Finite Group Databasebeta

← #25966752

Subgroups — #25966752

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#19147985C211yesmaximal, characteristic, complemented
2C2×#14583520C211yesmaximal, characteristic, complemented
3#19145278C214yesmaximal, complemented
4#19145263C214yesmaximal, complemented
5#19145234C214yesmaximal, complemented
6#19145212C214yesmaximal, complemented
7#19145141C211yesmaximal, characteristic, complemented
8#19145061C211yesmaximal, characteristic, complemented
9#19144989C211yesmaximal, characteristic, complemented
10#19144982C211yesmaximal, characteristic, complemented
11#19144225C212yesmaximal, complemented
12#19144214C212yesmaximal, complemented
13C4×#13063358C212yesmaximal, complemented
14C4×#13063353C212yesmaximal, complemented
15C43×#2873C211yesmaximal, characteristic, complemented
16C2×#13063358C2212yes—
17C2×#13063353C2212yes—
18#14583520—22no—
19#14583520—22no—
20#14583520C2214yes—
21#14583520C2214yes—
22#14583520C2212yescomplemented
23#14583520C2212yescomplemented
24#14583511C2212yescomplemented
25#14583504C2212yescomplemented
26#14583496—21no—
27#14583496—21no—
28#14583487—21no—
29#14583487—21no—
30#14583456C2211yescharacteristic
31#14583449C2211yescharacteristic
32C2×#13063325C2211yescharacteristic
33#14583427—22no—
34#14583427—22no—
35C2×#13063320—21no—
36C2×#13063313C2211yescharacteristic
37C2×#13063311—21no—
38#14583410C2212yes—
39C2×#13063307—21no—
40C2×#13063304C2211yescharacteristic
41C2×#13063303—21no—
42C2×#13063299C2211yescharacteristic
43C4×#10621898C2212yes—
44C2×C4×Dic86C2211yescharacteristic
45C2×C4×D172C2211yescharacteristic
46#14583308C2214yescomplemented
47#14583304C2212yescomplemented
48#14583297C2212yescomplemented
49#14583293C2212yescomplemented
50#14583288C2212yescomplemented
51#14583283C2214yescomplemented
52#14583259C2212yescomplemented
53#14583259C2214yescomplemented
54#14583259C2212yescomplemented
55#14583254C2214yescomplemented
56#14583250C2212yescomplemented
57#14583246C2212yescomplemented
58#14583157C2214yescomplemented
59#14583152C2214yes—
60#14583145C2214yes—
61#14583145C2214yescomplemented
62#14583140C2214yescomplemented
63#14583135C2214yes—
64#14583128C2214yes—
65#14583128C2214yescomplemented
66#14583012C2214yescomplemented
67#14583007C2214yescomplemented
68#14583001C2214yescomplemented
69#14583001C2214yescomplemented
70C4×Dic172C2214yescomplemented
71C4×#10621873C2214yescomplemented
72C4×#10621873C2214yescomplemented
73C4×D344C2214yescomplemented
74#14582941C2212yes—
75#14582941C2212yes—
76#14582909C2212yes—
77#14582905C2212yes—
78#14582901C2212yes—
79#14582901C2212yes—
80C22×M16×C43C2212yes—
81C2×#117×C43C2211yescharacteristic
82C43×#405C2214yescomplemented
83C43×#405C2214yescomplemented
84C4×M16×C43C2211yescharacteristic
85C4×M16×C43C2211yescharacteristic
86C4×M16×C43C2212yes—
87C2×#10621898C2312yes—
88C22×Dic86—21no—
89C22×Dic86C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C4×D43—21no—
93#13063358—28no—
94#13063353—28no—
95C2×Dic172C2314yes—
96C2×#10621873C2314yes—
97C2×#10621873C2314yes—
98C2×D344C2314yes—
99#13063325—21no—
100#13063325—21no—
101#13063325C2311yescharacteristic
102#13063325C2311yescharacteristic
103#13063325C2312yes—
104#13063325C2311yescharacteristic
105#13063325C2312yes—
106#13063322C2311yescharacteristic
107#13063320—24no—
108#13063320—24no—
109#13063320—22no—
110#13063320—22no—
111#13063318—22no—
112#13063318—22no—
113#13063317C2312yes—
114#13063315—22no—
115#13063315—22no—
116#13063313—21no—
117#13063313—21no—
118#13063313C2312yes—
119#13063313C2312yes—
120#13063313C2312yes—
121#13063311—24no—
122#13063311—24no—
123#13063311—22no—
124#13063311—22no—
125#13063310—22no—
126#13063310—22no—
127#13063308—22no—
128#13063307—24no—
129#13063307—24no—
130#13063307—22no—
131#13063307—22no—
132#13063304—22no—
133#13063304—21no—
134#13063304—21no—
135#13063304C2312yes—
136#13063304C2314yes—
137#13063304C2312yes—
138#13063303—24no—
139#13063303—24no—
140#13063303—22no—
141#13063303—22no—
142#13063299—22no—
143#13063299—21no—
144#13063299—21no—
145#13063299C2314yes—
146#13063299C2312yes—
147#13063299C2312yes—
148#13063298—22no—
149#13063298—22no—
150#13063294—22no—
151C4×Dic86—22no—
152C4×Dic86—21no—
153C4×Dic86—21no—
154C4×Dic86C2314yes—
155C4×Dic86C2312yes—
156C4×Dic86C2312yes—
157C4×D172—22no—
158C4×D172—21no—
159C4×D172—21no—
160C4×D172C2314yes—
161C4×D172C2312yes—
162C4×D172C2312yes—
163C4×C22⋊D43—22no—
164C4×C22⋊D43—22no—
165C4×C22⋊D43—22no—
166C4×C22⋊D43—22no—
167#13063284C2312yes—
168#13063282—22no—
169C2×C4⋊Dic43—21no—
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2311yescharacteristic
172C2×Dic43⋊C4—21no—
173C2×Dic43⋊C4—21no—
174C2×C22⋊Dic43—21no—
175C2×(C2×D43)⋊C4—21no—
176C2×(C2×D43)⋊C4—21no—
177C2×(C2×D43)⋊C4—21no—
178C2×(C2×D43)⋊C4—21no—
179C2×C4×Dic43—21no—
180C42×D43—22no—
181#13063259C2314yes—
182#13063259C2314yes—
183#13063257C2314yes—
184#13063257C2314yes—
185#13063250C2314yes—
186#13063250C2314yes—
187#13063250C2314yes—
188#13063250C2314yes—
189#13063247C2314yes—
190#13063247C2314yes—
191#13063247C2314yes—
192#13063247C2314yes—
193C23×C4×C43C2311yescharacteristic
194C2×M16×C43—28no—
195C2×M16×C43C2314yes—
196C2×M16×C43C2312yes—
197C2×M16×C43C2312yes—
198C22×C8×C43C2314yes—
199#117×C43D412yes—
200#117×C43D412yes—
201#117×C43C2312yes—
202#117×C43C2312yes—
203C2×C4⋊C4×C43D411yescharacteristic
204C2×C4⋊C4×C43D411yescharacteristic
205C2×C22⋊C4×C43D411yescharacteristic
206C2×C22⋊C4×C43D411yescharacteristic
207C2×C42×C43C2311yescharacteristic
208C2×C42×C43C2311yescharacteristic
209#97×C43C2312yes—
210#97×C43C2314yes—
211#97×C43C2312yes—
212C4×C8×C43C2312yes—
213C4×C8×C43C2314yes—
214C4×C8×C43C2312yes—
215C24×C43C2×D411yescharacteristic
216C23×D43—21no—
217C22×C4×C43—24no—
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D412yes—
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2412yes—
225C22×C4×C43C2411yescharacteristic
226C2×C22⋊D43—22no—
227C2×C22⋊D43—22no—
228C2×C22⋊D43—22no—
229C2×C22⋊D43—24no—
230C2×C22⋊D43—82no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234#10621898—24no—
235#10621898—24no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172—24no—
240C2×D172C2412yes—
241C2×D172C2412yes—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—22no—
245C2×C4×D43—24no—
246C2×C4×D43—82no—
247C2×Dic86—24no—
248C2×Dic86—21no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86—22no—
252C2×Dic86—22no—
253C2×Dic86—82no—
254C2×Dic86C2412yes—
255C2×Dic86C2412yes—
256M16×C43—24no—
257M16×C43—28no—
258M16×C43#4118yes—
259C2×C8×C43—28no—
260C2×C8×C43C2414yes—
261C2×C8×C43C2414yes—
262C4⋊C4×C43C2×D412yes—
263C4⋊C4×C43C2×D412yes—
264C4⋊C4×C43C2×D412yes—
265C4⋊C4×C43C2×D412yes—
266C22⋊C4×C43C2×D412yes—
267C22⋊C4×C43C2×D412yes—
268C22⋊C4×C43C2×D412yes—
269C22⋊C4×C43C2×D412yes—
270C42×C43C2×D412yes—
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2412yes—
274C42×C43C2411yescharacteristic
275C42×C43C2411yescharacteristic
276C22⋊Dic43—24no—
277C22⋊Dic43—22no—
278C22⋊Dic43—22no—
279C22⋊Dic43—22no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—22no—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—22no—
292C4⋊Dic43—22no—
293C4⋊Dic43—22no—
294C4⋊Dic43—21no—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43C2412yes—
301C4⋊Dic43C2412yes—
302C4⋊Dic43C2412yes—
303C4⋊Dic43C2412yes—
304Dic43⋊C4—24no—
305Dic43⋊C4—24no—
306Dic43⋊C4—22no—
307Dic43⋊C4—22no—
308Dic43⋊C4—22no—
309Dic43⋊C4—22no—
310Dic43⋊C4—22no—
311Dic43⋊C4—22no—
312C4×Dic43—22no—
313C4×Dic43—22no—
314C4×Dic43—22no—
315C4×Dic43—24no—
316Dic172—28no—
317D344—28no—
318#10621873—28no—
319#10621873—28no—
320C23×C43—22no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43C22×D412yes—
324C23×C43C22×D411yescharacteristic
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—42no—
330C2×C4×C43—22no—
331C2×C4×C43—24no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43C22×D412yes—
339C2×C4×C43C22×D412yes—
340C2×C4×C43C22×D412yes—
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4114yes—
347C2×C4×C43C2511yescharacteristic
348C22⋊D43—44no—
349C22⋊D43—82no—
350C22⋊D43—82no—
351C22⋊D43—84no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—42no—
359C2×Dic43—42no—
360C2×Dic43—42no—
361D172—22no—
362D172—24no—
363D172—22no—
364D172—42no—
365D172—81no—
366D172—81no—
367C4×D43—44no—
368C4×D43—82no—
369C4×D43—82no—
370C4×D43—84no—
371Dic86—22no—
372Dic86—24no—
373Dic86—22no—
374Dic86—42no—
375Dic86—81no—
376Dic86—81no—
377Dic86—82no—
378Dic86—82no—
379C8×C43—24no—
380C8×C43C2×#4118yes—
381#60703—431nomaximal, Sylow
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—82no—
388C22×C43#53212yes—
389C22×C43C23×D411yescharacteristic
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—84no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—22no—
400C4×C43—21no—
401C4×C43—22no—
402C4×C43—21no—
403C4×C43—22no—
404C4×C43#53212yes—
405C4×C43C22×#4112yes—
406Dic43—42no—
407Dic43—42no—
408Dic43—42no—
409Dic43—42no—
410Dic43—42no—
411Dic43—42no—
412#3455—431no—
413C2×#542—431no—
414#3179—434no—
415#3178—434no—
416#3175—434no—
417#3173—434no—
418#3165—431no—
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#2873D4311yescharacteristic, complemented
427C2×C43—22no—
428C2×C43—42no—
429C2×C43C2×#53211yescharacteristic
430C2×C43#358511yescharacteristic
431C2×C43#358611yescharacteristic
432D43—82no—
433D43—82no—
434C2×#137—432no—
435C2×AGL(1,ℤ/8)—432no—
436C22×M16C2×D4312yes—
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#533—431no—
450#532—431no—
451C2×C4⋊Q8—431no—
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×#117C2×D4311yescharacteristic
466#501—434no—
467#500—432no—
468#498—432no—
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#428—432no—
495#428—432no—
496#419—432no—
497#418—432no—
498#417—432no—
499#417—432no—
500#405C2×D4314yescomplemented
501#405C2×D4314yescomplemented
502C4×M16C2×D4311yescharacteristic
503C4×M16C2×D4311yescharacteristic
504C4×M16C2×D4312yes—
505C43#6070311yescharacteristic, complemented, Sylow
506C2×#41—432no—
507C22×Q8—431no—
508C22×Q8—861no—
509C22×D4—431no—
510C22×D4—861no—
511C23×C4—861no—
512C23×C4C22×D4311yescharacteristic
513#137—868no—
514AGL(1,ℤ/8)—868no—
515C2×Q16—434no—
516C2×SD16—434no—
517C2×SD16—434no—
518C2×D8—434no—
519C2×M16—28no—
520C2×M16C22×D4312yes—
521C2×M16C22×D4314yes—
522C2×M16C22×D4312yes—
523C22×C8C22×D4314yes—
524C4⋊Q8—432no—
525C4⋊Q8—432no—
526C4⋊Q8—431no—
527C4⋊Q8—431no—
528C4⋊Q8—431no—
529C4⋊Q8—861no—
530C4⋊Q8—861no—
531#127—431no—
532#126—864no—
533#126—864no—
534#126—862no—
535#126—862no—
536#126—862no—
537#126—862no—
538#125—432no—
539#125—862no—
540#125—862no—
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—862no—
552#123—862no—
553#123—864no—
554#123—864no—
555#123—862no—
556#123—862no—
557C22⋊Q8—434no—
558C22⋊Q8—432no—
559C22⋊Q8—432no—
560C22⋊Q8—862no—
561C22⋊Q8—861no—
562C22⋊Q8—861no—
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—861no—
572#121—861no—
573#121—862no—
574#121—862no—
575#120—862no—
576C4×Q8—434no—
577C4×Q8—432no—
578C4×Q8—432no—
579C4×Q8—862no—
580C4×Q8—861no—
581C4×Q8—861no—
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—862no—
594#117D17212yes—
595#117D17212yes—
596#117C22×D4312yes—
597#117C22×D4312yes—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4D17211yescharacteristic
604C2×C4⋊C4D17211yescharacteristic
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C22⋊C4—861no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4D17211yescharacteristic
611C2×C22⋊C4D17211yescharacteristic
612C2×C42—861no—
613C2×C42—862no—
614C2×C42C22×D4311yescharacteristic
615C2×C42C22×D4311yescharacteristic
616#107—434no—
617#107—434no—
618#106—434no—
619#106—434no—
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#97C22×D4314yes—
629#97C22×D4312yes—
630#97C22×D4312yes—
631C4×C8C22×D4314yes—
632C4×C8C22×D4312yes—
633C4×C8C22×D4312yes—
634C24—861no—
635C24C2×D17211yescharacteristic
636#41—864no—
637#41—864no—
638C2×Q8—432no—
639C2×Q8—432no—
640C2×Q8—861no—
641C2×Q8—861no—
642C2×Q8—862no—
643C2×Q8—862no—
644C2×Q8—861no—
645C2×Q8—864no—
646C2×Q8—3442no—
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—24no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—864no—
665C22×C4—862no—
666C22×C4—3442no—
667C22×C4C2×D17211yescharacteristic
668C22×C4C2×D17212yes—
669C22×C4C2×D17211yescharacteristic
670C22×C4C2×D17211yescharacteristic
671C22×C4C2×D17211yescharacteristic
672C22×C4C2×D17211yescharacteristic
673C22×C4C23×D4312yes—
674C22×C4C23×D4311yescharacteristic
675Q16—868no—
676SD16—868no—
677SD16—868no—
678D8—868no—
679M16—24no—
680M16—28no—
681M16#1062189818yes—
682C2×C8—28no—
683C2×C8C23×D4314yes—
684C2×C8C23×D4314yes—
685C4⋊C4—432no—
686C4⋊C4—432no—
687C4⋊C4—432no—
688C4⋊C4—432no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—864no—
692C4⋊C4—864no—
693C4⋊C4—862no—
694C4⋊C4—862no—
695C4⋊C4—862no—
696C4⋊C4—862no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—862no—
700C4⋊C4—862no—
701C4⋊C4—862no—
702C4⋊C4—862no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4C2×D17212yes—
706C4⋊C4C2×D17212yes—
707C4⋊C4C2×D17212yes—
708C4⋊C4C2×D17212yes—
709C22⋊C4—864no—
710C22⋊C4—862no—
711C22⋊C4—862no—
712C22⋊C4—862no—
713C22⋊C4—864no—
714C22⋊C4—864no—
715C22⋊C4—862no—
716C22⋊C4—862no—
717C22⋊C4—862no—
718C22⋊C4—862no—
719C22⋊C4—862no—
720C22⋊C4—862no—
721C22⋊C4—862no—
722C22⋊C4—862no—
723C22⋊C4—862no—
724C22⋊C4—862no—
725C22⋊C4C2×D17212yes—
726C22⋊C4C2×D17212yes—
727C22⋊C4C2×D17212yes—
728C22⋊C4C2×D17212yes—
729C42—862no—
730C42—862no—
731C42—862no—
732C42—864no—
733C42C2×D17212yes—
734C42C2×D17211yescharacteristic
735C42C2×D17211yescharacteristic
736C42C23×D4312yes—
737C42C23×D4311yescharacteristic
738C42C23×D4311yescharacteristic
739C23—22no—
740C23—41no—
741C23—41no—
742C23—862no—
743C23—862no—
744C23—1722no—
745C23—1722no—
746C23—1722no—
747C23C22×D17212yes—
748C23C22×D17211yescharacteristic
749Q8—862no—
750Q8—864no—
751Q8—862no—
752Q8—3442no—
753Q8—3442no—
754Q8—3441no—
755Q8—3441no—
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—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—3444no—
782C2×C4—3442no—
783C2×C4—3442no—
784C2×C4—1722no—
785C2×C4—1722no—
786C2×C4—1722no—
787C2×C4—1724no—
788C2×C4C22×D17212yes—
789C2×C4C22×D17212yes—
790C2×C4C22×D17211yescharacteristic
791C2×C4C22×D17211yescharacteristic
792C2×C4C22×D17211yescharacteristic
793C2×C4C22×D17211yescharacteristic
794C2×C4C22×D17212yes—
795C2×C4C22×D17211yescharacteristic
796C2×C4C2×#1062189814yes—
797C2×C4C24×D4311yescharacteristic
798C8—24no—
799C8C2×#1062189818yes—
800C22—21no—
801C22—21no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—82no—
806C22—3444no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1722no—
813C22#1458344912yes—
814C22C23×D17211yescharacteristic
815C4—22no—
816C4—21no—
817C4—21no—
818C4—22no—
819C4—21no—
820C4—21no—
821C4—22no—
822C4—1722no—
823C4—1722no—
824C4—1722no—
825C4—1722no—
826C4—1722no—
827C4—1722no—
828C4#1458344912yes—
829C4C22×#1062189812yes—
830C2—22no—
831C2—42no—
832C2—3442no—
833C2—3442no—
834C2C2×#1458344911yescharacteristic
835C2#1914937611yescharacteristic
836C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2873C2
socleC22×C43C23×D4
hypercenter#2873D43
hypocenterC43#60703
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2873

Complements

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

NH ≅ G/Ntype
1. #19147985C2semidirect
2. C2×#14583520C2semidirect
3. #19145278C2semidirect
4. #19145263C2semidirect
5. #19145234C2semidirect
6. #19145212C2semidirect
7. #19145141C2semidirect
8. #19145061C2semidirect
9. #19144989C2semidirect
10. #19144982C2semidirect
11. #19144225C2semidirect
12. #19144214C2semidirect
13. C4×#13063358C2semidirect
14. C4×#13063353C2semidirect
15. C43×#2873C2semidirect
22. #14583520C22semidirect
23. #14583520C22semidirect
24. #14583511C22semidirect
25. #14583504C22semidirect
46. #14583308C22semidirect
47. #14583304C22semidirect
48. #14583297C22semidirect
49. #14583293C22semidirect
50. #14583288C22semidirect
51. #14583283C22semidirect
52. #14583259C22semidirect
53. #14583259C22semidirect
54. #14583259C22semidirect
55. #14583254C22semidirect
56. #14583250C22semidirect
57. #14583246C22semidirect
58. #14583157C22semidirect
61. #14583145C22semidirect
62. #14583140C22semidirect
65. #14583128C22semidirect
66. #14583012C22semidirect
67. #14583007C22semidirect
68. #14583001C22semidirect
69. #14583001C22semidirect
70. C4×Dic172C22semidirect
71. C4×#10621873C22semidirect
72. C4×#10621873C22semidirect
73. C4×D344C22semidirect
82. C43×#405C22semidirect
83. C43×#405C22semidirect
426. #2873D43semidirect
500. #405C2×D43semidirect
501. #405C2×D43semidirect
505. C43#60703semidirect

Maximal subgroups

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

subgroupindex
#191479852
C2×#145835202
#191452782
#191452632
#191452342
#191452122
#191451412
#191450612
#191449892
#191449822
#191442252
#191442142
C4×#130633582
C4×#130633532
C43×#28732
#6070343