Finite Group Databasebeta

← #25140453

Subgroups — #25140453

Order 11008.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic43C211yesmaximal, characteristic, complemented
2#19138116C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic43C211yesmaximal, characteristic
4#19136126C211yesmaximal, characteristic, complemented
5#19136028C211yesmaximal, characteristic, complemented
6#19135908C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135275C211yesmaximal, characteristic, complemented
9#19135198C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic, complemented
11#19134931C211yesmaximal, characteristic, complemented
12#19134854C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic
15C2×C43×#450C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic, complemented
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C22×C22⋊Dic43—21no—
20SD16×Dic43—24no—
21C2×#13063257C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23C2×Dic43⋊C8C2211yescharacteristic, complemented
24C2×#13063249C2211yescharacteristic, complemented
25C2×#13063249C2211yescharacteristic, complemented
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic, complemented
32#14582835—21no—
33#14582829—21no—
34#14582806C2211yescharacteristic, complemented
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582795C2211yescharacteristic, complemented
38#14582787—21no—
39#14582780—21no—
40#14582779—21no—
41#14582779—21no—
42#14582768C2211yescharacteristic, complemented
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582755—21no—
46C4×C22⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C23×D4×C43C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C43×#450—24no—
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65Q8×Dic43—22no—
66Q8×Dic43—41no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—41no—
70D4×Dic43—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—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⋊Dic43—21no—
87C2×C22⋊Dic43—44no—
88C2×C22⋊Dic43D411yescharacteristic
89C2×C22⋊Dic43D411yescharacteristic
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063257—22no—
94#13063256—41no—
95Dic43⋊C8—41no—
96#13063249—22no—
97#13063249—41no—
98#13063246—22no—
99#13063246—22no—
100#13063246—22no—
101#13063246—41no—
102C22⋊(C43⋊C8)—41no—
103C8×Dic43—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C25×C43—21no—
112C22×Q8×C43C2311yescharacteristic
113C22×D4×C43—22no—
114C22×D4×C43—22no—
115C22×D4×C43—22no—
116C22×D4×C43—22no—
117C22×D4×C43—21no—
118C22×D4×C43—41no—
119C22×D4×C43—41no—
120C22×D4×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C2×SD16×C43—22no—
124C2×SD16×C43—22no—
125C2×SD16×C43—22no—
126C2×SD16×C43—22no—
127C2×SD16×C43—41no—
128C2×SD16×C43D414yes—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43—41no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136#102×C43—22no—
137#102×C43—22no—
138C22⋊C8×C43—22no—
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—21no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C2×D412yes—
155C2×D4×C43—24no—
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—42no—
165C2×D4×C43—42no—
166C2×D4×C43—44no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43C2×D412yes—
171C2×D4×C43#4112yes—
172C2×D4×C43#4112yes—
173C2×D4×C43#4112yes—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2411yescharacteristic
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43—81no—
193C22×Dic43—81no—
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198SD16×C43—28no—
199SD16×C43—44no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43C2×D412yes—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊Dic43—41no—
211C22⋊Dic43—42no—
212C22⋊Dic43—42no—
213C22⋊Dic43—42no—
214C22⋊Dic43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—81no—
217C22⋊Dic43—81no—
218C22⋊Dic43—81no—
219C22⋊Dic43SD1614yescomplemented
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—42no—
229Dic43⋊C4—42no—
230Dic43⋊C4—81no—
231Dic43⋊C4—81no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—42no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C23×C43—21no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—21no—
247C23×C43—22no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—22no—
253C23×C43—48no—
254C23×C43—48no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—84no—
266C23×C43—84no—
267C23×C43—84no—
268C23×C43—84no—
269C23×C43—84no—
270C23×C43C2×SD1612yes—
271C23×C43C22×D411yescharacteristic
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—41no—
275Q8×C43—41no—
276D4×C43—22no—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—22no—
281D4×C43—48no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43#12314yes—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
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×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
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—21no—
313C2×Dic43—21no—
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—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—84no—
327C2×Dic43—84no—
328C2×Dic43C2×SD1612yes—
329C2×Dic43C2×SD1612yes—
330C8×C43—22no—
331C8×C43—41no—
332C43⋊C8—41no—
333C43⋊C8—41no—
334#24901—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—24no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—42no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—816no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43#52511yescharacteristic
358C22×C43D4211yescharacteristic
359C22×C43#54611yescharacteristic
360C22×C43C22×SD1611yescharacteristic
361C22×C43#57511yescharacteristic
362C22×C43#57611yescharacteristic
363C22×C43#57711yescharacteristic
364C4×C43—41no—
365C4×C43—42no—
366C4×C43—81no—
367C4×C43C2×#12311yescharacteristic
368C4×C43#53811yescharacteristic
369C4×C43#54611yescharacteristic
370C4×C43#55111yescharacteristic
371Dic43—22no—
372Dic43—22no—
373Dic43—41no—
374Dic43—41no—
375Dic43—81no—
376Dic43—81no—
377Dic43—81no—
378Dic43—81no—
379C2×#450D4311yescharacteristic
380C2×C4×SD16—431no—
381#2423—431no—
382D4×C22⋊C4—431no—
383#2094—431no—
384#2077—431no—
385#2055—431no—
386#2035—431no—
387#1934—431no—
388#1923—431no—
389#1880—431no—
390#1877—431no—
391#1864—431no—
392#1802—431no—
393#1786—431no—
394C2×C43—42no—
395C2×C43—44no—
396C2×C43—82no—
397C2×C43#241811yescharacteristic
398C2×C43#310111yescharacteristic
399C2×C43#311811yescharacteristic
400C2×C43#326811yescharacteristic
401C2×C43D4×SD1611yescharacteristic
402C2×C43#329511yescharacteristic
403C2×C43#332311yescharacteristic
404C23×D4C2×D4311yescharacteristic
405C22×SD16C2×D4311yescharacteristic
406C22×SD16C2×D4311yescharacteristic
407C2×C22⋊Q8C2×D4311yescharacteristic
408C2×C4×Q8—431no—
409C2×C4×D4—431no—
410C2×C4×D4—431no—
411C22×C22⋊C4—861no—
412#450—24no—
413C4×SD16—864no—
414C2×#106—431no—
415C2×#106—431no—
416C2×C4⋊C8—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102C2×D4311yescharacteristic
424C2×#102C2×D4311yescharacteristic
425C2×C22⋊C8—431no—
426C2×C22⋊C8C2×D4311yescharacteristic
427C2×C4×C8—431no—
428#399—861no—
429#398—861no—
430#391—431no—
431#390—431no—
432#390—431no—
433#389—431no—
434#388—861no—
435#387—861no—
436#386—861no—
437#386—861no—
438#384—431no—
439#380—431no—
440#380—431no—
441#379—861no—
442C4×C22⋊C4—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#336—431no—
448#336—431no—
449C43#2490111yescharacteristic, complemented, Sylow
450C25—21no—
451C22×Q8C22×D4311yescharacteristic
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C22×D4311yescharacteristic
460C22×D4C22×D4311yescharacteristic
461C23×C4—861no—
462C23×C4—861no—
463C23×C4C22×D4311yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×SD16C22⋊D4314yes—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C4×Q8—862no—
477C4×Q8—1721no—
478C4×D4—862no—
479C4×D4—862no—
480C4×D4—1721no—
481C4×D4—1721no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—431no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—1724no—
504C2×C42—431no—
505C2×C42—431no—
506C2×C42—861no—
507#106—862no—
508#106—1721no—
509C4⋊C8—1721no—
510#103—862no—
511#103—1721no—
512#102—22no—
513#102—22no—
514#102—862no—
515#102—862no—
516#102—862no—
517#102—1721no—
518C22⋊C8—22no—
519C22⋊C8—1721no—
520C4×C8—862no—
521#95—431no—
522#95—431no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24D4×D4311yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C22⋊D4312yes—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4#1062190012yes—
560C2×D4#1062190012yes—
561C2×D4#1062190012yes—
562C2×D4C2×C22⋊D4312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—3441no—
580C22×C4—3441no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4—1722no—
584C22×C4—1722no—
585C22×C4D4×D4311yescharacteristic
586C22×C4C23×D4311yescharacteristic
587SD16—28no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8C2×C22⋊D4312yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—3441no—
613C4⋊C4—3441no—
614C4⋊C4—1722no—
615C4⋊C4—1722no—
616C22⋊C4—42no—
617C22⋊C4—434no—
618C22⋊C4—3441no—
619C22⋊C4—3441no—
620C22⋊C4—3441no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C22⋊C4—1721no—
624C22⋊C4—1722no—
625C22⋊C4—1722no—
626C22⋊C4—1722no—
627C42—861no—
628C42—861no—
629C42—861no—
630C42—861no—
631C42—1722no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23SD16×D4312yes—
660C23C2×D4×D4311yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#1306330614yes—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—3444no—
700C2×C4—3444no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4C22×C22⋊D4311yescharacteristic
714C2×C4C2×#1062190011yescharacteristic
715C2×C4C2×#1062190011yescharacteristic
716C2×C4C2×#1062190011yescharacteristic
717C2×C4#1306337011yescharacteristic
718C2×C4#1306337011yescharacteristic
719C8—22no—
720C8—41no—
721C8—1721no—
722C8—1721no—
723C22—24no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#1458340511yescharacteristic
746C22D4×C22⋊D4311yescharacteristic
747C22#1458353611yescharacteristic
748C22C2×SD16×D4311yescharacteristic
749C22#1458369511yescharacteristic
750C22#1458370311yescharacteristic
751C22#1458370511yescharacteristic
752C4—41no—
753C4—42no—
754C4—81no—
755C4—862no—
756C4—862no—
757C4—3441no—
758C4—3441no—
759C4—3441no—
760C4—3441no—
761C4—1721no—
762C4—1721no—
763C4C2×#1306330611yescharacteristic
764C4#1458348411yescharacteristic
765C4#1458354311yescharacteristic
766C4#1458358011yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2#1913805311yescharacteristic
771C2#1914459811yescharacteristic
772C2#1914478011yescharacteristic
773C2#1914612911yescharacteristic
774C2SD16×C22⋊D4311yescharacteristic
775C2#1914641211yescharacteristic
776C2#1914681511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#450C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenterC2×#450D43
hypocenterC43#24901
LCSG ▷ C22×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. C2×SD16×Dic43C2semidirect
2. #19138116C2semidirect
4. #19136126C2semidirect
5. #19136028C2semidirect
6. #19135908C2semidirect
7. #19135788C2semidirect
8. #19135275C2semidirect
9. #19135198C2semidirect
10. #19134952C2semidirect
11. #19134931C2semidirect
12. #19134854C2semidirect
13. #19134593C2semidirect
16. C2×Q8×Dic43C22semidirect
21. C2×#13063257C22semidirect
22. C2×#13063256C22semidirect
23. C2×Dic43⋊C8C22semidirect
24. C2×#13063249C22semidirect
25. C2×#13063249C22semidirect
31. C2×C8×Dic43C22semidirect
34. #14582806C22semidirect
37. #14582795C22semidirect
42. #14582768C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
219. C22⋊Dic43SD16semidirect
449. C43#24901semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic432
#191381162
D4×C22⋊Dic432
#191361262
#191360282
#191359082
#191357882
#191352752
#191351982
#191349522
#191349312
#191348542
#191345932
#191345262
C2×C43×#4502
#2490143