Finite Group Databasebeta

← #25149726

Subgroups — #25149726

Order 11008.

1108 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583588C211yesmaximal, characteristic
2C2×#14583155C211yesmaximal, characteristic, complemented
3#19138047C211yesmaximal, characteristic
4#19135931C211yesmaximal, characteristic, complemented
5#19135800C211yesmaximal, characteristic, complemented
6#19135744C211yesmaximal, characteristic, complemented
7#19135604C211yesmaximal, characteristic, complemented
8#19134933C211yesmaximal, characteristic, complemented
9#19134900C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic, complemented
11#19134890C211yesmaximal, characteristic
12#19134860C211yesmaximal, characteristic, complemented
13#19134786C211yesmaximal, characteristic, complemented
14#19134316C211yesmaximal, characteristic, complemented
15C2×C43×#485C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18#14583588—24no—
19#14583588—24no—
20C2×#13063318—21no—
21C2×#13063317—21no—
22C2×#13063316C2211yescharacteristic
23C2×#13063307—21no—
24C2×#13063305C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26C2×#13063301C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063282—21no—
30C22×C4⋊Dic43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14583155—24no—
33C2×#13063256C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40#14582832—21no—
41#14582821—21no—
42#14582806C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582776—21no—
45#14582757—21no—
46#14582756C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C22⋊Q8×C43C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C43×#485—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43D411yescharacteristic
65C23×Dic43—21no—
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—41no—
71C2×#10621877—22no—
72C2×#10621877—22no—
73C2×#10621877—41no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063318—28no—
77#13063317—28no—
78#13063316—22no—
79#13063316—22no—
80#13063307—28no—
81#13063305—22no—
82#13063305—22no—
83#13063304—22no—
84#13063304D414yes—
85#13063301—22no—
86#13063301—41no—
87#13063290—22no—
88#13063290—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91#13063282—28no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—41no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4D411yescharacteristic
107C4⋊C4×D43—22no—
108C4⋊C4×D43—22no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43D411yescharacteristic
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4D411yescharacteristic
115C2×C4×Dic43—21no—
116C2×C4×Dic43C2311yescharacteristic
117#13063256—22no—
118#13063250—22no—
119#13063250—41no—
120#13063249—22no—
121#13063248—22no—
122(C2×D43)⋊C8—22no—
123(C2×D43)⋊C8—41no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×Q8×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22⋊Q8×C43—22no—
133C22⋊Q8×C43—22no—
134#117×C43—22no—
135#117×C43D414yes—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C42×C43—21no—
143#107×C43—22no—
144#106×C43—22no—
145#103×C43—22no—
146#103×C43—22no—
147C22⋊C8×C43—22no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×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—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C2×D412yes—
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—41no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—81no—
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C2×C4×D43—24no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86C2×D412yes—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43C2×D412yes—
208C4⋊C4×C43C2×D412yes—
209C22⋊C4×C43—24no—
210C22⋊C4×C43—42no—
211C42×C43—24no—
212C22⋊Dic43—24no—
213C22⋊Dic43—22no—
214#10621885—44no—
215(C2×D43)⋊C4—24no—
216(C2×D43)⋊C4—22no—
217(C2×D43)⋊C4—42no—
218(C2×D43)⋊C4—81no—
219C4⋊Dic43—24no—
220C4⋊Dic43—24no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—42no—
226C4⋊Dic43C2×D412yes—
227C4⋊Dic43#4112yes—
228Dic43⋊C4—24no—
229Dic43⋊C4—24no—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232Dic43⋊C4—22no—
233Dic43⋊C4—42no—
234Dic43⋊C4—81no—
235C4×Dic43—24no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238#10621877—44no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8#4112yes—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43#12012yes—
252C23×C43C22×D411yescharacteristic
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43#13712yes—
260Q8×C43—41no—
261Q8×C43—41no—
262Q8×C43—41no—
263Q8×C43—41no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43#12012yes—
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C2×C4×C432−1+411yescharacteristic
289C22⋊D43—44no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—22no—
293C2×Dic43—21no—
294C2×Dic43—22no—
295C2×Dic43—21no—
296C2×Dic43—22no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—84no—
312C4×D43—48no—
313C4×D43—41no—
314C4×D43—41no—
315C4×D43—41no—
316C4×D43—41no—
317Dic86—22no—
318Dic86—22no—
319Dic86—41no—
320Dic86—41no—
321C8×C43—41no—
322C8×C43—41no—
323C43⋊C8—22no—
324C43⋊C8—41no—
325#25562—431nomaximal, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43C2×#12011yescharacteristic
334C22×C43#54611yescharacteristic
335C22×C43#54711yescharacteristic
336C22×C43C2×#13711yescharacteristic
337C22×C43#57511yescharacteristic
338C22×C43#57711yescharacteristic
339C22×C43#57811yescharacteristic
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C2×D43—41no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—81no—
351C4×C43—81no—
352C4×C43#53211yescharacteristic
353C4×C43#53711yescharacteristic
354C4×C43#54611yescharacteristic
355C4×C43#54711yescharacteristic
356Dic43—42no—
357Dic43—41no—
358Dic43—42no—
359Dic43—41no—
360Dic43—41no—
361Dic43—42no—
362Dic43—81no—
363C2×#552—431no—
364C2×#485D4311yescharacteristic, complemented
365C2×#470—431no—
366#2417—431no—
367#2059—431no—
368#2036—431no—
369#2026—431no—
370#2001—431no—
371#1878—431no—
372#1872—431no—
373#1872—431no—
374#1870—431no—
375#1865—431no—
376#1853—431no—
377#1736—431no—
378C2×C43—42no—
379C2×C43#243011yescharacteristic
380C2×C43#300711yescharacteristic
381C2×C43#301311yescharacteristic
382C2×C43#331211yescharacteristic
383C2×C43#332311yescharacteristic
384C2×C43#334411yescharacteristic
385C2×C43#335211yescharacteristic
386D43—42no—
387C22×Q16—431no—
388C22×M16—431no—
389#552—864no—
390#552—864no—
391C2×#126—861no—
392C2×#125—431no—
393C2×#125—861no—
394C2×#123—861no—
395C2×C22⋊Q8—431no—
396C2×C22⋊Q8—431no—
397C2×C22⋊Q8—431no—
398C2×C22⋊Q8C2×D4311yescharacteristic
399C2×C4×Q8—431no—
400C2×C4×D4—431no—
401C2×#117—861no—
402C2×#117C2×D4311yescharacteristic
403C22×C4⋊C4—431no—
404C22×C4⋊C4—431no—
405#485—24no—
406#470—864no—
407C2×#107C2×D4311yescharacteristic
408C2×#106—431no—
409C2×#106C2×D4311yescharacteristic
410C2×#103—431no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#103—431no—
414C2×#103C2×D4311yescharacteristic
415C2×#103C2×D4311yescharacteristic
416C2×C22⋊C8—431no—
417C2×C22⋊C8—431no—
418C2×C22⋊C8C2×D4311yescharacteristic
419#398—861no—
420#396—861no—
421#391—431no—
422#389—431no—
423#386—861no—
424#380—431no—
425#380—861no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#336—431no—
433#336—431no—
434C43#2556211yescharacteristic, complemented, Sylow
435C22×Q8—431no—
436C22×Q8C22×D4311yescharacteristic
437C22×D4—431no—
438C23×C4—431no—
439C23×C4—861no—
440C23×C4—861no—
441C23×C4C22×D4311yescharacteristic
442C2×Q16—862no—
443C2×Q16—862no—
444C2×Q16—1721no—
445C2×M16—862no—
446C2×M16—862no—
447C2×M16—1721no—
448C22×C8—431no—
449C22×C8—431no—
450C22×C8C22×D4311yescharacteristic
451C22×C8C22×D4311yescharacteristic
452#126—868no—
453#125—868no—
454#125—862no—
455#125—862no—
456#123—868no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—434no—
460C22⋊Q8—862no—
461C22⋊Q8—862no—
462C22⋊Q8—862no—
463C22⋊Q8—862no—
464C22⋊Q8—1721no—
465C4×Q8—862no—
466C4×Q8—862no—
467C4×D4—862no—
468C4×D4—862no—
469#117—22no—
470#117—868no—
471#117C22⋊D4314yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—862no—
478C2×C4⋊C4—862no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—862no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—1721no—
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—431no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C42—21no—
502C2×C42—431no—
503C2×C42—861no—
504#107—22no—
505#106—22no—
506#106—862no—
507#103—22no—
508#103—22no—
509#103—862no—
510#103—862no—
511#103—862no—
512#103—1721no—
513C22⋊C8—22no—
514C22⋊C8—862no—
515C22⋊C8—1721no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520C24—431no—
521C24D4×D4311yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—432no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×D4—862no—
535C2×D4—862no—
536C2×D4—1721no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—864no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—3441no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4D4×D4311yescharacteristic
565C22×C4D4×D4312yes—
566C22×C4C2×C22⋊D4312yes—
567C22×C4C23×D4311yescharacteristic
568Q16—1724no—
569M16—1724no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—432no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—42no—
587C4⋊C4—432no—
588C4⋊C4—432no—
589C4⋊C4—864no—
590C4⋊C4—864no—
591C4⋊C4—864no—
592C4⋊C4—864no—
593C4⋊C4—864no—
594C4⋊C4—862no—
595C4⋊C4—864no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—3441no—
601C4⋊C4—1722no—
602C4⋊C4—1722no—
603C4⋊C4C2×C22⋊D4312yes—
604C4⋊C4C2×C22⋊D4312yes—
605C22⋊C4—24no—
606C22⋊C4—42no—
607C22⋊C4—864no—
608C22⋊C4—862no—
609C22⋊C4—864no—
610C22⋊C4—862no—
611C22⋊C4—3441no—
612C22⋊C4—1722no—
613C42—24no—
614C42—864no—
615C42—861no—
616C42—861no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—432no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23#1306329312yes—
631C23C2×D4×D4311yescharacteristic
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—862no—
637Q8—862no—
638Q8—1721no—
639Q8—1721no—
640D4—1724no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—861no—
660C2×C4—862no—
661C2×C4—861no—
662C2×C4—862no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—862no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—3444no—
672C2×C4—1728no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4#1306329312yes—
687C2×C4C2×D4×D4311yescharacteristic
688C2×C4C22×C22⋊D4311yescharacteristic
689C2×C4#41×D4311yescharacteristic
690C2×C4#41×D4311yescharacteristic
691C2×C4#1306337111yescharacteristic
692C2×C4#1306337211yescharacteristic
693C8—41no—
694C8—41no—
695C8—862no—
696C8—1721no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—1721no—
708C22—1721no—
709C22—1721no—
710C22—1721no—
711C22C2×#1306329311yescharacteristic
712C22#1458354111yescharacteristic
713C22#1458354711yescharacteristic
714C22#137×D4311yescharacteristic
715C22#1458369811yescharacteristic
716C22#1458370611yescharacteristic
717C22#1458371311yescharacteristic
718C4—22no—
719C4—42no—
720C4—42no—
721C4—81no—
722C4—81no—
723C4—3441no—
724C4—1722no—
725C4—1721no—
726C4—1722no—
727C4—1721no—
728C4—1722no—
729C4—1721no—
730C4#1458344511yescharacteristic
731C4#1458347711yescharacteristic
732C4#1458354111yescharacteristic
733C4#1458354711yescharacteristic
734C2—42no—
735C2—1722no—
736C2#1913820711yescharacteristic
737C2#1914385111yescharacteristic
738C2#1914390611yescharacteristic
739C2#1914664911yescharacteristic
740C2#1914680911yescharacteristic
741C2#1914704311yescharacteristic
742C2#1914716311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#485C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#485D43
hypocenterC43#25562
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#14583155C2semidirect
4. #19135931C2semidirect
5. #19135800C2semidirect
6. #19135744C2semidirect
7. #19135604C2semidirect
8. #19134933C2semidirect
9. #19134900C2semidirect
10. #19134899C2semidirect
12. #19134860C2semidirect
13. #19134786C2semidirect
14. #19134316C2semidirect
15. C2×C43×#485C2semidirect
364. C2×#485D43semidirect
434. C43#25562semidirect

Maximal subgroups

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

subgroupindex
C2×#145835882
C2×#145831552
#191380472
#191359312
#191358002
#191357442
#191356042
#191349332
#191349002
#191348992
#191348902
#191348602
#191347862
#191343162
C2×C43×#4852
#2556243