Finite Group Databasebeta

← #25107882

Subgroups — #25107882

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
1#19137279C211yesmaximal, characteristic, complemented
2#19137177C211yesmaximal, characteristic
3#19135478C211yesmaximal, characteristic, complemented
4#19135451C211yesmaximal, characteristic, complemented
5#19135294C211yesmaximal, characteristic, complemented
6#19135280C211yesmaximal, characteristic, complemented
7#19135224C211yesmaximal, characteristic, complemented
8#19135217C211yesmaximal, characteristic, complemented
9#19134952C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic, complemented
11#19134908C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic
14#19134363C211yesmaximal, characteristic, complemented
15C2×C43×#450C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic, complemented
17C2×#13063284C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063259C2211yescharacteristic, complemented
20C2×#13063257C2211yescharacteristic, complemented
21C2×#13063249C2211yescharacteristic, complemented
22C2×#13063249C2211yescharacteristic, complemented
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063235C2211yescharacteristic, complemented
29C2×C8×Dic43C2211yescharacteristic, complemented
30#14582806C2211yescharacteristic, complemented
31#14582802—21no—
32#14582802—21no—
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582798—21no—
38#14582798C2211yescharacteristic, complemented
39#14582792—21no—
40#14582792—21no—
41#14582785—21no—
42#14582759C2211yescharacteristic
43#14582755—21no—
44#14582755—21no—
45C4⋊C4×Dic43C2211yescharacteristic, complemented
46#14582662C2211yescharacteristic, complemented
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582653C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52C23×D4×C43C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C22⋊Q8×C43C2211yescharacteristic
56C43×#450C418yescomplemented
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62Q8×Dic43—41no—
63Q8×Dic43—41no—
64#13063284—41no—
65#13063284—41no—
66#13063284—41no—
67#13063284—41no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43D411yescharacteristic
87C2×C22⋊Dic43D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063259—41no—
94#13063257—41no—
95#13063249—41no—
96#13063249—41no—
97#13063246—41no—
98#13063246—41no—
99#13063246—41no—
100#13063246—41no—
101C22⋊(C43⋊C8)—22no—
102#13063235—41no—
103C8×Dic43—41no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C25×C43—21no—
110C22×Q8×C43C2311yescharacteristic
111C22×D4×C43—21no—
112C22×D4×C43—22no—
113C22×D4×C43—41no—
114C22×D4×C43—41no—
115C22×D4×C43—41no—
116C22×D4×C43—41no—
117C22×D4×C43C2×C414yes—
118C22×D4×C43C2311yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C2×SD16×C43—41no—
122C2×SD16×C43—41no—
123C2×SD16×C43—41no—
124C2×SD16×C43—41no—
125C2×SD16×C43C2×C414yes—
126C2×SD16×C43C2×C414yes—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22⋊Q8×C43—22no—
130C22⋊Q8×C43C2×C414yes—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134#102×C43C2×C414yes—
135#102×C43C2×C414yes—
136C22⋊C8×C43C2×C414yes—
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×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C22×C412yes—
153C2×D4×C43—24no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—44no—
165C2×D4×C43—44no—
166C2×D4×C43—44no—
167C2×D4×C43—44no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43C22×C412yes—
171C2×D4×C43C22×C412yes—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43C22×C412yes—
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43#4112yes—
181C22×C4×C43C2411yescharacteristic
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190SD16×C43—44no—
191SD16×C43—44no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43C22×C412yes—
197C2×C8×C43C22×C412yes—
198C4⋊C4×C43—24no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43C22×C412yes—
201C22⋊C4×C43—24no—
202C22⋊Dic43—41no—
203C22⋊Dic43—41no—
204C22⋊Dic43—42no—
205C22⋊Dic43—81no—
206C22⋊Dic43—81no—
207C22⋊Dic43—81no—
208C22⋊Dic43—81no—
209C22⋊Dic43—81no—
210C22⋊Dic43—81no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213C22⋊Dic43—81no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—41no—
223C4⋊Dic43—41no—
224C4⋊Dic43—42no—
225C4⋊Dic43—81no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—42no—
231C4×Dic43—42no—
232C4×Dic43—81no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
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
268Q8×C43—22no—
269Q8×C43—22no—
270Q8×C43—41no—
271Q8×C43—41no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—48no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43C4×D412yes—
294C2×C4×C43C23×C411yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43H(5,𝔽2)11yescharacteristic
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C8×C43—22no—
325C8×C43—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—42no—
360C4×C43—42no—
361C4×C43#51811yescharacteristic
362C4×C43#51811yescharacteristic
363C4×C43#53811yescharacteristic
364C4×C43#53811yescharacteristic
365Dic43—41no—
366Dic43—41no—
367Dic43—41no—
368Dic43—41no—
369Dic43—81no—
370Dic43—81no—
371Dic43—81no—
372Dic43—81no—
373C2×#450D4311yescharacteristic
374#2323—431no—
375#2309—431no—
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×SD16C2×D4311yescharacteristic
400C22×SD16C2×D4311yescharacteristic
401C2×C22⋊Q8C2×D4311yescharacteristic
402C2×C4×Q8—431no—
403C2×#117—431no—
404C2×#117—431no—
405#450Dic4318yescomplemented
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×#102C2×D4311yescharacteristic
415C2×#102C2×D4311yescharacteristic
416C2×C22⋊C8—431no—
417C2×C22⋊C8C2×D4311yescharacteristic
418C2×#97—431no—
419C2×C4×C8—431no—
420#391—431no—
421#390—431no—
422#390—431no—
423#390—431no—
424#390—431no—
425#390—861no—
426#390—861no—
427#389—431no—
428#389—861no—
429#388—861no—
430#388—861no—
431#387—861no—
432#380—431no—
433#379—861no—
434#379—861no—
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×Q8C22×D4311yescharacteristic
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—41no—
448C22×D4—41no—
449C22×D4—41no—
450C22×D4—41no—
451C22×D4C2×Dic4314yes—
452C22×D4C22×D4311yescharacteristic
453C22×D4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C2×SD16—41no—
456C2×SD16—41no—
457C2×SD16—41no—
458C2×SD16—41no—
459C2×SD16C2×Dic4314yes—
460C2×SD16C2×Dic4314yes—
461C22×C8—431no—
462C22×C8—431no—
463C22×C8C22×D4311yescharacteristic
464C22×C8C22×D4311yescharacteristic
465C22⋊Q8—22no—
466C22⋊Q8C2×Dic4314yes—
467C4×Q8—1721no—
468C4×Q8—1721no—
469#117—1721no—
470#117—1721no—
471#117—1721no—
472#117—1721no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—431no—
485C2×C22⋊C4—431no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C42—431no—
497C2×C42—431no—
498C2×C42—861no—
499C2×C42—861no—
500C2×C42—861no—
501#107—1721no—
502#106—1721no—
503#103—1721no—
504#103—1721no—
505#102—1721no—
506#102—1721no—
507#102—1721no—
508#102—1721no—
509#102C2×Dic4314yes—
510#102C2×Dic4314yes—
511C22⋊C8—862no—
512C22⋊C8C2×Dic4314yes—
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—
529C24D4×D4311yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8C22×Dic4312yes—
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×D4C22×Dic4312yes—
554C2×D4C22×Dic4312yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4D4×D4311yescharacteristic
570C22×C4#1062190012yes—
571C22×C4C22×Dic4312yes—
572C22×C4C23×D4311yescharacteristic
573SD16—44no—
574SD16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8C22×Dic4312yes—
586C2×C8C22×Dic4312yes—
587C4⋊C4—24no—
588C4⋊C4—21no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—3441no—
598C4⋊C4—1721no—
599C4⋊C4—1721no—
600C4⋊C4—1722no—
601C4⋊C4C22×Dic4312yes—
602C22⋊C4—24no—
603C22⋊C4—3441no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—3441no—
608C22⋊C4—3441no—
609C22⋊C4—3441no—
610C22⋊C4—3441no—
611C22⋊C4—3441no—
612C22⋊C4—1721no—
613C22⋊C4—1721no—
614C22⋊C4—1722no—
615C42—861no—
616C42—861no—
617C42—861no—
618C42—861no—
619C42—3441no—
620C42—1722no—
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—
649C23D4×Dic4312yes—
650C23C2×D4×D4311yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
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—22no—
671C2×C4—22no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—1721no—
689C2×C4—1721no—
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×C4D4×Dic4312yes—
701C2×C4C23×Dic4311yescharacteristic
702C2×C4C2×#1062190011yescharacteristic
703C2×C4#1306337011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337011yescharacteristic
706C2×C4#1306337011yescharacteristic
707C8—22no—
708C8—22no—
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×D4×Dic4311yescharacteristic
734C22#1458345911yescharacteristic
735C22#1458346411yescharacteristic
736C22#1458370311yescharacteristic
737C22#1458370511yescharacteristic
738C22#1458370511yescharacteristic
739C22#1458370911yescharacteristic
740C4—22no—
741C4—42no—
742C4—42no—
743C4—3441no—
744C4—3441no—
745C4—3441no—
746C4—3441no—
747C4—1721no—
748C4—1721no—
749C4—1721no—
750C4—1721no—
751C4#1458337411yescharacteristic
752C4#1458337411yescharacteristic
753C4#1458348411yescharacteristic
754C4#1458348411yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#1913725611yescharacteristic
759C2#1914342811yescharacteristic
760C2#1914345511yescharacteristic
761C2#1914545111yescharacteristic
762C2#1914546411yescharacteristic
763C2#1914566311yescharacteristic
764C2#1914569311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#450C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#450D43
hypocenterC43#22052
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. #19137279C2semidirect
3. #19135478C2semidirect
4. #19135451C2semidirect
5. #19135294C2semidirect
6. #19135280C2semidirect
7. #19135224C2semidirect
8. #19135217C2semidirect
9. #19134952C2semidirect
10. #19134952C2semidirect
11. #19134908C2semidirect
12. #19134796C2semidirect
14. #19134363C2semidirect
16. C2×Q8×Dic43C22semidirect
19. C2×#13063259C22semidirect
20. C2×#13063257C22semidirect
21. C2×#13063249C22semidirect
22. C2×#13063249C22semidirect
28. C2×#13063235C22semidirect
29. C2×C8×Dic43C22semidirect
30. #14582806C22semidirect
38. #14582798C22semidirect
45. C4⋊C4×Dic43C22semidirect
46. #14582662C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582653C22semidirect
51. #14582653C22semidirect
56. C43×#450C4semidirect
405. #450Dic43semidirect
442. C43#22052semidirect

Maximal subgroups

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

subgroupindex
#191372792
#191371772
#191354782
#191354512
#191352942
#191352802
#191352242
#191352172
#191349522
#191349082
#191347962
#191345262
#191343632
C2×C43×#4502
#2205243