Finite Group Databasebeta

← #25140439

Subgroups — #25140439

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583042C211yesmaximal, characteristic
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3#19137435C211yesmaximal, characteristic, complemented
4#19136119C211yesmaximal, characteristic, complemented
5#19136031C211yesmaximal, characteristic, complemented
6#19135905C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134848C211yesmaximal, characteristic, complemented
13#19134607C211yesmaximal, characteristic, complemented
14#19134533C211yesmaximal, characteristic, complemented
15C43×#2420C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21#14583042—24no—
22C4×#10621883—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582799—21no—
40#14582799—21no—
41#14582759C2211yescharacteristic
42#14582758—21no—
43#14582746—21no—
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×#121×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C43×#397—21no—
53C43×#394—21no—
54C43×#390C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#386—21no—
57C43×#382C2211yescharacteristic
58C43×#381—21no—
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C22×Dic86C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C22⋊D43—21no—
70C22×C4×D43—21no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883D414yes—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—41no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86—41no—
84C4×Dic86—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96#13063258—41no—
97#13063256—22no—
98C4⋊(C43⋊C8)—41no—
99#13063248—22no—
100#13063248—22no—
101#13063248—22no—
102#13063246—22no—
103#13063246—41no—
104#13063245—22no—
105#13063245—22no—
106#13063245—41no—
107C22⋊(C43⋊C8)—22no—
108C22⋊(C43⋊C8)—41no—
109C4×C43⋊C8—22no—
110C43⋊#95—21no—
111C22×D4×C43—21no—
112C22×D4×C43C2311yescharacteristic
113C23×C4×C43—21no—
114C23×C4×C43C2311yescharacteristic
115#121×C43—22no—
116#121×C43—41no—
117C4×D4×C43—22no—
118C4×D4×C43—41no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
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×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C23×D43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—42no—
147C2×D4×C43—42no—
148C2×D4×C43—81no—
149C2×D4×C43C2×D412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—42no—
160C22×C4×C43—42no—
161C22×C4×C43—81no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—24no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43—42no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174#10621898—44no—
175#10621898—44no—
176#10621898—44no—
177#10621898—44no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172#4112yes—
184C2×C4×D43—24no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86C2×D412yes—
191C2×Dic86#4112yes—
192C2×Dic86#4112yes—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—81no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—42no—
204C22⋊C4×C43—81no—
205C22⋊C4×C43—81no—
206C22⋊C4×C43—81no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—21no—
210C42×C43—21no—
211C22⋊Dic43—81no—
212#10621883—28no—
213#10621882—44no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—81no—
217(C2×D43)⋊C4—81no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222Dic43⋊C4—42no—
223Dic43⋊C4—42no—
224C4×Dic43—42no—
225C4×Dic43—42no—
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—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8C2×D412yes—
238C23×C43—21no—
239C23×C43—22no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43C22×D411yescharacteristic
253C22×D43—22no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—41no—
263D4×C43—41no—
264D4×C43—84no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
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×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—84no—
293C2×C4×C43#13512yes—
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C22⋊D43—48no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310D172—22no—
311D172—22no—
312D172—41no—
313D172—41no—
314C4×D43—48no—
315Dic86—22no—
316Dic86—22no—
317Dic86—22no—
318Dic86#12314yes—
319C43⋊C8—22no—
320C43⋊C8—41no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323#24900—431nomaximal, Sylow
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—42no—
328C22×C43—41no—
329C22×C43—42no—
330C22×C43—41no—
331C22×C43—42no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43#52511yescharacteristic
339C22×C43D4211yescharacteristic
340C22×C43#54611yescharacteristic
341C22×C43C2×#13511yescharacteristic
342C22×C43#57511yescharacteristic
343C22×C43#57611yescharacteristic
344C22×C43#57711yescharacteristic
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—81no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C4×C43—22no—
353C4×C43—41no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43—81no—
358C4×C43—81no—
359C4×C43—81no—
360C4×C43C2×#12311yescharacteristic
361C4×C43#53811yescharacteristic
362C4×C43#54611yescharacteristic
363C4×C43#55111yescharacteristic
364Dic43—24no—
365Dic43—81no—
366Dic43—81no—
367C2×#449—431no—
368C2×C4×SD16—431no—
369#2420D4311yescharacteristic, complemented
370#2341—431no—
371#2092—431no—
372#2077—431no—
373#2054—431no—
374#2033—431no—
375#1934—431no—
376#1923—431no—
377#1880—431no—
378#1879—431no—
379#1863—431no—
380#1805—431no—
381#1788—431no—
382C2×C43—81no—
383C2×C43—82no—
384C2×C43#241811yescharacteristic
385C2×C43#310211yescharacteristic
386C2×C43#311911yescharacteristic
387C2×C43#326811yescharacteristic
388C2×C43#328211yescharacteristic
389C2×C43#330511yescharacteristic
390C2×C43#332611yescharacteristic
391D43—82no—
392C22×#41—431no—
393C22×SD16—431no—
394C22×D8—431no—
395C2×#121C2×D4311yescharacteristic
396C2×C4×Q8—431no—
397C2×C4×Q8—431no—
398C2×C4×D4C2×D4311yescharacteristic
399#449—864no—
400C4×SD16—864no—
401C2×#107—431no—
402C2×#106—431no—
403C2×C4⋊C8—431no—
404C2×#103—431no—
405C2×#103—431no—
406C2×#103—431no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×C22⋊C8—431no—
413C2×C22⋊C8—431no—
414C2×C4×C8—431no—
415#397—21no—
416#394—21no—
417#390—431no—
418#390—431no—
419#390—861no—
420#390—861no—
421#390C2×D4311yescharacteristic
422#389C2×D4311yescharacteristic
423#386—21no—
424#382C2×D4311yescharacteristic
425#381—21no—
426#380—431no—
427#380—861no—
428#380C2×D4311yescharacteristic
429C4×C22⋊C4—861no—
430C4×C22⋊C4C2×D4311yescharacteristic
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#336—431no—
436#336—431no—
437C43#2490011yescharacteristic, complemented, Sylow
438C2×#41—862no—
439C2×#41—862no—
440C2×#41—862no—
441C2×#41—862no—
442C2×#41—1721no—
443C2×#41—1721no—
444C22×Q8—431no—
445C22×D4—21no—
446C22×D4—431no—
447C22×D4—861no—
448C22×D4C22×D4311yescharacteristic
449C23×C4—21no—
450C23×C4—861no—
451C23×C4C22×D4311yescharacteristic
452C2×SD16—434no—
453C2×SD16—862no—
454C2×SD16—862no—
455C2×D8—862no—
456C2×D8—862no—
457C2×D8—1721no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—431no—
461C22×C8—431no—
462#121—22no—
463#121—41no—
464C4×Q8—862no—
465C4×Q8—862no—
466C4×Q8—1721no—
467C4×Q8—1721no—
468C4×D4—22no—
469C4×D4—41no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4C22⋊D4311yescharacteristic
489C2×C22⋊C4C22⋊D4311yescharacteristic
490C2×C42—861no—
491C2×C42—861no—
492C2×C42C22×D4311yescharacteristic
493C2×C42C22×D4311yescharacteristic
494#107—1721no—
495#106—862no—
496C4⋊C8—1721no—
497#103—862no—
498#103—862no—
499#103—862no—
500#102—862no—
501#102—862no—
502#102—862no—
503#102—1721no—
504#102—1721no—
505C22⋊C8—862no—
506C22⋊C8—1721no—
507C4×C8—862no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—861no—
513#95C22⋊D4311yescharacteristic
514#95C22⋊D4311yescharacteristic
515C24—21no—
516C24—861no—
517C24C2×C22⋊D4311yescharacteristic
518#41—1724no—
519#41—1724no—
520#41—1724no—
521#41—1724no—
522C2×Q8—432no—
523C2×Q8—432no—
524C2×Q8—432no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—81no—
536C2×D4—432no—
537C2×D4—864no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—1722no—
544C2×D4—1722no—
545C2×D4D4×D4312yes—
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—42no—
556C22×C4—42no—
557C22×C4—81no—
558C22×C4—864no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4C2×C22⋊D4311yescharacteristic
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C2×C22⋊D4311yescharacteristic
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C2×C22⋊D4311yescharacteristic
569C22×C4C23×D4311yescharacteristic
570SD16—868no—
571D8—1724no—
572C2×C8—432no—
573C2×C8—861no—
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—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—81no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—1722no—
596C4⋊C4—1722no—
597C22⋊C4—22no—
598C22⋊C4—41no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—1722no—
614C42—1722no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—21no—
622C23—21no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—862no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23C22×C22⋊D4311yescharacteristic
637Q8—434no—
638Q8—862no—
639Q8—862no—
640Q8—862no—
641D4—22no—
642D4—22no—
643D4—41no—
644D4—41no—
645D4—84no—
646D4—862no—
647D4—862no—
648D4—1728no—
649D4—1721no—
650D4—1721no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
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—41no—
678C2×C4—84no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—1728no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4#1306334512yes—
690C2×C4C2×D4×D4311yescharacteristic
691C2×C4#41×D4311yescharacteristic
692C2×C4#41×D4311yescharacteristic
693C2×C4#41×D4311yescharacteristic
694C2×C4#1306337011yescharacteristic
695C2×C4#1306337111yescharacteristic
696C8—862no—
697C8—1721no—
698C8—1721no—
699C8—1721no—
700C22—41no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—41no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—3441no—
715C22—3441no—
716C22—3441no—
717C22—3441no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22#1458340611yescharacteristic
722C22D4×C22⋊D4311yescharacteristic
723C22#1458353711yescharacteristic
724C22C2×#1306334511yescharacteristic
725C22#1458369711yescharacteristic
726C22#1458370211yescharacteristic
727C22#1458371011yescharacteristic
728C4—22no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4—864no—
737C4—3441no—
738C4—3441no—
739C4#123×D4311yescharacteristic
740C4#1458348511yescharacteristic
741C4#1458354111yescharacteristic
742C4#1458357711yescharacteristic
743C2—81no—
744C2—82no—
745C2—3442no—
746C2#1913805411yescharacteristic
747C2#1914460711yescharacteristic
748C2#1914478811yescharacteristic
749C2#1914613111yescharacteristic
750C2#1914629811yescharacteristic
751C2#1914653911yescharacteristic
752C2#1914684211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2420C2
socleC23×C43C22×D4
prime radicalC2×#14583042C2
hypercenter#2420D43
hypocenterC43#24900
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2420

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621883C2semidirect
3. #19137435C2semidirect
4. #19136119C2semidirect
5. #19136031C2semidirect
6. #19135905C2semidirect
7. #19135774C2semidirect
8. #19135277C2semidirect
9. #19135203C2semidirect
10. #19134953C2semidirect
11. #19134943C2semidirect
12. #19134848C2semidirect
13. #19134607C2semidirect
14. #19134533C2semidirect
15. C43×#2420C2semidirect
369. #2420D43semidirect
437. C43#24900semidirect

Maximal subgroups

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

subgroupindex
C2×#145830422
C2×C4×#106218832
#191374352
#191361192
#191360312
#191359052
#191357742
#191352772
#191352032
#191349532
#191349432
#191348482
#191346072
#191345332
C43×#24202
#2490043