirect
6. #71563C2semidirect
7. #71563C2semidirect
8. #71563C2semidirect
10. #69424C2semidirect
11. #69414C2semidirect
61. C23×C3×C4Q8semidirect
96. C2×#217Q8semidirect
284. C23×C4Dic6semidirect
367. C23×C3C4⋊Q8semidirect
619. C3×C4#393semidirect
660. C23#888semidirect
823. C4#4947semidirect
824. C3#15125semidirect

Maximal subgroups

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

subgroupindex
C22×#8882
C2×C3×#3802
C2×#52122
C2×C4×#2172
C2×#49472
#715632
#715472
#694242
#694142
#151253