Finite Group Databasebeta

← #25107746

Subgroups — #25107746

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583059C211yesmaximal, characteristic
2#19137085C211yesmaximal, characteristic
3#19135455C211yesmaximal, characteristic, complemented
4#19135452C211yesmaximal, characteristic, complemented
5#19135277C211yesmaximal, characteristic, complemented
6#19135270C211yesmaximal, characteristic, complemented
7#19135229C211yesmaximal, characteristic, complemented
8#19135215C211yesmaximal, characteristic, complemented
9#19134950C211yesmaximal, characteristic, complemented
10#19134936C211yesmaximal, characteristic, complemented
11#19134908C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134533C211yesmaximal, characteristic
14C4×C22⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20#14583059C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582805C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582778—21no—
40#14582778—21no—
41C4×(C2×D43)⋊C4—21no—
42C4×(C2×D43)⋊C4—21no—
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×C22⋊Q8×C43C2211yescharacteristic
50C2×C4×Q8×C43C2211yescharacteristic
51C22×C42×C43C2211yescharacteristic
52C43×#391C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#385—21no—
56C43×#380C2211yescharacteristic
57C4×C4⋊C4×C43—21no—
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C22⋊C4×C43—21no—
60C2×#10621898—22no—
61C2×#10621898—41no—
62C2×#10621898—41no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898C2×C414yes—
66C22×Dic86C2311yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C22⋊D43—21no—
69C22×C4×D43—21no—
70C2×#10621885—41no—
71C2×#10621885—41no—
72C2×#10621885C2×C414yescomplemented
73C2×#10621884—41no—
74C2×#10621884—41no—
75C2×#10621884C2×C414yescomplemented
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063284—41no—
81#13063284—41no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90#13063258—41no—
91#13063256—41no—
92#13063249—41no—
93#13063249—41no—
94#13063248—41no—
95#13063248—41no—
96#13063248C2×C414yescomplemented
97#13063245—41no—
98#13063245—41no—
99#13063245C2×C414yescomplemented
100C22⋊(C43⋊C8)—22no—
101C22⋊(C43⋊C8)C2×C414yes—
102C4×C43⋊C8—41no—
103C4×C43⋊C8—41no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C23×C4×C43D411yescharacteristic
110C23×C4×C43D411yescharacteristic
111C23×C4×C43C2311yescharacteristic
112C22⋊Q8×C43—22no—
113C22⋊Q8×C43C2×C414yes—
114C4×Q8×C43—41no—
115C4×Q8×C43—41no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43—21no—
125C2×C42×C43—21no—
126C2×C42×C43—41no—
127C2×C42×C43—41no—
128C2×C42×C43D411yescharacteristic
129C2×C42×C43D411yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137C24×C43C2×D411yescharacteristic
138C23×D43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C22×C412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43#4112yes—
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—42no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173#10621898—44no—
174#10621898—44no—
175#10621898—44no—
176#10621898—44no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172C22×C412yes—
183C2×C4×D43—24no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86C22×C412yes—
192C4⋊C4×C43—24no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—42no—
199C4⋊C4×C43—42no—
200C4⋊C4×C43C22×C412yes—
201C22⋊C4×C43—24no—
202C22⋊C4×C43—42no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—41no—
208C42×C43—41no—
209C42×C43—42no—
210C42×C43—42no—
211C22⋊Dic43—42no—
212#10621885—44no—
213#10621884—44no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—42no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4×Dic43—42no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8C22×C412yes—
234C2×C43⋊C8C22×C412yes—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43C4×D412yes—
242C23×C43C22×D411yescharacteristic
243C22×D43—22no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250Q8×C43—22no—
251Q8×C43—22no—
252Q8×C43—41no—
253Q8×C43—41no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—44no—
272C2×C4×C43—44no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43C4×D412yes—
284C2×C4×C43#13512yes—
285C2×C4×C43#13512yes—
286C2×C4×C43#13712yes—
287C2×C4×C43C23×C411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C22⋊D43—48no—
294C2×Dic43—22no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303D172—22no—
304D172—22no—
305D172—41no—
306D172—41no—
307C4×D43—48no—
308Dic86—22no—
309Dic86—22no—
310Dic86—41no—
311Dic86—41no—
312C43⋊C8—22no—
313C43⋊C8—22no—
314C43⋊C8—41no—
315C43⋊C8—41no—
316#22042—431nomaximal, Sylow
317C22×C43—22no—
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43C2×C4×D411yescharacteristic
325C22×C43#53411yescharacteristic
326C22×C43#53511yescharacteristic
327C22×C43C2×#13511yescharacteristic
328C22×C43C2×#13511yescharacteristic
329C22×C43C2×#13711yescharacteristic
330C22×C43#57511yescharacteristic
331C2×D43—42no—
332C2×D43—42no—
333C2×D43—42no—
334C2×D43—81no—
335C2×D43—81no—
336C2×D43—81no—
337C2×D43—81no—
338C4×C43—22no—
339C4×C43—22no—
340C4×C43—22no—
341C4×C43—22no—
342C4×C43—42no—
343C4×C43—41no—
344C4×C43—42no—
345C4×C43—81no—
346C4×C43—81no—
347C4×C43#51811yescharacteristic
348C4×C43#51811yescharacteristic
349C4×C43#53811yescharacteristic
350C4×C43#53811yescharacteristic
351Dic43—42no—
352Dic43—81no—
353Dic43—81no—
354C2×#452—431no—
355C4×C22⋊Q8D4311yescharacteristic, complemented
356#2297—431no—
357#1969—431no—
358#1968—431no—
359#1934—431no—
360#1933—431no—
361#1927—431no—
362#1925—431no—
363#1880—431no—
364#1878—431no—
365#1873—431no—
366#1854—431no—
367#1788—431no—
368C4×C22⋊C8—431no—
369C2×C43—42no—
370C2×C43#232111yescharacteristic
371C2×C43C4×#13511yescharacteristic
372C2×C43C4×#13711yescharacteristic
373C2×C43#319011yescharacteristic
374C2×C43#319111yescharacteristic
375C2×C43#321011yescharacteristic
376C2×C43#321211yescharacteristic
377D43—82no—
378C22×#41—431no—
379C22×Q16—431no—
380C22×SD16—431no—
381C2×C22⋊Q8C2×D4311yescharacteristic
382C2×C4×Q8C2×D4311yescharacteristic
383C2×#117—431no—
384C22×C42C2×D4311yescharacteristic
385#452—438no—
386C2×#107—431no—
387C2×#106—431no—
388C2×#103—431no—
389C2×#103—431no—
390C2×#103—431no—
391C2×#103—431no—
392C2×#103—431no—
393C2×#102—431no—
394C2×#102—431no—
395C2×#102—431no—
396C2×C22⋊C8—431no—
397C2×C22⋊C8—431no—
398C2×C4×C8—431no—
399C2×C4×C8—431no—
400#391—431no—
401#391—431no—
402#391C2×D4311yescharacteristic
403#390—431no—
404#390—431no—
405#389C2×D4311yescharacteristic
406#387—21no—
407#386—861no—
408#386—861no—
409#385—21no—
410#380C2×D4311yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4C2×D4311yescharacteristic
413C4×C22⋊C4—21no—
414C4×C22⋊C4—861no—
415C4×C22⋊C4—861no—
416#340—431no—
417#340—431no—
418#340—431no—
419#340—431no—
420#336—431no—
421#336—431no—
422C43#2204211yescharacteristic, complemented, Sylow
423C2×#41—434no—
424C2×#41—862no—
425C2×#41—1721no—
426C2×#41—1721no—
427C2×#41—1721no—
428C2×#41—1721no—
429C22×Q8—431no—
430C22×Q8C22×D4311yescharacteristic
431C22×D4—431no—
432C22×D4—861no—
433C23×C4—861no—
434C23×C4C22⋊D4311yescharacteristic
435C23×C4C22⋊D4311yescharacteristic
436C23×C4C22×D4311yescharacteristic
437C2×Q16—434no—
438C2×Q16—1721no—
439C2×Q16—1721no—
440C2×SD16—434no—
441C2×SD16—1721no—
442C2×SD16—1721no—
443C22×C8—431no—
444C22×C8—431no—
445C22×C8—431no—
446C22×C8—431no—
447C22⋊Q8—22no—
448C22⋊Q8C4×D4314yes—
449C4×Q8—41no—
450C4×Q8—41no—
451#117—1721no—
452#117—1721no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4C22×D4311yescharacteristic
459C2×C4⋊C4C22×D4311yescharacteristic
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—861no—
464C2×C22⋊C4—861no—
465C2×C22⋊C4—861no—
466C2×C22⋊C4—861no—
467C2×C22⋊C4—861no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—41no—
471C2×C42—41no—
472C2×C42—861no—
473C2×C42C22⋊D4311yescharacteristic
474C2×C42C22⋊D4311yescharacteristic
475C2×C42C22×D4311yescharacteristic
476C2×C42C22×D4311yescharacteristic
477#107—1721no—
478#106—1721no—
479#103—434no—
480#103—1721no—
481#103—1721no—
482#103—1721no—
483#103—1721no—
484#102—434no—
485#102—1721no—
486#102—1721no—
487C22⋊C8—434no—
488C22⋊C8—862no—
489C4×C8—1721no—
490C4×C8—1721no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—861no—
497#95—861no—
498#95—861no—
499#95—861no—
500C24—861no—
501C24C2×C22⋊D4311yescharacteristic
502#41—1724no—
503#41—1724no—
504#41—1724no—
505#41—1724no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—432no—
512C2×Q8—861no—
513C2×Q8—861no—
514C2×Q8—861no—
515C2×Q8—861no—
516C2×Q8—861no—
517C2×Q8C2×C4×D4312yes—
518C2×D4—432no—
519C2×D4—864no—
520C2×D4—861no—
521C2×D4—861no—
522C2×D4—861no—
523C2×D4—861no—
524C2×D4—861no—
525C2×D4—1722no—
526C2×D4—1722no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—861no—
542C22×C4—864no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—1722no—
546C22×C4—1722no—
547C22×C4C2×C4×D4312yes—
548C22×C4#1062189812yes—
549C22×C4C2×C22⋊D4311yescharacteristic
550C22×C4C2×C22⋊D4311yescharacteristic
551C22×C4C2×C22⋊D4311yescharacteristic
552C22×C4C2×C22⋊D4311yescharacteristic
553C22×C4C2×C22⋊D4311yescharacteristic
554C22×C4C23×D4311yescharacteristic
555Q16—1724no—
556SD16—1724no—
557C2×C8—432no—
558C2×C8—432no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8—861no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4C2×C4×D4312yes—
582C22⋊C4—24no—
583C22⋊C4—42no—
584C22⋊C4—1722no—
585C22⋊C4—1722no—
586C22⋊C4—1722no—
587C22⋊C4—1722no—
588C22⋊C4—1722no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—41no—
594C42—41no—
595C42—42no—
596C42—42no—
597C42—1722no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—862no—
605C23—1721no—
606C23—1721no—
607C23—1721no—
608C23—1721no—
609C23—1721no—
610C23—1721no—
611C23C4×C22⋊D4312yes—
612C23C22×C22⋊D4311yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—862no—
618Q8—862no—
619Q8—1721no—
620Q8—1721no—
621D4—862no—
622D4—862no—
623D4—1728no—
624D4—1721no—
625D4—1721no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—862no—
656C2×C4—1728no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4—1721no—
665C2×C4C4×C22⋊D4312yes—
666C2×C4#1306334512yes—
667C2×C4#1306334512yes—
668C2×C4#1306335612yes—
669C2×C4C22×C4×D4311yescharacteristic
670C2×C4C2×#1062189811yescharacteristic
671C2×C4#1306337011yescharacteristic
672C2×C4#1306337011yescharacteristic
673C2×C4#1306337111yescharacteristic
674C2×C4#1306337111yescharacteristic
675C8—862no—
676C8—862no—
677C8—1721no—
678C8—1721no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—3441no—
687C22—3441no—
688C22—3441no—
689C22—3441no—
690C22—1722no—
691C22—1722no—
692C22—1722no—
693C22C2×C4×C22⋊D4311yescharacteristic
694C22#1458345811yescharacteristic
695C22#1458346311yescharacteristic
696C22C2×#1306334511yescharacteristic
697C22C2×#1306334511yescharacteristic
698C22C2×#1306335611yescharacteristic
699C22#1458369711yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—41no—
705C4—42no—
706C4—42no—
707C4—81no—
708C4—81no—
709C4—3441no—
710C4—3441no—
711C4—1722no—
712C4#1458337111yescharacteristic
713C4#1458337111yescharacteristic
714C4#1458348211yescharacteristic
715C4#1458348211yescharacteristic
716C2—42no—
717C2—3442no—
718C2#1913724911yescharacteristic
719C2C4×#1306334511yescharacteristic
720C2C4×#1306335611yescharacteristic
721C2#1914537611yescharacteristic
722C2#1914538311yescharacteristic
723C2#1914554711yescharacteristic
724C2#1914556711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×C22⋊Q8×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC4×C22⋊Q8D43
hypocenterC43#22042
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #19135455C2semidirect
4. #19135452C2semidirect
5. #19135277C2semidirect
6. #19135270C2semidirect
7. #19135229C2semidirect
8. #19135215C2semidirect
9. #19134950C2semidirect
10. #19134936C2semidirect
11. #19134908C2semidirect
12. #19134792C2semidirect
14. C4×C22⋊(C43⋊C8)C2semidirect
15. C4×C22⋊Q8×C43C2semidirect
20. #14583059C4semidirect
72. C2×#10621885C2×C4semidirect
75. C2×#10621884C2×C4semidirect
96. #13063248C2×C4semidirect
99. #13063245C2×C4semidirect
355. C4×C22⋊Q8D43semidirect
422. C43#22042semidirect

Maximal subgroups

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

subgroupindex
C2×#145830592
#191370852
#191354552
#191354522
#191352772
#191352702
#191352292
#191352152
#191349502
#191349362
#191349082
#191347922
#191345332
C4×C22⋊(C43⋊C8)2
C4×C22⋊Q8×C432
#2204243