Finite Group Databasebeta

← #25123950

Subgroups — #25123950

Order 11008.

1250 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×#14583529C211yesmaximal, characteristic, complemented
2C2×#14582899C211yesmaximal, characteristic
3C2×#14582894C211yesmaximal, characteristic
4#19137186C211yesmaximal, characteristic
5#19135744C211yesmaximal, characteristic, complemented
6#19135740C211yesmaximal, characteristic, complemented
7#19135738C211yesmaximal, characteristic, complemented
8#19135736C211yesmaximal, characteristic, complemented
9#19135734C211yesmaximal, characteristic, complemented
10#19135732C211yesmaximal, characteristic, complemented
11#19135730C211yesmaximal, characteristic, complemented
12#19134313C211yesmaximal, characteristic, complemented
13#340×D43C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#2026C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583529—24no—
20#14583529—24no—
21C2×#13063325C2211yescharacteristic
22C2×#13063324—21no—
23C2×#13063324C2211yescharacteristic
24C2×#13063316C2211yescharacteristic
25C2×#13063315—21no—
26C2×#13063305—21no—
27C2×#13063303—21no—
28C2×#13063283C2211yescharacteristic
29C2×#13063282C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582899—24no—
33#14582894—24no—
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40#14582806C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582800C2211yescharacteristic
43#14582777—21no—
44#14582777—21no—
45#14582758—21no—
46#14582758—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#10621902—22no—
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902Q814yescomplemented
69C22×Dic86—21no—
70C22×Dic86—21no—
71C22×D172—21no—
72C22×D172C2311yescharacteristic
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—22no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C2×C8×D43—22no—
83C2×C8×D43—22no—
84C2×C8×D43—22no—
85#13063325—22no—
86#13063325—22no—
87#13063324—28no—
88#13063324—22no—
89#13063324—22no—
90#13063316—22no—
91#13063316—22no—
92#13063315—28no—
93#13063305—28no—
94#13063303—28no—
95#13063283—22no—
96#13063283D414yes—
97#13063282—22no—
98#13063282—22no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4D411yescharacteristic
109C2×Dic43⋊C4D411yescharacteristic
110C4⋊C4×D43—22no—
111C4⋊C4×D43—22no—
112C4⋊C4×D43—22no—
113C4⋊C4×D43D414yes—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4D411yescharacteristic
120C2×(C2×D43)⋊C4D411yescharacteristic
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123#13063249—22no—
124#13063249—22no—
125#13063247—22no—
126#13063247—22no—
127#13063245—22no—
128#13063245—22no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×Q8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134#125×C43—22no—
135#125×C43—22no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C42×C43C2311yescharacteristic
142#103×C43—22no—
143#103×C43—22no—
144#95×C43—21no—
145#95×C43—21no—
146C23×D43—21no—
147C23×D43C2×D411yescharacteristic
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43C2×Q812yes—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167#10621902—28no—
168#10621902—28no—
169#10621902—44no—
170#10621902—44no—
171C2×D172—21no—
172C2×D172—24no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—42no—
178C2×D172—42no—
179C2×D172C2×Q812yes—
180C2×C4×D43—24no—
181C2×C4×D43—24no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—42no—
185C2×C4×D43—81no—
186C2×C4×D43—81no—
187C2×C4×D43—81no—
188C2×C4×D43—81no—
189C2×C4×D43C2×D412yes—
190C2×C4×D43C2×D412yes—
191C2×C4×D43C2×Q812yes—
192C2×C4×D43#4112yes—
193C2×C4×D43#4112yes—
194C2×C4×D43#4112yes—
195C2×Dic86—24no—
196C2×Dic86—24no—
197C2×Dic86—81no—
198C2×Dic86—81no—
199C2×Dic86—81no—
200C2×Dic86—81no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C4⋊C4×C43—24no—
208C4⋊C4×C43—24no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C2×D412yes—
214C4⋊C4×C43C2×D412yes—
215C42×C43—21no—
216C42×C43—21no—
217(C2×D43)⋊C4—24no—
218(C2×D43)⋊C4—22no—
219(C2×D43)⋊C4—22no—
220(C2×D43)⋊C4—81no—
221(C2×D43)⋊C4—81no—
222(C2×D43)⋊C4—81no—
223(C2×D43)⋊C4—81no—
224C4⋊Dic43—24no—
225C4⋊Dic43—24no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43C2×D412yes—
231C4⋊Dic43C2×D412yes—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4—24no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4—42no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—24no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247#10621872—44no—
248C8×D43—44no—
249C23×C43C22×D411yescharacteristic
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—22no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43#12012yes—
262C22×D43C22⋊Q812yes—
263C22×D43#12412yes—
264Q8×C43—22no—
265Q8×C43—22no—
266Q8×C43—41no—
267Q8×C43—41no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C22×Q811yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43#12012yes—
308C2×Dic43C22⋊Q812yes—
309C2×Dic43#12412yes—
310D172—22no—
311D172—22no—
312D172—48no—
313D172—41no—
314D172—41no—
315C4×D43—48no—
316C4×D43—84no—
317C4×D43—84no—
318C4×D43C22⋊Q814yes—
319C4×D43C22⋊Q814yes—
320C4×D43#12414yes—
321C4×D43#12414yes—
322Dic86—84no—
323Dic86—84no—
324C8×C43—41no—
325C8×C43—41no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#23458—431nomaximal, Sylow
329C22×C43C2×#12011yescharacteristic
330C22×C43C2×C22⋊Q811yescharacteristic
331C22×C43C2×#12411yescharacteristic
332C22×C43#57611yescharacteristic
333C22×C43#57711yescharacteristic
334C22×C43#57711yescharacteristic
335C22×C43#57811yescharacteristic
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C2×D43#39314yes—
350C4×C43—42no—
351C4×C43—41no—
352C4×C43—42no—
353C4×C43—41no—
354C4×C43—42no—
355C4×C43—81no—
356C4×C43C2×C22⋊Q811yescharacteristic
357C4×C43C2×C22⋊Q811yescharacteristic
358C4×C43C2×#12411yescharacteristic
359C4×C43C2×#12411yescharacteristic
360Dic43—41no—
361Dic43—42no—
362Dic43—42no—
363Dic43—41no—
364Dic43—81no—
365Dic43#39314yes—
366C2×#544—431no—
367C2×#417—431no—
368C2×#416—431no—
369#2311—431no—
370#2026—431no—
371#2026D4311yescharacteristic, complemented
372#2025—431no—
373#2025—431no—
374#2024—431no—
375#2024—431no—
376#2023—431no—
377#2023—431no—
378#1736—431no—
379C2×#340—431no—
380#1729—431no—
381C2×C43C2×#39311yescharacteristic
382C2×C43#301211yescharacteristic
383C2×C43#301311yescharacteristic
384C2×C43#308311yescharacteristic
385C2×C43#308411yescharacteristic
386C2×C43#313611yescharacteristic
387C2×C43#313711yescharacteristic
388D43—24no—
389D43—82no—
390C22×#41—431no—
391C22×M16—431no—
392C23×C8—431no—
393#544—864no—
394#544—864no—
395C2×C4⋊Q8—431no—
396C2×C4⋊Q8—431no—
397C2×C4⋊Q8—861no—
398C2×#125—431no—
399C2×#125—861no—
400C2×#125C2×D4311yescharacteristic
401C2×C22⋊Q8—861no—
402C2×C22⋊Q8—861no—
403C2×#117—431no—
404C2×#117—431no—
405C22×C4⋊C4—431no—
406C22×C4⋊C4—431no—
407#417—864no—
408#416—864no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103C2×D4311yescharacteristic
412C2×#103C2×D4311yescharacteristic
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417#391—431no—
418#391C2×D4311yescharacteristic
419#390—431no—
420#390—431no—
421#386—861no—
422#386—861no—
423#380—861no—
424#380—861no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340C2×D4311yescharacteristic
432#340C2×D4311yescharacteristic
433#336—431no—
434#336—431no—
435#336—431no—
436#336C2×D4311yescharacteristic
437C43#2345811yescharacteristic, complemented, Sylow
438C2×#41—434no—
439C2×#41—862no—
440C2×#41—862no—
441C2×#41—862no—
442C2×#41—862no—
443C2×#41—862no—
444C22×Q8—861no—
445C22×Q8—861no—
446C22×Q8C22×D4311yescharacteristic
447C22×D4—431no—
448C22×D4—861no—
449C23×C4—431no—
450C23×C4—861no—
451C23×C4—861no—
452C23×C4—861no—
453C2×M16—862no—
454C2×M16—862no—
455C2×M16—862no—
456C22×C8—431no—
457C22×C8—431no—
458C22×C8—862no—
459C22×C8—862no—
460C22×C8—862no—
461C22×C8C22×D4311yescharacteristic
462C22×C8C22×D4311yescharacteristic
463C4⋊Q8—862no—
464C4⋊Q8—862no—
465C4⋊Q8—862no—
466C4⋊Q8—868no—
467C4⋊Q8—862no—
468#125—22no—
469#125—22no—
470#125—862no—
471#125—868no—
472#125—862no—
473C22⋊Q8—868no—
474C22⋊Q8—868no—
475#117—434no—
476#117—862no—
477#117—862no—
478#117—862no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—862no—
488C2×C4⋊C4—862no—
489C2×C4⋊C4—862no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4C22×D4311yescharacteristic
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—431no—
500C2×C22⋊C4—431no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C42—431no—
507C2×C42—861no—
508C2×C42C22×D4311yescharacteristic
509#103—22no—
510#103—22no—
511#103—862no—
512#103—862no—
513#102—862no—
514#102—862no—
515#102—862no—
516#102—862no—
517#95—21no—
518#95—21no—
519#95—861no—
520#95—861no—
521C24—431no—
522C24—861no—
523#41—868no—
524#41—868no—
525#41—1724no—
526#41—1724no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—864no—
533C2×Q8—864no—
534C2×Q8—3441no—
535C2×Q8—3441no—
536C2×Q8—3441no—
537C2×Q8—3441no—
538C2×Q8Q8×D4312yes—
539C2×D4—432no—
540C2×D4—864no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—1722no—
547C2×D4—1722no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—431no—
553C22×C4—432no—
554C22×C4—432no—
555C22×C4—432no—
556C22×C4—432no—
557C22×C4—432no—
558C22×C4—432no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—864no—
562C22×C4—864no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—3441no—
567C22×C4—3441no—
568C22×C4—3441no—
569C22×C4—3441no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4—1722no—
573C22×C4D4×D4311yescharacteristic
574C22×C4D4×D4311yescharacteristic
575C22×C4C23×D4311yescharacteristic
576M16—1724no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—1724no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—432no—
597C4⋊C4—432no—
598C4⋊C4—864no—
599C4⋊C4—862no—
600C4⋊C4—862no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4—864no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—1722no—
610C4⋊C4D4×D4312yes—
611C4⋊C4D4×D4312yes—
612C22⋊C4—862no—
613C22⋊C4—862no—
614C22⋊C4—864no—
615C22⋊C4—3441no—
616C22⋊C4—3441no—
617C22⋊C4—3441no—
618C22⋊C4—3441no—
619C42—21no—
620C42—21no—
621C42—864no—
622C42—861no—
623C42—861no—
624C23—432no—
625C23—432no—
626C23—432no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—862no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23C2×D4×D4311yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—41no—
642Q8—41no—
643Q8—3444no—
644Q8—3444no—
645D4—862no—
646D4—862no—
647D4—1728no—
648D4—1721no—
649D4—1721no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—434no—
672C2×C4—434no—
673C2×C4—434no—
674C2×C4—434no—
675C2×C4—862no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—862no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—3444no—
684C2×C4—3444no—
685C2×C4—1728no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C2×D4×D4311yescharacteristic
695C2×C4C2×Q8×D4311yescharacteristic
696C2×C4#41×D4311yescharacteristic
697C2×C4#41×D4311yescharacteristic
698C2×C4#41×D4311yescharacteristic
699C8—41no—
700C8—41no—
701C8—1721no—
702C8—1721no—
703C22—434no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—862no—
709C22—862no—
710C22—3441no—
711C22—3441no—
712C22—3441no—
713C22—3441no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22#120×D4311yescharacteristic
718C22C22⋊Q8×D4311yescharacteristic
719C22#124×D4311yescharacteristic
720C22#1458370111yescharacteristic
721C22#1458370611yescharacteristic
722C22#1458370811yescharacteristic
723C22#1458371511yescharacteristic
724C4—42no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—81no—
730C4—434no—
731C4—3441no—
732C4—1721no—
733C4—1722no—
734C4—1722no—
735C4—1721no—
736C4C22⋊Q8×D4311yescharacteristic
737C4C22⋊Q8×D4311yescharacteristic
738C4#124×D4311yescharacteristic
739C4#124×D4311yescharacteristic
740C2—864no—
741C2—3442no—
742C2#393×D4311yescharacteristic
743C2#1914390311yescharacteristic
744C2#1914391411yescharacteristic
745C2#1914444911yescharacteristic
746C2#1914446011yescharacteristic
747C2#1914494811yescharacteristic
748C2#1914496111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2026C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
hypercenter#2026D43
hypocenterC43#23458
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2026

Complements

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

NH ≅ G/Ntype
1. C2×#14583529C2semidirect
5. #19135744C2semidirect
6. #19135740C2semidirect
7. #19135738C2semidirect
8. #19135736C2semidirect
9. #19135734C2semidirect
10. #19135732C2semidirect
11. #19135730C2semidirect
12. #19134313C2semidirect
13. #340×D43C2semidirect
14. #19134290C2semidirect
15. C43×#2026C2semidirect
68. C2×#10621902Q8semidirect
371. #2026D43semidirect
437. C43#23458semidirect

Maximal subgroups

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

subgroupindex
C2×#145835292
C2×#145828992
C2×#145828942
#191371862
#191357442
#191357402
#191357382
#191357362
#191357342
#191357322
#191357302
#191343132
#340×D432
#191342902
C43×#20262
#2345843