Finite Group Databasebeta

← #25968946

Subgroups — #25968946

Order 11008.

1686 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
1#19147985C211yesmaximal, characteristic
2#19145893C214yesmaximal, complemented
3#19145878C214yesmaximal, complemented
4#19145863C214yesmaximal, complemented
5#19145848C214yesmaximal, complemented
6#19145144C211yesmaximal, characteristic, complemented
7#19145137C211yesmaximal, characteristic, complemented
8#19144998C211yesmaximal, characteristic, complemented
9#19144991C211yesmaximal, characteristic, complemented
10#19144526C212yesmaximal, complemented
11#19144518C212yesmaximal, complemented
12#19144413C212yesmaximal, complemented
13#19144404C212yesmaximal, complemented
14#19143233C211yesmaximal, characteristic, complemented
15C2×C43×#544C211yesmaximal, characteristic, complemented
16#14583520C2212yes—
17#14583520C2212yes—
18#14583511C2212yes—
19#14583504C2212yes—
20#14583496—21no—
21#14583496—21no—
22#14583487—21no—
23#14583487—21no—
24#14583456C2211yescharacteristic
25#14583449C2211yescharacteristic
26#14583427—22no—
27#14583427—22no—
28#14583410C2212yes—
29C4×#10621898C2212yes—
30#14583309C2212yescomplemented
31#14583309C2212yescomplemented
32#14583305C2214yescomplemented
33#14583302C2212yescomplemented
34#14583298C2214yescomplemented
35#14583295C2212yescomplemented
36#14583269C2212yescomplemented
37#14583265C2212yescomplemented
38#14583261C2214yescomplemented
39#14583256C2214yescomplemented
40#14583251C2212yescomplemented
41#14583247C2212yescomplemented
42#14583240C2214yes—
43#14583240C2214yes—
44#14583234C2214yes—
45#14583229C2214yes—
46#14583223C2214yes—
47#14583223C2214yes—
48#14583217C2214yes—
49#14583212C2214yes—
50#14583203C2214yescomplemented
51#14583203C2214yescomplemented
52#14583196C2214yescomplemented
53#14583196C2214yescomplemented
54#14583191C2214yescomplemented
55#14583186C2214yescomplemented
56#14583181C2214yescomplemented
57#14583176C2214yescomplemented
58#14582960C2214yes—
59#14582960C2214yes—
60#14582939C2212yes—
61#14582939C2212yes—
62#14582939C2212yes—
63#14582939C2212yes—
64#14582923C2212yes—
65#14582898C2212yes—
66#14582898C2212yes—
67#14582898C2212yes—
68#14582898C2212yes—
69#14582863C2212yes—
70C4×#10621877C2211yescharacteristic
71C4×#10621877C2211yescharacteristic
72C43×#544—22no—
73C43×#544—22no—
74C43×#544C2214yes—
75C43×#544C2214yes—
76C2×C4⋊Q8×C43—21no—
77C2×C4⋊Q8×C43C2211yescharacteristic
78C2×C4⋊Q8×C43C2211yescharacteristic
79C2×#125×C43—21no—
80C2×#125×C43C2211yescharacteristic
81C2×#125×C43C2211yescharacteristic
82C2×C22⋊Q8×C43—21no—
83C2×C22⋊Q8×C43—21no—
84C2×#117×C43C2211yescharacteristic
85C2×#117×C43C2211yescharacteristic
86C22×C4⋊C4×C43C2211yescharacteristic
87C2×#10621898C2312yes—
88C2×#10621877C2312yes—
89C2×#10621877C2312yes—
90#13063325C2311yescharacteristic
91#13063325C2311yescharacteristic
92#13063325C2311yescharacteristic
93#13063322C2311yescharacteristic
94#13063320—22no—
95#13063320—22no—
96#13063318—22no—
97#13063318—22no—
98#13063317C2312yes—
99#13063315—22no—
100#13063315—22no—
101#13063313C2312yes—
102#13063311—22no—
103#13063311—22no—
104#13063310—22no—
105#13063310—22no—
106#13063308—22no—
107#13063307—22no—
108#13063307—22no—
109#13063304—21no—
110#13063304—21no—
111#13063304C2312yes—
112#13063304C2312yes—
113#13063303—22no—
114#13063303—22no—
115#13063299—21no—
116#13063299—21no—
117#13063299C2312yes—
118#13063299C2312yes—
119#13063298—22no—
120#13063298—22no—
121#13063294—22no—
122C4×Dic86—21no—
123C4×Dic86—21no—
124C4×Dic86C2312yes—
125C4×Dic86C2312yes—
126C4×D172—21no—
127C4×D172—21no—
128C4×D172C2312yes—
129C4×D172C2312yes—
130C4×C22⋊D43—22no—
131C4×C22⋊D43—22no—
132C4×C22⋊D43—22no—
133C4×C22⋊D43—22no—
134#13063284C2312yes—
135#13063282—22no—
136C42×D43—22no—
137#13063258C2314yes—
138#13063258C2314yes—
139#13063258C2314yes—
140#13063258C2314yes—
141#13063256C2314yes—
142#13063256C2314yes—
143#13063256C2314yes—
144#13063256C2314yes—
145C4⋊(C43⋊C8)C2314yes—
146C4⋊(C43⋊C8)C2314yes—
147#13063248C2314yes—
148#13063248C2314yes—
149#13063248C2314yes—
150#13063248C2314yes—
151#13063245C2314yes—
152#13063245C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155C22⋊(C43⋊C8)C2314yes—
156C22⋊(C43⋊C8)C2314yes—
157#13063236C2312yes—
158#13063236C2312yes—
159C4×C43⋊C8C2312yes—
160C4×C43⋊C8C2312yes—
161C22×Q8×C43—21no—
162C22×Q8×C43—21no—
163C23×C4×C43—21no—
164C23×C4×C43C2311yescharacteristic
165C4⋊Q8×C43—24no—
166C4⋊Q8×C43—24no—
167C4⋊Q8×C43—22no—
168C4⋊Q8×C43—21no—
169C4⋊Q8×C43—21no—
170C4⋊Q8×C43C2312yes—
171C4⋊Q8×C43C2312yes—
172C4⋊Q8×C43C2314yes—
173#125×C43—24no—
174#125×C43—24no—
175#125×C43—22no—
176#125×C43—21no—
177#125×C43—21no—
178#125×C43C2312yes—
179#125×C43C2312yes—
180#125×C43C2314yes—
181C22⋊Q8×C43—24no—
182C22⋊Q8×C43—24no—
183C22⋊Q8×C43—24no—
184C22⋊Q8×C43—24no—
185#117×C43—22no—
186#117×C43D412yes—
187#117×C43D412yes—
188#117×C43C2314yes—
189#117×C43C2312yes—
190#117×C43C2312yes—
191C2×C4⋊C4×C43—21no—
192C2×C4⋊C4×C43—22no—
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43—21no—
195C2×C4⋊C4×C43—21no—
196C2×C4⋊C4×C43—21no—
197C2×C4⋊C4×C43—21no—
198C2×C4⋊C4×C43—21no—
199C2×C4⋊C4×C43D411yescharacteristic
200C2×C4⋊C4×C43D411yescharacteristic
201C2×C4⋊C4×C43C2311yescharacteristic
202C2×C4⋊C4×C43C2311yescharacteristic
203C2×C4⋊C4×C43C2314yes—
204C2×C4⋊C4×C43C2311yescharacteristic
205C2×C4⋊C4×C43C2311yescharacteristic
206C2×C22⋊C4×C43—21no—
207C2×C22⋊C4×C43D411yescharacteristic
208C2×C22⋊C4×C43D411yescharacteristic
209C2×C42×C43—21no—
210C2×C42×C43C2311yescharacteristic
211C2×C42×C43C2311yescharacteristic
212C24×C43C2×D411yescharacteristic
213C2×Q8×C43—24no—
214C2×Q8×C43—22no—
215C2×Q8×C43—22no—
216C2×Q8×C43—82no—
217C2×Q8×C43—82no—
218C22×C4×C43—24no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—24no—
224C22×C4×C43—82no—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2412yes—
232C22×C4×C43C2411yescharacteristic
233C2×C22⋊D43—22no—
234C2×C22⋊D43—22no—
235C2×C22⋊D43—22no—
236#10621898—28no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172C2412yes—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—22no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86C2412yes—
246C4⋊C4×C43—24no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—22no—
251C4⋊C4×C43—22no—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—22no—
254C4⋊C4×C43—22no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—22no—
257C4⋊C4×C43—22no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43C2×D412yes—
261C4⋊C4×C43C2×D412yes—
262C4⋊C4×C43C2×D412yes—
263C4⋊C4×C43C2×D412yes—
264C4⋊C4×C43C2412yes—
265C4⋊C4×C43C2412yes—
266C4⋊C4×C43C2412yes—
267C4⋊C4×C43C2412yes—
268C22⋊C4×C43—24no—
269C22⋊C4×C43C2×D412yes—
270C22⋊C4×C43C2×D412yes—
271C22⋊C4×C43C2×D412yes—
272C22⋊C4×C43C2×D412yes—
273C42×C43—24no—
274C42×C43C2×D412yes—
275C42×C43C2×D411yescharacteristic
276C42×C43C2×D411yescharacteristic
277C42×C43C2411yescharacteristic
278C42×C43C2411yescharacteristic
279C42×C43C2412yes—
280C22⋊Dic43—22no—
281C22⋊Dic43—22no—
282C22⋊Dic43—22no—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—22no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43—21no—
292C4⋊Dic43—21no—
293C4⋊Dic43C2412yes—
294C4⋊Dic43C2412yes—
295Dic43⋊C4—22no—
296Dic43⋊C4—22no—
297Dic43⋊C4—22no—
298Dic43⋊C4—22no—
299Dic43⋊C4—22no—
300Dic43⋊C4—22no—
301C4×Dic43—22no—
302C4×Dic43—22no—
303C4×Dic43—22no—
304#10621877—24no—
305#10621877—24no—
306C2×C43⋊C8C2414yes—
307C2×C43⋊C8C2414yes—
308C23×C43—22no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43C22×D412yes—
312C23×C43C22×D411yescharacteristic
313C22×D43—22no—
314Q8×C43—82no—
315Q8×C43—84no—
316Q8×C43—82no—
317C2×C4×C43—22no—
318C2×C4×C43—24no—
319C2×C4×C43—24no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43—84no—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D412yes—
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C432−1+414yes—
342C2×C4×C43C2511yescharacteristic
343C22⋊D43—44no—
344C22⋊D43—82no—
345C22⋊D43—82no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349D172—24no—
350D172—81no—
351D172—81no—
352C4×D43—44no—
353C4×D43—82no—
354C4×D43—82no—
355Dic86—24no—
356Dic86—81no—
357Dic86—81no—
358C43⋊C8—24no—
359C43⋊C8—24no—
360#60867—431nomaximal, Sylow
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—44no—
367C22×C43#53612yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C4×C43—21no—
373C4×C43—22no—
374C4×C43—21no—
375C4×C43—21no—
376C4×C43—22no—
377C4×C43—21no—
378C4×C43—22no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43#53612yes—
384C4×C43C2×2−1+412yes—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388C2×#544D4311yescharacteristic, complemented
389#3455—431no—
390#3244—434no—
391#3243—434no—
392#3242—434no—
393#3241—434no—
394#3166—431no—
395#3165—431no—
396#3142—431no—
397#3141—431no—
398#3093—432no—
399#3092—432no—
400#3080—432no—
401#3079—432no—
402#2921—431no—
403C2×C43—22no—
404C2×C43—42no—
405C2×C43C2×#53611yescharacteristic
406C2×C43#358511yescharacteristic
407C2×C43#358611yescharacteristic
408D43—82no—
409#544—22no—
410#544—22no—
411#544C2×D4314yes—
412#544C2×D4314yes—
413#542—432no—
414#542—432no—
415#541—432no—
416#540—432no—
417#539—861no—
418#539—861no—
419#538—861no—
420#538—861no—
421#533—431no—
422#532—431no—
423C2×C4⋊Q8—21no—
424C2×C4⋊Q8C2×D4311yescharacteristic
425C2×C4⋊Q8C2×D4311yescharacteristic
426#529—862no—
427#529—862no—
428C2×#125—21no—
429C2×#125C2×D4311yescharacteristic
430C2×#125C2×D4311yescharacteristic
431#525—432no—
432C2×C22⋊Q8—21no—
433C2×C22⋊Q8—21no—
434C4×#41—432no—
435C2×#117C2×D4311yescharacteristic
436C2×#117C2×D4311yescharacteristic
437C22×C4⋊C4C2×D4311yescharacteristic
438#501—434no—
439#501—432no—
440#501—432no—
441#500—432no—
442#499—434no—
443#498—432no—
444#491—432no—
445#490—432no—
446#489—434no—
447#488—434no—
448#487—432no—
449#486—432no—
450#485—434no—
451#485—434no—
452#484—434no—
453#483—434no—
454#482—434no—
455#482—434no—
456#481—434no—
457#480—434no—
458#479—434no—
459#479—434no—
460#478—434no—
461#478—434no—
462#477—434no—
463#476—434no—
464#475—434no—
465#474—434no—
466#433—434no—
467#433—434no—
468#428—432no—
469#428—432no—
470#428—432no—
471#428—432no—
472#423—432no—
473#417—432no—
474#417—432no—
475#417—432no—
476#417—432no—
477#407—432no—
478C4×M16—431no—
479C4×M16—431no—
480C43#6086711yescharacteristic, complemented, Sylow
481C2×#41—432no—
482C22×Q8—21no—
483C22×Q8—21no—
484C23×C4—21no—
485C23×C4C22×D4311yescharacteristic
486C2×M16—432no—
487C2×M16—432no—
488C4⋊Q8—24no—
489C4⋊Q8—24no—
490C4⋊Q8—22no—
491C4⋊Q8—21no—
492C4⋊Q8—21no—
493C4⋊Q8—431no—
494C4⋊Q8—431no—
495C4⋊Q8—431no—
496C4⋊Q8C22×D4314yes—
497C4⋊Q8C22×D4312yes—
498C4⋊Q8C22×D4312yes—
499#127—431no—
500#126—862no—
501#126—862no—
502#126—862no—
503#126—862no—
504#125—24no—
505#125—24no—
506#125—22no—
507#125—21no—
508#125—21no—
509#125—432no—
510#125—862no—
511#125—862no—
512#125C22×D4314yes—
513#125C22×D4312yes—
514#125C22×D4312yes—
515#124—432no—
516#124—862no—
517#124—862no—
518#123—862no—
519#123—862no—
520#123—862no—
521#123—862no—
522#123—862no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—24no—
526C22⋊Q8—24no—
527C22⋊Q8—432no—
528C22⋊Q8—432no—
529C22⋊Q8—861no—
530C22⋊Q8—861no—
531C22⋊Q8—862no—
532C22⋊Q8—862no—
533#121—432no—
534#121—432no—
535#121—861no—
536#121—861no—
537#121—862no—
538#121—862no—
539#120—862no—
540C4×Q8—432no—
541C4×Q8—432no—
542C4×Q8—861no—
543C4×Q8—861no—
544C4×D4—432no—
545C4×D4—432no—
546C4×D4—862no—
547C4×D4—862no—
548C4×D4—862no—
549C4×D4—862no—
550C4×D4—861no—
551C4×D4—861no—
552#117—22no—
553#117—432no—
554#117—862no—
555#117C22⋊D4312yes—
556#117C22⋊D4312yes—
557#117C22×D4314yes—
558#117C22×D4312yes—
559#117C22×D4312yes—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4C22⋊D4311yescharacteristic
569C2×C4⋊C4C22⋊D4311yescharacteristic
570C2×C4⋊C4C22×D4311yescharacteristic
571C2×C4⋊C4C22×D4311yescharacteristic
572C2×C4⋊C4C22×D4314yes—
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C4⋊C4C22×D4311yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4C22⋊D4311yescharacteristic
577C2×C22⋊C4C22⋊D4311yescharacteristic
578C2×C42—21no—
579C2×C42—862no—
580C2×C42C22×D4311yescharacteristic
581C2×C42C22×D4311yescharacteristic
582#107—434no—
583#107—434no—
584#107—434no—
585#107—434no—
586#106—434no—
587#106—434no—
588#106—434no—
589#106—434no—
590C4⋊C8—434no—
591C4⋊C8—434no—
592#103—434no—
593#103—434no—
594#103—434no—
595#103—434no—
596#102—434no—
597#102—434no—
598#102—434no—
599#102—434no—
600C22⋊C8—434no—
601C22⋊C8—434no—
602#97—432no—
603#97—432no—
604C4×C8—432no—
605C4×C8—432no—
606C24C2×C22⋊D4311yescharacteristic
607#41—868no—
608C2×Q8—24no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—82no—
612C2×Q8—82no—
613C2×Q8—432no—
614C2×Q8—861no—
615C2×Q8—861no—
616C2×D4—432no—
617C2×D4—862no—
618C2×D4—862no—
619C2×D4—862no—
620C2×D4—861no—
621C2×D4—861no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C2×C22⋊D4312yes—
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C2×C22⋊D4311yescharacteristic
636C22×C4C2×C22⋊D4311yescharacteristic
637C22×C4C2×C22⋊D4311yescharacteristic
638C22×C4C23×D4312yes—
639C22×C4C23×D4311yescharacteristic
640M16—864no—
641M16—864no—
642C2×C8—434no—
643C2×C8—434no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—24no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—432no—
659C4⋊C4—432no—
660C4⋊C4—862no—
661C4⋊C4—862no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—862no—
665C4⋊C4—862no—
666C4⋊C4—862no—
667C4⋊C4—862no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4C2×C22⋊D4312yes—
671C4⋊C4C2×C22⋊D4312yes—
672C4⋊C4C2×C22⋊D4312yes—
673C4⋊C4C2×C22⋊D4312yes—
674C4⋊C4C23×D4312yes—
675C4⋊C4C23×D4312yes—
676C4⋊C4C23×D4312yes—
677C4⋊C4C23×D4312yes—
678C22⋊C4—24no—
679C22⋊C4—862no—
680C22⋊C4—862no—
681C22⋊C4—862no—
682C22⋊C4—862no—
683C22⋊C4—862no—
684C22⋊C4—862no—
685C22⋊C4—862no—
686C22⋊C4—862no—
687C22⋊C4—862no—
688C22⋊C4C2×C22⋊D4312yes—
689C22⋊C4C2×C22⋊D4312yes—
690C22⋊C4C2×C22⋊D4312yes—
691C22⋊C4C2×C22⋊D4312yes—
692C42—24no—
693C42—862no—
694C42—862no—
695C42—862no—
696C42C2×C22⋊D4312yes—
697C42C2×C22⋊D4311yescharacteristic
698C42C2×C22⋊D4311yescharacteristic
699C42C23×D4311yescharacteristic
700C42C23×D4311yescharacteristic
701C42C23×D4312yes—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—862no—
706C23C22×C22⋊D4312yes—
707C23C22×C22⋊D4311yescharacteristic
708Q8—84no—
709Q8—82no—
710Q8—82no—
711Q8—864no—
712Q8—3441no—
713Q8—3441no—
714D4—864no—
715D4—3441no—
716D4—3441no—
717D4—3442no—
718D4—3442no—
719D4—1724no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—84no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—3442no—
740C2×C4—3442no—
741C2×C4—1724no—
742C2×C4C22×C22⋊D4312yes—
743C2×C4C22×C22⋊D4312yes—
744C2×C4C22×C22⋊D4312yes—
745C2×C4C22×C22⋊D4311yescharacteristic
746C2×C4C22×C22⋊D4311yescharacteristic
747C2×C4C22×C22⋊D4311yescharacteristic
748C2×C4C22×C22⋊D4311yescharacteristic
749C2×C4C22×C22⋊D4311yescharacteristic
750C2×C4#1306337314yes—
751C2×C4C24×D4311yescharacteristic
752C8—864no—
753C8—864no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—1722no—
761C22—1722no—
762C22—1722no—
763C22#1458347312yes—
764C22C23×C22⋊D4311yescharacteristic
765C4—22no—
766C4—21no—
767C4—21no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—1722no—
777C4—1722no—
778C4—1722no—
779C4#1458347312yes—
780C4C2×#1306337312yes—
781C2—22no—
782C2—42no—
783C2—3442no—
784C2C2×#1458347311yescharacteristic
785C2#1914937511yescharacteristic
786C2#1914938211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#544C2
socleC22×C43C23×D4
prime radical#19147985C2
hypercenterC2×#544D43
hypocenterC43#60867
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #19145893C2semidirect
3. #19145878C2semidirect
4. #19145863C2semidirect
5. #19145848C2semidirect
6. #19145144C2semidirect
7. #19145137C2semidirect
8. #19144998C2semidirect
9. #19144991C2semidirect
10. #19144526C2semidirect
11. #19144518C2semidirect
12. #19144413C2semidirect
13. #19144404C2semidirect
14. #19143233C2semidirect
15. C2×C43×#544C2semidirect
30. #14583309C22semidirect
31. #14583309C22semidirect
32. #14583305C22semidirect
33. #14583302C22semidirect
34. #14583298C22semidirect
35. #14583295C22semidirect
36. #14583269C22semidirect
37. #14583265C22semidirect
38. #14583261C22semidirect
39. #14583256C22semidirect
40. #14583251C22semidirect
41. #14583247C22semidirect
50. #14583203C22semidirect
51. #14583203C22semidirect
52. #14583196C22semidirect
53. #14583196C22semidirect
54. #14583191C22semidirect
55. #14583186C22semidirect
56. #14583181C22semidirect
57. #14583176C22semidirect
388. C2×#544D43semidirect
480. C43#60867semidirect

Maximal subgroups

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

subgroupindex
#191479852
#191458932
#191458782
#191458632
#191458482
#191451442
#191451372
#191449982
#191449912
#191445262
#191445182
#191444132
#191444042
#191432332
C2×C43×#5442
#6086743