Finite Group Databasebeta

← #25147368

Subgroups — #25147368

Order 11008.

1116 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583133C211yesmaximal, characteristic, complemented
2C2×#14583130C211yesmaximal, characteristic, complemented
3C2×#14583111C211yesmaximal, characteristic, complemented
4C2×D4×C43⋊C8C211yesmaximal, characteristic, complemented
5#19139496C211yesmaximal, characteristic, complemented
6#19135795C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135596C211yesmaximal, characteristic, complemented
9#19135591C211yesmaximal, characteristic, complemented
10#19135407C211yesmaximal, characteristic, complemented
11#19135363C211yesmaximal, characteristic, complemented
12#19135024C211yesmaximal, characteristic, complemented
13#19135019C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#2540C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583133—24no—
24#14583130—24no—
25#14583111—24no—
26D4×C43⋊C8—24no—
27C2×#13063258C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41#14582825—21no—
42#14582807—21no—
43#14582775—21no—
44#14582775—21no—
45#14582765C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×#124×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×#121×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#399—21no—
59C43×#392—21no—
60C43×#390—21no—
61C43×#390—21no—
62C4×C4⋊C4×C43C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—41no—
70C2×#10621882—22no—
71C2×#10621882—22no—
72C2×#10621882—41no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—22no—
75C22×C43⋊C8—22no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—41no—
78C22×C43⋊C8—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063299—22no—
84#13063299—22no—
85#13063299—41no—
86#13063299—41no—
87C4×D172—22no—
88C4×D172—22no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97#13063258—22no—
98#13063256—22no—
99C4⋊(C43⋊C8)D414yescomplemented
100#13063249—22no—
101#13063249—22no—
102#13063249—41no—
103#13063246—22no—
104#13063246—22no—
105#13063246—41no—
106#13063245—22no—
107#13063245D414yescomplemented
108C22⋊(C43⋊C8)—22no—
109C22⋊(C43⋊C8)—22no—
110C4×C43⋊C8—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43D411yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122#124×C43—22no—
123#124×C43—22no—
124C22⋊Q8×C43—22no—
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—41no—
127C22⋊Q8×C43—41no—
128#121×C43—22no—
129#121×C43—22no—
130#121×C43—41no—
131#121×C43—41no—
132C4×D4×C43—22no—
133C4×D4×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#95×C43—21no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C24×C43C2×D411yescharacteristic
153C23×D43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×D4×C43—22no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—42no—
199C2×C22⋊D43—81no—
200C2×C22⋊D43—81no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172C2×D412yes—
210C2×C4×D43—42no—
211C2×C4×D43—81no—
212C2×C4×D43—81no—
213C4⋊C4×C43—22no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—42no—
217C4⋊C4×C43—42no—
218C4⋊C4×C43C2×D412yes—
219C4⋊C4×C43#4112yes—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C42×C43—81no—
229C42×C43C2×D412yes—
230C42×C43#4112yes—
231C22⋊Dic43—81no—
232C22⋊Dic43—81no—
233#10621884—44no—
234#10621882—44no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237(C2×D43)⋊C4—42no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—44no—
254C2×C43⋊C8—44no—
255C2×C43⋊C8C2×D412yes—
256C2×C43⋊C8C2×D412yes—
257C2×C43⋊C8C2×D412yes—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43#13512yes—
278C23×C43#13512yes—
279C23×C43C22×D411yescharacteristic
280C22×D43—22no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287Q8×C43—41no—
288Q8×C43—41no—
289Q8×C43—41no—
290Q8×C43—41no—
291D4×C43—28no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—84no—
297D4×C43—84no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43#12112yes—
326C2×C4×C43#12112yes—
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C22⋊D43—84no—
334C22⋊D43—84no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344D172—22no—
345D172—22no—
346D172—41no—
347D172—41no—
348C4×D43—84no—
349C43⋊C8—22no—
350C43⋊C8—22no—
351C43⋊C8—22no—
352C43⋊C8—41no—
353#25388—431nomaximal, Sylow
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43C2×#12111yescharacteristic
376C22×C43D4211yescharacteristic
377C22×C43#54611yescharacteristic
378C22×C43C2×#13511yescharacteristic
379C22×C43C2×#13511yescharacteristic
380C22×C43#57611yescharacteristic
381C22×C43#57711yescharacteristic
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43—81no—
389C4×C43—22no—
390C4×C43—22no—
391C4×C43—41no—
392C4×C43—41no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—81no—
396C4×C43#53211yescharacteristic
397C4×C43#54011yescharacteristic
398C4×C43D4211yescharacteristic
399C4×C43#55011yescharacteristic
400Dic43—81no—
401Dic43—81no—
402Dic43—81no—
403C2×#466—431no—
404C2×#465—431no—
405C2×#463—431no—
406C2×C8×D4—431no—
407#2540D4311yescharacteristic, complemented
408#2535—431no—
409#2036—431no—
410#2034—431no—
411#2000—431no—
412#1999—431no—
413#1958—431no—
414#1949—431no—
415#1893—431no—
416#1892—431no—
417C4×#102—431no—
418C2×C43—42no—
419C2×C43—42no—
420C2×C43—161no—
421C2×C43#242811yescharacteristic
422C2×C43#305011yescharacteristic
423C2×C43#306211yescharacteristic
424C2×C43#328011yescharacteristic
425C2×C43#328211yescharacteristic
426C2×C43#329711yescharacteristic
427C2×C43#330111yescharacteristic
428D43—82no—
429C22×SD16—431no—
430C22×D8—431no—
431C23×C8—431no—
432C23×C8—431no—
433C2×#124C2×D4311yescharacteristic
434C2×C22⋊Q8C2×D4311yescharacteristic
435C2×C22⋊Q8C2×D4311yescharacteristic
436C2×#121—431no—
437C2×#121—431no—
438C2×#121C2×D4311yescharacteristic
439C2×#121C2×D4311yescharacteristic
440C2×C4×D4—431no—
441C2×C4×D4C2×D4311yescharacteristic
442#466—864no—
443#465—864no—
444#463—864no—
445C8×D4—864no—
446C2×#107—431no—
447C2×#106—431no—
448C2×C4⋊C8—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—431no—
457C2×C22⋊C8—431no—
458C2×C22⋊C8—431no—
459C2×C4×C8—431no—
460#399—21no—
461#397—861no—
462#392—21no—
463#392—861no—
464#390—21no—
465#390—21no—
466#386—861no—
467#386—861no—
468#382—431no—
469#380—431no—
470#380—431no—
471C4×C4⋊C4C2×D4311yescharacteristic
472#340—431no—
473#340—431no—
474#340—431no—
475#340—431no—
476C43#2538811yescharacteristic, complemented, Sylow
477C22×Q8C22×D4311yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—431no—
481C22×D4—861no—
482C22×D4—861no—
483C22×D4C22⋊D4311yescharacteristic
484C22×D4C22×D4311yescharacteristic
485C23×C4—861no—
486C23×C4C22×D4311yescharacteristic
487C23×C4C22×D4311yescharacteristic
488C2×SD16—862no—
489C2×SD16—862no—
490C2×SD16—1721no—
491C2×D8—862no—
492C2×D8—862no—
493C2×D8—1721no—
494C22×C8—431no—
495C22×C8—431no—
496C22×C8—431no—
497C22×C8—431no—
498C22×C8—862no—
499C22×C8—862no—
500C22×C8—862no—
501C22×C8—862no—
502C22×C8—1721no—
503C22×C8—1721no—
504#124—22no—
505#124—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510#121—22no—
511#121—22no—
512#121—41no—
513#121—41no—
514#121—862no—
515#121—862no—
516#121—1721no—
517#121—1721no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—862no—
521C4×D4—862no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—431no—
526C2×C4⋊C4—431no—
527C2×C4⋊C4C22⋊D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C4⋊C4C22×D4311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4C22⋊D4311yescharacteristic
542C2×C22⋊C4C22⋊D4311yescharacteristic
543C2×C42—21no—
544C2×C42C22×D4311yescharacteristic
545#107—862no—
546#106—862no—
547C4⋊C8—434no—
548#103—862no—
549#103—862no—
550#103—1721no—
551#102—434no—
552#102—862no—
553#102—862no—
554#102—862no—
555#102—1721no—
556C22⋊C8—862no—
557C22⋊C8—862no—
558C4×C8—862no—
559#95—21no—
560#95—861no—
561#95—861no—
562#95—861no—
563#95—861no—
564C24—21no—
565C24—861no—
566C24C2×C22⋊D4311yescharacteristic
567C24C2×C22⋊D4311yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—432no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—3441no—
596C2×D4—3441no—
597C2×D4—1722no—
598C2×D4—1722no—
599C2×D4—1722no—
600C2×D4—1722no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—3441no—
620C22×C4—3441no—
621C22×C4—1722no—
622C22×C4C2×C22⋊D4311yescharacteristic
623C22×C4C2×C22⋊D4311yescharacteristic
624C22×C4C2×C22⋊D4311yescharacteristic
625C22×C4C2×C22⋊D4311yescharacteristic
626C22×C4C23×D4311yescharacteristic
627SD16—1724no—
628D8—1724no—
629C2×C8—432no—
630C2×C8—432no—
631C2×C8—432no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—1724no—
642C2×C8—1724no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4D4×D4312yes—
655C4⋊C4#1062190012yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—3441no—
665C22⋊C4—3441no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C42—81no—
670C42D4×D4312yes—
671C42#1062190012yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—862no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23—1721no—
696C23—1721no—
697C23—1721no—
698C23#1306334512yes—
699C23#1306334512yes—
700C23C22×C22⋊D4311yescharacteristic
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705D4—28no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712D4—862no—
713D4—862no—
714D4—3444no—
715D4—3444no—
716D4—1721no—
717D4—1721no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—3444no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4#1306329712yes—
756C2×C4#1306329712yes—
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4C2×#1062190011yescharacteristic
760C2×C4C2×#1062190011yescharacteristic
761C2×C4#1306337011yescharacteristic
762C2×C4#1306337011yescharacteristic
763C8—862no—
764C8—862no—
765C8—862no—
766C8—1721no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—3441no—
789C22—3441no—
790C22—3441no—
791C22—3441no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22C2×#1306329711yescharacteristic
796C22D4×C22⋊D4311yescharacteristic
797C22#1458354311yescharacteristic
798C22C2×#1306334511yescharacteristic
799C22C2×#1306334511yescharacteristic
800C22#1458370211yescharacteristic
801C22#1458370711yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—81no—
809C4—3441no—
810C4—3441no—
811C4—3441no—
812C4#1458344711yescharacteristic
813C4#1458350311yescharacteristic
814C4#1458353411yescharacteristic
815C4#1458356911yescharacteristic
816C2—42no—
817C2—42no—
818C2—161no—
819C2—3442no—
820C2#1913818611yescharacteristic
821C2#1914417311yescharacteristic
822C2#1914427711yescharacteristic
823C2#1914627611yescharacteristic
824C2#1914630311yescharacteristic
825C2#1914644511yescharacteristic
826C2#1914649711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2540C2
socleC23×C43C22×D4
hypercenter#2540D43
hypocenterC43#25388
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#14583133C2semidirect
2. C2×#14583130C2semidirect
3. C2×#14583111C2semidirect
4. C2×D4×C43⋊C8C2semidirect
5. #19139496C2semidirect
6. #19135795C2semidirect
7. #19135781C2semidirect
8. #19135596C2semidirect
9. #19135591C2semidirect
10. #19135407C2semidirect
11. #19135363C2semidirect
12. #19135024C2semidirect
13. #19135019C2semidirect
14. C4×#13063245C2semidirect
15. C43×#2540C2semidirect
99. C4⋊(C43⋊C8)D4semidirect
107. #13063245D4semidirect
407. #2540D43semidirect
476. C43#25388semidirect

Maximal subgroups

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

subgroupindex
C2×#145831332
C2×#145831302
C2×#145831112
C2×D4×C43⋊C82
#191394962
#191357952
#191357812
#191355962
#191355912
#191354072
#191353632
#191350242
#191350192
C4×#130632452
C43×#25402
#2538843