Finite Group Databasebeta

← #25129280

Subgroups — #25129280

Order 11008.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583237C211yesmaximal, characteristic, complemented
2C2×#14583220C211yesmaximal, characteristic, complemented
3#19136978C211yesmaximal, characteristic, complemented
4#19135795C211yesmaximal, characteristic, complemented
5#19135788C211yesmaximal, characteristic, complemented
6#19135781C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19134918C211yesmaximal, characteristic, complemented
9#19134908C211yesmaximal, characteristic, complemented
10#19134794C211yesmaximal, characteristic, complemented
11#19134794C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134505C211yesmaximal, characteristic, complemented
15C2×C43×#525C211yesmaximal, characteristic
16C2×#13063284C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18#14583237—24no—
19#14583220—24no—
20C2×#13063258C2211yescharacteristic, complemented
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24C2×#13063249C2211yescharacteristic, complemented
25C2×#13063249C2211yescharacteristic, complemented
26C2×#13063249C2211yescharacteristic, complemented
27C2×#13063249C2211yescharacteristic, complemented
28C2×#13063246C2211yescharacteristic, complemented
29C2×#13063246C2211yescharacteristic, complemented
30C2×#13063246C2211yescharacteristic, complemented
31C2×#13063246C2211yescharacteristic, complemented
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38#14582762—21no—
39#14582759C2211yescharacteristic
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582755—21no—
44C4×C22⋊Dic43—21no—
45C4×C22⋊Dic43—21no—
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50C22×#41×C43C2211yescharacteristic
51C24×C4×C43C2211yescharacteristic
52C43×#525—24no—
53C43×#525—24no—
54C2×#123×C43—21no—
55C2×C22⋊Q8×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#120×C43—21no—
60C2×C4×D4×C43—21no—
61C2×C4×D4×C43—21no—
62C2×#117×C43C2211yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063284—22no—
68#13063284—22no—
69#13063284—41no—
70#13063284—41no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83#13063258—22no—
84#13063258—22no—
85#13063256—22no—
86#13063256—22no—
87#13063249—22no—
88#13063249—22no—
89#13063249—41no—
90#13063249—41no—
91#13063246—22no—
92#13063246—22no—
93#13063246—41no—
94#13063246—41no—
95C22⋊(C43⋊C8)—22no—
96C22⋊(C43⋊C8)—22no—
97C22⋊(C43⋊C8)—22no—
98C22⋊(C43⋊C8)—22no—
99C22⋊(C43⋊C8)—41no—
100C22⋊(C43⋊C8)—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C25×C43D411yescharacteristic
106C2×#41×C43—22no—
107C2×#41×C43—22no—
108C2×#41×C43—22no—
109C2×#41×C43—22no—
110C2×#41×C43—41no—
111C2×#41×C43—41no—
112C22×Q8×C43C2311yescharacteristic
113C22×D4×C43—21no—
114C22×D4×C43—21no—
115C22×D4×C43—21no—
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43—22no—
119C23×C4×C43—22no—
120C23×C4×C43—22no—
121C23×C4×C43—22no—
122C23×C4×C43—41no—
123C23×C4×C43—41no—
124C23×C4×C43D411yescharacteristic
125C23×C4×C43D411yescharacteristic
126C23×C4×C43D411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130#123×C43—28no—
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43—22no—
133C22⋊Q8×C43—22no—
134C22⋊Q8×C43D414yes—
135#121×C43—22no—
136#121×C43—22no—
137#121×C43—22no—
138#121×C43D414yes—
139#120×C43—28no—
140C4×D4×C43—28no—
141C4×D4×C43—28no—
142#117×C43—22no—
143#117×C43—22no—
144C2×C4⋊C4×C43—21no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151C2×C22⋊C4×C43—21no—
152C2×C22⋊C4×C43—21no—
153C2×C42×C43—21no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—21no—
158C24×C43—41no—
159C24×C43—41no—
160C24×C43—41no—
161C24×C43—41no—
162C24×C43C2×D411yescharacteristic
163C24×C43C2×D411yescharacteristic
164C24×C43C2×D411yescharacteristic
165#41×C43—44no—
166#41×C43—44no—
167#41×C43—44no—
168#41×C43—44no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43C2×D412yes—
175C2×D4×C43—24no—
176C2×D4×C43—24no—
177C2×D4×C43—21no—
178C2×D4×C43—24no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43C2×D412yes—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—24no—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—41no—
215C22×C4×C43—41no—
216C22×C4×C43—41no—
217C22×C4×C43—44no—
218C22×C4×C43—44no—
219C22×C4×C43—44no—
220C22×C4×C43—44no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43C2×D412yes—
224C22×C4×C43C2×D412yes—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43#4112yes—
229C22×C4×C43#4112yes—
230C22×C4×C43C2411yescharacteristic
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C2×D412yes—
240C4⋊C4×C43C2×D412yes—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—24no—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C42×C43—24no—
247C22⋊Dic43—42no—
248C22⋊Dic43—42no—
249C22⋊Dic43—42no—
250C22⋊Dic43—42no—
251C22⋊Dic43—42no—
252C22⋊Dic43—42no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4×Dic43—42no—
262C4×Dic43—42no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—22no—
294C23×C43—44no—
295C23×C43—44no—
296C23×C43—44no—
297C23×C43—44no—
298C23×C43—44no—
299C23×C43—44no—
300C23×C43—44no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43#12012yes—
308C23×C43#12312yes—
309C23×C43#13512yes—
310C23×C43C22×D411yescharacteristic
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—41no—
314Q8×C43—41no—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—48no—
318D4×C43—48no—
319D4×C43—48no—
320D4×C43—41no—
321D4×C43—41no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—21no—
337C2×C4×C43—22no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—44no—
341C2×C4×C43—44no—
342C2×C4×C43—44no—
343C2×C4×C43—48no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43#12012yes—
355C2×C4×C43#12312yes—
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C2×#4111yescharacteristic
359C2×C4×C43C2×#4111yescharacteristic
360C2×C4×C43H(5,𝔽2)11yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C43⋊C8—41no—
375C43⋊C8—41no—
376C43⋊C8—41no—
377C43⋊C8—41no—
378#24008—431nomaximal, Sylow
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—416no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43—81no—
408C22×C43C2×#12011yescharacteristic
409C22×C43C2×#12311yescharacteristic
410C22×C43#53411yescharacteristic
411C22×C43C2×#13511yescharacteristic
412C22×C43#57511yescharacteristic
413C22×C43#57511yescharacteristic
414C22×C43#57511yescharacteristic
415C4×C43—22no—
416C4×C43—22no—
417C4×C43—41no—
418C4×C43—42no—
419C4×C43—42no—
420C4×C43—42no—
421C4×C43#54611yescharacteristic
422C4×C43#54611yescharacteristic
423C4×C43#54611yescharacteristic
424C4×C43#54611yescharacteristic
425Dic43—81no—
426Dic43—81no—
427Dic43—81no—
428Dic43—81no—
429C2×#525D4311yescharacteristic
430C2×#485—431no—
431C2×#482—431no—
432#2280—431no—
433#2036—431no—
434#2035—431no—
435#2034—431no—
436#2033—431no—
437#1875—431no—
438#1873—431no—
439#1854—431no—
440#1854—431no—
441#1788—431no—
442#1788—431no—
443#1779—431no—
444C2×C43—42no—
445C2×C43—42no—
446C2×C43—42no—
447C2×C43—82no—
448C2×C43#240511yescharacteristic
449C2×C43#300211yescharacteristic
450C2×C43#300511yescharacteristic
451C2×C43#309111yescharacteristic
452C2×C43#309311yescharacteristic
453C2×C43#319111yescharacteristic
454C2×C43#319711yescharacteristic
455C22×#41C2×D4311yescharacteristic
456C24×C4C2×D4311yescharacteristic
457#525—24no—
458#525—24no—
459C2×#123—21no—
460C2×C22⋊Q8C2×D4311yescharacteristic
461C2×C22⋊Q8C2×D4311yescharacteristic
462C2×#121C2×D4311yescharacteristic
463C2×#121C2×D4311yescharacteristic
464C2×#120—21no—
465C2×C4×D4—21no—
466C2×C4×D4—21no—
467C2×#117—431no—
468C2×#117—431no—
469C2×#117C2×D4311yescharacteristic
470#485—864no—
471#482—864no—
472C2×#107—431no—
473C2×#107—431no—
474C2×#106—431no—
475C2×#106—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×C22⋊C8—431no—
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—431no—
489C2×C22⋊C8—431no—
490#381—861no—
491#380—431no—
492#380—431no—
493#380—431no—
494#380—431no—
495#379—861no—
496C4×C22⋊C4—861no—
497C4×C22⋊C4—861no—
498#340—431no—
499#340—431no—
500#340—431no—
501#340—431no—
502C43#2400811yescharacteristic, complemented, Sylow
503C25C22⋊D4311yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C22×D4311yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C22×D4311yescharacteristic
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—21no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4C22⋊D4311yescharacteristic
523C23×C4C22⋊D4311yescharacteristic
524C23×C4C22⋊D4311yescharacteristic
525C23×C4C22×D4311yescharacteristic
526C23×C4C22×D4311yescharacteristic
527C23×C4C22×D4311yescharacteristic
528C22×C8—431no—
529C22×C8—431no—
530C22×C8—431no—
531C22×C8—431no—
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8C22⋊D4314yes—
537#121—22no—
538#121—22no—
539#121—22no—
540#121C22⋊D4314yes—
541#120—28no—
542C4×D4—28no—
543C4×D4—28no—
544#117—22no—
545#117—22no—
546#117—862no—
547#117—862no—
548#117—1721no—
549#117—1721no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C42—21no—
570C2×C42—861no—
571C2×C42—861no—
572#107—862no—
573#107—862no—
574#106—862no—
575#106—862no—
576#103—862no—
577#103—862no—
578#103—1721no—
579#103—1721no—
580#102—862no—
581#102—862no—
582#102—1721no—
583#102—1721no—
584C22⋊C8—862no—
585C22⋊C8—862no—
586C22⋊C8—862no—
587C22⋊C8—862no—
588C22⋊C8—1721no—
589C22⋊C8—1721no—
590#95—861no—
591#95—861no—
592#95—861no—
593#95—861no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C2×C22⋊D4311yescharacteristic
603C24C2×C22⋊D4311yescharacteristic
604C24C2×C22⋊D4311yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×C22⋊D4312yes—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×C22⋊D4312yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4#1062190012yes—
668C22×C4#1062190012yes—
669C22×C4C2×C22⋊D4311yescharacteristic
670C22×C4C2×C22⋊D4311yescharacteristic
671C22×C4C2×C22⋊D4312yes—
672C22×C4C2×C22⋊D4312yes—
673C22×C4C2×C22⋊D4311yescharacteristic
674C22×C4C23×D4311yescharacteristic
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4C2×C22⋊D4312yes—
700C4⋊C4C2×C22⋊D4312yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—1722no—
707C22⋊C4—1722no—
708C22⋊C4—1722no—
709C22⋊C4—1722no—
710C22⋊C4—1722no—
711C22⋊C4—1722no—
712C42—24no—
713C42—1722no—
714C42—1722no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23#1306329412yes—
748C23#1306330612yes—
749C23#1306334512yes—
750C23C22×C22⋊D4311yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4#1306329412yes—
807C2×C4#1306330612yes—
808C2×C4C22×C22⋊D4311yescharacteristic
809C2×C4C22×C22⋊D4311yescharacteristic
810C2×C4C2×#1062190011yescharacteristic
811C2×C4C2×#1062190011yescharacteristic
812C2×C4#1306337011yescharacteristic
813C2×C4#1306337011yescharacteristic
814C8—1721no—
815C8—1721no—
816C8—1721no—
817C8—1721no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×#1306329411yescharacteristic
848C22C2×#1306330611yescharacteristic
849C22#1458345811yescharacteristic
850C22C2×#1306334511yescharacteristic
851C22#1458369711yescharacteristic
852C22#1458369711yescharacteristic
853C22#1458369711yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—3441no—
861C4—3441no—
862C4—3441no—
863C4—3441no—
864C4#1458354311yescharacteristic
865C4#1458354311yescharacteristic
866C4#1458354311yescharacteristic
867C4#1458354311yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2#1913791811yescharacteristic
873C2#1914381311yescharacteristic
874C2#1914383711yescharacteristic
875C2#1914450411yescharacteristic
876C2#1914452411yescharacteristic
877C2#1914538311yescharacteristic
878C2#1914543211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#525C2
socleC23×C43C22×D4
hypercenterC2×#525D43
hypocenterC43#24008
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#14583237C2semidirect
2. C2×#14583220C2semidirect
3. #19136978C2semidirect
4. #19135795C2semidirect
5. #19135788C2semidirect
6. #19135781C2semidirect
7. #19135774C2semidirect
8. #19134918C2semidirect
9. #19134908C2semidirect
10. #19134794C2semidirect
11. #19134794C2semidirect
12. #19134535C2semidirect
13. #19134535C2semidirect
14. #19134505C2semidirect
20. C2×#13063258C22semidirect
21. C2×#13063258C22semidirect
22. C2×#13063256C22semidirect
23. C2×#13063256C22semidirect
24. C2×#13063249C22semidirect
25. C2×#13063249C22semidirect
26. C2×#13063249C22semidirect
27. C2×#13063249C22semidirect
28. C2×#13063246C22semidirect
29. C2×#13063246C22semidirect
30. C2×#13063246C22semidirect
31. C2×#13063246C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
502. C43#24008semidirect

Maximal subgroups

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

subgroupindex
C2×#145832372
C2×#145832202
#191369782
#191357952
#191357882
#191357812
#191357742
#191349182
#191349082
#191347942
#191345352
#191345052
C2×C43×#5252
#2400843