Finite Group Databasebeta

← #25140457

Subgroups — #25140457

Order 11008.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583050C211yesmaximal, characteristic
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3#19138120C211yesmaximal, characteristic, complemented
4#19136128C211yesmaximal, characteristic, complemented
5#19136031C211yesmaximal, characteristic, complemented
6#19135912C211yesmaximal, characteristic, complemented
7#19135791C211yesmaximal, characteristic, complemented
8#19135281C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic, complemented
12#19134856C211yesmaximal, characteristic, complemented
13#19134595C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic
15D4×C22⋊C4×C43C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic, complemented
20#14583050—24no—
21C4×#10621883—24no—
22C2×#13063256C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
25C2×#13063248C2211yescharacteristic, complemented
26C2×#13063248C2211yescharacteristic, complemented
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic, complemented
36#14582835—21no—
37#14582833—21no—
38#14582805C2211yescharacteristic, complemented
39#14582797C2211yescharacteristic, complemented
40#14582792—21no—
41#14582782—21no—
42#14582769C2211yescharacteristic, complemented
43#14582759C2211yescharacteristic
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C23×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C22×C22⋊C4×C43—21no—
54C43×#390C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#386—21no—
57C43×#386—21no—
58C43×#380C2211yescharacteristic
59C43×#379—21no—
60C4×C22⋊C4×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883—41no—
67C2×#10621883D414yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063304—22no—
73#13063304—41no—
74C4×Dic86—22no—
75C4×Dic86—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87#13063256—22no—
88#13063256—41no—
89C4⋊(C43⋊C8)—41no—
90#13063248—22no—
91#13063248—41no—
92#13063246—22no—
93#13063246—22no—
94#13063246—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—41no—
98C22⋊(C43⋊C8)—22no—
99C22⋊(C43⋊C8)—41no—
100C4×C43⋊C8—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C25×C43—21no—
106C22×D4×C43—22no—
107C22×D4×C43—22no—
108C22×D4×C43—22no—
109C22×D4×C43—22no—
110C22×D4×C43—21no—
111C22×D4×C43—41no—
112C22×D4×C43—41no—
113C22×D4×C43C2311yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C23×C4×C43—21no—
116C23×C4×C43—21no—
117C23×C4×C43C2311yescharacteristic
118C4×D4×C43—22no—
119C4×D4×C43—22no—
120C4×D4×C43—41no—
121C4×D4×C43—41no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—44no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43D411yescharacteristic
138#95×C43D411yescharacteristic
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—21no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C2×D4×C43—24no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—44no—
161C2×D4×C43—44no—
162C2×D4×C43—44no—
163C2×D4×C43—44no—
164C2×D4×C43C2×D412yes—
165C2×D4×C43#4112yes—
166C2×D4×C43#4112yes—
167C2×D4×C43#4112yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43—42no—
179C22×C4×C43—42no—
180C22×C4×C43—81no—
181C22×C4×C43—81no—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86C2×D412yes—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—42no—
204C22⋊C4×C43—42no—
205C22⋊C4×C43—42no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—81no—
209C22⋊C4×C43—81no—
210C22⋊C4×C43SD1614yescomplemented
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C22⋊Dic43—42no—
216C22⋊Dic43—81no—
217#10621883—28no—
218#10621883—44no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—42no—
226C4⋊Dic43—81no—
227Dic43⋊C4—42no—
228Dic43⋊C4—42no—
229Dic43⋊C4—81no—
230C4×Dic43—42no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8C2×D412yes—
243C23×C43—21no—
244C23×C43—22no—
245C23×C43—21no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—22no—
253C23×C43—48no—
254C23×C43—48no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—84no—
266C23×C43—84no—
267C23×C43—84no—
268C23×C43—84no—
269C23×C43—84no—
270C23×C43C2×SD1612yes—
271C23×C43C22×D411yescharacteristic
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—48no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43#12314yes—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—84no—
305C2×C4×C43—84no—
306C2×C4×C43C2×SD1612yes—
307C2×C4×C43C2×SD1612yes—
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C2×Dic43—22no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326Dic86—22no—
327Dic86—22no—
328Dic86—41no—
329Dic86—41no—
330C43⋊C8—22no—
331C43⋊C8—41no—
332C43⋊C8—41no—
333C43⋊C8—41no—
334#24901—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—24no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—42no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—816no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43#52511yescharacteristic
358C22×C43D4211yescharacteristic
359C22×C43#54611yescharacteristic
360C22×C43C22×SD1611yescharacteristic
361C22×C43#57511yescharacteristic
362C22×C43#57611yescharacteristic
363C22×C43#57711yescharacteristic
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—41no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43—81no—
370C4×C43—81no—
371C4×C43C2×#12311yescharacteristic
372C4×C43#53811yescharacteristic
373C4×C43#54611yescharacteristic
374C4×C43#55111yescharacteristic
375Dic43—42no—
376Dic43—81no—
377Dic43—81no—
378Dic43—81no—
379C2×#450—431no—
380C2×C4×SD16—431no—
381#2423—431no—
382D4×C22⋊C4D4311yescharacteristic
383#2094—431no—
384#2077—431no—
385#2055—431no—
386#2035—431no—
387#1934—431no—
388#1923—431no—
389#1880—431no—
390#1877—431no—
391#1864—431no—
392#1802—431no—
393#1786—431no—
394C2×C43—42no—
395C2×C43—44no—
396C2×C43—82no—
397C2×C43#241811yescharacteristic
398C2×C43#310111yescharacteristic
399C2×C43#311811yescharacteristic
400C2×C43#326811yescharacteristic
401C2×C43D4×SD1611yescharacteristic
402C2×C43#329511yescharacteristic
403C2×C43#332311yescharacteristic
404C23×D4C2×D4311yescharacteristic
405C22×SD16—431no—
406C22×SD16—431no—
407C2×C22⋊Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×D4C2×D4311yescharacteristic
410C2×C4×D4C2×D4311yescharacteristic
411C22×C22⋊C4—21no—
412#450—864no—
413C4×SD16—864no—
414C2×#106—431no—
415C2×#106—431no—
416C2×C4⋊C8—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×C22⋊C8—431no—
426C2×C22⋊C8—431no—
427C2×C4×C8—431no—
428#399—861no—
429#398—861no—
430#391—431no—
431#390C2×D4311yescharacteristic
432#390C2×D4311yescharacteristic
433#389—431no—
434#388—861no—
435#387—861no—
436#386—21no—
437#386—21no—
438#384—431no—
439#380—431no—
440#380C2×D4311yescharacteristic
441#379—21no—
442C4×C22⋊C4C2×D4311yescharacteristic
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#336—431no—
448#336—431no—
449C43#2490111yescharacteristic, complemented, Sylow
450C25—21no—
451C22×Q8—431no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C22×D4311yescharacteristic
460C22×D4C22×D4311yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C22×D4311yescharacteristic
464C2×SD16—434no—
465C2×SD16—862no—
466C2×SD16—862no—
467C2×SD16—862no—
468C2×SD16—862no—
469C2×SD16—1721no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—431no—
474C22⋊Q8—862no—
475C22⋊Q8—1721no—
476C4×Q8—862no—
477C4×Q8—1721no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—44no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4C22⋊D4311yescharacteristic
503C2×C22⋊C4C22⋊D4311yescharacteristic
504C2×C42—861no—
505C2×C42C22×D4311yescharacteristic
506C2×C42C22×D4311yescharacteristic
507#106—862no—
508#106—1721no—
509C4⋊C8—1721no—
510#103—862no—
511#103—1721no—
512#102—862no—
513#102—862no—
514#102—862no—
515#102—862no—
516#102—862no—
517#102—1721no—
518C22⋊C8—862no—
519C22⋊C8—1721no—
520C4×C8—862no—
521#95—21no—
522#95—861no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95C22⋊D4311yescharacteristic
527#95C22⋊D4311yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×C22⋊D4311yescharacteristic
538C2×Q8—432no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4#1062189812yes—
560C2×D4#1062189812yes—
561C2×D4D4×D4312yes—
562C2×D4#1062190012yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4C2×C22⋊D4311yescharacteristic
582C22×C4C2×C22⋊D4311yescharacteristic
583C22×C4C2×C22⋊D4311yescharacteristic
584C22×C4C2×C22⋊D4311yescharacteristic
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C23×D4311yescharacteristic
587SD16—868no—
588SD16—1724no—
589C2×C8—432no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—3441no—
612C4⋊C4—3441no—
613C4⋊C4—1722no—
614C4⋊C4—1722no—
615C4⋊C4—1722no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—3441no—
625C22⋊C4—1722no—
626C22⋊C4#1062188314yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—1722no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×#1062188312yes—
660C23C22×C22⋊D4311yescharacteristic
661Q8—862no—
662Q8—862no—
663Q8—1721no—
664Q8—1721no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#1306330714yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—862no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4C2×#1062188312yes—
712C2×C4C2×#1062188312yes—
713C2×C4C2×D4×D4311yescharacteristic
714C2×C4C2×#1062190011yescharacteristic
715C2×C4C2×#1062189811yescharacteristic
716C2×C4C2×#1062189811yescharacteristic
717C2×C4#1306337011yescharacteristic
718C2×C4#1306337011yescharacteristic
719C8—862no—
720C8—1721no—
721C8—1721no—
722C8—1721no—
723C22—24no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#1458341011yescharacteristic
746C22D4×C22⋊D4311yescharacteristic
747C22#1458354311yescharacteristic
748C22C22×#1062188311yescharacteristic
749C22#1458369711yescharacteristic
750C22#1458370211yescharacteristic
751C22#1458371011yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—81no—
758C4—81no—
759C4—3441no—
760C4—3441no—
761C4—3441no—
762C4—1722no—
763C4C2×#1306330711yescharacteristic
764C4#1458348711yescharacteristic
765C4#1458353911yescharacteristic
766C4#1458357511yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2#1913805711yescharacteristic
771C2#1914460311yescharacteristic
772C2#1914477911yescharacteristic
773C2#1914613111yescharacteristic
774C2D4×#1062188311yescharacteristic
775C2#1914641911yescharacteristic
776C2#1914681111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenterD4×C22⋊C4D43
hypocenterC43#24901
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621883C2semidirect
3. #19138120C2semidirect
4. #19136128C2semidirect
5. #19136031C2semidirect
6. #19135912C2semidirect
7. #19135791C2semidirect
8. #19135281C2semidirect
9. #19135203C2semidirect
10. #19134953C2semidirect
11. #19134929C2semidirect
12. #19134856C2semidirect
13. #19134595C2semidirect
19. C2×C4×Dic86C22semidirect
22. C2×#13063256C22semidirect
23. C2×#13063256C22semidirect
24. C2×C4⋊(C43⋊C8)C22semidirect
25. C2×#13063248C22semidirect
26. C2×#13063248C22semidirect
35. C2×C4×C43⋊C8C22semidirect
38. #14582805C22semidirect
39. #14582797C22semidirect
42. #14582769C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
210. C22⋊C4×C43SD16semidirect
449. C43#24901semidirect
626. C22⋊C4#10621883semidirect

Maximal subgroups

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

subgroupindex
C2×#145830502
C2×C4×#106218832
#191381202
#191361282
#191360312
#191359122
#191357912
#191352812
#191352032
#191349532
#191349292
#191348562
#191345952
#191345262
D4×C22⋊C4×C432
#2490143