Finite Group Databasebeta

← #25139001

Subgroups — #25139001

Order 11008.

1026 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583143C211yesmaximal, characteristic, complemented
2C2×#14583143C211yesmaximal, characteristic, complemented
3C2×#14582977C211yesmaximal, characteristic, complemented
4C2×#14582939C211yesmaximal, characteristic, complemented
5#19138024C211yesmaximal, characteristic, complemented
6#19135983C211yesmaximal, characteristic, complemented
7#19135973C211yesmaximal, characteristic, complemented
8#19135798C211yesmaximal, characteristic, complemented
9#19135781C211yesmaximal, characteristic, complemented
10#19135448C211yesmaximal, characteristic, complemented
11#19135325C211yesmaximal, characteristic, complemented
12#19134918C211yesmaximal, characteristic, complemented
13#19134902C211yesmaximal, characteristic, complemented
14#19134626C211yesmaximal, characteristic, complemented
15C43×#2416C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14583143—24no—
23#14583143—24no—
24#14582977—24no—
25#14582939—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063258C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41#14582827—21no—
42#14582813—21no—
43#14582805C2211yescharacteristic
44#14582797C2211yescharacteristic
45#14582794—21no—
46#14582793—21no—
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×#121×C43—21no—
53C2×#121×C43C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C22×C4⋊C4×C43C2211yescharacteristic
57C43×#396—21no—
58C43×#394—21no—
59C43×#390C2211yescharacteristic
60C43×#389C2211yescharacteristic
61C43×#386—21no—
62C43×#380C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621877—22no—
68C2×#10621877—22no—
69C2×#10621877—22no—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877D414yescomplemented
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063304—22no—
78#13063304—22no—
79#13063304—22no—
80#13063304—41no—
81#13063284—22no—
82#13063284—41no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C4×Dic43—21no—
94#13063258—22no—
95#13063258—22no—
96#13063258D414yescomplemented
97#13063256—22no—
98#13063256—22no—
99C4⋊(C43⋊C8)—22no—
100#13063248—22no—
101#13063248—22no—
102#13063248—41no—
103#13063246—22no—
104#13063246—22no—
105#13063246—41no—
106C22⋊(C43⋊C8)—22no—
107C22⋊(C43⋊C8)—22no—
108C4×C43⋊C8—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×D4×C43—21no—
114C22×D4×C43—21no—
115C22×D4×C43D411yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2311yescharacteristic
120#121×C43—22no—
121#121×C43—22no—
122#121×C43—22no—
123#121×C43—41no—
124#121×C43—44no—
125C4×D4×C43—22no—
126C4×D4×C43—22no—
127C2×C4⋊C4×C43—22no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—41no—
131C2×C4⋊C4×C43D411yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43D411yescharacteristic
141C2×C22⋊C4×C43D411yescharacteristic
142C2×C42×C43C2311yescharacteristic
143#95×C43—21no—
144#95×C43—21no—
145C24×C43—21no—
146C24×C43C2×D411yescharacteristic
147C24×C43C2×D411yescharacteristic
148C2×D4×C43—22no—
149C2×D4×C43—22no—
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—41no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—81no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
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×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43—81no—
179C22×C4×C43C2×D412yes—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43#4112yes—
185C22×C4×C43C2411yescharacteristic
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C4⋊C4×C43—22no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—42no—
203C4⋊C4×C43—42no—
204C4⋊C4×C43C2×D412yes—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—81no—
212C42×C43—21no—
213C42×C43—21no—
214C22⋊Dic43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218#10621883—44no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43C2×D412yes—
225Dic43⋊C4—42no—
226Dic43⋊C4—42no—
227Dic43⋊C4—42no—
228C4×Dic43—42no—
229#10621877—28no—
230#10621877—44no—
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⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8C2×D412yes—
240C2×C43⋊C8C2×D412yes—
241C2×C43⋊C8C2×D412yes—
242C2×C43⋊C8#4112yes—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43#12112yes—
264C23×C43C22×D411yescharacteristic
265D4×C43—44no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—84no—
271D4×C43—84no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—84no—
300C2×C4×C43#12112yes—
301C2×C4×C43AGL(1,ℤ/8)12yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C432−1+411yescharacteristic
308C2×Dic43—22no—
309C2×Dic43—41no—
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—41no—
321Dic86—41no—
322Dic86—41no—
323Dic86—41no—
324C43⋊C8—22no—
325C43⋊C8—41no—
326C43⋊C8—41no—
327C43⋊C8#12114yescomplemented
328#24794—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—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43C2×#12111yescharacteristic
351C22×C43D4211yescharacteristic
352C22×C43#54711yescharacteristic
353C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C43#57511yescharacteristic
355C22×C43#57711yescharacteristic
356C22×C43#57811yescharacteristic
357C4×C43—22no—
358C4×C43—22no—
359C4×C43—41no—
360C4×C43—42no—
361C4×C43—41no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43C2×#12111yescharacteristic
365C4×C43#53711yescharacteristic
366C4×C43#54811yescharacteristic
367C4×C43#55311yescharacteristic
368Dic43—42no—
369Dic43—81no—
370Dic43—81no—
371Dic43—81no—
372C2×#468—431no—
373C2×#468—431no—
374C2×#436—431no—
375C2×#428—431no—
376#2416D4311yescharacteristic
377#2415—431no—
378#2067—431no—
379#2066—431no—
380#2036—431no—
381#2034—431no—
382#1968—431no—
383#1942—431no—
384#1875—431no—
385#1872—431no—
386#1809—431no—
387C2×C43—42no—
388C2×C43—81no—
389C2×C43—161no—
390C2×C43#241611yescharacteristic
391C2×C43#305511yescharacteristic
392C2×C43#306311yescharacteristic
393C2×C43#327211yescharacteristic
394C2×C43#327711yescharacteristic
395C2×C43#335111yescharacteristic
396C2×C43#335311yescharacteristic
397C22×SD16—431no—
398C22×M16—431no—
399C22×M16—431no—
400C2×C22⋊Q8—431no—
401C2×C22⋊Q8—431no—
402C2×#121—21no—
403C2×#121C2×D4311yescharacteristic
404C2×#121C2×D4311yescharacteristic
405C2×C4×D4C2×D4311yescharacteristic
406C2×#117—431no—
407C22×C4⋊C4C2×D4311yescharacteristic
408#468—864no—
409#468—864no—
410#436—864no—
411#428—864no—
412C2×#107—431no—
413C2×#107—431no—
414C2×#107—431no—
415C2×#106—431no—
416C2×#106—431no—
417C2×C4⋊C8—431no—
418C2×#103—431no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×C22⋊C8—431no—
425C2×C22⋊C8—431no—
426C2×C4×C8—431no—
427#397—861no—
428#396—21no—
429#394—21no—
430#394—861no—
431#391—431no—
432#390C2×D4311yescharacteristic
433#389—431no—
434#389—861no—
435#389C2×D4311yescharacteristic
436#388—861no—
437#386—21no—
438#380—431no—
439#380C2×D4311yescharacteristic
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444C43#2479411yescharacteristic, complemented, Sylow
445C22×Q8—431no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22⋊D4311yescharacteristic
449C22×D4C22×D4311yescharacteristic
450C23×C4—21no—
451C23×C4C22×D4311yescharacteristic
452C23×C4C22×D4311yescharacteristic
453C2×SD16—862no—
454C2×SD16—862no—
455C2×SD16—862no—
456C2×M16—434no—
457C2×M16—862no—
458C2×M16—862no—
459C2×M16—862no—
460C2×M16—862no—
461C2×M16—862no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8—431no—
466C22⋊Q8—862no—
467C22⋊Q8—862no—
468C22⋊Q8—862no—
469C22⋊Q8—1721no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121—41no—
474#121—44no—
475C4×D4—22no—
476C4×D4—22no—
477#117—862no—
478#117—1721no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4C22⋊D4311yescharacteristic
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4C22⋊D4311yescharacteristic
503C2×C22⋊C4C22⋊D4311yescharacteristic
504C2×C42—861no—
505C2×C42C22×D4311yescharacteristic
506#107—434no—
507#107—862no—
508#107—862no—
509#106—862no—
510#106—862no—
511C4⋊C8—862no—
512#103—862no—
513#103—862no—
514#103—1721no—
515#102—862no—
516#102—862no—
517#102—1721no—
518C22⋊C8—862no—
519C22⋊C8—862no—
520C4×C8—862no—
521#95—21no—
522#95—21no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95—861no—
527C24—21no—
528C24C2×C22⋊D4311yescharacteristic
529C24C2×C22⋊D4311yescharacteristic
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—81no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4D4×D4312yes—
572C22×C4#1062190012yes—
573C22×C4C2×C22⋊D4311yescharacteristic
574C22×C4C2×C22⋊D4311yescharacteristic
575C22×C4C2×C22⋊D4311yescharacteristic
576C22×C4C2×C22⋊D4311yescharacteristic
577C22×C4C23×D4311yescharacteristic
578SD16—1724no—
579M16—868no—
580M16—1724no—
581C2×C8—432no—
582C2×C8—432no—
583C2×C8—432no—
584C2×C8—432no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—432no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—1722no—
608C4⋊C4—1722no—
609C4⋊C4—1722no—
610C4⋊C4D4×D4312yes—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—81no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C42—21no—
623C42—21no—
624C42—1722no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23#1306329712yes—
646C23C22×C22⋊D4311yescharacteristic
647Q8—1721no—
648Q8—1721no—
649Q8—1721no—
650Q8—1721no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4—862no—
687C2×C4—1721no—
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#1306329712yes—
699C2×C4#1306335112yes—
700C2×C4C2×D4×D4311yescharacteristic
701C2×C4C2×D4×D4311yescharacteristic
702C2×C4#41×D4311yescharacteristic
703C2×C4C2×#1062190011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337211yescharacteristic
706C8—434no—
707C8—862no—
708C8—1721no—
709C8—1721no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×#1306329711yescharacteristic
732C22D4×C22⋊D4311yescharacteristic
733C22#1458354811yescharacteristic
734C22C2×#1306335111yescharacteristic
735C22#1458369711yescharacteristic
736C22#1458371011yescharacteristic
737C22#1458371411yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—42no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—3441no—
746C4—3441no—
747C4—3441no—
748C4—1722no—
749C4#121×D4311yescharacteristic
750C4#1458347611yescharacteristic
751C4#1458355511yescharacteristic
752C4#1458359211yescharacteristic
753C2—42no—
754C2—81no—
755C2—161no—
756C2#1913803211yescharacteristic
757C2#1914421011yescharacteristic
758C2#1914428811yescharacteristic
759C2#1914619111yescharacteristic
760C2#1914624811yescharacteristic
761C2#1914714911yescharacteristic
762C2#1914717911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2416C2
socleC23×C43C22×D4
hypercenter#2416D43
hypocenterC43#24794
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#14583143C2semidirect
2. C2×#14583143C2semidirect
3. C2×#14582977C2semidirect
4. C2×#14582939C2semidirect
5. #19138024C2semidirect
6. #19135983C2semidirect
7. #19135973C2semidirect
8. #19135798C2semidirect
9. #19135781C2semidirect
10. #19135448C2semidirect
11. #19135325C2semidirect
12. #19134918C2semidirect
13. #19134902C2semidirect
14. #19134626C2semidirect
72. C2×#10621877D4semidirect
96. #13063258D4semidirect
327. C43⋊C8#121semidirect
444. C43#24794semidirect

Maximal subgroups

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

subgroupindex
C2×#145831432
C2×#145829772
C2×#145829392
#191380242
#191359832
#191359732
#191357982
#191357812
#191354482
#191353252
#191349182
#191349022
#191346262
C43×#24162
#2479443