Finite Group Databasebeta

← #25132213

Subgroups — #25132213

Order 11008.

1566 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583118C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic, complemented
3C2×#14583050C211yesmaximal, characteristic, complemented
4C2×#14582999C211yesmaximal, characteristic, complemented
5#19139517C211yesmaximal, characteristic, complemented
6#19135795C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135603C211yesmaximal, characteristic, complemented
9#19135598C211yesmaximal, characteristic, complemented
10#19135412C211yesmaximal, characteristic, complemented
11#19135394C211yesmaximal, characteristic, complemented
12#19134595C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic, complemented
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic, complemented
21C2×C4×Dic86C2211yescharacteristic, complemented
22#14583118—24no—
23#14583061—24no—
24#14583050—24no—
25#14582999—24no—
26C2×#13063258C2211yescharacteristic, complemented
27C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
28C2×#13063249C2211yescharacteristic, complemented
29C2×#13063249C2211yescharacteristic, complemented
30C2×#13063249C2211yescharacteristic, complemented
31C2×#13063248C2211yescharacteristic, complemented
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
41C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
42C2×#13063236C2211yescharacteristic, complemented
43#14582822—21no—
44#14582822—21no—
45#14582802—21no—
46#14582795—21no—
47#14582769C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic
49#14582759C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52C22×#41×C43C2211yescharacteristic
53C23×D4×C43C2211yescharacteristic
54C43×#546—24no—
55C43×#546—24no—
56C2×#124×C43C2211yescharacteristic
57C2×#123×C43—21no—
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#121×C43—21no—
60C2×#121×C43C2211yescharacteristic
61C2×#120×C43—21no—
62C2×C4×D4×C43C2211yescharacteristic
63C2×C4×D4×C43C2211yescharacteristic
64C22×C22⋊C4×C43—21no—
65C22×Dic86C2311yescharacteristic
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—41no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883—41no—
74C2×#10621883D414yescomplemented
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063304—22no—
80#13063304—22no—
81#13063304—41no—
82#13063304—41no—
83C4×Dic86—22no—
84C4×Dic86—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C4×Dic43—21no—
98#13063258—22no—
99C4⋊(C43⋊C8)—22no—
100#13063249—22no—
101#13063249—22no—
102#13063249—41no—
103#13063248—22no—
104#13063246—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246—41no—
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—41no—
113C22⋊(C43⋊C8)—41no—
114#13063236—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—41no—
123C2×#41×C43—41no—
124C22×Q8×C43C2311yescharacteristic
125C22×D4×C43—21no—
126C22×D4×C43—21no—
127C22×D4×C43—22no—
128C22×D4×C43—22no—
129C22×D4×C43—22no—
130C22×D4×C43—22no—
131C22×D4×C43—21no—
132C22×D4×C43—41no—
133C22×D4×C43—41no—
134C22×D4×C43D411yescharacteristic
135C22×D4×C43C2311yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43—21no—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141#124×C43—22no—
142#124×C43D414yes—
143#123×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146#121×C43—28no—
147#121×C43—22no—
148#121×C43—22no—
149#120×C43—28no—
150C4×D4×C43—22no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C4×D4×C43D414yes—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43D411yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43—28no—
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43—21no—
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×C43—24no—
168C24×C43—21no—
169C24×C43—42no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43—42no—
173C24×C43—81no—
174C24×C43—81no—
175C24×C43C2×D411yescharacteristic
176C24×C43C2×D411yescharacteristic
177#41×C43—44no—
178#41×C43—44no—
179#41×C43—44no—
180#41×C43—44no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43C2×D412yes—
187C2×D4×C43—24no—
188C2×D4×C43—24no—
189C2×D4×C43—24no—
190C2×D4×C43—22no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—22no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—41no—
201C2×D4×C43—42no—
202C2×D4×C43—42no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—44no—
206C2×D4×C43—44no—
207C2×D4×C43—44no—
208C2×D4×C43—44no—
209C2×D4×C43—81no—
210C2×D4×C43—81no—
211C2×D4×C43C2×D412yes—
212C2×D4×C43C2×D412yes—
213C2×D4×C43C2×D412yes—
214C2×D4×C43#4112yes—
215C22×C4×C43—24no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—24no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—42no—
232C22×C4×C43—42no—
233C22×C4×C43—81no—
234C22×C4×C43—81no—
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2411yescharacteristic
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86C2×D412yes—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—22no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C2×D412yes—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—24no—
256C22⋊C4×C43—22no—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—22no—
261C42×C43C2×D412yes—
262C42×C43C2×D412yes—
263C22⋊Dic43—42no—
264C22⋊Dic43—42no—
265C22⋊Dic43—81no—
266C22⋊Dic43—81no—
267#10621885—44no—
268#10621883—28no—
269#10621883—44no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—42no—
277C4⋊Dic43—81no—
278Dic43⋊C4—42no—
279Dic43⋊C4—42no—
280Dic43⋊C4—42no—
281C4×Dic43—42no—
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—21no—
293C2×C43⋊C8C2×D412yes—
294C23×C43—21no—
295C23×C43—22no—
296C23×C43—21no—
297C23×C43—22no—
298C23×C43—21no—
299C23×C43—22no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—22no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—48no—
312C23×C43—48no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—84no—
324C23×C43—84no—
325C23×C43—84no—
326C23×C43—84no—
327C23×C43—84no—
328C23×C43#13712yes—
329C23×C43C22×D411yescharacteristic
330Q8×C43—22no—
331Q8×C43—22no—
332Q8×C43—41no—
333Q8×C43—41no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—22no—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—44no—
340D4×C43—48no—
341D4×C43—48no—
342D4×C43—41no—
343D4×C43—41no—
344D4×C43—84no—
345D4×C43#12114yes—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—22no—
351C2×C4×C43—21no—
352C2×C4×C43—22no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—48no—
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—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—84no—
372C2×C4×C43#12012yes—
373C2×C4×C43#12012yes—
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C22×D411yescharacteristic
377C2×C4×C43C2×#4111yescharacteristic
378C2×C4×C43H(5,𝔽2)11yescharacteristic
379C2×C4×C43H(5,𝔽2)11yescharacteristic
380C2×Dic43—22no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392Dic86—22no—
393Dic86—22no—
394Dic86—41no—
395Dic86—41no—
396C43⋊C8—22no—
397C43⋊C8—41no—
398C43⋊C8—41no—
399C43⋊C8—41no—
400#24259—431nomaximal, Sylow
401C22×C43—24no—
402C22×C43—22no—
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—41no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43—41no—
409C22×C43—42no—
410C22×C43—41no—
411C22×C43—42no—
412C22×C43—41no—
413C22×C43—42no—
414C22×C43—42no—
415C22×C43—41no—
416C22×C43—42no—
417C22×C43—41no—
418C22×C43—42no—
419C22×C43—41no—
420C22×C43—41no—
421C22×C43—42no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—816no—
426C22×C43—81no—
427C22×C43—81no—
428C22×C43—81no—
429C22×C43—81no—
430C22×C43C2×#12011yescharacteristic
431C22×C43D4211yescharacteristic
432C22×C43#54611yescharacteristic
433C22×C43C2×#13711yescharacteristic
434C22×C43#57511yescharacteristic
435C22×C43#57611yescharacteristic
436C22×C43#57711yescharacteristic
437C4×C43—22no—
438C4×C43—22no—
439C4×C43—41no—
440C4×C43—41no—
441C4×C43—42no—
442C4×C43—42no—
443C4×C43C2×#12111yescharacteristic
444C4×C43#53511yescharacteristic
445C4×C43D4211yescharacteristic
446C4×C43#54611yescharacteristic
447Dic43—42no—
448Dic43—81no—
449Dic43—81no—
450Dic43—81no—
451C2×#546D4311yescharacteristic
452C2×#464—431no—
453C2×#452—431no—
454C2×#450—431no—
455C2×#440—431no—
456#2538—431no—
457#2036—431no—
458#2033—431no—
459#2001—431no—
460#2000—431no—
461#1959—431no—
462#1955—431no—
463#1802—431no—
464#1788—431no—
465#1786—431no—
466C2×C43—42no—
467C2×C43—44no—
468C2×C43—81no—
469C2×C43—82no—
470C2×C43#240811yescharacteristic
471C2×C43#300711yescharacteristic
472C2×C43#301211yescharacteristic
473C2×C43#326611yescharacteristic
474C2×C43#326811yescharacteristic
475C2×C43#331111yescharacteristic
476C2×C43#331411yescharacteristic
477C22×#41C2×D4311yescharacteristic
478C23×D4C2×D4311yescharacteristic
479C22×Q16—431no—
480C22×SD16—431no—
481C22×SD16—431no—
482#546—24no—
483#546—24no—
484C2×#124C2×D4311yescharacteristic
485C2×#123—21no—
486C2×C22⋊Q8—431no—
487C2×C22⋊Q8—431no—
488C2×C22⋊Q8C2×D4311yescharacteristic
489C2×#121—21no—
490C2×#121C2×D4311yescharacteristic
491C2×#120—21no—
492C2×C4×Q8—431no—
493C2×C4×D4C2×D4311yescharacteristic
494C2×C4×D4C2×D4311yescharacteristic
495C22×C22⋊C4—21no—
496#464—864no—
497#452—864no—
498#450—864no—
499#440—864no—
500C2×#107—431no—
501C2×C4⋊C8—431no—
502C2×#103—431no—
503C2×#103—431no—
504C2×#103—431no—
505C2×#103—431no—
506C2×#102—431no—
507C2×#102—431no—
508C2×#102—431no—
509C2×#102—431no—
510C2×#102—431no—
511C2×#102—431no—
512C2×C22⋊C8—431no—
513C2×C22⋊C8—431no—
514C2×C22⋊C8—431no—
515C2×C22⋊C8—431no—
516C2×#97—431no—
517#396—861no—
518#396—861no—
519#390—861no—
520#389—861no—
521#384—431no—
522#380—431no—
523#380—431no—
524#340—431no—
525#340—431no—
526C43#2425911yescharacteristic, complemented, Sylow
527C25—21no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8—431no—
535C22×Q8C22×D4311yescharacteristic
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—21no—
543C22×D4—41no—
544C22×D4—41no—
545C22×D4C22⋊D4311yescharacteristic
546C22×D4C22×D4311yescharacteristic
547C22×D4C22×D4311yescharacteristic
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C22×D4311yescharacteristic
551C23×C4C22×D4311yescharacteristic
552C2×Q16—862no—
553C2×Q16—862no—
554C2×Q16—1721no—
555C2×SD16—434no—
556C2×SD16—862no—
557C2×SD16—862no—
558C2×SD16—862no—
559C2×SD16—862no—
560C2×SD16—1721no—
561C22×C8—431no—
562C22×C8—431no—
563C22×C8—431no—
564C22×C8—431no—
565#124—22no—
566#124C22⋊D4314yes—
567#123—28no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—862no—
571C22⋊Q8—862no—
572C22⋊Q8—1721no—
573C22⋊Q8—1721no—
574#121—28no—
575#121—22no—
576#121—22no—
577#120—28no—
578C4×Q8—862no—
579C4×Q8—862no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4C22⋊D4314yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—431no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4C22⋊D4311yescharacteristic
594C2×C4⋊C4C22×D4311yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4C22⋊D4311yescharacteristic
606C2×C22⋊C4C22⋊D4311yescharacteristic
607C2×C42—861no—
608C2×C42C22×D4311yescharacteristic
609#107—862no—
610C4⋊C8—862no—
611#103—862no—
612#103—862no—
613#103—862no—
614#103—1721no—
615#102—862no—
616#102—862no—
617#102—862no—
618#102—862no—
619#102—862no—
620#102—1721no—
621C22⋊C8—862no—
622C22⋊C8—862no—
623C22⋊C8—1721no—
624C22⋊C8—1721no—
625#97—862no—
626#95—861no—
627#95—861no—
628C24—21no—
629C24—24no—
630C24—21no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24C2×C22⋊D4311yescharacteristic
638C24C2×C22⋊D4311yescharacteristic
639#41—44no—
640#41—44no—
641#41—44no—
642#41—44no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—432no—
649C2×Q8—861no—
650C2×Q8—861no—
651C2×Q8—861no—
652C2×Q8—861no—
653C2×Q8—861no—
654C2×Q8C2×C22⋊D4312yes—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—41no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—44no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4D4×D4312yes—
680C2×D4#1062190012yes—
681C2×D4C2×C22⋊D4312yes—
682C2×D4C2×C22⋊D4312yes—
683C22×C4—24no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—81no—
702C22×C4—81no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4C2×C22⋊D4311yescharacteristic
708C22×C4C2×C22⋊D4311yescharacteristic
709C22×C4C2×C22⋊D4311yescharacteristic
710C22×C4C2×C22⋊D4311yescharacteristic
711C22×C4C23×D4311yescharacteristic
712Q16—1724no—
713SD16—868no—
714SD16—1724no—
715C2×C8—432no—
716C2×C8—861no—
717C2×C8—861no—
718C2×C8—861no—
719C2×C8—861no—
720C2×C8—861no—
721C2×C8—861no—
722C2×C8—861no—
723C2×C8—861no—
724C2×C8—861no—
725C2×C8—861no—
726C2×C8—861no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—861no—
735C4⋊C4—861no—
736C4⋊C4—3441no—
737C4⋊C4—1722no—
738C4⋊C4—1722no—
739C4⋊C4—1722no—
740C4⋊C4—1722no—
741C4⋊C4C2×C22⋊D4312yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—3441no—
750C22⋊C4—3441no—
751C22⋊C4—1722no—
752C22⋊C4—1722no—
753C42—1722no—
754C42C2×C22⋊D4312yes—
755C42C2×C22⋊D4312yes—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—22no—
763C23—21no—
764C23—22no—
765C23—22no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—48no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23#1306335512yes—
791C23C22×C22⋊D4311yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—41no—
795Q8—41no—
796Q8—862no—
797Q8—862no—
798Q8—1721no—
799Q8—1721no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—44no—
806D4—48no—
807D4—48no—
808D4—41no—
809D4—41no—
810D4—84no—
811D4#1306329614yes—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—48no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—84no—
838C2×C4—862no—
839C2×C4—1721no—
840C2×C4—1721no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4—1721no—
844C2×C4—1721no—
845C2×C4—1721no—
846C2×C4—1721no—
847C2×C4—1721no—
848C2×C4—1721no—
849C2×C4—1721no—
850C2×C4#1306329412yes—
851C2×C4#1306329412yes—
852C2×C4C2×D4×D4311yescharacteristic
853C2×C4C22×C22⋊D4311yescharacteristic
854C2×C4C22×C22⋊D4311yescharacteristic
855C2×C4C2×#1062190011yescharacteristic
856C2×C4#1306337011yescharacteristic
857C2×C4#1306337011yescharacteristic
858C8—862no—
859C8—1721no—
860C8—1721no—
861C8—1721no—
862C22—22no—
863C22—24no—
864C22—22no—
865C22—22no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—42no—
886C22—816no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22C2×#1306329411yescharacteristic
892C22D4×C22⋊D4311yescharacteristic
893C22#1458354311yescharacteristic
894C22C2×#1306335511yescharacteristic
895C22#1458369711yescharacteristic
896C22#1458370211yescharacteristic
897C22#1458371011yescharacteristic
898C4—22no—
899C4—22no—
900C4—41no—
901C4—41no—
902C4—42no—
903C4—42no—
904C4—3441no—
905C4—3441no—
906C4—3441no—
907C4—1722no—
908C4C2×#1306329611yescharacteristic
909C4#1458346611yescharacteristic
910C4D4×C22⋊D4311yescharacteristic
911C4#1458354311yescharacteristic
912C2—42no—
913C2—44no—
914C2—81no—
915C2—82no—
916C2#1913794511yescharacteristic
917C2#1914385511yescharacteristic
918C2#1914389911yescharacteristic
919C2#1914610111yescharacteristic
920C2#1914613111yescharacteristic
921C2#1914663111yescharacteristic
922C2#1914667611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#546C2
socleC23×C43C22×D4
hypercenterC2×#546D43
hypocenterC43#24259
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#14583118C2semidirect
2. C2×#14583061C2semidirect
3. C2×#14583050C2semidirect
4. C2×#14582999C2semidirect
5. #19139517C2semidirect
6. #19135795C2semidirect
7. #19135774C2semidirect
8. #19135603C2semidirect
9. #19135598C2semidirect
10. #19135412C2semidirect
11. #19135394C2semidirect
12. #19134595C2semidirect
13. #19134535C2semidirect
14. #19134526C2semidirect
16. C22×#10621885C22semidirect
20. C2×#13063304C22semidirect
21. C2×C4×Dic86C22semidirect
26. C2×#13063258C22semidirect
27. C2×C4⋊(C43⋊C8)C22semidirect
28. C2×#13063249C22semidirect
29. C2×#13063249C22semidirect
30. C2×#13063249C22semidirect
31. C2×#13063248C22semidirect
40. C2×C22⋊(C43⋊C8)C22semidirect
41. C2×C22⋊(C43⋊C8)C22semidirect
42. C2×#13063236C22semidirect
47. #14582769C22semidirect
49. #14582759C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
74. C2×#10621883D4semidirect
526. C43#24259semidirect

Maximal subgroups

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

subgroupindex
C2×#145831182
C2×#145830612
C2×#145830502
C2×#145829992
#191395172
#191357952
#191357742
#191356032
#191355982
#191354122
#191353942
#191345952
#191345352
#191345262
C2×C43×#5462
#2425943