Finite Group Databasebeta

← #25129517

Subgroups — #25129517

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144524C211yesmaximal, characteristic, complemented
2#19143114C211yesmaximal, characteristic, complemented
3#19139058C211yesmaximal, characteristic, complemented
4#19135821C211yesmaximal, characteristic, complemented
5#19135816C211yesmaximal, characteristic, complemented
6#19135802C211yesmaximal, characteristic, complemented
7#19135802C211yesmaximal, characteristic, complemented
8#19135059C211yesmaximal, characteristic, complemented
9#19134898C211yesmaximal, characteristic, complemented
10#19134828C211yesmaximal, characteristic, complemented
11#19134821C211yesmaximal, characteristic, complemented
12#19134549C211yesmaximal, characteristic, complemented
13#19134549C211yesmaximal, characteristic, complemented
14#19134539C211yesmaximal, characteristic, complemented
15C43×#3488C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic, complemented
17C2×#13063284C2211yescharacteristic, complemented
18#14583237—21no—
19#14583237—21no—
20#14583220—21no—
21#14583220—21no—
22#14582942C2211yescharacteristic, complemented
23#14582942C2211yescharacteristic, complemented
24C2×#13063252C2211yescharacteristic
25C2×#13063252C2211yescharacteristic
26C2×#13063252C2211yescharacteristic, complemented
27C2×#13063252C2211yescharacteristic, complemented
28C2×#13063252C2211yescharacteristic, complemented
29C2×#13063252C2211yescharacteristic, complemented
30#14582908—21no—
31#14582904—21no—
32#14582900C2211yescharacteristic
33#14582900C2211yescharacteristic
34#14582900C2211yescharacteristic, complemented
35#14582900C2211yescharacteristic, complemented
36#14582900C2211yescharacteristic, complemented
37#14582900C2211yescharacteristic, complemented
38#14582895—21no—
39#14582895—21no—
40C2×#13063242C2211yescharacteristic, complemented
41C2×#13063242C2211yescharacteristic, complemented
42#14582863C2211yescharacteristic, complemented
43#14582813—22no—
44#14582802C2211yescharacteristic, complemented
45#14582802C2211yescharacteristic, complemented
46#14582787—22no—
47#14582768C2211yescharacteristic, complemented
48#14582764C2211yescharacteristic, complemented
49C4×C22⋊Dic43C2211yescharacteristic, complemented
50#14582668C2211yescharacteristic, complemented
51#14582668C2211yescharacteristic, complemented
52#14582658C2211yescharacteristic, complemented
53#14582658C2211yescharacteristic, complemented
54C2×H(5,𝔽2)×C43C2211yescharacteristic
55C22×#41×C43C2211yescharacteristic
56C43×#550—21no—
57C43×#548—21no—
58C43×#546—21no—
59C43×#546—22no—
60D42×C43—22no—
61D42×C43—21no—
62C43×#537—21no—
63C43×#537C2211yescharacteristic
64C43×#535—21no—
65C43×#535C2211yescharacteristic
66C43×#525—21no—
67C43×#525C2211yescharacteristic
68C2×#121×C43—21no—
69C2×#121×C43C2211yescharacteristic
70C43×#520C2211yescharacteristic
71C2×#10621877—21no—
72C2×#10621877—41no—
73C2×#10621877—41no—
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C22×C43⋊C8—21no—
79#13063284—21no—
80#13063284—21no—
81#13063284—21no—
82#13063284—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—22no—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—22no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95#13063256—21no—
96#13063256—21no—
97#13063252—22no—
98#13063252—22no—
99#13063252—41no—
100#13063252—41no—
101#13063252—41no—
102#13063252—41no—
103#13063249—21no—
104#13063249—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063249—21no—
109#13063246—21no—
110#13063246—21no—
111#13063246—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063242—41no—
116#13063242—41no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119C43⋊#95—21no—
120C43⋊#95—22no—
121H(5,𝔽2)×C43—22no—
122H(5,𝔽2)×C43—22no—
123H(5,𝔽2)×C43—41no—
124H(5,𝔽2)×C43—41no—
125C2×#41×C43—21no—
126C2×#41×C43—21no—
127C2×#41×C43—21no—
128C2×#41×C43—21no—
129C2×#41×C43—22no—
130C2×#41×C43—22no—
131C2×#41×C43—41no—
132C2×#41×C43—41no—
133C2×#41×C43D411yescharacteristic
134C2×#41×C43D411yescharacteristic
135C2×#41×C43C2311yescharacteristic
136C2×#41×C43C2311yescharacteristic
137C2×#41×C43C2311yescharacteristic
138C22×Q8×C43D411yescharacteristic
139C22×D4×C43—21no—
140C22×D4×C43—22no—
141C22×D4×C43—22no—
142C22×D4×C43—21no—
143C22×D4×C43—21no—
144C22×D4×C43D411yescharacteristic
145C22×D4×C43D412yes—
146C22×D4×C43C2311yescharacteristic
147C23×C4×C43—21no—
148C23×C4×C43C2311yescharacteristic
149#127×C43—22no—
150#127×C43—21no—
151#124×C43—22no—
152#124×C43—21no—
153#123×C43—22no—
154#123×C43—21no—
155C22⋊Q8×C43—22no—
156C22⋊Q8×C43—21no—
157C22⋊Q8×C43—21no—
158C22⋊Q8×C43D411yescharacteristic
159C22⋊Q8×C43D411yescharacteristic
160#121×C43—22no—
161#121×C43—22no—
162#121×C43—22no—
163#121×C43—22no—
164#121×C43—22no—
165#121×C43—21no—
166#121×C43—21no—
167#121×C43—21no—
168#121×C43—21no—
169#121×C43—21no—
170#121×C43—21no—
171#121×C43—22no—
172#121×C43—21no—
173#121×C43—21no—
174#121×C43D411yescharacteristic
175#121×C43D411yescharacteristic
176#120×C43—22no—
177#120×C43—22no—
178#120×C43—22no—
179#120×C43—21no—
180#120×C43—22no—
181C4×Q8×C43—21no—
182C4×D4×C43—22no—
183C4×D4×C43—22no—
184C4×D4×C43—21no—
185C4×D4×C43—22no—
186C4×D4×C43—21no—
187C4×D4×C43—21no—
188#117×C43—21no—
189#117×C43C2311yescharacteristic
190C2×C4⋊C4×C43—21no—
191C2×C4⋊C4×C43C2311yescharacteristic
192C2×C22⋊C4×C43—22no—
193C2×C22⋊C4×C43D412yes—
194C24×C43—22no—
195C24×C43—21no—
196C24×C43C2×D412yes—
197C24×C43C2×D411yescharacteristic
198#41×C43—21no—
199#41×C43—21no—
200#41×C43—22no—
201#41×C43—22no—
202#41×C43—21no—
203#41×C43—21no—
204#41×C43—21no—
205#41×C43—21no—
206#41×C43—21no—
207#41×C43—21no—
208#41×C43—21no—
209#41×C43—21no—
210#41×C43—42no—
211#41×C43—42no—
212#41×C43—41no—
213#41×C43—41no—
214#41×C43—42no—
215#41×C43—42no—
216#41×C43—42no—
217#41×C43—42no—
218#41×C43—42no—
219#41×C43—42no—
220#41×C43#4112yes—
221#41×C43#4112yes—
222C2×Q8×C43—21no—
223C2×Q8×C43—22no—
224C2×Q8×C43—41no—
225C2×Q8×C43C2×D411yescharacteristic
226C2×Q8×C43C2×D411yescharacteristic
227C2×Q8×C43C2×D411yescharacteristic
228C2×D4×C43—22no—
229C2×D4×C43—22no—
230C2×D4×C43—22no—
231C2×D4×C43—22no—
232C2×D4×C43—22no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—21no—
236C2×D4×C43—21no—
237C2×D4×C43—21no—
238C2×D4×C43—21no—
239C2×D4×C43—21no—
240C2×D4×C43—22no—
241C2×D4×C43—21no—
242C2×D4×C43—21no—
243C2×D4×C43—21no—
244C2×D4×C43—21no—
245C2×D4×C43—22no—
246C2×D4×C43—21no—
247C2×D4×C43—21no—
248C2×D4×C43—21no—
249C2×D4×C43—22no—
250C2×D4×C43—42no—
251C2×D4×C43—42no—
252C2×D4×C43—44no—
253C2×D4×C43—44no—
254C2×D4×C43—41no—
255C2×D4×C43—42no—
256C2×D4×C43—42no—
257C2×D4×C43—42no—
258C2×D4×C43—42no—
259C2×D4×C43—82no—
260C2×D4×C43—84no—
261C2×D4×C43C2×D411yescharacteristic
262C2×D4×C43C2×D411yescharacteristic
263C2×D4×C43C2×D411yescharacteristic
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43—21no—
268C22×C4×C43—21no—
269C22×C4×C43—22no—
270C22×C4×C43—22no—
271C22×C4×C43—21no—
272C22×C4×C43—21no—
273C22×C4×C43—21no—
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—42no—
277C22×C4×C43—42no—
278C22×C4×C43C2×D411yescharacteristic
279C22×C4×C43C2×D411yescharacteristic
280C22×C4×C43C2×D411yescharacteristic
281C22×C4×C43C2×D411yescharacteristic
282C22×C4×C43C2×D411yescharacteristic
283C22×C4×C43C2×D412yes—
284C22×C4×C43C2411yescharacteristic
285C22×Dic43—21no—
286C22×Dic43—21no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C4⋊C4×C43—22no—
290C4⋊C4×C43—22no—
291C4⋊C4×C43—21no—
292C4⋊C4×C43—21no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43—21no—
295C4⋊C4×C43C2×D411yescharacteristic
296C4⋊C4×C43C2×D411yescharacteristic
297C22⋊C4×C43—22no—
298C22⋊C4×C43—22no—
299C22⋊C4×C43—22no—
300C22⋊C4×C43—22no—
301C22⋊C4×C43—22no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—22no—
304C22⋊C4×C43—22no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C42×C43—22no—
310C42×C43—21no—
311C22⋊Dic43—42no—
312C22⋊Dic43—44no—
313C22⋊Dic43—41no—
314C22⋊Dic43—41no—
315C22⋊Dic43—82no—
316C4⋊Dic43—21no—
317C4⋊Dic43—21no—
318C4⋊Dic43—21no—
319C4⋊Dic43—21no—
320Dic43⋊C4—82no—
321C4×Dic43—21no—
322C4×Dic43—21no—
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—41no—
326C4×Dic43—41no—
327#10621877—21no—
328#10621877—21no—
329#10621877—21no—
330#10621877—21no—
331#10621877—21no—
332#10621877—21no—
333#10621877—21no—
334#10621877—21no—
335#10621877—42no—
336C2×C43⋊C8—21no—
337C2×C43⋊C8—21no—
338C2×C43⋊C8—21no—
339C2×C43⋊C8—21no—
340C2×C43⋊C8—42no—
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43—22no—
345C23×C43—21no—
346C23×C43—21no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—42no—
352C23×C43—42no—
353C23×C43—44no—
354C23×C43—42no—
355C23×C43—42no—
356C23×C43—81no—
357C23×C43—82no—
358C23×C43—82no—
359C23×C43#12011yescharacteristic
360C23×C43#12011yescharacteristic
361C23×C43C22×D411yescharacteristic
362Q8×C43—21no—
363Q8×C43—21no—
364Q8×C43—21no—
365Q8×C43—21no—
366Q8×C43—21no—
367Q8×C43—42no—
368Q8×C43#12312yes—
369D4×C43—22no—
370D4×C43—22no—
371D4×C43—21no—
372D4×C43—21no—
373D4×C43—21no—
374D4×C43—21no—
375D4×C43—21no—
376D4×C43—42no—
377D4×C43—42no—
378D4×C43—44no—
379D4×C43—42no—
380D4×C43—44no—
381D4×C43—44no—
382D4×C43—42no—
383D4×C43—41no—
384D4×C43—41no—
385D4×C43—41no—
386D4×C43—41no—
387D4×C43—41no—
388D4×C43—41no—
389D4×C43—41no—
390D4×C43—41no—
391D4×C43—81no—
392D4×C43—82no—
393D4×C43—82no—
394D4×C43—82no—
395D4×C43—82no—
396D4×C43#12312yes—
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—21no—
402C2×C4×C43—21no—
403C2×C4×C43—21no—
404C2×C4×C43—21no—
405C2×C4×C43—21no—
406C2×C4×C43—21no—
407C2×C4×C43—21no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—21no—
411C2×C4×C43—22no—
412C2×C4×C43—21no—
413C2×C4×C43—21no—
414C2×C4×C43—21no—
415C2×C4×C43—42no—
416C2×C4×C43—42no—
417C2×C4×C43—42no—
418C2×C4×C43—44no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—42no—
424C2×C4×C43—82no—
425C2×C4×C43#12011yescharacteristic
426C2×C4×C43#12011yescharacteristic
427C2×C4×C43C22×D411yescharacteristic
428C2×C4×C43C22×D411yescharacteristic
429C2×C4×C43C2×#4111yescharacteristic
430C2×C4×C43C2×#4111yescharacteristic
431C2×C4×C43H(5,𝔽2)11yescharacteristic
432C2×C4×C43H(5,𝔽2)11yescharacteristic
433C2×Dic43—22no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43—42no—
437C2×Dic43—41no—
438C2×Dic43—42no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43—41no—
442C2×Dic43—41no—
443C43⋊C8—41no—
444C43⋊C8—41no—
445C43⋊C8—41no—
446C43⋊C8—41no—
447#24031—431nomaximal, Sylow
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—22no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—21no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43—42no—
460C22×C43—41no—
461C22×C43—41no—
462C22×C43—42no—
463C22×C43—41no—
464C22×C43—41no—
465C22×C43—41no—
466C22×C43—42no—
467C22×C43—41no—
468C22×C43—81no—
469C22×C43—81no—
470C22×C43—82no—
471C22×C43—82no—
472C22×C43—84no—
473C22×C43—164no—
474C22×C43C2×#12011yescharacteristic
475C22×C43#54611yescharacteristic
476C22×C43#54611yescharacteristic
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—22no—
480C4×C43—41no—
481C4×C43—41no—
482C4×C43—41no—
483C4×C43—42no—
484C4×C43—41no—
485C4×C43C2×#12311yescharacteristic
486C4×C43#53411yescharacteristic
487C4×C43#54611yescharacteristic
488C4×C43#54611yescharacteristic
489Dic43—42no—
490Dic43—81no—
491Dic43—81no—
492Dic43—81no—
493#3488D4311yescharacteristic
494#3093—431no—
495#2896—431no—
496#2500—431no—
497#2040—431no—
498#2039—431no—
499#2037—431no—
500#2037—431no—
501#1900—431no—
502#1871—431no—
503#1860—431no—
504#1859—431no—
505#1792—431no—
506#1792—431no—
507#1789—431no—
508C2×C43—21no—
509C2×C43—21no—
510C2×C43—41no—
511C2×C43—41no—
512C2×C43—42no—
513C2×C43—81no—
514C2×C43—82no—
515C2×C43—81no—
516C2×C43#240511yescharacteristic
517C2×C43#301811yescharacteristic
518C2×C43#301911yescharacteristic
519C2×H(5,𝔽2)C2×D4311yescharacteristic
520C22×#41C2×D4311yescharacteristic
521C22×M16—431no—
522#550—21no—
523#548—21no—
524#546—21no—
525#546—22no—
526D42—22no—
527D42—21no—
528#537—21no—
529#537C2×D4311yescharacteristic
530#535—21no—
531#535C2×D4311yescharacteristic
532#525—21no—
533#525C2×D4311yescharacteristic
534C2×#121—21no—
535C2×#121C2×D4311yescharacteristic
536#520C2×D4311yescharacteristic
537C2×#117—431no—
538#485—861no—
539#485—861no—
540#482—861no—
541#482—861no—
542#428—431no—
543#428—431no—
544C2×#104—431no—
545C2×#104—431no—
546C2×#104—431no—
547C2×#104—431no—
548C2×#104—431no—
549C2×#104—431no—
550#419—861no—
551#418—861no—
552#417—431no—
553#417—431no—
554#417—431no—
555#417—431no—
556#417—431no—
557#417—431no—
558#416—861no—
559#416—861no—
560C2×#100—431no—
561C2×#100—431no—
562#407—431no—
563#394—862no—
564#390—431no—
565#390—431no—
566#388—862no—
567#384—431no—
568#382—431no—
569C4×C22⋊C4—431no—
570#343—431no—
571#343—431no—
572#339—431no—
573#339—431no—
574C43#2403111yescharacteristic, complemented, Sylow
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41C22⋊D4311yescharacteristic
588C2×#41C22⋊D4311yescharacteristic
589C2×#41C22×D4311yescharacteristic
590C2×#41C22×D4311yescharacteristic
591C2×#41C22×D4311yescharacteristic
592C22×Q8C22⋊D4311yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4C22⋊D4311yescharacteristic
599C22×D4C22⋊D4312yes—
600C22×D4C22×D4311yescharacteristic
601C23×C4—21no—
602C23×C4C22×D4311yescharacteristic
603C2×M16—431no—
604C2×M16—431no—
605C2×M16—431no—
606C2×M16—431no—
607C2×M16—861no—
608C2×M16—1721no—
609C2×M16—1721no—
610C22×C8—861no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8C22⋊D4311yescharacteristic
621C22⋊Q8C22⋊D4311yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121C22⋊D4311yescharacteristic
637#121C22⋊D4311yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—861no—
652#117—861no—
653#117—861no—
654#117—861no—
655#117C22×D4311yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—431no—
658C2×C4⋊C4—431no—
659C2×C4⋊C4—862no—
660C2×C4⋊C4C22×D4311yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—862no—
663C2×C22⋊C4—861no—
664C2×C22⋊C4—861no—
665C2×C22⋊C4—862no—
666C2×C22⋊C4C22⋊D4312yes—
667C2×C42—431no—
668C2×C42—431no—
669C2×C42—861no—
670#107—861no—
671#107—861no—
672#106—861no—
673#106—861no—
674#104—862no—
675#104—862no—
676#104—1721no—
677#104—1721no—
678#104—1721no—
679#104—1721no—
680#103—861no—
681#103—861no—
682#103—861no—
683#103—861no—
684#103—861no—
685#103—861no—
686#102—861no—
687#102—861no—
688#102—861no—
689#102—861no—
690#102—861no—
691#102—861no—
692#100—1721no—
693#100—1721no—
694C22⋊C8—861no—
695C22⋊C8—861no—
696#95—861no—
697#95—862no—
698C24—22no—
699C24—21no—
700C24C2×C22⋊D4312yes—
701C24C2×C22⋊D4311yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#1062190012yes—
725#41#1062190012yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×C22⋊D4311yescharacteristic
730C2×Q8C2×C22⋊D4311yescharacteristic
731C2×Q8C2×C22⋊D4311yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×C22⋊D4311yescharacteristic
766C2×D4C2×C22⋊D4311yescharacteristic
767C2×D4C2×C22⋊D4311yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—861no—
785C22×C4—861no—
786C22×C4C2×C22⋊D4311yescharacteristic
787C22×C4C2×C22⋊D4311yescharacteristic
788C22×C4C2×C22⋊D4311yescharacteristic
789C22×C4C2×C22⋊D4311yescharacteristic
790C22×C4C2×C22⋊D4311yescharacteristic
791C22×C4C2×C22⋊D4312yes—
792C22×C4C23×D4311yescharacteristic
793M16—861no—
794M16—861no—
795M16—861no—
796M16—861no—
797M16—861no—
798M16—861no—
799M16—861no—
800M16—861no—
801M16—1722no—
802C2×C8—861no—
803C2×C8—861no—
804C2×C8—861no—
805C2×C8—861no—
806C2×C8—1722no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—861no—
814C4⋊C4—861no—
815C4⋊C4—861no—
816C4⋊C4—861no—
817C4⋊C4—3442no—
818C4⋊C4C2×C22⋊D4311yescharacteristic
819C4⋊C4C2×C22⋊D4311yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—3442no—
833C22⋊C4—1722no—
834C22⋊C4—1724no—
835C22⋊C4—1721no—
836C22⋊C4—1721no—
837C42—22no—
838C42—21no—
839C42—861no—
840C42—861no—
841C42—861no—
842C42—861no—
843C42—1721no—
844C42—1721no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#1306329411yescharacteristic
864C23#1306329411yescharacteristic
865C23C22×C22⋊D4311yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#1306330612yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#1306330612yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—44no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—82no—
929C2×C4—862no—
930C2×C4—1721no—
931C2×C4—1722no—
932C2×C4—1721no—
933C2×C4—1722no—
934C2×C4—1721no—
935C2×C4—1721no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4#1306329411yescharacteristic
940C2×C4#1306329411yescharacteristic
941C2×C4C22×C22⋊D4311yescharacteristic
942C2×C4C22×C22⋊D4311yescharacteristic
943C2×C4C2×#1062190011yescharacteristic
944C2×C4C2×#1062190011yescharacteristic
945C2×C4#1306337011yescharacteristic
946C2×C4#1306337011yescharacteristic
947C8—1721no—
948C8—1721no—
949C8—1721no—
950C8—1721no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#1306329411yescharacteristic
978C22#1458354311yescharacteristic
979C22#1458354311yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—41no—
986C4—41no—
987C4—41no—
988C4—3441no—
989C4—3441no—
990C4—3441no—
991C4—1722no—
992C4C2×#1306330611yescharacteristic
993C4#1458345811yescharacteristic
994C4#1458354311yescharacteristic
995C4#1458354311yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2#1913791811yescharacteristic
1005C2#1914394411yescharacteristic
1006C2#1914395211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3488C2
socleC22×C43C2×#120
hypercenter#3488D43
hypocenterC43#24031
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #19144524C2semidirect
2. #19143114C2semidirect
3. #19139058C2semidirect
4. #19135821C2semidirect
5. #19135816C2semidirect
6. #19135802C2semidirect
7. #19135802C2semidirect
8. #19135059C2semidirect
9. #19134898C2semidirect
10. #19134828C2semidirect
11. #19134821C2semidirect
12. #19134549C2semidirect
13. #19134549C2semidirect
14. #19134539C2semidirect
16. C22×#10621877C22semidirect
17. C2×#13063284C22semidirect
22. #14582942C22semidirect
23. #14582942C22semidirect
26. C2×#13063252C22semidirect
27. C2×#13063252C22semidirect
28. C2×#13063252C22semidirect
29. C2×#13063252C22semidirect
34. #14582900C22semidirect
35. #14582900C22semidirect
36. #14582900C22semidirect
37. #14582900C22semidirect
40. C2×#13063242C22semidirect
41. C2×#13063242C22semidirect
42. #14582863C22semidirect
44. #14582802C22semidirect
45. #14582802C22semidirect
47. #14582768C22semidirect
48. #14582764C22semidirect
49. C4×C22⋊Dic43C22semidirect
50. #14582668C22semidirect
51. #14582668C22semidirect
52. #14582658C22semidirect
53. #14582658C22semidirect
574. C43#24031semidirect

Maximal subgroups

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

subgroupindex
#191445242
#191431142
#191390582
#191358212
#191358162
#191358022
#191350592
#191348982
#191348282
#191348212
#191345492
#191345392
C43×#34882
#2403143