Finite Group Databasebeta

← #25153684

Subgroups — #25153684

Order 11008.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583199C211yesmaximal, characteristic, complemented
2C22×#13063246C211yesmaximal, characteristic
3#19138319C211yesmaximal, characteristic, complemented
4#19136116C211yesmaximal, characteristic, complemented
5#19135983C211yesmaximal, characteristic, complemented
6#19135969C211yesmaximal, characteristic, complemented
7#19135741C211yesmaximal, characteristic, complemented
8#19134856C211yesmaximal, characteristic, complemented
9#19134842C211yesmaximal, characteristic, complemented
10#19134787C211yesmaximal, characteristic, complemented
11#19134775C211yesmaximal, characteristic, complemented
12#19134622C211yesmaximal, characteristic, complemented
13#19134605C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic
15D4×C22⋊C4×C43C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063317C2211yescharacteristic, complemented
18C22×C4⋊Dic43C2211yescharacteristic
19#14583199—24no—
20C2×#13063258C2211yescharacteristic, complemented
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
25C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
26C2×#13063246—24no—
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36#14582841—21no—
37#14582833—21no—
38#14582797C2211yescharacteristic, complemented
39#14582797C2211yescharacteristic, complemented
40#14582771—21no—
41#14582765C2211yescharacteristic, complemented
42#14582759C2211yescharacteristic
43#14582757—21no—
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C23×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C22×C22⋊C4×C43—21no—
54C43×#390C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#386—21no—
57C43×#386—21no—
58C43×#380C2211yescharacteristic
59C43×#379—21no—
60C4×C22⋊C4×C43C2211yescharacteristic
61C23×Dic43—21no—
62C22×C43⋊C8—22no—
63C22×C43⋊C8—22no—
64C22×C43⋊C8—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063317—22no—
70#13063317—41no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—41no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83#13063258—22no—
84#13063258—41no—
85#13063256—22no—
86#13063256—41no—
87C4⋊(C43⋊C8)—22no—
88C4⋊(C43⋊C8)—41no—
89#13063246—22no—
90#13063246—22no—
91#13063246—22no—
92#13063246—22no—
93#13063246—22no—
94#13063246—41no—
95#13063246—41no—
96#13063246D414yes—
97C22⋊(C43⋊C8)—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C25×C43—21no—
104C22×D4×C43—22no—
105C22×D4×C43—22no—
106C22×D4×C43—21no—
107C22×D4×C43—22no—
108C22×D4×C43—41no—
109C22×D4×C43—41no—
110C22×D4×C43Q814yes—
111C22×D4×C43C2311yescharacteristic
112C22×D4×C43C2311yescharacteristic
113C23×C4×C43—21no—
114C23×C4×C43—21no—
115C23×C4×C43C2311yescharacteristic
116C4×D4×C43—22no—
117C4×D4×C43—22no—
118C4×D4×C43—41no—
119C4×D4×C43—41no—
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—44no—
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134#95×C43—21no—
135#95×C43D411yescharacteristic
136#95×C43D411yescharacteristic
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—24no—
140C24×C43—42no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—81no—
145C24×C43—81no—
146C24×C43C2×D411yescharacteristic
147C2×D4×C43—24no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—28no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43—44no—
160C2×D4×C43—44no—
161C2×D4×C43—44no—
162C2×D4×C43C2×D412yes—
163C2×D4×C43C2×Q812yes—
164C2×D4×C43C2×Q812yes—
165C2×D4×C43#4112yes—
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—42no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43—81no—
177C22×C4×C43—81no—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×Q812yes—
184C22×C4×C43#4112yes—
185C22×C4×C43C2411yescharacteristic
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43—81no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—22no—
199C22⋊C4×C43—42no—
200C22⋊C4×C43—42no—
201C22⋊C4×C43—42no—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—42no—
204C22⋊C4×C43—81no—
205C22⋊C4×C43—81no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—21no—
210C22⋊Dic43—42no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—42no—
219C4⋊Dic43C2×D412yes—
220Dic43⋊C4—42no—
221Dic43⋊C4—42no—
222Dic43⋊C4—81no—
223Dic43⋊C4—81no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—44no—
236C2×C43⋊C8C2×D412yes—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—48no—
246C23×C43—41no—
247C23×C43—41no—
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—48no—
257C23×C43—84no—
258C23×C43—84no—
259C23×C43—84no—
260C23×C43—84no—
261C23×C43—84no—
262C23×C43C22⋊Q812yes—
263C23×C43#13512yes—
264C23×C43AGL(1,ℤ/8)12yes—
265C23×C43C22×D411yescharacteristic
266D4×C43—22no—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—48no—
272D4×C43—41no—
273D4×C43—41no—
274D4×C43C22⋊Q814yes—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—84no—
300C2×C4×C43—84no—
301C2×C4×C43C22⋊Q812yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×Q811yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
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—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—84no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324C43⋊C8—41no—
325#25952—431nomaximal, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—24no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—816no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43#47814yescomplemented
348C22×C43C2×C22⋊Q811yescharacteristic
349C22×C43D4211yescharacteristic
350C22×C43#54611yescharacteristic
351C22×C43C2×#13511yescharacteristic
352C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C43#57611yescharacteristic
354C22×C43#57711yescharacteristic
355C4×C43—22no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43—81no—
361C4×C43—81no—
362C4×C43C2×C22⋊Q811yescharacteristic
363C4×C43#54311yescharacteristic
364C4×C43#54611yescharacteristic
365C4×C43#55111yescharacteristic
366Dic43—42no—
367Dic43—81no—
368Dic43—81no—
369Dic43—81no—
370C2×#478—431no—
371C22×#102—431no—
372#2442—431no—
373D4×C22⋊C4D4311yescharacteristic
374#2092—431no—
375#2067—431no—
376#2065—431no—
377#2025—431no—
378#1864—431no—
379#1862—431no—
380#1853—431no—
381#1850—431no—
382#1808—431no—
383#1804—431no—
384#1786—431no—
385C2×C43—24no—
386C2×C43—44no—
387C2×C43—82no—
388C2×C43#243711yescharacteristic
389C2×C43C2×#47811yescharacteristic
390C2×C43#308111yescharacteristic
391C2×C43#326511yescharacteristic
392C2×C43#328011yescharacteristic
393C2×C43#329611yescharacteristic
394C2×C43#331811yescharacteristic
395C23×D4C2×D4311yescharacteristic
396C23×C8—431no—
397C2×#125—431no—
398C2×C4×D4C2×D4311yescharacteristic
399C2×C4×D4C2×D4311yescharacteristic
400C22×C4⋊C4—431no—
401C22×C22⋊C4—21no—
402#478—864no—
403C2×#107—431no—
404C2×#107—431no—
405C2×#106—431no—
406C2×#106—431no—
407C2×C4⋊C8—431no—
408C2×C4⋊C8—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×#102—864no—
418C2×C22⋊C8—431no—
419#400—861no—
420#398—861no—
421#390C2×D4311yescharacteristic
422#390C2×D4311yescharacteristic
423#389—431no—
424#389—431no—
425#386—21no—
426#386—21no—
427#385—861no—
428#382—431no—
429#380—431no—
430#380—861no—
431#380C2×D4311yescharacteristic
432#379—21no—
433C4×C22⋊C4C2×D4311yescharacteristic
434#340—431no—
435#340—431no—
436#340—431no—
437#340—431no—
438#336—431no—
439#336—431no—
440C43#2595211yescharacteristic, complemented, Sylow
441C25—21no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—21no—
446C22×D4—41no—
447C22×D4—41no—
448C22×D4Dic8614yes—
449C22×D4C22×D4311yescharacteristic
450C22×D4C22×D4311yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—861no—
454C23×C4C22×D4311yescharacteristic
455C22×C8—431no—
456C22×C8—431no—
457C22×C8—431no—
458C22×C8—431no—
459C22×C8—862no—
460C22×C8—862no—
461C22×C8—1721no—
462#125—862no—
463#125—1721no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—41no—
467C4×D4—41no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—862no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—1721no—
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—44no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4C22⋊D4311yescharacteristic
491C2×C22⋊C4C22⋊D4311yescharacteristic
492C2×C42C22×D4311yescharacteristic
493C2×C42C22×D4311yescharacteristic
494#107—862no—
495#107—1721no—
496#106—862no—
497#106—1721no—
498C4⋊C8—862no—
499C4⋊C8—1721no—
500#102—434no—
501#102—862no—
502#102—862no—
503#102—862no—
504#102—862no—
505#102—862no—
506#102—1721no—
507#102—1721no—
508C22⋊C8—862no—
509#95—21no—
510#95—861no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95C22⋊D4311yescharacteristic
516#95C22⋊D4311yescharacteristic
517C24—21no—
518C24—21no—
519C24—24no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24C2×C22⋊D4311yescharacteristic
527C2×D4—28no—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4C2×Dic8612yes—
543C2×D4C2×Dic8612yes—
544C2×D4D4×D4312yes—
545C2×D4#1062190012yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—3441no—
563C22×C4—1722no—
564C22×C4—1722no—
565C22×C4C2×Dic8612yes—
566C22×C4#1062189812yes—
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C2×C22⋊D4311yescharacteristic
569C22×C4C2×C22⋊D4311yescharacteristic
570C22×C4C2×C22⋊D4311yescharacteristic
571C22×C4C2×C22⋊D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573C2×C8—432no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
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—1724no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—432no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—3441no—
599C4⋊C4—3441no—
600C4⋊C4—1722no—
601C4⋊C4—1722no—
602C4⋊C4—1722no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—1722no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—48no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—48no—
635C23—41no—
636C23—41no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23#1306330412yes—
643C23#1306334512yes—
644C23#1306335112yes—
645C23C22×C22⋊D4311yescharacteristic
646D4—22no—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4#1306330214yes—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—84no—
681C2×C4—862no—
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—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4#1306330412yes—
695C2×C4C2×D4×D4311yescharacteristic
696C2×C4C22×Dic8611yescharacteristic
697C2×C4C2×#1062190011yescharacteristic
698C2×C4C2×#1062189811yescharacteristic
699C2×C4#1306337011yescharacteristic
700C2×C4#1306337011yescharacteristic
701C8—862no—
702C8—1721no—
703C8—1721no—
704C8—1721no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—24no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—816no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22#1458319914yescomplemented
727C22C2×#1306330411yescharacteristic
728C22D4×C22⋊D4311yescharacteristic
729C22#1458354311yescharacteristic
730C22C2×#1306334511yescharacteristic
731C22C2×#1306335111yescharacteristic
732C22#1458370211yescharacteristic
733C22#1458371011yescharacteristic
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—81no—
740C4—81no—
741C4—3441no—
742C4—3441no—
743C4—3441no—
744C4—1722no—
745C4C2×#1306330211yescharacteristic
746C4#1458352511yescharacteristic
747C4#1458353911yescharacteristic
748C4#1458357511yescharacteristic
749C2—24no—
750C2—44no—
751C2—82no—
752C2#1913825611yescharacteristic
753C2C2×#1458319911yescharacteristic
754C2#1914442611yescharacteristic
755C2#1914608611yescharacteristic
756C2#1914627611yescharacteristic
757C2#1914643011yescharacteristic
758C2#1914673611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenterD4×C22⋊C4D43
hypocenterC43#25952
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14583199C2semidirect
3. #19138319C2semidirect
4. #19136116C2semidirect
5. #19135983C2semidirect
6. #19135969C2semidirect
7. #19135741C2semidirect
8. #19134856C2semidirect
9. #19134842C2semidirect
10. #19134787C2semidirect
11. #19134775C2semidirect
12. #19134622C2semidirect
13. #19134605C2semidirect
17. C2×#13063317C22semidirect
20. C2×#13063258C22semidirect
21. C2×#13063258C22semidirect
22. C2×#13063256C22semidirect
23. C2×#13063256C22semidirect
24. C2×C4⋊(C43⋊C8)C22semidirect
25. C2×C4⋊(C43⋊C8)C22semidirect
38. #14582797C22semidirect
39. #14582797C22semidirect
41. #14582765C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
347. C22×C43#478semidirect
440. C43#25952semidirect
726. C22#14583199semidirect

Maximal subgroups

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

subgroupindex
C2×#145831992
C22×#130632462
#191383192
#191361162
#191359832
#191359692
#191357412
#191348562
#191348422
#191347872
#191347752
#191346222
#191346052
#191345262
D4×C22⋊C4×C432
#2595243