Finite Group Databasebeta

← #25134368

Subgroups — #25134368

Order 11008.

1498 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583130C211yesmaximal, characteristic, complemented
2C2×#14583044C211yesmaximal, characteristic, complemented
3C2×#14583044C211yesmaximal, characteristic, complemented
4C2×#14582895C211yesmaximal, characteristic, complemented
5#19138013C211yesmaximal, characteristic, complemented
6#19135838C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135678C211yesmaximal, characteristic, complemented
9#19135596C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134908C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#547C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23#14583130—24no—
24#14583044—24no—
25#14583044—24no—
26C2×#13063256C2211yescharacteristic
27#14582895—24no—
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41#14582814—21no—
42#14582807—21no—
43#14582801C2211yescharacteristic
44#14582799—21no—
45#14582797C2211yescharacteristic
46#14582789—21no—
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C22×#41×C43C2211yescharacteristic
54C43×#547—24no—
55C43×#547—24no—
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#123×C43—21no—
58C2×#123×C43—21no—
59C2×C22⋊Q8×C43C2211yescharacteristic
60C2×C22⋊Q8×C43C2211yescharacteristic
61C2×#121×C43—21no—
62C2×C4×D4×C43C2211yescharacteristic
63C2×C4×D4×C43C2211yescharacteristic
64C22×C4⋊C4×C43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621884—41no—
72C2×#10621884—41no—
73C2×#10621884—41no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—22no—
77C22×C43⋊C8—22no—
78C22×C43⋊C8—22no—
79C22×C43⋊C8—41no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84#13063299—22no—
85#13063299—22no—
86#13063299—22no—
87#13063299—41no—
88#13063284—22no—
89#13063284—41no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101#13063256—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—22no—
106#13063249—22no—
107#13063249—41no—
108#13063246—22no—
109#13063246—22no—
110#13063246D414yescomplemented
111#13063245—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—41no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C2×#41×C43—22no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43—41no—
125C2×#41×C43—41no—
126C2×#41×C43—41no—
127C2×#41×C43—41no—
128C2×#41×C43D414yescomplemented
129C22×Q8×C43C2311yescharacteristic
130C22×Q8×C43C2311yescharacteristic
131C22×D4×C43—21no—
132C22×D4×C43—21no—
133C22×D4×C43D411yescharacteristic
134C22×D4×C43C2311yescharacteristic
135C23×C4×C43—21no—
136C23×C4×C43—21no—
137C23×C4×C43—21no—
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C4⋊Q8×C43—22no—
141C4⋊Q8×C43—22no—
142#123×C43—28no—
143#123×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43D414yescomplemented
148#121×C43—28no—
149C4×D4×C43—22no—
150C4×D4×C43—22no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C2×C4⋊C4×C43—28no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43D411yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43D411yescharacteristic
164C2×C22⋊C4×C43D411yescharacteristic
165C2×C42×C43C2311yescharacteristic
166C24×C43—21no—
167C24×C43C2×D411yescharacteristic
168C24×C43C2×D411yescharacteristic
169C23×D43—21no—
170#41×C43—28no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175#41×C43—44no—
176#41×C43—44no—
177#41×C43—44no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43C2×D412yes—
189C2×Q8×C43C2×D412yes—
190C2×D4×C43—24no—
191C2×D4×C43—22no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—22no—
196C2×D4×C43—24no—
197C2×D4×C43—41no—
198C2×D4×C43—42no—
199C2×D4×C43—42no—
200C2×D4×C43—42no—
201C2×D4×C43—42no—
202C2×D4×C43C2×D412yes—
203C2×D4×C43C2×D412yes—
204C2×D4×C43#4112yes—
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—24no—
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—21no—
220C22×C4×C43—21no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43—42no—
224C22×C4×C43—42no—
225C22×C4×C43—42no—
226C22×C4×C43—42no—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C2×C22⋊D43—42no—
235C2×C22⋊D43—42no—
236C2×C22⋊D43—42no—
237C2×C22⋊D43—81no—
238C2×C22⋊D43—81no—
239C2×C22⋊D43—81no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C2×D172—21no—
244C2×D172—21no—
245C2×D172—21no—
246C2×D172—21no—
247C2×D172—21no—
248C2×D172—21no—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—22no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C2×D412yes—
256C22⋊C4×C43—24no—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—22no—
261C42×C43—21no—
262C42×C43—21no—
263C22⋊Dic43—42no—
264C22⋊Dic43—81no—
265#10621884—44no—
266#10621884—44no—
267#10621882—44no—
268(C2×D43)⋊C4—42no—
269(C2×D43)⋊C4—42no—
270(C2×D43)⋊C4—42no—
271(C2×D43)⋊C4—81no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43C2×D412yes—
278Dic43⋊C4—81no—
279C4×Dic43—42no—
280C2×C43⋊C8—21no—
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—44no—
292C2×C43⋊C8C2×D412yes—
293C23×C43—22no—
294C23×C43—21no—
295C23×C43—22no—
296C23×C43—21no—
297C23×C43—22no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43#12012yes—
314C23×C43C22×D411yescharacteristic
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—41no—
321C22×D43—41no—
322Q8×C43—22no—
323Q8×C43—22no—
324Q8×C43—22no—
325Q8×C43—22no—
326Q8×C43—41no—
327Q8×C43—41no—
328Q8×C43—41no—
329Q8×C43—41no—
330D4×C43—22no—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—44no—
334D4×C43—48no—
335D4×C43—48no—
336D4×C43#12114yes—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—21no—
346C2×C4×C43—22no—
347C2×C4×C43—21no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—48no—
355C2×C4×C43—48no—
356C2×C4×C43—48no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43#12012yes—
368C2×C4×C43#13512yes—
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C2×C4×C43C22×D411yescharacteristic
372C2×C4×C43C2×#4111yescharacteristic
373C2×C4×C43H(5,𝔽2)11yescharacteristic
374C2×C4×C43H(5,𝔽2)11yescharacteristic
375C22⋊D43—84no—
376C22⋊D43—84no—
377C2×Dic43—22no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386D172—41no—
387D172—41no—
388D172—41no—
389D172—41no—
390C43⋊C8—22no—
391C43⋊C8—41no—
392C43⋊C8—41no—
393C43⋊C8—41no—
394#24438—431nomaximal, Sylow
395C22×C43—24no—
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—41no—
402C22×C43—42no—
403C22×C43—41no—
404C22×C43—42no—
405C22×C43—41no—
406C22×C43—42no—
407C22×C43—41no—
408C22×C43—42no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43C2×#12011yescharacteristic
417C22×C43D4211yescharacteristic
418C22×C43#54611yescharacteristic
419C22×C43C2×#13511yescharacteristic
420C22×C43#57511yescharacteristic
421C22×C43#57711yescharacteristic
422C22×C43#57711yescharacteristic
423C2×D43—81no—
424C2×D43—81no—
425C2×D43—81no—
426C2×D43—81no—
427C2×D43—81no—
428C2×D43—81no—
429C2×D43—81no—
430C4×C43—22no—
431C4×C43—22no—
432C4×C43—41no—
433C4×C43—42no—
434C4×C43—42no—
435C4×C43—42no—
436C4×C43—41no—
437C4×C43C2×#12111yescharacteristic
438C4×C43#53411yescharacteristic
439C4×C43D4211yescharacteristic
440C4×C43#54611yescharacteristic
441Dic43—42no—
442Dic43—81no—
443Dic43—81no—
444C2×#547D4311yescharacteristic, complemented
445C2×#465—431no—
446C2×#449—431no—
447C2×#449—431no—
448C2×#416—431no—
449#2414—431no—
450#2043—431no—
451#2035—431no—
452#2013—431no—
453#2000—431no—
454#1879—431no—
455#1873—431no—
456#1869—431no—
457#1864—431no—
458#1788—431no—
459C2×C43—42no—
460C2×C43—44no—
461C2×C43—81no—
462C2×C43#241011yescharacteristic
463C2×C43#300211yescharacteristic
464C2×C43#301011yescharacteristic
465C2×C43#326711yescharacteristic
466C2×C43#328411yescharacteristic
467C2×C43#330311yescharacteristic
468C2×C43#330711yescharacteristic
469D43—161no—
470C22×#41C2×D4311yescharacteristic
471C22×#41C2×D4311yescharacteristic
472C22×SD16—431no—
473C22×SD16—431no—
474C22×D8—431no—
475C23×C8—431no—
476#547—24no—
477#547—24no—
478C2×C4⋊Q8C2×D4311yescharacteristic
479C2×#123—21no—
480C2×#123—21no—
481C2×C22⋊Q8C2×D4311yescharacteristic
482C2×C22⋊Q8C2×D4311yescharacteristic
483C2×#121—21no—
484C2×#121—431no—
485C2×#121—431no—
486C2×C4×D4C2×D4311yescharacteristic
487C2×C4×D4C2×D4311yescharacteristic
488C2×#117—431no—
489C22×C4⋊C4—21no—
490#465—864no—
491#449—864no—
492#449—864no—
493C2×#106—431no—
494#416—864no—
495C2×#103—431no—
496C2×#103—431no—
497C2×#103—431no—
498C2×#103—431no—
499C2×#103—431no—
500C2×#103—431no—
501C2×#102—431no—
502C2×#102—431no—
503C2×#102—431no—
504C2×#102—431no—
505C2×C22⋊C8—431no—
506C2×C22⋊C8—431no—
507C2×C22⋊C8—431no—
508#394—861no—
509#392—861no—
510#390—431no—
511#390—861no—
512#389—431no—
513#388—861no—
514#380—431no—
515#340—431no—
516#340—431no—
517#336—431no—
518#336—431no—
519C43#2443811yescharacteristic, complemented, Sylow
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41C22⋊D4314yescomplemented
532C22×Q8C22×D4311yescharacteristic
533C22×Q8C22×D4311yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—431no—
537C22×D4—861no—
538C22×D4—861no—
539C22×D4C22⋊D4311yescharacteristic
540C22×D4C22×D4311yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C22×D4311yescharacteristic
545C23×C4C22×D4311yescharacteristic
546C2×SD16—862no—
547C2×SD16—862no—
548C2×SD16—862no—
549C2×SD16—1721no—
550C2×SD16—1721no—
551C2×SD16—1721no—
552C2×D8—862no—
553C2×D8—862no—
554C2×D8—862no—
555C22×C8—431no—
556C22×C8—431no—
557C22×C8—431no—
558C22×C8—431no—
559C22×C8—862no—
560C22×C8—862no—
561C22×C8—1721no—
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564#123—28no—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8C22⋊D4314yescomplemented
570#121—28no—
571#121—862no—
572#121—862no—
573#121—862no—
574#121—1721no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579#117—862no—
580#117—1721no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4C22⋊D4311yescharacteristic
591C2×C4⋊C4C22×D4311yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—861no—
596C2×C22⋊C4—861no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4C22⋊D4311yescharacteristic
602C2×C22⋊C4C22⋊D4311yescharacteristic
603C2×C42—861no—
604C2×C42C22×D4311yescharacteristic
605#106—862no—
606#103—862no—
607#103—862no—
608#103—862no—
609#103—862no—
610#103—862no—
611#103—1721no—
612#102—434no—
613#102—862no—
614#102—862no—
615#102—862no—
616C22⋊C8—862no—
617C22⋊C8—862no—
618C22⋊C8—1721no—
619#95—861no—
620#95—861no—
621C24—21no—
622C24—861no—
623C24C2×C22⋊D4311yescharacteristic
624C24C2×C22⋊D4311yescharacteristic
625#41—28no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×C22⋊D4312yes—
644C2×Q8C2×C22⋊D4312yes—
645C2×D4—24no—
646C2×D4—22no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—41no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—861no—
658C2×D4—861no—
659C2×D4—861no—
660C2×D4—861no—
661C2×D4—861no—
662C2×D4—861no—
663C2×D4—3441no—
664C2×D4—3441no—
665C2×D4—3441no—
666C2×D4—1722no—
667C2×D4—1722no—
668C2×D4—1722no—
669C2×D4D4×D4312yes—
670C2×D4#1062190012yes—
671C2×D4C2×C22⋊D4312yes—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4C2×C22⋊D4311yescharacteristic
698C22×C4C2×C22⋊D4311yescharacteristic
699C22×C4C2×C22⋊D4311yescharacteristic
700C22×C4C2×C22⋊D4312yes—
701C22×C4C2×C22⋊D4312yes—
702C22×C4C2×C22⋊D4311yescharacteristic
703C22×C4C23×D4311yescharacteristic
704SD16—1724no—
705SD16—1724no—
706D8—1724no—
707C2×C8—432no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—861no—
713C2×C8—861no—
714C2×C8—861no—
715C2×C8—861no—
716C2×C8—861no—
717C2×C8—861no—
718C2×C8—861no—
719C2×C8—1724no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—22no—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—432no—
727C4⋊C4—861no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—3441no—
733C4⋊C4C2×C22⋊D4312yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—3441no—
740C22⋊C4—3441no—
741C22⋊C4—1722no—
742C22⋊C4—1722no—
743C22⋊C4—1722no—
744C22⋊C4—1722no—
745C42—21no—
746C42—21no—
747C42—1722no—
748C23—22no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—22no—
755C23—21no—
756C23—22no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—1721no—
769C23—1721no—
770C23—1721no—
771C23—1721no—
772C23—1721no—
773C23—1721no—
774C23—1721no—
775C23#1306329412yes—
776C23C22×C22⋊D4311yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—48no—
790D4—48no—
791D4—3444no—
792D4—3444no—
793D4—1721no—
794D4—1721no—
795D4—1721no—
796D4—1721no—
797D4#1306329714yes—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—48no—
816C2×C4—48no—
817C2×C4—48no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—862no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4—1721no—
832C2×C4—1721no—
833C2×C4—1721no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4#1306329412yes—
838C2×C4#1306334512yes—
839C2×C4C2×D4×D4311yescharacteristic
840C2×C4C22×C22⋊D4311yescharacteristic
841C2×C4C22×C22⋊D4311yescharacteristic
842C2×C4C2×#1062190011yescharacteristic
843C2×C4#1306337011yescharacteristic
844C2×C4#1306337011yescharacteristic
845C8—862no—
846C8—1721no—
847C8—1721no—
848C8—1721no—
849C22—22no—
850C22—22no—
851C22—24no—
852C22—22no—
853C22—41no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—3441no—
871C22—3441no—
872C22—3441no—
873C22—3441no—
874C22—3441no—
875C22—3441no—
876C22—3441no—
877C22C2×#1306329411yescharacteristic
878C22D4×C22⋊D4311yescharacteristic
879C22#1458354311yescharacteristic
880C22C2×#1306334511yescharacteristic
881C22#1458369711yescharacteristic
882C22#1458370711yescharacteristic
883C22#1458370711yescharacteristic
884C4—22no—
885C4—22no—
886C4—42no—
887C4—41no—
888C4—42no—
889C4—42no—
890C4—41no—
891C4—3441no—
892C4—3441no—
893C4—1722no—
894C4C2×#1306329711yescharacteristic
895C4#1458345811yescharacteristic
896C4D4×C22⋊D4311yescharacteristic
897C4#1458354311yescharacteristic
898C2—42no—
899C2—44no—
900C2—81no—
901C2—6881no—
902C2#1913796911yescharacteristic
903C2#1914381311yescharacteristic
904C2#1914388111yescharacteristic
905C2#1914612111yescharacteristic
906C2#1914632111yescharacteristic
907C2#1914652311yescharacteristic
908C2#1914657111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#547C2
socleC23×C43C22×D4
hypercenterC2×#547D43
hypocenterC43#24438
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#14583130C2semidirect
2. C2×#14583044C2semidirect
3. C2×#14583044C2semidirect
4. C2×#14582895C2semidirect
5. #19138013C2semidirect
6. #19135838C2semidirect
7. #19135788C2semidirect
8. #19135678C2semidirect
9. #19135596C2semidirect
10. #19134943C2semidirect
11. #19134908C2semidirect
12. #19134888C2semidirect
13. #19134856C2semidirect
14. #19134535C2semidirect
15. C2×C43×#547C2semidirect
110. #13063246D4semidirect
128. C2×#41×C43D4semidirect
147. C22⋊Q8×C43D4semidirect
444. C2×#547D43semidirect
519. C43#24438semidirect
531. C2×#41C22⋊D43semidirect
569. C22⋊Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831302
C2×#145830442
C2×#145828952
#191380132
#191358382
#191357882
#191356782
#191355962
#191349432
#191349082
#191348882
#191348562
#191345352
C2×C43×#5472
#2443843