Finite Group Databasebeta

← #25113436

Subgroups — #25113436

Order 11008.

1366 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583569C211yesmaximal, characteristic
2C2×#14583028C211yesmaximal, characteristic, complemented
3#19137553C211yesmaximal, characteristic, complemented
4#19135520C211yesmaximal, characteristic, complemented
5#19135520C211yesmaximal, characteristic, complemented
6#19135420C211yesmaximal, characteristic, complemented
7#19135417C211yesmaximal, characteristic, complemented
8#19135399C211yesmaximal, characteristic, complemented
9#19134606C211yesmaximal, characteristic, complemented
10#19134603C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134423C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#1982C211yesmaximal, characteristic, complemented
16C22×#10621900—21no—
17#14583569—24no—
18#14583569C418yescomplemented
19C2×#13063321C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21C2×#13063297—21no—
22C2×#13063297—21no—
23C2×#13063296—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28#14583028—24no—
29C2×Dic43⋊C8C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063236C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42#14582803—21no—
43#14582783—21no—
44#14582782—21no—
45#14582768C2211yescharacteristic
46#14582765C2211yescharacteristic
47#14582764C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50C4×Dic43⋊C4—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#127×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C2×#10621900—28no—
63C2×#10621900—44no—
64C2×#10621900—44no—
65C22×Dic86D411yescharacteristic
66C22×D172C2311yescharacteristic
67C22×C22⋊D43—21no—
68C22×C22⋊D43—21no—
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C23×Dic43—21no—
72C23×Dic43—21no—
73C22×C4×D43—21no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063321—22no—
77#13063321—22no—
78#13063321C2×C414yes—
79#13063321C2×C414yes—
80#13063297—28no—
81#13063297—28no—
82#13063296—28no—
83C4×Dic86C2×C414yes—
84C4×Dic86D414yes—
85C4×D172—22no—
86C4×D172C2×C414yes—
87D4×Dic43—22no—
88D4×Dic43—22no—
89D4×Dic43C2×C414yes—
90D4×Dic43C2×C414yes—
91C2×C4⋊Dic43D411yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4D411yescharacteristic
98C2×Dic43⋊C4D411yescharacteristic
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106Dic43⋊C8—22no—
107Dic43⋊C8—22no—
108#13063247—41no—
109#13063247—41no—
110#13063246—22no—
111#13063246—22no—
112#13063246—41no—
113#13063246—41no—
114#13063245—22no—
115#13063245—22no—
116#13063236—22no—
117#13063235—22no—
118C8×Dic43—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×D4×C43—21no—
126C22×D4×C43—21no—
127C22×D4×C43C2311yescharacteristic
128C22×D4×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131#127×C43—22no—
132#127×C43C2×C414yes—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—41no—
141#102×C43—41no—
142#95×C43—21no—
143C24×C43—21no—
144C24×C43—21no—
145C23×D43—21no—
146C2×D4×C43—24no—
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—42no—
159C2×D4×C43—42no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
162C2×D4×C43C22×C412yes—
163C2×D4×C43C22×C412yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×C22⋊D43—24no—
170C2×C22⋊D43—24no—
171C2×C22⋊D43—24no—
172C2×C22⋊D43—24no—
173C2×C22⋊D43—42no—
174C2×C22⋊D43—42no—
175C2×C22⋊D43—42no—
176C2×C22⋊D43—42no—
177C2×C22⋊D43—81no—
178C2×C22⋊D43—81no—
179C2×C22⋊D43—81no—
180C2×C22⋊D43—81no—
181C22×Dic43—24no—
182C22×Dic43—24no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—42no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194#10621900—432no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172C22×C412yes—
201C2×C4×D43—24no—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×Dic86—22no—
205C2×Dic86—22no—
206C2×Dic86C22⋊C414yes—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43#4112yescomplemented
217C42×C43—81no—
218C42×C43C22×C412yes—
219C42×C43C2×D412yes—
220C22⋊Dic43—24no—
221C22⋊Dic43—24no—
222(C2×D43)⋊C4—24no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43C22⋊C414yes—
229C4⋊Dic43C22×C412yes—
230Dic43⋊C4—42no—
231Dic43⋊C4—81no—
232Dic43⋊C4C22⋊C414yes—
233Dic43⋊C4C22⋊C414yes—
234C4×Dic43—42no—
235C4×Dic43—81no—
236C4×Dic43C22×C412yes—
237C4×Dic43C22×C412yes—
238C4×Dic43C2×D412yes—
239C4×Dic43C2×D412yes—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8#4112yescomplemented
246C23×C43—22no—
247C23×C43—22no—
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×C43C22×D411yescharacteristic
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
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—
277D4×C43—84no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43C2×C22⋊C412yes—
289C2×C4×C43C2×C22⋊C412yes—
290C2×C4×C43C23×C411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C432−1+411yescharacteristic
296C22⋊D43—48no—
297C22⋊D43—48no—
298C22⋊D43—84no—
299C22⋊D43—84no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—22no—
307C2×Dic43—48no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—48no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43C2×C22⋊C412yes—
318C2×Dic43C2×C22⋊C412yes—
319C2×Dic43C2×C22⋊C412yes—
320C2×Dic43C2×C22⋊C412yes—
321C2×Dic43AGL(1,ℤ/8)12yes—
322C2×Dic43AGL(1,ℤ/8)12yes—
323D172—22no—
324D172—22no—
325D172—41no—
326D172—41no—
327C4×D43—48no—
328Dic86—28no—
329C8×C43—41no—
330C8×C43—41no—
331C43⋊C8—22no—
332C43⋊C8—41no—
333#22545—431nomaximal, Sylow
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43C22×C22⋊C411yescharacteristic
349C22×C43#54811yescharacteristic
350C22×C43#55011yescharacteristic
351C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C43#57611yescharacteristic
354C22×C43#57711yescharacteristic
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—81no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—81no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43—42no—
365C4×C43—81no—
366C4×C43C4×#4111yescharacteristic
367C4×C43#52011yescharacteristic
368C4×C43#54811yescharacteristic
369C4×C43#55011yescharacteristic
370Dic43—22no—
371Dic43—22no—
372Dic43—22no—
373Dic43—42no—
374Dic43—81no—
375Dic43—81no—
376Dic43#41814yes—
377C2×#550—431no—
378C2×#446—431no—
379#2355—431no—
380#1982—431no—
381#1982—431no—
382#1982D4311yescharacteristic, complemented
383#1961—431no—
384#1961—431no—
385#1957—431no—
386#1804—431no—
387#1804—431no—
388#1802—431no—
389#1762—431no—
390#1762—431no—
391C4×#102—431no—
392C2×C43—82no—
393C2×C43—82no—
394C2×C43#234111yescharacteristic
395C2×C43C2×#41811yescharacteristic
396C2×C43#289711yescharacteristic
397C2×C43#336611yescharacteristic
398C2×C43#336811yescharacteristic
399C2×C43#339711yescharacteristic
400C2×C43#339911yescharacteristic
401D43—82no—
402C22×#41—861no—
403#550—438no—
404#550—864no—
405C2×#127—431no—
406C2×#127—431no—
407C2×#127C2×D4311yescharacteristic
408C2×#121—861no—
409C2×#121—861no—
410C2×#121—861no—
411C2×C4×Q8—431no—
412C2×C4×D4—431no—
413C2×C4×D4—431no—
414C2×C4×D4—431no—
415#446—864no—
416C2×C4⋊C8—431no—
417C2×C4⋊C8—431no—
418C2×C4⋊C8C2×D4311yescharacteristic
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102—431no—
427C2×#102C2×D4311yescharacteristic
428C2×#102C2×D4311yescharacteristic
429C2×#102C2×D4311yescharacteristic
430C2×#102C2×D4311yescharacteristic
431C2×#97—431no—
432C2×#97—431no—
433C2×C4×C8—431no—
434#391—861no—
435#387—861no—
436#387—861no—
437#384—431no—
438#382—431no—
439#382—431no—
440C4×C4⋊C4—431no—
441C4×C4⋊C4—431no—
442C4×C4⋊C4—861no—
443C4×C4⋊C4C2×D4311yescharacteristic
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448C43#2254511yescharacteristic, complemented, Sylow
449C2×#41—868no—
450C2×#41—1724no—
451C2×#41—1724no—
452C22×Q8—431no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—431no—
456C22×D4—861no—
457C22×D4—861no—
458C22×D4—861no—
459C22×D4—861no—
460C22×D4C22×D4311yescharacteristic
461C22×D4C22×D4311yescharacteristic
462C23×C4—861no—
463C23×C4—861no—
464C23×C4—861no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469#127—22no—
470#127—434no—
471#127—434no—
472#127—862no—
473#127—862no—
474#127C4×D4314yes—
475#121—868no—
476#121—868no—
477#121—868no—
478C4×Q8—434no—
479C4×Q8—434no—
480C4×D4—434no—
481C4×D4—434no—
482C4×D4—434no—
483C4×D4—862no—
484C4×D4—862no—
485C4×D4—862no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4C22×D4311yescharacteristic
495C2×C4⋊C4C22×D4311yescharacteristic
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C42—21no—
500C2×C42—431no—
501C2×C42—431no—
502C2×C42—861no—
503C2×C42—861no—
504C2×C42C22×D4311yescharacteristic
505C4⋊C8—22no—
506C4⋊C8—862no—
507C4⋊C8—862no—
508#102—22no—
509#102—22no—
510#102—41no—
511#102—41no—
512#102—862no—
513#102—862no—
514#102—862no—
515#102—862no—
516#102—1721no—
517#102—1721no—
518#102—1721no—
519#102—1721no—
520#97—862no—
521#97—862no—
522C4×C8—862no—
523#95—21no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528#95—861no—
529#95—861no—
530C24—21no—
531C24—21no—
532C24—861no—
533#41—17232no—
534C2×Q8—434no—
535C2×Q8—862no—
536C2×Q8—862no—
537C2×D4—24no—
538C2×D4—24no—
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—21no—
548C2×D4—21no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—432no—
554C2×D4—864no—
555C2×D4—864no—
556C2×D4—864no—
557C2×D4—864no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—861no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—3441no—
564C2×D4—3441no—
565C2×D4—3441no—
566C2×D4—3441no—
567C2×D4—1722no—
568C2×D4—1722no—
569C2×D4—1722no—
570C2×D4—1722no—
571C2×D4C2×C4×D4312yes—
572C2×D4C2×C4×D4312yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—864no—
580C22×C4—864no—
581C22×C4—861no—
582C22×C4—864no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4—1722no—
588C22×C4—1722no—
589C22×C4—1722no—
590C22×C4—1722no—
591C22×C4D4×D4311yescharacteristic
592C22×C4D4×D4311yescharacteristic
593C22×C4C23×D4311yescharacteristic
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—432no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—434no—
610C4⋊C4—434no—
611C4⋊C4—434no—
612C4⋊C4—432no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—3441no—
619C4⋊C4—1722no—
620C4⋊C4#1062190012yescomplemented
621C22⋊C4—864no—
622C22⋊C4—864no—
623C22⋊C4—864no—
624C42—81no—
625C42—432no—
626C42—432no—
627C42—432no—
628C42—432no—
629C42—3441no—
630C42—1722no—
631C42C2×C4×D4312yes—
632C42D4×D4312yes—
633C23—22no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—862no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23C2×D4×D4311yescharacteristic
655Q8—868no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—48no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—84no—
666D4—862no—
667D4—862no—
668D4—3444no—
669D4—3444no—
670D4—1728no—
671D4—1728no—
672D4—1721no—
673D4—1721no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—432no—
685C2×C4—432no—
686C2×C4—432no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—432no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—862no—
697C2×C4—1728no—
698C2×C4—1728no—
699C2×C4—1728no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4C22⋊C4×D4312yes—
709C2×C4C22⋊C4×D4312yes—
710C2×C4C22×C4×D4311yescharacteristic
711C2×C4C2×D4×D4311yescharacteristic
712C2×C4#41×D4311yescharacteristic
713C2×C4C2×#1062190011yescharacteristic
714C2×C4#1306337011yescharacteristic
715C2×C4#1306337211yescharacteristic
716C8—41no—
717C8—41no—
718C8—862no—
719C8—1721no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—3441no—
735C22—3441no—
736C22—3441no—
737C22—3441no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22C2×C22⋊C4×D4311yescharacteristic
742C22#1458355511yescharacteristic
743C22#1458356711yescharacteristic
744C22AGL(1,ℤ/8)×D4311yescharacteristic
745C22AGL(1,ℤ/8)×D4311yescharacteristic
746C22#1458370011yescharacteristic
747C22#1458370511yescharacteristic
748C4—22no—
749C4—22no—
750C4—42no—
751C4—81no—
752C4—434no—
753C4—862no—
754C4—862no—
755C4—862no—
756C4—3441no—
757C4—3441no—
758C4—1722no—
759C4C4×#1062190011yescharacteristic
760C4#1458337811yescharacteristic
761C4#1458355711yescharacteristic
762C4#1458356911yescharacteristic
763C2—82no—
764C2—82no—
765C2—3442no—
766C2#1913743411yescharacteristic
767C2#418×D4311yescharacteristic
768C2#1914311611yescharacteristic
769C2#1914729711yescharacteristic
770C2#1914731911yescharacteristic
771C2#1914761011yescharacteristic
772C2#1914764011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1982C2
socleC23×C43C22×D4
prime radicalC2×#14583569C2
cosocleC22×C4×C43C24
hypercenter#1982D43
hypocenterC43#22545
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#14583028C2semidirect
3. #19137553C2semidirect
4. #19135520C2semidirect
5. #19135520C2semidirect
6. #19135420C2semidirect
7. #19135417C2semidirect
8. #19135399C2semidirect
9. #19134606C2semidirect
10. #19134603C2semidirect
11. #19134593C2semidirect
12. #19134423C2semidirect
13. #19134422C2semidirect
14. #102×Dic43C2semidirect
15. C43×#1982C2semidirect
18. #14583569C4semidirect
216. C4⋊C4×C43#41semidirect
245. C2×C43⋊C8#41semidirect
382. #1982D43semidirect
448. C43#22545semidirect
620. C4⋊C4#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145835692
C2×#145830282
#191375532
#191355202
#191354202
#191354172
#191353992
#191346062
#191346032
#191345932
#191344232
#191344222
#102×Dic432
C43×#19822
#2254543