Finite Group Databasebeta

← #25124442

Subgroups — #25124442

Order 11008.

1332 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583697C211yesmaximal, characteristic
2C2×#14582948C211yesmaximal, characteristic, complemented
3C2×#14582915C211yesmaximal, characteristic, complemented
4#19143114C211yesmaximal, characteristic, complemented
5C2×#14582881C211yesmaximal, characteristic, complemented
6#19135874C214yesmaximal, complemented
7#19135867C214yesmaximal, complemented
8C2×#14582670C211yesmaximal, characteristic, complemented
9C2×C43×#413C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11#14583697—22no—
12#14583697—22no—
13#14583697—22no—
14#14583697—22no—
15C2×#13063356C2212yes—
16C2×#13063355—21no—
17C2×#13063351C2212yes—
18C2×#13063350—21no—
19C2×#13063345—22no—
20C22×#10621877C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23#14582948—22no—
24#14582948C2214yescomplemented
25C2×#13063261—22no—
26#14582915—22no—
27#14582915C2214yes—
28C2×#13063251—22no—
29#14582908C2212yescomplemented
30#14582904C2212yescomplemented
31#14582900—22no—
32#14582895—22no—
33#14582881—22no—
34#14582881C2214yes—
35C2×#13063243—21no—
36C2×#13063241—21no—
37#14582670C2214yescomplemented
38C22×#41×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C22×M16×C43C2211yescharacteristic
41C43×#413—22no—
42C43×#413—22no—
43C2×#101×C43C2212yescomplemented
44C2×#100×C43C2212yescomplemented
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C2×#10621898—21no—
53C2×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621898D412yes—
56C2×#10621898C2312yes—
57C22×Dic86D411yescharacteristic
58C22×D172D411yescharacteristic
59C22×C22⋊D43—21no—
60C22×C4×D43—21no—
61#13063356—24no—
62#13063356—24no—
63#13063355—24no—
64#13063355—24no—
65#13063351—24no—
66#13063351—24no—
67#13063350—24no—
68#13063350—24no—
69#13063345—28no—
70#13063345—28no—
71C2×#10621885—22no—
72C2×#10621883—22no—
73C2×#10621884—22no—
74C2×#10621882—22no—
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621877—21no—
78C2×#10621877—21no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877D412yes—
84C2×#10621877D412yes—
85C2×#10621877C2312yes—
86C2×#10621877C2312yes—
87C22×C43⋊C8—21no—
88C22×C43⋊C8—21no—
89#13063284—21no—
90#13063284—21no—
91#13063284—21no—
92#13063284C2312yes—
93C2×C4⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C4×Dic43—21no—
96#13063261—28no—
97#13063251—28no—
98#13063249—24no—
99#13063246—24no—
100#13063243—24no—
101#13063241—24no—
102C2×#41×C43—21no—
103C2×#41×C43—21no—
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×C43D412yes—
113C2×#41×C43D412yes—
114C22×Q8×C43C2311yescharacteristic
115C22×D4×C43—21no—
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119C2×M16×C43—21no—
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43—21no—
123C2×M16×C43—21no—
124C2×M16×C43—21no—
125C2×M16×C43—21no—
126C2×M16×C43—21no—
127C2×M16×C43D412yes—
128C2×M16×C43D412yes—
129C2×M16×C43C2312yes—
130C2×M16×C43C2312yes—
131C22×C8×C43—21no—
132C22×C8×C43—21no—
133#101×C43—24no—
134#100×C43—24no—
135C24×C43—21no—
136C24×C43#4111yescharacteristic
137C23×D43—21no—
138#41×C43—22no—
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—41no—
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—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C2×D412yes—
160C2×D4×C43—21no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—41no—
168C2×D4×C43—41no—
169C2×D4×C43—41no—
170C2×D4×C43—41no—
171C2×D4×C43C2×D412yes—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—21no—
175C22×C4×C43—41no—
176C22×C4×C43—41no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43#4111yescharacteristic
188C22×C4×C43#4111yescharacteristic
189C22×C4×C43#4111yescharacteristic
190C22×C4×C43#4111yescharacteristic
191C22×C4×C43#4111yescharacteristic
192C22×C4×C43C2411yescharacteristic
193C2×C22⋊D43—22no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43—41no—
196C2×C22⋊D43—41no—
197C2×C22⋊D43—41no—
198C2×C22⋊D43—41no—
199C22×Dic43—21no—
200C22×Dic43—41no—
201#10621898—22no—
202#10621898—22no—
203#10621898—22no—
204#10621898—22no—
205#10621898—22no—
206#10621898—22no—
207#10621898—22no—
208#10621898—22no—
209#10621898—41no—
210#10621898—41no—
211#10621898—41no—
212#10621898—41no—
213#10621898—41no—
214#10621898—41no—
215#10621898—41no—
216#10621898—41no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172C2×D412yes—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—41no—
226C2×C4×D43—41no—
227C2×C4×D43—41no—
228C2×C4×D43—41no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86C2×D412yes—
235M16×C43—22no—
236M16×C43—22no—
237M16×C43—22no—
238M16×C43—22no—
239M16×C43—22no—
240M16×C43—41no—
241M16×C43—41no—
242M16×C43C2×D414yes—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C2×C8×C43—22no—
246C2×C8×C43—22no—
247C2×C8×C43—41no—
248C2×C8×C43—41no—
249C22⋊Dic43—22no—
250C22⋊Dic43—41no—
251#10621885—28no—
252#10621884—28no—
253#10621883—28no—
254#10621882—28no—
255C4⋊Dic43—22no—
256C4⋊Dic43—41no—
257C4×Dic43—22no—
258C4×Dic43—41no—
259#10621877—22no—
260#10621877—22no—
261#10621877—22no—
262#10621877—22no—
263#10621877—22no—
264#10621877—41no—
265#10621877—41no—
266#10621877C2×D414yes—
267C2×C43⋊C8—22no—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—41no—
272C2×C43⋊C8—41no—
273C23×C43—22no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—81no—
277C23×C43—82no—
278C23×C43#12111yescharacteristic
279C23×C43#12111yescharacteristic
280C23×C43#12311yescharacteristic
281C23×C43#12311yescharacteristic
282C23×C43#12411yescharacteristic
283C23×C43#12411yescharacteristic
284C23×C43C2×#4111yescharacteristic
285C22×D43—22no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—82no—
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43—41no—
292Q8×C43—41no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—41no—
300D4×C43—41no—
301C2×C4×C43—22no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12011yescharacteristic
311C2×C4×C43#12011yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12111yescharacteristic
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12111yescharacteristic
318C2×C4×C43#12111yescharacteristic
319C2×C4×C43#12111yescharacteristic
320C2×C4×C43#12111yescharacteristic
321C2×C4×C43#12111yescharacteristic
322C2×C4×C43#12311yescharacteristic
323C2×C4×C43#12311yescharacteristic
324C2×C4×C43#12311yescharacteristic
325C2×C4×C43#12311yescharacteristic
326C2×C4×C43#12311yescharacteristic
327C2×C4×C43#12311yescharacteristic
328C2×C4×C43#12411yescharacteristic
329C2×C4×C43#12411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C2×#4111yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C22⋊D43—42no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C22⋊D43—42no—
340C2×Dic43—22no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—42no—
344C2×Dic43—82no—
345D172—22no—
346D172—22no—
347D172—41no—
348D172—41no—
349C4×D43—42no—
350C4×D43—42no—
351C4×D43—42no—
352C4×D43—42no—
353Dic86—22no—
354Dic86—22no—
355Dic86—41no—
356Dic86—41no—
357C8×C43—24no—
358C8×C43—42no—
359C43⋊C8—24no—
360C43⋊C8—42no—
361#23525—431nomaximal, Sylow
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—42no—
370C22×C43—82no—
371C22×C43—82no—
372C22×C43—82no—
373C22×C43#39411yescharacteristic
374C22×C43#39411yescharacteristic
375C22×C43#39411yescharacteristic
376C22×C43#39411yescharacteristic
377C22×C43C2×#12111yescharacteristic
378C22×C43C2×#12311yescharacteristic
379C22×C43C2×#12411yescharacteristic
380C2×D43—42no—
381C2×D43—82no—
382C2×D43—82no—
383C2×D43—82no—
384C4×C43—42no—
385C4×C43#39411yescharacteristic
386C4×C43#39411yescharacteristic
387C4×C43#39411yescharacteristic
388C4×C43#39411yescharacteristic
389C4×C43C2×#12011yescharacteristic
390C4×C43C2×#12111yescharacteristic
391C4×C43C2×#12111yescharacteristic
392C4×C43C2×#12311yescharacteristic
393Dic43—42no—
394Dic43—82no—
395C2×#575—431no—
396C2×#430—431no—
397C2×#421—431no—
398#2896—431no—
399C2×#413—431no—
400C2×#413D4311yescharacteristic, complemented
401#2049—434no—
402#2048—434no—
403C2×#344—431no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43—21no—
407C2×C43—21no—
408C2×C43—21no—
409C2×C43—21no—
410C2×C43—21no—
411C2×C43—82no—
412C2×C43C2×#39411yescharacteristic
413D43—82no—
414C22×#41—431no—
415C22×#41C2×D4311yescharacteristic
416#575—862no—
417#575—862no—
418#575—862no—
419#575—862no—
420C2×#137—432no—
421C2×#137—861no—
422C2×AGL(1,ℤ/8)—432no—
423C2×AGL(1,ℤ/8)—861no—
424C2×#135—862no—
425C22×M16—431no—
426C22×M16—431no—
427C22×M16C2×D4311yescharacteristic
428C22×M16C2×D4311yescharacteristic
429C2×#117—431no—
430#430—434no—
431#430—862no—
432C2×#108—862no—
433#421—434no—
434#421—862no—
435C2×#104—862no—
436#419—432no—
437#418—432no—
438#417—862no—
439#416—862no—
440#413—22no—
441#413—22no—
442#413—434no—
443#413—862no—
444C2×#101—861no—
445C2×#101C2×D4312yescomplemented
446C2×#100—861no—
447C2×#100C2×D4312yescomplemented
448#344—434no—
449C43#2352511yescharacteristic, complemented, Sylow
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—432no—
461C2×#41—432no—
462C2×#41—861no—
463C2×#41—861no—
464C2×#41—861no—
465C2×#41—861no—
466C2×#41—861no—
467C2×#41—861no—
468C2×#41—861no—
469C2×#41—861no—
470C2×#41—861no—
471C2×#41—861no—
472C2×#41D17212yes—
473C2×#41D17212yes—
474C22×Q8—431no—
475C22×Q8C22×D4311yescharacteristic
476C22×D4—21no—
477C22×D4—431no—
478C22×D4—861no—
479C22×D4C22×D4311yescharacteristic
480C23×C4—21no—
481C23×C4—861no—
482C23×C4C22×D4311yescharacteristic
483#137—864no—
484#137—864no—
485#137—864no—
486#137—864no—
487AGL(1,ℤ/8)—864no—
488AGL(1,ℤ/8)—864no—
489AGL(1,ℤ/8)—864no—
490AGL(1,ℤ/8)—864no—
491#135—868no—
492#135—868no—
493C2×Q16—862no—
494C2×SD16—862no—
495C2×SD16—862no—
496C2×D8—862no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—432no—
506C2×M16—432no—
507C2×M16—432no—
508C2×M16—432no—
509C2×M16—861no—
510C2×M16—861no—
511C2×M16—861no—
512C2×M16—861no—
513C2×M16—861no—
514C2×M16—861no—
515C2×M16—861no—
516C2×M16—861no—
517C2×M16C22⋊D4312yes—
518C2×M16C22⋊D4312yes—
519C2×M16C22×D4312yes—
520C2×M16C22×D4312yes—
521C22×C8—21no—
522C22×C8—21no—
523C22×C8—861no—
524C22×C8—861no—
525#117—432no—
526#117—861no—
527#117—861no—
528#117—861no—
529C2×C4⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C42—861no—
532#108—868no—
533#104—868no—
534#103—864no—
535#102—864no—
536#101—24no—
537#101—864no—
538#100—24no—
539#100—864no—
540C24—21no—
541C24—861no—
542C24#1062189811yescharacteristic
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—862no—
560#41—862no—
561#41—862no—
562#41—862no—
563#41—862no—
564#41—862no—
565#41—862no—
566#41—862no—
567#41—1721no—
568#41—1721no—
569#41—1721no—
570#41—1721no—
571#41—1721no—
572#41—1721no—
573#41—1721no—
574#41—1721no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—432no—
581C2×Q8—861no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8—861no—
585C2×Q8—861no—
586C2×Q8C2×D17212yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—432no—
599C2×D4—862no—
600C2×D4—862no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—1721no—
607C2×D4—1721no—
608C2×D4—1721no—
609C2×D4—1721no—
610C2×D4C2×D17212yes—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—861no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—1721no—
622C22×C4—1721no—
623C22×C4—1721no—
624C22×C4—1721no—
625C22×C4—1721no—
626C22×C4C2×D17211yescharacteristic
627C22×C4C2×D17211yescharacteristic
628C22×C4#1062189811yescharacteristic
629C22×C4D4×D4311yescharacteristic
630C22×C4D4×D4311yescharacteristic
631C22×C4D4×D4311yescharacteristic
632C22×C4D4×D4311yescharacteristic
633C22×C4#1062190011yescharacteristic
634C22×C4#1062190011yescharacteristic
635C22×C4#1062190011yescharacteristic
636C22×C4#1062190011yescharacteristic
637C22×C4C2×C22⋊D4311yescharacteristic
638C22×C4C2×C22⋊D4311yescharacteristic
639C22×C4C23×D4311yescharacteristic
640Q16—868no—
641SD16—868no—
642SD16—868no—
643D8—868no—
644M16—22no—
645M16—22no—
646M16—22no—
647M16—22no—
648M16—22no—
649M16—41no—
650M16—41no—
651M16—434no—
652M16—862no—
653M16—862no—
654M16—862no—
655M16—862no—
656M16—862no—
657M16—1721no—
658M16—1721no—
659M16C2×C22⋊D4314yes—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—862no—
667C2×C8—862no—
668C2×C8—862no—
669C2×C8—862no—
670C2×C8—1721no—
671C2×C8—1721no—
672C4⋊C4—862no—
673C4⋊C4—1721no—
674C22⋊C4—862no—
675C22⋊C4—1721no—
676C42—862no—
677C42—1721no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—82no—
683C23—862no—
684C23—3442no—
685C23—1721no—
686C23—1721no—
687C23#1306329911yescharacteristic
688C23#1306329911yescharacteristic
689C23#1306330711yescharacteristic
690C23#1306330711yescharacteristic
691C23#1306331111yescharacteristic
692C23#1306331111yescharacteristic
693C23C2×#1062189811yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698Q8—862no—
699Q8—862no—
700Q8—1721no—
701Q8—1721no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4—862no—
711D4—862no—
712D4—1722no—
713D4—1722no—
714D4—1722no—
715D4—1722no—
716D4—1721no—
717D4—1721no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—862no—
726C2×C4—3442no—
727C2×C4—1722no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4#1306329511yescharacteristic
735C2×C4#1306329511yescharacteristic
736C2×C4#1306329511yescharacteristic
737C2×C4#1306329511yescharacteristic
738C2×C4#1306329611yescharacteristic
739C2×C4#1306329611yescharacteristic
740C2×C4#1306329611yescharacteristic
741C2×C4#1306329611yescharacteristic
742C2×C4#1306329711yescharacteristic
743C2×C4#1306329711yescharacteristic
744C2×C4#1306329711yescharacteristic
745C2×C4#1306329711yescharacteristic
746C2×C4#1306329911yescharacteristic
747C2×C4#1306329911yescharacteristic
748C2×C4#1306330711yescharacteristic
749C2×C4#1306330711yescharacteristic
750C2×C4#1306330911yescharacteristic
751C2×C4#1306330911yescharacteristic
752C2×C4#1306330911yescharacteristic
753C2×C4#1306330911yescharacteristic
754C2×C4#1306331111yescharacteristic
755C2×C4#1306331111yescharacteristic
756C2×C4C2×D4×D4311yescharacteristic
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4C22×C22⋊D4311yescharacteristic
759C2×C4C22×D17211yescharacteristic
760C2×C4C2×#1062190011yescharacteristic
761C2×C4C2×#1062190011yescharacteristic
762C8—24no—
763C8—42no—
764C8—864no—
765C8—1722no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—3442no—
778C22—3442no—
779C22—3442no—
780C22—1722no—
781C22#1458281511yescharacteristic
782C22#1458281511yescharacteristic
783C22#1458281511yescharacteristic
784C22#1458281511yescharacteristic
785C22C2×#1306329911yescharacteristic
786C22C2×#1306330711yescharacteristic
787C22C2×#1306331111yescharacteristic
788C4—42no—
789C4—3442no—
790C4—1722no—
791C4#1458281511yescharacteristic
792C4#1458281511yescharacteristic
793C4#1458281511yescharacteristic
794C4#1458281511yescharacteristic
795C4C2×#1306329511yescharacteristic
796C4C2×#1306329611yescharacteristic
797C4C2×#1306329711yescharacteristic
798C4C2×#1306330911yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—82no—
807C2—3442no—
808C2C2×#1458281511yescharacteristic
subgroupG/H
centerC4#14582815
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#413C2
socleC2×C43C2×#394
prime radicalC2×#14583697C2
hypercenterC2×#413D43
hypocenterC43#23525
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#14582948C2semidirect
3. C2×#14582915C2semidirect
4. #19143114C2semidirect
5. C2×#14582881C2semidirect
6. #19135874C2semidirect
7. #19135867C2semidirect
8. C2×#14582670C2semidirect
9. C2×C43×#413C2semidirect
24. #14582948C22semidirect
29. #14582908C22semidirect
30. #14582904C22semidirect
37. #14582670C22semidirect
43. C2×#101×C43C22semidirect
44. C2×#100×C43C22semidirect
400. C2×#413D43semidirect
445. C2×#101C2×D43semidirect
447. C2×#100C2×D43semidirect
449. C43#23525semidirect

Maximal subgroups

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

subgroupindex
C2×#145836972
C2×#145829482
C2×#145829152
#191431142
C2×#145828812
#191358742
#191358672
C2×#145826702
C2×C43×#4132
#2352543