Finite Group Databasebeta

← #25969663

Subgroups — #25969663

Order 11008.

1758 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147984C211yesmaximal, characteristic
2C2×#14583507C211yesmaximal, characteristic, complemented
3#19146047C214yesmaximal, complemented
4#19146039C214yesmaximal, complemented
5#19146026C214yesmaximal, complemented
6#19146018C214yesmaximal, complemented
7#19144415C212yesmaximal, complemented
8#19144402C211yesmaximal, characteristic, complemented
9#19144400C211yesmaximal, characteristic, complemented
10#19144228C212yesmaximal, complemented
11#19144219C212yesmaximal, complemented
12#19144080C212yesmaximal, complemented
13#19144063C211yesmaximal, characteristic, complemented
14#19143157C211yesmaximal, characteristic, complemented
15C43×#3037C211yesmaximal, characteristic, complemented
16C2×#13063355C2212yes—
17C2×M16×D43C2212yes—
18#14583518C2212yes—
19#14583518C2212yes—
20#14583510C2212yes—
21#14583507—22no—
22#14583507—22no—
23#14583507C2214yes—
24#14583507C2214yes—
25#14583503C2212yes—
26#14583494—21no—
27#14583494—21no—
28#14583486—21no—
29#14583486—21no—
30#14583456C2211yescharacteristic
31C2×#13063323C2211yescharacteristic
32#14583429—22no—
33#14583429—22no—
34C2×#13063320—21no—
35C2×#13063319—21no—
36C2×#13063317—21no—
37C2×#13063316C2211yescharacteristic
38C2×#13063315—21no—
39#14583406C2212yes—
40C2×#13063305C2211yescharacteristic
41C2×#13063301C2211yescharacteristic
42#41×Dic43C2212yes—
43C2×C4×Dic86C2211yescharacteristic
44C2×#13063282C2211yescharacteristic
45#14583208C2214yescomplemented
46#14583207C2214yescomplemented
47#14583206C2214yescomplemented
48#14583204C2214yescomplemented
49#14583201C2214yescomplemented
50#14583197C2214yescomplemented
51#14583195C2212yescomplemented
52#14583194C2212yescomplemented
53#14583185C2212yescomplemented
54#14583184C2212yescomplemented
55#14583156C2214yes—
56#14583154C2214yes—
57#14583144C2214yes—
58#14583142C2214yes—
59#14583139C2214yes—
60#14583137C2214yes—
61#14583127C2214yes—
62#14583125C2214yes—
63#14583118C2214yescomplemented
64#14583107C2214yescomplemented
65#14583107C2214yescomplemented
66#14583106C2212yescomplemented
67#14583102C2214yescomplemented
68#14583102C2214yescomplemented
69#14583096C2212yescomplemented
70#14582941C2212yes—
71#14582939C2212yes—
72#14582924C2214yes—
73#14582924C2214yes—
74#14582923C2211yescharacteristic
75#14582922C2212yes—
76#14582909C2212yes—
77#14582908C2212yes—
78#14582900C2212yes—
79C2×#137×C43C2212yes—
80C43×#532C2211yescharacteristic
81C2×C4×Q8×C43C2211yescharacteristic
82C43×#464C2214yescomplemented
83C43×#462C2212yescomplemented
84C43×#460C2212yescomplemented
85C43×#423C2211yescharacteristic
86C43×#417C2212yes—
87C22×Dic86C2311yescharacteristic
88C22×C4×D43C2311yescharacteristic
89#13063355—44no—
90C2×#10621885C2314yes—
91C2×#10621883C2314yes—
92C2×#10621877C2312yes—
93C2×#10621872C2314yes—
94M16×D43—44no—
95C2×C8×D43C2314yes—
96#13063325C2311yescharacteristic
97#13063325C2311yescharacteristic
98#13063323—22no—
99#13063323C2314yes—
100#13063320—24no—
101#13063320—24no—
102#13063320—22no—
103#13063320—22no—
104#13063319—24no—
105#13063319—24no—
106#13063318—22no—
107#13063318—22no—
108#13063317—24no—
109#13063317—24no—
110#13063317C2312yes—
111#13063316—22no—
112#13063316C2314yes—
113#13063315—24no—
114#13063315—24no—
115#13063315—22no—
116#13063315—22no—
117#13063311—22no—
118#13063311—22no—
119#13063309—22no—
120#13063309—22no—
121#13063306—22no—
122#13063306—22no—
123#13063306—22no—
124#13063305—22no—
125#13063305C2314yes—
126#13063304—21no—
127#13063304—21no—
128#13063302—22no—
129#13063302—22no—
130#13063301—22no—
131#13063301C2314yes—
132#13063301C2312yes—
133#13063301C2312yes—
134#13063297—22no—
135#13063297—22no—
136#13063296C2312yes—
137#13063296C2312yes—
138#13063293—22no—
139Q8×Dic43C2312yes—
140Q8×Dic43C2312yes—
141C4×Dic86—21no—
142C4×Dic86—21no—
143C4×Dic86—21no—
144C4×Dic86—21no—
145C4×Dic86C2312yes—
146C4×Dic86C2312yes—
147D4×Dic43—22no—
148D4×Dic43—22no—
149D4×Dic43C2312yes—
150D4×Dic43C2312yes—
151C4×C22⋊D43—22no—
152C4×C22⋊D43—22no—
153#13063284—22no—
154#13063284C2312yes—
155#13063282D412yes—
156#13063282D412yes—
157#13063282C2312yes—
158#13063282C2312yes—
159C2×C4⋊Dic43—21no—
160C2×C4⋊Dic43—21no—
161C2×C4⋊Dic43C2311yescharacteristic
162C2×Dic43⋊C4—21no—
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4—21no—
165C2×Dic43⋊C4—21no—
166C2×Dic43⋊C4—21no—
167C2×Dic43⋊C4D411yescharacteristic
168C2×Dic43⋊C4D411yescharacteristic
169C2×(C2×D43)⋊C4—21no—
170C2×(C2×D43)⋊C4—21no—
171C2×(C2×D43)⋊C4D411yescharacteristic
172C2×(C2×D43)⋊C4D411yescharacteristic
173C2×C4×Dic43—21no—
174C2×C4×Dic43—22no—
175C2×C4×Dic43C2311yescharacteristic
176#13063259C2314yes—
177#13063258C2314yes—
178#13063257C2314yes—
179#13063256C2314yes—
180C4⋊(C43⋊C8)C2312yes—
181C4⋊(C43⋊C8)C2312yes—
182Dic43⋊C8C2314yes—
183Dic43⋊C8C2314yes—
184#13063250C2314yes—
185#13063250C2314yes—
186#13063249C2314yes—
187#13063249C2314yes—
188#13063249C2314yes—
189#13063246C2314yes—
190C2×#41×C43C2312yes—
191C22×Q8×C43C2311yescharacteristic
192#137×C43—44no—
193C2×Q16×C43C2314yes—
194C2×SD16×C43C2314yes—
195C2×M16×C43C2312yes—
196C4⋊Q8×C43C2311yescharacteristic
197#127×C43C2311yescharacteristic
198#124×C43C2312yes—
199#121×C43—21no—
200#121×C43—21no—
201C4×Q8×C43—21no—
202C4×Q8×C43—21no—
203C4×Q8×C43C2312yes—
204C4×Q8×C43C2312yes—
205C4×D4×C43—21no—
206C4×D4×C43—21no—
207C2×C4⋊C4×C43—21no—
208C2×C4⋊C4×C43C2311yescharacteristic
209C2×C42×C43—21no—
210C2×C42×C43C2311yescharacteristic
211C4⋊C8×C43C2312yes—
212C4⋊C8×C43C2312yes—
213#103×C43C2314yes—
214#102×C43C2314yes—
215C23×D43C2×D411yescharacteristic
216#41×C43—24no—
217#41×C43—24no—
218C2×Q8×C43—21no—
219C2×Q8×C43—22no—
220C2×Q8×C43—22no—
221C2×Q8×C43C2412yes—
222C2×Q8×C43C2412yes—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—22no—
226C2×D4×C43C2412yes—
227C22×C4×C43—22no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C2×C22⋊D43—22no—
234C2×C22⋊D43—22no—
235C22×Dic43—22no—
236C22×Dic43—22no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43C2×D411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241C22×Dic43C2×D411yescharacteristic
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2412yes—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86—21no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86C2412yes—
252Q16×C43—44no—
253SD16×C43—44no—
254M16×C43—24no—
255C2×C8×C43C2414yes—
256C4⋊C4×C43—22no—
257C4⋊C4×C43—22no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C2412yes—
262C22⋊C4×C43—22no—
263C22⋊C4×C43—22no—
264C42×C43—22no—
265C42×C43—22no—
266C42×C43C2×D411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2411yescharacteristic
269C42×C43C2411yescharacteristic
270C22⋊Dic43—22no—
271C22⋊Dic43—22no—
272C22⋊Dic43—22no—
273C22⋊Dic43—22no—
274C22⋊Dic43—22no—
275#10621885—44no—
276#10621883—44no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—22no—
280(C2×D43)⋊C4—22no—
281(C2×D43)⋊C4C2×D412yes—
282(C2×D43)⋊C4C2×D412yes—
283(C2×D43)⋊C4C2×D412yes—
284(C2×D43)⋊C4C2×D412yes—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—24no—
289C4⋊Dic43—24no—
290C4⋊Dic43—22no—
291C4⋊Dic43—22no—
292C4⋊Dic43C2412yes—
293C4⋊Dic43C2412yes—
294C4⋊Dic43C2412yes—
295Dic43⋊C4—22no—
296Dic43⋊C4—22no—
297Dic43⋊C4—22no—
298Dic43⋊C4—22no—
299Dic43⋊C4—24no—
300Dic43⋊C4—24no—
301Dic43⋊C4—24no—
302Dic43⋊C4—24no—
303Dic43⋊C4—22no—
304Dic43⋊C4—22no—
305Dic43⋊C4C2×D412yes—
306Dic43⋊C4C2×D412yes—
307Dic43⋊C4C2×D412yes—
308Dic43⋊C4C2×D412yes—
309C4×Dic43—22no—
310C4×Dic43—22no—
311C4×Dic43—22no—
312C4×Dic43—22no—
313C4×Dic43—22no—
314C4×Dic43C2×D412yes—
315C4×Dic43C2412yes—
316#10621877—24no—
317C2×C43⋊C8C2414yes—
318#10621872—44no—
319C8×D43—44no—
320C23×C43—22no—
321C23×C43C22×D411yescharacteristic
322C22×D43—22no—
323C22×D43—41no—
324C22×D43—41no—
325C22×D43C22×D412yes—
326Q8×C43—22no—
327Q8×C43—22no—
328Q8×C43—22no—
329Q8×C43—22no—
330Q8×C43—42no—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—44no—
334D4×C43—81no—
335D4×C43—81no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43—44no—
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43H(5,𝔽2)12yes—
350C2×C4×C432−1+412yes—
351C2×C4×C43C2511yescharacteristic
352C22⋊D43—82no—
353C22⋊D43—82no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—42no—
362C2×Dic43—42no—
363C2×Dic43—82no—
364C2×Dic43—82no—
365C2×Dic43C22×D412yes—
366C2×Dic43C22×D412yes—
367C2×Dic43C22×D412yes—
368C4×D43—24no—
369C4×D43—22no—
370C4×D43—22no—
371Dic86—22no—
372Dic86—22no—
373Dic86—42no—
374Dic86—81no—
375Dic86—81no—
376C8×C43—24no—
377C43⋊C8—24no—
378#60921—431nomaximal, Sylow
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43#53712yes—
385C22×C43C23×D411yescharacteristic
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—82no—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—21no—
393C4×C43—21no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43—42no—
397C4×C43#53712yes—
398C4×C43C2×H(5,𝔽2)11yescharacteristic
399C4×C43C2×2−1+411yescharacteristic
400Dic43—22no—
401Dic43—22no—
402Dic43—22no—
403Dic43—42no—
404Dic43—42no—
405Dic43—42no—
406Dic43—42no—
407#3455—431no—
408C2×#541—431no—
409#3261—434no—
410#3260—434no—
411#3258—434no—
412#3258—434no—
413#3080—432no—
414#3078—431no—
415#3078—431no—
416#3056—432no—
417#3056—432no—
418#3039—432no—
419#3037—431no—
420#3037D4311yescharacteristic, complemented
421#2905—431no—
422C2×C43—22no—
423C2×C43—82no—
424C2×C43C2×#53711yescharacteristic
425C2×C43#358611yescharacteristic
426C2×C43#358611yescharacteristic
427D43—42no—
428C2×#137—432no—
429C2×#137C2×D4312yes—
430C22×M16—432no—
431#542—432no—
432#542—432no—
433#541—432no—
434#541—434no—
435#541—434no—
436#541—862no—
437#541—862no—
438#540—432no—
439#539—861no—
440#539—861no—
441#538—861no—
442#538—861no—
443#533—431no—
444#532C2×D4311yescharacteristic
445C2×C4⋊Q8—431no—
446#529—862no—
447#529—862no—
448C2×#126—861no—
449C2×#126—861no—
450C2×#125—431no—
451C2×#125—861no—
452C2×#125—861no—
453#525—432no—
454C2×C22⋊Q8—431no—
455C2×C22⋊Q8—431no—
456C4×#41—432no—
457C2×C4×Q8—431no—
458C2×C4×Q8C2×D4311yescharacteristic
459C2×#117—431no—
460#479—434no—
461#479—434no—
462#479—434no—
463#479—434no—
464#478—434no—
465#478—434no—
466#477—432no—
467#477—432no—
468#475—432no—
469#475—432no—
470#470—434no—
471#470—434no—
472#468—434no—
473#468—434no—
474#467—434no—
475#467—434no—
476#465—434no—
477#465—434no—
478#464—434no—
479#464C2×D4314yescomplemented
480#462—434no—
481#462—434no—
482#462—432no—
483#462C2×D4312yescomplemented
484#461—434no—
485#461—434no—
486#460—432no—
487#460C2×D4312yescomplemented
488#428—432no—
489#428—432no—
490#424—434no—
491#424—434no—
492#423—432no—
493#423—431no—
494#423C2×D4311yescharacteristic
495#419—432no—
496#419—432no—
497#417—432no—
498#417C2×D4312yes—
499C43#6092111yescharacteristic, complemented, Sylow
500C2×#41C22×D4312yes—
501C22×Q8—431no—
502C22×Q8C22×D4311yescharacteristic
503C23×C4—431no—
504#137—44no—
505#137—1724no—
506C2×Q16—434no—
507C2×Q16C22×D4314yes—
508C2×SD16—434no—
509C2×SD16C22×D4314yes—
510C2×M16—432no—
511C2×M16—434no—
512C2×M16—1724no—
513C2×M16C22×D4312yes—
514C22×C8—434no—
515C4⋊Q8—434no—
516C4⋊Q8—431no—
517C4⋊Q8—431no—
518C4⋊Q8—862no—
519C4⋊Q8C22×D4311yescharacteristic
520#127C22×D4311yescharacteristic
521#126—864no—
522#126—864no—
523#126—862no—
524#126—862no—
525#126—864no—
526#126—864no—
527#126—862no—
528#126—862no—
529#125—434no—
530#125—432no—
531#125—864no—
532#125—864no—
533#125—862no—
534#125—864no—
535#125—864no—
536#125—862no—
537#125—862no—
538#124—862no—
539#124—862no—
540#124C22×D4312yes—
541#123—862no—
542#123—862no—
543#123—862no—
544#123—862no—
545#123—862no—
546C22⋊Q8—434no—
547C22⋊Q8—432no—
548C22⋊Q8—432no—
549C22⋊Q8—434no—
550C22⋊Q8—862no—
551C22⋊Q8—862no—
552C22⋊Q8—862no—
553C22⋊Q8—862no—
554C22⋊Q8—861no—
555C22⋊Q8—861no—
556#121—21no—
557#121—21no—
558#121—432no—
559#121—432no—
560#121—862no—
561#121—862no—
562#120—862no—
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8—432no—
566C4×Q8—432no—
567C4×Q8—432no—
568C4×Q8—432no—
569C4×Q8—861no—
570C4×Q8—861no—
571C4×Q8—861no—
572C4×Q8—861no—
573C4×Q8C22×D4312yes—
574C4×Q8C22×D4312yes—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4—432no—
578C4×D4—432no—
579C4×D4—862no—
580C4×D4—862no—
581C4×D4—862no—
582C4×D4—862no—
583#117—432no—
584#117—432no—
585#117—432no—
586#117—432no—
587#117—432no—
588#117—862no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4—861no—
596C2×C4⋊C4—861no—
597C2×C4⋊C4—861no—
598C2×C4⋊C4—861no—
599C2×C4⋊C4—861no—
600C2×C4⋊C4C22×D4311yescharacteristic
601C2×C22⋊C4—431no—
602C2×C22⋊C4—431no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C42—21no—
606C2×C42—431no—
607C2×C42—862no—
608C2×C42—861no—
609C2×C42C22×D4311yescharacteristic
610#107—434no—
611#107—434no—
612#106—434no—
613#106—434no—
614C4⋊C8—434no—
615C4⋊C8—434no—
616C4⋊C8—432no—
617C4⋊C8—432no—
618C4⋊C8C22×D4312yes—
619C4⋊C8C22×D4312yes—
620#103—434no—
621#103—434no—
622#103—434no—
623#103—434no—
624#103—434no—
625#103C22×D4314yes—
626#102—434no—
627#102C22×D4314yes—
628C24—431no—
629#41—24no—
630#41—24no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—432no—
635C2×Q8—861no—
636C2×Q8—861no—
637C2×Q8—861no—
638C2×Q8—862no—
639C2×Q8—862no—
640C2×Q8C23×D4312yes—
641C2×Q8C23×D4312yes—
642C2×D4—22no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—862no—
646C2×D4—862no—
647C2×D4C23×D4312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—22no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—432no—
655C22×C4—432no—
656C22×C4—862no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—862no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4D4×D4311yescharacteristic
663C22×C4D4×D4311yescharacteristic
664C22×C4C23×D4311yescharacteristic
665Q16—44no—
666Q16—1724no—
667SD16—44no—
668SD16—1724no—
669M16—24no—
670M16—864no—
671M16—1724no—
672C2×C8—434no—
673C2×C8—1724no—
674C2×C8C23×D4314yes—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—432no—
681C4⋊C4—432no—
682C4⋊C4—432no—
683C4⋊C4—432no—
684C4⋊C4—432no—
685C4⋊C4—432no—
686C4⋊C4—432no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—864no—
692C4⋊C4—864no—
693C4⋊C4—862no—
694C4⋊C4—862no—
695C4⋊C4—862no—
696C4⋊C4—862no—
697C4⋊C4—861no—
698C4⋊C4—862no—
699C4⋊C4—862no—
700C4⋊C4—862no—
701C4⋊C4—862no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4C23×D4312yes—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—432no—
708C22⋊C4—432no—
709C22⋊C4—432no—
710C22⋊C4—432no—
711C22⋊C4—864no—
712C22⋊C4—864no—
713C22⋊C4—862no—
714C22⋊C4—862no—
715C22⋊C4—862no—
716C22⋊C4—862no—
717C22⋊C4—862no—
718C22⋊C4—862no—
719C22⋊C4—862no—
720C42—22no—
721C42—22no—
722C42—432no—
723C42—432no—
724C42—862no—
725C42—862no—
726C42—862no—
727C42—862no—
728C42—862no—
729C42D4×D4311yescharacteristic
730C42D4×D4311yescharacteristic
731C42C23×D4311yescharacteristic
732C42C23×D4311yescharacteristic
733C23—22no—
734C23—432no—
735C23—862no—
736C23—1721no—
737C23—1721no—
738C23C2×D4×D4311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—862no—
745Q8—862no—
746Q8—3441no—
747Q8—3441no—
748Q8—1722no—
749D4—22no—
750D4—22no—
751D4—44no—
752D4—81no—
753D4—81no—
754D4—3442no—
755D4—3442no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—432no—
765C2×C4—432no—
766C2×C4—432no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—864no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—3442no—
776C2×C4—3442no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1722no—
780C2×C4—1722no—
781C2×C4C2×D4×D4311yescharacteristic
782C2×C4C2×D4×D4311yescharacteristic
783C2×C4C2×D4×D4311yescharacteristic
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4C2×D4×D4311yescharacteristic
786C2×C4#1306337012yes—
787C2×C4#1306337212yes—
788C2×C4C24×D4311yescharacteristic
789C8—24no—
790C8—864no—
791C22—21no—
792C22—21no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—862no—
797C22—862no—
798C22—862no—
799C22—3442no—
800C22#1458347812yes—
801C22C22×D4×D4311yescharacteristic
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—862no—
810C4—862no—
811C4—862no—
812C4—1722no—
813C4—1722no—
814C4—1722no—
815C4—1722no—
816C4#1458347812yes—
817C4C2×#1306337011yescharacteristic
818C4C2×#1306337211yescharacteristic
819C2—22no—
820C2—82no—
821C2—1722no—
822C2C2×#1458347811yescharacteristic
823C2#1914937811yescharacteristic
824C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3037C2
socleC22×C43C23×D4
prime radical#19147984C2
hypercenter#3037D43
hypocenterC43#60921
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. C2×#14583507C2semidirect
3. #19146047C2semidirect
4. #19146039C2semidirect
5. #19146026C2semidirect
6. #19146018C2semidirect
7. #19144415C2semidirect
8. #19144402C2semidirect
9. #19144400C2semidirect
10. #19144228C2semidirect
11. #19144219C2semidirect
12. #19144080C2semidirect
13. #19144063C2semidirect
14. #19143157C2semidirect
15. C43×#3037C2semidirect
45. #14583208C22semidirect
46. #14583207C22semidirect
47. #14583206C22semidirect
48. #14583204C22semidirect
49. #14583201C22semidirect
50. #14583197C22semidirect
51. #14583195C22semidirect
52. #14583194C22semidirect
53. #14583185C22semidirect
54. #14583184C22semidirect
63. #14583118C22semidirect
64. #14583107C22semidirect
65. #14583107C22semidirect
66. #14583106C22semidirect
67. #14583102C22semidirect
68. #14583102C22semidirect
69. #14583096C22semidirect
82. C43×#464C22semidirect
83. C43×#462C22semidirect
84. C43×#460C22semidirect
420. #3037D43semidirect
479. #464C2×D43semidirect
483. #462C2×D43semidirect
487. #460C2×D43semidirect
499. C43#60921semidirect

Maximal subgroups

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

subgroupindex
#191479842
C2×#145835072
#191460472
#191460392
#191460262
#191460182
#191444152
#191444022
#191444002
#191442282
#191442192
#191440802
#191440632
#191431572
C43×#30372
#6092143