Finite Group Databasebeta

← #25967392

Subgroups — #25967392

Order 11008.

2130 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147924C211yesmaximal, characteristic
2C2×#14583472C211yesmaximal, characteristic, complemented
3#19145488C214yesmaximal, complemented
4#19145476C214yesmaximal, complemented
5#19145474C214yesmaximal, complemented
6#19145464C214yesmaximal, complemented
7#19144544C211yesmaximal, characteristic, complemented
8#19144539C211yesmaximal, characteristic, complemented
9#19144525C212yesmaximal, complemented
10#19144228C212yesmaximal, complemented
11#19144219C212yesmaximal, complemented
12#19143855C211yesmaximal, characteristic, complemented
13#19143827C212yesmaximal, complemented
14#19143038C211yesmaximal, characteristic, complemented
15C43×#3007C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic, complemented
18C2×#13063355C2212yes—
19C2×M16×D43C2212yescomplemented
20#14583477C2212yes—
21#14583477C2212yes—
22#14583473C2212yes—
23#14583472—22no—
24#14583472—22no—
25#14583472C2214yes—
26#14583472C2214yescomplemented
27#14583470—21no—
28#14583466C2212yes—
29#14583463—21no—
30#14583458—21no—
31#14583458—21no—
32#14583445—22no—
33C2×#13063324—21no—
34C2×#13063311—21no—
35#14583410—22no—
36#14583406C2212yes—
37#14583406C2212yes—
38C2×#13063310—21no—
39C2×#13063307—21no—
40C2×#13063305C2211yescharacteristic, complemented
41C2×#13063304C2211yescharacteristic
42C2×#13063301C2211yescharacteristic, complemented
43C2×#13063284C2211yescharacteristic
44C2×#13063283C2211yescharacteristic, complemented
45#14583241C2214yescomplemented
46#14583239C2214yescomplemented
47#14583238C2214yescomplemented
48#14583237C2214yescomplemented
49#14583235C2212yescomplemented
50#14583232C2212yescomplemented
51#14583230C2212yescomplemented
52#14583227C2212yescomplemented
53#14583222C2214yescomplemented
54#14583221C2214yescomplemented
55#14583156C2214yescomplemented
56#14583154C2214yescomplemented
57#14583144C2214yescomplemented
58#14583142C2214yescomplemented
59#14583139C2214yescomplemented
60#14583137C2214yescomplemented
61#14583127C2214yescomplemented
62#14583125C2214yescomplemented
63#14583061C2214yescomplemented
64#14583055C2212yescomplemented
65#14583053C2214yescomplemented
66#14583053C2214yescomplemented
67#14583050C2212yescomplemented
68#14583036C2214yescomplemented
69#14583036C2214yescomplemented
70#14582941C2212yescomplemented
71#14582939C2212yescomplemented
72#14582909C2212yescomplemented
73#14582908C2212yescomplemented
74#14582900C2212yes—
75#14582864C2214yes—
76#14582864C2214yescomplemented
77#14582863C2211yescharacteristic
78#14582862C2212yescomplemented
79C22×#41×C43C2211yescharacteristic
80C2×#137×C43C2212yes—
81C2×C22⋊Q8×C43C2211yescharacteristic
82C43×#452C2214yescomplemented
83C43×#451C2212yescomplemented
84C43×#450C2212yescomplemented
85C43×#417C2212yes—
86C43×#407C2211yescharacteristic
87C2×#10621898—44no—
88C2×#10621898D412yes—
89C2×#10621898D412yes—
90C2×#10621898C2312yes—
91C2×#10621898C2312yes—
92C22×Dic86—21no—
93C22×Dic86D411yescharacteristic
94C22×Dic86C2311yescharacteristic
95C2×Q8×D43—22no—
96C2×Q8×D43—44no—
97C2×Q8×D43C2314yes—
98C22×D172D411yescharacteristic
99C22×C22⋊D43D411yescharacteristic
100C22×C22⋊D43D411yescharacteristic
101C22×C4×D43—21no—
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2311yescharacteristic
104#13063355—44no—
105C2×#10621885C2314yes—
106C2×#10621883C2314yes—
107C2×#10621877C2312yes—
108C2×#10621872C2314yes—
109M16×D43—44no—
110C2×C8×D43C2314yes—
111#13063324—24no—
112#13063324—24no—
113#13063323—22no—
114#13063321—22no—
115#13063314—22no—
116#13063312—22no—
117#13063311—24no—
118#13063311—24no—
119#13063310—24no—
120#13063310—24no—
121#13063308—22no—
122#13063308—22no—
123#13063307—24no—
124#13063307—24no—
125#13063306—22no—
126#13063306—22no—
127#13063305—22no—
128#13063305C2314yes—
129#13063304—21no—
130#13063304—21no—
131#13063304—22no—
132#13063304—22no—
133#13063304C2312yes—
134#13063304C2312yes—
135#13063301—22no—
136#13063301C2312yes—
137#13063301C2312yes—
138#13063301C2314yes—
139#13063301C2312yes—
140#13063301C2312yes—
141#13063299—22no—
142#13063299—22no—
143#13063297—22no—
144#13063297—22no—
145#13063297—22no—
146#13063297—22no—
147#13063296C2312yes—
148#13063296C2312yes—
149#13063296C2312yes—
150#13063296C2312yes—
151#13063294—22no—
152#13063294—22no—
153#13063293—22no—
154#13063293—22no—
155C4×C22⋊D43—22no—
156C4×C22⋊D43—22no—
157C4×C22⋊D43—22no—
158C4×C22⋊D43—22no—
159#13063284—21no—
160#13063284—21no—
161#13063284C2312yes—
162#13063284C2312yes—
163#13063283—22no—
164#13063283C2314yes—
165C2×C4⋊Dic43—21no—
166C2×C4⋊Dic43C2311yescharacteristic
167C2×C4⋊Dic43C2311yescharacteristic
168C2×C4⋊Dic43C2311yescharacteristic
169C2×Dic43⋊C4—21no—
170C2×Dic43⋊C4—21no—
171C2×C22⋊Dic43—21no—
172C2×C22⋊Dic43—21no—
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4—21no—
175C2×(C2×D43)⋊C4—21no—
176C2×C4×Dic43—21no—
177C2×C4×Dic43—21no—
178#13063259C2314yes—
179#13063258C2314yes—
180#13063257C2314yes—
181#13063256C2314yes—
182#13063250C2314yes—
183#13063250C2314yes—
184#13063249C2314yes—
185#13063249C2314yes—
186#13063249C2314yes—
187#13063246C2314yes—
188C22⋊(C43⋊C8)C2312yes—
189C22⋊(C43⋊C8)C2312yes—
190(C2×D43)⋊C8C2314yes—
191(C2×D43)⋊C8C2314yes—
192C2×#41×C43—21no—
193C2×#41×C43—21no—
194C2×#41×C43—44no—
195C2×#41×C43C2312yes—
196C2×#41×C43C2312yes—
197C22×Q8×C43C2311yescharacteristic
198C22×Q8×C43C2311yescharacteristic
199C22×D4×C43—21no—
200C22×D4×C43C2311yescharacteristic
201C23×C4×C43—21no—
202C23×C4×C43C2311yescharacteristic
203#137×C43—44no—
204C2×Q16×C43C2314yes—
205C2×SD16×C43C2314yes—
206C2×M16×C43C2312yes—
207C22⋊Q8×C43—21no—
208C22⋊Q8×C43—21no—
209C22⋊Q8×C43C2312yes—
210C22⋊Q8×C43C2312yes—
211C2×C4⋊C4×C43—21no—
212C2×C4⋊C4×C43C2311yescharacteristic
213C2×C22⋊C4×C43—21no—
214#103×C43C2314yes—
215#102×C43C2314yes—
216C22⋊C8×C43C2312yes—
217C22⋊C8×C43C2312yes—
218C24×C43—21no—
219C24×C43C2×D411yescharacteristic
220C23×D43C2×D411yescharacteristic
221C23×D43C2×D411yescharacteristic
222#41×C43—24no—
223#41×C43—24no—
224#41×C43—42no—
225#41×C43—42no—
226#41×C43—44no—
227#41×C43—44no—
228C2×Q8×C43—21no—
229C2×Q8×C43—21no—
230C2×Q8×C43—24no—
231C2×Q8×C43—42no—
232C2×Q8×C43C2412yes—
233C2×Q8×C43C2412yes—
234C2×D4×C43—21no—
235C2×D4×C43—22no—
236C2×D4×C43—22no—
237C2×D4×C43—44no—
238C2×D4×C43—42no—
239C2×D4×C43C2412yes—
240C22×C4×C43—24no—
241C22×C4×C43—22no—
242C22×C4×C43—22no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—44no—
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2411yescharacteristic
251C22×C4×C43C2411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253C2×C22⋊D43—22no—
254C2×C22⋊D43—22no—
255C2×C22⋊D43—22no—
256C2×C22⋊D43—22no—
257C2×C22⋊D43—42no—
258C2×C22⋊D43—42no—
259C2×C22⋊D43C2×D412yes—
260C2×C22⋊D43C2×D412yes—
261C2×C22⋊D43C2×D412yes—
262C2×C22⋊D43C2×D412yes—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43C2×D411yescharacteristic
268C22×Dic43C2×D411yescharacteristic
269Q8×D43—44no—
270Q8×D43—44no—
271Q8×D43—48no—
272#10621898—44no—
273#10621898—44no—
274#10621898—42no—
275#10621898—42no—
276#10621898—42no—
277#10621898—42no—
278C2×D172—42no—
279C2×D172C2×D412yes—
280C2×D172C2×D412yes—
281C2×C4×D43—24no—
282C2×C4×D43—24no—
283C2×C4×D43—24no—
284C2×C4×D43—44no—
285C2×C4×D43C2×D412yes—
286C2×C4×D43C2×D412yes—
287C2×C4×D43C2412yes—
288C2×C4×D43C2412yes—
289C2×Dic86—24no—
290C2×Dic86—21no—
291C2×Dic86—24no—
292C2×Dic86—42no—
293C2×Dic86—44no—
294C2×Dic86C2×D412yes—
295C2×Dic86C2×D412yes—
296C2×Dic86C2412yes—
297Q16×C43—44no—
298SD16×C43—44no—
299M16×C43—24no—
300C2×C8×C43C2414yes—
301C4⋊C4×C43—22no—
302C4⋊C4×C43—22no—
303C4⋊C4×C43—21no—
304C4⋊C4×C43C2412yes—
305C22⋊C4×C43—22no—
306C22⋊C4×C43—22no—
307C22⋊Dic43—22no—
308C22⋊Dic43—22no—
309C22⋊Dic43—22no—
310C22⋊Dic43—22no—
311C22⋊Dic43—22no—
312C22⋊Dic43—22no—
313C22⋊Dic43—22no—
314C22⋊Dic43—22no—
315#10621885—44no—
316#10621883—44no—
317(C2×D43)⋊C4—24no—
318(C2×D43)⋊C4—24no—
319(C2×D43)⋊C4—24no—
320(C2×D43)⋊C4—22no—
321(C2×D43)⋊C4—22no—
322(C2×D43)⋊C4—22no—
323(C2×D43)⋊C4—22no—
324C4⋊Dic43—21no—
325C4⋊Dic43—21no—
326C4⋊Dic43—21no—
327C4⋊Dic43—24no—
328C4⋊Dic43C2412yes—
329C4⋊Dic43C2412yes—
330C4⋊Dic43C2412yes—
331Dic43⋊C4—22no—
332Dic43⋊C4—22no—
333Dic43⋊C4—24no—
334Dic43⋊C4—22no—
335Dic43⋊C4—22no—
336Dic43⋊C4—22no—
337Dic43⋊C4—22no—
338C4×Dic43—22no—
339C4×Dic43—22no—
340C4×Dic43—24no—
341#10621877—24no—
342C2×C43⋊C8C2414yes—
343#10621872—44no—
344C8×D43—44no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—42no—
350C23×C43—81no—
351C23×C43—81no—
352C23×C43C22×D411yescharacteristic
353C23×C43C22×D411yescharacteristic
354C23×C43C22×D411yescharacteristic
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—41no—
358C22×D43—41no—
359C22×D43—41no—
360C22×D43—41no—
361C22×D43C22×D412yes—
362C22×D43C22×D412yes—
363Q8×C43—22no—
364Q8×C43—24no—
365Q8×C43—22no—
366Q8×C43—42no—
367Q8×C43—42no—
368D4×C43—22no—
369D4×C43—22no—
370D4×C43—42no—
371D4×C43—44no—
372D4×C43—44no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—44no—
382C2×C4×C43—42no—
383C2×C4×C43—42no—
384C2×C4×C43—42no—
385C2×C4×C43—44no—
386C2×C4×C43C22×D411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43H(5,𝔽2)14yes—
390C2×C4×C43C2511yescharacteristic
391C22⋊D43—42no—
392C22⋊D43—42no—
393C22⋊D43—42no—
394C22⋊D43—42no—
395C22⋊D43—82no—
396C22⋊D43—82no—
397C22⋊D43—82no—
398C22⋊D43—82no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—42no—
406C2×Dic43—42no—
407C2×Dic43—81no—
408C2×Dic43—81no—
409C2×Dic43C22×D412yes—
410C2×Dic43C22×D412yes—
411D172—42no—
412D172—42no—
413C4×D43—24no—
414C4×D43—24no—
415C4×D43—22no—
416C4×D43—22no—
417C4×D43—22no—
418C4×D43—22no—
419C4×D43—48no—
420Dic86—24no—
421Dic86—42no—
422Dic86—42no—
423Dic86—48no—
424Dic86—42no—
425C8×C43—24no—
426C43⋊C8—24no—
427#60754—431nomaximal, Sylow
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—42no—
437C22×C43—42no—
438C22×C43—42no—
439C22×C43—82no—
440C22×C43—84no—
441C22×C43#53412yes—
442C22×C43C23×D411yescharacteristic
443C2×D43—22no—
444C2×D43—22no—
445C2×D43—22no—
446C2×D43—22no—
447C2×D43—22no—
448C2×D43—22no—
449C2×D43—44no—
450C2×D43—82no—
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—42no—
454C4×C43—42no—
455C4×C43—42no—
456C4×C43#53412yes—
457C4×C43C2×H(5,𝔽2)12yes—
458Dic43—22no—
459Dic43—22no—
460Dic43—42no—
461Dic43—42no—
462Dic43—42no—
463Dic43—42no—
464#3449—431no—
465C2×#536—431no—
466#3202—434no—
467#3201—434no—
468#3201—434no—
469#3200—434no—
470#3095—431no—
471#3095—431no—
472#3093—432no—
473#3056—432no—
474#3056—432no—
475#3007—431no—
476#3007D4311yescharacteristic, complemented
477#3004—432no—
478#2879—431no—
479C2×C43—22no—
480C2×C43—41no—
481C2×C43—41no—
482C2×C43—82no—
483C2×C43C2×#53411yescharacteristic
484C2×C43#358611yescharacteristic
485C2×C43#358611yescharacteristic
486D43—42no—
487D43—42no—
488C22×#41—431no—
489C22×#41C2×D4311yescharacteristic
490C23×Q8—431no—
491C2×#137—432no—
492C2×#137C2×D4312yes—
493C22×M16—432no—
494#537—432no—
495#537—432no—
496#536—432no—
497#536—434no—
498#536—434no—
499#536—862no—
500#536—862no—
501#536—861no—
502#535—432no—
503#535—861no—
504#534—861no—
505#534—861no—
506#532—862no—
507C2×C4⋊Q8—861no—
508C2×#124—861no—
509#525—432no—
510#525—432no—
511#525—862no—
512C2×#123—861no—
513C2×#123—861no—
514C2×C22⋊Q8—431no—
515C2×C22⋊Q8—431no—
516C2×C22⋊Q8—431no—
517C2×C22⋊Q8C2×D4311yescharacteristic
518C2×#117—431no—
519C2×#117—431no—
520#485—434no—
521#485—434no—
522#485—434no—
523#485—434no—
524#484—432no—
525#484—432no—
526#483—432no—
527#483—432no—
528#482—434no—
529#482—434no—
530#470—434no—
531#470—434no—
532#468—434no—
533#468—434no—
534#467—434no—
535#467—434no—
536#465—434no—
537#465—434no—
538#452—434no—
539#452C2×D4314yescomplemented
540#451—432no—
541#451—434no—
542#451—434no—
543#451C2×D4312yescomplemented
544#450—432no—
545#450C2×D4312yescomplemented
546#448—434no—
547#448—434no—
548#428—432no—
549#428—432no—
550#419—432no—
551#419—432no—
552#417—432no—
553#417C2×D4312yes—
554#408—434no—
555#408—434no—
556#407—431no—
557#407—432no—
558#407C2×D4311yescharacteristic
559C43#6075411yescharacteristic, complemented, Sylow
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—44no—
563C2×#41—432no—
564C2×#41—432no—
565C2×#41—432no—
566C2×#41—432no—
567C2×#41—1724no—
568C2×#41C22×D4312yes—
569C2×#41C22×D4312yes—
570C22×Q8—431no—
571C22×Q8—434no—
572C22×Q8—431no—
573C22×Q8—861no—
574C22×Q8—862no—
575C22×Q8—1724no—
576C22×Q8C22×D4311yescharacteristic
577C22×Q8C22×D4311yescharacteristic
578C22×D4—21no—
579C22×D4—431no—
580C22×D4—431no—
581C22×D4—431no—
582C22×D4C22×D4311yescharacteristic
583C23×C4—21no—
584C23×C4—431no—
585C23×C4—431no—
586C23×C4—861no—
587C23×C4C22×D4311yescharacteristic
588#137—44no—
589#137—1724no—
590C2×Q16—434no—
591C2×Q16C22×D4314yes—
592C2×SD16—434no—
593C2×SD16C22×D4314yes—
594C2×M16—432no—
595C2×M16—434no—
596C2×M16—1724no—
597C2×M16C22×D4312yes—
598C22×C8—434no—
599C4⋊Q8—864no—
600C4⋊Q8—864no—
601C4⋊Q8—862no—
602#127—862no—
603#124—864no—
604#124—864no—
605#124—862no—
606#124—862no—
607#123—864no—
608#123—864no—
609#123—864no—
610#123—864no—
611#123—862no—
612#123—862no—
613#123—862no—
614#123—862no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—434no—
618C22⋊Q8—432no—
619C22⋊Q8—432no—
620C22⋊Q8—432no—
621C22⋊Q8—432no—
622C22⋊Q8—432no—
623C22⋊Q8—432no—
624C22⋊Q8—434no—
625C22⋊Q8—862no—
626C22⋊Q8—862no—
627C22⋊Q8—862no—
628C22⋊Q8—862no—
629C22⋊Q8—861no—
630C22⋊Q8—861no—
631C22⋊Q8C22×D4312yes—
632C22⋊Q8C22×D4312yes—
633#121—432no—
634#121—432no—
635#121—432no—
636#121—432no—
637#121—862no—
638#121—862no—
639#121—862no—
640#121—862no—
641#121—862no—
642#121—862no—
643#120—862no—
644#120—862no—
645#120—862no—
646#120—862no—
647C4×D4—862no—
648C4×D4—862no—
649C4×D4—862no—
650C4×D4—862no—
651#117—432no—
652#117—432no—
653#117—434no—
654#117—862no—
655#117—861no—
656#117—861no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—431no—
659C2×C4⋊C4—431no—
660C2×C4⋊C4—431no—
661C2×C4⋊C4—861no—
662C2×C4⋊C4—861no—
663C2×C4⋊C4—861no—
664C2×C4⋊C4C22×D4311yescharacteristic
665C2×C22⋊C4—21no—
666C2×C22⋊C4—861no—
667C2×C22⋊C4—861no—
668C2×C22⋊C4—861no—
669C2×C22⋊C4—861no—
670C2×C22⋊C4—861no—
671C2×C42—861no—
672C2×C42—861no—
673#107—434no—
674#107—434no—
675#106—434no—
676#106—434no—
677#103—434no—
678#103—434no—
679#103—434no—
680#103—434no—
681#103—434no—
682#103C22×D4314yes—
683#102—434no—
684#102C22×D4314yes—
685C22⋊C8—432no—
686C22⋊C8—432no—
687C22⋊C8—434no—
688C22⋊C8—434no—
689C22⋊C8C22×D4312yes—
690C22⋊C8C22×D4312yes—
691C24—21no—
692C24—431no—
693C24—431no—
694C24D4×D4311yescharacteristic
695#41—24no—
696#41—24no—
697#41—42no—
698#41—42no—
699#41—44no—
700#41—44no—
701#41—1724no—
702#41—1724no—
703#41—1722no—
704#41—1722no—
705#41—1722no—
706#41—1722no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—24no—
710C2×Q8—42no—
711C2×Q8—432no—
712C2×Q8—432no—
713C2×Q8—432no—
714C2×Q8—864no—
715C2×Q8—861no—
716C2×Q8—864no—
717C2×Q8—1722no—
718C2×Q8—1724no—
719C2×Q8—1724no—
720C2×Q8—1724no—
721C2×Q8—1728no—
722C2×Q8C23×D4312yes—
723C2×Q8C23×D4312yes—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—42no—
728C2×D4—44no—
729C2×D4—432no—
730C2×D4—432no—
731C2×D4—432no—
732C2×D4—432no—
733C2×D4—432no—
734C2×D4—432no—
735C2×D4—862no—
736C2×D4—862no—
737C2×D4—862no—
738C2×D4—862no—
739C2×D4—1722no—
740C2×D4—1722no—
741C2×D4—1722no—
742C2×D4C23×D4312yes—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—44no—
750C22×C4—431no—
751C22×C4—431no—
752C22×C4—432no—
753C22×C4—432no—
754C22×C4—432no—
755C22×C4—432no—
756C22×C4—864no—
757C22×C4—864no—
758C22×C4—864no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—1724no—
764C22×C4D4×D4311yescharacteristic
765C22×C4D4×D4311yescharacteristic
766C22×C4D4×D4311yescharacteristic
767C22×C4C23×D4311yescharacteristic
768C22×C4C23×D4311yescharacteristic
769C22×C4C23×D4311yescharacteristic
770Q16—44no—
771Q16—1724no—
772SD16—44no—
773SD16—1724no—
774M16—24no—
775M16—864no—
776M16—1724no—
777C2×C8—434no—
778C2×C8—1724no—
779C2×C8C23×D4314yes—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—432no—
784C4⋊C4—432no—
785C4⋊C4—432no—
786C4⋊C4—864no—
787C4⋊C4—864no—
788C4⋊C4—862no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4—862no—
792C4⋊C4—861no—
793C4⋊C4—861no—
794C4⋊C4—861no—
795C4⋊C4—862no—
796C4⋊C4—862no—
797C4⋊C4C23×D4312yes—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—864no—
801C22⋊C4—864no—
802C22⋊C4—864no—
803C22⋊C4—862no—
804C22⋊C4—862no—
805C22⋊C4—862no—
806C22⋊C4—862no—
807C22⋊C4—862no—
808C22⋊C4—862no—
809C22⋊C4—862no—
810C22⋊C4—862no—
811C22⋊C4—862no—
812C22⋊C4—862no—
813C22⋊C4—862no—
814C22⋊C4—862no—
815C42—864no—
816C42—862no—
817C42—862no—
818C23—22no—
819C23—22no—
820C23—41no—
821C23—41no—
822C23—42no—
823C23—81no—
824C23—81no—
825C23—432no—
826C23—432no—
827C23—862no—
828C23—862no—
829C23—1721no—
830C23—1721no—
831C23—1721no—
832C23—1721no—
833C23C2×D4×D4311yescharacteristic
834C23C2×D4×D4311yescharacteristic
835C23C2×D4×D4311yescharacteristic
836Q8—24no—
837Q8—22no—
838Q8—22no—
839Q8—42no—
840Q8—42no—
841Q8—864no—
842Q8—1722no—
843Q8—1722no—
844Q8—1728no—
845Q8—1722no—
846D4—22no—
847D4—22no—
848D4—42no—
849D4—44no—
850D4—44no—
851D4—3442no—
852D4—3442no—
853D4—3442no—
854D4—3442no—
855D4—1722no—
856D4—1722no—
857D4—1722no—
858D4—1722no—
859D4—1722no—
860D4—1722no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—44no—
874C2×C4—432no—
875C2×C4—432no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—864no—
879C2×C4—864no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—3441no—
889C2×C4—3441no—
890C2×C4—1728no—
891C2×C4—1722no—
892C2×C4—1722no—
893C2×C4C2×D4×D4311yescharacteristic
894C2×C4C2×D4×D4311yescharacteristic
895C2×C4C2×D4×D4311yescharacteristic
896C2×C4#1306337014yes—
897C2×C4C24×D4311yescharacteristic
898C8—24no—
899C8—864no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—82no—
912C22—84no—
913C22—862no—
914C22—862no—
915C22—862no—
916C22—862no—
917C22—862no—
918C22—862no—
919C22—3442no—
920C22—1724no—
921C22#1458345912yes—
922C22C22×D4×D4311yescharacteristic
923C4—21no—
924C4—21no—
925C4—42no—
926C4—42no—
927C4—42no—
928C4—862no—
929C4—862no—
930C4—1722no—
931C4—1722no—
932C4—1722no—
933C4—1722no—
934C4#1458345912yes—
935C4C2×#1306337012yes—
936C2—22no—
937C2—41no—
938C2—41no—
939C2—82no—
940C2—1722no—
941C2—1722no—
942C2C2×#1458345911yescharacteristic
943C2#1914937811yescharacteristic
944C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3007C2
socleC22×C43C23×D4
prime radical#19147924C2
hypercenter#3007D43
hypocenterC43#60754
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
2. C2×#14583472C2semidirect
3. #19145488C2semidirect
4. #19145476C2semidirect
5. #19145474C2semidirect
6. #19145464C2semidirect
7. #19144544C2semidirect
8. #19144539C2semidirect
9. #19144525C2semidirect
10. #19144228C2semidirect
11. #19144219C2semidirect
12. #19143855C2semidirect
13. #19143827C2semidirect
14. #19143038C2semidirect
15. C43×#3007C2semidirect
17. C22×Q8×D43C22semidirect
19. C2×M16×D43C22semidirect
26. #14583472C22semidirect
40. C2×#13063305C22semidirect
42. C2×#13063301C22semidirect
44. C2×#13063283C22semidirect
45. #14583241C22semidirect
46. #14583239C22semidirect
47. #14583238C22semidirect
48. #14583237C22semidirect
49. #14583235C22semidirect
50. #14583232C22semidirect
51. #14583230C22semidirect
52. #14583227C22semidirect
53. #14583222C22semidirect
54. #14583221C22semidirect
55. #14583156C22semidirect
56. #14583154C22semidirect
57. #14583144C22semidirect
58. #14583142C22semidirect
59. #14583139C22semidirect
60. #14583137C22semidirect
61. #14583127C22semidirect
62. #14583125C22semidirect
63. #14583061C22semidirect
64. #14583055C22semidirect
65. #14583053C22semidirect
66. #14583053C22semidirect
67. #14583050C22semidirect
68. #14583036C22semidirect
69. #14583036C22semidirect
70. #14582941C22semidirect
71. #14582939C22semidirect
72. #14582909C22semidirect
73. #14582908C22semidirect
76. #14582864C22semidirect
78. #14582862C22semidirect
82. C43×#452C22semidirect
83. C43×#451C22semidirect
84. C43×#450C22semidirect
476. #3007D43semidirect
539. #452C2×D43semidirect
543. #451C2×D43semidirect
545. #450C2×D43semidirect
559. C43#60754semidirect

Maximal subgroups

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

subgroupindex
#191479242
C2×#145834722
#191454882
#191454762
#191454742
#191454642
#191445442
#191445392
#191445252
#191442282
#191442192
#191438552
#191438272
#191430382
C43×#30072
#6075443