Finite Group Databasebeta

← #25033312

Subgroups — #25033312

Order 11008.

2214 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063323C211yesmaximal, characteristic, complemented
2C2×#14582812C211yesmaximal, characteristic, complemented
3C2×#14582811C211yesmaximal, characteristic, complemented
4C2×#14582810C211yesmaximal, characteristic, complemented
5C2×#14582799C211yesmaximal, characteristic
6C2×#14582799C212yesmaximal
7#19132839C212yesmaximal, complemented
8#19132838C212yesmaximal, complemented
9Dic43⋊#95C212yesmaximal, complemented
10#95×Dic43C211yesmaximal, characteristic, complemented
11C2×C43×#393C211yesmaximal, characteristic, complemented
12C23×Dic86C2211yescharacteristic
13C23×C22⋊D43C2211yescharacteristic
14C2×#13063323—28no—
15C2×#13063323—24no—
16C22×Dic43⋊C4C2211yescharacteristic
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2212yes—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2212yes—
24C22×(C2×D43)⋊C4C2212yes—
25C22×C4×Dic43C2212yes—
26C22×C4×Dic43C2211yescharacteristic
27#14582812—24no—
28#14582811—24no—
29#14582810—24no—
30#14582799—28no—
31#14582799—24no—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C2×C43⋊#95C2211yescharacteristic
37C23×Q8×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2212yes—
40C43×#393—24no—
41C2×#95×C43C2212yes—
42C2×#95×C43C2211yescharacteristic
43C24×D43C2311yescharacteristic
44C22×Dic86—22no—
45C22×Dic86—24no—
46C22×Dic86—22no—
47C22×Dic86—22no—
48C22×Dic86—42no—
49C22×C22⋊D43—24no—
50C22×C22⋊D43—22no—
51C22×C22⋊D43—22no—
52C22×C22⋊D43—24no—
53C22×C22⋊D43Q814yescomplemented
54C23×Dic43C2311yescharacteristic
55C23×Dic43C2312yes—
56C23×Dic43C2312yes—
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59#13063323—232no—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—24no—
64C2×Dic43⋊C4—24no—
65C2×Dic43⋊C4—22no—
66C2×Dic43⋊C4—24no—
67C2×Dic43⋊C4D418yes—
68C2×C22⋊Dic43—24no—
69C2×C22⋊Dic43—22no—
70C2×C22⋊Dic43—24no—
71C2×C22⋊Dic43—24no—
72C2×C22⋊Dic43—42no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—22no—
75C2×(C2×D43)⋊C4—22no—
76C2×(C2×D43)⋊C4—24no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—24no—
81C2×(C2×D43)⋊C4—24no—
82C2×(C2×D43)⋊C4—42no—
83C2×(C2×D43)⋊C4—42no—
84C2×C4×Dic43—24no—
85C2×C4×Dic43—24no—
86C2×C4×Dic43—24no—
87C2×C4×Dic43—24no—
88C2×C4×Dic43D414yes—
89C43⋊#95—24no—
90C43⋊#95—24no—
91C43⋊#95—24no—
92C43⋊#95—24no—
93C43⋊#95D414yescomplemented
94C25×C43C2311yescharacteristic
95C22×Q8×C43—24no—
96C22×Q8×C43—22no—
97C22×Q8×C43—22no—
98C22×Q8×C43—22no—
99C22×Q8×C43—42no—
100C23×C4×C43C2311yescharacteristic
101C23×C4×C43C2312yes—
102C23×C4×C43C2312yes—
103C23×C4×C43C2311yescharacteristic
104C2×C22⋊C4×C43—24no—
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—24no—
108C2×C22⋊C4×C43—22no—
109C2×C22⋊C4×C43—42no—
110#95×C43—24no—
111#95×C43D414yescomplemented
112C24×C43—21no—
113C24×C43—21no—
114C24×C43—21no—
115C24×C43—22no—
116C24×C43—22no—
117C24×C43—22no—
118C24×C43—21no—
119C24×C43—22no—
120C24×C43—21no—
121C24×C43—21no—
122C24×C43C2×Q812yes—
123C24×C43C2411yescharacteristic
124C23×D43—21no—
125C23×D43—21no—
126C23×D43—21no—
127C23×D43—22no—
128C23×D43—22no—
129C23×D43—22no—
130C23×D43—21no—
131C23×D43—22no—
132C23×D43—21no—
133C23×D43—21no—
134C23×D43C2×Q812yes—
135C2×Q8×C43—28no—
136C2×Q8×C43—48no—
137C2×Q8×C43—48no—
138C2×Q8×C43—44no—
139C2×Q8×C43—44no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43C2×D414yes—
160C22×C4×C43C2×D412yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D414yes—
163C22×C4×C43C2×D412yes—
164C2×C22⋊D43—28no—
165C2×C22⋊D43—216no—
166C2×C22⋊D43—44no—
167C2×C22⋊D43—48no—
168C2×C22⋊D43—44no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—22no—
189C22×Dic43C2×D414yes—
190C22×Dic43C2×D414yes—
191C22×Dic43C2×D412yes—
192C22×Dic43C2×D414yes—
193C22×Dic43C2×D412yes—
194C22×Dic43C2×Q812yes—
195C22×Dic43#4114yes—
196C22×Dic43#4112yes—
197C22×Dic43#4114yes—
198C2×Dic86—28no—
199C2×Dic86—48no—
200C2×Dic86—48no—
201C2×Dic86—44no—
202C2×Dic86—44no—
203C22⋊C4×C43—48no—
204C22⋊C4×C43—44no—
205C22⋊Dic43—48no—
206C22⋊Dic43—44no—
207(C2×D43)⋊C4—48no—
208(C2×D43)⋊C4—48no—
209(C2×D43)⋊C4—44no—
210(C2×D43)⋊C4—44no—
211Dic43⋊C4—216no—
212Dic43⋊C4—216no—
213Dic43⋊C4—44no—
214C4×Dic43—28no—
215C4×Dic43—48no—
216C23×C43—22no—
217C23×C43—24no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—24no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—42no—
225C23×C43—41no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—42no—
237C23×C43—42no—
238C23×C43—42no—
239C23×C43C22×D411yescharacteristic
240C23×C43C22×D412yes—
241C23×C43C22×D411yescharacteristic
242C23×C43C22×D411yescharacteristic
243C23×C43C22×Q811yescharacteristic
244C23×C43C2×#4112yes—
245C23×C43C2×#4111yescharacteristic
246C23×C43C2×#4112yes—
247C23×C43H(5,𝔽2)12yes—
248C23×C432−1+411yescharacteristic
249C23×C432−1+411yescharacteristic
250C22×D43—22no—
251C22×D43—24no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—24no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—42no—
259C22×D43—41no—
260C22×D43—42no—
261C22×D43—42no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—42no—
265C22×D43—42no—
266C22×D43—42no—
267C22×D43—42no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43—42no—
273Q8×C43—416no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—24no—
277C2×C4×C43—24no—
278C2×C4×C43—24no—
279C2×C4×C43—24no—
280C2×C4×C43—24no—
281C2×C4×C43—24no—
282C2×C4×C43—24no—
283C2×C4×C43—24no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43#12714yes—
298C22⋊D43—416no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—24no—
305C2×Dic43—24no—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43#12014yes—
323C2×Dic43C22⋊Q814yes—
324C2×Dic43C22⋊Q818yes—
325C2×Dic43#12414yes—
326C2×Dic43#12418yes—
327C2×Dic43#12414yes—
328Dic86—416no—
329#15144—431nomaximal, Sylow
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—44no—
333C22×C43—44no—
334C22×C43—42no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—82no—
340C22×C43—82no—
341C22×C43C2×#12011yescharacteristic
342C22×C43C2×C22⋊Q811yescharacteristic
343C22×C43C2×C22⋊Q812yes—
344C22×C43C2×#12411yescharacteristic
345C22×C43C2×#12411yescharacteristic
346C22×C43C2×#12412yes—
347C22×C43C2×#12711yescharacteristic
348C22×C43#53212yes—
349C22×C43#53212yes—
350C22×C43#53511yescharacteristic
351C22×C43#53611yescharacteristic
352C22×C43#54212yes—
353C22×C43#54212yes—
354C22×C43D4212yes—
355C22×C43D4212yes—
356C22×C43#54711yescharacteristic
357C22×C43#54711yescharacteristic
358C22×C43#54812yes—
359C22×C43#54812yes—
360C22×C43D4×Q811yescharacteristic
361C22×C43D4×Q811yescharacteristic
362C22×C43#55412yes—
363C22×C43#55512yes—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—44no—
367C2×D43—44no—
368C2×D43—42no—
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43—81no—
373C2×D43—82no—
374C2×D43—82no—
375C4×C43—24no—
376C4×C43—44no—
377C4×C43—44no—
378C4×C43—81no—
379Dic43—24no—
380Dic43—44no—
381Dic43—44no—
382Dic43—81no—
383Dic43#39318yescomplemented
384C22×C4⋊Q8—431no—
385C2×#393—431no—
386C2×#393—431no—
387C2×#393—431no—
388C2×#393D4311yescharacteristic, complemented
389C2×#390—431no—
390C2×#390—432no—
391#1439—432no—
392#1439—432no—
393C4⋊#95—432no—
394C4×#95—431no—
395C2×C43—82no—
396C2×C43C2×#39311yescharacteristic
397C2×C43#243311yescharacteristic
398C2×C43#243611yescharacteristic
399C2×C43#245212yes—
400C2×C43#245212yes—
401C2×C43#249112yes—
402C2×C43#249112yes—
403C2×C43#254211yescharacteristic
404C2×C43#256311yescharacteristic
405C2×C43#264011yescharacteristic
406C2×C43#285811yescharacteristic
407D43—82no—
408C23×Q8—431no—
409C23×Q8C2×D4311yescharacteristic
410C23×D4—431no—
411C2×C4⋊Q8—864no—
412C2×C4⋊Q8—868no—
413C22×C4⋊C4—432no—
414C22×C4⋊C4—432no—
415C22×C4⋊C4—431no—
416C22×C22⋊C4—431no—
417C22×C22⋊C4—431no—
418C22×C22⋊C4—431no—
419C22×C22⋊C4—432no—
420C22×C22⋊C4—432no—
421C22×C22⋊C4—432no—
422C22×C22⋊C4C2×D4311yescharacteristic
423C22×C22⋊C4C2×D4312yes—
424C22×C42—431no—
425C22×C42—432no—
426#393—24no—
427#393—864no—
428#393—864no—
429#393—864no—
430#390—864no—
431#390—868no—
432C2×#95—431no—
433C2×#95—432no—
434C2×#95—432no—
435C2×#95—432no—
436C2×#95—432no—
437C2×#95C2×D4312yes—
438C2×#95C2×D4311yescharacteristic
439C43#1514411yescharacteristic, complemented, Sylow
440C25—431no—
441C25C22×D4311yescharacteristic
442C22×Q8—24no—
443C22×Q8—22no—
444C22×Q8—22no—
445C22×Q8—22no—
446C22×Q8—42no—
447C22×Q8—864no—
448C22×Q8—862no—
449C22×Q8—862no—
450C22×Q8—862no—
451C22×Q8—1722no—
452C22×D4—434no—
453C22×D4—862no—
454C22×D4—864no—
455C22×D4—862no—
456C22×D4—864no—
457C23×C4—431no—
458C23×C4—431no—
459C23×C4—432no—
460C23×C4—432no—
461C23×C4—431no—
462C23×C4C22×D4311yescharacteristic
463C23×C4C22×D4312yes—
464C23×C4C22×D4312yes—
465C23×C4C22×D4311yescharacteristic
466C4⋊Q8—8632no—
467C2×C4⋊C4—438no—
468C2×C4⋊C4—864no—
469C2×C4⋊C4—864no—
470C2×C4⋊C4—864no—
471C2×C4⋊C4—864no—
472C2×C4⋊C4—864no—
473C2×C4⋊C4—864no—
474C2×C4⋊C4—862no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—864no—
482C2×C22⋊C4—864no—
483C2×C22⋊C4—862no—
484C2×C22⋊C4—864no—
485C2×C22⋊C4—864no—
486C2×C22⋊C4—862no—
487C2×C22⋊C4—864no—
488C2×C22⋊C4—864no—
489C2×C22⋊C4—864no—
490C2×C22⋊C4—862no—
491C2×C22⋊C4—862no—
492C2×C22⋊C4—864no—
493C2×C22⋊C4—862no—
494C2×C22⋊C4—1722no—
495C2×C22⋊C4—1722no—
496C2×C22⋊C4—1722no—
497C2×C42—434no—
498C2×C42—864no—
499C2×C42—864no—
500C2×C42—864no—
501C2×C42—864no—
502#95—24no—
503#95—434no—
504#95—864no—
505#95—864no—
506#95—864no—
507#95—864no—
508#95C22⋊D4314yescomplemented
509C24—21no—
510C24—22no—
511C24—21no—
512C24—21no—
513C24—22no—
514C24—21no—
515C24—22no—
516C24—22no—
517C24—21no—
518C24—21no—
519C24—432no—
520C24—861no—
521C24—862no—
522C24—861no—
523C24—861no—
524C24—862no—
525C24—861no—
526C24—862no—
527C24—862no—
528C24—861no—
529C24—861no—
530C24Q8×D4312yes—
531C24C23×D4311yescharacteristic
532C2×Q8—28no—
533C2×Q8—48no—
534C2×Q8—48no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8—868no—
538C2×Q8—1728no—
539C2×Q8—1728no—
540C2×Q8—1724no—
541C2×Q8—1724no—
542C2×D4—8616no—
543C2×D4—868no—
544C2×D4—1724no—
545C2×D4—1728no—
546C2×D4—1724no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—432no—
567C22×C4—434no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—434no—
571C22×C4—432no—
572C22×C4—434no—
573C22×C4—434no—
574C22×C4—434no—
575C22×C4—862no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4D4×D4314yes—
596C22×C4D4×D4312yes—
597C22×C4D4×D4312yes—
598C22×C4C2×C22⋊D4314yes—
599C22×C4C2×C22⋊D4312yes—
600C4⋊C4—8616no—
601C4⋊C4—8616no—
602C4⋊C4—1724no—
603C22⋊C4—48no—
604C22⋊C4—44no—
605C22⋊C4—1728no—
606C22⋊C4—1728no—
607C22⋊C4—1724no—
608C22⋊C4—1724no—
609C22⋊C4—1728no—
610C22⋊C4—1724no—
611C42—868no—
612C42—1728no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—41no—
629C23—41no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—862no—
637C23—862no—
638C23—864no—
639C23—864no—
640C23—862no—
641C23—1722no—
642C23—1722no—
643C23—1722no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1722no—
648C23—1721no—
649C23—1722no—
650C23—1722no—
651C23—1721no—
652C23—1721no—
653C23—1722no—
654C23—1722no—
655C23—1722no—
656C23—1722no—
657C23—1721no—
658C23—1721no—
659C23C2×D4×D4312yes—
660C23C2×D4×D4311yescharacteristic
661C23C2×D4×D4311yescharacteristic
662C23C22×C22⋊D4311yescharacteristic
663C23C2×Q8×D4311yescharacteristic
664C23#41×D4312yes—
665C23#41×D4311yescharacteristic
666C23#41×D4312yes—
667C23#1306337012yes—
668C23#1306337211yescharacteristic
669C23#1306337311yescharacteristic
670Q8—416no—
671Q8—17216no—
672D4—17216no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—434no—
697C2×C4—438no—
698C2×C4—434no—
699C2×C4—438no—
700C2×C4—434no—
701C2×C4—434no—
702C2×C4—864no—
703C2×C4—864no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—864no—
707C2×C4—864no—
708C2×C4—864no—
709C2×C4—864no—
710C2×C4—864no—
711C2×C4—864no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4#1306332114yes—
726C22—42no—
727C22—44no—
728C22—44no—
729C22—42no—
730C22—42no—
731C22—81no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—3441no—
738C22—3442no—
739C22—3442no—
740C22—3441no—
741C22—3441no—
742C22—3441no—
743C22—1722no—
744C22—1724no—
745C22—1724no—
746C22—1722no—
747C22—1722no—
748C22#120×D4311yescharacteristic
749C22C22⋊Q8×D4312yes—
750C22C22⋊Q8×D4311yescharacteristic
751C22#124×D4311yescharacteristic
752C22#124×D4312yes—
753C22#124×D4311yescharacteristic
754C22C2×#1306332111yescharacteristic
755C22#1458344512yes—
756C22#1458344812yes—
757C22#1458346411yescharacteristic
758C22#1458347211yescharacteristic
759C22#1458351312yes—
760C22#1458351912yes—
761C22#1458353112yes—
762C22D4×C22⋊D4312yes—
763C22#1458354811yescharacteristic
764C22#1458355111yescharacteristic
765C22#1458355712yes—
766C22#1458355912yes—
767C22#1458356211yescharacteristic
768C22Q8×C22⋊D4311yescharacteristic
769C22#1458360312yes—
770C22#1458361112yes—
771C4—24no—
772C4—44no—
773C4—44no—
774C4—81no—
775C4—438no—
776C4—864no—
777C4—3441no—
778C4—1724no—
779C4—1724no—
780C2—82no—
781C2—3442no—
782C2#393×D4311yescharacteristic
783C2#1913823011yescharacteristic
784C2#1913824811yescharacteristic
785C2#1913844012yes—
786C2#1913844412yes—
787C2#1913895312yes—
788C2#1913895512yes—
789C2#1913954511yescharacteristic
790C2#1913976311yescharacteristic
791C2#1914053311yescharacteristic
792C2#1914295011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC2×C43×#393C2
prime radicalC23×C22⋊D43C22
hypercenterC2×#393D43
hypocenterC43#15144
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#13063323C2semidirect
2. C2×#14582812C2semidirect
3. C2×#14582811C2semidirect
4. C2×#14582810C2semidirect
7. #19132839C2semidirect
8. #19132838C2semidirect
9. Dic43⋊#95C2semidirect
10. #95×Dic43C2semidirect
11. C2×C43×#393C2semidirect
53. C22×C22⋊D43Q8semidirect
93. C43⋊#95D4semidirect
111. #95×C43D4semidirect
383. Dic43#393semidirect
388. C2×#393D43semidirect
439. C43#15144semidirect
508. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633232
C2×#145828122
C2×#145828112
C2×#145828102
C2×#145827992
#191328392
#191328382
Dic43⋊#952
#95×Dic432
C2×C43×#3932
#1514443