Finite Group Databasebeta

← #25974740

Subgroups — #25974740

Order 11008.

2078 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148444C211yesmaximal, characteristic, complemented
2#19148375C211yesmaximal, characteristic, complemented
3#19146901C212yesmaximal, complemented
4#19146890C212yesmaximal, complemented
5#19146768C214yesmaximal, complemented
6#19146573C214yesmaximal, complemented
7#19146524C212yesmaximal, complemented
8#19146461C212yesmaximal, complemented
9#19144976C211yesmaximal, characteristic, complemented
10#19144565C212yesmaximal, complemented
11#19144385C211yesmaximal, characteristic, complemented
12#19144234C212yesmaximal, complemented
13C2×#14583105C211yesmaximal, characteristic, complemented
14#19143883C212yesmaximal, complemented
15C4×#13063353C211yesmaximal, characteristic, complemented
16#19143129C212yesmaximal, complemented
17C43×#2935C211yesmaximal, characteristic, complemented
18C2×#13063372C2212yes—
19C2×#13063353C2211yescharacteristic
20C22×#10621873C2212yes—
21#14583631—22no—
22#14583623—21no—
23#14583614C2212yes—
24#14583595C2214yes—
25#14583569—21no—
26D4×Dic86C2212yescomplemented
27D4×Dic86C2212yescomplemented
28#14583554C2212yescomplemented
29#14583554C2212yescomplemented
30#14583553C2212yes—
31#14583549—22no—
32#14583549—22no—
33#14583486—22no—
34#14583470C2212yes—
35#14583469—22no—
36#14583463C2212yes—
37#14583456C2211yescharacteristic
38#14583447—21no—
39C2×#13063325C2211yescharacteristic
40C4⋊Q8×D43—21no—
41#14583409—22no—
42#14583382C2212yes—
43C4×#10621898C2211yescharacteristic
44C2×C4×D172C2211yescharacteristic
45#14583268C2214yescomplemented
46#14583250C2212yescomplemented
47#14583250C2212yescomplemented
48#14583241C2214yescomplemented
49#14583241C2214yescomplemented
50#14583235C2214yescomplemented
51#14583230C2214yescomplemented
52#14583207C2212yescomplemented
53#14583200C2212yescomplemented
54#14583195C2211yescharacteristic, complemented
55#14583190C2211yescharacteristic, complemented
56#14583185C2211yescharacteristic, complemented
57#14583180C2211yescharacteristic, complemented
58#14583145C2214yes—
59#14583145C2214yes—
60#14583128C2214yes—
61#14583128C2214yes—
62#14583105C2214yes—
63#14583105C2212yes—
64#14583105C2212yes—
65#14583046C2214yes—
66#14583046C2214yes—
67#14583040C2214yes—
68#14583040C2214yes—
69#14583012C2212yes—
70#14583001C2212yes—
71C4×#10621873C2212yes—
72C4×D344C2212yes—
73#14582941C2211yescharacteristic
74#14582937C2212yes—
75#14582909C2212yes—
76#14582909C2212yes—
77#14582909C2214yescomplemented
78#14582905C2211yescharacteristic
79#14582901C2211yescharacteristic
80#14582901C2214yescomplemented
81#14582896C2212yes—
82#14582896C2214yescomplemented
83C2×#13063250C2212yes—
84C2×#13063250C2214yescomplemented
85C2×#131×C43C2212yes—
86C43×#532C2211yescharacteristic
87C43×#436C2212yescomplemented
88C43×#435C2214yescomplemented
89C8×D4×C43C2212yescomplemented
90C2×C4⋊C8×C43C2211yescharacteristic
91C43×#408C2212yes—
92C4×M16×C43C2211yescharacteristic
93#13063372—28no—
94#13063372—44no—
95C2×#10621898C2314yes—
96C2×#10621898C2311yescharacteristic
97C2×#10621900—22no—
98C2×#10621900—24no—
99C2×#10621900—22no—
100C22×Dic86C2312yes—
101C22×Dic86C2314yes—
102C2×Q8×D43—22no—
103C22×D172C2311yescharacteristic
104C22×C4×D43—21no—
105#13063353—24no—
106C2×#10621873—44no—
107C2×#10621873C2312yes—
108C2×#10621873C2314yes—
109C2×#10621873C2314yes—
110C2×D344C2312yes—
111#13063325—21no—
112#13063325—21no—
113#13063325C2312yes—
114#13063325C2312yes—
115#13063325C2311yescharacteristic
116#13063325C2311yescharacteristic
117#13063324—22no—
118#13063324—22no—
119#13063323—22no—
120#13063321—22no—
121#13063320—24no—
122#13063317C2312yes—
123#13063314—22no—
124#13063312—22no—
125#13063311—24no—
126#13063309—24no—
127#13063307—24no—
128#13063307—24no—
129#13063307—24no—
130#13063306—24no—
131#13063305—22no—
132#13063304—21no—
133#13063304—21no—
134#13063304C2314yes—
135#13063304C2314yes—
136#13063302—24no—
137#13063302—24no—
138#13063299C2314yes—
139#13063299C2314yes—
140#13063297—24no—
141#13063296—22no—
142#13063296—22no—
143#13063296—22no—
144#13063293—24no—
145Q8×Dic43—22no—
146C4×Dic86—21no—
147C4×Dic86—21no—
148C4×Dic86C2311yescharacteristic
149C4×Dic86C2311yescharacteristic
150C4×D172—21no—
151C4×D172—21no—
152C4×D172C2312yes—
153C4×D172C2311yescharacteristic
154C4×D172C2311yescharacteristic
155C4×D172C2312yes—
156D4×Dic43—22no—
157D4×Dic43—22no—
158D4×Dic43—22no—
159D4×Dic43—24no—
160C4×C22⋊D43—21no—
161C4×C22⋊D43—21no—
162(C22⋊D43)⋊C4—24no—
163#13063284C2314yes—
164#13063284C2311yescharacteristic
165#13063284C2312yes—
166#13063283—22no—
167#13063282—21no—
168C2×C4⋊Dic43—21no—
169C2×C4⋊Dic43—21no—
170C2×C4⋊Dic43C2314yes—
171C2×C4⋊Dic43C2311yescharacteristic
172C4⋊C4×D43—22no—
173C4⋊C4×D43—22no—
174C2×(C2×D43)⋊C4—21no—
175C42×D43—21no—
176#13063259C2312yes—
177#13063259C2312yes—
178#13063259C2312yes—
179#13063257C2312yes—
180#13063257C2312yes—
181#13063257C2312yes—
182#13063250C2312yes—
183#13063250C2312yes—
184#13063250C2314yes—
185#13063250C2314yes—
186#13063250C2314yes—
187#13063250C2314yes—
188#13063250C2314yes—
189#13063250C2314yes—
190#13063250C2312yes—
191#13063247C2312yes—
192#13063247C2312yes—
193#13063247C2312yes—
194#13063247C2312yes—
195#13063247C2312yes—
196C2×#41×C43C2312yes—
197#131×C43—44no—
198C2×M16×C43C2311yescharacteristic
199C2×M16×C43C2311yescharacteristic
200C2×M16×C43C2314yes—
201C22×C8×C43C2312yes—
202C22×C8×C43C2314yes—
203C4⋊Q8×C43D411yescharacteristic
204#127×C43D411yescharacteristic
205#124×C43D412yes—
206#121×C43D412yes—
207#121×C43D412yes—
208C4×D4×C43C2312yes—
209C4×D4×C43C2312yes—
210C2×C42×C43C2311yescharacteristic
211C4⋊C8×C43C2311yescharacteristic
212C4⋊C8×C43C2311yescharacteristic
213C4⋊C8×C43C2312yes—
214C22⋊C8×C43C2314yes—
215C22⋊C8×C43C2314yes—
216#97×C43C2312yes—
217C4×C8×C43C2312yes—
218C23×D43—21no—
219#41×C43—24no—
220#41×C43—24no—
221C2×Q8×C43C2×D412yes—
222C2×D4×C43C2×D412yes—
223C2×D4×C43C2×D414yes—
224C2×D4×C43C2×D412yes—
225C2×D4×C43C2×D412yes—
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2414yes—
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43—21no—
231C2×C22⋊D43—24no—
232C2×C22⋊D43—24no—
233C2×C22⋊D43—24no—
234C22×Dic43—22no—
235C22×Dic43—24no—
236C22×Dic43—21no—
237C22×Dic43—24no—
238Q8×D43—48no—
239#10621900—48no—
240#10621900—416no—
241#10621900—84no—
242#10621898—22no—
243#10621898—28no—
244#10621898—44no—
245#10621898#4114yescomplemented
246C2×D172—21no—
247C2×D172—22no—
248C2×D172—22no—
249C2×D172C2412yes—
250C2×D172C2411yescharacteristic
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—24no—
255C2×C4×D43—22no—
256C2×C4×D43—22no—
257C2×C4×D43—82no—
258C2×Dic86—24no—
259C2×Dic86—24no—
260C2×Dic86—28no—
261C2×Dic86—21no—
262C2×Dic86—24no—
263C2×Dic86—22no—
264C2×Dic86—21no—
265C2×Dic86—44no—
266C2×Dic86C2414yes—
267C2×Dic86C2411yescharacteristic
268M16×C43—22no—
269M16×C43—22no—
270M16×C43—44no—
271C2×C8×C43—24no—
272C2×C8×C43—44no—
273C2×C8×C43C2412yes—
274C2×C8×C43C2412yes—
275C2×C8×C43C2412yes—
276C2×C8×C43C2412yes—
277C4⋊C4×C43C2×D412yes—
278C4⋊C4×C43C2×D412yes—
279C22⋊C4×C43C2×D414yes—
280C22⋊C4×C43C2×D414yes—
281C42×C43C2×D411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C42×C43C2411yescharacteristic
284C42×C43C2411yescharacteristic
285C22⋊Dic43—21no—
286C22⋊Dic43—22no—
287C22⋊Dic43—24no—
288C22⋊Dic43—24no—
289C22⋊Dic43—24no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—24no—
295(C2×D43)⋊C4—24no—
296C4⋊Dic43—22no—
297C4⋊Dic43—22no—
298C4⋊Dic43—22no—
299C4⋊Dic43—22no—
300C4⋊Dic43—21no—
301C4⋊Dic43—24no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43C2411yescharacteristic
305C4⋊Dic43C2411yescharacteristic
306C4⋊Dic43C2412yes—
307C4⋊Dic43C2412yes—
308C4⋊Dic43C2412yes—
309Dic43⋊C4—24no—
310Dic43⋊C4—24no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—22no—
314Dic43⋊C4—22no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—24no—
319C4×Dic43—22no—
320D344—24no—
321#10621873—24no—
322#10621873—44no—
323#10621873—44no—
324C23×C43C22×D414yes—
325C23×C43C22×D411yescharacteristic
326C22×D43—21no—
327C22×D43—22no—
328C22×D43—42no—
329C22×D43—81no—
330C22×D43—81no—
331Q8×C43—24no—
332D4×C43—28no—
333D4×C43—24no—
334D4×C43—24no—
335D4×C43—42no—
336C2×C4×C43—22no—
337C2×C4×C43—24no—
338C2×C4×C43—24no—
339C2×C4×C43—41no—
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D414yes—
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4112yes—
347C2×C4×C43H(5,𝔽2)12yes—
348C2×C4×C43C2511yescharacteristic
349C22⋊D43—24no—
350C22⋊D43—48no—
351C22⋊D43—84no—
352C22⋊D43—84no—
353C2×Dic43—21no—
354C2×Dic43—22no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—24no—
360C2×Dic43—48no—
361C2×Dic43—44no—
362C2×Dic43—81no—
363C2×Dic43—84no—
364D172—22no—
365D172—21no—
366D172—22no—
367D172—42no—
368D172C2×#4112yes—
369C4×D43—24no—
370C4×D43—48no—
371C4×D43—42no—
372C4×D43—42no—
373C4×D43—44no—
374C4×D43—82no—
375Dic86—21no—
376Dic86—24no—
377Dic86—24no—
378Dic86—48no—
379Dic86—44no—
380Dic86—42no—
381Dic86—81no—
382Dic86C2×#4112yes—
383C8×C43—22no—
384C8×C43—22no—
385C8×C43—22no—
386C8×C43—22no—
387#61209—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—24no—
391C22×C43—24no—
392C22×C43—24no—
393C22×C43#54612yes—
394C22×C43C23×D411yescharacteristic
395C2×D43—22no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—84no—
402C4×C43—21no—
403C4×C43—21no—
404C4×C43—24no—
405C4×C43—21no—
406C4×C43#54612yes—
407C4×C43#57712yes—
408C4×C43C22×#4111yescharacteristic
409C4×C43C2×H(5,𝔽2)11yescharacteristic
410Dic43—22no—
411Dic43—42no—
412Dic43—41no—
413Dic43—44no—
414Dic43—42no—
415Dic43—42no—
416Dic43—41no—
417#3506—431no—
418#3499—431no—
419#3330—432no—
420#3329—432no—
421#3320—434no—
422#3307—434no—
423#3303—432no—
424#3298—432no—
425#3139—431no—
426#3097—432no—
427#3076—431no—
428#3057—432no—
429C2×#461—431no—
430#3010—432no—
431C4×AGL(1,ℤ/8)—431no—
432#2935D4311yescharacteristic, complemented
433#2898—432no—
434C2×C43—22no—
435C2×C43—44no—
436C2×C43C2×#54611yescharacteristic
437C2×C43C2×#57711yescharacteristic
438C2×C43#358611yescharacteristic
439D43—42no—
440D43—82no—
441C2×2−1+4—432no—
442C2×AGL(1,ℤ/8)—431no—
443C22×SD16—432no—
444C2×#131C2×D4312yes—
445#559—862no—
446#556—861no—
447#555—432no—
448#553—434no—
449#550—861no—
450D4×Q8—432no—
451D4×Q8—432no—
452#547—432no—
453#547—432no—
454#547—432no—
455#547—862no—
456#547—862no—
457#538—862no—
458#536—432no—
459#536—862no—
460#535—432no—
461#533—431no—
462#532—861no—
463#532C2×D4311yescharacteristic
464C2×C4⋊Q8—431no—
465C2×C4⋊Q8—861no—
466#525—862no—
467#520—432no—
468C4×#41—431no—
469C2×C4×D4—431no—
470#491—434no—
471#487—432no—
472#487—432no—
473#485—434no—
474#485—434no—
475#484—434no—
476#483—434no—
477#479—432no—
478#478—432no—
479#477—431no—
480#476—431no—
481#475—431no—
482#474—431no—
483#468—434no—
484#468—434no—
485#465—434no—
486#465—434no—
487#461—432no—
488#461—432no—
489#461—434no—
490#449—434no—
491#449—434no—
492#448—434no—
493#448—434no—
494#442—432no—
495#440—432no—
496C4×SD16—432no—
497C4×D8—432no—
498#436C2×D4312yescomplemented
499#435C2×D4314yescomplemented
500C8×D4C2×D4312yescomplemented
501#428—431no—
502#427—432no—
503C2×C4⋊C8C2×D4311yescharacteristic
504#419—434no—
505#419—432no—
506#419—432no—
507#418—431no—
508#417—434no—
509#417—431no—
510#416—432no—
511#416—434no—
512C2×#103—432no—
513C2×#103—434no—
514#408C2×D4312yes—
515C4×M16C2×D4311yescharacteristic
516C43#6120911yescharacteristic, complemented, Sylow
5172−1+4—868no—
5182−1+4—1724no—
519C2×#41—431no—
520C2×#41—434no—
521C2×#41—862no—
522C2×#41—862no—
523C2×#41—864no—
524C2×#41C22×D4312yes—
525C22×Q8—432no—
526C22×Q8—434no—
527C22×Q8—862no—
528C22×D4—431no—
529C23×C4—861no—
530AGL(1,ℤ/8)—864no—
531C2×SD16—432no—
532C2×SD16—434no—
533C2×SD16—434no—
534C2×SD16—1724no—
535C2×D8—432no—
536#131—44no—
537C2×M16C22×D4311yescharacteristic
538C2×M16C22×D4311yescharacteristic
539C2×M16C22×D4314yes—
540C22×C8C22×D4312yes—
541C22×C8C22×D4314yes—
542C4⋊Q8—431no—
543C4⋊Q8—431no—
544C4⋊Q8—432no—
545C4⋊Q8—432no—
546C4⋊Q8—862no—
547C4⋊Q8—862no—
548C4⋊Q8—862no—
549C4⋊Q8—861no—
550C4⋊Q8—861no—
551C4⋊Q8D17211yescharacteristic
552#127—862no—
553#127D17211yescharacteristic
554#126—864no—
555#125—432no—
556#124—862no—
557#124—862no—
558#124—864no—
559#124D17212yes—
560#123—864no—
561#123—864no—
562#123—864no—
563#123—864no—
564#123—864no—
565C22⋊Q8—434no—
566C22⋊Q8—434no—
567C22⋊Q8—861no—
568C22⋊Q8—861no—
569C22⋊Q8—862no—
570C22⋊Q8—864no—
571C22⋊Q8—864no—
572#121—434no—
573#121—434no—
574#121—862no—
575#121—862no—
576#121—862no—
577#121—864no—
578#121D17212yes—
579#121D17212yes—
580#120—864no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—862no—
584C4×Q8—861no—
585C4×Q8—861no—
586C4×D4—432no—
587C4×D4—432no—
588C4×D4—431no—
589C4×D4—431no—
590C4×D4—864no—
591C4×D4—862no—
592C4×D4—862no—
593C4×D4—862no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—864no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4C22×D4312yes—
600C4×D4C22×D4312yes—
601#117—431no—
602#117—432no—
603#117—434no—
604#117—862no—
605#117—861no—
606C2×C4⋊C4—431no—
607C2×C4⋊C4—434no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4—862no—
611C2×C4⋊C4—862no—
612C2×C22⋊C4—861no—
613C2×C42—861no—
614C2×C42C22×D4311yescharacteristic
615#107—432no—
616#107—432no—
617#107—432no—
618#106—432no—
619#106—432no—
620#106—432no—
621C4⋊C8C22×D4311yescharacteristic
622C4⋊C8C22×D4312yes—
623C4⋊C8C22×D4311yescharacteristic
624#103—432no—
625#103—434no—
626#103—432no—
627#103—434no—
628#103—434no—
629#103—432no—
630#103—434no—
631#103—434no—
632#103—434no—
633#102—432no—
634#102—432no—
635#102—432no—
636#102—432no—
637#102—432no—
638C22⋊C8C22×D4314yes—
639C22⋊C8C22×D4314yes—
640#97C22×D4312yes—
641C4×C8C22×D4312yes—
642C24—861no—
643#41—24no—
644#41—24no—
645#41—434no—
646#41—868no—
647#41—862no—
648#41—3444no—
649#41—1724no—
650#41—1728no—
651#41—17216no—
652C2×Q8—431no—
653C2×Q8—434no—
654C2×Q8—868no—
655C2×Q8—861no—
656C2×Q8—861no—
657C2×Q8—864no—
658C2×Q8—862no—
659C2×Q8—864no—
660C2×Q8—864no—
661C2×Q8—1724no—
662C2×Q8—1728no—
663C2×Q8C2×D17212yes—
664C2×D4—431no—
665C2×D4—432no—
666C2×D4—861no—
667C2×D4—864no—
668C2×D4—864no—
669C2×D4—864no—
670C2×D4—861no—
671C2×D4—862no—
672C2×D4—862no—
673C2×D4C2×D17212yes—
674C2×D4C2×D17214yes—
675C2×D4C2×D17212yes—
676C2×D4C2×D17212yes—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—864no—
680C22×C4—862no—
681C22×C4—864no—
682C22×C4—862no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—864no—
686C22×C4—862no—
687C22×C4—3442no—
688C22×C4C2×D17211yescharacteristic
689C22×C4C2×D17211yescharacteristic
690C22×C4C23×D4314yes—
691C22×C4C23×D4311yescharacteristic
692SD16—864no—
693SD16—1724no—
694SD16—1724no—
695D8—864no—
696M16—22no—
697M16—22no—
698M16—44no—
699C2×C8—24no—
700C2×C8—44no—
701C2×C8C23×D4312yes—
702C2×C8C23×D4312yes—
703C2×C8C23×D4312yes—
704C2×C8C23×D4312yes—
705C4⋊C4—431no—
706C4⋊C4—431no—
707C4⋊C4—432no—
708C4⋊C4—432no—
709C4⋊C4—432no—
710C4⋊C4—861no—
711C4⋊C4—864no—
712C4⋊C4—862no—
713C4⋊C4—862no—
714C4⋊C4—864no—
715C4⋊C4—864no—
716C4⋊C4—862no—
717C4⋊C4—862no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—862no—
722C4⋊C4—862no—
723C4⋊C4—861no—
724C4⋊C4C2×D17212yes—
725C4⋊C4C2×D17212yes—
726C22⋊C4—862no—
727C22⋊C4—864no—
728C22⋊C4—861no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—862no—
732C22⋊C4—862no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C22⋊C4C2×D17214yes—
738C22⋊C4C2×D17214yes—
739C42—861no—
740C42—861no—
741C42—861no—
742C42—864no—
743C42—862no—
744C42C2×D17211yescharacteristic
745C42C2×D17211yescharacteristic
746C42C23×D4311yescharacteristic
747C42C23×D4311yescharacteristic
748C23—861no—
749C23—862no—
750C23—3441no—
751C23—3441no—
752C23—1722no—
753C23C22×D17214yes—
754C23C22×D17211yescharacteristic
755Q8—24no—
756Q8—432no—
757Q8—861no—
758Q8—864no—
759Q8—864no—
760Q8—3441no—
761Q8—1728no—
762Q8—1722no—
763Q8—1724no—
764D4—28no—
765D4—24no—
766D4—24no—
767D4—42no—
768D4—432no—
769D4—864no—
770D4—862no—
771D4—861no—
772D4—862no—
773D4—3444no—
774D4—3444no—
775D4—1728no—
776D4—1722no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—41no—
781C2×C4—861no—
782C2×C4—864no—
783C2×C4—862no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—864no—
789C2×C4—3442no—
790C2×C4—3441no—
791C2×C4—3444no—
792C2×C4—1728no—
793C2×C4—1722no—
794C2×C4—1728no—
795C2×C4—1724no—
796C2×C4—1724no—
797C2×C4—1722no—
798C2×C4C22×D17211yescharacteristic
799C2×C4C22×D17214yes—
800C2×C4C22×D17211yescharacteristic
801C2×C4C22×D17211yescharacteristic
802C2×C4C22×D17211yescharacteristic
803C2×C4C22×D17211yescharacteristic
804C2×C4#41×D4312yes—
805C2×C4#1306337012yes—
806C2×C4C24×D4311yescharacteristic
807C8—22no—
808C8—22no—
809C8—22no—
810C8—22no—
811C22—21no—
812C22—21no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—862no—
817C22—3444no—
818C22—1722no—
819C22—1722no—
820C22—1722no—
821C22—1721no—
822C22—1721no—
823C22#1458354412yes—
824C22C23×D17211yescharacteristic
825C4—24no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—862no—
830C4—1724no—
831C4—1722no—
832C4—1722no—
833C4—1721no—
834C4—1721no—
835C4—1722no—
836C4#1458354412yes—
837C4#1458371112yes—
838C4C2×#41×D4311yescharacteristic
839C4C2×#1306337011yescharacteristic
840C2—22no—
841C2—44no—
842C2—3442no—
843C2—1722no—
844C2C2×#1458354411yescharacteristic
845C2C2×#1458371111yescharacteristic
846C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2935C2
socleC22×C43C23×D4
hypercenter#2935D43
hypocenterC43#61209
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #532 ◁ #2935

Complements

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

NH ≅ G/Ntype
1. #19148444C2semidirect
2. #19148375C2semidirect
3. #19146901C2semidirect
4. #19146890C2semidirect
5. #19146768C2semidirect
6. #19146573C2semidirect
7. #19146524C2semidirect
8. #19146461C2semidirect
9. #19144976C2semidirect
10. #19144565C2semidirect
11. #19144385C2semidirect
12. #19144234C2semidirect
13. C2×#14583105C2semidirect
14. #19143883C2semidirect
15. C4×#13063353C2semidirect
16. #19143129C2semidirect
17. C43×#2935C2semidirect
26. D4×Dic86C22semidirect
27. D4×Dic86C22semidirect
28. #14583554C22semidirect
29. #14583554C22semidirect
45. #14583268C22semidirect
46. #14583250C22semidirect
47. #14583250C22semidirect
48. #14583241C22semidirect
49. #14583241C22semidirect
50. #14583235C22semidirect
51. #14583230C22semidirect
52. #14583207C22semidirect
53. #14583200C22semidirect
54. #14583195C22semidirect
55. #14583190C22semidirect
56. #14583185C22semidirect
57. #14583180C22semidirect
77. #14582909C22semidirect
80. #14582901C22semidirect
82. #14582896C22semidirect
84. C2×#13063250C22semidirect
87. C43×#436C22semidirect
88. C43×#435C22semidirect
89. C8×D4×C43C22semidirect
245. #10621898#41semidirect
432. #2935D43semidirect
498. #436C2×D43semidirect
499. #435C2×D43semidirect
500. C8×D4C2×D43semidirect
516. C43#61209semidirect

Maximal subgroups

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

subgroupindex
#191484442
#191483752
#191469012
#191468902
#191467682
#191465732
#191465242
#191464612
#191449762
#191445652
#191443852
#191442342
C2×#145831052
#191438832
C4×#130633532
#191431292
C43×#29352
#6120943