Finite Group Databasebeta

← #25149715

Subgroups — #25149715

Order 11008.

1124 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583606C211yesmaximal, characteristic
2C2×#14583227C211yesmaximal, characteristic, complemented
3C2×#14583155C211yesmaximal, characteristic, complemented
4#19135928C211yesmaximal, characteristic, complemented
5#19135791C211yesmaximal, characteristic, complemented
6#19135736C211yesmaximal, characteristic, complemented
7#19135603C211yesmaximal, characteristic, complemented
8#19134939C211yesmaximal, characteristic, complemented
9#19134907C211yesmaximal, characteristic, complemented
10#19134903C211yesmaximal, characteristic, complemented
11#19134893C211yesmaximal, characteristic
12#19134862C211yesmaximal, characteristic, complemented
13#19134787C211yesmaximal, characteristic, complemented
14#19134316C211yesmaximal, characteristic, complemented
15C43×#2415C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18#14583606—24no—
19#14583606—24no—
20C2×#13063325C2211yescharacteristic
21C2×#13063316—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063302—21no—
25C2×#13063302—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×D4×Dic43—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30#14583227—24no—
31#14583155—24no—
32C2×#13063256C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C43×#397—21no—
57C43×#394—21no—
58C43×#391C2211yescharacteristic
59C43×#389—21no—
60C43×#389C2211yescharacteristic
61C43×#388—21no—
62C43×#380C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—41no—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063325—22no—
78#13063325—22no—
79#13063316—28no—
80#13063304—22no—
81#13063304—22no—
82#13063304—22no—
83#13063304D414yes—
84#13063302—28no—
85#13063302—28no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88D4×Dic43—28no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—22no—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43D414yes—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C4×Dic43—21no—
105#13063256—22no—
106#13063256—22no—
107#13063256—22no—
108#13063249—22no—
109#13063249—22no—
110#13063249—22no—
111#13063248—22no—
112#13063248—22no—
113#13063248—41no—
114C22⋊(C43⋊C8)—22no—
115C22⋊(C43⋊C8)—22no—
116C22⋊(C43⋊C8)—41no—
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43D411yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C22⋊Q8×C43—22no—
122C22⋊Q8×C43—22no—
123C22⋊Q8×C43—22no—
124C22⋊Q8×C43—41no—
125C4×D4×C43—22no—
126C4×D4×C43—22no—
127#117×C43—22no—
128#117×C43—41no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
143C2×C42×C43C2311yescharacteristic
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
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×C43C2×D412yes—
174C22×C4×C43C2×D412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C22×Dic43—24no—
181C22×Dic43—24no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—81no—
187C22×Dic43—81no—
188C22×Dic43—81no—
189C22×Dic43—81no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—24no—
196C2×Dic86—81no—
197C2×Dic86—81no—
198C2×Dic86C2×D412yes—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—42no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43#4112yes—
209C22⋊C4×C43—22no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—42no—
218C22⋊Dic43—24no—
219C22⋊Dic43—24no—
220#10621885—44no—
221C4⋊Dic43—24no—
222C4⋊Dic43—24no—
223C4⋊Dic43—24no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43C2×D412yes—
228C4⋊Dic43C2×D412yes—
229C4⋊Dic43C2×D412yes—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232Dic43⋊C4—24no—
233C4×Dic43—24no—
234#10621877—44no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8#4112yes—
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—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43#12012yes—
260C23×C43#13712yes—
261C23×C43C22×D411yescharacteristic
262Q8×C43—41no—
263Q8×C43—41no—
264Q8×C43—41no—
265Q8×C43—41no—
266D4×C43—28no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
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#12012yes—
298C2×C4×C43#13712yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C432−1+411yescharacteristic
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
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—84no—
318C2×Dic43—84no—
319Dic86—22no—
320Dic86—22no—
321Dic86—41no—
322Dic86—41no—
323Dic86—84no—
324C43⋊C8—22no—
325C43⋊C8—41no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#25561—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
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×C43C2×#12011yescharacteristic
344C22×C43#54611yescharacteristic
345C22×C43#54711yescharacteristic
346C22×C43C2×#13711yescharacteristic
347C22×C43C2×#13711yescharacteristic
348C22×C43#57711yescharacteristic
349C22×C43#57711yescharacteristic
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—41no—
354C4×C43—41no—
355C4×C43—81no—
356C4×C43—81no—
357C4×C43—81no—
358C4×C43#53211yescharacteristic
359C4×C43#53711yescharacteristic
360C4×C43#54611yescharacteristic
361C4×C43#54711yescharacteristic
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365Dic43—42no—
366C2×#554—431no—
367C2×#483—431no—
368C2×#470—431no—
369#2415D4311yescharacteristic
370#2058—431no—
371#2035—431no—
372#2024—431no—
373#2001—431no—
374#1878—431no—
375#1873—431no—
376#1872—431no—
377#1870—431no—
378#1865—431no—
379#1853—431no—
380#1736—431no—
381C2×C43—42no—
382C2×C43—42no—
383C2×C43#243011yescharacteristic
384C2×C43#300411yescharacteristic
385C2×C43#300911yescharacteristic
386C2×C43#331611yescharacteristic
387C2×C43#333111yescharacteristic
388C2×C43#334411yescharacteristic
389C2×C43#335611yescharacteristic
390C22×Q16—431no—
391C22×M16—431no—
392#554—864no—
393#554—864no—
394C2×C4⋊Q8—431no—
395C2×#125—861no—
396C2×C22⋊Q8—431no—
397C2×C22⋊Q8—431no—
398C2×C22⋊Q8—861no—
399C2×C22⋊Q8—861no—
400C2×C22⋊Q8C2×D4311yescharacteristic
401C2×C22⋊Q8C2×D4311yescharacteristic
402C2×C4×Q8—431no—
403C2×C4×D4—861no—
404C2×C4×D4C2×D4311yescharacteristic
405C2×#117C2×D4311yescharacteristic
406C22×C4⋊C4—431no—
407C22×C4⋊C4—431no—
408#483—864no—
409#470—864no—
410C2×#106—431no—
411C2×#106—431no—
412C2×#106—431no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×C22⋊C8—431no—
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422#397—21no—
423#394—21no—
424#391C2×D4311yescharacteristic
425#389—21no—
426#389C2×D4311yescharacteristic
427#388—21no—
428#380C2×D4311yescharacteristic
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#336—431no—
436#336—431no—
437C43#2556111yescharacteristic, complemented, Sylow
438C22×Q8—431no—
439C22×Q8—861no—
440C22×Q8C22×D4311yescharacteristic
441C22×D4C22⋊D4311yescharacteristic
442C23×C4—861no—
443C23×C4—861no—
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4311yescharacteristic
446C2×Q16—862no—
447C2×Q16—862no—
448C2×Q16—1721no—
449C2×M16—862no—
450C2×M16—862no—
451C2×M16—1721no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8—431no—
456C4⋊Q8—862no—
457C4⋊Q8—862no—
458#125—868no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463C22⋊Q8—434no—
464C22⋊Q8—868no—
465C22⋊Q8—868no—
466C22⋊Q8—862no—
467C22⋊Q8—862no—
468C22⋊Q8—862no—
469C4×Q8—862no—
470C4×Q8—862no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—868no—
474#117—22no—
475#117—41no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—434no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—862no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4C22⋊D4311yescharacteristic
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C4⋊C4C22×D4311yescharacteristic
495C2×C4⋊C4C22×D4311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4C22⋊D4311yescharacteristic
503C2×C22⋊C4C22⋊D4311yescharacteristic
504C2×C42—21no—
505C2×C42—861no—
506C2×C42C22×D4311yescharacteristic
507#106—862no—
508#106—862no—
509#106—862no—
510#103—862no—
511#103—862no—
512#103—862no—
513#103—862no—
514#103—862no—
515#103—1721no—
516C22⋊C8—862no—
517C22⋊C8—862no—
518C22⋊C8—1721no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523C24C2×C22⋊D4311yescharacteristic
524C24C2×C22⋊D4311yescharacteristic
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—432no—
532C2×Q8—864no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8—3441no—
539C2×Q8—3441no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—864no—
558C22×C4—864no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—3441no—
564C22×C4—3441no—
565C22×C4—3441no—
566C22×C4—3441no—
567C22×C4D4×D4312yes—
568C22×C4D4×D4312yes—
569C22×C4C2×C22⋊D4311yescharacteristic
570C22×C4C2×C22⋊D4311yescharacteristic
571C22×C4C2×C22⋊D4311yescharacteristic
572C22×C4C2×C22⋊D4311yescharacteristic
573C22×C4C23×D4311yescharacteristic
574Q16—1724no—
575M16—1724no—
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—
587C2×C8—861no—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—432no—
598C4⋊C4—432no—
599C4⋊C4—432no—
600C4⋊C4—864no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4#1062190012yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—864no—
617C22⋊C4—864no—
618C42—21no—
619C42—21no—
620C42—42no—
621C42—864no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23#1306329312yes—
635C23#1306335512yes—
636C23C22×C22⋊D4311yescharacteristic
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—862no—
642Q8—862no—
643Q8—3444no—
644Q8—1721no—
645Q8—1721no—
646D4—28no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—3444no—
682C2×C4—3444no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4#1306329312yes—
692C2×C4#1306335512yes—
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C2×D4×D4311yescharacteristic
695C2×C4#41×D4311yescharacteristic
696C2×C4C2×#1062190011yescharacteristic
697C2×C4#1306337011yescharacteristic
698C2×C4#1306337211yescharacteristic
699C8—862no—
700C8—1721no—
701C8—1721no—
702C8—1721no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C2×#1306329311yescharacteristic
718C22#1458354311yescharacteristic
719C22#1458354811yescharacteristic
720C22C2×#1306335511yescharacteristic
721C22C2×#1306335511yescharacteristic
722C22#1458370711yescharacteristic
723C22#1458370711yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4—1722no—
733C4—1722no—
734C4—1722no—
735C4—1722no—
736C4#1458344411yescharacteristic
737C4#1458347611yescharacteristic
738C4#1458353811yescharacteristic
739C4#1458354911yescharacteristic
740C2—42no—
741C2—42no—
742C2#1913820111yescharacteristic
743C2#1914382811yescharacteristic
744C2#1914387011yescharacteristic
745C2#1914670611yescharacteristic
746C2#1914691111yescharacteristic
747C2#1914705011yescharacteristic
748C2#1914720411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2415C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#2415D43
hypocenterC43#25561
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
2. C2×#14583227C2semidirect
3. C2×#14583155C2semidirect
4. #19135928C2semidirect
5. #19135791C2semidirect
6. #19135736C2semidirect
7. #19135603C2semidirect
8. #19134939C2semidirect
9. #19134907C2semidirect
10. #19134903C2semidirect
12. #19134862C2semidirect
13. #19134787C2semidirect
14. #19134316C2semidirect
437. C43#25561semidirect

Maximal subgroups

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

subgroupindex
C2×#145836062
C2×#145832272
C2×#145831552
#191359282
#191357912
#191357362
#191356032
#191349392
#191349072
#191349032
#191348932
#191348622
#191347872
#191343162
C43×#24152
#2556143