Finite Group Databasebeta

← #25129379

Subgroups — #25129379

Order 11008.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 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#19137187C211yesmaximal, characteristic, complemented
4#19135795C211yesmaximal, characteristic, complemented
5#19135788C211yesmaximal, characteristic, complemented
6#19135781C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19134913C211yesmaximal, characteristic, complemented
9#19134903C211yesmaximal, characteristic, complemented
10#19134788C211yesmaximal, characteristic, complemented
11#19134783C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134507C211yesmaximal, characteristic, complemented
15C2×C43×#537C211yesmaximal, characteristic
16C2×#13063284C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18#14583237—24no—
19#14583220—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
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#14582806—21no—
39#14582802—21no—
40#14582779—21no—
41#14582779—21no—
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C22×#41×C43C2211yescharacteristic
51C22×#41×C43C2211yescharacteristic
52C43×#537—24no—
53C43×#537—24no—
54C2×C22⋊Q8×C43—21no—
55C2×C22⋊Q8×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×#121×C43—21no—
58C2×#121×C43—21no—
59C2×#121×C43—21no—
60C2×#121×C43C2211yescharacteristic
61C2×#121×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C23×Dic43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063284—22no—
69#13063284—22no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—41no—
72C2×C4⋊Dic43—41no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊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—
105C2×#41×C43—22no—
106C2×#41×C43—22no—
107C2×#41×C43—22no—
108C2×#41×C43—22no—
109C2×#41×C43—22no—
110C2×#41×C43—22no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—41no—
114C2×#41×C43—41no—
115C2×#41×C43—41no—
116C2×#41×C43—41no—
117C22×Q8×C43D411yescharacteristic
118C22×Q8×C43C2311yescharacteristic
119C22×D4×C43—21no—
120C22×D4×C43—21no—
121C22×D4×C43—21no—
122C22×D4×C43D411yescharacteristic
123C22×D4×C43D411yescharacteristic
124C22×D4×C43D411yescharacteristic
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C23×C4×C43—21no—
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C22⋊Q8×C43—28no—
132C22⋊Q8×C43—22no—
133C22⋊Q8×C43—22no—
134C22⋊Q8×C43—22no—
135C22⋊Q8×C43D414yes—
136#121×C43—28no—
137#121×C43—28no—
138#121×C43—28no—
139#121×C43—22no—
140#121×C43—22no—
141#121×C43—22no—
142#121×C43D414yes—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43—21no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43—22no—
147C2×C4⋊C4×C43—22no—
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C22⋊C4×C43—21no—
151C2×C22⋊C4×C43—21no—
152C2×C22⋊C4×C43—21no—
153C2×C22⋊C4×C43—21no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157C24×C43C2×D411yescharacteristic
158#41×C43—44no—
159#41×C43—44no—
160#41×C43—44no—
161#41×C43—44no—
162#41×C43—44no—
163#41×C43—44no—
164#41×C43—44no—
165#41×C43—44no—
166C2×Q8×C43—22no—
167C2×Q8×C43—22no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—41no—
174C2×Q8×C43C2×D412yes—
175C2×D4×C43—24no—
176C2×D4×C43—24no—
177C2×D4×C43—22no—
178C2×D4×C43—22no—
179C2×D4×C43—21no—
180C2×D4×C43—22no—
181C2×D4×C43—22no—
182C2×D4×C43—24no—
183C2×D4×C43—22no—
184C2×D4×C43—22no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—41no—
190C2×D4×C43—41no—
191C2×D4×C43—41no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43—81no—
195C2×D4×C43—81no—
196C2×D4×C43—81no—
197C2×D4×C43—81no—
198C2×D4×C43C2×D412yes—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—24no—
208C22×C4×C43—24no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—42no—
219C22×C4×C43—42no—
220C22×C4×C43—81no—
221C22×C4×C43—81no—
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2×D412yes—
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43#4112yes—
228C22×C4×C43#4112yes—
229C22×C4×C43C2411yescharacteristic
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—42no—
235C22×Dic43—81no—
236C22×Dic43—81no—
237C4⋊C4×C43—24no—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—24no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C2×D412yes—
243C4⋊C4×C43C2×D412yes—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—24no—
248C22⋊Dic43—42no—
249C22⋊Dic43—81no—
250C22⋊Dic43—81no—
251C22⋊Dic43—81no—
252C22⋊Dic43—81no—
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—22no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43#12012yes—
302C23×C43#12312yes—
303C23×C43C22×D411yescharacteristic
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—44no—
307Q8×C43—41no—
308Q8×C43—41no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—44no—
312D4×C43—44no—
313D4×C43—44no—
314D4×C43—48no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—84no—
318D4×C43—84no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
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—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—48no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—84no—
349C2×C4×C43#12012yes—
350C2×C4×C43#12312yes—
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C2×#4111yescharacteristic
354C2×C4×C43C2×#4111yescharacteristic
355C2×C4×C43H(5,𝔽2)11yescharacteristic
356C2×C4×C43H(5,𝔽2)11yescharacteristic
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—84no—
370C43⋊C8—41no—
371C43⋊C8—41no—
372C43⋊C8—41no—
373C43⋊C8—41no—
374#24017—431nomaximal, Sylow
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—42no—
397C22×C43—41no—
398C22×C43—42no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43C2×#12011yescharacteristic
404C22×C43C2×#12311yescharacteristic
405C22×C43#53411yescharacteristic
406C22×C43#57611yescharacteristic
407C22×C43#57711yescharacteristic
408C22×C43#57711yescharacteristic
409C22×C43#57811yescharacteristic
410C4×C43—22no—
411C4×C43—22no—
412C4×C43—41no—
413C4×C43—42no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43#54611yescharacteristic
417C4×C43#54611yescharacteristic
418C4×C43#54611yescharacteristic
419C4×C43#54611yescharacteristic
420Dic43—81no—
421Dic43—81no—
422Dic43—81no—
423Dic43—81no—
424C2×#537D4311yescharacteristic
425C2×#485—431no—
426C2×#482—431no—
427#2311—431no—
428#2036—431no—
429#2035—431no—
430#2034—431no—
431#2033—431no—
432#1874—431no—
433#1872—431no—
434#1853—431no—
435#1852—431no—
436#1788—431no—
437#1788—431no—
438#1780—431no—
439C2×C43—42no—
440C2×C43—42no—
441C2×C43—81no—
442C2×C43—82no—
443C2×C43#240511yescharacteristic
444C2×C43#301211yescharacteristic
445C2×C43#301311yescharacteristic
446C2×C43#309811yescharacteristic
447C2×C43#309911yescharacteristic
448C2×C43#319811yescharacteristic
449C2×C43#320111yescharacteristic
450C22×#41C2×D4311yescharacteristic
451C22×#41C2×D4311yescharacteristic
452#537—24no—
453#537—24no—
454C2×C22⋊Q8—21no—
455C2×C22⋊Q8C2×D4311yescharacteristic
456C2×C22⋊Q8C2×D4311yescharacteristic
457C2×#121—21no—
458C2×#121—21no—
459C2×#121—21no—
460C2×#121C2×D4311yescharacteristic
461C2×#121C2×D4311yescharacteristic
462C2×#117—431no—
463C22×C4⋊C4—431no—
464C22×C4⋊C4C2×D4311yescharacteristic
465#485—864no—
466#482—864no—
467C2×#107—431no—
468C2×#107—431no—
469C2×#106—431no—
470C2×#106—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×C22⋊C8—431no—
484C2×C22⋊C8—431no—
485#391—861no—
486#390—861no—
487#386—861no—
488#386—861no—
489#380—431no—
490#380—431no—
491#380—431no—
492#380—431no—
493#340—431no—
494#340—431no—
495#340—431no—
496#340—431no—
497C43#2401711yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C22⋊D4311yescharacteristic
511C22×Q8C22×D4311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C22⋊D4311yescharacteristic
516C22×D4C22⋊D4311yescharacteristic
517C22×D4C22⋊D4311yescharacteristic
518C22×D4C22×D4311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—861no—
522C23×C4C22×D4311yescharacteristic
523C23×C4C22×D4311yescharacteristic
524C23×C4C22×D4311yescharacteristic
525C22×C8—431no—
526C22×C8—431no—
527C22×C8—431no—
528C22×C8—431no—
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8C22⋊D4314yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121C22⋊D4314yes—
541#117—862no—
542#117—862no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—1721no—
554C2×C4⋊C4—1721no—
555C2×C4⋊C4C22×D4311yescharacteristic
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C42—861no—
567#107—862no—
568#107—862no—
569#106—862no—
570#106—862no—
571#103—862no—
572#103—862no—
573#103—1721no—
574#103—1721no—
575#102—862no—
576#102—862no—
577#102—1721no—
578#102—1721no—
579C22⋊C8—862no—
580C22⋊C8—862no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—1721no—
584C22⋊C8—1721no—
585#95—861no—
586#95—861no—
587#95—861no—
588#95—861no—
589C24—21no—
590C24C2×C22⋊D4311yescharacteristic
591C24C2×C22⋊D4311yescharacteristic
592C24C2×C22⋊D4311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×C22⋊D4312yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×C22⋊D4312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—81no—
656C22×C4—81no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—3441no—
662C22×C4—3441no—
663C22×C4—1722no—
664C22×C4#1062190012yes—
665C22×C4#1062190012yes—
666C22×C4C2×C22⋊D4311yescharacteristic
667C22×C4C2×C22⋊D4311yescharacteristic
668C22×C4C2×C22⋊D4312yes—
669C22×C4C2×C22⋊D4312yes—
670C22×C4C2×C22⋊D4311yescharacteristic
671C22×C4C23×D4311yescharacteristic
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
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—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—1722no—
698C4⋊C4C2×C22⋊D4312yes—
699C4⋊C4C2×C22⋊D4312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—3441no—
705C22⋊C4—3441no—
706C22⋊C4—3441no—
707C22⋊C4—3441no—
708C22⋊C4—1722no—
709C42—1722no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#1306329412yes—
737C23#1306330612yes—
738C23C22×C22⋊D4311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—3444no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4#1306329412yes—
798C2×C4#1306330612yes—
799C2×C4C22×C22⋊D4311yescharacteristic
800C2×C4C22×C22⋊D4311yescharacteristic
801C2×C4C2×#1062190011yescharacteristic
802C2×C4C2×#1062190011yescharacteristic
803C2×C4#1306337011yescharacteristic
804C2×C4#1306337011yescharacteristic
805C8—1721no—
806C8—1721no—
807C8—1721no—
808C8—1721no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#1306329411yescharacteristic
838C22C2×#1306330611yescharacteristic
839C22#1458345811yescharacteristic
840C22#1458370211yescharacteristic
841C22#1458370711yescharacteristic
842C22#1458371011yescharacteristic
843C22#1458371411yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—3441no—
851C4—3441no—
852C4—3441no—
853C4—3441no—
854C4#1458354311yescharacteristic
855C4#1458354311yescharacteristic
856C4#1458354311yescharacteristic
857C4#1458354311yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2#1913791811yescharacteristic
863C2#1914389911yescharacteristic
864C2#1914391011yescharacteristic
865C2#1914456911yescharacteristic
866C2#1914458011yescharacteristic
867C2#1914544111yescharacteristic
868C2#1914547111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#537C2
socleC23×C43C22×D4
hypercenterC2×#537D43
hypocenterC43#24017
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#14583237C2semidirect
2. C2×#14583220C2semidirect
3. #19137187C2semidirect
4. #19135795C2semidirect
5. #19135788C2semidirect
6. #19135781C2semidirect
7. #19135774C2semidirect
8. #19134913C2semidirect
9. #19134903C2semidirect
10. #19134788C2semidirect
11. #19134783C2semidirect
12. #19134535C2semidirect
13. #19134535C2semidirect
14. #19134507C2semidirect
497. C43#24017semidirect

Maximal subgroups

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

subgroupindex
C2×#145832372
C2×#145832202
#191371872
#191357952
#191357882
#191357812
#191357742
#191349132
#191349032
#191347882
#191347832
#191345352
#191345072
C2×C43×#5372
#2401743