Finite Group Databasebeta

← #25134230

Subgroups — #25134230

Order 11008.

1508 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic86C211yesmaximal, characteristic, complemented
2C2×#14583126C211yesmaximal, characteristic, complemented
3C2×#14583037C211yesmaximal, characteristic, complemented
4C2×#14583037C211yesmaximal, characteristic, complemented
5C22×#13063248C211yesmaximal, characteristic, complemented
6#19135841C211yesmaximal, characteristic, complemented
7#19135791C211yesmaximal, characteristic, complemented
8#19135677C211yesmaximal, characteristic, complemented
9#19135598C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic, complemented
11#19134902C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic, complemented
13#19134862C211yesmaximal, characteristic, complemented
14#19134529C211yesmaximal, characteristic, complemented
15C43×#2416C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C23×C43⋊C8C2211yescharacteristic
22D4×Dic86—24no—
23D4×Dic86—24no—
24C2×#13063325C2211yescharacteristic
25C2×#13063324—21no—
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×#13063302—21no—
29C2×#13063302—21no—
30C2×C4×Dic86C2211yescharacteristic
31C2×D4×Dic43—21no—
32#14583126—24no—
33#14583037—24no—
34#14583037—24no—
35C2×#13063256C2211yescharacteristic
36C2×#13063248—24no—
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063248C2211yescharacteristic
45C2×#13063248C2211yescharacteristic
46C2×#13063246C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48C2×C22⋊(C43⋊C8)C2211yescharacteristic
49C2×C22⋊(C43⋊C8)C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582654C2211yescharacteristic
54C2×#121×C43—21no—
55C2×#121×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C43×#396—21no—
60C43×#394—21no—
61C43×#390C2211yescharacteristic
62C43×#389C2211yescharacteristic
63C43×#386—21no—
64C43×#380C2211yescharacteristic
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—22no—
68C22×Dic86—21no—
69C22×Dic86—21no—
70C22×Dic86—22no—
71C22×Dic86—22no—
72C22×Dic86—22no—
73C22×Dic86—22no—
74C22×Dic86—41no—
75C22×Dic86—41no—
76C22×Dic86—41no—
77C22×Dic86—41no—
78C22×Dic86D414yescomplemented
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C22×Dic86C2311yescharacteristic
82C23×Dic43—21no—
83C23×Dic43—21no—
84C2×#10621883—22no—
85C2×#10621883—22no—
86C2×#10621883—22no—
87C2×#10621883—22no—
88C2×#10621883—22no—
89C2×#10621883—22no—
90C2×#10621883—41no—
91C2×#10621883—41no—
92C2×#10621883—41no—
93C22×C43⋊C8—22no—
94C22×C43⋊C8—22no—
95C22×C43⋊C8—41no—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100#13063325—22no—
101#13063325—22no—
102#13063324—28no—
103#13063304—22no—
104#13063304—22no—
105#13063304—22no—
106#13063304D414yescomplemented
107#13063302—28no—
108#13063302—28no—
109C4×Dic86—22no—
110C4×Dic86—22no—
111D4×Dic43—28no—
112C2×C4⋊Dic43—21no—
113C2×C4⋊Dic43—21no—
114C2×C4⋊Dic43C2311yescharacteristic
115C2×Dic43⋊C4—21no—
116C2×Dic43⋊C4—21no—
117C2×Dic43⋊C4—21no—
118C2×C22⋊Dic43—21no—
119C2×C22⋊Dic43—21no—
120C2×C4×Dic43—21no—
121#13063256—22no—
122#13063248—22no—
123#13063248—22no—
124#13063248—22no—
125#13063248—22no—
126#13063248—22no—
127#13063248—22no—
128#13063248—22no—
129#13063248—41no—
130#13063248D414yescomplemented
131#13063246—22no—
132C22⋊(C43⋊C8)—22no—
133C22⋊(C43⋊C8)—22no—
134C22⋊(C43⋊C8)—41no—
135C22×D4×C43—21no—
136C22×D4×C43—21no—
137C22×D4×C43D411yescharacteristic
138C22×D4×C43C2311yescharacteristic
139C23×C4×C43—21no—
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142#121×C43—22no—
143#121×C43—22no—
144#121×C43—22no—
145#121×C43—41no—
146#121×C43—44no—
147C4×D4×C43—22no—
148C4×D4×C43—22no—
149C2×C4⋊C4×C43—22no—
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43—21no—
152C2×C4⋊C4×C43—41no—
153C2×C4⋊C4×C43D411yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C4⋊C4×C43C2311yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43—21no—
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43D411yescharacteristic
163C2×C22⋊C4×C43D411yescharacteristic
164C2×C42×C43C2311yescharacteristic
165#95×C43—21no—
166#95×C43—21no—
167C24×C43—21no—
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170C2×D4×C43—22no—
171C2×D4×C43—22no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43—81no—
184C2×D4×C43SD1614yescomplemented
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
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—42no—
199C22×C4×C43—42no—
200C22×C4×C43—81no—
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2×D412yes—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2411yescharacteristic
208C22×Dic43—24no—
209C22×Dic43—24no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—42no—
215C22×Dic43—42no—
216C22×Dic43—42no—
217C22×Dic43—42no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—28no—
230C2×Dic86—24no—
231C2×Dic86—24no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—44no—
235C2×Dic86—44no—
236C2×Dic86—44no—
237C2×Dic86—44no—
238C2×Dic86—44no—
239C2×Dic86—44no—
240C2×Dic86—42no—
241C2×Dic86—42no—
242C2×Dic86—42no—
243C2×Dic86—42no—
244C2×Dic86—44no—
245C2×Dic86C2×D412yes—
246C2×Dic86C2×D412yes—
247C2×Dic86C2×D412yes—
248C2×Dic86C2×D412yes—
249C2×Dic86#4112yes—
250C4⋊C4×C43—22no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—42no—
257C4⋊C4×C43—42no—
258C4⋊C4×C43C2×D412yes—
259C22⋊C4×C43—22no—
260C22⋊C4×C43—22no—
261C22⋊C4×C43—42no—
262C22⋊C4×C43—42no—
263C22⋊C4×C43—42no—
264C22⋊C4×C43—42no—
265C22⋊C4×C43—81no—
266C42×C43—21no—
267C42×C43—21no—
268C22⋊Dic43—24no—
269C22⋊Dic43—24no—
270#10621883—44no—
271#10621883—44no—
272#10621883—44no—
273C4⋊Dic43—24no—
274C4⋊Dic43—24no—
275C4⋊Dic43—21no—
276C4⋊Dic43C2×D412yes—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280C4×Dic43—24no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—44no—
293C2×C43⋊C8C2×D412yes—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43#12012yes—
312C23×C43C2×SD1612yes—
313C23×C43C2×SD1612yes—
314C23×C43#13712yes—
315C23×C43C22×D411yescharacteristic
316D4×C43—28no—
317D4×C43—41no—
318D4×C43—41no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—84no—
322D4×C43—84no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—22no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
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—41no—
349C2×C4×C43—41no—
350C2×C4×C43—84no—
351C2×C4×C43#12012yes—
352C2×C4×C43C2×SD1612yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
358C2×C4×C43H(5,𝔽2)11yescharacteristic
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—48no—
366C2×Dic43—48no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373Dic86—22no—
374Dic86—22no—
375Dic86—22no—
376Dic86—22no—
377Dic86—22no—
378Dic86—22no—
379Dic86—22no—
380Dic86—48no—
381Dic86—48no—
382Dic86—41no—
383Dic86—41no—
384Dic86—41no—
385Dic86—41no—
386Dic86#12114yescomplemented
387C43⋊C8—22no—
388C43⋊C8—41no—
389C43⋊C8—41no—
390C43⋊C8—41no—
391#24429—431nomaximal, Sylow
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43—41no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43—81no—
408C22×C43—81no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43#44814yescomplemented
413C22×C43C2×#12011yescharacteristic
414C22×C43D4211yescharacteristic
415C22×C43#54611yescharacteristic
416C22×C43C22×SD1611yescharacteristic
417C22×C43C2×#13711yescharacteristic
418C22×C43#57711yescharacteristic
419C22×C43#57811yescharacteristic
420C4×C43—22no—
421C4×C43—22no—
422C4×C43—41no—
423C4×C43—41no—
424C4×C43—42no—
425C4×C43—81no—
426C4×C43—81no—
427C4×C43C2×#12111yescharacteristic
428C4×C43#53411yescharacteristic
429C4×C43D4211yescharacteristic
430C4×C43#54611yescharacteristic
431Dic43—24no—
432Dic43—42no—
433Dic43—42no—
434Dic43—42no—
435C2×D4×Q8—431no—
436C2×#465—431no—
437C2×#448—431no—
438C2×#448—431no—
439C22×#103—431no—
440#2416D4311yescharacteristic
441#2043—431no—
442#2035—431no—
443#2013—431no—
444#2000—431no—
445#1880—431no—
446#1872—431no—
447#1869—431no—
448#1865—431no—
449#1787—431no—
450C2×C43—24no—
451C2×C43—42no—
452C2×C43—161no—
453C2×C43#241011yescharacteristic
454C2×C43C2×#44811yescharacteristic
455C2×C43#301311yescharacteristic
456C2×C43#327011yescharacteristic
457C2×C43D4×SD1611yescharacteristic
458C2×C43#329811yescharacteristic
459C2×C43#332011yescharacteristic
460C23×Q8—431no—
461C23×Q8—431no—
462C22×SD16—431no—
463C22×SD16—431no—
464C22×SD16—431no—
465C23×C8—431no—
466D4×Q8—864no—
467D4×Q8—864no—
468C2×C4⋊Q8—431no—
469C2×C4⋊Q8—861no—
470C2×C22⋊Q8—431no—
471C2×C22⋊Q8—431no—
472C2×C22⋊Q8—861no—
473C2×C22⋊Q8—861no—
474C2×#121—21no—
475C2×#121C2×D4311yescharacteristic
476C2×#121C2×D4311yescharacteristic
477C2×C4×Q8—431no—
478C2×C4×D4—861no—
479C2×C4×D4C2×D4311yescharacteristic
480C22×C4⋊C4C2×D4311yescharacteristic
481#465—864no—
482#448—864no—
483#448—864no—
484C2×#106—431no—
485C2×#103—431no—
486C2×#103—431no—
487C2×#103—431no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103—431no—
491C2×#103—431no—
492C2×#103—431no—
493C2×#103—431no—
494C2×#103—864no—
495C2×#102—431no—
496C2×C22⋊C8—431no—
497C2×C22⋊C8—431no—
498C2×C22⋊C8—431no—
499#396—21no—
500#394—21no—
501#390C2×D4311yescharacteristic
502#389C2×D4311yescharacteristic
503#386—21no—
504#380C2×D4311yescharacteristic
505#340—431no—
506#340—431no—
507#336—431no—
508#336—431no—
509C43#2442911yescharacteristic, complemented, Sylow
510C22×Q8—434no—
511C22×Q8—431no—
512C22×Q8—431no—
513C22×Q8—431no—
514C22×Q8—862no—
515C22×Q8—862no—
516C22×Q8—862no—
517C22×Q8—862no—
518C22×Q8—862no—
519C22×Q8—862no—
520C22×Q8—862no—
521C22×Q8—861no—
522C22×Q8—861no—
523C22×Q8—1721no—
524C22×Q8—1721no—
525C22×Q8—1721no—
526C22×Q8—1721no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4C22⋊D4311yescharacteristic
530C22×D4C22×D4311yescharacteristic
531C23×C4—21no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535C23×C4C22×D4311yescharacteristic
536C2×SD16—862no—
537C2×SD16—862no—
538C2×SD16—862no—
539C2×SD16—862no—
540C2×SD16—862no—
541C2×SD16—862no—
542C2×SD16—1721no—
543C2×SD16—1721no—
544C2×SD16—1721no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—431no—
548C22×C8—431no—
549C22×C8—862no—
550C22×C8—862no—
551C22×C8—1721no—
552C4⋊Q8—862no—
553C4⋊Q8—862no—
554C4⋊Q8—868no—
555C22⋊Q8—434no—
556C22⋊Q8—868no—
557C22⋊Q8—868no—
558C22⋊Q8—862no—
559C22⋊Q8—862no—
560C22⋊Q8—862no—
561#121—22no—
562#121—22no—
563#121—22no—
564#121—41no—
565#121—44no—
566C4×Q8—862no—
567C4×Q8—862no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—868no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4C22⋊D4311yescharacteristic
582C2×C4⋊C4C22×D4311yescharacteristic
583C2×C4⋊C4C22×D4311yescharacteristic
584C2×C4⋊C4C22×D4311yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4C22⋊D4311yescharacteristic
593C2×C22⋊C4C22⋊D4311yescharacteristic
594C2×C42—861no—
595C2×C42C22×D4311yescharacteristic
596#106—862no—
597#103—434no—
598#103—862no—
599#103—862no—
600#103—862no—
601#103—862no—
602#103—862no—
603#103—862no—
604#103—862no—
605#103—1721no—
606#102—862no—
607C22⋊C8—862no—
608C22⋊C8—862no—
609C22⋊C8—1721no—
610#95—21no—
611#95—21no—
612C24—21no—
613C24C2×C22⋊D4311yescharacteristic
614C24C2×C22⋊D4311yescharacteristic
615C2×Q8—432no—
616C2×Q8—432no—
617C2×Q8—432no—
618C2×Q8—432no—
619C2×Q8—432no—
620C2×Q8—864no—
621C2×Q8—868no—
622C2×Q8—864no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×Q8—861no—
627C2×Q8—861no—
628C2×Q8—861no—
629C2×Q8—861no—
630C2×Q8—861no—
631C2×Q8—861no—
632C2×Q8—861no—
633C2×Q8—861no—
634C2×Q8—861no—
635C2×Q8—861no—
636C2×Q8—1722no—
637C2×Q8—1722no—
638C2×Q8—1722no—
639C2×Q8—1722no—
640C2×Q8—1724no—
641C2×Q8—1724no—
642C2×Q8—1724no—
643C2×Q8—1724no—
644C2×Q8—1724no—
645C2×Q8—1724no—
646C2×Q8—1724no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—81no—
661C2×D4#1062188314yescomplemented
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—81no—
678C22×C4—861no—
679C22×C4—864no—
680C22×C4—864no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—1722no—
685C22×C4—1722no—
686C22×C4—1722no—
687C22×C4—1722no—
688C22×C4D4×D4312yes—
689C22×C4D4×D4312yes—
690C22×C4C2×C22⋊D4311yescharacteristic
691C22×C4C2×C22⋊D4311yescharacteristic
692C22×C4C2×C22⋊D4311yescharacteristic
693C22×C4C2×C22⋊D4311yescharacteristic
694C22×C4C23×D4311yescharacteristic
695SD16—1724no—
696SD16—1724no—
697SD16—1724no—
698C2×C8—432no—
699C2×C8—861no—
700C2×C8—861no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—1724no—
711C4⋊C4—22no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—432no—
720C4⋊C4—864no—
721C4⋊C4—864no—
722C4⋊C4—864no—
723C4⋊C4—864no—
724C4⋊C4—864no—
725C4⋊C4—861no—
726C4⋊C4D4×D4312yes—
727C22⋊C4—22no—
728C22⋊C4—22no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4—81no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C42—21no—
737C42—21no—
738C42—864no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23#1306329312yes—
757C23C2×#1062188312yes—
758C23C2×#1062188312yes—
759C23#1306335512yes—
760C23C22×C22⋊D4311yescharacteristic
761Q8—434no—
762Q8—862no—
763Q8—862no—
764Q8—862no—
765Q8—862no—
766Q8—862no—
767Q8—862no—
768Q8—862no—
769Q8—1728no—
770Q8—1728no—
771Q8—1721no—
772Q8—1721no—
773Q8—1721no—
774Q8—1721no—
775D4—28no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—84no—
781D4—84no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—84no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—862no—
815C2×C4—862no—
816C2×C4—1728no—
817C2×C4—1728no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4#1306329312yes—
825C2×C4C2×#1062188312yes—
826C2×C4C2×D4×D4311yescharacteristic
827C2×C4C2×D4×D4311yescharacteristic
828C2×C4C2×D4×D4311yescharacteristic
829C2×C4#41×D4311yescharacteristic
830C2×C4#1306337011yescharacteristic
831C2×C4#1306337111yescharacteristic
832C8—862no—
833C8—1721no—
834C8—1721no—
835C8—1721no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22#1458303714yescomplemented
857C22C2×#1306329311yescharacteristic
858C22D4×C22⋊D4311yescharacteristic
859C22#1458353711yescharacteristic
860C22C22×#1062188311yescharacteristic
861C22C2×#1306335511yescharacteristic
862C22#1458371011yescharacteristic
863C22#1458371411yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—41no—
868C4—41no—
869C4—81no—
870C4—81no—
871C4—864no—
872C4—1722no—
873C4—1722no—
874C4—1722no—
875C4#121×D4311yescharacteristic
876C4#1458345711yescharacteristic
877C4#1458353311yescharacteristic
878C4#1458353811yescharacteristic
879C2—24no—
880C2—42no—
881C2—161no—
882C2#1913796611yescharacteristic
883C2C2×#1458303711yescharacteristic
884C2#1914390711yescharacteristic
885C2#1914616111yescharacteristic
886C2D4×#1062188311yescharacteristic
887C2#1914645411yescharacteristic
888C2#1914676011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2416C2
socleC23×C43C22×D4
hypercenter#2416D43
hypocenterC43#24429
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic86C2semidirect
2. C2×#14583126C2semidirect
3. C2×#14583037C2semidirect
4. C2×#14583037C2semidirect
5. C22×#13063248C2semidirect
6. #19135841C2semidirect
7. #19135791C2semidirect
8. #19135677C2semidirect
9. #19135598C2semidirect
10. #19134953C2semidirect
11. #19134902C2semidirect
12. #19134888C2semidirect
13. #19134862C2semidirect
14. #19134529C2semidirect
78. C22×Dic86D4semidirect
106. #13063304D4semidirect
130. #13063248D4semidirect
184. C2×D4×C43SD16semidirect
386. Dic86#121semidirect
412. C22×C43#448semidirect
509. C43#24429semidirect
661. C2×D4#10621883semidirect
856. C22#14583037semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic862
C2×#145831262
C2×#145830372
C22×#130632482
#191358412
#191357912
#191356772
#191355982
#191349532
#191349022
#191348882
#191348622
#191345292
C43×#24162
#2442943