Finite Group Databasebeta

← #25098040

Subgroups — #25098040

Order 11008.

1690 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D43C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic
3C2×#14582906C211yesmaximal, characteristic
4C2×#14582906C211yesmaximal, characteristic
5#19137178C211yesmaximal, characteristic
6#19134939C211yesmaximal, characteristic, complemented
7#19134938C211yesmaximal, characteristic, complemented
8#19134937C211yesmaximal, characteristic, complemented
9#19134936C211yesmaximal, characteristic, complemented
10#19134935C211yesmaximal, characteristic, complemented
11#19134934C211yesmaximal, characteristic, complemented
12#19134933C211yesmaximal, characteristic, complemented
13#19134310C211yesmaximal, characteristic
14#19134290C211yesmaximal, characteristic
15C43×#1878C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C2×Q16×D43—24no—
22C2×Q16×D43—24no—
23C2×Q16×D43C418yescomplemented
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583375—24no—
27#14583375—24no—
28C2×Q8×Dic43C2211yescharacteristic
29C2×C4×Dic86—21no—
30C2×C4×Dic86C2211yescharacteristic
31C2×#13063290—21no—
32C2×#13063290C2211yescharacteristic
33C2×#13063283—21no—
34C2×#13063283C2211yescharacteristic
35C2×#13063283C2211yescharacteristic
36C2×#13063282—21no—
37C2×#13063282C2211yescharacteristic
38#14582906—24no—
39#14582906—24no—
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063249C2211yescharacteristic
44C2×#13063248C2211yescharacteristic
45C2×#13063248C2211yescharacteristic
46#14582806C2211yescharacteristic
47#14582805C2211yescharacteristic
48#14582804C2211yescharacteristic
49#14582803—21no—
50#14582803—21no—
51#14582761—21no—
52#14582761—21no—
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582654C2211yescharacteristic
57#14582653C2211yescharacteristic
58#14582653C2211yescharacteristic
59C22×Q16×C43C2211yescharacteristic
60C2×C4×Q8×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C43×#391C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C43×#336C2211yescharacteristic
66C22×Dic86—21no—
67C22×Dic86—21no—
68C22×Dic86C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C2×Q8×D43—22no—
71C2×Q8×D43—22no—
72C2×Q8×D43—22no—
73C2×Q8×D43—22no—
74C2×Q8×D43—22no—
75C2×Q8×D43—22no—
76C2×Q8×D43—22no—
77C2×Q8×D43—22no—
78C2×Q8×D43C2×C414yes—
79C2×Q8×D43C2×C414yes—
80C2×Q8×D43D414yes—
81C2×Q8×D43D414yes—
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×Dic172—22no—
86C2×Dic172—22no—
87C2×Dic172C2×C414yes—
88C2×#10621885—22no—
89C2×#10621885—22no—
90C2×#10621885—22no—
91C2×#10621885—22no—
92C2×#10621885C2×C414yes—
93C2×#10621885C2×C414yes—
94Q16×D43—232no—
95C2×#10621872—22no—
96C2×#10621872—22no—
97C2×#10621872—22no—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C2×C8×D43—22no—
101C2×C8×D43—22no—
102C2×C8×D43C2×C414yes—
103Q8×Dic43—22no—
104Q8×Dic43—22no—
105C4×Dic86—28no—
106C4×Dic86—22no—
107C4×Dic86—22no—
108#13063290—28no—
109#13063290—22no—
110#13063290—22no—
111#13063283—28no—
112#13063283—22no—
113#13063283—22no—
114#13063283—22no—
115#13063283D414yes—
116#13063282—28no—
117#13063282—22no—
118#13063282—22no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4D411yescharacteristic
125C2×Dic43⋊C4D411yescharacteristic
126C2×(C2×D43)⋊C4—21no—
127C2×(C2×D43)⋊C4—21no—
128C2×(C2×D43)⋊C4D411yescharacteristic
129C2×(C2×D43)⋊C4D411yescharacteristic
130C2×C4×Dic43—21no—
131C2×C4×Dic43—21no—
132C2×C4×Dic43—21no—
133C2×C4×Dic43—21no—
134C2×C4×Dic43—21no—
135C2×C4×Dic43C2311yescharacteristic
136#13063250—22no—
137#13063250—22no—
138#13063249—22no—
139#13063249—22no—
140#13063248—22no—
141#13063248—22no—
142C43⋊#95—21no—
143C43⋊#95—21no—
144C43⋊#95—21no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C43⋊#95—21no—
148C22×Q8×C43C2311yescharacteristic
149C22×Q8×C43C2311yescharacteristic
150C2×Q16×C43—22no—
151C2×Q16×C43—22no—
152C2×Q16×C43C2×C414yes—
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C4×Q8×C43—22no—
156C4×Q8×C43—22no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C42×C43—21no—
161C2×C42×C43C2311yescharacteristic
162#103×C43—22no—
163#103×C43—22no—
164#95×C43—21no—
165#95×C43—21no—
166C23×D43C2×D411yescharacteristic
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C22×C412yes—
176C2×Q8×C43C22×C412yes—
177C2×Q8×C43C2×D412yes—
178C2×Q8×C43C2×D412yes—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193Q8×D43—28no—
194Q8×D43—28no—
195Q8×D43—28no—
196Q8×D43—28no—
197Q8×D43—28no—
198Q8×D43—44no—
199Q8×D43—44no—
200Q8×D43C22⋊C4116yes—
201C2×C4×D43—24no—
202C2×C4×D43—24no—
203C2×C4×D43—24no—
204C2×C4×D43—24no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43C22×C412yes—
208C2×C4×D43C2×D412yes—
209C2×C4×D43C2×D412yes—
210C2×C4×D43C2×D412yes—
211C2×C4×D43#4112yes—
212C2×C4×D43#4112yes—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—24no—
217C2×Dic86—24no—
218C2×Dic86—24no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—24no—
225C2×Dic86—42no—
226C2×Dic86—42no—
227C2×Dic86C22×C412yes—
228C2×Dic86C22×C412yes—
229C2×Dic86C2×D412yes—
230C2×Dic86C2×D412yes—
231Q16×C43—28no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43C22×C412yes—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C2×D412yes—
243C42×C43—24no—
244C42×C43—21no—
245C42×C43—21no—
246#10621885—28no—
247#10621885—28no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—22no—
250(C2×D43)⋊C4—22no—
251(C2×D43)⋊C4—42no—
252C4⋊Dic43—24no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43C2×D412yes—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—22no—
260Dic43⋊C4—22no—
261C4×Dic43—24no—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43—21no—
265C4×Dic43—21no—
266C4×Dic43—24no—
267C4×Dic43—42no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8C22×C412yes—
274Dic172—28no—
275#10621872—44no—
276C8×D43—28no—
277C23×C43C22×D411yescharacteristic
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43C4×D412yes—
283C22×D43#12012yes—
284C22×D43#12112yes—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—22no—
289Q8×C43—22no—
290Q8×C43—41no—
291Q8×C43—41no—
292Q8×C43C2×C22⋊C414yes—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—21no—
298C2×C4×C43—22no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43C23×C411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—22no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43C4×D412yes—
336C2×Dic43#12012yes—
337C2×Dic43#12112yes—
338C4×D43—216no—
339C4×D43—48no—
340C4×D43C2×C22⋊C414yes—
341C4×D43C4×D414yes—
342C4×D43#12114yes—
343C4×D43#12314yes—
344Dic86—22no—
345Dic86—22no—
346Dic86—22no—
347Dic86—216no—
348Dic86—22no—
349Dic86—22no—
350Dic86—41no—
351Dic86—41no—
352Dic86—48no—
353Dic86C2×C22⋊C414yes—
354C8×C43—22no—
355C8×C43—41no—
356C43⋊C8—22no—
357C43⋊C8—41no—
358#20935—431nomaximal, Sylow
359C22×C43C2×C4×D411yescharacteristic
360C22×C43C2×#12011yescharacteristic
361C22×C43C2×#12111yescharacteristic
362C22×C43#57811yescharacteristic
363C22×C43#57811yescharacteristic
364C22×C43#57811yescharacteristic
365C22×C43#57811yescharacteristic
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43#38614yes—
373C4×C43—24no—
374C4×C43—41no—
375C4×C43—41no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43—81no—
379C4×C43C22×C22⋊C411yescharacteristic
380C4×C43C2×C4×D411yescharacteristic
381C4×C43C2×#12111yescharacteristic
382C4×C43C2×#12311yescharacteristic
383Dic43—24no—
384Dic43—41no—
385Dic43—41no—
386Dic43—42no—
387Dic43—42no—
388Dic43—81no—
389Dic43#38614yes—
390C23×Q16—431no—
391C2×#519—431no—
392C2×#419—431no—
393C2×#419—431no—
394#2310—431no—
395#1878—431no—
396#1878—431no—
397#1878—431no—
398#1878—431no—
399#1878—431no—
400#1878—431no—
401#1878—431no—
402#1878D4311yescharacteristic, complemented
403#1735—431no—
404#1729—431no—
405C2×C43C2×#38611yescharacteristic
406C2×C43#295011yescharacteristic
407C2×C43#295011yescharacteristic
408C2×C43#301111yescharacteristic
409C2×C43#301111yescharacteristic
410C2×C43#304411yescharacteristic
411C2×C43#304411yescharacteristic
412D43—24no—
413C23×Q8—431no—
414C23×Q8—431no—
415C22×Q16—431no—
416C22×Q16—431no—
417C22×Q16—438no—
418C22×Q16—431no—
419C22×Q16—864no—
420C22×Q16—864no—
421C22×Q16C2×D4311yescharacteristic
422C22×M16—431no—
423C23×C8—431no—
424#519—864no—
425#519—864no—
426C2×C4×Q8—431no—
427C2×C4×Q8—431no—
428C2×C4×Q8—431no—
429C2×C4×Q8—861no—
430C2×C4×Q8—861no—
431C2×C4×Q8C2×D4311yescharacteristic
432C2×#117—431no—
433C2×#117—431no—
434C2×#117—431no—
435C2×#117—861no—
436C2×#117—861no—
437#419—864no—
438#419—864no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#103C2×D4311yescharacteristic
446C2×#103C2×D4311yescharacteristic
447#391—431no—
448#391—431no—
449#391—431no—
450#391—861no—
451#391—861no—
452#391C2×D4311yescharacteristic
453#381—861no—
454#381—861no—
455#340—431no—
456#340—431no—
457#340—431no—
458#340C2×D4311yescharacteristic
459#336—431no—
460#336—431no—
461#336—431no—
462#336C2×D4311yescharacteristic
463C43#2093511yescharacteristic, complemented, Sylow
464C22×Q8—434no—
465C22×Q8—434no—
466C22×Q8—434no—
467C22×Q8—434no—
468C22×Q8—431no—
469C22×Q8—431no—
470C22×Q8—861no—
471C22×Q8—861no—
472C22×Q8—862no—
473C22×Q8—862no—
474C22×Q8—862no—
475C22×Q8—862no—
476C22×Q8—862no—
477C22×Q8—862no—
478C22×Q8—862no—
479C22×Q8—862no—
480C22×Q8C22×D4311yescharacteristic
481C22×Q8C22×D4311yescharacteristic
482C23×C4—431no—
483C23×C4—861no—
484C23×C4—861no—
485C2×Q16—22no—
486C2×Q16—22no—
487C2×Q16—434no—
488C2×Q16—434no—
489C2×Q16—434no—
490C2×Q16—862no—
491C2×Q16—862no—
492C2×Q16—8632no—
493C2×Q16—862no—
494C2×Q16—862no—
495C2×Q16—862no—
496C2×Q16—862no—
497C2×Q16C4×D4314yes—
498C2×M16—862no—
499C2×M16—862no—
500C2×M16—862no—
501C22×C8—431no—
502C22×C8—434no—
503C22×C8—431no—
504C22×C8—862no—
505C22×C8—862no—
506C22×C8C22×D4311yescharacteristic
507C22×C8C22×D4311yescharacteristic
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—862no—
511C4×Q8—862no—
512C4×Q8—868no—
513C4×Q8—862no—
514C4×Q8—868no—
515C4×Q8—862no—
516C4×Q8—862no—
517C4×Q8—862no—
518#117—434no—
519#117—862no—
520#117—862no—
521#117—868no—
522#117—862no—
523#117—868no—
524#117—862no—
525#117—862no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—431no—
528C2×C4⋊C4—431no—
529C2×C4⋊C4—431no—
530C2×C4⋊C4—431no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C22⋊C4—431no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C42—21no—
541C2×C42—431no—
542C2×C42—861no—
543C2×C42—861no—
544C2×C42—861no—
545C2×C42—861no—
546C2×C42—861no—
547C2×C42C22×D4311yescharacteristic
548#103—22no—
549#103—22no—
550#103—862no—
551#103—862no—
552#103—862no—
553#103—862no—
554#103—862no—
555#103—862no—
556#95—21no—
557#95—21no—
558#95—861no—
559#95—861no—
560#95—861no—
561#95—861no—
562#95—861no—
563#95—861no—
564C24—431no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—4316no—
574C2×Q8—432no—
575C2×Q8—432no—
576C2×Q8—432no—
577C2×Q8—432no—
578C2×Q8—864no—
579C2×Q8—864no—
580C2×Q8—864no—
581C2×Q8—864no—
582C2×Q8—868no—
583C2×Q8—868no—
584C2×Q8—868no—
585C2×Q8—868no—
586C2×Q8—868no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8—861no—
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—1722no—
596C2×Q8—1722no—
597C2×Q8—1724no—
598C2×Q8—1724no—
599C2×Q8C2×C4×D4312yes—
600C2×Q8C2×C4×D4312yes—
601C2×Q8D4×D4312yes—
602C2×Q8D4×D4312yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—431no—
608C22×C4—432no—
609C22×C4—432no—
610C22×C4—432no—
611C22×C4—432no—
612C22×C4—432no—
613C22×C4—432no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—864no—
617C22×C4—864no—
618C22×C4—864no—
619C22×C4—864no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4D4×D4311yescharacteristic
627C22×C4D4×D4311yescharacteristic
628C22×C4C23×D4311yescharacteristic
629Q16—28no—
630Q16—868no—
631Q16—868no—
632Q16—868no—
633M16—1724no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—432no—
640C2×C8—868no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8C2×C4×D4312yes—
647C4⋊C4—24no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—432no—
652C4⋊C4—862no—
653C4⋊C4—862no—
654C4⋊C4—864no—
655C4⋊C4—864no—
656C4⋊C4—864no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4D4×D4312yes—
661C22⋊C4—862no—
662C22⋊C4—862no—
663C22⋊C4—864no—
664C22⋊C4—1722no—
665C42—24no—
666C42—21no—
667C42—21no—
668C42—864no—
669C42—864no—
670C42—864no—
671C42—864no—
672C42—861no—
673C42—861no—
674C42—1722no—
675C23—432no—
676C23—432no—
677C23—432no—
678C23—861no—
679C23—861no—
680C23—861no—
681C23—861no—
682C23C2×D4×D4311yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—41no—
689Q8—41no—
690Q8—434no—
691Q8—8616no—
692Q8—862no—
693Q8—862no—
694Q8—862no—
695Q8—862no—
696Q8—862no—
697Q8—1728no—
698Q8—1721no—
699Q8—1721no—
700Q8C22⋊C4×D4314yes—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—432no—
722C2×C4—434no—
723C2×C4—434no—
724C2×C4—434no—
725C2×C4—434no—
726C2×C4—8616no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—1728no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4C22×C4×D4311yescharacteristic
747C2×C4C2×D4×D4311yescharacteristic
748C2×C4C2×D4×D4311yescharacteristic
749C2×C4C2×D4×D4311yescharacteristic
750C2×C4#41×D4311yescharacteristic
751C2×C4#41×D4311yescharacteristic
752C8—22no—
753C8—41no—
754C8—862no—
755C8—1721no—
756C22—434no—
757C22—862no—
758C22—862no—
759C22—862no—
760C22—862no—
761C22—862no—
762C22—862no—
763C22C4×D4×D4311yescharacteristic
764C22#120×D4311yescharacteristic
765C22#121×D4311yescharacteristic
766C22#1458371211yescharacteristic
767C22#1458371311yescharacteristic
768C22#1458371511yescharacteristic
769C22#1458371511yescharacteristic
770C4—24no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—42no—
775C4—81no—
776C4—434no—
777C4—864no—
778C4—3441no—
779C4—1721no—
780C4—1722no—
781C4—1721no—
782C4—1722no—
783C4C2×C22⋊C4×D4311yescharacteristic
784C4C4×D4×D4311yescharacteristic
785C4#121×D4311yescharacteristic
786C4#123×D4311yescharacteristic
787C2—864no—
788C2#386×D4311yescharacteristic
789C2#1914345811yescharacteristic
790C2#1914346011yescharacteristic
791C2#1914388511yescharacteristic
792C2#1914388711yescharacteristic
793C2#1914412011yescharacteristic
794C2#1914412311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1878C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1878D43
hypocenterC43#20935
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
6. #19134939C2semidirect
7. #19134938C2semidirect
8. #19134937C2semidirect
9. #19134936C2semidirect
10. #19134935C2semidirect
11. #19134934C2semidirect
12. #19134933C2semidirect
15. C43×#1878C2semidirect
23. C2×Q16×D43C4semidirect
402. #1878D43semidirect
463. C43#20935semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×D432
C2×#145833752
C2×#145829062
#191371782
#191349392
#191349382
#191349372
#191349362
#191349352
#191349342
#191349332
#191343102
#191342902
C43×#18782
#2093543