Finite Group Databasebeta

← #25107878

Subgroups — #25107878

Order 11008.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583050C211yesmaximal, characteristic
2#19137277C211yesmaximal, characteristic, complemented
3#19135475C211yesmaximal, characteristic, complemented
4#19135448C211yesmaximal, characteristic, complemented
5#19135295C211yesmaximal, characteristic, complemented
6#19135281C211yesmaximal, characteristic, complemented
7#19135219C211yesmaximal, characteristic, complemented
8#19135212C211yesmaximal, characteristic, complemented
9#19134953C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic, complemented
11#19134907C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic
14#19134361C211yesmaximal, characteristic, complemented
15C43×#2309C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic, complemented
20#14583050C418yescomplemented
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23C2×#13063248C2211yescharacteristic, complemented
24C2×#13063248C2211yescharacteristic, complemented
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063236C2211yescharacteristic, complemented
34C2×C4×C43⋊C8C2211yescharacteristic, complemented
35#14582805C2211yescharacteristic, complemented
36#14582797C2211yescharacteristic, complemented
37#14582794—21no—
38#14582793—21no—
39#14582787—21no—
40#14582780—21no—
41#14582759C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic, complemented
43#14582661C2211yescharacteristic, complemented
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582654C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49C23×D4×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C43×#390—21no—
53C43×#390—21no—
54C43×#390C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#379—21no—
59C43×#379—21no—
60C22×Dic86C2311yescharacteristic
61C2×#10621883—41no—
62C2×#10621883—41no—
63C2×#10621883—41no—
64C2×#10621883—41no—
65C2×#10621883C2×C414yes—
66C2×#10621883C2×C414yes—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063304—22no—
72#13063304C2×C414yes—
73C4×Dic86—41no—
74C4×Dic86—41no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85#13063258—41no—
86#13063256—41no—
87#13063248—41no—
88#13063248—41no—
89#13063246—41no—
90#13063246—41no—
91#13063246—41no—
92#13063246—41no—
93#13063246C2×C414yes—
94#13063246C2×C414yes—
95C22⋊(C43⋊C8)—22no—
96C22⋊(C43⋊C8)C2×C414yes—
97#13063236—41no—
98C4×C43⋊C8—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C25×C43—21no—
105C22×D4×C43—21no—
106C22×D4×C43—22no—
107C22×D4×C43—41no—
108C22×D4×C43—41no—
109C22×D4×C43—41no—
110C22×D4×C43—41no—
111C22×D4×C43C2×C414yes—
112C22×D4×C43C2311yescharacteristic
113C22×D4×C43C2311yescharacteristic
114C23×C4×C43C2311yescharacteristic
115#117×C43—41no—
116#117×C43—41no—
117#117×C43—41no—
118#117×C43—41no—
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—24no—
140C24×C43—42no—
141C24×C43—42no—
142C24×C43—81no—
143C24×C43—81no—
144C24×C43—81no—
145C24×C43—81no—
146C24×C43C2×D411yescharacteristic
147C2×D4×C43—24no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—44no—
159C2×D4×C43—44no—
160C2×D4×C43—44no—
161C2×D4×C43—44no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43C22×C412yes—
165C2×D4×C43C22×C412yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43C22×C412yes—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43#4112yes—
179C22×C4×C43C2411yescharacteristic
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86C22×C412yes—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—42no—
199C22⋊C4×C43—81no—
200C22⋊C4×C43—81no—
201C22⋊C4×C43—81no—
202C22⋊C4×C43—81no—
203C22⋊C4×C43—81no—
204C22⋊C4×C43—81no—
205C22⋊C4×C43—81no—
206C22⋊C4×C43—81no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—21no—
210C42×C43—21no—
211C42×C43—42no—
212C22⋊Dic43—24no—
213C22⋊Dic43—81no—
214#10621883—44no—
215#10621883—44no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43C22×C412yes—
222Dic43⋊C4—24no—
223Dic43⋊C4—42no—
224Dic43⋊C4—81no—
225C4×Dic43—42no—
226C4×Dic43—81no—
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⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8C22×C412yes—
238C2×C43⋊C8C22×C412yes—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—48no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—84no—
261C23×C43—84no—
262C23×C43—84no—
263C23×C43—84no—
264C23×C43—84no—
265C23×C43—84no—
266C23×C43C4×D412yes—
267C23×C43C22×D411yescharacteristic
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—48no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—41no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43C4×D412yes—
302C2×C4×C43C23×C411yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320Dic86—22no—
321Dic86—22no—
322Dic86—41no—
323Dic86—41no—
324C43⋊C8—22no—
325C43⋊C8—22no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#22052—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—816no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43C2×C4×D411yescharacteristic
352C22×C43#53411yescharacteristic
353C22×C43#53511yescharacteristic
354C22×C43#57611yescharacteristic
355C22×C43#57711yescharacteristic
356C22×C43#57711yescharacteristic
357C22×C43#57711yescharacteristic
358C4×C43—22no—
359C4×C43—41no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43—41no—
363C4×C43—81no—
364C4×C43—81no—
365C4×C43#51811yescharacteristic
366C4×C43#51811yescharacteristic
367C4×C43#53811yescharacteristic
368C4×C43#53811yescharacteristic
369Dic43—42no—
370Dic43—42no—
371Dic43—81no—
372Dic43—81no—
373C2×#450—431no—
374#2323—431no—
375#2309D4311yescharacteristic
376#1973—431no—
377#1968—431no—
378#1936—431no—
379#1934—431no—
380#1926—431no—
381#1925—431no—
382#1880—431no—
383#1880—431no—
384#1873—431no—
385#1854—431no—
386#1786—431no—
387#1750—431no—
388C2×C43—42no—
389C2×C43—82no—
390C2×C43—82no—
391C2×C43#232111yescharacteristic
392C2×C43#294611yescharacteristic
393C2×C43#294911yescharacteristic
394C2×C43#319811yescharacteristic
395C2×C43#320011yescharacteristic
396C2×C43#322211yescharacteristic
397C2×C43#322411yescharacteristic
398C23×D4C2×D4311yescharacteristic
399C22×SD16—431no—
400C22×SD16—431no—
401C2×C22⋊Q8—431no—
402C2×C4×Q8—431no—
403C2×#117C2×D4311yescharacteristic
404C2×#117C2×D4311yescharacteristic
405#450—438no—
406C2×#107—431no—
407C2×#106—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×C22⋊C8—431no—
417C2×C22⋊C8—431no—
418C2×#97—431no—
419C2×C4×C8—431no—
420#391—431no—
421#390—21no—
422#390—21no—
423#390C2×D4311yescharacteristic
424#390C2×D4311yescharacteristic
425#390C2×D4311yescharacteristic
426#390C2×D4311yescharacteristic
427#389—431no—
428#389—861no—
429#388—861no—
430#388—861no—
431#387—861no—
432#380—431no—
433#379—21no—
434#379—21no—
435C4×C4⋊C4—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#336—431no—
441#336—431no—
442C43#2205211yescharacteristic, complemented, Sylow
443C25—21no—
444C22×Q8—431no—
445C22×D4—22no—
446C22×D4—21no—
447C22×D4—41no—
448C22×D4—41no—
449C22×D4—41no—
450C22×D4—41no—
451C22×D4C4×D4314yes—
452C22×D4C22×D4311yescharacteristic
453C22×D4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C2×SD16—434no—
456C2×SD16—434no—
457C2×SD16—1721no—
458C2×SD16—1721no—
459C2×SD16—1721no—
460C2×SD16—1721no—
461C22×C8—431no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—431no—
465C22⋊Q8—434no—
466C22⋊Q8—862no—
467C4×Q8—1721no—
468C4×Q8—1721no—
469#117—41no—
470#117—41no—
471#117—41no—
472#117—41no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4C22⋊D4311yescharacteristic
480C2×C4⋊C4C22⋊D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4C22⋊D4311yescharacteristic
495C2×C22⋊C4C22⋊D4311yescharacteristic
496C2×C42—21no—
497C2×C42—861no—
498C2×C42—861no—
499C2×C42C22×D4311yescharacteristic
500C2×C42C22×D4311yescharacteristic
501#107—1721no—
502#106—1721no—
503#103—1721no—
504#103—1721no—
505#102—434no—
506#102—434no—
507#102—1721no—
508#102—1721no—
509#102—1721no—
510#102—1721no—
511C22⋊C8—434no—
512C22⋊C8—862no—
513#97—1721no—
514C4×C8—1721no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520C24—21no—
521C24—21no—
522C24—24no—
523C24—42no—
524C24—42no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24—81no—
529C24C2×C22⋊D4311yescharacteristic
530C2×Q8—432no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4C2×C4×D4312yes—
554C2×D4C2×C4×D4312yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4C2×C4×D4312yes—
566C22×C4#1062189812yes—
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C2×C22⋊D4311yescharacteristic
569C22×C4C2×C22⋊D4311yescharacteristic
570C22×C4C2×C22⋊D4311yescharacteristic
571C22×C4C2×C22⋊D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573SD16—1724no—
574SD16—1724no—
575C2×C8—432no—
576C2×C8—432no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—432no—
594C4⋊C4—864no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—3441no—
601C4⋊C4—1722no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—864no—
614C22⋊C4—3441no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—3441no—
621C42—1722no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—22no—
630C23—48no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23C4×C22⋊D4312yes—
650C23C22×C22⋊D4311yescharacteristic
651Q8—862no—
652Q8—862no—
653Q8—1721no—
654Q8—1721no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4C4×C22⋊D4312yes—
701C2×C4C22×C4×D4311yescharacteristic
702C2×C4C2×#1062189811yescharacteristic
703C2×C4#1306337011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337011yescharacteristic
706C2×C4#1306337011yescharacteristic
707C8—862no—
708C8—862no—
709C8—1721no—
710C8—1721no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—816no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×C4×C22⋊D4311yescharacteristic
734C22#1458345811yescharacteristic
735C22#1458346611yescharacteristic
736C22#1458370211yescharacteristic
737C22#1458371011yescharacteristic
738C22#1458371011yescharacteristic
739C22#1458371011yescharacteristic
740C4—22no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—3441no—
748C4—3441no—
749C4—1722no—
750C4—1722no—
751C4#1458337211yescharacteristic
752C4#1458337211yescharacteristic
753C4#1458348711yescharacteristic
754C4#1458348711yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#1913725311yescharacteristic
759C2#1914342711yescharacteristic
760C2#1914345211yescharacteristic
761C2#1914544711yescharacteristic
762C2#1914546711yescharacteristic
763C2#1914566711yescharacteristic
764C2#1914568911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2309C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenter#2309D43
hypocenterC43#22052
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #19137277C2semidirect
3. #19135475C2semidirect
4. #19135448C2semidirect
5. #19135295C2semidirect
6. #19135281C2semidirect
7. #19135219C2semidirect
8. #19135212C2semidirect
9. #19134953C2semidirect
10. #19134953C2semidirect
11. #19134907C2semidirect
12. #19134794C2semidirect
14. #19134361C2semidirect
19. C2×C4×Dic86C22semidirect
20. #14583050C4semidirect
21. C2×#13063258C22semidirect
22. C2×#13063256C22semidirect
23. C2×#13063248C22semidirect
24. C2×#13063248C22semidirect
33. C2×#13063236C22semidirect
34. C2×C4×C43⋊C8C22semidirect
35. #14582805C22semidirect
36. #14582797C22semidirect
42. C4×C4⋊Dic43C22semidirect
43. #14582661C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582654C22semidirect
48. #14582654C22semidirect
442. C43#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#145830502
#191372772
#191354752
#191354482
#191352952
#191352812
#191352192
#191352122
#191349532
#191349072
#191347942
#191345262
#191343612
C43×#23092
#2205243