Finite Group Databasebeta

← #25135397

Subgroups — #25135397

Order 11008.

986 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×#14583044C211yesmaximal, characteristic
2C2×#14582960C211yesmaximal, characteristic, complemented
3#19140384C211yesmaximal, characteristic, complemented
4#19135990C211yesmaximal, characteristic, complemented
5#19135983C211yesmaximal, characteristic, complemented
6#19135910C211yesmaximal, characteristic, complemented
7#19135905C211yesmaximal, characteristic, complemented
8#19135479C211yesmaximal, characteristic, complemented
9#19135460C211yesmaximal, characteristic, complemented
10#19135295C211yesmaximal, characteristic, complemented
11#19135274C211yesmaximal, characteristic, complemented
12#19134912C211yesmaximal, characteristic, complemented
13#19134783C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C43×#2311C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19#14583044—24no—
20#14582960—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582834—21no—
38#14582825—21no—
39#14582814—21no—
40#14582814—21no—
41#14582801C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582797C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C22×#41×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C43×#391C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#386—21no—
58C43×#386—21no—
59C43×#380—21no—
60C43×#380—21no—
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C2×#10621884—22no—
64C2×#10621884—22no—
65C2×#10621884—41no—
66C2×#10621882—22no—
67C2×#10621882—22no—
68C2×#10621882—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063299—22no—
74#13063299—22no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86#13063258—41no—
87#13063258—41no—
88C4⋊(C43⋊C8)—22no—
89C4⋊(C43⋊C8)—22no—
90#13063249—22no—
91#13063249—22no—
92#13063249—41no—
93#13063246—22no—
94#13063246—22no—
95#13063246—41no—
96#13063245—41no—
97#13063245—41no—
98C22⋊(C43⋊C8)—22no—
99C22⋊(C43⋊C8)D414yes—
100#13063236—22no—
101C4×C43⋊C8—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C2×#41×C43—22no—
106C2×#41×C43—22no—
107C2×#41×C43—22no—
108C2×#41×C43—22no—
109C2×#41×C43—41no—
110C2×#41×C43—41no—
111C22×Q8×C43C2311yescharacteristic
112C22×D4×C43—21no—
113C22×D4×C43C2311yescharacteristic
114C23×C4×C43—21no—
115C23×C4×C43—21no—
116C23×C4×C43C2311yescharacteristic
117#117×C43—22no—
118#117×C43—22no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—41no—
121C2×C4⋊C4×C43—41no—
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C23×D43—21no—
141#41×C43—44no—
142#41×C43—44no—
143#41×C43—44no—
144#41×C43—44no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43#4112yes—
151C2×D4×C43—24no—
152C2×D4×C43—21no—
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#4112yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—24no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—42no—
169C22×C4×C43—42no—
170C22×C4×C43—42no—
171C22×C4×C43—81no—
172C22×C4×C43—81no—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43#4112yes—
180C22×C4×C43C2411yescharacteristic
181C2×C22⋊D43—42no—
182C2×C22⋊D43—81no—
183C2×C22⋊D43—81no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C4⋊C4×C43—22no—
194C4⋊C4×C43—22no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—42no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—81no—
203C22⋊C4×C43—81no—
204C22⋊C4×C43—81no—
205C22⋊C4×C43—81no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—21no—
210C22⋊Dic43—81no—
211#10621884—44no—
212#10621882—44no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—81no—
215(C2×D43)⋊C4—81no—
216(C2×D43)⋊C4—81no—
217(C2×D43)⋊C4—81no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224Dic43⋊C4—81no—
225Dic43⋊C4—81no—
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⋊C8C2×D412yes—
237C2×C43⋊C8C2×D412yes—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—22no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43#12112yes—
252C23×C43C22×D411yescharacteristic
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—48no—
267D4×C43—41no—
268D4×C43—41no—
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—21no—
278C2×C4×C43—21no—
279C2×C4×C43—22no—
280C2×C4×C43—21no—
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—48no—
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—84no—
298C2×C4×C43#12112yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C22⋊D43—84no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315D172—41no—
316D172—41no—
317D172—41no—
318D172—41no—
319C43⋊C8—22no—
320C43⋊C8—22no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323#24513—431nomaximal, Sylow
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43C2×#12111yescharacteristic
339C22×C43#52511yescharacteristic
340C22×C43#53511yescharacteristic
341C22×C43#57611yescharacteristic
342C22×C43#57611yescharacteristic
343C22×C43#57711yescharacteristic
344C22×C43#57811yescharacteristic
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C4×C43—22no—
353C4×C43—42no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43—81no—
359C4×C43—81no—
360C4×C43#54611yescharacteristic
361C4×C43#54611yescharacteristic
362C4×C43#55111yescharacteristic
363C4×C43#55111yescharacteristic
364Dic43—81no—
365Dic43—81no—
366Dic43—81no—
367C2×#449—431no—
368C2×#433—431no—
369#2624—431no—
370#2311D4311yescharacteristic, complemented
371#2068—431no—
372#2067—431no—
373#2055—431no—
374#2054—431no—
375#1973—431no—
376#1970—431no—
377#1936—431no—
378#1933—431no—
379#1874—431no—
380#1852—431no—
381#1788—431no—
382C2×C43—42no—
383C2×C43—82no—
384C2×C43#241111yescharacteristic
385C2×C43#306111yescharacteristic
386C2×C43#306211yescharacteristic
387C2×C43#311911yescharacteristic
388C2×C43#312411yescharacteristic
389C2×C43#322011yescharacteristic
390C2×C43#322511yescharacteristic
391D43—161no—
392C22×#41C2×D4311yescharacteristic
393C22×SD16—431no—
394C22×D8—431no—
395C2×#121—431no—
396C2×#117C2×D4311yescharacteristic
397C22×C4⋊C4C2×D4311yescharacteristic
398#449—864no—
399#433—864no—
400C2×#107—431no—
401C2×#107—431no—
402C2×C4⋊C8—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×#97—431no—
415C2×C4×C8—431no—
416#399—861no—
417#397—861no—
418#394—861no—
419#394—861no—
420#391C2×D4311yescharacteristic
421#391C2×D4311yescharacteristic
422#390—431no—
423#390—431no—
424#390C2×D4311yescharacteristic
425#390C2×D4311yescharacteristic
426#389—431no—
427#389—431no—
428#386—21no—
429#386—21no—
430#380—21no—
431#380—21no—
432#380—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#340—431no—
437C43#2451311yescharacteristic, complemented, Sylow
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—41no—
443C2×#41—41no—
444C22×Q8C22×D4311yescharacteristic
445C22×D4—21no—
446C22×D4—431no—
447C22×D4—861no—
448C22×D4C22×D4311yescharacteristic
449C23×C4—21no—
450C23×C4—21no—
451C23×C4C22×D4311yescharacteristic
452C2×SD16—862no—
453C2×SD16—862no—
454C2×SD16—1721no—
455C2×D8—862no—
456C2×D8—862no—
457C2×D8—1721no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—431no—
461C22×C8—431no—
462#121—862no—
463#121—862no—
464#117—22no—
465#117—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4C22⋊D4311yescharacteristic
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—861no—
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×C42C22×D4311yescharacteristic
491C2×C42C22×D4311yescharacteristic
492#107—1721no—
493#107—1721no—
494C4⋊C8—862no—
495C4⋊C8—862no—
496#103—862no—
497#103—862no—
498#103—1721no—
499#102—862no—
500#102—862no—
501#102—1721no—
502#102—1721no—
503#102—1721no—
504C22⋊C8—434no—
505C22⋊C8—862no—
506#97—862no—
507C4×C8—862no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—861no—
513#95—861no—
514#95—861no—
515C24—21no—
516C24—861no—
517C24C2×C22⋊D4311yescharacteristic
518#41—44no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8#1062189812yes—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—3441no—
543C2×D4—3441no—
544C2×D4—1722no—
545C2×D4#1062189812yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4D4×D4312yes—
563C22×C4#1062190012yes—
564C22×C4C2×C22⋊D4311yescharacteristic
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C2×C22⋊D4311yescharacteristic
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C2×C22⋊D4311yescharacteristic
569C22×C4C23×D4311yescharacteristic
570SD16—1724no—
571D8—1724no—
572C2×C8—432no—
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—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—42no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—3441no—
598C4⋊C4—3441no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—3441no—
608C22⋊C4—3441no—
609C22⋊C4—3441no—
610C22⋊C4—1722no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23#1306329712yes—
636C23C22×C22⋊D4311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641D4—22no—
642D4—22no—
643D4—48no—
644D4—41no—
645D4—41no—
646D4—3444no—
647D4—1721no—
648D4—1721no—
649D4—1721no—
650D4—1721no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
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—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4#1306329712yes—
690C2×C4C2×D4×D4311yescharacteristic
691C2×C4C2×#1062190011yescharacteristic
692C2×C4C2×#1062189811yescharacteristic
693C2×C4C2×#1062189811yescharacteristic
694C2×C4#1306337011yescharacteristic
695C2×C4#1306337011yescharacteristic
696C8—862no—
697C8—862no—
698C8—1721no—
699C8—1721no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—3441no—
715C22—3441no—
716C22—3441no—
717C22—3441no—
718C22—3441no—
719C22—3441no—
720C22—3441no—
721C22C2×#1306329711yescharacteristic
722C22#1458341011yescharacteristic
723C22#1458346611yescharacteristic
724C22#1458370211yescharacteristic
725C22#1458370211yescharacteristic
726C22#1458370711yescharacteristic
727C22#1458371411yescharacteristic
728C4—22no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—42no—
734C4—81no—
735C4—81no—
736C4—3441no—
737C4—3441no—
738C4—3441no—
739C4#1458353911yescharacteristic
740C4#1458353911yescharacteristic
741C4#1458357511yescharacteristic
742C4#1458357511yescharacteristic
743C2—42no—
744C2—82no—
745C2—6881no—
746C2#1913798011yescharacteristic
747C2#1914426211yescharacteristic
748C2#1914427711yescharacteristic
749C2#1914479411yescharacteristic
750C2#1914485711yescharacteristic
751C2#1914564511yescharacteristic
752C2#1914570411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2311C2
socleC23×C43C22×D4
prime radicalC2×#14583044C2
hypercenter#2311D43
hypocenterC43#24513
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#14582960C2semidirect
3. #19140384C2semidirect
4. #19135990C2semidirect
5. #19135983C2semidirect
6. #19135910C2semidirect
7. #19135905C2semidirect
8. #19135479C2semidirect
9. #19135460C2semidirect
10. #19135295C2semidirect
11. #19135274C2semidirect
12. #19134912C2semidirect
13. #19134783C2semidirect
14. #19134535C2semidirect
15. C43×#2311C2semidirect
370. #2311D43semidirect
437. C43#24513semidirect

Maximal subgroups

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

subgroupindex
C2×#145830442
C2×#145829602
#191403842
#191359902
#191359832
#191359102
#191359052
#191354792
#191354602
#191352952
#191352742
#191349122
#191347832
#191345352
C43×#23112
#2451343