Finite Group Databasebeta

← #25129554

Subgroups — #25129554

Order 11008.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583220C211yesmaximal, characteristic, complemented
2C2×#14582895C211yesmaximal, characteristic, complemented
3#19138892C211yesmaximal, characteristic, complemented
4#19135826C211yesmaximal, characteristic, complemented
5#19135826C211yesmaximal, characteristic, complemented
6#19135781C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134888C211yesmaximal, characteristic, complemented
10#19134863C211yesmaximal, characteristic, complemented
11#19134849C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#550C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18#14583220—24no—
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21#14582895—24no—
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37#14582827—21no—
38#14582813—21no—
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582787—21no—
42#14582780—21no—
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C22×#41×C43C2211yescharacteristic
51C22×#41×C43C2211yescharacteristic
52C43×#550—24no—
53C43×#550—24no—
54C2×#127×C43—21no—
55C2×#127×C43C2211yescharacteristic
56C2×#121×C43—21no—
57C2×#121×C43—21no—
58C2×#121×C43C2211yescharacteristic
59C2×#121×C43C2211yescharacteristic
60C2×C4×Q8×C43C2211yescharacteristic
61C2×C4×D4×C43—21no—
62C2×C4×D4×C43C2211yescharacteristic
63C22×C43⋊C8—22no—
64C22×C43⋊C8—41no—
65C22×C43⋊C8—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063284—22no—
71#13063284—22no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—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#13063256—22no—
85#13063249—22no—
86#13063249—22no—
87#13063249—22no—
88#13063249—22no—
89#13063246—22no—
90#13063246—22no—
91#13063246—22no—
92#13063246—22no—
93#13063246—41no—
94#13063246—41no—
95#13063246—41no—
96#13063246—41no—
97C22⋊(C43⋊C8)—22no—
98C22⋊(C43⋊C8)—41no—
99C22⋊(C43⋊C8)—41no—
100C43⋊#95—21no—
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—41no—
113C2×#41×C43—41no—
114C2×#41×C43—41no—
115C2×#41×C43—41no—
116C2×#41×C43D414yes—
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43—21no—
119C22×D4×C43—21no—
120C22×D4×C43—21no—
121C22×D4×C43—21no—
122C22×D4×C43—21no—
123C22×D4×C43—21no—
124C22×D4×C43D411yescharacteristic
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43—21no—
128C23×C4×C43—21no—
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131#127×C43—28no—
132#127×C43—22no—
133#127×C43—22no—
134#121×C43—28no—
135#121×C43—28no—
136#121×C43—22no—
137#121×C43—22no—
138#121×C43—22no—
139#121×C43D414yes—
140C4×Q8×C43—22no—
141C4×Q8×C43—22no—
142C4×D4×C43—28no—
143C4×D4×C43—22no—
144C4×D4×C43—22no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43D411yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C42×C43—21no—
153C2×C42×C43C2311yescharacteristic
154C24×C43—21no—
155C24×C43—21no—
156C24×C43C2×D411yescharacteristic
157C24×C43C2×D411yescharacteristic
158#41×C43—28no—
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—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43C2×D412yes—
170C2×Q8×C43#4112yes—
171C2×Q8×C43#4112yes—
172C2×D4×C43—24no—
173C2×D4×C43—24no—
174C2×D4×C43—24no—
175C2×D4×C43—24no—
176C2×D4×C43—22no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—22no—
180C2×D4×C43—24no—
181C2×D4×C43—24no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—41no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43—42no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—81no—
198C2×D4×C43—81no—
199C2×D4×C43—81no—
200C2×D4×C43—81no—
201C2×D4×C43—81no—
202C2×D4×C43—81no—
203C2×D4×C43C2×D412yes—
204C2×D4×C43C2×D412yes—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—24no—
210C22×C4×C43—24no—
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—21no—
219C22×C4×C43—42no—
220C22×C4×C43—42no—
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×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—22no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2×D412yes—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—22no—
241C22⋊C4×C43—22no—
242C42×C43—24no—
243C42×C43—21no—
244C42×C43—21no—
245C22⋊Dic43—42no—
246C22⋊Dic43—42no—
247C22⋊Dic43—81no—
248C22⋊Dic43—81no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257Dic43⋊C4—42no—
258Dic43⋊C4—81no—
259C4×Dic43—42no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
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—44no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43#12012yes—
301C23×C43C22×D411yescharacteristic
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43#12314yes—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—44no—
311D4×C43—48no—
312D4×C43—48no—
313D4×C43—48no—
314D4×C43—41no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—84no—
319D4×C43—84no—
320D4×C43—84no—
321C2×C4×C43—21no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—48no—
340C2×C4×C43—48no—
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#12012yes—
348C2×C4×C43#13512yes—
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C2×#4111yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43H(5,𝔽2)11yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C2×Dic43—41no—
356C2×Dic43—41no—
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—
367C43⋊C8—41no—
368C43⋊C8—41no—
369C43⋊C8—41no—
370C43⋊C8—41no—
371#24034—431nomaximal, Sylow
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—41no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—41no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43—81no—
400C22×C43C2×#12011yescharacteristic
401C22×C43#54611yescharacteristic
402C22×C43#54611yescharacteristic
403C22×C43C2×#13511yescharacteristic
404C22×C43#57511yescharacteristic
405C22×C43#57611yescharacteristic
406C22×C43#57711yescharacteristic
407C4×C43—22no—
408C4×C43—24no—
409C4×C43—22no—
410C4×C43—41no—
411C4×C43—41no—
412C4×C43—42no—
413C4×C43C2×#12311yescharacteristic
414C4×C43#53411yescharacteristic
415C4×C43#54611yescharacteristic
416C4×C43#54611yescharacteristic
417Dic43—81no—
418Dic43—81no—
419Dic43—81no—
420Dic43—81no—
421C2×#550D4311yescharacteristic
422C2×#482—431no—
423C2×#416—431no—
424#2485—431no—
425#2041—431no—
426#2041—431no—
427#2034—431no—
428#2033—431no—
429#1893—431no—
430#1869—431no—
431#1865—431no—
432#1863—431no—
433#1788—431no—
434#1788—431no—
435#1788—431no—
436C2×C43—42no—
437C2×C43—81no—
438C2×C43—82no—
439C2×C43—82no—
440C2×C43#240511yescharacteristic
441C2×C43#300211yescharacteristic
442C2×C43#301211yescharacteristic
443C2×C43#330411yescharacteristic
444C2×C43#330511yescharacteristic
445C2×C43#330911yescharacteristic
446C2×C43#331711yescharacteristic
447C22×#41C2×D4311yescharacteristic
448C22×#41C2×D4311yescharacteristic
449C23×C8—431no—
450#550—24no—
451#550—24no—
452C2×#127—21no—
453C2×#127C2×D4311yescharacteristic
454C2×#121—21no—
455C2×#121—21no—
456C2×#121C2×D4311yescharacteristic
457C2×#121C2×D4311yescharacteristic
458C2×C4×Q8C2×D4311yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C2×D4311yescharacteristic
461C2×#117—431no—
462#482—864no—
463C2×#107—431no—
464C2×#106—431no—
465#416—864no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#102—431no—
471C2×#102—431no—
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×C22⋊C8—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481#397—861no—
482#394—861no—
483#389—431no—
484#389—431no—
485#388—861no—
486#387—861no—
487#380—431no—
488#380—431no—
489#380—431no—
490#340—431no—
491#340—431no—
492#336—431no—
493#336—431no—
494C43#2403411yescharacteristic, complemented, Sylow
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C22⋊D4314yes—
507C22×Q8C22×D4311yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C22⋊D4311yescharacteristic
515C22×D4C22×D4311yescharacteristic
516C22×D4C22×D4311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C22×D4311yescharacteristic
520C23×C4C22×D4311yescharacteristic
521C22×C8—431no—
522C22×C8—431no—
523C22×C8—431no—
524C22×C8—431no—
525C22×C8—862no—
526C22×C8—1721no—
527C22×C8—1721no—
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121C22⋊D4314yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—862no—
543#117—862no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4C22⋊D4311yescharacteristic
552C2×C4⋊C4C22×D4311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4C22⋊D4311yescharacteristic
560C2×C22⋊C4C22⋊D4311yescharacteristic
561C2×C42—21no—
562C2×C42—861no—
563C2×C42C22×D4311yescharacteristic
564#107—862no—
565#106—862no—
566#103—862no—
567#103—862no—
568#103—862no—
569#103—862no—
570#102—862no—
571#102—862no—
572#102—862no—
573#102—862no—
574#102—1721no—
575#102—1721no—
576#102—1721no—
577#102—1721no—
578C22⋊C8—862no—
579C22⋊C8—1721no—
580C22⋊C8—1721no—
581#95—861no—
582#95—861no—
583#95—861no—
584#95—861no—
585#95—861no—
586C24—21no—
587C24—21no—
588C24C2×C22⋊D4311yescharacteristic
589C24C2×C22⋊D4311yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8#1062190012yes—
602C2×Q8#1062190012yes—
603C2×Q8C2×C22⋊D4312yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×C22⋊D4312yes—
636C2×D4C2×C22⋊D4312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4C2×C22⋊D4311yescharacteristic
660C22×C4C2×C22⋊D4311yescharacteristic
661C22×C4C2×C22⋊D4311yescharacteristic
662C22×C4C2×C22⋊D4312yes—
663C22×C4C2×C22⋊D4312yes—
664C22×C4C2×C22⋊D4311yescharacteristic
665C22×C4C23×D4311yescharacteristic
666C2×C8—861no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—861no—
670C2×C8—861no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—1724no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—3441no—
691C4⋊C4—1722no—
692C4⋊C4C2×C22⋊D4312yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—3441no—
698C22⋊C4—3441no—
699C22⋊C4—1722no—
700C22⋊C4—1722no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—1722no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#1306329412yes—
733C23C22×C22⋊D4311yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#1306330614yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
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—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4#1306329412yes—
792C2×C4#1306334512yes—
793C2×C4C22×C22⋊D4311yescharacteristic
794C2×C4C22×C22⋊D4311yescharacteristic
795C2×C4C2×#1062190011yescharacteristic
796C2×C4C2×#1062190011yescharacteristic
797C2×C4#1306337011yescharacteristic
798C2×C4#1306337011yescharacteristic
799C8—1721no—
800C8—1721no—
801C8—1721no—
802C8—1721no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—42no—
814C22—42no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#1306329411yescharacteristic
832C22#1458354311yescharacteristic
833C22#1458354311yescharacteristic
834C22C2×#1306334511yescharacteristic
835C22#1458369711yescharacteristic
836C22#1458370211yescharacteristic
837C22#1458371011yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—3441no—
845C4—3441no—
846C4—3441no—
847C4—3441no—
848C4C2×#1306330611yescharacteristic
849C4#1458345811yescharacteristic
850C4#1458354311yescharacteristic
851C4#1458354311yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2#1913791811yescharacteristic
857C2#1914381311yescharacteristic
858C2#1914389911yescharacteristic
859C2#1914653411yescharacteristic
860C2#1914654511yescharacteristic
861C2#1914660111yescharacteristic
862C2#1914672111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#550C2
socleC23×C43C22×D4
hypercenterC2×#550D43
hypocenterC43#24034
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#14583220C2semidirect
2. C2×#14582895C2semidirect
3. #19138892C2semidirect
4. #19135826C2semidirect
5. #19135826C2semidirect
6. #19135781C2semidirect
7. #19135774C2semidirect
8. #19135024C2semidirect
9. #19134888C2semidirect
10. #19134863C2semidirect
11. #19134849C2semidirect
12. #19134535C2semidirect
13. #19134535C2semidirect
14. #19134535C2semidirect
494. C43#24034semidirect

Maximal subgroups

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

subgroupindex
C2×#145832202
C2×#145828952
#191388922
#191358262
#191357812
#191357742
#191350242
#191348882
#191348632
#191348492
#191345352
C2×C43×#5502
#2403443