Finite Group Databasebeta

← #25130601

Subgroups — #25130601

Order 11008.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583601C211yesmaximal, characteristic
2C2×#14583204C211yesmaximal, characteristic, complemented
3C2×SD16×Dic43C211yesmaximal, characteristic, complemented
4#19139502C211yesmaximal, characteristic, complemented
5#19135783C211yesmaximal, characteristic, complemented
6#19135774C211yesmaximal, characteristic, complemented
7#19135595C211yesmaximal, characteristic, complemented
8#19135558C211yesmaximal, characteristic, complemented
9#19135387C211yesmaximal, characteristic, complemented
10#19134904C211yesmaximal, characteristic, complemented
11#19134903C211yesmaximal, characteristic, complemented
12#19134795C211yesmaximal, characteristic, complemented
13#19134790C211yesmaximal, characteristic, complemented
14#19134603C211yesmaximal, characteristic, complemented
15C43×#2000C211yesmaximal, characteristic, complemented
16#14583601—24no—
17#14583601—24no—
18C2×#13063318—21no—
19C2×#13063316C2211yescharacteristic
20C2×#13063309—21no—
21C2×#13063301C2211yescharacteristic
22C2×#13063297—21no—
23C2×#13063296C2211yescharacteristic
24C2×Q8×Dic43C2211yescharacteristic
25C2×D4×Dic43—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30#14583204—24no—
31SD16×Dic43—24no—
32C2×#13063258C2211yescharacteristic
33C2×#13063257C2211yescharacteristic
34C2×#13063257C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44#14582832—21no—
45#14582815—21no—
46#14582793—21no—
47#14582789—21no—
48#14582764C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43D411yescharacteristic
65C23×Dic43—21no—
66C23×Dic43—21no—
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063318—28no—
71#13063316—22no—
72#13063316D414yes—
73#13063309—28no—
74#13063301—22no—
75#13063301—41no—
76#13063297—28no—
77#13063296—22no—
78#13063296—22no—
79Q8×Dic43—22no—
80Q8×Dic43—22no—
81D4×Dic43—28no—
82D4×Dic43—22no—
83D4×Dic43D414yes—
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86#13063283—22no—
87#13063283—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4D411yescharacteristic
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43D411yescharacteristic
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111#13063258—22no—
112#13063257—22no—
113#13063257—22no—
114Dic43⋊C8—22no—
115#13063249—22no—
116#13063249—22no—
117#13063246—22no—
118#13063246—41no—
119C22⋊(C43⋊C8)—41no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—41no—
122C8×Dic43—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×Q8×C43C2311yescharacteristic
128C22×D4×C43—21no—
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C2×SD16×C43—22no—
132C2×SD16×C43—22no—
133C2×SD16×C43—22no—
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C22⋊Q8×C43—22no—
137C22⋊Q8×C43—41no—
138#121×C43—22no—
139#121×C43—22no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145#103×C43—22no—
146#102×C43—41no—
147C22⋊C8×C43—22no—
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C23×D43C2×D411yescharacteristic
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43#4112yes—
157C2×D4×C43—24no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43C2×D412yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—24no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—22no—
180C2×C22⋊D43—41no—
181C2×C22⋊D43—81no—
182C2×C22⋊D43—81no—
183C22×Dic43—24no—
184C22×Dic43—24no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—81no—
190C22×Dic43—81no—
191C22×Dic43—81no—
192C22×Dic43—81no—
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202SD16×C43—28no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43#4112yes—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43C2×D412yes—
214C22⋊C4×C43—24no—
215C22⋊C4×C43—42no—
216C22⋊Dic43—24no—
217C22⋊Dic43—24no—
218C22⋊Dic43—22no—
219C22⋊Dic43—42no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—22no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224C4⋊Dic43—24no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—24no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—42no—
233C4⋊Dic43C2×D412yes—
234C4⋊Dic43C2×D412yes—
235Dic43⋊C4—24no—
236Dic43⋊C4—22no—
237Dic43⋊C4—42no—
238C4×Dic43—24no—
239C4×Dic43—42no—
240C4×Dic43C2×D412yes—
241C4×Dic43C2×D412yes—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—22no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43#13512yes—
262C23×C43C22×D411yescharacteristic
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270Q8×C43—22no—
271Q8×C43—22no—
272Q8×C43—41no—
273Q8×C43—41no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—48no—
277D4×C43—41no—
278D4×C43—41no—
279C2×C4×C43—22no—
280C2×C4×C43—21no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×C4×C432−1+411yescharacteristic
301C22⋊D43—44no—
302C22⋊D43—84no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—41no—
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—84no—
323C2×Dic43—84no—
324C2×Dic43#12012yes—
325C2×Dic43#12012yes—
326C4×D43—41no—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330C8×C43—22no—
331C8×C43—41no—
332C43⋊C8—41no—
333C43⋊C8—41no—
334#24126—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43C2×#12011yescharacteristic
350C22×C43#54611yescharacteristic
351C22×C43#54711yescharacteristic
352C22×C43C2×#13511yescharacteristic
353C22×C43#57511yescharacteristic
354C22×C43#57711yescharacteristic
355C22×C43#57711yescharacteristic
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—41no—
363C4×C43—41no—
364C4×C43—42no—
365C4×C43—42no—
366C4×C43—81no—
367C4×C43#52511yescharacteristic
368C4×C43#53711yescharacteristic
369C4×C43#54811yescharacteristic
370C4×C43#55011yescharacteristic
371Dic43—22no—
372Dic43—22no—
373Dic43—41no—
374Dic43—42no—
375Dic43—42no—
376Dic43—81no—
377Dic43—81no—
378C2×#553—431no—
379C2×#479—431no—
380C2×C4×SD16—431no—
381#2536—431no—
382#2034—431no—
383#2033—431no—
384#2000—431no—
385#2000D4311yescharacteristic, complemented
386#1991—431no—
387#1954—431no—
388#1873—431no—
389#1872—431no—
390#1854—431no—
391#1853—431no—
392#1804—431no—
393C2×C43—42no—
394C2×C43—82no—
395C2×C43#240711yescharacteristic
396C2×C43#300211yescharacteristic
397C2×C43#300911yescharacteristic
398C2×C43#330111yescharacteristic
399C2×C43#332611yescharacteristic
400C2×C43#333711yescharacteristic
401C2×C43#335111yescharacteristic
402D43—81no—
403C22×SD16C2×D4311yescharacteristic
404#553—864no—
405#553—864no—
406C2×#126—861no—
407C2×#125—431no—
408C2×#123—861no—
409C2×C22⋊Q8—431no—
410C2×C22⋊Q8C2×D4311yescharacteristic
411C2×#121—431no—
412C2×#121—861no—
413C2×#121C2×D4311yescharacteristic
414C2×C4×Q8—431no—
415C2×C4×D4—431no—
416C2×C4×D4—431no—
417C2×C4×D4—861no—
418C2×#117—431no—
419C22×C4⋊C4—431no—
420#479—864no—
421C4×SD16—864no—
422C2×#107—431no—
423C2×#106—431no—
424C2×#106—431no—
425C2×C4⋊C8—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103C2×D4311yescharacteristic
429C2×#102—431no—
430C2×#102—431no—
431C2×#102C2×D4311yescharacteristic
432C2×C22⋊C8—431no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8C2×D4311yescharacteristic
436C2×C4×C8—431no—
437#398—861no—
438#394—861no—
439#388—861no—
440#388—861no—
441#382—431no—
442#380—431no—
443#380—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340C2×D4311yescharacteristic
450C43#2412611yescharacteristic, complemented, Sylow
451C22×Q8C22×D4311yescharacteristic
452C22×D4—21no—
453C22×D4—431no—
454C22×D4—861no—
455C22×D4C22×D4311yescharacteristic
456C23×C4—431no—
457C23×C4—861no—
458C23×C4—861no—
459C23×C4C22×D4311yescharacteristic
460C2×SD16—22no—
461C2×SD16—22no—
462C2×SD16—22no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8C22×D4311yescharacteristic
466C22×C8C22×D4311yescharacteristic
467#126—868no—
468#125—434no—
469#125—862no—
470#123—868no—
471C22⋊Q8—22no—
472C22⋊Q8—41no—
473C22⋊Q8—862no—
474C22⋊Q8—1721no—
475#121—22no—
476#121—22no—
477#121—862no—
478#121—868no—
479#121—862no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×D4—434no—
483C4×D4—862no—
484C4×D4—862no—
485C4×D4—862no—
486C4×D4—868no—
487#117—862no—
488#117—862no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—862no—
496C2×C4⋊C4—862no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C42—431no—
515C2×C42—861no—
516C2×C42—861no—
517#107—862no—
518#106—862no—
519#106—862no—
520C4⋊C8—862no—
521#103—22no—
522#103—862no—
523#103—862no—
524#102—41no—
525#102—862no—
526#102—1721no—
527C22⋊C8—22no—
528C22⋊C8—862no—
529C22⋊C8—1721no—
530C22⋊C8—1721no—
531C4×C8—862no—
532#95—861no—
533#95—861no—
534#95—861no—
535#95—861no—
536C24—21no—
537C24—431no—
538C24D4×D4311yescharacteristic
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8#1062190012yes—
545C2×D4—24no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—862no—
554C2×D4—864no—
555C2×D4—862no—
556C2×D4—3441no—
557C2×D4—3441no—
558C2×D4—1721no—
559C2×D4D4×D4312yes—
560C22×C4—21no—
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—431no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—864no—
573C22×C4—864no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—3441no—
585C22×C4—3441no—
586C22×C4—3441no—
587C22×C4—3441no—
588C22×C4D4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590SD16—28no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8#1062190012yes—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—42no—
607C4⋊C4—432no—
608C4⋊C4—432no—
609C4⋊C4—862no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—1722no—
620C4⋊C4—1722no—
621C4⋊C4D4×D4312yes—
622C22⋊C4—24no—
623C22⋊C4—42no—
624C22⋊C4—862no—
625C22⋊C4—864no—
626C22⋊C4—862no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C22⋊C4—1722no—
632C42—432no—
633C42—432no—
634C42—864no—
635C42—1722no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23#1306334612yes—
657C23C2×D4×D4311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—22no—
663D4—22no—
664D4—48no—
665D4—41no—
666D4—41no—
667D4—3444no—
668D4—1724no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—432no—
686C2×C4—432no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—3444no—
697C2×C4—3444no—
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—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4C2×D4×D4311yescharacteristic
714C2×C4C2×#1062190011yescharacteristic
715C2×C4C2×#1062190011yescharacteristic
716C2×C4#1306337011yescharacteristic
717C2×C4#1306337211yescharacteristic
718C8—22no—
719C8—41no—
720C8—1721no—
721C8—1721no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—1721no—
737C22—1721no—
738C22—1721no—
739C22—1721no—
740C22—1721no—
741C22—1721no—
742C22—1721no—
743C22#120×D4311yescharacteristic
744C22#1458353611yescharacteristic
745C22#1458354911yescharacteristic
746C22C2×#1306334611yescharacteristic
747C22#1458369511yescharacteristic
748C22#1458370611yescharacteristic
749C22#1458370811yescharacteristic
750C4—42no—
751C4—41no—
752C4—42no—
753C4—81no—
754C4—862no—
755C4—862no—
756C4—3441no—
757C4—3441no—
758C4—1721no—
759C4—1722no—
760C4—1722no—
761C4#1458340511yescharacteristic
762C4#1458347611yescharacteristic
763C4#1458355511yescharacteristic
764C4#1458356911yescharacteristic
765C2—42no—
766C2—82no—
767C2—3441no—
768C2#1913793311yescharacteristic
769C2#1914381411yescharacteristic
770C2#1914386911yescharacteristic
771C2#1914650111yescharacteristic
772C2#1914684111yescharacteristic
773C2#1914698011yescharacteristic
774C2#1914715011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2000C2
socleC23×C43C22×D4
prime radicalC2×#14583601C2
hypercenter#2000D43
hypocenterC43#24126
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
2. C2×#14583204C2semidirect
3. C2×SD16×Dic43C2semidirect
4. #19139502C2semidirect
5. #19135783C2semidirect
6. #19135774C2semidirect
7. #19135595C2semidirect
8. #19135558C2semidirect
9. #19135387C2semidirect
10. #19134904C2semidirect
11. #19134903C2semidirect
12. #19134795C2semidirect
13. #19134790C2semidirect
14. #19134603C2semidirect
15. C43×#2000C2semidirect
385. #2000D43semidirect
450. C43#24126semidirect

Maximal subgroups

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

subgroupindex
C2×#145836012
C2×#145832042
C2×SD16×Dic432
#191395022
#191357832
#191357742
#191355952
#191355582
#191353872
#191349042
#191349032
#191347952
#191347902
#191346032
C43×#20002
#2412643