Finite Group Databasebeta

← #25098076

Subgroups — #25098076

Order 11008.

1668 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583697C211yesmaximal, characteristic
2C2×#14583665C211yesmaximal, characteristic, complemented
3#19143112C211yesmaximal, characteristic, complemented
4#19143040C211yesmaximal, characteristic, complemented
5#19134954C218yesmaximal, complemented
6C2×#14582669C211yesmaximal, characteristic, complemented
7#19134321C211yesmaximal, characteristic, complemented
8C2×C43×#421C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583697—22no—
11#14583697—22no—
12#14583697C414yescomplemented
13#14583697C2214yes—
14C2×#13063356C412yescomplemented
15C2×#13063355—21no—
16C2×#13063351C412yescomplemented
17C2×#13063350—21no—
18C2×#13063345—22no—
19#14583665—22no—
20#14583665—22no—
21#14583665—22no—
22#14583665C2214yescomplemented
23C2×#13063333—22no—
24C2×#13063331—22no—
25C22×#10621877C2211yescharacteristic
26C22×#10621877C2211yescharacteristic
27C22×#10621877C2211yescharacteristic
28C2×M16×D43—22no—
29#14582907—21no—
30#14582903—21no—
31#14582898—22no—
32#14582893C2214yescomplemented
33#14582866—22no—
34#14582866C2214yescomplemented
35#14582863—22no—
36#14582669C2214yescomplemented
37#14582663C2214yescomplemented
38C22×#41×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C43×#421—22no—
42C43×#421C2214yescomplemented
43C2×#104×C43—22no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898C2×C412yes—
51C2×#10621898C2×C412yes—
52C2×#10621898D412yes—
53C2×#10621898D412yes—
54C2×#10621898D412yes—
55C2×#10621898C2312yes—
56C22×Dic86D411yescharacteristic
57C22×D172D411yescharacteristic
58C22×C22⋊D43—21no—
59C22×C4×D43—21no—
60#13063356—24no—
61#13063356C2×C418yescomplemented
62#13063355—24no—
63#13063355—24no—
64#13063351—24no—
65#13063351C2×C418yescomplemented
66#13063350—24no—
67#13063350—24no—
68#13063345—28no—
69#13063345—28no—
70C2×#10621885—22no—
71C2×#10621883—22no—
72C2×#10621884—22no—
73C2×#10621882—22no—
74#13063333—28no—
75#13063333—28no—
76#13063331—28no—
77#13063331—28no—
78C2×#10621877—21no—
79C2×#10621877—21no—
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×#10621877C2×C412yes—
92C2×#10621877C2×C412yes—
93C2×#10621877D412yes—
94C2×#10621877C2312yes—
95C2×#10621877C2312yes—
96C2×#10621872—24no—
97M16×D43—28no—
98M16×D43—28no—
99C22×C43⋊C8—21no—
100C22×C43⋊C8D412yes—
101C22×C43⋊C8C2312yes—
102C2×C8×D43—24no—
103#13063248—24no—
104#13063245—24no—
105C22⋊(C43⋊C8)—28no—
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×C43—21no—
115C2×#41×C43—21no—
116C2×#41×C43C2×C412yes—
117C2×#41×C43C2312yes—
118C22×Q8×C43C2×C411yescharacteristic
119C22×D4×C43—21no—
120C22×D4×C43C2×C411yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C2×M16×C43—21no—
124C2×M16×C43—21no—
125C2×M16×C43—21no—
126C2×M16×C43D412yes—
127C2×M16×C43D412yes—
128C2×M16×C43C2312yes—
129C22×C8×C43—21no—
130#117×C43—21no—
131#117×C43—21no—
132#117×C43—21no—
133#117×C43C2312yes—
134C2×C4⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C42×C43—21no—
137#104×C43—28no—
138C24×C43—21no—
139C24×C43#4111yescharacteristic
140C23×D43—21no—
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—22no—
148#41×C43—22no—
149#41×C43—41no—
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—41no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43C22×C412yes—
163C2×D4×C43—21no—
164C2×D4×C43—22no—
165C2×D4×C43—22no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—41no—
171C2×D4×C43—41no—
172C2×D4×C43—41no—
173C2×D4×C43—41no—
174C2×D4×C43C22×C412yes—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—21no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43—41no—
181C22×C4×C43—41no—
182C22×C4×C43—41no—
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43#4111yescharacteristic
194C22×C4×C43#4111yescharacteristic
195C22×C4×C43#4111yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—22no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—22no—
203C22×Dic43—21no—
204#10621898—22no—
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#10621898C22⋊C414yes—
217#10621898C22⋊C414yes—
218#10621898C22×C414yes—
219#10621898C2×D414yes—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172C22⋊C412yes—
224C2×D172C22⋊C412yes—
225C2×D172C2×D412yes—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—22no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86C22⋊C412yes—
236C2×Dic86C22⋊C412yes—
237C2×Dic86C2×D412yes—
238M16×C43—22no—
239M16×C43—22no—
240M16×C43—22no—
241M16×C43C2×D414yes—
242C2×C8×C43—22no—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C4⋊C4×C43—22no—
246C4⋊C4×C43—41no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—41no—
249C42×C43—22no—
250C42×C43—41no—
251#10621885—28no—
252#10621884—28no—
253#10621883—28no—
254#10621882—28no—
255#10621877—22no—
256#10621877—22no—
257#10621877—22no—
258#10621877—22no—
259#10621877—22no—
260#10621877—22no—
261#10621877—22no—
262#10621877—41no—
263#10621877—41no—
264#10621877—41no—
265#10621877—41no—
266#10621877C22×C414yes—
267C2×C43⋊C8—22no—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8C2×D414yes—
276#10621872—216no—
277C8×D43—216no—
278C23×C43—22no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—81no—
282C23×C43—82no—
283C23×C43C4×D411yescharacteristic
284C23×C43C4×D411yescharacteristic
285C23×C43#12111yescharacteristic
286C23×C43#12111yescharacteristic
287C23×C43#12311yescharacteristic
288C23×C43#12311yescharacteristic
289C23×C43C2×#4111yescharacteristic
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—82no—
294Q8×C43—22no—
295Q8×C43—22no—
296Q8×C43—41no—
297Q8×C43—41no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43—42no—
301D4×C43—42no—
302D4×C43—42no—
303D4×C43—42no—
304D4×C43—41no—
305D4×C43—41no—
306C2×C4×C43—22no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—82no—
315C2×C4×C43C2×C22⋊C411yescharacteristic
316C2×C4×C43C2×C22⋊C411yescharacteristic
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C4×D411yescharacteristic
320C2×C4×C43C4×D411yescharacteristic
321C2×C4×C43C4×D411yescharacteristic
322C2×C4×C43C4×D411yescharacteristic
323C2×C4×C43C4×D411yescharacteristic
324C2×C4×C43C4×D411yescharacteristic
325C2×C4×C43#12011yescharacteristic
326C2×C4×C43#12011yescharacteristic
327C2×C4×C43#12011yescharacteristic
328C2×C4×C43#12011yescharacteristic
329C2×C4×C43#12111yescharacteristic
330C2×C4×C43#12111yescharacteristic
331C2×C4×C43#12111yescharacteristic
332C2×C4×C43#12111yescharacteristic
333C2×C4×C43#12111yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12311yescharacteristic
336C2×C4×C43#12311yescharacteristic
337C2×C4×C43C23×C411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C22⋊D43—24no—
344C22⋊D43—24no—
345C22⋊D43—24no—
346C22⋊D43—24no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350D172—22no—
351D172—22no—
352D172—22no—
353D172C2×C22⋊C414yes—
354C4×D43—24no—
355C4×D43—24no—
356C4×D43—24no—
357C4×D43—24no—
358Dic86—22no—
359Dic86—22no—
360Dic86—22no—
361Dic86C2×C22⋊C414yes—
362C8×C43—24no—
363C43⋊C8—24no—
364C43⋊C8—24no—
365C43⋊C8—42no—
366#20939—431nomaximal, Sylow
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—44no—
375C22×C43—42no—
376C22×C43—82no—
377C22×C43—82no—
378C22×C43#38611yescharacteristic
379C22×C43#38611yescharacteristic
380C22×C43#38611yescharacteristic
381C22×C43#38611yescharacteristic
382C22×C43C2×C4×D411yescharacteristic
383C22×C43C2×#12111yescharacteristic
384C22×C43C2×#12311yescharacteristic
385C2×D43—24no—
386C2×D43—44no—
387C2×D43—82no—
388C2×D43—82no—
389C4×C43—42no—
390C4×C43—82no—
391C4×C43#38611yescharacteristic
392C4×C43#38611yescharacteristic
393C4×C43#38611yescharacteristic
394C4×C43#38611yescharacteristic
395C4×C43C22×C22⋊C411yescharacteristic
396C4×C43C2×C4×D411yescharacteristic
397C4×C43C2×#12011yescharacteristic
398C4×C43C2×#12111yescharacteristic
399Dic43—24no—
400C2×#575—431no—
401C2×#568—431no—
402C2×#421D4311yescharacteristic, complemented
403#2896—431no—
404#2879—431no—
405#1881—438no—
406C2×#344—431no—
407#1738—431no—
408C2×C43—21no—
409C2×C43—21no—
410C2×C43—21no—
411C2×C43—21no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—82no—
416C2×C43C2×#38611yescharacteristic
417D43—44no—
418C22×#41—431no—
419C22×#41C2×D4311yescharacteristic
420#575—434no—
421#575—434no—
422#575—862no—
423#575—862no—
424C2×#137—432no—
425C2×#137—861no—
426C2×AGL(1,ℤ/8)—432no—
427C2×AGL(1,ℤ/8)—861no—
428C2×#135—862no—
429#568—434no—
430#568—862no—
431#568—862no—
432#568—862no—
433C2×#131—862no—
434C2×#131—862no—
435C22×M16—431no—
436C22×M16—431no—
437C22×M16—431no—
438C22×M16—862no—
439C22×M16C2×D4311yescharacteristic
440C2×#117C2×D4311yescharacteristic
441#421—22no—
442#421C2×D4314yescomplemented
443C2×#104—22no—
444#419—861no—
445#418—861no—
446#417—862no—
447#416—434no—
448#408—434no—
449#408—862no—
450#407—862no—
451#344—434no—
452#341—434no—
453C43#2093911yescharacteristic, complemented, Sylow
454C2×#41—21no—
455C2×#41—21no—
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—432no—
465C2×#41—432no—
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×#41C4×D4312yes—
477C2×#41C22×D4312yes—
478C22×Q8—431no—
479C22×Q8C4×D4311yescharacteristic
480C22×D4—21no—
481C22×D4—431no—
482C22×D4—861no—
483C22×D4C4×D4311yescharacteristic
484C23×C4—21no—
485C23×C4—861no—
486C23×C4C22×D4311yescharacteristic
487#137—438no—
488#137—864no—
489#137—864no—
490#137—864no—
491AGL(1,ℤ/8)—438no—
492AGL(1,ℤ/8)—864no—
493AGL(1,ℤ/8)—864no—
494AGL(1,ℤ/8)—864no—
495#135—868no—
496#135—868no—
497C2×Q16—862no—
498C2×SD16—862no—
499C2×SD16—862no—
500C2×D8—862no—
501#131—868no—
502#131—868no—
503#131—868no—
504#131—868no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—432no—
509C2×M16—432no—
510C2×M16—432no—
511C2×M16—432no—
512C2×M16—432no—
513C2×M16—864no—
514C2×M16—868no—
515C2×M16—861no—
516C2×M16—861no—
517C2×M16—861no—
518C2×M16—861no—
519C2×M16—861no—
520C2×M16—861no—
521C2×M16—861no—
522C2×M16—868no—
523C2×M16—861no—
524C2×M16—861no—
525C2×M16—861no—
526C2×M16—861no—
527C2×M16—861no—
528C2×M16—861no—
529C2×M16C22⋊D4312yes—
530C2×M16C22⋊D4312yes—
531C2×M16C22×D4312yes—
532C22×C8—21no—
533C22×C8—432no—
534C22×C8—432no—
535C22×C8—864no—
536C22×C8—861no—
537#117—21no—
538#117—21no—
539#117—21no—
540#117C22×D4312yes—
541C2×C4⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C42—21no—
544#104—28no—
545#103—864no—
546#102—864no—
547C22⋊C8—868no—
548C24—21no—
549C24—861no—
550C24#1062190011yescharacteristic
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—434no—
568#41—434no—
569#41—434no—
570#41—434no—
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—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—432no—
589C2×Q8—432no—
590C2×Q8—432no—
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8C2×C4×D4312yes—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—432no—
607C2×D4—432no—
608C2×D4—432no—
609C2×D4—862no—
610C2×D4—862no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—862no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4C2×C4×D4312yes—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—861no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4C2×C4×D4311yescharacteristic
636C22×C4#1062189811yescharacteristic
637C22×C4#1062189811yescharacteristic
638C22×C4D4×D4311yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4#1062190011yescharacteristic
645C22×C4C2×C22⋊D4311yescharacteristic
646C22×C4C2×C22⋊D4311yescharacteristic
647C22×C4C23×D4311yescharacteristic
648Q16—868no—
649SD16—868no—
650SD16—868no—
651D8—868no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—434no—
656M16—8616no—
657M16—862no—
658M16—862no—
659M16—862no—
660M16—862no—
661M16—862no—
662M16—862no—
663M16—862no—
664M16—1721no—
665M16—1721no—
666M16—1721no—
667M16—1721no—
668M16C2×C22⋊D4314yes—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—434no—
673C2×C8—8616no—
674C2×C8—862no—
675C2×C8—862no—
676C2×C8—862no—
677C2×C8—862no—
678C2×C8—862no—
679C2×C8—862no—
680C2×C8—862no—
681C2×C8—862no—
682C4⋊C4—22no—
683C4⋊C4—41no—
684C22⋊C4—22no—
685C22⋊C4—41no—
686C42—22no—
687C42—41no—
688C23—22no—
689C23—41no—
690C23—41no—
691C23—81no—
692C23—82no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—3442no—
697C23(C22⋊D43)⋊C411yescharacteristic
698C23(C22⋊D43)⋊C411yescharacteristic
699C23#1306329611yescharacteristic
700C23#1306329611yescharacteristic
701C23#1306330711yescharacteristic
702C23#1306330711yescharacteristic
703C23C2×#1062190011yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—41no—
707Q8—41no—
708Q8—434no—
709Q8—862no—
710Q8—862no—
711Q8—862no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—434no—
721D4—864no—
722D4—864no—
723D4—864no—
724D4—864no—
725D4—862no—
726D4—862no—
727D4—862no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—82no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—864no—
741C2×C4—864no—
742C2×C4—864no—
743C2×C4—864no—
744C2×C4C22⋊C4×D4311yescharacteristic
745C2×C4C22⋊C4×D4311yescharacteristic
746C2×C4C22⋊C4×D4311yescharacteristic
747C2×C4C22⋊C4×D4311yescharacteristic
748C2×C4(C22⋊D43)⋊C411yescharacteristic
749C2×C4(C22⋊D43)⋊C411yescharacteristic
750C2×C4C4×C22⋊D4311yescharacteristic
751C2×C4C4×C22⋊D4311yescharacteristic
752C2×C4C4×C22⋊D4311yescharacteristic
753C2×C4C4×C22⋊D4311yescharacteristic
754C2×C4#1306329311yescharacteristic
755C2×C4#1306329311yescharacteristic
756C2×C4#1306329311yescharacteristic
757C2×C4#1306329311yescharacteristic
758C2×C4#1306329611yescharacteristic
759C2×C4#1306329611yescharacteristic
760C2×C4#1306329811yescharacteristic
761C2×C4#1306329811yescharacteristic
762C2×C4#1306329811yescharacteristic
763C2×C4#1306329811yescharacteristic
764C2×C4#1306330711yescharacteristic
765C2×C4#1306330711yescharacteristic
766C2×C4C22×C4×D4311yescharacteristic
767C2×C4C2×D4×D4311yescharacteristic
768C2×C4C2×D4×D4311yescharacteristic
769C2×C4C2×D4×D4311yescharacteristic
770C2×C4C22×C22⋊D4311yescharacteristic
771C2×C4C2×#1062189811yescharacteristic
772C8—24no—
773C8—864no—
774C8—864no—
775C8—1722no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—44no—
784C22—42no—
785C22—82no—
786C22—82no—
787C22—864no—
788C22—3442no—
789C22—3442no—
790C22—1724no—
791C22#1458277511yescharacteristic
792C22#1458277511yescharacteristic
793C22#1458277511yescharacteristic
794C22#1458277511yescharacteristic
795C22C2×(C22⋊D43)⋊C411yescharacteristic
796C22C2×#1306329611yescharacteristic
797C22C2×#1306330711yescharacteristic
798C4—42no—
799C4—82no—
800C4—864no—
801C4#1458277511yescharacteristic
802C4#1458277511yescharacteristic
803C4#1458277511yescharacteristic
804C4#1458277511yescharacteristic
805C4C2×C22⋊C4×D4311yescharacteristic
806C4C2×C4×C22⋊D4311yescharacteristic
807C4C2×#1306329311yescharacteristic
808C4C2×#1306329811yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—82no—
817C2—1724no—
818C2C2×#1458277511yescharacteristic
subgroupG/H
centerC4C2×#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC2×C43C2×#386
prime radicalC2×#14583697C2
cosocleC22×C4×C43C24
hypercenterC2×#421D43
hypocenterC43#20939
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
2. C2×#14583665C2semidirect
3. #19143112C2semidirect
4. #19143040C2semidirect
5. #19134954C2semidirect
6. C2×#14582669C2semidirect
7. #19134321C2semidirect
8. C2×C43×#421C2semidirect
12. #14583697C4semidirect
14. C2×#13063356C4semidirect
16. C2×#13063351C4semidirect
22. #14583665C22semidirect
32. #14582893C22semidirect
34. #14582866C22semidirect
36. #14582669C22semidirect
37. #14582663C22semidirect
42. C43×#421C22semidirect
61. #13063356C2×C4semidirect
65. #13063351C2×C4semidirect
402. C2×#421D43semidirect
442. #421C2×D43semidirect
453. C43#20939semidirect

Maximal subgroups

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

subgroupindex
C2×#145836972
C2×#145836652
#191431122
#191430402
#191349542
C2×#145826692
#191343212
C2×C43×#4212
#2093943