Finite Group Databasebeta

← #25140517

Subgroups — #25140517

Order 11008.

1148 conjugacy classes of subgroups.

The subgroup lattice has 774 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#19138098C211yesmaximal, characteristic, complemented
4#19136116C211yesmaximal, characteristic, complemented
5#19136032C211yesmaximal, characteristic, complemented
6#19135912C211yesmaximal, characteristic, complemented
7#19135798C211yesmaximal, characteristic, complemented
8#19135281C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic, complemented
12#19134842C211yesmaximal, characteristic, complemented
13#19134605C211yesmaximal, 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×#13063258C2211yescharacteristic, 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#14582840—21no—
37#14582827—21no—
38#14582805C2211yescharacteristic, complemented
39#14582797C2211yescharacteristic, complemented
40#14582793—21no—
41#14582781—21no—
42#14582765C2211yescharacteristic, 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⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85#13063258—41no—
86#13063256—22no—
87C4⋊(C43⋊C8)—41no—
88#13063248—22no—
89#13063248—41no—
90#13063246—22no—
91#13063246—22no—
92#13063246—22no—
93#13063246—22no—
94#13063246—22no—
95#13063246—41no—
96C22⋊(C43⋊C8)—22no—
97C22⋊(C43⋊C8)—41no—
98C4×C43⋊C8—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
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—22no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—42no—
205C22⋊C4×C43—42no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—81no—
210C22⋊C4×C43—81no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217#10621883—28no—
218#10621883—44no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225Dic43⋊C4—42no—
226Dic43⋊C4—42no—
227Dic43⋊C4—42no—
228C4×Dic43—42no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
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⋊C8C2×D412yes—
241C23×C43—21no—
242C23×C43—22no—
243C23×C43—21no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—22no—
251C23×C43—48no—
252C23×C43—48no—
253C23×C43—41no—
254C23×C43—41no—
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—84no—
264C23×C43—84no—
265C23×C43—84no—
266C23×C43—84no—
267C23×C43—84no—
268C23×C43#13512yes—
269C23×C43C22×D411yescharacteristic
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—48no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43#12314yes—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
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—41no—
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—84no—
304C2×C4×C43—84no—
305C2×C4×C43AGL(1,ℤ/8)12yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×Dic43—22no—
313C2×Dic43—41no—
314C2×Dic43—41no—
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—
324Dic86—22no—
325Dic86—22no—
326Dic86—41no—
327Dic86—41no—
328C43⋊C8—22no—
329C43⋊C8—41no—
330C43⋊C8—41no—
331C43⋊C8—41no—
332#24905—431nomaximal, Sylow
333C22×C43—22no—
334C22×C43—24no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—42no—
338C22×C43—41no—
339C22×C43—42no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—816no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43#52511yescharacteristic
356C22×C43D4211yescharacteristic
357C22×C43#54611yescharacteristic
358C22×C43C2×#13511yescharacteristic
359C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C43#57711yescharacteristic
361C22×C43#57711yescharacteristic
362C4×C43—22no—
363C4×C43—41no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43—81no—
368C4×C43—81no—
369C4×C43C2×#12311yescharacteristic
370C4×C43#53811yescharacteristic
371C4×C43#54611yescharacteristic
372C4×C43#55111yescharacteristic
373Dic43—42no—
374Dic43—81no—
375Dic43—81no—
376Dic43—81no—
377C2×#450—431no—
378C2×C4×SD16—431no—
379#2421—431no—
380D4×C22⋊C4D4311yescharacteristic
381#2092—431no—
382#2077—431no—
383#2055—431no—
384#2036—431no—
385#1934—431no—
386#1923—431no—
387#1880—431no—
388#1877—431no—
389#1862—431no—
390#1804—431no—
391#1786—431no—
392C2×C43—42no—
393C2×C43—44no—
394C2×C43—82no—
395C2×C43#241811yescharacteristic
396C2×C43#310511yescharacteristic
397C2×C43#312311yescharacteristic
398C2×C43#326511yescharacteristic
399C2×C43#328211yescharacteristic
400C2×C43#329611yescharacteristic
401C2×C43#332411yescharacteristic
402C23×D4C2×D4311yescharacteristic
403C22×SD16—431no—
404C22×SD16—431no—
405C2×C22⋊Q8—431no—
406C2×C4×Q8—431no—
407C2×C4×D4C2×D4311yescharacteristic
408C2×C4×D4C2×D4311yescharacteristic
409C22×C22⋊C4—21no—
410#450—864no—
411C4×SD16—864no—
412C2×#107—431no—
413C2×#106—431no—
414C2×C4⋊C8—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×C22⋊C8—431no—
424C2×C22⋊C8—431no—
425C2×C4×C8—431no—
426#400—861no—
427#397—861no—
428#391—431no—
429#390C2×D4311yescharacteristic
430#390C2×D4311yescharacteristic
431#389—431no—
432#388—861no—
433#387—861no—
434#386—21no—
435#386—21no—
436#382—431no—
437#380—431no—
438#380C2×D4311yescharacteristic
439#379—21no—
440C4×C22⋊C4C2×D4311yescharacteristic
441#340—431no—
442#340—431no—
443#340—431no—
444#340—431no—
445#336—431no—
446#336—431no—
447C43#2490511yescharacteristic, complemented, Sylow
448C25—21no—
449C22×Q8—431no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—21no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4C22×D4311yescharacteristic
458C22×D4C22×D4311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C22×D4311yescharacteristic
462C2×SD16—434no—
463C2×SD16—862no—
464C2×SD16—862no—
465C2×SD16—862no—
466C2×SD16—862no—
467C2×SD16—1721no—
468C22×C8—431no—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8—431no—
472C22⋊Q8—862no—
473C22⋊Q8—1721no—
474C4×Q8—862no—
475C4×Q8—1721no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—41no—
479C4×D4—41no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—44no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4C22⋊D4311yescharacteristic
499C2×C22⋊C4C22⋊D4311yescharacteristic
500C2×C42—861no—
501C2×C42C22×D4311yescharacteristic
502C2×C42C22×D4311yescharacteristic
503#107—1721no—
504#106—862no—
505C4⋊C8—1721no—
506#103—862no—
507#103—1721no—
508#102—862no—
509#102—862no—
510#102—862no—
511#102—862no—
512#102—862no—
513#102—1721no—
514C22⋊C8—862no—
515C22⋊C8—1721no—
516C4×C8—862no—
517#95—21no—
518#95—861no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95—861no—
523#95—861no—
524#95C22⋊D4311yescharacteristic
525#95C22⋊D4311yescharacteristic
526C24—21no—
527C24—24no—
528C24—21no—
529C24—42no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—81no—
534C24—81no—
535C24C2×C22⋊D4311yescharacteristic
536C2×Q8—432no—
537C2×Q8—861no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4#1062189812yes—
558C2×D4#1062189812yes—
559C2×D4D4×D4312yes—
560C2×D4#1062190012yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4C2×C22⋊D4311yescharacteristic
580C22×C4C2×C22⋊D4311yescharacteristic
581C22×C4C2×C22⋊D4311yescharacteristic
582C22×C4C2×C22⋊D4311yescharacteristic
583C22×C4C2×C22⋊D4311yescharacteristic
584C22×C4C23×D4311yescharacteristic
585SD16—868no—
586SD16—1724no—
587C2×C8—432no—
588C2×C8—861no—
589C2×C8—861no—
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—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—1722no—
610C4⋊C4—1722no—
611C4⋊C4—1722no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—81no—
620C22⋊C4—81no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—1722no—
628C23—21no—
629C23—22no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—48no—
639C23—48no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23#1306334512yes—
656C23C22×C22⋊D4311yescharacteristic
657Q8—862no—
658Q8—862no—
659Q8—1721no—
660Q8—1721no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4#1306330714yes—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
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—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4—862no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
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#1306335112yes—
709C2×C4C2×D4×D4311yescharacteristic
710C2×C4C2×#1062190011yescharacteristic
711C2×C4C2×#1062189811yescharacteristic
712C2×C4C2×#1062189811yescharacteristic
713C2×C4#1306337011yescharacteristic
714C2×C4#1306337011yescharacteristic
715C8—862no—
716C8—1721no—
717C8—1721no—
718C8—1721no—
719C22—24no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—816no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22#1458341011yescharacteristic
742C22D4×C22⋊D4311yescharacteristic
743C22#1458354311yescharacteristic
744C22C2×#1306334511yescharacteristic
745C22C2×#1306335111yescharacteristic
746C22#1458371011yescharacteristic
747C22#1458371011yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—81no—
754C4—81no—
755C4—3441no—
756C4—3441no—
757C4—3441no—
758C4—1722no—
759C4C2×#1306330711yescharacteristic
760C4#1458348711yescharacteristic
761C4#1458353911yescharacteristic
762C4#1458357511yescharacteristic
763C2—42no—
764C2—44no—
765C2—82no—
766C2#1913805711yescharacteristic
767C2#1914464211yescharacteristic
768C2#1914484711yescharacteristic
769C2#1914608611yescharacteristic
770C2#1914629811yescharacteristic
771C2#1914643011yescharacteristic
772C2#1914682611yescharacteristic
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#24905
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. #19138098C2semidirect
4. #19136116C2semidirect
5. #19136032C2semidirect
6. #19135912C2semidirect
7. #19135798C2semidirect
8. #19135281C2semidirect
9. #19135203C2semidirect
10. #19134953C2semidirect
11. #19134929C2semidirect
12. #19134842C2semidirect
13. #19134605C2semidirect
19. C2×C4×Dic86C22semidirect
22. C2×#13063258C22semidirect
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. #14582765C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
447. C43#24905semidirect

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
#191380982
#191361162
#191360322
#191359122
#191357982
#191352812
#191352032
#191349532
#191349292
#191348422
#191346052
#191345262
D4×C22⋊C4×C432
#2490543