Finite Group Databasebeta

← #25966756

Subgroups — #25966756

Order 11008.

1910 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147987C211yesmaximal, characteristic, complemented
2C2×#14583523C211yesmaximal, characteristic, complemented
3#19145283C214yesmaximal, complemented
4#19145268C214yesmaximal, complemented
5#19145237C214yesmaximal, complemented
6#19145214C214yesmaximal, complemented
7#19145061C211yesmaximal, characteristic, complemented
8#19144991C211yesmaximal, characteristic, complemented
9#19144984C211yesmaximal, characteristic, complemented
10#19144226C212yesmaximal, complemented
11#19144215C212yesmaximal, complemented
12#19143413C212yesmaximal, complemented
13#19143402C212yesmaximal, complemented
14#19143012C211yesmaximal, characteristic, complemented
15C43×#3165C211yesmaximal, characteristic, complemented
16C2×#13063358C2212yes—
17C2×#13063353C2212yes—
18C2×M16×D43C2212yes—
19#14583523—22no—
20#14583523—22no—
21#14583523C2214yes—
22#14583523C2214yes—
23#14583523C2212yescomplemented
24#14583523C2212yescomplemented
25#14583512C2212yescomplemented
26#14583505C2212yescomplemented
27#14583498—21no—
28#14583498—21no—
29#14583489—21no—
30#14583489—21no—
31#14583449C2211yescharacteristic
32#14583436—22no—
33#14583436—22no—
34C2×#13063320—21no—
35C2×#13063314—21no—
36C2×#13063313C2211yescharacteristic
37#14583411C2212yes—
38C2×#13063310—21no—
39C2×#13063305C2211yescharacteristic
40C2×#13063301—21no—
41C2×#13063300C2211yescharacteristic
42#14583367C2212yes—
43C2×#13063290C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063282C2211yescharacteristic
46#14583293C2212yescomplemented
47#14583288C2212yescomplemented
48#14583283C2214yescomplemented
49#14583261C2212yescomplemented
50#14583261C2214yescomplemented
51#14583261C2212yescomplemented
52#14583256C2214yescomplemented
53#14583251C2212yescomplemented
54#14583247C2212yescomplemented
55#14583158C2214yescomplemented
56#14583153C2214yes—
57#14583146C2214yes—
58#14583146C2214yescomplemented
59#14583141C2214yescomplemented
60#14583136C2214yes—
61#14583129C2214yes—
62#14583129C2214yescomplemented
63#14583010C2214yescomplemented
64#14583005C2214yescomplemented
65#14582998C2214yescomplemented
66#14582998C2214yescomplemented
67#14582993C2214yescomplemented
68#14582986C2214yescomplemented
69#14582986C2214yescomplemented
70#14582981C2214yescomplemented
71#14582907C2212yes—
72#14582903C2212yes—
73#14582898C2212yes—
74#14582898C2212yes—
75#14582856C2214yescomplemented
76#14582853C2214yescomplemented
77C4×#10621877C2211yescharacteristic
78M16×Dic43C2212yes—
79C43×#533C2211yescharacteristic
80C2×C4⋊Q8×C43C2211yescharacteristic
81C43×#501C2214yescomplemented
82C43×#500C2212yescomplemented
83C43×#498C2212yescomplemented
84C43×#428C2212yes—
85C43×#428C2212yes—
86C4×M16×C43C2211yescharacteristic
87C2×#10621898C2312yes—
88C22×Dic86C2311yescharacteristic
89C22×D172—21no—
90C22×D172C2311yescharacteristic
91C22×C4×D43—21no—
92C22×C4×D43C2311yescharacteristic
93#13063358—28no—
94#13063353—28no—
95C2×Dic172C2314yes—
96C2×#10621873C2314yes—
97C2×#10621873C2314yes—
98C2×D344C2314yes—
99C2×#10621877C2312yes—
100C2×#10621872C2314yes—
101M16×D43—28no—
102C2×C8×D43C2314yes—
103#13063325C2311yescharacteristic
104#13063322C2311yescharacteristic
105#13063320—22no—
106#13063320—22no—
107#13063320—24no—
108#13063320—24no—
109#13063320—22no—
110#13063320—22no—
111#13063316—22no—
112#13063316—22no—
113#13063314—24no—
114#13063314—24no—
115#13063314—22no—
116#13063314—22no—
117#13063313—21no—
118#13063313—21no—
119#13063313C2312yes—
120#13063313C2312yes—
121#13063313C2312yes—
122#13063310—24no—
123#13063310—24no—
124#13063310—22no—
125#13063310—22no—
126#13063310—22no—
127#13063310—22no—
128#13063309—22no—
129#13063305—22no—
130#13063305C2312yes—
131#13063305C2314yes—
132#13063305C2312yes—
133#13063301—24no—
134#13063301—24no—
135#13063301—22no—
136#13063301—22no—
137#13063300—22no—
138#13063300—22no—
139#13063300—22no—
140#13063300C2314yes—
141#13063300C2312yes—
142#13063300C2312yes—
143#13063299—21no—
144#13063299—21no—
145#13063295—22no—
146#13063290—22no—
147#13063290C2314yes—
148#13063290C2312yes—
149#13063290C2312yes—
150C4×D172—22no—
151C4×D172—22no—
152C4×D172—21no—
153C4×D172—21no—
154#13063287—22no—
155#13063287C2314yes—
156#13063287C2312yes—
157#13063287C2312yes—
158(C22⋊D43)⋊C4—22no—
159(C22⋊D43)⋊C4—22no—
160#13063282—22no—
161#13063282D412yes—
162#13063282D412yes—
163#13063282C2312yes—
164#13063282C2312yes—
165C2×C4⋊Dic43—21no—
166C2×Dic43⋊C4—21no—
167C2×Dic43⋊C4D411yescharacteristic
168C2×Dic43⋊C4D411yescharacteristic
169C2×(C2×D43)⋊C4—21no—
170C2×(C2×D43)⋊C4—21no—
171C2×(C2×D43)⋊C4—21no—
172C2×(C2×D43)⋊C4—21no—
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4D411yescharacteristic
175C2×(C2×D43)⋊C4D411yescharacteristic
176C2×C4×Dic43—21no—
177C2×C4×Dic43C2311yescharacteristic
178C42×D43—22no—
179#13063248C2314yes—
180#13063248C2314yes—
181#13063248C2314yes—
182#13063248C2314yes—
183#13063245C2314yes—
184#13063245C2314yes—
185#13063245C2314yes—
186#13063245C2314yes—
187#13063236C2312yes—
188#13063235C2314yes—
189C4×C43⋊C8C2312yes—
190C8×Dic43C2314yes—
191C22×Q8×C43—21no—
192C2×M16×C43C2312yes—
193C4⋊Q8×C43—21no—
194C4⋊Q8×C43—21no—
195C4⋊Q8×C43C2311yescharacteristic
196C4⋊Q8×C43C2312yes—
197C4⋊Q8×C43C2311yescharacteristic
198C4⋊Q8×C43C2312yes—
199#125×C43C2312yes—
200C22⋊Q8×C43—21no—
201C22⋊Q8×C43—21no—
202C4×Q8×C43—21no—
203C4×Q8×C43—21no—
204#117×C43C2312yes—
205C2×C4⋊C4×C43—21no—
206C2×C4⋊C4×C43C2311yescharacteristic
207C2×C4⋊C4×C43C2311yescharacteristic
208C2×C42×C43C2311yescharacteristic
209#107×C43C2314yes—
210#107×C43C2314yes—
211#106×C43C2314yes—
212#106×C43C2314yes—
213#97×C43C2312yes—
214C4×C8×C43C2312yes—
215C23×D43—21no—
216C23×D43C2×D411yescharacteristic
217C2×Q8×C43—21no—
218C2×Q8×C43—21no—
219C2×Q8×C43—22no—
220C2×Q8×C43—22no—
221C2×Q8×C43—82no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227C2×C22⋊D43—22no—
228C22×Dic43—21no—
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232#10621898—24no—
233#10621898—24no—
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172—22no—
238C2×D172—22no—
239C2×D172—24no—
240C2×D172—24no—
241C2×D172—82no—
242C2×D172C2412yes—
243C2×D172C2412yes—
244C2×C4×D43—24no—
245C2×C4×D43—22no—
246C2×C4×D43—22no—
247C2×C4×D43—22no—
248C2×C4×D43—24no—
249C2×C4×D43—82no—
250C2×C4×D43C2×D412yes—
251C2×C4×D43C2412yes—
252C2×Dic86—24no—
253C2×Dic86—21no—
254C2×Dic86C2412yes—
255C2×Dic86C2412yes—
256M16×C43#4118yes—
257C2×C8×C43C2414yes—
258C4⋊C4×C43—22no—
259C4⋊C4×C43—22no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—22no—
263C4⋊C4×C43—22no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43C2412yes—
267C4⋊C4×C43C2412yes—
268C4⋊C4×C43C2412yes—
269C4⋊C4×C43C2412yes—
270C22⋊C4×C43—22no—
271C42×C43—22no—
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2411yescharacteristic
275C42×C43C2411yescharacteristic
276(C2×D43)⋊C4—22no—
277(C2×D43)⋊C4—22no—
278(C2×D43)⋊C4—22no—
279(C2×D43)⋊C4—22no—
280(C2×D43)⋊C4—22no—
281(C2×D43)⋊C4—22no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4C2×D412yes—
292(C2×D43)⋊C4C2×D412yes—
293(C2×D43)⋊C4C2×D412yes—
294(C2×D43)⋊C4C2×D412yes—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—24no—
298C4⋊Dic43—22no—
299C4⋊Dic43—22no—
300Dic43⋊C4—24no—
301Dic43⋊C4—22no—
302Dic43⋊C4—22no—
303Dic43⋊C4C2×D412yes—
304Dic43⋊C4C2×D412yes—
305Dic43⋊C4C2×D412yes—
306Dic43⋊C4C2×D412yes—
307C4×Dic43—22no—
308C4×Dic43—22no—
309C4×Dic43—24no—
310C4×Dic43C2×D412yes—
311C4×Dic43C2412yes—
312#10621877—24no—
313C2×C43⋊C8C2414yes—
314Dic172—28no—
315D344—28no—
316#10621873—28no—
317#10621873—28no—
318#10621872—28no—
319C8×D43—28no—
320C23×C43C22×D411yescharacteristic
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—41no—
325C22×D43—41no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43C22×D412yes—
330Q8×C43—81no—
331Q8×C43—81no—
332Q8×C43—82no—
333Q8×C43—82no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—42no—
341C2×C4×C43—42no—
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C2×#4114yes—
348C2×C4×C43C2511yescharacteristic
349C22⋊D43—44no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—42no—
356C2×Dic43C22×D412yes—
357C2×Dic43C22×D412yes—
358C2×Dic43C22×D412yes—
359D172—22no—
360D172—24no—
361D172—22no—
362D172—42no—
363D172—81no—
364D172—81no—
365D172—82no—
366D172—82no—
367D172—84no—
368C4×D43—24no—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—44no—
372C4×D43—82no—
373C4×D43—82no—
374C4×D43—84no—
375Dic86—22no—
376Dic86—24no—
377Dic86—22no—
378Dic86—42no—
379C8×C43C2×#4118yes—
380C43⋊C8—24no—
381#60703—431nomaximal, Sylow
382C22×C43—21no—
383C22×C43—21no—
384C22×C43#53212yes—
385C22×C43C23×D411yescharacteristic
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—82no—
396C2×D43—84no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43#53212yes—
406C4×C43C22×#4112yes—
407Dic43—22no—
408Dic43—22no—
409Dic43—22no—
410Dic43—42no—
411Dic43—42no—
412#3455—431no—
413C2×#542—431no—
414#3179—434no—
415#3178—434no—
416#3175—434no—
417#3173—434no—
418#3165D4311yescharacteristic, complemented
419#3153—431no—
420#3141—431no—
421#3140—431no—
422#3056—432no—
423#3055—432no—
424C4×#137—432no—
425C4×AGL(1,ℤ/8)—432no—
426#2873—431no—
427C2×C43—22no—
428C2×C43C2×#53211yescharacteristic
429C2×C43#358511yescharacteristic
430C2×C43#358611yescharacteristic
431D43—42no—
432D43—82no—
433D43—82no—
434C2×#137—432no—
435C2×AGL(1,ℤ/8)—432no—
436C22×M16—432no—
437#542—432no—
438#542—434no—
439#542—432no—
440#542—434no—
441#542—862no—
442#542—862no—
443#541—432no—
444#540—432no—
445#539—861no—
446#539—861no—
447#538—861no—
448#538—861no—
449#533C2×D4311yescharacteristic
450#532—431no—
451C2×C4⋊Q8C2×D4311yescharacteristic
452#529—862no—
453#529—862no—
454C2×#126—861no—
455C2×#124—431no—
456C2×#124—861no—
457#525—432no—
458C2×#123—861no—
459C2×C22⋊Q8—431no—
460C2×C22⋊Q8—861no—
461C2×#121—431no—
462C4×#41—432no—
463C2×C4×Q8—431no—
464C2×C4×D4—431no—
465C2×#117—431no—
466#501C2×D4314yescomplemented
467#500C2×D4312yescomplemented
468#498C2×D4312yescomplemented
469#497—432no—
470#496—432no—
471#495—434no—
472#489—432no—
473#489—432no—
474#489—434no—
475#488—434no—
476#487—432no—
477#486—432no—
478#470—434no—
479#469—434no—
480#468—434no—
481#468—434no—
482#467—434no—
483#466—434no—
484#465—434no—
485#465—434no—
486#442—434no—
487#441—434no—
488#440—434no—
489#440—434no—
490C4×Q16—434no—
491C4×SD16—434no—
492C4×SD16—434no—
493C4×D8—434no—
494#428C2×D4312yes—
495#428C2×D4312yes—
496#419—432no—
497#418—432no—
498#417—432no—
499#417—432no—
500#405—434no—
501#405—434no—
502C4×M16—432no—
503C4×M16—431no—
504C4×M16C2×D4311yescharacteristic
505C43#6070311yescharacteristic, complemented, Sylow
506C2×#41—432no—
507C22×Q8—21no—
508C22×Q8—431no—
509C22×D4—431no—
510C22×D4—861no—
511C23×C4—431no—
512C23×C4—861no—
513#137—868no—
514AGL(1,ℤ/8)—868no—
515C2×Q16—434no—
516C2×SD16—434no—
517C2×SD16—434no—
518C2×D8—434no—
519C2×M16—432no—
520C2×M16—434no—
521C2×M16—868no—
522C2×M16C22×D4312yes—
523C22×C8—434no—
524C4⋊Q8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—431no—
527C4⋊Q8C22×D4312yes—
528C4⋊Q8C22×D4312yes—
529C4⋊Q8C22×D4311yescharacteristic
530C4⋊Q8C22×D4311yescharacteristic
531#127—431no—
532#126—862no—
533#126—862no—
534#126—864no—
535#126—864no—
536#126—862no—
537#126—862no—
538#125—862no—
539#125—862no—
540#125C22×D4312yes—
541#124—432no—
542#124—432no—
543#124—432no—
544#124—864no—
545#124—864no—
546#124—862no—
547#124—862no—
548#124—861no—
549#124—861no—
550#123—862no—
551#123—864no—
552#123—864no—
553#123—862no—
554#123—862no—
555#123—862no—
556#123—862no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—434no—
560C22⋊Q8—432no—
561C22⋊Q8—432no—
562C22⋊Q8—862no—
563C22⋊Q8—864no—
564C22⋊Q8—864no—
565C22⋊Q8—862no—
566C22⋊Q8—862no—
567#121—434no—
568#121—432no—
569#121—432no—
570#121—862no—
571#121—862no—
572#121—862no—
573#121—861no—
574#121—861no—
575#120—862no—
576C4×Q8—21no—
577C4×Q8—21no—
578C4×Q8—434no—
579C4×Q8—432no—
580C4×Q8—432no—
581C4×Q8—862no—
582C4×D4—434no—
583C4×D4—432no—
584C4×D4—432no—
585C4×D4—862no—
586C4×D4—862no—
587C4×D4—862no—
588C4×D4—862no—
589C4×D4—862no—
590C4×D4—861no—
591C4×D4—861no—
592#117—432no—
593#117—432no—
594#117—432no—
595#117—432no—
596#117—862no—
597#117C22×D4312yes—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4C22×D4311yescharacteristic
604C2×C4⋊C4C22×D4311yescharacteristic
605C2×C22⋊C4—431no—
606C2×C22⋊C4—431no—
607C2×C22⋊C4—861no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C42—431no—
613C2×C42—862no—
614C2×C42—861no—
615C2×C42C22×D4311yescharacteristic
616#107C22×D4314yes—
617#107C22×D4314yes—
618#106C22×D4314yes—
619#106C22×D4314yes—
620#103—434no—
621#103—434no—
622#103—434no—
623#103—434no—
624#102—434no—
625#102—434no—
626#102—434no—
627#102—434no—
628#97—434no—
629#97—432no—
630#97C22×D4312yes—
631C4×C8—434no—
632C4×C8—432no—
633C4×C8C22×D4312yes—
634C24—431no—
635C24—861no—
636#41—864no—
637#41—864no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—82no—
643C2×Q8—432no—
644C2×Q8—432no—
645C2×Q8—861no—
646C2×Q8—864no—
647C2×D4—432no—
648C2×D4—432no—
649C2×D4—862no—
650C2×D4—862no—
651C2×D4—864no—
652C2×D4—862no—
653C2×D4—861no—
654C2×D4—861no—
655C2×D4—861no—
656C2×D4—864no—
657C2×D4—3442no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—862no—
666C22×C4—862no—
667C22×C4—864no—
668C22×C4—864no—
669C22×C4—861no—
670C22×C4—862no—
671C22×C4—3442no—
672C22×C4D4×D4311yescharacteristic
673C22×C4D4×D4311yescharacteristic
674C22×C4C23×D4311yescharacteristic
675Q16—868no—
676SD16—868no—
677SD16—868no—
678D8—868no—
679M16—864no—
680M16—868no—
681M16#1062190218yes—
682C2×C8—434no—
683C2×C8—868no—
684C2×C8C23×D4314yes—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—432no—
694C4⋊C4—432no—
695C4⋊C4—432no—
696C4⋊C4—432no—
697C4⋊C4—864no—
698C4⋊C4—864no—
699C4⋊C4—862no—
700C4⋊C4—862no—
701C4⋊C4—862no—
702C4⋊C4—862no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4C23×D4312yes—
706C4⋊C4C23×D4312yes—
707C4⋊C4C23×D4312yes—
708C4⋊C4C23×D4312yes—
709C22⋊C4—22no—
710C22⋊C4—432no—
711C22⋊C4—432no—
712C22⋊C4—432no—
713C22⋊C4—432no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—862no—
717C22⋊C4—862no—
718C22⋊C4—862no—
719C22⋊C4—862no—
720C22⋊C4—864no—
721C22⋊C4—862no—
722C22⋊C4—862no—
723C22⋊C4—862no—
724C22⋊C4—862no—
725C22⋊C4—862no—
726C22⋊C4—862no—
727C22⋊C4—862no—
728C22⋊C4—862no—
729C42—22no—
730C42—432no—
731C42—432no—
732C42—862no—
733C42—862no—
734C42—864no—
735C42D4×D4311yescharacteristic
736C42D4×D4311yescharacteristic
737C42C23×D4311yescharacteristic
738C42C23×D4311yescharacteristic
739C23—432no—
740C23—862no—
741C23—862no—
742C23—862no—
743C23—1721no—
744C23—1721no—
745C23—1722no—
746C23—1722no—
747C23—1722no—
748C23C2×D4×D4311yescharacteristic
749Q8—82no—
750Q8—82no—
751Q8—81no—
752Q8—81no—
753Q8—862no—
754Q8—864no—
755Q8—862no—
756Q8—1722no—
757D4—862no—
758D4—864no—
759D4—862no—
760D4—3441no—
761D4—3441no—
762D4—3444no—
763D4—3442no—
764D4—3442no—
765D4—1724no—
766D4—1722no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—432no—
778C2×C4—862no—
779C2×C4—864no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—3444no—
785C2×C4—3442no—
786C2×C4—3442no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1722no—
790C2×C4—1724no—
791C2×C4C2×D4×D4311yescharacteristic
792C2×C4C2×D4×D4311yescharacteristic
793C2×C4C2×D4×D4311yescharacteristic
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4C2×D4×D4311yescharacteristic
796C2×C4C2×#1062190214yes—
797C2×C4C24×D4311yescharacteristic
798C8—864no—
799C8C2×#1062190218yes—
800C22—21no—
801C22—21no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—3444no—
806C22—3442no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1722no—
813C22#1458345012yes—
814C22C22×D4×D4311yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—862no—
824C4—862no—
825C4—862no—
826C4—1722no—
827C4—1722no—
828C4#1458345012yes—
829C4C22×#1062190212yes—
830C2—22no—
831C2—3442no—
832C2—3442no—
833C2—1722no—
834C2C2×#1458345011yescharacteristic
835C2#1914937111yescharacteristic
836C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3165C2
socleC22×C43C23×D4
hypercenter#3165D43
hypocenterC43#60703
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
1. #19147987C2semidirect
2. C2×#14583523C2semidirect
3. #19145283C2semidirect
4. #19145268C2semidirect
5. #19145237C2semidirect
6. #19145214C2semidirect
7. #19145061C2semidirect
8. #19144991C2semidirect
9. #19144984C2semidirect
10. #19144226C2semidirect
11. #19144215C2semidirect
12. #19143413C2semidirect
13. #19143402C2semidirect
14. #19143012C2semidirect
15. C43×#3165C2semidirect
23. #14583523C22semidirect
24. #14583523C22semidirect
25. #14583512C22semidirect
26. #14583505C22semidirect
46. #14583293C22semidirect
47. #14583288C22semidirect
48. #14583283C22semidirect
49. #14583261C22semidirect
50. #14583261C22semidirect
51. #14583261C22semidirect
52. #14583256C22semidirect
53. #14583251C22semidirect
54. #14583247C22semidirect
55. #14583158C22semidirect
58. #14583146C22semidirect
59. #14583141C22semidirect
62. #14583129C22semidirect
63. #14583010C22semidirect
64. #14583005C22semidirect
65. #14582998C22semidirect
66. #14582998C22semidirect
67. #14582993C22semidirect
68. #14582986C22semidirect
69. #14582986C22semidirect
70. #14582981C22semidirect
75. #14582856C22semidirect
76. #14582853C22semidirect
81. C43×#501C22semidirect
82. C43×#500C22semidirect
83. C43×#498C22semidirect
418. #3165D43semidirect
466. #501C2×D43semidirect
467. #500C2×D43semidirect
468. #498C2×D43semidirect
505. C43#60703semidirect

Maximal subgroups

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

subgroupindex
#191479872
C2×#145835232
#191452832
#191452682
#191452372
#191452142
#191450612
#191449912
#191449842
#191442262
#191442152
#191434132
#191434022
#191430122
C43×#31652
#6070343