Finite Group Databasebeta

← #25132183

Subgroups — #25132183

Order 11008.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583111C211yesmaximal, characteristic, complemented
2C2×#14583044C211yesmaximal, characteristic, complemented
3C2×#14583033C211yesmaximal, characteristic, complemented
4C2×#14583009C211yesmaximal, characteristic, complemented
5#19139508C211yesmaximal, characteristic, complemented
6#19135788C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135596C211yesmaximal, characteristic, complemented
9#19135591C211yesmaximal, characteristic, complemented
10#19135412C211yesmaximal, characteristic, complemented
11#19135394C211yesmaximal, characteristic, complemented
12#19134595C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic, complemented
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063299C2211yescharacteristic, complemented
21C2×#13063296—21no—
22C2×C4×D172C2211yescharacteristic, complemented
23#14583111—24no—
24#14583044—24no—
25#14583033—24no—
26#14583009—24no—
27C2×#13063256C2211yescharacteristic, complemented
28C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
29C2×#13063249C2211yescharacteristic, complemented
30C2×#13063249C2211yescharacteristic, complemented
31C2×#13063249C2211yescharacteristic, complemented
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic, complemented
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
42C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
43C2×#13063236C2211yescharacteristic, complemented
44#14582815—21no—
45#14582815—21no—
46#14582769C2211yescharacteristic, complemented
47#14582759C2211yescharacteristic
48#14582759C2211yescharacteristic, complemented
49#14582756—21no—
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52C22×#41×C43C2211yescharacteristic
53C23×D4×C43C2211yescharacteristic
54C43×#546—24no—
55C43×#546—24no—
56C2×#124×C43C2211yescharacteristic
57C2×#123×C43—21no—
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#121×C43—21no—
60C2×#121×C43C2211yescharacteristic
61C2×#120×C43—21no—
62C2×C4×D4×C43C2211yescharacteristic
63C2×C4×D4×C43C2211yescharacteristic
64C22×C22⋊C4×C43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C4×D43—21no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—41no—
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—41no—
77C2×#10621882D414yescomplemented
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063299—22no—
83#13063299—22no—
84#13063299—41no—
85#13063299—41no—
86#13063296—44no—
87C4×D172—22no—
88C4×D172—22no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99#13063256—22no—
100C4⋊(C43⋊C8)—22no—
101#13063249—22no—
102#13063249—22no—
103#13063249—41no—
104#13063246—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246—41no—
110#13063245—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—41no—
114C22⋊(C43⋊C8)—41no—
115#13063236—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C25×C43—21no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—41no—
124C2×#41×C43—41no—
125C22×Q8×C43C2311yescharacteristic
126C22×D4×C43—21no—
127C22×D4×C43—21no—
128C22×D4×C43—22no—
129C22×D4×C43—22no—
130C22×D4×C43—22no—
131C22×D4×C43—22no—
132C22×D4×C43—21no—
133C22×D4×C43—41no—
134C22×D4×C43—41no—
135C22×D4×C43D411yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C22×D4×C43C2311yescharacteristic
138C23×C4×C43—21no—
139C23×C4×C43—21no—
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142#124×C43—22no—
143#124×C43D414yescomplemented
144#123×C43—28no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43—22no—
147#121×C43—28no—
148#121×C43—22no—
149#121×C43—22no—
150#120×C43—28no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C4×D4×C43—22no—
154C4×D4×C43D414yescomplemented
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43D411yescharacteristic
157C2×C4⋊C4×C43C2311yescharacteristic
158C2×C22⋊C4×C43—28no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43—21no—
164C2×C22⋊C4×C43D411yescharacteristic
165C2×C22⋊C4×C43D411yescharacteristic
166C2×C42×C43C2311yescharacteristic
167C24×C43—21no—
168C24×C43—24no—
169C24×C43—21no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43—42no—
173C24×C43—42no—
174C24×C43—81no—
175C24×C43—81no—
176C24×C43C2×D411yescharacteristic
177C24×C43C2×D411yescharacteristic
178C23×D43—21no—
179#41×C43—44no—
180#41×C43—44no—
181#41×C43—44no—
182#41×C43—44no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43C2×D412yes—
189C2×D4×C43—24no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—22no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—22no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—41no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43—42no—
207C2×D4×C43—44no—
208C2×D4×C43—44no—
209C2×D4×C43—44no—
210C2×D4×C43—44no—
211C2×D4×C43—81no—
212C2×D4×C43—81no—
213C2×D4×C43C2×D412yes—
214C2×D4×C43C2×D412yes—
215C2×D4×C43C2×D412yes—
216C2×D4×C43#4112yes—
217C22×C4×C43—24no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—24no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—42no—
234C22×C4×C43—42no—
235C22×C4×C43—81no—
236C22×C4×C43—81no—
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2411yescharacteristic
242C2×C22⋊D43—42no—
243C2×C22⋊D43—42no—
244C2×C22⋊D43—42no—
245C2×C22⋊D43—42no—
246C2×C22⋊D43—81no—
247C2×C22⋊D43—81no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C2×D172—21no—
252C2×D172—21no—
253C2×D172—21no—
254C2×D172—21no—
255C2×D172—21no—
256C2×D172C2×D412yes—
257C2×C4×D43—42no—
258C2×C4×D43—42no—
259C2×C4×D43—42no—
260C4⋊C4×C43—24no—
261C4⋊C4×C43—22no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2×D412yes—
264C22⋊C4×C43—24no—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—22no—
267C22⋊C4×C43—24no—
268C22⋊C4×C43—24no—
269C22⋊C4×C43—24no—
270C22⋊C4×C43—22no—
271C42×C43C2×D412yes—
272C42×C43C2×D412yes—
273C22⋊Dic43—42no—
274C22⋊Dic43—42no—
275#10621884—44no—
276#10621882—28no—
277#10621882—44no—
278(C2×D43)⋊C4—42no—
279(C2×D43)⋊C4—42no—
280(C2×D43)⋊C4—42no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—42no—
288C4⋊Dic43—81no—
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—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8C2×D412yes—
301C23×C43—21no—
302C23×C43—22no—
303C23×C43—21no—
304C23×C43—22no—
305C23×C43—21no—
306C23×C43—22no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—22no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—48no—
319C23×C43—48no—
320C23×C43—41no—
321C23×C43—41no—
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—84no—
331C23×C43—84no—
332C23×C43—84no—
333C23×C43—84no—
334C23×C43—84no—
335C23×C43AGL(1,ℤ/8)12yes—
336C23×C43C22×D411yescharacteristic
337C22×D43—22no—
338C22×D43—41no—
339C22×D43—41no—
340C22×D43—41no—
341C22×D43—41no—
342C22×D43—41no—
343C22×D43—41no—
344Q8×C43—22no—
345Q8×C43—22no—
346Q8×C43—41no—
347Q8×C43—41no—
348D4×C43—22no—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—22no—
353D4×C43—44no—
354D4×C43—48no—
355D4×C43—48no—
356D4×C43—41no—
357D4×C43—41no—
358D4×C43—84no—
359D4×C43#12114yescomplemented
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—22no—
365C2×C4×C43—21no—
366C2×C4×C43—22no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—48no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
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—84no—
386C2×C4×C43#12012yes—
387C2×C4×C43#12012yes—
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C2×C4×C43C22×D411yescharacteristic
391C2×C4×C43C2×#4111yescharacteristic
392C2×C4×C43H(5,𝔽2)11yescharacteristic
393C2×C4×C43H(5,𝔽2)11yescharacteristic
394C22⋊D43—84no—
395C22⋊D43—84no—
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—
405D172—22no—
406D172—22no—
407D172—41no—
408D172—41no—
409C4×D43—84no—
410C43⋊C8—22no—
411C43⋊C8—41no—
412C43⋊C8—41no—
413C43⋊C8—41no—
414#24257—431nomaximal, Sylow
415C22×C43—24no—
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—41no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—41no—
423C22×C43—42no—
424C22×C43—41no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43—41no—
428C22×C43—42no—
429C22×C43—41no—
430C22×C43—42no—
431C22×C43—41no—
432C22×C43—42no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—42no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—816no—
440C22×C43—81no—
441C22×C43—81no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43C2×#12011yescharacteristic
445C22×C43D4211yescharacteristic
446C22×C43#54611yescharacteristic
447C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
448C22×C43#57511yescharacteristic
449C22×C43#57611yescharacteristic
450C22×C43#57711yescharacteristic
451C2×D43—42no—
452C2×D43—42no—
453C2×D43—42no—
454C2×D43—81no—
455C2×D43—81no—
456C2×D43—81no—
457C2×D43—81no—
458C4×C43—22no—
459C4×C43—22no—
460C4×C43—41no—
461C4×C43—41no—
462C4×C43—42no—
463C4×C43—42no—
464C4×C43C2×#12111yescharacteristic
465C4×C43#53511yescharacteristic
466C4×C43D4211yescharacteristic
467C4×C43#54611yescharacteristic
468Dic43—81no—
469Dic43—81no—
470Dic43—81no—
471C2×#546D4311yescharacteristic, complemented
472C2×#463—431no—
473C2×#449—431no—
474C2×#447—431no—
475C2×#442—431no—
476#2537—431no—
477#2035—431no—
478#2034—431no—
479#2000—431no—
480#1999—431no—
481#1959—431no—
482#1955—431no—
483#1802—431no—
484#1788—431no—
485#1786—431no—
486C2×C43—42no—
487C2×C43—44no—
488C2×C43—81no—
489C2×C43—82no—
490C2×C43#240811yescharacteristic
491C2×C43#300611yescharacteristic
492C2×C43#301211yescharacteristic
493C2×C43#326411yescharacteristic
494C2×C43#326711yescharacteristic
495C2×C43#330611yescharacteristic
496C2×C43#331911yescharacteristic
497D43—82no—
498C22×#41C2×D4311yescharacteristic
499C23×D4C2×D4311yescharacteristic
500C22×SD16—431no—
501C22×D8—431no—
502C22×D8—431no—
503#546—24no—
504#546—24no—
505C2×#124C2×D4311yescharacteristic
506C2×#123—21no—
507C2×C22⋊Q8C2×D4311yescharacteristic
508C2×#121—21no—
509C2×#121—431no—
510C2×#121—431no—
511C2×#121—861no—
512C2×#121C2×D4311yescharacteristic
513C2×#120—21no—
514C2×C4×D4—431no—
515C2×C4×D4C2×D4311yescharacteristic
516C2×C4×D4C2×D4311yescharacteristic
517C22×C22⋊C4—21no—
518#463—864no—
519#449—864no—
520#447—864no—
521#442—864no—
522C2×#106—431no—
523C2×C4⋊C8—431no—
524C2×#103—431no—
525C2×#103—431no—
526C2×#103—431no—
527C2×#102—431no—
528C2×#102—431no—
529C2×#102—431no—
530C2×#102—431no—
531C2×#102—431no—
532C2×#102—431no—
533C2×#102—431no—
534C2×C22⋊C8—431no—
535C2×C22⋊C8—431no—
536C2×C22⋊C8—431no—
537C2×C22⋊C8—431no—
538C2×#97—431no—
539#394—861no—
540#394—861no—
541#384—431no—
542#380—431no—
543#380—431no—
544#380—861no—
545#340—431no—
546#340—431no—
547C43#2425711yescharacteristic, complemented, Sylow
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C22×D4311yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—41no—
564C22×D4—41no—
565C22×D4—431no—
566C22×D4—861no—
567C22×D4—861no—
568C22×D4C22⋊D4311yescharacteristic
569C22×D4C22×D4311yescharacteristic
570C22×D4C22×D4311yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—861no—
574C23×C4C22×D4311yescharacteristic
575C23×C4C22×D4311yescharacteristic
576C2×SD16—862no—
577C2×SD16—862no—
578C2×SD16—1721no—
579C2×D8—434no—
580C2×D8—862no—
581C2×D8—862no—
582C2×D8—862no—
583C2×D8—862no—
584C2×D8—1721no—
585C22×C8—431no—
586C22×C8—431no—
587C22×C8—431no—
588C22×C8—431no—
589#124—22no—
590#124C22⋊D4314yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—862no—
598#121—862no—
599#121—1721no—
600#121—1721no—
601#121—1724no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—862no—
607C4×D4—862no—
608C4×D4C22⋊D4314yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4C22⋊D4311yescharacteristic
616C2×C4⋊C4C22×D4311yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4C22⋊D4311yescharacteristic
629C2×C22⋊C4C22⋊D4311yescharacteristic
630C2×C42C22×D4311yescharacteristic
631#106—862no—
632C4⋊C8—862no—
633#103—862no—
634#103—862no—
635#103—1721no—
636#102—862no—
637#102—862no—
638#102—862no—
639#102—862no—
640#102—862no—
641#102—862no—
642#102—1721no—
643C22⋊C8—862no—
644C22⋊C8—862no—
645C22⋊C8—1721no—
646C22⋊C8—1721no—
647#97—862no—
648#95—861no—
649#95—861no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—81no—
658C24—81no—
659C24—861no—
660C24C2×C22⋊D4311yescharacteristic
661C24C2×C22⋊D4311yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×C22⋊D4312yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—41no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—432no—
697C2×D4—861no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—3441no—
703C2×D4—3441no—
704C2×D4—1722no—
705C2×D4—1722no—
706C2×D4—1722no—
707C2×D4—1722no—
708C2×D4D4×D4312yes—
709C2×D4#1062190012yes—
710C2×D4C2×C22⋊D4312yes—
711C2×D4C2×C22⋊D4312yes—
712C22×C4—24no—
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—24no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—1722no—
736C22×C4—1722no—
737C22×C4—1722no—
738C22×C4C2×C22⋊D4311yescharacteristic
739C22×C4C2×C22⋊D4311yescharacteristic
740C22×C4C2×C22⋊D4311yescharacteristic
741C22×C4C2×C22⋊D4311yescharacteristic
742C22×C4C23×D4311yescharacteristic
743SD16—1724no—
744D8—868no—
745D8—1724no—
746C2×C8—432no—
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—861no—
757C2×C8—861no—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—3441no—
768C4⋊C4—1722no—
769C4⋊C4C2×C22⋊D4312yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—1722no—
778C22⋊C4—1722no—
779C22⋊C4—1722no—
780C22⋊C4—1722no—
781C22⋊C4—1722no—
782C42C2×C22⋊D4312yes—
783C42C2×C22⋊D4312yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—48no—
802C23—48no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—862no—
819C23—1721no—
820C23—1721no—
821C23—1721no—
822C23—1721no—
823C23—1721no—
824C23—1721no—
825C23#1306335012yes—
826C23C22×C22⋊D4311yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—44no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4—862no—
843D4—862no—
844D4—3444no—
845D4—3444no—
846D4—1721no—
847D4—1721no—
848D4#1306329614yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
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—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—84no—
875C2×C4—3444no—
876C2×C4—1721no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4#1306329412yes—
886C2×C4#1306329412yes—
887C2×C4C2×D4×D4311yescharacteristic
888C2×C4C22×C22⋊D4311yescharacteristic
889C2×C4C22×C22⋊D4311yescharacteristic
890C2×C4C2×#1062190011yescharacteristic
891C2×C4#1306337011yescharacteristic
892C2×C4#1306337011yescharacteristic
893C8—862no—
894C8—1721no—
895C8—1721no—
896C8—1721no—
897C22—22no—
898C22—22no—
899C22—24no—
900C22—22no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—816no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—3441no—
927C22—3441no—
928C22—3441no—
929C22—3441no—
930C22—1722no—
931C22—1722no—
932C22—1722no—
933C22C2×#1306329411yescharacteristic
934C22D4×C22⋊D4311yescharacteristic
935C22#1458354311yescharacteristic
936C22C2×#1306335011yescharacteristic
937C22#1458369711yescharacteristic
938C22#1458370211yescharacteristic
939C22#1458371011yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—3441no—
947C4—3441no—
948C4—3441no—
949C4C2×#1306329611yescharacteristic
950C4#1458346611yescharacteristic
951C4D4×C22⋊D4311yescharacteristic
952C4#1458354311yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—3442no—
958C2#1913794511yescharacteristic
959C2#1914384711yescharacteristic
960C2#1914389911yescharacteristic
961C2#1914607611yescharacteristic
962C2#1914611611yescharacteristic
963C2#1914655611yescharacteristic
964C2#1914675111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#546C2
socleC23×C43C22×D4
hypercenterC2×#546D43
hypocenterC43#24257
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#14583111C2semidirect
2. C2×#14583044C2semidirect
3. C2×#14583033C2semidirect
4. C2×#14583009C2semidirect
5. #19139508C2semidirect
6. #19135788C2semidirect
7. #19135781C2semidirect
8. #19135596C2semidirect
9. #19135591C2semidirect
10. #19135412C2semidirect
11. #19135394C2semidirect
12. #19134595C2semidirect
13. #19134535C2semidirect
14. #19134526C2semidirect
15. C2×C43×#546C2semidirect
16. C22×#10621884C22semidirect
20. C2×#13063299C22semidirect
22. C2×C4×D172C22semidirect
27. C2×#13063256C22semidirect
28. C2×C4⋊(C43⋊C8)C22semidirect
29. C2×#13063249C22semidirect
30. C2×#13063249C22semidirect
31. C2×#13063249C22semidirect
38. C2×#13063245C22semidirect
41. C2×C22⋊(C43⋊C8)C22semidirect
42. C2×C22⋊(C43⋊C8)C22semidirect
43. C2×#13063236C22semidirect
46. #14582769C22semidirect
48. #14582759C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
77. C2×#10621882D4semidirect
143. #124×C43D4semidirect
154. C4×D4×C43D4semidirect
359. D4×C43#121semidirect
471. C2×#546D43semidirect
547. C43#24257semidirect
590. #124C22⋊D43semidirect
608. C4×D4C22⋊D43semidirect
848. D4#13063296semidirect

Maximal subgroups

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

subgroupindex
C2×#145831112
C2×#145830442
C2×#145830332
C2×#145830092
#191395082
#191357882
#191357812
#191355962
#191355912
#191354122
#191353942
#191345952
#191345352
#191345262
C2×C43×#5462
#2425743