Finite Group Databasebeta

← #25960177

Subgroups — #25960177

Order 11008.

4902 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583735C211yesmaximal, characteristic
2C2×#14583665C211yesmaximal, characteristic, complemented
3C2×#14583380C211yesmaximal, characteristic, complemented
4#19143126C214yesmaximal, complemented
5#19143123C214yesmaximal, complemented
6#19143119C214yesmaximal, complemented
7#19143116C214yesmaximal, complemented
8#19143115C211yesmaximal, characteristic, complemented
9#19143114C211yesmaximal, characteristic, complemented
10#19143111C214yesmaximal, complemented
11C2×#14582898C211yesmaximal, characteristic, complemented
12#417×D43C214yesmaximal, complemented
13C2×C43×#417C211yesmaximal, characteristic, complemented
14#14583735—28no—
15#14583735C4116yescomplemented
16C2×#13063373C2212yes—
17C2×#13063372—21no—
18C2×#13063372C2212yes—
19C2×#13063371—21no—
20C2×#13063371C2212yes—
21C2×#13063370—22no—
22C2×#13063370C2212yes—
23C22×#10621898—22no—
24C22×#10621898C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26C2×#41×D43—22no—
27C2×#41×D43C2214yes—
28#14583665—28no—
29C2×#13063333C2214yescomplemented
30C2×#13063331C2214yescomplemented
31C22×#10621877C2211yescharacteristic, complemented
32C2×M16×D43C2214yescomplemented
33#14583380—22no—
34#14583380—22no—
35#14583380C2214yescomplemented
36#14583380C2214yescomplemented
37C2×#13063290—21no—
38C2×#13063287—21no—
39C2×C4×C22⋊D43—22no—
40C2×#13063284C2211yescharacteristic, complemented
41C2×#13063283C2212yescomplemented
42C2×C4⋊C4×D43C2212yescomplemented
43#14582909C2212yescomplemented
44#14582908C2212yescomplemented
45#14582906C2218yescomplemented
46#14582905C2212yescomplemented
47#14582904C2212yescomplemented
48#14582902C2218yescomplemented
49#14582901C2212yescomplemented
50#14582901C2212yescomplemented
51#14582900C2212yescomplemented
52#14582900C2212yescomplemented
53#14582899C2218yescomplemented
54#14582898C2214yescomplemented
55#14582898C2214yescomplemented
56#14582897C2218yescomplemented
57#14582896C2214yescomplemented
58#14582895C2214yescomplemented
59#14582894C2218yescomplemented
60#14582892C2218yescomplemented
61C2×#13063248C2212yescomplemented
62#103×D43C2218yescomplemented
63C2×#13063245C2212yescomplemented
64#102×D43C2218yescomplemented
65C22×#41×C43C2211yescharacteristic
66C22×M16×C43C2211yescharacteristic, complemented
67C22×C4⋊C4×C43C2211yescharacteristic, complemented
68C43×#417C2214yescomplemented
69C43×#417C2214yescomplemented
70C2×#103×C43C2212yescomplemented
71C2×#102×C43C2212yescomplemented
72#13063373—28no—
73#13063373C2×C4116yescomplemented
74#13063372—28no—
75#13063372—216no—
76#13063372C2×C4116yescomplemented
77#13063371—28no—
78#13063371—216no—
79#13063371C2×C4116yescomplemented
80#13063370—232no—
81#13063370—28no—
82#13063370C2×C4116yescomplemented
83C2×#10621902—22no—
84C2×#10621902C2314yes—
85C2×#10621898—21no—
86C2×#10621898—21no—
87C2×#10621898—24no—
88C2×#10621898—24no—
89C2×#10621898—232no—
90C2×#10621898—22no—
91C2×#10621898—24no—
92C2×#10621898—22no—
93C2×#10621898C2×C418yes—
94C2×#10621898C2×C418yescomplemented
95C2×#10621898D418yes—
96C2×#10621898D412yes—
97C2×#10621898D412yes—
98C2×#10621898C2312yes—
99C2×#10621898C2312yes—
100C2×#10621898C2312yes—
101C2×#10621898C2312yes—
102C2×#10621900—24no—
103C2×#10621900—24no—
104C2×#10621900—22no—
105C2×#10621900C2314yes—
106#41×D43—232no—
107#41×D43—216no—
108#41×D43C2×C4132yescomplemented
109C22×Dic86—22no—
110C22×Dic86D411yescharacteristic
111C22×Dic86C2311yescharacteristic
112C2×Q8×D43—22no—
113C2×Q8×D43C2314yes—
114C22×D172—22no—
115C22×D172D411yescharacteristic
116C22×D172C2311yescharacteristic
117C22×C22⋊D43—21no—
118C22×C22⋊D43—24no—
119C22×C22⋊D43D412yes—
120C2×D4×D43—24no—
121C2×D4×D43—24no—
122C2×D4×D43—22no—
123C2×D4×D43C2314yes—
124C22×C4×D43—21no—
125C22×C4×D43—24no—
126C22×C4×D43—22no—
127C22×C4×D43C2312yes—
128#13063333—216no—
129#13063331—216no—
130C2×#10621877—24no—
131C2×#10621877C2312yes—
132C2×#10621877C2312yes—
133C2×#10621872C2318yes—
134M16×D43—216no—
135C22×C43⋊C8C2312yes—
136C2×C8×D43C2318yes—
137#13063290—24no—
138#13063290—24no—
139#13063287—24no—
140#13063287—24no—
141C4×C22⋊D43—28no—
142C4×C22⋊D43—28no—
143#13063284—21no—
144#13063284—21no—
145#13063284C2312yes—
146#13063284C2312yes—
147#13063283—24no—
148#13063283C2318yes—
149C2×C4⋊Dic43C2311yescharacteristic
150C2×C4⋊Dic43C2311yescharacteristic
151C2×Dic43⋊C4—22no—
152C4⋊C4×D43—24no—
153C4⋊C4×D43C2318yes—
154C2×C22⋊Dic43—21no—
155C2×(C2×D43)⋊C4—22no—
156C2×C4×Dic43—21no—
157C2×C4×Dic43—22no—
158#13063250C2314yes—
159#13063250C2314yes—
160#13063249C2314yes—
161#13063249C2314yes—
162#13063248C2318yes—
163#13063247C2314yes—
164#13063247C2314yes—
165#13063246C2314yes—
166#13063246C2314yes—
167#13063245C2318yes—
168C2×#41×C43—21no—
169C2×#41×C43—21no—
170C2×#41×C43—24no—
171C2×#41×C43C2×C418yescomplemented
172C2×#41×C43C2312yes—
173C2×#41×C43C2312yes—
174C22×Q8×C43C2311yescharacteristic
175C22×D4×C43—21no—
176C22×D4×C43C2311yescharacteristic
177C23×C4×C43—21no—
178C23×C4×C43—21no—
179C23×C4×C43C2311yescharacteristic
180C2×M16×C43—24no—
181C2×M16×C43C2312yes—
182C2×M16×C43C2312yes—
183C22×C8×C43C2312yes—
184C2×C4⋊C4×C43—21no—
185C2×C4⋊C4×C43—21no—
186C2×C4⋊C4×C43—21no—
187C2×C4⋊C4×C43C2312yes—
188C2×C4⋊C4×C43C2312yes—
189C2×C4⋊C4×C43C2312yes—
190#103×C43C2318yes—
191#102×C43C2318yes—
192C24×C43—21no—
193C24×C43C2×D411yescharacteristic
194C23×D43—21no—
195C23×D43—24no—
196C23×D43C2×D412yes—
197#41×C43—28no—
198#41×C43—28no—
199#41×C43—24no—
200#41×C43—24no—
201#41×C43C22×C418yes—
202#41×C43C22×C418yescomplemented
203C2×Q8×C43—21no—
204C2×Q8×C43—22no—
205C2×Q8×C43C22×C414yescomplemented
206C2×Q8×C43C2412yes—
207C2×D4×C43—21no—
208C2×D4×C43—22no—
209C2×D4×C43—28no—
210C2×D4×C43—22no—
211C2×D4×C43—22no—
212C2×D4×C43C22×C414yescomplemented
213C2×D4×C43C2412yes—
214C22×C4×C43—28no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—21no—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43—22no—
221C22×C4×C43—82no—
222C22×C4×C43C22×C414yes—
223C22×C4×C43C2×D414yes—
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43—232no—
231C2×C22⋊D43—24no—
232C2×C22⋊D43—28no—
233C2×C22⋊D43—22no—
234C2×C22⋊D43—22no—
235C2×C22⋊D43—24no—
236C2×C22⋊D43C22⋊C4116yes—
237C2×C22⋊D43C2×D414yes—
238C2×C22⋊D43C2×D414yes—
239C22×Dic43—24no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43C2×D412yes—
244#10621902—216no—
245#10621902—28no—
246#10621902C22×C4116yescomplemented
247Q8×D43—28no—
248Q8×D43—216no—
249Q8×D43C22×C4116yescomplemented
250#10621900—232no—
251#10621900—232no—
252#10621900—28no—
253#10621900—216no—
254#10621900C22×C4116yescomplemented
255D4×D43—232no—
256D4×D43—216no—
257D4×D43—28no—
258D4×D43—232no—
259D4×D43C22×C4116yescomplemented
260#10621898—28no—
261#10621898—28no—
262#10621898—24no—
263#10621898—24no—
264#10621898—232no—
265#10621898—216no—
266#10621898—232no—
267#10621898—216no—
268#10621898C22⋊C4116yes—
269#10621898C22⋊C4116yes—
270#10621898C22×C418yes—
271#10621898C22×C418yes—
272#10621898C22×C418yes—
273#10621898C22×C418yescomplemented
274#10621898C2×D418yes—
275#10621898C2×D418yes—
276C2×D172—21no—
277C2×D172—22no—
278C2×D172—216no—
279C2×D172—24no—
280C2×D172C22⋊C418yes—
281C2×D172C22×C414yescomplemented
282C2×D172C2×D412yes—
283C2×D172C2×D412yes—
284C2×D172C2412yes—
285C2×C4×D43—28no—
286C2×C4×D43—22no—
287C2×C4×D43—22no—
288C2×C4×D43—24no—
289C2×C4×D43—232no—
290C2×C4×D43—24no—
291C2×C4×D43—28no—
292C2×C4×D43—84no—
293C2×C4×D43C22×C418yes—
294C2×C4×D43C2×D418yes—
295C2×C4×D43C2×D414yes—
296C2×C4×D43C2414yes—
297C2×Dic86—21no—
298C2×Dic86—22no—
299C2×Dic86—24no—
300C2×Dic86—216no—
301C2×Dic86C22⋊C418yes—
302C2×Dic86C22×C414yescomplemented
303C2×Dic86C2×D412yes—
304C2×Dic86C2×D412yes—
305C2×Dic86C2412yes—
306M16×C43—24no—
307M16×C43—24no—
308C2×C8×C43—24no—
309C2×C8×C43C2414yes—
310C4⋊C4×C43—22no—
311C4⋊C4×C43—22no—
312C4⋊C4×C43—22no—
313C4⋊C4×C43C2414yes—
314C22⋊Dic43—22no—
315C22⋊Dic43—22no—
316(C2×D43)⋊C4—28no—
317C4⋊Dic43—21no—
318C4⋊Dic43—21no—
319C4⋊Dic43C2412yes—
320C4⋊Dic43C2412yes—
321Dic43⋊C4—28no—
322C4×Dic43—22no—
323C4×Dic43—22no—
324C4×Dic43—28no—
325#10621877—24no—
326#10621877—24no—
327C2×C43⋊C8—24no—
328C2×C43⋊C8C2414yes—
329#10621872—216no—
330C8×D43—216no—
331C23×C43—22no—
332C23×C43—24no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—81no—
336C23×C43—81no—
337C23×C43C2×C22⋊C414yes—
338C23×C43C22×D411yescharacteristic
339C23×C43C22×D411yescharacteristic
340C23×C43C22×D411yescharacteristic
341C22×D43—22no—
342C22×D43—24no—
343C22×D43—216no—
344C22×D43—42no—
345C22×D43—42no—
346C22×D43—84no—
347C22×D43—84no—
348C22×D43—81no—
349C22×D43—81no—
350C22×D43C2×C22⋊C418yes—
351C22×D43C22×D414yes—
352Q8×C43—24no—
353Q8×C43—22no—
354Q8×C43C23×C414yes—
355D4×C43—28no—
356D4×C43—28no—
357D4×C43—24no—
358D4×C43—22no—
359D4×C43C23×C414yes—
360C2×C4×C43—24no—
361C2×C4×C43—22no—
362C2×C4×C43—28no—
363C2×C4×C43—28no—
364C2×C4×C43—24no—
365C2×C4×C43—44no—
366C2×C4×C43—82no—
367C2×C4×C43—82no—
368C2×C4×C43C2×C22⋊C414yes—
369C2×C4×C43C2×C22⋊C414yes—
370C2×C4×C43C2×C22⋊C414yes—
371C2×C4×C43C23×C412yes—
372C2×C4×C43C23×C412yes—
373C2×C4×C43C23×C412yes—
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C22×D411yescharacteristic
377C2×C4×C43C22×D412yes—
378C2×C4×C43C22×D412yes—
379C2×C4×C43C22×D412yes—
380C2×C4×C43C2511yescharacteristic
381C22⋊D43—28no—
382C22⋊D43—28no—
383C22⋊D43—216no—
384C22⋊D43—216no—
385C22⋊D43C2×C22⋊C4116yes—
386C22⋊D43C2×C22⋊C4116yes—
387C2×Dic43—24no—
388C2×Dic43—22no—
389C2×Dic43—216no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—42no—
393C2×Dic43—42no—
394C2×Dic43C2×C22⋊C418yes—
395C2×Dic43C22×D414yes—
396D172—216no—
397D172—24no—
398D172—22no—
399D172C2×C22⋊C418yes—
400D172C2×C22⋊C418yes—
401D172C23×C414yes—
402C4×D43—216no—
403C4×D43—28no—
404C4×D43—28no—
405C4×D43—216no—
406C4×D43—88no—
407C4×D43C2×C22⋊C4116yes—
408C4×D43C23×C418yes—
409C4×D43C22×D418yes—
410Dic86—24no—
411Dic86—22no—
412Dic86—216no—
413Dic86C2×C22⋊C418yes—
414Dic86C2×C22⋊C418yes—
415Dic86C23×C414yes—
416C8×C43—24no—
417C43⋊C8—24no—
418#60089—431nomaximal, Sylow
419C22×C43—21no—
420C22×C43—21no—
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—24no—
426C22×C43—44no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43—84no—
430C22×C43C22×C22⋊C412yes—
431C22×C43C22×C22⋊C412yes—
432C22×C43C22×C22⋊C412yes—
433C22×C43C23×D411yescharacteristic
434C2×D43—24no—
435C2×D43—24no—
436C2×D43—24no—
437C2×D43—48no—
438C2×D43—42no—
439C2×D43—42no—
440C2×D43—816no—
441C2×D43—84no—
442C2×D43C22×C22⋊C418yes—
443C4×C43—24no—
444C4×C43—44no—
445C4×C43C22×C22⋊C412yes—
446C4×C43C22×C22⋊C412yes—
447C4×C43C22×C22⋊C412yes—
448C4×C43C24×C411yescharacteristic
449C4×C43C23×D411yescharacteristic
450Dic43—24no—
451Dic43—42no—
452Dic43—42no—
453Dic43C22×C22⋊C418yes—
454C2×#585—431no—
455C2×#568—431no—
456C2×#520—431no—
457#2898—434no—
458#2898—434no—
459#2897—434no—
460#2897—434no—
461#2896—434no—
462#2896—431no—
463#2896—431no—
464C2×#417—434no—
465C2×#417—431no—
466C2×#417D4311yescharacteristic, complemented
467C2×C43—22no—
468C2×C43—22no—
469C2×C43—22no—
470C2×C43—44no—
471C2×C43C23×C22⋊C411yescharacteristic
472C2×C43#358511yescharacteristic
473C2×C43#358611yescharacteristic
474D43—28no—
475D43—44no—
476#585—4316no—
477#585—868no—
478C2×2−1+4—432no—
479C2×2−1+4—432no—
480C2×2−1+4—861no—
481C2×H(5,𝔽2)—432no—
482C2×H(5,𝔽2)—432no—
483C2×H(5,𝔽2)—862no—
484C2×H(5,𝔽2)—861no—
485C22×#41—431no—
486C22×#41—434no—
487C22×#41—431no—
488C22×#41—862no—
489C22×#41—862no—
490C22×#41C2×D4311yescharacteristic
491#568—868no—
492C2×#131—434no—
493C2×#131—434no—
494C22×M16—431no—
495C22×M16—434no—
496C22×M16C2×D4311yescharacteristic, complemented
497#520—434no—
498#520—434no—
499#520—862no—
500#520—862no—
501C2×C4×Q8—861no—
502C2×C4×D4—861no—
503C2×C4×D4—862no—
504C2×#117—431no—
505C2×#117—432no—
506C22×C4⋊C4—432no—
507C22×C4⋊C4C2×D4311yescharacteristic, complemented
508#419—432no—
509#419—432no—
510#419—438no—
511#418—432no—
512#418—432no—
513#418—438no—
514#417—432no—
515#417—432no—
516#417—432no—
517#417—432no—
518#417—434no—
519#417—434no—
520#417—438no—
521#417—438no—
522#417C2×D4314yescomplemented
523#417C2×D4314yescomplemented
524#416—434no—
525#416—434no—
526#416—438no—
527#416—438no—
528C2×#103—432no—
529C2×#103—438no—
530C2×#103C2×D4312yescomplemented
531C2×#102—432no—
532C2×#102—438no—
533C2×#102C2×D4312yescomplemented
534C43#6008911yescharacteristic, complemented, Sylow
5352−1+4—4316no—
5362−1+4—4316no—
5372−1+4—868no—
5382−1+4—8616no—
5392−1+4—868no—
540H(5,𝔽2)—4316no—
541H(5,𝔽2)—4316no—
542H(5,𝔽2)—8632no—
543H(5,𝔽2)—868no—
544H(5,𝔽2)—8616no—
545H(5,𝔽2)—868no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—24no—
549C2×#41—438no—
550C2×#41—432no—
551C2×#41—432no—
552C2×#41—438no—
553C2×#41—432no—
554C2×#41—432no—
555C2×#41—4332no—
556C2×#41—434no—
557C2×#41—434no—
558C2×#41—438no—
559C2×#41—432no—
560C2×#41—432no—
561C2×#41—864no—
562C2×#41—864no—
563C2×#41—862no—
564C2×#41—862no—
565C2×#41—8632no—
566C2×#41—864no—
567C2×#41—8616no—
568C2×#41—864no—
569C2×#41—862no—
570C2×#41—862no—
571C2×#41—8632no—
572C2×#41—861no—
573C2×#41—861no—
574C2×#41—864no—
575C2×#41C4×D4318yescomplemented
576C2×#41C22×D4312yes—
577C2×#41C22×D4312yes—
578C22×Q8—431no—
579C22×Q8—434no—
580C22×Q8—431no—
581C22×Q8—862no—
582C22×Q8—862no—
583C22×Q8C22×D4311yescharacteristic
584C22×D4—21no—
585C22×D4—432no—
586C22×D4—434no—
587C22×D4—431no—
588C22×D4—431no—
589C22×D4—862no—
590C22×D4—864no—
591C22×D4—862no—
592C22×D4—864no—
593C22×D4—864no—
594C22×D4—861no—
595C22×D4C22×D4311yescharacteristic
596C23×C4—21no—
597C23×C4—21no—
598C23×C4—432no—
599C23×C4—864no—
600C23×C4—862no—
601C23×C4—861no—
602C23×C4C22×D4311yescharacteristic
603#131—8616no—
604#131—8616no—
605C2×M16—24no—
606C2×M16—432no—
607C2×M16—432no—
608C2×M16—438no—
609C2×M16—8616no—
610C2×M16—864no—
611C2×M16C22×D4312yes—
612C2×M16C22×D4312yes—
613C22×C8—432no—
614C22×C8—438no—
615C22×C8C22×D4312yes—
616C4×Q8—864no—
617C4×Q8—864no—
618C4×D4—864no—
619C4×D4—864no—
620C4×D4—868no—
621C4×D4—868no—
622#117—432no—
623#117—432no—
624#117—438no—
625#117—864no—
626#117—861no—
627#117—861no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—431no—
632C2×C4⋊C4—431no—
633C2×C4⋊C4—438no—
634C2×C4⋊C4—864no—
635C2×C4⋊C4—862no—
636C2×C4⋊C4C22×D4312yes—
637C2×C4⋊C4C22×D4312yes—
638C2×C4⋊C4C22×D4312yes—
639C2×C22⋊C4—862no—
640C2×C22⋊C4—861no—
641C2×C42—862no—
642C2×C42—861no—
643#103—434no—
644#103—434no—
645#103—434no—
646#103—434no—
647#103—438no—
648#103C22×D4318yes—
649#102—434no—
650#102—434no—
651#102—434no—
652#102—434no—
653#102—438no—
654#102C22×D4318yes—
655C24—21no—
656C24—432no—
657C24—864no—
658C24—861no—
659C24D4×D4311yescharacteristic
660#41—28no—
661#41—28no—
662#41—24no—
663#41—24no—
664#41—4316no—
665#41—4316no—
666#41—438no—
667#41—438no—
668#41—438no—
669#41—438no—
670#41—4316no—
671#41—4316no—
672#41—438no—
673#41—438no—
674#41—8632no—
675#41—8632no—
676#41—8616no—
677#41—8616no—
678#41—8632no—
679#41—868no—
680#41—868no—
681#41—8632no—
682#41—8616no—
683#41—8616no—
684#41—868no—
685#41—868no—
686#41—864no—
687#41—864no—
688#41C2×C4×D4318yes—
689#41C2×C4×D4318yescomplemented
690C2×Q8—21no—
691C2×Q8—22no—
692C2×Q8—438no—
693C2×Q8—432no—
694C2×Q8—432no—
695C2×Q8—4316no—
696C2×Q8—434no—
697C2×Q8—432no—
698C2×Q8—864no—
699C2×Q8—8616no—
700C2×Q8—868no—
701C2×Q8—8616no—
702C2×Q8—861no—
703C2×Q8—862no—
704C2×Q8C2×C4×D4314yescomplemented
705C2×Q8C23×D4312yes—
706C2×D4—28no—
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—21no—
710C2×D4—22no—
711C2×D4—4316no—
712C2×D4—434no—
713C2×D4—434no—
714C2×D4—4316no—
715C2×D4—438no—
716C2×D4—434no—
717C2×D4—432no—
718C2×D4—432no—
719C2×D4—432no—
720C2×D4—8616no—
721C2×D4—864no—
722C2×D4—868no—
723C2×D4—864no—
724C2×D4—8632no—
725C2×D4—8616no—
726C2×D4—8632no—
727C2×D4—8632no—
728C2×D4—864no—
729C2×D4—868no—
730C2×D4—862no—
731C2×D4—862no—
732C2×D4—861no—
733C2×D4—862no—
734C2×D4C2×C4×D4314yescomplemented
735C2×D4C23×D4312yes—
736C22×C4—21no—
737C22×C4—28no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—82no—
744C22×C4—432no—
745C22×C4—438no—
746C22×C4—434no—
747C22×C4—438no—
748C22×C4—434no—
749C22×C4—864no—
750C22×C4—8632no—
751C22×C4—864no—
752C22×C4—868no—
753C22×C4—864no—
754C22×C4—861no—
755C22×C4—868no—
756C22×C4—862no—
757C22×C4—862no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—3444no—
761C22×C4C2×C4×D4314yes—
762C22×C4D4×D4311yescharacteristic
763C22×C4D4×D4311yescharacteristic
764C22×C4D4×D4311yescharacteristic
765C22×C4D4×D4314yes—
766C22×C4C23×D4311yescharacteristic
767C22×C4C23×D4311yescharacteristic
768C22×C4C23×D4311yescharacteristic
769M16—24no—
770M16—24no—
771M16—8616no—
772M16—864no—
773M16—864no—
774C2×C8—24no—
775C2×C8—434no—
776C2×C8—8616no—
777C2×C8—864no—
778C2×C8C23×D4314yes—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—432no—
783C4⋊C4—432no—
784C4⋊C4—868no—
785C4⋊C4—861no—
786C4⋊C4—861no—
787C4⋊C4C23×D4314yes—
788C22⋊C4—868no—
789C22⋊C4—862no—
790C22⋊C4—862no—
791C42—868no—
792C42—862no—
793C42—862no—
794C23—22no—
795C23—24no—
796C23—41no—
797C23—41no—
798C23—81no—
799C23—81no—
800C23—434no—
801C23—438no—
802C23—8616no—
803C23—864no—
804C23—862no—
805C23—3441no—
806C23—3441no—
807C23—3444no—
808C23—3444no—
809C23—1722no—
810C23—1722no—
811C23C22⋊C4×D4314yes—
812C23C2×D4×D4311yescharacteristic
813C23C2×D4×D4311yescharacteristic
814C23C2×D4×D4311yescharacteristic
815Q8—24no—
816Q8—22no—
817Q8—438no—
818Q8—438no—
819Q8—434no—
820Q8—8616no—
821Q8—864no—
822Q8—862no—
823Q8C22×C4×D4314yes—
824D4—28no—
825D4—28no—
826D4—24no—
827D4—22no—
828D4—4316no—
829D4—4316no—
830D4—438no—
831D4—438no—
832D4—434no—
833D4—8616no—
834D4—8616no—
835D4—8616no—
836D4—868no—
837D4—868no—
838D4—864no—
839D4—862no—
840D4C22×C4×D4314yes—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—28no—
844C2×C4—28no—
845C2×C4—24no—
846C2×C4—44no—
847C2×C4—82no—
848C2×C4—82no—
849C2×C4—438no—
850C2×C4—434no—
851C2×C4—4316no—
852C2×C4—438no—
853C2×C4—438no—
854C2×C4—8616no—
855C2×C4—8616no—
856C2×C4—8616no—
857C2×C4—864no—
858C2×C4—862no—
859C2×C4—868no—
860C2×C4—868no—
861C2×C4—862no—
862C2×C4—862no—
863C2×C4—3448no—
864C2×C4—1722no—
865C2×C4—1722no—
866C2×C4C22⋊C4×D4314yes—
867C2×C4C22⋊C4×D4314yes—
868C2×C4C22⋊C4×D4314yes—
869C2×C4C22×C4×D4312yes—
870C2×C4C22×C4×D4312yes—
871C2×C4C22×C4×D4312yes—
872C2×C4C2×D4×D4311yescharacteristic
873C2×C4C2×D4×D4311yescharacteristic
874C2×C4C2×D4×D4311yescharacteristic
875C2×C4C2×D4×D4312yes—
876C2×C4C2×D4×D4312yes—
877C2×C4C2×D4×D4312yes—
878C2×C4C24×D4311yescharacteristic
879C8—24no—
880C8—864no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—24no—
888C22—44no—
889C22—42no—
890C22—42no—
891C22—84no—
892C22—438no—
893C22—864no—
894C22—864no—
895C22—864no—
896C22—3444no—
897C22—34416no—
898C22—1728no—
899C22—1722no—
900C22—1722no—
901C22C2×C22⋊C4×D4312yes—
902C22C2×C22⋊C4×D4312yes—
903C22C2×C22⋊C4×D4312yes—
904C22C22×D4×D4311yescharacteristic
905C4—24no—
906C4—44no—
907C4—438no—
908C4—864no—
909C4—1722no—
910C4—1722no—
911C4C2×C22⋊C4×D4312yes—
912C4C2×C22⋊C4×D4312yes—
913C4C2×C22⋊C4×D4312yes—
914C4C23×C4×D4311yescharacteristic
915C4C22×D4×D4311yescharacteristic
916C2—22no—
917C2—22no—
918C2—22no—
919C2—44no—
920C2—868no—
921C2—1724no—
922C2C22×C22⋊C4×D4311yescharacteristic
923C2#1914937111yescharacteristic
924C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#417C2
socleC22×C43C23×D4
prime radicalC2×#14583735C2
cosocleC2×C4×C43C25
hypercenterC2×#417D43
hypocenterC43#60089
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14583665C2semidirect
3. C2×#14583380C2semidirect
4. #19143126C2semidirect
5. #19143123C2semidirect
6. #19143119C2semidirect
7. #19143116C2semidirect
8. #19143115C2semidirect
9. #19143114C2semidirect
10. #19143111C2semidirect
11. C2×#14582898C2semidirect
12. #417×D43C2semidirect
13. C2×C43×#417C2semidirect
15. #14583735C4semidirect
29. C2×#13063333C22semidirect
30. C2×#13063331C22semidirect
31. C22×#10621877C22semidirect
32. C2×M16×D43C22semidirect
35. #14583380C22semidirect
36. #14583380C22semidirect
40. C2×#13063284C22semidirect
41. C2×#13063283C22semidirect
42. C2×C4⋊C4×D43C22semidirect
43. #14582909C22semidirect
44. #14582908C22semidirect
45. #14582906C22semidirect
46. #14582905C22semidirect
47. #14582904C22semidirect
48. #14582902C22semidirect
49. #14582901C22semidirect
50. #14582901C22semidirect
51. #14582900C22semidirect
52. #14582900C22semidirect
53. #14582899C22semidirect
54. #14582898C22semidirect
55. #14582898C22semidirect
56. #14582897C22semidirect
57. #14582896C22semidirect
58. #14582895C22semidirect
59. #14582894C22semidirect
60. #14582892C22semidirect
61. C2×#13063248C22semidirect
62. #103×D43C22semidirect
63. C2×#13063245C22semidirect
64. #102×D43C22semidirect
66. C22×M16×C43C22semidirect
67. C22×C4⋊C4×C43C22semidirect
68. C43×#417C22semidirect
69. C43×#417C22semidirect
70. C2×#103×C43C22semidirect
71. C2×#102×C43C22semidirect
73. #13063373C2×C4semidirect
76. #13063372C2×C4semidirect
79. #13063371C2×C4semidirect
82. #13063370C2×C4semidirect
94. C2×#10621898C2×C4semidirect
108. #41×D43C2×C4semidirect
171. C2×#41×C43C2×C4semidirect
202. #41×C43C22×C4semidirect
205. C2×Q8×C43C22×C4semidirect
212. C2×D4×C43C22×C4semidirect
246. #10621902C22×C4semidirect
249. Q8×D43C22×C4semidirect
254. #10621900C22×C4semidirect
259. D4×D43C22×C4semidirect
273. #10621898C22×C4semidirect
281. C2×D172C22×C4semidirect
302. C2×Dic86C22×C4semidirect
466. C2×#417D43semidirect
496. C22×M16C2×D43semidirect
507. C22×C4⋊C4C2×D43semidirect
522. #417C2×D43semidirect
523. #417C2×D43semidirect
530. C2×#103C2×D43semidirect
533. C2×#102C2×D43semidirect
534. C43#60089semidirect
575. C2×#41C4×D43semidirect
689. #41C2×C4×D43semidirect
704. C2×Q8C2×C4×D43semidirect
734. C2×D4C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145837352
C2×#145836652
C2×#145833802
#191431262
#191431232
#191431192
#191431162
#191431152
#191431142
#191431112
C2×#145828982
#417×D432
C2×C43×#4172
#6008943