Finite Group Databasebeta

← #25098140

Subgroups — #25098140

Order 11008.

1708 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2#19147924C211yesmaximal, characteristic
3C2×#14582916C211yesmaximal, characteristic, complemented
4C2×#14582872C211yesmaximal, characteristic, complemented
5#19134975C218yesmaximal, complemented
6#19134306C211yesmaximal, characteristic, complemented
7#19134304C211yesmaximal, characteristic, complemented
8C2×C43×#421C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583665—22no—
11#14583665—22no—
12#14583665—22no—
13#14583665C2214yescomplemented
14C2×#13063333—22no—
15C2×#13063331—22no—
16C22×#10621877C2211yescharacteristic
17C2×M16×D43—22no—
18#14583477—22no—
19#14583473C412yescomplemented
20#14583470C412yescomplemented
21#14583466C412yescomplemented
22#14583463C412yescomplemented
23#14583458—22no—
24#14583445C2214yes—
25#14583410—22no—
26#14583406—22no—
27C2×#13063284C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29#14582916—22no—
30#14582916C2214yescomplemented
31C2×#13063252—22no—
32#14582872—22no—
33#14582872C2214yescomplemented
34C2×#13063239—22no—
35#14582660C2214yescomplemented
36#14582658C2214yescomplemented
37C22×#41×C43C2211yescharacteristic
38C22×M16×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C43×#421—22no—
41C43×#421C2214yescomplemented
42C2×#104×C43—22no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898C2×C412yes—
52C2×#10621898D412yes—
53C2×#10621898D412yes—
54C2×#10621898C2312yes—
55C22×Dic86C2×C411yescharacteristic
56C22×D172C2×C411yescharacteristic
57C22×C22⋊D43D412yes—
58C22×C4×D43D412yes—
59#13063333—28no—
60#13063333—28no—
61#13063331—28no—
62#13063331—28no—
63C2×#10621877—21no—
64C2×#10621877—21no—
65C2×#10621877—21no—
66C2×#10621877D412yescomplemented
67C2×#10621877D412yescomplemented
68C2×#10621877C2312yes—
69C2×#10621872—24no—
70M16×D43—28no—
71M16×D43—28no—
72C22×C43⋊C8—21no—
73C2×C8×D43—24no—
74#13063323C2×C414yescomplemented
75#13063321C2×C414yescomplemented
76#13063314C2×C414yescomplemented
77#13063312C2×C414yescomplemented
78#13063308—24no—
79#13063306—24no—
80#13063304—24no—
81#13063301—24no—
82#13063299—24no—
83#13063297—28no—
84#13063296—24no—
85#13063294—24no—
86#13063293—24no—
87C4×C22⋊D43—28no—
88#13063284—21no—
89#13063284—21no—
90#13063284—21no—
91#13063284—21no—
92#13063284—21no—
93#13063284C2×C412yes—
94#13063284C2×C412yes—
95#13063284C2312yes—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2312yes—
102#13063252—28no—
103#13063239—28no—
104C2×#41×C43—21no—
105C2×#41×C43—21no—
106C2×#41×C43—21no—
107C2×#41×C43—21no—
108C2×#41×C43—21no—
109C2×#41×C43—21no—
110C2×#41×C43—21no—
111C2×#41×C43—21no—
112C2×#41×C43—21no—
113C2×#41×C43—21no—
114C2×#41×C43C2×C412yes—
115C2×#41×C43C2312yes—
116C22×Q8×C43C2×C411yescharacteristic
117C22×D4×C43—21no—
118C22×D4×C43C2×C411yescharacteristic
119C23×C4×C43—21no—
120C23×C4×C43C2311yescharacteristic
121C2×M16×C43—21no—
122C2×M16×C43—21no—
123C2×M16×C43—21no—
124C2×M16×C43D412yescomplemented
125C2×M16×C43D412yescomplemented
126C2×M16×C43C2312yes—
127C22×C8×C43—21no—
128#117×C43—21no—
129#117×C43—21no—
130#117×C43—21no—
131#117×C43C2312yes—
132C2×C4⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43—21no—
135#104×C43—28no—
136C24×C43—21no—
137C24×C43C2×D411yescharacteristic
138C23×D43C22⋊C412yes—
139#41×C43—22no—
140#41×C43—22no—
141#41×C43—22no—
142#41×C43—22no—
143#41×C43—22no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—22no—
147#41×C43—41no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C22×C412yes—
161C2×D4×C43—21no—
162C2×D4×C43—22no—
163C2×D4×C43—22no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—41no—
169C2×D4×C43—41no—
170C2×D4×C43—41no—
171C2×D4×C43—41no—
172C2×D4×C43C22×C412yes—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—21no—
176C22×C4×C43—41no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43—41no—
181C22×C4×C43C22×C411yescharacteristic
182C22×C4×C43C22×C411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43#4111yescharacteristic
191C22×C4×C43#4111yescharacteristic
192C22×C4×C43#4111yescharacteristic
193C22×C4×C43#4111yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—22no—
196C2×C22⋊D43—22no—
197C2×C22⋊D43—22no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—28no—
200C2×C22⋊D43C22⋊C414yes—
201C2×C22⋊D43C2×D414yes—
202C22×Dic43—22no—
203C22×Dic43—41no—
204C22×Dic43C22⋊C412yes—
205#10621898—22no—
206#10621898—22no—
207#10621898—22no—
208#10621898—22no—
209#10621898—22no—
210#10621898—22no—
211#10621898—22no—
212#10621898—22no—
213#10621898—22no—
214#10621898—22no—
215#10621898—22no—
216#10621898—22no—
217#10621898—22no—
218#10621898—22no—
219#10621898—22no—
220#10621898—22no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172C22⋊C412yes—
226C2×D172C22×C412yes—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43C22⋊C414yes—
232C2×C4×D43C2×D414yes—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86C22⋊C412yes—
238C2×Dic86C22×C412yes—
239M16×C43—22no—
240M16×C43—22no—
241M16×C43—22no—
242M16×C43C2×D414yes—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C2×C8×C43—22no—
246C4⋊C4×C43—22no—
247C4⋊C4×C43—41no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—41no—
250C42×C43—22no—
251C42×C43—41no—
252C22⋊Dic43—28no—
253C22⋊Dic43—22no—
254C22⋊Dic43—22no—
255C22⋊Dic43—22no—
256C22⋊Dic43—41no—
257(C2×D43)⋊C4—28no—
258C4⋊Dic43—22no—
259C4⋊Dic43—22no—
260C4⋊Dic43—22no—
261C4⋊Dic43—41no—
262Dic43⋊C4—28no—
263C4×Dic43—22no—
264C4×Dic43—22no—
265C4×Dic43—41no—
266C4×Dic43C22×C414yes—
267#10621877—22no—
268#10621877—22no—
269#10621877—22no—
270#10621877C2×D414yes—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274#10621872—216no—
275C8×D43—216no—
276C23×C43—22no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—81no—
280C23×C43—82no—
281C23×C43C2×C22⋊C411yescharacteristic
282C23×C43C2×C22⋊C411yescharacteristic
283C23×C43#12111yescharacteristic
284C23×C43#12111yescharacteristic
285C23×C43#12111yescharacteristic
286C23×C43#12111yescharacteristic
287C23×C43C22×D411yescharacteristic
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—82no—
291C22×D43C2×C22⋊C414yes—
292Q8×C43—22no—
293Q8×C43—22no—
294Q8×C43—41no—
295Q8×C43—41no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—42no—
299D4×C43—42no—
300D4×C43—42no—
301D4×C43—42no—
302D4×C43—41no—
303D4×C43—41no—
304C2×C4×C43—22no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—82no—
313C2×C4×C43C2×C22⋊C411yescharacteristic
314C2×C4×C43C2×C22⋊C411yescharacteristic
315C2×C4×C43C4×D411yescharacteristic
316C2×C4×C43C4×D411yescharacteristic
317C2×C4×C43C4×D411yescharacteristic
318C2×C4×C43C4×D411yescharacteristic
319C2×C4×C43C4×D411yescharacteristic
320C2×C4×C43C4×D411yescharacteristic
321C2×C4×C43C4×D411yescharacteristic
322C2×C4×C43C4×D411yescharacteristic
323C2×C4×C43#12011yescharacteristic
324C2×C4×C43#12011yescharacteristic
325C2×C4×C43#12011yescharacteristic
326C2×C4×C43#12011yescharacteristic
327C2×C4×C43#12111yescharacteristic
328C2×C4×C43#12111yescharacteristic
329C2×C4×C43#12111yescharacteristic
330C2×C4×C43#12111yescharacteristic
331C2×C4×C43#12311yescharacteristic
332C2×C4×C43#12311yescharacteristic
333C2×C4×C43#12311yescharacteristic
334C2×C4×C43#12311yescharacteristic
335C2×C4×C43C23×C411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C2×#4111yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C22⋊D43—24no—
342C22⋊D43—24no—
343C22⋊D43—24no—
344C22⋊D43—24no—
345C22⋊D43—88no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—24no—
349C2×Dic43—42no—
350C2×Dic43—82no—
351C2×Dic43—82no—
352C2×Dic43C2×C22⋊C414yes—
353D172—22no—
354D172—22no—
355D172—22no—
356D172—22no—
357C4×D43—24no—
358C4×D43—24no—
359C4×D43—24no—
360C4×D43—24no—
361Dic86—22no—
362Dic86—22no—
363Dic86—22no—
364Dic86—22no—
365C8×C43—24no—
366C43⋊C8—24no—
367#20947—431nomaximal, Sylow
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—44no—
376C22×C43—42no—
377C22×C43—82no—
378C22×C43—82no—
379C22×C43#38611yescharacteristic
380C22×C43#38611yescharacteristic
381C22×C43#38611yescharacteristic
382C22×C43#38611yescharacteristic
383C22×C43C22×C22⋊C411yescharacteristic
384C22×C43C2×#12111yescharacteristic
385C22×C43C2×#12111yescharacteristic
386C2×D43—24no—
387C2×D43—44no—
388C2×D43—44no—
389C2×D43—82no—
390C4×C43—42no—
391C4×C43—82no—
392C4×C43#38611yescharacteristic
393C4×C43#38611yescharacteristic
394C4×C43#38611yescharacteristic
395C4×C43#38611yescharacteristic
396C4×C43C2×C4×D411yescharacteristic
397C4×C43C2×C4×D411yescharacteristic
398C4×C43C2×#12011yescharacteristic
399C4×C43C2×#12311yescharacteristic
400Dic43—24no—
401Dic43—44no—
402Dic43—82no—
403C2×#568—431no—
404#3449—431no—
405C2×#421—431no—
406C2×#421D4311yescharacteristic, complemented
407C2×#410—431no—
408#1884—438no—
409#1733—431no—
410#1733—431no—
411C2×C43—21no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43—82no—
419C2×C43C2×#38611yescharacteristic
420D43—44no—
421C22×#41—431no—
422C22×#41C2×D4311yescharacteristic
423#568—434no—
424#568—862no—
425#568—862no—
426#568—862no—
427C2×#131—862no—
428C2×#131—862no—
429C22×M16—431no—
430C22×M16—862no—
431C22×M16C2×D4311yescharacteristic
432#537—862no—
433#536—432no—
434#536—432no—
435#535—432no—
436#535—432no—
437#534—862no—
438#532—434no—
439#525—862no—
440#525—862no—
441C2×#117—431no—
442C2×#117—431no—
443C2×#117C2×D4311yescharacteristic
444#421—22no—
445#421—434no—
446#421—862no—
447#421C2×D4314yescomplemented
448C2×#104—22no—
449C2×#104—862no—
450#410—434no—
451#410—862no—
452C2×#99—862no—
453#339—434no—
454#339—434no—
455C43#2094711yescharacteristic, complemented, Sylow
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—432no—
467C2×#41—432no—
468C2×#41—432no—
469C2×#41—432no—
470C2×#41—861no—
471C2×#41—861no—
472C2×#41—861no—
473C2×#41—861no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41—861no—
477C2×#41—861no—
478C2×#41C4×D4312yes—
479C2×#41C22×D4312yes—
480C22×Q8—431no—
481C22×Q8C4×D4311yescharacteristic
482C22×D4—21no—
483C22×D4—432no—
484C22×D4—431no—
485C22×D4C4×D4311yescharacteristic
486C23×C4—21no—
487C23×C4—432no—
488C23×C4C22×D4311yescharacteristic
489#131—868no—
490#131—868no—
491#131—868no—
492#131—868no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—432no—
497C2×M16—432no—
498C2×M16—432no—
499C2×M16—864no—
500C2×M16—868no—
501C2×M16—868no—
502C2×M16—861no—
503C2×M16—861no—
504C2×M16—861no—
505C2×M16C22⋊D4312yescomplemented
506C2×M16C22⋊D4312yescomplemented
507C2×M16C22×D4312yes—
508C22×C8—21no—
509C22×C8—864no—
510C22×C8—861no—
511C4⋊Q8—434no—
512#127—434no—
513#124—434no—
514#124—434no—
515#123—864no—
516#123—864no—
517C22⋊Q8—864no—
518C22⋊Q8—864no—
519#121—864no—
520#121—864no—
521#121—868no—
522#120—864no—
523#120—864no—
524C4×D4—868no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—432no—
529#117—432no—
530#117—432no—
531#117—861no—
532#117—861no—
533#117—861no—
534#117—861no—
535#117—861no—
536#117C22×D4312yes—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C42—21no—
544C2×C42—432no—
545C2×C42—861no—
546#104—28no—
547#104—868no—
548#99—868no—
549C24—21no—
550C24—432no—
551C24D4×D4311yescharacteristic
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—862no—
569#41—862no—
570#41—862no—
571#41—862no—
572#41—862no—
573#41—862no—
574#41—862no—
575#41—862no—
576#41—862no—
577#41—862no—
578#41—862no—
579#41—862no—
580#41—862no—
581#41—862no—
582#41—862no—
583#41—862no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—432no—
590C2×Q8—432no—
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8C2×C4×D4312yes—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—434no—
608C2×D4—434no—
609C2×D4—432no—
610C2×D4—432no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—862no—
615C2×D4—868no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4C2×C4×D4312yes—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—432no—
630C22×C4—434no—
631C22×C4—434no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—1721no—
638C22×C4C2×C4×D4311yescharacteristic
639C22×C4C2×C4×D4311yescharacteristic
640C22×C4#1062189811yescharacteristic
641C22×C4#1062189811yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4D4×D4311yescharacteristic
645C22×C4D4×D4311yescharacteristic
646C22×C4D4×D4311yescharacteristic
647C22×C4#1062190011yescharacteristic
648C22×C4#1062190011yescharacteristic
649C22×C4C2×C22⋊D4311yescharacteristic
650C22×C4C2×C22⋊D4311yescharacteristic
651C22×C4C23×D4311yescharacteristic
652M16—22no—
653M16—22no—
654M16—22no—
655M16—434no—
656M16—8616no—
657M16—862no—
658M16—862no—
659M16—862no—
660M16C2×C22⋊D4314yes—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—8616no—
665C2×C8—862no—
666C2×C8—862no—
667C2×C8—862no—
668C4⋊C4—22no—
669C4⋊C4—41no—
670C4⋊C4—868no—
671C4⋊C4—862no—
672C4⋊C4—862no—
673C4⋊C4—862no—
674C4⋊C4—1721no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—868no—
678C22⋊C4—868no—
679C22⋊C4—862no—
680C22⋊C4—862no—
681C22⋊C4—862no—
682C22⋊C4—1721no—
683C42—22no—
684C42—41no—
685C42—434no—
686C42—862no—
687C42—862no—
688C42—1721no—
689C23—22no—
690C23—41no—
691C23—41no—
692C23—81no—
693C23—82no—
694C23—434no—
695C23—862no—
696C23—862no—
697C23—3442no—
698C23C22⋊C4×D4311yescharacteristic
699C23C22⋊C4×D4311yescharacteristic
700C23#1306329611yescharacteristic
701C23#1306329611yescharacteristic
702C23#1306329811yescharacteristic
703C23#1306329811yescharacteristic
704C23C2×D4×D4311yescharacteristic
705Q8—22no—
706Q8—22no—
707Q8—41no—
708Q8—41no—
709Q8—862no—
710Q8—862no—
711Q8—862no—
712Q8—862no—
713D4—22no—
714D4—22no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—41no—
720D4—41no—
721D4—864no—
722D4—864no—
723D4—864no—
724D4—864no—
725D4—862no—
726D4—862no—
727D4—862no—
728D4—862no—
729D4—3448no—
730C2×C4—22no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—82no—
739C2×C4—434no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—864no—
743C2×C4—864no—
744C2×C4—864no—
745C2×C4—864no—
746C2×C4—864no—
747C2×C4—3442no—
748C2×C4—3442no—
749C2×C4—1722no—
750C2×C4C22⋊C4×D4311yescharacteristic
751C2×C4C22⋊C4×D4311yescharacteristic
752C2×C4(C22⋊D43)⋊C411yescharacteristic
753C2×C4(C22⋊D43)⋊C411yescharacteristic
754C2×C4(C22⋊D43)⋊C411yescharacteristic
755C2×C4(C22⋊D43)⋊C411yescharacteristic
756C2×C4C4×C22⋊D4311yescharacteristic
757C2×C4C4×C22⋊D4311yescharacteristic
758C2×C4C4×C22⋊D4311yescharacteristic
759C2×C4C4×C22⋊D4311yescharacteristic
760C2×C4#1306329311yescharacteristic
761C2×C4#1306329311yescharacteristic
762C2×C4#1306329311yescharacteristic
763C2×C4#1306329311yescharacteristic
764C2×C4#1306329611yescharacteristic
765C2×C4#1306329611yescharacteristic
766C2×C4#1306329811yescharacteristic
767C2×C4#1306329811yescharacteristic
768C2×C4#1306330711yescharacteristic
769C2×C4#1306330711yescharacteristic
770C2×C4#1306330711yescharacteristic
771C2×C4#1306330711yescharacteristic
772C2×C4C22×C4×D4311yescharacteristic
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C22×C22⋊D4311yescharacteristic
776C2×C4C2×#1062190011yescharacteristic
777C2×C4C2×#1062189811yescharacteristic
778C8—24no—
779C8—864no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—44no—
788C22—42no—
789C22—82no—
790C22—82no—
791C22—864no—
792C22—3442no—
793C22—1724no—
794C22—1724no—
795C22#1458277511yescharacteristic
796C22#1458277511yescharacteristic
797C22#1458277511yescharacteristic
798C22#1458277511yescharacteristic
799C22C2×C22⋊C4×D4311yescharacteristic
800C22C2×#1306329611yescharacteristic
801C22C2×#1306329811yescharacteristic
802C4—42no—
803C4—82no—
804C4—864no—
805C4—3442no—
806C4—1724no—
807C4#1458277511yescharacteristic
808C4#1458277511yescharacteristic
809C4#1458277511yescharacteristic
810C4#1458277511yescharacteristic
811C4C2×(C22⋊D43)⋊C411yescharacteristic
812C4C2×C4×C22⋊D4311yescharacteristic
813C4C2×#1306329311yescharacteristic
814C4C2×#1306330711yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—82no—
823C2—1724no—
824C2C2×#1458277511yescharacteristic
subgroupG/H
centerC4C2×#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC2×C43C2×#386
prime radical#19147924C2
cosocleC22×C4×C43C24
hypercenterC2×#421D43
hypocenterC43#20947
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582916C2semidirect
4. C2×#14582872C2semidirect
5. #19134975C2semidirect
6. #19134306C2semidirect
7. #19134304C2semidirect
8. C2×C43×#421C2semidirect
13. #14583665C22semidirect
19. #14583473C4semidirect
20. #14583470C4semidirect
21. #14583466C4semidirect
22. #14583463C4semidirect
30. #14582916C22semidirect
33. #14582872C22semidirect
35. #14582660C22semidirect
36. #14582658C22semidirect
41. C43×#421C22semidirect
66. C2×#10621877D4semidirect
67. C2×#10621877D4semidirect
74. #13063323C2×C4semidirect
75. #13063321C2×C4semidirect
76. #13063314C2×C4semidirect
77. #13063312C2×C4semidirect
124. C2×M16×C43D4semidirect
125. C2×M16×C43D4semidirect
406. C2×#421D43semidirect
447. #421C2×D43semidirect
455. C43#20947semidirect
505. C2×M16C22⋊D43semidirect
506. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191479242
C2×#145829162
C2×#145828722
#191349752
#191343062
#191343042
C2×C43×#4212
#2094743