Finite Group Databasebeta

← #25098359

Subgroups — #25098359

Order 11008.

1954 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic, complemented
3C2×#14582916C211yesmaximal, characteristic, complemented
4C2×#14582862C211yesmaximal, characteristic, complemented
5#19135040C214yesmaximal, complemented
6#19135035C214yesmaximal, complemented
7#19134306C211yesmaximal, characteristic, complemented
8#19134305C211yesmaximal, characteristic, complemented
9C2×C43×#421C211yesmaximal, characteristic, complemented
10C23×C4×D43C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12#14583406—21no—
13#14583406—21no—
14#14583406—22no—
15#14583406C414yescomplemented
16#14583406C2212yes—
17#14583406C2212yes—
18C2×#13063306—21no—
19C2×#13063301C412yescomplemented
20C2×#13063296C412yescomplemented
21C2×#13063293—21no—
22C2×C4×C22⋊D43—22no—
23C2×#13063284C2211yescharacteristic
24C2×#13063284C2211yescharacteristic
25C2×#13063283—21no—
26C2×#13063282C2212yescomplemented
27C2×#13063281—21no—
28#117×D43—24no—
29#117×D43—24no—
30C2×C4⋊C4×D43—21no—
31C2×C22⋊C4×D43—21no—
32C2×C42×D43C2212yescomplemented
33#14582916—24no—
34C2×#13063252C2214yescomplemented
35#14582862—22no—
36#14582862C2212yescomplemented
37#14582862C2212yescomplemented
38C2×(C2×D43)⋊C8—22no—
39#14582660C2214yescomplemented
40#14582659C2214yescomplemented
41C22×#41×C43C2211yescharacteristic
42C22×M16×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C43×#421—24no—
45C2×#104×C43C2214yescomplemented
46C24×D43D411yescharacteristic
47C22×C22⋊D43—22no—
48C23×Dic43D411yescharacteristic
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43C2×C412yes—
55C22×C4×D43C2×C412yes—
56C22×C4×D43D411yescharacteristic
57C22×C4×D43D411yescharacteristic
58C22×C4×D43D412yes—
59C22×C4×D43D412yes—
60C22×C4×D43C2311yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C2×#10621877—21no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C2×#10621877C2312yes—
66C22×C43⋊C8—21no—
67#13063306—24no—
68#13063306—22no—
69#13063306—22no—
70#13063301—22no—
71#13063301—22no—
72#13063301C2×C414yes—
73#13063301C2×C414yescomplemented
74#13063296—22no—
75#13063296—22no—
76#13063296C2×C414yes—
77#13063296C2×C414yescomplemented
78#13063293—24no—
79#13063293—22no—
80#13063293—22no—
81C4×C22⋊D43—24no—
82C4×C22⋊D43—24no—
83C4×C22⋊D43—24no—
84C4×C22⋊D43—24no—
85#13063284—22no—
86#13063284—21no—
87#13063284—21no—
88#13063284C2×C412yescomplemented
89#13063284D414yescomplemented
90#13063284C2312yes—
91#13063283—28no—
92#13063282—24no—
93#13063282—24no—
94#13063281—28no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2×C412yescomplemented
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C4⋊C4×D43—28no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C22⋊C4×D43—28no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43C2312yes—
109C42×D43—24no—
110C42×D43—24no—
111#13063252—28no—
112(C2×D43)⋊C8—24no—
113(C2×D43)⋊C8—24no—
114C2×#41×C43—21no—
115C2×#41×C43—21no—
116C2×#41×C43—22no—
117C2×#41×C43—22no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43C2×C412yescomplemented
121C2×#41×C43C2312yes—
122C22×Q8×C43C2×C411yescharacteristic, complemented
123C22×D4×C43—21no—
124C22×D4×C43C2×C411yescharacteristic, complemented
125C23×C4×C43—21no—
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43—21no—
128C2×M16×C43—22no—
129C2×M16×C43—22no—
130C2×M16×C43C2312yes—
131C22×C8×C43—21no—
132#117×C43—22no—
133#117×C43D414yescomplemented
134C2×C4⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C42×C43C2312yes—
137#104×C43—28no—
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C23×D43—22no—
141C23×D43—22no—
142C23×D43—44no—
143C23×D43C22⋊C412yes—
144C23×D43C22⋊C412yes—
145C23×D43C2×D411yescharacteristic
146C23×D43C2×D411yescharacteristic
147#41×C43—24no—
148#41×C43—24no—
149#41×C43—22no—
150#41×C43—22no—
151#41×C43—22no—
152#41×C43—22no—
153#41×C43—42no—
154#41×C43—42no—
155#41×C43—42no—
156#41×C43—42no—
157C2×Q8×C43—21no—
158C2×Q8×C43—22no—
159C2×Q8×C43—22no—
160C2×Q8×C43C22×C412yes—
161C2×D4×C43—21no—
162C2×D4×C43—22no—
163C2×D4×C43—22no—
164C2×D4×C43—22no—
165C2×D4×C43—22no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43C22×C412yes—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—21no—
172C22×C4×C43—22no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43C22×C411yescharacteristic
176C22×C4×C43C22×C411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D412yes—
180C22×C4×C43C2×D412yes—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43#4112yes—
183C22×C4×C43#4112yes—
184C22×C4×C43C2411yescharacteristic
185C2×C22⋊D43—24no—
186C2×C22⋊D43—24no—
187C2×C22⋊D43—48no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43C22⋊C412yes—
193C22×Dic43C22⋊C412yes—
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C2×C4×D43—24no—
197C2×C4×D43—24no—
198C2×C4×D43—24no—
199C2×C4×D43—24no—
200C2×C4×D43—22no—
201C2×C4×D43—22no—
202C2×C4×D43—24no—
203C2×C4×D43—24no—
204C2×C4×D43—24no—
205C2×C4×D43—24no—
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—28no—
217C2×C4×D43—48no—
218C2×C4×D43C22⋊C412yes—
219C2×C4×D43C22⋊C412yes—
220C2×C4×D43C22⋊C412yes—
221C2×C4×D43C22⋊C412yes—
222C2×C4×D43C22×C412yes—
223C2×C4×D43C22×C412yes—
224C2×C4×D43C2×D412yes—
225C2×C4×D43C2×D412yes—
226M16×C43—22no—
227M16×C43—22no—
228M16×C43—42no—
229C2×C8×C43—22no—
230C2×C8×C43—42no—
231C4⋊C4×C43—24no—
232C22⋊C4×C43—24no—
233C42×C43—22no—
234C42×C43C2×D414yescomplemented
235C22⋊Dic43—24no—
236C22⋊Dic43—24no—
237C22⋊Dic43—22no—
238C22⋊Dic43—24no—
239C22⋊Dic43—22no—
240(C2×D43)⋊C4—28no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243C4⋊Dic43—22no—
244C4⋊Dic43—24no—
245C4⋊Dic43C22×C414yes—
246Dic43⋊C4—28no—
247Dic43⋊C4—24no—
248Dic43⋊C4—24no—
249C4×Dic43—28no—
250C4×Dic43—22no—
251C4×Dic43—22no—
252C4×Dic43—22no—
253C4×Dic43C2×D414yescomplemented
254#10621877—22no—
255#10621877—22no—
256#10621877—42no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—42no—
259C23×C43—22no—
260C23×C43—42no—
261C23×C43—44no—
262C23×C43—42no—
263C23×C43C2×C22⋊C411yescharacteristic
264C23×C43C2×C22⋊C411yescharacteristic
265C23×C43#12012yes—
266C23×C43#12312yes—
267C23×C43C22×D411yescharacteristic
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—24no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—24no—
274C22×D43—24no—
275C22×D43—24no—
276C22×D43—24no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—48no—
281C22×D43—48no—
282C22×D43C2×C22⋊C412yes—
283C22×D43C2×C22⋊C412yes—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—42no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—42no—
290D4×C43—42no—
291D4×C43—44no—
292D4×C43—42no—
293C2×C4×C43—22no—
294C2×C4×C43—24no—
295C2×C4×C43—44no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—44no—
300C2×C4×C43C2×C22⋊C411yescharacteristic
301C2×C4×C43C2×C22⋊C411yescharacteristic
302C2×C4×C43C4×D412yes—
303C2×C4×C43C4×D412yes—
304C2×C4×C43C4×D412yes—
305C2×C4×C43C4×D412yes—
306C2×C4×C43#12012yes—
307C2×C4×C43#12112yes—
308C2×C4×C43#12112yes—
309C2×C4×C43#12112yes—
310C2×C4×C43#12112yes—
311C2×C4×C43#12312yes—
312C2×C4×C43C23×C411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C22⋊D43—48no—
319C22⋊D43—48no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—24no—
325C2×Dic43—24no—
326C2×Dic43—24no—
327C2×Dic43—24no—
328C2×Dic43—44no—
329C2×Dic43—44no—
330C2×Dic43C2×C22⋊C412yes—
331C2×Dic43C2×C22⋊C412yes—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—24no—
341C4×D43—24no—
342C4×D43—24no—
343C4×D43—24no—
344C4×D43—416no—
345C8×C43—42no—
346C43⋊C8—42no—
347#20979—431nomaximal, Sylow
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—44no—
354C22×C43—42no—
355C22×C43—84no—
356C22×C43#38612yes—
357C22×C43#38612yes—
358C22×C43C22×C22⋊C411yescharacteristic
359C22×C43C2×#12011yescharacteristic
360C22×C43C2×#12311yescharacteristic
361C2×D43—24no—
362C2×D43—24no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—48no—
369C2×D43—48no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43#42114yescomplemented
373C4×C43—44no—
374C4×C43—42no—
375C4×C43#38612yes—
376C4×C43#38612yes—
377C4×C43C2×C4×D411yescharacteristic
378C4×C43C2×C4×D411yescharacteristic
379C4×C43C2×#12111yescharacteristic
380C4×C43C2×#12111yescharacteristic
381Dic43—22no—
382Dic43—22no—
383Dic43—44no—
384Dic43—44no—
385C2×#525—431no—
386C22×#117—431no—
387C2×#421—431no—
388C2×#421D4311yescharacteristic, complemented
389C2×#407—431no—
390#1897—434no—
391#1896—434no—
392#1733—431no—
393#1733—431no—
394C2×C43—21no—
395C2×C43—21no—
396C2×C43—22no—
397C2×C43—22no—
398C2×C43—82no—
399C2×C43C2×#38611yescharacteristic
400C2×C43C2×#42112yes—
401D43—24no—
402D43—42no—
403C22×#41C2×D4311yescharacteristic
404C24×C4—431no—
405C22×M16—431no—
406C22×M16C2×D4311yescharacteristic
407#525—432no—
408#525—432no—
409#525—434no—
410#525—861no—
411#525—861no—
412#525—862no—
413C2×#123—861no—
414C2×C22⋊Q8—432no—
415C2×#121—432no—
416C2×#120—861no—
417C2×C4×D4—862no—
418C2×#117—431no—
419C2×#117—432no—
420C2×#117—431no—
421C2×#117—861no—
422C2×#117—861no—
423C2×#117—864no—
424C2×#117—864no—
425C2×#117C2×D4311yescharacteristic
426C22×C4⋊C4—861no—
427C22×C22⋊C4—861no—
428C22×C42—432no—
429#421—24no—
430#421—864no—
431C2×#104—434no—
432C2×#104C2×D4314yescomplemented
433#407—432no—
434#407—432no—
435#407—862no—
436C2×C22⋊C8—862no—
437#339—434no—
438#339—434no—
439C43#2097911yescharacteristic, complemented, Sylow
440C25—431no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41C4×D4312yescomplemented
448C2×#41C22×D4312yes—
449C22×Q8C4×D4311yescharacteristic, complemented
450C22×D4—21no—
451C22×D4—862no—
452C22×D4C4×D4311yescharacteristic, complemented
453C23×C4—21no—
454C23×C4—431no—
455C23×C4—432no—
456C23×C4—432no—
457C23×C4—431no—
458C23×C4—431no—
459C23×C4—432no—
460C23×C4—432no—
461C23×C4—431no—
462C23×C4—431no—
463C23×C4—862no—
464C23×C4—862no—
465C23×C4—862no—
466C23×C4—862no—
467C23×C4—862no—
468C23×C4C22×D4311yescharacteristic
469C2×M16—21no—
470C2×M16—22no—
471C2×M16—22no—
472C2×M16—432no—
473C2×M16—861no—
474C2×M16—862no—
475C2×M16—862no—
476C2×M16C22×D4312yes—
477C22×C8—21no—
478C22×C8—861no—
479#123—864no—
480#123—862no—
481#123—862no—
482C22⋊Q8—434no—
483C22⋊Q8—434no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486#121—434no—
487#121—434no—
488#121—862no—
489#121—862no—
490#120—864no—
491#120—862no—
492#120—862no—
493C4×D4—864no—
494C4×D4—864no—
495C4×D4—864no—
496C4×D4—864no—
497#117—22no—
498#117—434no—
499#117—432no—
500#117—432no—
501#117—864no—
502#117—868no—
503#117—868no—
504#117—861no—
505#117—861no—
506#117—862no—
507#117—864no—
508#117C22⋊D4314yescomplemented
509C2×C4⋊C4—21no—
510C2×C4⋊C4—432no—
511C2×C4⋊C4—868no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—862no—
514C2×C4⋊C4—861no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—868no—
517C2×C22⋊C4—862no—
518C2×C22⋊C4—862no—
519C2×C22⋊C4—862no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C42—432no—
523C2×C42—864no—
524C2×C42—862no—
525C2×C42—861no—
526C2×C42—864no—
527C2×C42C22×D4312yes—
528#104—28no—
529#104—868no—
530C22⋊C8—864no—
531C22⋊C8—864no—
532C24—21no—
533C24—431no—
534C24—432no—
535C24—432no—
536C24—431no—
537C24—862no—
538C24—862no—
539C24—1724no—
540C24D4×D4311yescharacteristic
541#41—24no—
542#41—24no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—42no—
548#41—42no—
549#41—42no—
550#41—42no—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8C2×C4×D4312yes—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—864no—
563C2×D4—864no—
564C2×D4—1728no—
565C2×D4C2×C4×D4312yes—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—432no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—432no—
580C22×C4—432no—
581C22×C4—432no—
582C22×C4—432no—
583C22×C4—432no—
584C22×C4—868no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—864no—
590C22×C4—864no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—864no—
594C22×C4—864no—
595C22×C4—864no—
596C22×C4—864no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—1728no—
610C22×C4C2×C4×D4311yescharacteristic
611C22×C4C2×C4×D4311yescharacteristic
612C22×C4#1062189812yes—
613C22×C4D4×D4311yescharacteristic
614C22×C4D4×D4311yescharacteristic
615C22×C4D4×D4311yescharacteristic
616C22×C4D4×D4312yes—
617C22×C4#1062190012yes—
618C22×C4C2×C22⋊D4312yes—
619C22×C4C23×D4311yescharacteristic
620M16—22no—
621M16—22no—
622M16—42no—
623M16—862no—
624M16—862no—
625M16—1722no—
626C2×C8—22no—
627C2×C8—42no—
628C2×C8—862no—
629C2×C8—1722no—
630C4⋊C4—24no—
631C4⋊C4—434no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—868no—
635C4⋊C4—862no—
636C4⋊C4—864no—
637C22⋊C4—24no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C22⋊C4—868no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—862no—
644C22⋊C4—864no—
645C22⋊C4—862no—
646C42—22no—
647C42—434no—
648C42—868no—
649C42—862no—
650C42—862no—
651C42—862no—
652C42C2×C22⋊D4314yescomplemented
653C23—22no—
654C23—42no—
655C23—44no—
656C23—42no—
657C23—432no—
658C23—432no—
659C23—864no—
660C23—864no—
661C23—864no—
662C23—861no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23—864no—
667C23—864no—
668C23—1722no—
669C23—1722no—
670C23—1722no—
671C23—1728no—
672C23—1728no—
673C23C22⋊C4×D4311yescharacteristic
674C23C22⋊C4×D4311yescharacteristic
675C23#1306329312yes—
676C23#1306330712yes—
677C23C2×D4×D4311yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—42no—
681D4—22no—
682D4—22no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—42no—
687D4—1728no—
688D4—1728no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—864no—
703C2×C4—864no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—864no—
713C2×C4—864no—
714C2×C4—864no—
715C2×C4—864no—
716C2×C4—864no—
717C2×C4—864no—
718C2×C4—17216no—
719C2×C4—1724no—
720C2×C4—1724no—
721C2×C4C22⋊C4×D4311yescharacteristic
722C2×C4C22⋊C4×D4311yescharacteristic
723C2×C4(C22⋊D43)⋊C412yes—
724C2×C4(C22⋊D43)⋊C412yes—
725C2×C4C4×C22⋊D4312yes—
726C2×C4C4×C22⋊D4312yes—
727C2×C4#1306329312yes—
728C2×C4#1306329612yes—
729C2×C4#1306329612yes—
730C2×C4#1306329812yes—
731C2×C4#1306329812yes—
732C2×C4#1306330712yes—
733C2×C4C22×C4×D4311yescharacteristic
734C2×C4C2×D4×D4311yescharacteristic
735C2×C4C2×D4×D4311yescharacteristic
736C2×C4C22×C22⋊D4311yescharacteristic
737C2×C4C2×#1062190011yescharacteristic
738C2×C4C2×#1062189811yescharacteristic
739C8—42no—
740C8—1722no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—84no—
749C22—434no—
750C22—864no—
751C22—864no—
752C22—862no—
753C22—862no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22—1728no—
758C22—1728no—
759C22—1722no—
760C22—1722no—
761C22#1458277512yes—
762C22#1458277512yes—
763C22C2×C22⋊C4×D4311yescharacteristic
764C22C2×#1306329311yescharacteristic
765C22C2×#1306330711yescharacteristic
766C4—44no—
767C4—42no—
768C4—862no—
769C4—862no—
770C4—1724no—
771C4—1724no—
772C4#1458277512yes—
773C4#1458277512yes—
774C4C2×(C22⋊D43)⋊C411yescharacteristic
775C4C2×C4×C22⋊D4311yescharacteristic
776C4C2×#1306329611yescharacteristic
777C4C2×#1306329811yescharacteristic
778C2—21no—
779C2—22no—
780C2—21no—
781C2—22no—
782C2—82no—
783C2—864no—
784C2—1722no—
785C2C2×#1458277511yescharacteristic
786C2#421×D4312yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583406C2
cosocleC22×C4×C43C24
hypercenterC2×#421D43
hypocenterC43#20979
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#117×D43C2semidirect
3. C2×#14582916C2semidirect
4. C2×#14582862C2semidirect
5. #19135040C2semidirect
6. #19135035C2semidirect
7. #19134306C2semidirect
8. #19134305C2semidirect
9. C2×C43×#421C2semidirect
15. #14583406C4semidirect
19. C2×#13063301C4semidirect
20. C2×#13063296C4semidirect
26. C2×#13063282C22semidirect
32. C2×C42×D43C22semidirect
34. C2×#13063252C22semidirect
36. #14582862C22semidirect
37. #14582862C22semidirect
39. #14582660C22semidirect
40. #14582659C22semidirect
45. C2×#104×C43C22semidirect
73. #13063301C2×C4semidirect
77. #13063296C2×C4semidirect
88. #13063284C2×C4semidirect
89. #13063284D4semidirect
96. C2×C4⋊Dic43C2×C4semidirect
120. C2×#41×C43C2×C4semidirect
122. C22×Q8×C43C2×C4semidirect
124. C22×D4×C43C2×C4semidirect
133. #117×C43D4semidirect
234. C42×C43C2×D4semidirect
253. C4×Dic43C2×D4semidirect
372. C2×D43#421semidirect
388. C2×#421D43semidirect
432. C2×#104C2×D43semidirect
439. C43#20979semidirect
447. C2×#41C4×D43semidirect
449. C22×Q8C4×D43semidirect
452. C22×D4C4×D43semidirect
508. #117C22⋊D43semidirect
652. C42C2×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#117×D432
C2×#145829162
C2×#145828622
#191350402
#191350352
#191343062
#191343052
C2×C43×#4212
#2097943