Finite Group Databasebeta

← #25098467

Subgroups — #25098467

Order 11008.

1664 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×#14583697C211yesmaximal, characteristic
2C2×#14583665C211yesmaximal, characteristic, complemented
3C2×#14582917C211yesmaximal, characteristic, complemented
4C2×#14582883C211yesmaximal, characteristic, complemented
5#19135072C214yesmaximal, complemented
6#19135065C214yesmaximal, complemented
7C2×#14582669C211yesmaximal, characteristic, complemented
8C2×C43⋊#338C211yesmaximal, characteristic, complemented
9C43×#2896C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11#14583697—22no—
12#14583697—22no—
13#14583697—22no—
14#14583697—22no—
15C2×#13063356C2212yes—
16C2×#13063355C412yescomplemented
17C2×#13063351C2212yes—
18C2×#13063350C412yescomplemented
19C2×#13063345C414yescomplemented
20#14583665—22no—
21#14583665—22no—
22#14583665—22no—
23#14583665C2214yes—
24C2×#13063333—22no—
25C2×#13063331—22no—
26C22×#10621877C2211yescharacteristic
27C22×#10621877C2211yescharacteristic
28C22×#10621877C2211yescharacteristic
29C2×M16×D43—22no—
30#14582917—22no—
31#14582917C2214yes—
32C2×#13063253—22no—
33#14582883—22no—
34#14582883—22no—
35C2×#13063244C2212yescomplemented
36C2×#13063242C2212yescomplemented
37#14582669C2214yescomplemented
38C43⋊#338C2214yescomplemented
39C22×#41×C43C2211yescharacteristic
40C22×M16×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C43×#419C2212yescomplemented
43C43×#418C2212yescomplemented
44C43×#417—22no—
45C43×#416—22no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C2×#10621898C2×C412yes—
53C2×#10621898D412yes—
54C2×#10621898D412yes—
55C2×#10621898D412yes—
56C2×#10621898D412yes—
57C2×#10621898C2312yes—
58C22×Dic86C2×C411yescharacteristic
59C22×D172C2×C411yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62#13063356—24no—
63#13063356—24no—
64#13063355—24no—
65#13063355—24no—
66#13063351—24no—
67#13063351—24no—
68#13063350—24no—
69#13063350—24no—
70#13063345—28no—
71#13063345—28no—
72C2×#10621885C2×C414yescomplemented
73C2×#10621883C2×C414yescomplemented
74C2×#10621884C2×C414yescomplemented
75C2×#10621882C2×C414yescomplemented
76#13063333—28no—
77#13063333—28no—
78#13063331—28no—
79#13063331—28no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C2×#10621877—21no—
86C2×#10621877—21no—
87C2×#10621877—21no—
88C2×#10621877—21no—
89C2×#10621877—21no—
90C2×#10621877—21no—
91C2×#10621877—21no—
92C2×#10621877C2×C412yes—
93C2×#10621877D412yes—
94C2×#10621877D412yes—
95C2×#10621877C2312yes—
96C2×#10621877C2312yes—
97C2×#10621877C2312yes—
98C2×#10621872—24no—
99M16×D43—28no—
100M16×D43—28no—
101C22×C43⋊C8—21no—
102C22×C43⋊C8—21no—
103C22×C43⋊C8C2×C412yes—
104C2×C8×D43—24no—
105#13063253—28no—
106#13063244—24no—
107#13063242—24no—
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×C43—21no—
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117C2×#41×C43—21no—
118C2×#41×C43C2×C412yes—
119C2×#41×C43C2×C412yes—
120C22×Q8×C43C2311yescharacteristic
121C22×D4×C43—21no—
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C2×M16×C43—21no—
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C2×M16×C43—21no—
129C2×M16×C43D412yes—
130C2×M16×C43C2312yes—
131C22×C8×C43D412yes—
132#117×C43—21no—
133#117×C43—21no—
134#117×C43—21no—
135#117×C43C2312yes—
136C2×C4⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43—21no—
139#103×C43—24no—
140#102×C43—24no—
141C24×C43—21no—
142C24×C43#4111yescharacteristic
143C23×D43—21no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—22no—
147#41×C43—22no—
148#41×C43—22no—
149#41×C43—22no—
150#41×C43—22no—
151#41×C43—22no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—41no—
157#41×C43—41no—
158#41×C43—41no—
159#41×C43—41no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43C22×C412yes—
166C2×D4×C43—21no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—41no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43—41no—
177C2×D4×C43C22×C412yes—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—21no—
181C22×C4×C43—41no—
182C22×C4×C43—41no—
183C22×C4×C43—41no—
184C22×C4×C43—41no—
185C22×C4×C43—41no—
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43#4111yescharacteristic
197C22×C4×C43#4111yescharacteristic
198C22×C4×C43#4111yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—22no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—22no—
205C2×C22⋊D43—22no—
206C22×Dic43—21no—
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#10621898C22⋊C414yes—
220#10621898C22⋊C414yes—
221#10621898C2×D414yes—
222#10621898C2×D414yes—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172C22⋊C412yes—
227C2×D172C22⋊C412yes—
228C2×D172C22×C412yes—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86C22⋊C412yes—
239C2×Dic86C22⋊C412yes—
240C2×Dic86C22×C412yes—
241M16×C43—22no—
242M16×C43—22no—
243M16×C43—22no—
244M16×C43—22no—
245C2×C8×C43—22no—
246C2×C8×C43—22no—
247C2×C8×C43C2×D414yes—
248C4⋊C4×C43—22no—
249C4⋊C4×C43—41no—
250C22⋊C4×C43—22no—
251C22⋊C4×C43—41no—
252C42×C43—22no—
253C42×C43—41no—
254#10621885—28no—
255#10621884—28no—
256#10621883—28no—
257#10621882—28no—
258#10621877—22no—
259#10621877—22no—
260#10621877—22no—
261#10621877—22no—
262#10621877—22no—
263#10621877—22no—
264#10621877—22no—
265#10621877—22no—
266#10621877—22no—
267#10621877—41no—
268#10621877—41no—
269#10621877C2×D414yes—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—22no—
276C2×C43⋊C8—41no—
277C2×C43⋊C8—41no—
278C2×C43⋊C8C22×C414yes—
279#10621872—216no—
280C8×D43—216no—
281C23×C43—22no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—81no—
285C23×C43—82no—
286C23×C43C4×D411yescharacteristic
287C23×C43C4×D411yescharacteristic
288C23×C43#12111yescharacteristic
289C23×C43#12111yescharacteristic
290C23×C43#12311yescharacteristic
291C23×C43#12311yescharacteristic
292C23×C43C2×#4111yescharacteristic
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—82no—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—41no—
300Q8×C43—41no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—42no—
304D4×C43—42no—
305D4×C43—42no—
306D4×C43—42no—
307D4×C43—41no—
308D4×C43—41no—
309C2×C4×C43—22no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—82no—
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C2×C22⋊C411yescharacteristic
322C2×C4×C43C4×D411yescharacteristic
323C2×C4×C43C4×D411yescharacteristic
324C2×C4×C43C4×D411yescharacteristic
325C2×C4×C43C4×D411yescharacteristic
326C2×C4×C43C4×D411yescharacteristic
327C2×C4×C43C4×D411yescharacteristic
328C2×C4×C43#12011yescharacteristic
329C2×C4×C43#12011yescharacteristic
330C2×C4×C43#12011yescharacteristic
331C2×C4×C43#12011yescharacteristic
332C2×C4×C43#12111yescharacteristic
333C2×C4×C43#12111yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12111yescharacteristic
336C2×C4×C43#12111yescharacteristic
337C2×C4×C43#12111yescharacteristic
338C2×C4×C43#12311yescharacteristic
339C2×C4×C43#12311yescharacteristic
340C2×C4×C43C23×C411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C22⋊D43—24no—
347C22⋊D43—24no—
348C22⋊D43—24no—
349C22⋊D43—24no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353D172—22no—
354D172—22no—
355D172—22no—
356D172C2×C22⋊C414yes—
357C4×D43—24no—
358C4×D43—24no—
359C4×D43—24no—
360C4×D43—24no—
361Dic86—22no—
362Dic86—22no—
363Dic86—22no—
364Dic86C2×C22⋊C414yes—
365C8×C43—24no—
366C43⋊C8—24no—
367C43⋊C8—24no—
368C43⋊C8—42no—
369#20995—431nomaximal, Sylow
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—42no—
378C22×C43—82no—
379C22×C43—82no—
380C22×C43—82no—
381C22×C43#38611yescharacteristic
382C22×C43#38611yescharacteristic
383C22×C43#38611yescharacteristic
384C22×C43#38611yescharacteristic
385C22×C43C2×C4×D411yescharacteristic
386C22×C43C2×#12111yescharacteristic
387C22×C43C2×#12311yescharacteristic
388C2×D43—24no—
389C2×D43—44no—
390C2×D43—82no—
391C2×D43—82no—
392C4×C43—42no—
393C4×C43—82no—
394C4×C43#38611yescharacteristic
395C4×C43#38611yescharacteristic
396C4×C43#38611yescharacteristic
397C4×C43#38611yescharacteristic
398C4×C43C22×C22⋊C411yescharacteristic
399C4×C43C2×C4×D411yescharacteristic
400C4×C43C2×#12011yescharacteristic
401C4×C43C2×#12111yescharacteristic
402Dic43—24no—
403C2×#575—431no—
404C2×#568—431no—
405C2×#421—431no—
406#2896D4311yescharacteristic, complemented
407C2×#413—431no—
408#1903—434no—
409#1902—434no—
410C2×#344—431no—
411C2×#338—431no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43—21no—
419C2×C43—82no—
420C2×C43C2×#38611yescharacteristic
421D43—44no—
422C22×#41—431no—
423C22×#41C2×D4311yescharacteristic
424#575—862no—
425#575—862no—
426#575—862no—
427#575—862no—
428C2×#137—432no—
429C2×#137—432no—
430C2×AGL(1,ℤ/8)—432no—
431C2×AGL(1,ℤ/8)—432no—
432C2×#135—434no—
433#568—434no—
434#568—862no—
435#568—862no—
436#568—862no—
437C2×#131—862no—
438C2×#131—862no—
439C22×M16—431no—
440C22×M16—431no—
441C22×M16—431no—
442C22×M16—862no—
443C22×M16C2×D4311yescharacteristic
444C2×#117C2×D4311yescharacteristic
445#421—434no—
446#421—862no—
447C2×#104—862no—
448#419C2×D4312yescomplemented
449#418C2×D4312yescomplemented
450#417—22no—
451#416—22no—
452#413—862no—
453#413—862no—
454C2×#101—432no—
455C2×#100—432no—
456#344—434no—
457#338—434no—
458C43#2099511yescharacteristic, complemented, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—432no—
470C2×#41—432no—
471C2×#41—432no—
472C2×#41—432no—
473C2×#41—432no—
474C2×#41—432no—
475C2×#41—861no—
476C2×#41—861no—
477C2×#41—861no—
478C2×#41—861no—
479C2×#41—861no—
480C2×#41—861no—
481C2×#41C4×D4312yes—
482C2×#41C4×D4312yes—
483C22×Q8—431no—
484C22×Q8C22×D4311yescharacteristic
485C22×D4—21no—
486C22×D4—431no—
487C22×D4—861no—
488C22×D4C22×D4311yescharacteristic
489C23×C4—21no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492#137—864no—
493#137—864no—
494#137—864no—
495#137—864no—
496AGL(1,ℤ/8)—864no—
497AGL(1,ℤ/8)—864no—
498AGL(1,ℤ/8)—864no—
499AGL(1,ℤ/8)—864no—
500#135—868no—
501#135—868no—
502C2×Q16—434no—
503C2×SD16—434no—
504C2×SD16—434no—
505C2×D8—434no—
506#131—868no—
507#131—868no—
508#131—868no—
509#131—868no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—432no—
515C2×M16—432no—
516C2×M16—432no—
517C2×M16—432no—
518C2×M16—432no—
519C2×M16—432no—
520C2×M16—864no—
521C2×M16—868no—
522C2×M16—868no—
523C2×M16—861no—
524C2×M16—861no—
525C2×M16—861no—
526C2×M16—861no—
527C2×M16—861no—
528C2×M16—861no—
529C2×M16—861no—
530C2×M16—861no—
531C2×M16—861no—
532C2×M16—861no—
533C2×M16—861no—
534C2×M16—861no—
535C2×M16C22⋊D4312yes—
536C2×M16C22×D4312yes—
537C22×C8—432no—
538C22×C8—864no—
539C22×C8—861no—
540C22×C8—861no—
541C22×C8C22⋊D4312yes—
542#117—21no—
543#117—21no—
544#117—21no—
545#117C22×D4312yes—
546C2×C4⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C42—21no—
549#104—868no—
550#103—24no—
551#102—24no—
552#101—864no—
553#100—864no—
554C24—21no—
555C24—861no—
556C24#1062190011yescharacteristic
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—434no—
574#41—434no—
575#41—434no—
576#41—434no—
577#41—862no—
578#41—862no—
579#41—862no—
580#41—862no—
581#41—862no—
582#41—862no—
583#41—862no—
584#41—862no—
585#41—862no—
586#41—862no—
587#41—862no—
588#41—862no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—432no—
595C2×Q8—432no—
596C2×Q8—432no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—861no—
600C2×Q8C2×C4×D4312yes—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—432no—
613C2×D4—432no—
614C2×D4—432no—
615C2×D4—862no—
616C2×D4—862no—
617C2×D4—862no—
618C2×D4—862no—
619C2×D4—862no—
620C2×D4—862no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4C2×C4×D4312yes—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—861no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4C2×C4×D4311yescharacteristic
641C22×C4C2×C4×D4311yescharacteristic
642C22×C4#1062189811yescharacteristic
643C22×C4#1062189811yescharacteristic
644C22×C4D4×D4311yescharacteristic
645C22×C4D4×D4311yescharacteristic
646C22×C4D4×D4311yescharacteristic
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4D4×D4311yescharacteristic
650C22×C4#1062190011yescharacteristic
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C23×D4311yescharacteristic
654Q16—868no—
655SD16—868no—
656SD16—868no—
657D8—868no—
658M16—22no—
659M16—22no—
660M16—22no—
661M16—22no—
662M16—434no—
663M16—8616no—
664M16—862no—
665M16—862no—
666M16—862no—
667M16—862no—
668M16—862no—
669M16—862no—
670M16—862no—
671M16—862no—
672M16—862no—
673M16—1721no—
674M16—1721no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—434no—
678C2×C8—8616no—
679C2×C8—862no—
680C2×C8—862no—
681C2×C8—862no—
682C2×C8—862no—
683C2×C8—862no—
684C2×C8—862no—
685C2×C8—1721no—
686C2×C8—1721no—
687C2×C8C2×C22⋊D4314yes—
688C4⋊C4—22no—
689C4⋊C4—41no—
690C22⋊C4—22no—
691C22⋊C4—41no—
692C42—22no—
693C42—41no—
694C23—22no—
695C23—41no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—3442no—
703C23(C22⋊D43)⋊C411yescharacteristic
704C23(C22⋊D43)⋊C411yescharacteristic
705C23#1306329611yescharacteristic
706C23#1306329611yescharacteristic
707C23#1306330711yescharacteristic
708C23#1306330711yescharacteristic
709C23C2×#1062190011yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—41no—
713Q8—41no—
714Q8—434no—
715Q8—862no—
716Q8—862no—
717Q8—862no—
718D4—22no—
719D4—22no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—41no—
725D4—41no—
726D4—434no—
727D4—864no—
728D4—864no—
729D4—864no—
730D4—864no—
731D4—862no—
732D4—862no—
733D4—862no—
734C2×C4—22no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—82no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—864no—
747C2×C4—864no—
748C2×C4—864no—
749C2×C4—864no—
750C2×C4C22⋊C4×D4311yescharacteristic
751C2×C4C22⋊C4×D4311yescharacteristic
752C2×C4C22⋊C4×D4311yescharacteristic
753C2×C4C22⋊C4×D4311yescharacteristic
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#1306329811yescharacteristic
769C2×C4#1306329811yescharacteristic
770C2×C4#1306330711yescharacteristic
771C2×C4#1306330711yescharacteristic
772C2×C4C22×C4×D4311yescharacteristic
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C2×D4×D4311yescharacteristic
776C2×C4C22×C22⋊D4311yescharacteristic
777C2×C4C2×#1062189811yescharacteristic
778C8—24no—
779C8—864no—
780C8—864no—
781C8—1722no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—864no—
794C22—3442no—
795C22—3442no—
796C22—1724no—
797C22#1458277511yescharacteristic
798C22#1458277511yescharacteristic
799C22#1458277511yescharacteristic
800C22#1458277511yescharacteristic
801C22C2×(C22⋊D43)⋊C411yescharacteristic
802C22C2×#1306329611yescharacteristic
803C22C2×#1306330711yescharacteristic
804C4—42no—
805C4—82no—
806C4—864no—
807C4#1458277511yescharacteristic
808C4#1458277511yescharacteristic
809C4#1458277511yescharacteristic
810C4#1458277511yescharacteristic
811C4C2×C22⋊C4×D4311yescharacteristic
812C4C2×C4×C22⋊D4311yescharacteristic
813C4C2×#1306329311yescharacteristic
814C4C2×#1306329811yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—82no—
823C2—1724no—
824C2C2×#1458277511yescharacteristic
subgroupG/H
centerC4#14582775
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2896C2
socleC2×C43C2×#386
prime radicalC2×#14583697C2
cosocleC22×C4×C43C24
hypercenter#2896D43
hypocenterC43#20995
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. C2×#14583665C2semidirect
3. C2×#14582917C2semidirect
4. C2×#14582883C2semidirect
5. #19135072C2semidirect
6. #19135065C2semidirect
7. C2×#14582669C2semidirect
8. C2×C43⋊#338C2semidirect
9. C43×#2896C2semidirect
16. C2×#13063355C4semidirect
18. C2×#13063350C4semidirect
19. C2×#13063345C4semidirect
35. C2×#13063244C22semidirect
36. C2×#13063242C22semidirect
37. #14582669C22semidirect
38. C43⋊#338C22semidirect
42. C43×#419C22semidirect
43. C43×#418C22semidirect
72. C2×#10621885C2×C4semidirect
73. C2×#10621883C2×C4semidirect
74. C2×#10621884C2×C4semidirect
75. C2×#10621882C2×C4semidirect
406. #2896D43semidirect
448. #419C2×D43semidirect
449. #418C2×D43semidirect
458. C43#20995semidirect

Maximal subgroups

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

subgroupindex
C2×#145836972
C2×#145836652
C2×#145829172
C2×#145828832
#191350722
#191350652
C2×#145826692
C2×C43⋊#3382
C43×#28962
#2099543