Finite Group Databasebeta

← #25133804

Subgroups — #25133804

Order 11008.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583143C211yesmaximal, characteristic, complemented
2C2×#14583126C211yesmaximal, characteristic, complemented
3C2×#14583050C211yesmaximal, characteristic, complemented
4C2×#14582866C211yesmaximal, characteristic, complemented
5#19140324C211yesmaximal, characteristic, complemented
6#19135781C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135598C211yesmaximal, characteristic, complemented
9#19135598C211yesmaximal, characteristic, complemented
10#19135034C211yesmaximal, characteristic, complemented
11#19135024C211yesmaximal, characteristic, complemented
12#19134907C211yesmaximal, characteristic, complemented
13#19134794C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×C43×#535C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621877C2211yescharacteristic, complemented
19C23×C43⋊C8C2211yescharacteristic, complemented
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic, complemented
22C2×#13063304C2211yescharacteristic, complemented
23#14583143—24no—
24#14583126—24no—
25#14583050—24no—
26C2×#13063258C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28C2×#13063248C2211yescharacteristic, complemented
29C2×#13063248C2211yescharacteristic, complemented
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36#14582866—24no—
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
40C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
41#14582818—21no—
42#14582813—21no—
43#14582813—21no—
44#14582813—21no—
45#14582759C2211yescharacteristic
46#14582759C2211yescharacteristic, complemented
47#14582759C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52C22×#41×C43C2211yescharacteristic
53C23×D4×C43C2211yescharacteristic
54C43×#535—24no—
55C43×#535—24no—
56C2×#127×C43—21no—
57C2×#124×C43—21no—
58C2×#121×C43C2211yescharacteristic
59C2×#121×C43C2211yescharacteristic
60C2×#121×C43C2211yescharacteristic
61C2×#121×C43C2211yescharacteristic
62C2×#120×C43—21no—
63C2×#120×C43—21no—
64C2×#117×C43C2211yescharacteristic
65C22×Dic86C2311yescharacteristic
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—41no—
71C2×#10621883—41no—
72C2×#10621877—22no—
73C2×#10621877—22no—
74C2×#10621877—41no—
75C22×C43⋊C8—22no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063304—22no—
83#13063304—22no—
84#13063304—22no—
85#13063304—22no—
86#13063304—41no—
87#13063304—41no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100#13063258—22no—
101#13063256—22no—
102#13063248—22no—
103#13063248—22no—
104#13063246—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—41no—
109#13063246—41no—
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)D414yescomplemented
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—41no—
123C2×#41×C43—41no—
124C22×Q8×C43D411yescharacteristic
125C22×D4×C43—21no—
126C22×D4×C43—21no—
127C22×D4×C43—21no—
128C22×D4×C43—21no—
129C22×D4×C43—22no—
130C22×D4×C43—22no—
131C22×D4×C43—21no—
132C22×D4×C43—22no—
133C22×D4×C43—22no—
134C22×D4×C43—41no—
135C22×D4×C43—41no—
136C22×D4×C43D411yescharacteristic
137C22×D4×C43D411yescharacteristic
138C22×D4×C43D411yescharacteristic
139C22×D4×C43C2311yescharacteristic
140C22×D4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144#127×C43—28no—
145#124×C43—28no—
146#121×C43—22no—
147#121×C43—22no—
148#121×C43—22no—
149#121×C43—22no—
150#121×C43—22no—
151#121×C43—22no—
152#121×C43D414yes—
153#121×C43D414yes—
154#120×C43—28no—
155#120×C43—28no—
156#117×C43—22no—
157#117×C43—22no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43—21no—
164C2×C22⋊C4×C43—21no—
165C2×C42×C43—21no—
166C24×C43—24no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—42no—
170C24×C43—42no—
171C24×C43—81no—
172C24×C43—81no—
173C24×C43—81no—
174C24×C43—81no—
175C24×C43C2×D411yescharacteristic
176C24×C43C2×D411yescharacteristic
177C24×C43C2×D411yescharacteristic
178#41×C43—44no—
179#41×C43—44no—
180#41×C43—44no—
181#41×C43—44no—
182C2×Q8×C43—22no—
183C2×Q8×C43—22no—
184C2×Q8×C43—41no—
185C2×D4×C43—24no—
186C2×D4×C43—24no—
187C2×D4×C43—24no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—24no—
195C2×D4×C43—24no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—41no—
207C2×D4×C43—41no—
208C2×D4×C43—41no—
209C2×D4×C43—44no—
210C2×D4×C43—44no—
211C2×D4×C43—44no—
212C2×D4×C43—44no—
213C2×D4×C43—42no—
214C2×D4×C43—42no—
215C2×D4×C43—81no—
216C2×D4×C43—81no—
217C2×D4×C43—81no—
218C2×D4×C43—81no—
219C2×D4×C43—81no—
220C2×D4×C43—81no—
221C2×D4×C43—81no—
222C2×D4×C43—81no—
223C2×D4×C43C2×D412yes—
224C2×D4×C43C2×D412yes—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43C2×D412yes—
242C22×C4×C43C2×D412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43#4112yes—
248C22×C4×C43C2411yescharacteristic
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C2×Dic86—21no—
254C2×Dic86—21no—
255C2×Dic86—21no—
256C2×Dic86—21no—
257C2×Dic86—21no—
258C2×Dic86—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C2×D412yes—
262C4⋊C4×C43C2×D412yes—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—24no—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—24no—
267C22⋊C4×C43—24no—
268C42×C43—24no—
269C22⋊Dic43—42no—
270C22⋊Dic43—42no—
271C22⋊Dic43—42no—
272C22⋊Dic43—81no—
273C22⋊Dic43—81no—
274C22⋊Dic43—81no—
275#10621883—44no—
276#10621883—44no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283Dic43⋊C4—42no—
284Dic43⋊C4—42no—
285Dic43⋊C4—42no—
286#10621877—44no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—44no—
298C2×C43⋊C8C2×D412yes—
299C2×C43⋊C8C2×D412yes—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—48no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—84no—
335C23×C43—84no—
336C23×C43—84no—
337C23×C43—84no—
338C23×C43—84no—
339C23×C43—84no—
340C23×C43#12012yes—
341C23×C43#12112yes—
342C23×C43C22×D411yescharacteristic
343Q8×C43—44no—
344D4×C43—22no—
345D4×C43—22no—
346D4×C43—22no—
347D4×C43—22no—
348D4×C43—44no—
349D4×C43—44no—
350D4×C43—48no—
351D4×C43—44no—
352D4×C43—41no—
353D4×C43—41no—
354D4×C43—41no—
355D4×C43—41no—
356D4×C43—84no—
357D4×C43—84no—
358D4×C43—84no—
359D4×C43—84no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43#12012yes—
386C2×C4×C43#12112yes—
387C2×C4×C43C22×D411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C2×C4×C43C2×#4111yescharacteristic
391C2×C4×C43H(5,𝔽2)11yescharacteristic
392C2×C4×C43H(5,𝔽2)11yescharacteristic
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405Dic86—41no—
406Dic86—41no—
407Dic86—41no—
408Dic86—41no—
409C43⋊C8—22no—
410C43⋊C8—22no—
411C43⋊C8—41no—
412C43⋊C8—41no—
413#24394—431nomaximal, Sylow
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—41no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—41no—
437C22×C43—42no—
438C22×C43—42no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—816no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43—81no—
446C22×C43—81no—
447C22×C43—81no—
448C22×C43—81no—
449C22×C43—81no—
450C22×C43C2×#12011yescharacteristic
451C22×C43C2×#12111yescharacteristic
452C22×C43#53411yescharacteristic
453C22×C43#57611yescharacteristic
454C22×C43#57711yescharacteristic
455C22×C43#57711yescharacteristic
456C22×C43#57711yescharacteristic
457C4×C43—22no—
458C4×C43—22no—
459C4×C43—41no—
460C4×C43—42no—
461C4×C43—42no—
462C4×C43D4211yescharacteristic
463C4×C43D4211yescharacteristic
464C4×C43#54611yescharacteristic
465C4×C43#54611yescharacteristic
466Dic43—81no—
467Dic43—81no—
468Dic43—81no—
469Dic43—81no—
470C2×#535D4311yescharacteristic
471C2×#468—431no—
472C2×#465—431no—
473C2×#450—431no—
474C2×#408—431no—
475#2616—431no—
476#2034—431no—
477#2033—431no—
478#2000—431no—
479#2000—431no—
480#1895—431no—
481#1893—431no—
482#1873—431no—
483#1854—431no—
484#1786—431no—
485C2×C43—42no—
486C2×C43—42no—
487C2×C43—81no—
488C2×C43—82no—
489C2×C43—82no—
490C2×C43#241011yescharacteristic
491C2×C43#300911yescharacteristic
492C2×C43#301211yescharacteristic
493C2×C43#305711yescharacteristic
494C2×C43#306211yescharacteristic
495C2×C43#319811yescharacteristic
496C2×C43#320011yescharacteristic
497C22×#41C2×D4311yescharacteristic
498C23×D4C2×D4311yescharacteristic
499C22×SD16—431no—
500C22×SD16—431no—
501C22×M16—431no—
502C23×C8—431no—
503#535—24no—
504#535—24no—
505C2×#127—21no—
506C2×#124—21no—
507C2×C22⋊Q8—431no—
508C2×C22⋊Q8—431no—
509C2×C22⋊Q8—431no—
510C2×#121C2×D4311yescharacteristic
511C2×#121C2×D4311yescharacteristic
512C2×#121C2×D4311yescharacteristic
513C2×#121C2×D4311yescharacteristic
514C2×#120—21no—
515C2×#120—21no—
516C2×#117C2×D4311yescharacteristic
517#468—864no—
518#465—864no—
519#450—864no—
520C2×#107—431no—
521C2×#106—431no—
522C2×#103—431no—
523C2×#103—431no—
524C2×#102—431no—
525C2×#102—431no—
526C2×#102—431no—
527C2×#102—431no—
528C2×#102—431no—
529C2×#102—431no—
530#408—864no—
531C2×C22⋊C8—431no—
532C2×C22⋊C8—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
535#395—861no—
536#394—861no—
537#394—861no—
538#394—861no—
539#380—431no—
540#380—431no—
541#380—431no—
542#340—431no—
543#340—431no—
544#340—431no—
545#340—431no—
546C43#2439411yescharacteristic, complemented, Sylow
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8—431no—
555C22×Q8C22⋊D4311yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—22no—
563C22×D4—22no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4C22⋊D4311yescharacteristic
568C22×D4C22⋊D4311yescharacteristic
569C22×D4C22⋊D4311yescharacteristic
570C22×D4C22×D4311yescharacteristic
571C22×D4C22×D4311yescharacteristic
572C23×C4C22×D4311yescharacteristic
573C23×C4C22×D4311yescharacteristic
574C23×C4C22×D4311yescharacteristic
575C2×SD16—862no—
576C2×SD16—862no—
577C2×SD16—862no—
578C2×SD16—862no—
579C2×SD16—1721no—
580C2×SD16—1721no—
581C2×M16—862no—
582C2×M16—862no—
583C2×M16—1721no—
584C22×C8—431no—
585C22×C8—431no—
586C22×C8—431no—
587C22×C8—431no—
588C22×C8—862no—
589C22×C8—862no—
590C22×C8—1721no—
591#127—28no—
592#124—28no—
593C22⋊Q8—862no—
594C22⋊Q8—862no—
595C22⋊Q8—862no—
596C22⋊Q8—862no—
597C22⋊Q8—1721no—
598C22⋊Q8—1721no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121C22⋊D4314yes—
606#121C22⋊D4314yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—431no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4C22×D4311yescharacteristic
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4—861no—
629C2×C22⋊C4—861no—
630C2×C42—21no—
631#107—862no—
632#106—862no—
633#103—862no—
634#103—862no—
635#102—862no—
636#102—862no—
637#102—862no—
638#102—862no—
639#102—1721no—
640#102—1721no—
641C22⋊C8—434no—
642C22⋊C8—862no—
643C22⋊C8—862no—
644C22⋊C8—862no—
645#95—861no—
646#95—861no—
647#95—861no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×C22⋊D4311yescharacteristic
658C24C2×C22⋊D4311yescharacteristic
659C24C2×C22⋊D4311yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—41no—
667C2×Q8—861no—
668C2×Q8—861no—
669C2×Q8—861no—
670C2×Q8—861no—
671C2×Q8—861no—
672C2×Q8—861no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×C22⋊D4312yes—
712C2×D4C2×C22⋊D4312yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4D4×D4312yes—
734C22×C4#1062190012yes—
735C22×C4C2×C22⋊D4311yescharacteristic
736C22×C4C2×C22⋊D4311yescharacteristic
737C22×C4C2×C22⋊D4312yes—
738C22×C4C2×C22⋊D4312yes—
739C22×C4C2×C22⋊D4311yescharacteristic
740C22×C4C23×D4311yescharacteristic
741SD16—1724no—
742SD16—1724no—
743M16—1724no—
744C2×C8—432no—
745C2×C8—432no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—861no—
749C2×C8—861no—
750C2×C8—861no—
751C2×C8—861no—
752C2×C8—861no—
753C2×C8—861no—
754C2×C8—861no—
755C2×C8—861no—
756C2×C8—1724no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—1722no—
766C4⋊C4—1722no—
767C4⋊C4—1722no—
768C4⋊C4C2×C22⋊D4312yes—
769C4⋊C4C2×C22⋊D4312yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—3441no—
776C22⋊C4—3441no—
777C22⋊C4—3441no—
778C22⋊C4—1722no—
779C22⋊C4—1722no—
780C22⋊C4—1722no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#1306329412yes—
823C23#1306329712yes—
824C23C22×C22⋊D4311yescharacteristic
825Q8—44no—
826Q8—1721no—
827Q8—1721no—
828Q8—1721no—
829Q8—1721no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4#1306329412yes—
884C2×C4#1306329712yes—
885C2×C4C2×D4×D4311yescharacteristic
886C2×C4C22×C22⋊D4311yescharacteristic
887C2×C4C22×C22⋊D4311yescharacteristic
888C2×C4C2×#1062190011yescharacteristic
889C2×C4#1306337011yescharacteristic
890C2×C4#1306337011yescharacteristic
891C8—862no—
892C8—862no—
893C8—1721no—
894C8—1721no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#1306329411yescharacteristic
932C22C2×#1306329711yescharacteristic
933C22#1458345811yescharacteristic
934C22#1458370211yescharacteristic
935C22#1458371011yescharacteristic
936C22#1458371011yescharacteristic
937C22#1458371011yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—3441no—
944C4—3441no—
945C4—3441no—
946C4—3441no—
947C4D4×C22⋊D4311yescharacteristic
948C4D4×C22⋊D4311yescharacteristic
949C4#1458354311yescharacteristic
950C4#1458354311yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2#1913796911yescharacteristic
957C2#1914387211yescharacteristic
958C2#1914389911yescharacteristic
959C2#1914423111yescharacteristic
960C2#1914427111yescharacteristic
961C2#1914544711yescharacteristic
962C2#1914546711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#535C2
socleC23×C43C22×D4
hypercenterC2×#535D43
hypocenterC43#24394
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#14583143C2semidirect
2. C2×#14583126C2semidirect
3. C2×#14583050C2semidirect
4. C2×#14582866C2semidirect
5. #19140324C2semidirect
6. #19135781C2semidirect
7. #19135774C2semidirect
8. #19135598C2semidirect
9. #19135598C2semidirect
10. #19135034C2semidirect
11. #19135024C2semidirect
12. #19134907C2semidirect
13. #19134794C2semidirect
14. #19134526C2semidirect
18. C22×#10621877C22semidirect
19. C23×C43⋊C8C22semidirect
21. C2×#13063304C22semidirect
22. C2×#13063304C22semidirect
26. C2×#13063258C22semidirect
27. C2×#13063256C22semidirect
28. C2×#13063248C22semidirect
29. C2×#13063248C22semidirect
39. C2×C22⋊(C43⋊C8)C22semidirect
40. C2×C22⋊(C43⋊C8)C22semidirect
46. #14582759C22semidirect
47. #14582759C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
113. C22⋊(C43⋊C8)D4semidirect
546. C43#24394semidirect

Maximal subgroups

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

subgroupindex
C2×#145831432
C2×#145831262
C2×#145830502
C2×#145828662
#191403242
#191357812
#191357742
#191355982
#191350342
#191350242
#191349072
#191347942
#191345262
C2×C43×#5352
#2439443