Finite Group Databasebeta

← C2×#19135899 #25124512

Subgroups — C2×#19135899 #25124512

Order 11008.

1366 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583697C211yesmaximal, characteristic
2C2×#14582925C211yesmaximal, characteristic, complemented
3C2×#14582896C211yesmaximal, characteristic, complemented
4C2×#14582873C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic, complemented
6#19135899C218yesmaximal, direct product factor
7C2×#14582655C211yesmaximal, characteristic, complemented
8C2×C43×#416C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583697—22no—
11#14583697—22no—
12#14583697—22no—
13#14583697C2214yes—
14C2×#13063356—21no—
15C2×#13063355—21no—
16C2×#13063351—21no—
17C2×#13063350—21no—
18C2×#13063345—22no—
19C22×#10621877C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14582925—22no—
23#14582925C2214yescomplemented
24C2×Dic43⋊C8—22no—
25#14582896—22no—
26#14582896C2214yescomplemented
27C2×#13063250—21no—
28C2×#13063247—21no—
29#14582873—22no—
30#14582873C2214yescomplemented
31#14582872—22no—
32#14582872C2214yescomplemented
33C2×#13063240—22no—
34C2×#13063239—22no—
35#14582655C2214yescomplemented
36C22×#41×C43C2211yescharacteristic
37C23×C8×C43C2211yescharacteristic
38C2×#117×C43C2211yescharacteristic
39C43×#416—22no—
40C43×#416C2214yescomplemented
41C2×#103×C43—21no—
42C2×#102×C43—21no—
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×#10621898—21no—
52C2×#10621898—21no—
53C2×#10621898D412yes—
54C2×#10621898C2312yes—
55C22×Dic86D411yescharacteristic
56C22×D172D411yescharacteristic
57C22×C22⋊D43—21no—
58C22×C4×D43—21no—
59#13063356—24no—
60#13063356—24no—
61#13063355—24no—
62#13063355—24no—
63#13063351—24no—
64#13063351—24no—
65#13063350—24no—
66#13063350—24no—
67#13063345—28no—
68#13063345—28no—
69C2×#10621885—22no—
70C2×#10621883—22no—
71C2×#10621884—22no—
72C2×#10621882—22no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621877D412yes—
78C2×#10621877C2312yes—
79C22×C43⋊C8D412yes—
80#13063284—21no—
81#13063284—21no—
82#13063284—21no—
83#13063284—21no—
84#13063284—21no—
85#13063284D412yes—
86#13063284C2312yes—
87#13063284C2312yes—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43D412yes—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94Dic43⋊C8—28no—
95#13063250—24no—
96#13063247—24no—
97#13063240—28no—
98#13063239—28no—
99C2×#41×C43—21no—
100C2×#41×C43—21no—
101C2×#41×C43—21no—
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×C43D412yes—
110C2×#41×C43C2312yes—
111C22×Q8×C43D411yescharacteristic
112C22×D4×C43—21no—
113C22×D4×C43D411yescharacteristic
114C23×C4×C43—21no—
115C23×C4×C43C2311yescharacteristic
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119C22×C8×C43—21no—
120C22×C8×C43—21no—
121C22×C8×C43—21no—
122C22×C8×C43C2312yes—
123#117×C43—21no—
124#117×C43—21no—
125#117×C43—21no—
126#117×C43C2312yes—
127C2×C4⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43—21no—
130#103×C43—24no—
131#102×C43—24no—
132C24×C43—21no—
133C24×C43C2×D411yescharacteristic
134C23×D43—21no—
135#41×C43—22no—
136#41×C43—22no—
137#41×C43—22no—
138#41×C43—22no—
139#41×C43—22no—
140#41×C43—22no—
141#41×C43—22no—
142#41×C43—22no—
143#41×C43—41no—
144#41×C43—41no—
145#41×C43—41no—
146#41×C43—41no—
147#41×C43—41no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43C2×D412yes—
157C2×D4×C43—21no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—41no—
165C2×D4×C43—41no—
166C2×D4×C43—41no—
167C2×D4×C43—41no—
168C2×D4×C43C2×D412yes—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—21no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43—41no—
176C22×C4×C43—41no—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43#4111yescharacteristic
185C22×C4×C43#4111yescharacteristic
186C22×C4×C43#4111yescharacteristic
187C22×C4×C43#4111yescharacteristic
188C22×C4×C43#4111yescharacteristic
189C22×C4×C43#4111yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—41no—
194C2×C22⋊D43—41no—
195C2×C22⋊D43—41no—
196C2×C22⋊D43—41no—
197C22×Dic43—22no—
198C22×Dic43—21no—
199C22×Dic43—41no—
200#10621898—22no—
201#10621898—22no—
202#10621898—22no—
203#10621898—22no—
204#10621898—22no—
205#10621898—22no—
206#10621898—22no—
207#10621898—22no—
208#10621898—41no—
209#10621898—41no—
210#10621898—41no—
211#10621898—41no—
212#10621898—41no—
213#10621898—41no—
214#10621898—41no—
215#10621898—41no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172C2×D412yes—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—41no—
225C2×C4×D43—41no—
226C2×C4×D43—41no—
227C2×C4×D43—41no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86C2×D412yes—
234C2×C8×C43—22no—
235C2×C8×C43—22no—
236C2×C8×C43—22no—
237C2×C8×C43—41no—
238C2×C8×C43—41no—
239C2×C8×C43—41no—
240C2×C8×C43—41no—
241C4⋊C4×C43—22no—
242C4⋊C4×C43—41no—
243C22⋊C4×C43—22no—
244C22⋊C4×C43—41no—
245C42×C43—22no—
246C42×C43—41no—
247C22⋊Dic43—22no—
248C22⋊Dic43—22no—
249C22⋊Dic43—41no—
250C22⋊Dic43C2×D414yes—
251#10621885—28no—
252#10621884—28no—
253#10621883—28no—
254#10621882—28no—
255C4⋊Dic43—22no—
256C4⋊Dic43—22no—
257C4⋊Dic43—22no—
258C4⋊Dic43—41no—
259C4×Dic43—22no—
260C4×Dic43—22no—
261C4×Dic43—22no—
262C4×Dic43—41no—
263#10621877—22no—
264#10621877—22no—
265#10621877—22no—
266#10621877—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8—22no—
269C2×C43⋊C8C2×D414yes—
270C23×C43—22no—
271C23×C43—42no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—82no—
275C23×C43#12111yescharacteristic
276C23×C43#12111yescharacteristic
277C23×C43#12111yescharacteristic
278C23×C43#12111yescharacteristic
279C23×C43#12111yescharacteristic
280C23×C43#12111yescharacteristic
281C23×C43C22×D411yescharacteristic
282C22×D43—22no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—82no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—41no—
289Q8×C43—41no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—42no—
293D4×C43—42no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—41no—
297D4×C43—41no—
298C2×C4×C43—22no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—82no—
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12011yescharacteristic
311C2×C4×C43#12111yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12111yescharacteristic
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12311yescharacteristic
318C2×C4×C43#12311yescharacteristic
319C2×C4×C43#12311yescharacteristic
320C2×C4×C43#12311yescharacteristic
321C2×C4×C43#12311yescharacteristic
322C2×C4×C43#12311yescharacteristic
323C2×C4×C43#12311yescharacteristic
324C2×C4×C43#12311yescharacteristic
325C2×C4×C43#12411yescharacteristic
326C2×C4×C43#12411yescharacteristic
327C2×C4×C43#12411yescharacteristic
328C2×C4×C43#12411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43C2×#4111yescharacteristic
334C2×C4×C43C2×#4111yescharacteristic
335C22⋊D43—42no—
336C22⋊D43—42no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C2×Dic43—24no—
340C2×Dic43—22no—
341C2×Dic43—44no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—42no—
345C2×Dic43—82no—
346D172—22no—
347D172—22no—
348D172—41no—
349D172—41no—
350C4×D43—42no—
351C4×D43—42no—
352C4×D43—42no—
353C4×D43—42no—
354Dic86—22no—
355Dic86—22no—
356Dic86—41no—
357Dic86—41no—
358C8×C43—42no—
359C43⋊C8—24no—
360C2×#2053—431nomaximal, Sylow
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—42no—
369C22×C43—82no—
370C22×C43—82no—
371C22×C43—82no—
372C22×C43#39411yescharacteristic
373C22×C43#39411yescharacteristic
374C22×C43#39411yescharacteristic
375C22×C43#39411yescharacteristic
376C22×C43C2×#12111yescharacteristic
377C22×C43C2×#12111yescharacteristic
378C22×C43C2×#12111yescharacteristic
379C2×D43—42no—
380C2×D43—82no—
381C2×D43—82no—
382C2×D43—82no—
383C4×C43—42no—
384C4×C43—82no—
385C4×C43#39411yescharacteristic
386C4×C43#39411yescharacteristic
387C4×C43#39411yescharacteristic
388C4×C43#39411yescharacteristic
389C4×C43C2×#12011yescharacteristic
390C4×C43C2×#12311yescharacteristic
391C4×C43C2×#12311yescharacteristic
392C4×C43C2×#12411yescharacteristic
393Dic43—44no—
394Dic43—42no—
395Dic43—82no—
396C2×#575—431no—
397C2×#424—431no—
398C2×#416—431no—
399C2×#416D4311yescharacteristic, complemented
400C2×#410—431no—
401C2×#410—431no—
402#2053—438no—
403C2×H(3,ℤ/4)—431no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43—21no—
407C2×C43—21no—
408C2×C43—21no—
409C2×C43—21no—
410C2×C43—82no—
411C2×C43#205312yescomplemented
412C2×C43C2×#39411yescharacteristic
413D43—82no—
414C22×#41—431no—
415C22×#41C2×D4311yescharacteristic
416#575—434no—
417#575—862no—
418#575—862no—
419#575—862no—
420C2×#137—861no—
421C2×#137—861no—
422C2×AGL(1,ℤ/8)—861no—
423C2×AGL(1,ℤ/8)—861no—
424C2×#135—862no—
425C22×M16—431no—
426C23×C8C2×D4311yescharacteristic
427C2×#117—431no—
428C2×#117—431no—
429C2×#117C2×D4311yescharacteristic
430#424—434no—
431#424—862no—
432C2×C4⋊C8—862no—
433#416—22no—
434#416—434no—
435#416—862no—
436#416C2×D4314yescomplemented
437C2×#103—21no—
438C2×#103—861no—
439C2×#102—21no—
440C2×#102—861no—
441#410—434no—
442#410—434no—
443#410—862no—
444#410—862no—
445C2×#99—862no—
446C2×#99—862no—
447H(3,ℤ/4)—434no—
448C43C2×#205311yescharacteristic, complemented, Sylow
449C2×#41—21no—
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—432no—
460C2×#41—432no—
461C2×#41—861no—
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×#41C22⋊D4312yes—
472C2×#41C22×D4312yes—
473C22×Q8—431no—
474C22×Q8C22⋊D4311yescharacteristic
475C22×D4—21no—
476C22×D4—431no—
477C22×D4—861no—
478C22×D4C22⋊D4311yescharacteristic
479C23×C4—21no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482#137—864no—
483#137—864no—
484#137—864no—
485#137—864no—
486AGL(1,ℤ/8)—864no—
487AGL(1,ℤ/8)—864no—
488AGL(1,ℤ/8)—864no—
489AGL(1,ℤ/8)—864no—
490#135—868no—
491#135—868no—
492C2×Q16—862no—
493C2×SD16—862no—
494C2×SD16—862no—
495C2×D8—862no—
496C2×M16—432no—
497C2×M16—432no—
498C2×M16—861no—
499C2×M16—861no—
500C2×M16—861no—
501C2×M16—861no—
502C22×C8—21no—
503C22×C8—21no—
504C22×C8—21no—
505C22×C8—21no—
506C22×C8—21no—
507C22×C8—21no—
508C22×C8—432no—
509C22×C8C22×D4312yes—
510#117—21no—
511#117—21no—
512#117—21no—
513#117—432no—
514#117—432no—
515#117—432no—
516#117—861no—
517#117—861no—
518#117—861no—
519#117—861no—
520#117—861no—
521#117C22×D4312yes—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—432no—
527C2×C22⋊C4—861no—
528C2×C42—21no—
529C2×C42—861no—
530C2×C42—861no—
531C4⋊C8—868no—
532#103—24no—
533#103—864no—
534#102—24no—
535#102—864no—
536#99—868no—
537#99—868no—
538C24—21no—
539C24—861no—
540C24D4×D4311yescharacteristic
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—862no—
558#41—862no—
559#41—862no—
560#41—862no—
561#41—862no—
562#41—862no—
563#41—862no—
564#41—862no—
565#41—1721no—
566#41—1721no—
567#41—1721no—
568#41—1721no—
569#41—1721no—
570#41—1721no—
571#41—1721no—
572#41—1721no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—432no—
579C2×Q8—861no—
580C2×Q8—861no—
581C2×Q8—861no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8C2×C22⋊D4312yes—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—432no—
597C2×D4—862no—
598C2×D4—862no—
599C2×D4—861no—
600C2×D4—861no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—1721no—
605C2×D4—1721no—
606C2×D4—1721no—
607C2×D4—1721no—
608C2×D4C2×C22⋊D4312yes—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—862no—
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×C4#1062189811yescharacteristic
627C22×C4#1062189811yescharacteristic
628C22×C4#1062189811yescharacteristic
629C22×C4#1062189811yescharacteristic
630C22×C4D4×D4311yescharacteristic
631C22×C4D4×D4311yescharacteristic
632C22×C4D4×D4311yescharacteristic
633C22×C4D4×D4311yescharacteristic
634C22×C4D4×D4311yescharacteristic
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—862no—
645M16—862no—
646M16—862no—
647M16—862no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—434no—
656C2×C8—862no—
657C2×C8—862no—
658C4⋊C4—22no—
659C4⋊C4—41no—
660C4⋊C4—862no—
661C4⋊C4—862no—
662C4⋊C4—862no—
663C4⋊C4—1721no—
664C22⋊C4—22no—
665C22⋊C4—41no—
666C22⋊C4—434no—
667C22⋊C4—862no—
668C22⋊C4—862no—
669C22⋊C4—1721no—
670C42—22no—
671C42—41no—
672C42—862no—
673C42—862no—
674C42—862no—
675C42—1721no—
676C23—22no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—82no—
681C23—862no—
682C23—3442no—
683C23—1721no—
684C23—1721no—
685C23#1306329711yescharacteristic
686C23#1306329711yescharacteristic
687C23#1306329811yescharacteristic
688C23#1306329811yescharacteristic
689C23#1306329811yescharacteristic
690C23#1306329811yescharacteristic
691C23C2×D4×D4311yescharacteristic
692Q8—22no—
693Q8—22no—
694Q8—41no—
695Q8—41no—
696Q8—862no—
697Q8—862no—
698Q8—1721no—
699Q8—1721no—
700D4—22no—
701D4—22no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—41no—
707D4—41no—
708D4—862no—
709D4—862no—
710D4—1722no—
711D4—1722no—
712D4—1722no—
713D4—1722no—
714D4—1721no—
715D4—1721no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—82no—
725C2×C4—864no—
726C2×C4—862no—
727C2×C4—3442no—
728C2×C4—1722no—
729C2×C4—1724no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4#1306329311yescharacteristic
737C2×C4#1306329311yescharacteristic
738C2×C4#1306329311yescharacteristic
739C2×C4#1306329311yescharacteristic
740C2×C4#1306329711yescharacteristic
741C2×C4#1306329711yescharacteristic
742C2×C4#1306329811yescharacteristic
743C2×C4#1306329811yescharacteristic
744C2×C4#1306329811yescharacteristic
745C2×C4#1306329811yescharacteristic
746C2×C4#1306330711yescharacteristic
747C2×C4#1306330711yescharacteristic
748C2×C4#1306330711yescharacteristic
749C2×C4#1306330711yescharacteristic
750C2×C4#1306330811yescharacteristic
751C2×C4#1306330811yescharacteristic
752C2×C4#1306330811yescharacteristic
753C2×C4#1306330811yescharacteristic
754C2×C4#1306331111yescharacteristic
755C2×C4#1306331111yescharacteristic
756C2×C4#1306331111yescharacteristic
757C2×C4#1306331111yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4C2×D4×D4311yescharacteristic
760C2×C4C22×C22⋊D4311yescharacteristic
761C2×C4C2×#1062190011yescharacteristic
762C2×C4C2×#1062189811yescharacteristic
763C2×C4C2×#1062189811yescharacteristic
764C8—42no—
765C8—864no—
766C22—22no—
767C22—22no—
768C22—22no—
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#1458281411yescharacteristic
782C22#1458281411yescharacteristic
783C22#1458281411yescharacteristic
784C22#1458281411yescharacteristic
785C22C2×#1306329711yescharacteristic
786C22C2×#1306329811yescharacteristic
787C22C2×#1306329811yescharacteristic
788C4—42no—
789C4—82no—
790C4—3442no—
791C4—1724no—
792C4—1722no—
793C4#1458281411yescharacteristic
794C4#1458281411yescharacteristic
795C4#1458281411yescharacteristic
796C4#1458281411yescharacteristic
797C4C2×#1306329311yescharacteristic
798C4C2×#1306330711yescharacteristic
799C4C2×#1306330811yescharacteristic
800C4C2×#1306331111yescharacteristic
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—82no—
808C2—3442no—
809C2#1913589912yesdirect product factor
810C2C2×#1458281411yescharacteristic
subgroupG/H
centerC2×C4#13063311
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#416C2
socleC22×C43#394
prime radicalC2×#14583697C2
hypercenterC2×#416D43
hypocenterC43C2×#2053
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#14582925C2semidirect
3. C2×#14582896C2semidirect
4. C2×#14582873C2semidirect
5. C2×#14582872C2semidirect
6. #19135899C2direct (N × H)
7. C2×#14582655C2semidirect
8. C2×C43×#416C2semidirect
23. #14582925C22semidirect
26. #14582896C22semidirect
30. #14582873C22semidirect
32. #14582872C22semidirect
35. #14582655C22semidirect
40. C43×#416C22semidirect
399. C2×#416D43semidirect
411. C2×C43#2053semidirect
436. #416C2×D43semidirect
448. C43C2×#2053semidirect
809. C2#19135899direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836972
C2×#145829252
C2×#145828962
C2×#145828732
C2×#145828722
#191358992
C2×#145826552
C2×C43×#4162
C2×#205343