Finite Group Databasebeta

← #25125239

Subgroups — #25125239

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582936C211yesmaximal, characteristic, complemented
2C2×#14582924C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic
4C2×#102×D43C211yesmaximal, characteristic
5#19137217C211yesmaximal, characteristic, complemented
6#19137174C211yesmaximal, characteristic
7#19135982C211yesmaximal, characteristic, complemented
8#19135981C211yesmaximal, characteristic, complemented
9#19135978C211yesmaximal, characteristic, complemented
10#19135970C211yesmaximal, characteristic, complemented
11#19135969C211yesmaximal, characteristic, complemented
12#19135966C211yesmaximal, characteristic, complemented
13#19135965C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#2067C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582936—24no—
24C2×#13063259C2211yescharacteristic, complemented
25C2×#13063256C2211yescharacteristic, complemented
26C2×#13063256C2211yescharacteristic, complemented
27#14582924—24no—
28C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
29C2×Dic43⋊C8C2211yescharacteristic, complemented
30C2×Dic43⋊C8C2211yescharacteristic, complemented
31#14582902—24no—
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38#102×D43—24no—
39#14582802C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582800C2211yescharacteristic
42#14582799—21no—
43#14582799—21no—
44#14582798C2211yescharacteristic, complemented
45#14582797C2211yescharacteristic, complemented
46#14582795C2211yescharacteristic, complemented
47#14582773—21no—
48#14582770—21no—
49#14582768—21no—
50#14582763—21no—
51#14582754—21no—
52#14582754—21no—
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C2×#107×C43C2211yescharacteristic, complemented
57C2×C4⋊C8×C43C2211yescharacteristic, complemented
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C43×#390C2211yescharacteristic
61C43×#389C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C24×D43—21no—
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43Q814yes—
72C22×C4×D43—21no—
73C22×C4×D43C2311yescharacteristic
74C2×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—22no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81C2×C8×D43D414yes—
82#13063283—22no—
83#13063283—22no—
84#13063283—22no—
85#13063283D414yes—
86#13063282—22no—
87#13063282—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4D411yescharacteristic
96C2×Dic43⋊C4D411yescharacteristic
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112#13063259—22no—
113#13063256—22no—
114#13063256—22no—
115C4⋊(C43⋊C8)—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118#13063247—22no—
119#13063247—22no—
120#13063246—22no—
121#13063246—22no—
122#13063245—22no—
123#13063245—22no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×D4×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137#107×C43—22no—
138C4⋊C8×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#95×C43—21no—
142C24×C43—21no—
143C23×D43—21no—
144C23×D43—24no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—81no—
148C23×D43—81no—
149C23×D43—81no—
150C23×D43—81no—
151C23×D43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43C2×Q812yes—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—24no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43—42no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173D4×D43—28no—
174D4×D43—28no—
175D4×D43—44no—
176D4×D43—44no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172C2×Q812yes—
183C2×C4×D43—42no—
184C2×C4×D43—81no—
185C2×C4×D43—81no—
186C2×C4×D43C2×D412yes—
187C2×C4×D43C2×D412yes—
188C2×C4×D43C2×Q812yes—
189C2×C4×D43#4112yes—
190C2×C4×D43#4112yes—
191C2×C4×D43#4112yes—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C2×D412yes—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—81no—
204C4⋊C4×C43C2×D412yes—
205C22⋊C4×C43—81no—
206C22⋊C4×C43—81no—
207C42×C43—21no—
208C42×C43—21no—
209C22⋊Dic43—81no—
210C22⋊Dic43—81no—
211(C2×D43)⋊C4—24no—
212(C2×D43)⋊C4—22no—
213(C2×D43)⋊C4—22no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—81no—
216(C2×D43)⋊C4—81no—
217(C2×D43)⋊C4—81no—
218(C2×D43)⋊C4—81no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—81no—
225C4⋊Dic43C2×D412yes—
226Dic43⋊C4—22no—
227Dic43⋊C4—22no—
228Dic43⋊C4—42no—
229Dic43⋊C4—81no—
230Dic43⋊C4—81no—
231C4×Dic43—21no—
232C4×Dic43—21no—
233C4×Dic43—24no—
234C4×Dic43—42no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8C2×D412yes—
241#10621872—44no—
242C8×D43—28no—
243C23×C43—22no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43C22×D411yescharacteristic
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—22no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—48no—
263C22×D43—84no—
264C22×D43—84no—
265C22×D43—84no—
266C22×D43—84no—
267C22×D43—84no—
268C22×D43—84no—
269C22×D43#12112yes—
270C22×D43#12112yes—
271C22×D43C22⋊Q812yes—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—41no—
275D4×C43—41no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C22×Q811yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C22⋊D43—48no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—22no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43#12112yes—
314C2×Dic43#12112yes—
315C2×Dic43C22⋊Q812yes—
316D172—22no—
317D172—22no—
318D172—41no—
319D172—41no—
320C4×D43—84no—
321C4×D43#12114yes—
322C4×D43C22⋊Q814yes—
323C4×D43C22⋊Q814yes—
324C4×D43#12614yes—
325C8×C43—22no—
326C8×C43—41no—
327C43⋊C8—22no—
328C43⋊C8—41no—
329#23612—431nomaximal, Sylow
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43C2×#12111yescharacteristic
338C22×C43C2×#12111yescharacteristic
339C22×C43C2×C22⋊Q811yescharacteristic
340C22×C43#57611yescharacteristic
341C22×C43#57611yescharacteristic
342C22×C43#57711yescharacteristic
343C22×C43#57711yescharacteristic
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—816no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43#39614yes—
359C4×C43—42no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43C2×#12111yescharacteristic
365C4×C43C2×C22⋊Q811yescharacteristic
366C4×C43C2×C22⋊Q811yescharacteristic
367C4×C43C2×#12611yescharacteristic
368Dic43—42no—
369Dic43—41no—
370Dic43—41no—
371Dic43—81no—
372Dic43—81no—
373Dic43#39614yes—
374C2×#427—431no—
375C2×#424—431no—
376C2×#418—431no—
377C22×#102—431no—
378#2317—431no—
379#2309—431no—
380#2067—431no—
381#2067—431no—
382#2067—431no—
383#2067D4311yescharacteristic, complemented
384#2065—431no—
385#2065—431no—
386#2065—431no—
387#2065—431no—
388#1736—431no—
389C2×C43—82no—
390C2×C43C2×#39611yescharacteristic
391C2×C43#304511yescharacteristic
392C2×C43#304511yescharacteristic
393C2×C43#305711yescharacteristic
394C2×C43#305811yescharacteristic
395C2×C43#308111yescharacteristic
396C2×C43#308111yescharacteristic
397D43—24no—
398D43—82no—
399C23×D4—431no—
400C22×M16—431no—
401C23×C8—431no—
402C2×#117—431no—
403C2×#117—431no—
404C2×#117—431no—
405C22×C4⋊C4—431no—
406#427—864no—
407C2×#107—431no—
408C2×#107C2×D4311yescharacteristic, complemented
409C2×#106—431no—
410C2×#106—431no—
411#424—864no—
412C2×C4⋊C8—431no—
413C2×C4⋊C8—431no—
414C2×C4⋊C8—431no—
415C2×C4⋊C8C2×D4311yescharacteristic, complemented
416#418—864no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—864no—
424C2×#102C2×D4311yescharacteristic
425C2×#102C2×D4311yescharacteristic
426#390—431no—
427#390—431no—
428#390—431no—
429#390—861no—
430#390—861no—
431#390C2×D4311yescharacteristic
432#389—431no—
433#389—431no—
434#389—431no—
435#389C2×D4311yescharacteristic, complemented
436#385—861no—
437#385—861no—
438#384—861no—
439#382—861no—
440#379—861no—
441#379—861no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340C2×D4311yescharacteristic, complemented
446C43#2361211yescharacteristic, complemented, Sylow
447C25—861no—
448C22×D4—434no—
449C22×D4—431no—
450C22×D4—862no—
451C22×D4—862no—
452C22×D4—862no—
453C22×D4—862no—
454C22×D4—862no—
455C22×D4—861no—
456C22×D4C22×D4311yescharacteristic
457C23×C4—431no—
458C23×C4—861no—
459C2×M16—862no—
460C2×M16—862no—
461C2×M16—862no—
462C22×C8—431no—
463C22×C8—434no—
464C22×C8—431no—
465C22×C8—862no—
466C22×C8—862no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469#117—434no—
470#117—862no—
471#117—862no—
472#117—862no—
473#117—862no—
474#117—862no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C42—431no—
503C2×C42—861no—
504C2×C42—861no—
505C2×C42C22×D4311yescharacteristic
506#107—22no—
507#107—862no—
508#106—862no—
509#106—862no—
510C4⋊C8—22no—
511C4⋊C8—862no—
512C4⋊C8—862no—
513C4⋊C8—862no—
514#102—22no—
515#102—22no—
516#102—862no—
517#102—862no—
518#102—862no—
519#102—862no—
520#102—862no—
521#102—862no—
522#95—21no—
523#95—861no—
524#95—861no—
525#95—861no—
526C24—21no—
527C24—431no—
528C24—864no—
529C24—861no—
530C24—3441no—
531C24—3441no—
532C24—3441no—
533C24—3441no—
534C24—1722no—
535C24—1722no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—432no—
542C2×D4—868no—
543C2×D4—868no—
544C2×D4—864no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—861no—
549C2×D4—861no—
550C2×D4—1724no—
551C2×D4—1724no—
552C2×D4—1722no—
553C2×D4—1722no—
554C2×D4Q8×D4312yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—431no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—431no—
566C22×C4—431no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—3441no—
571C22×C4—3441no—
572C22×C4—1722no—
573C22×C4D4×D4311yescharacteristic
574C22×C4D4×D4311yescharacteristic
575C22×C4C23×D4311yescharacteristic
576M16—1724no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—432no—
583C2×C8—868no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8D4×D4312yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—81no—
596C4⋊C4—432no—
597C4⋊C4—862no—
598C4⋊C4—862no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—3441no—
605C4⋊C4—3441no—
606C4⋊C4—3441no—
607C4⋊C4—1722no—
608C4⋊C4D4×D4312yes—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—862no—
612C22⋊C4—862no—
613C22⋊C4—864no—
614C22⋊C4—3441no—
615C22⋊C4—3441no—
616C22⋊C4—3441no—
617C22⋊C4—3441no—
618C22⋊C4—3441no—
619C22⋊C4—3441no—
620C22⋊C4—1722no—
621C42—21no—
622C42—21no—
623C42—864no—
624C42—861no—
625C42—861no—
626C42—1722no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—432no—
635C23—432no—
636C23—432no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23—862no—
642C23—3444no—
643C23—3444no—
644C23—3444no—
645C23—3444no—
646C23—3444no—
647C23—3444no—
648C23—1728no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23C2×D4×D4311yescharacteristic
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—862no—
661D4—862no—
662D4—1728no—
663D4—1721no—
664D4—1721no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—432no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—434no—
684C2×C4—434no—
685C2×C4—434no—
686C2×C4—434no—
687C2×C4—862no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—3444no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4C2×D4×D4311yescharacteristic
704C2×C4C2×D4×D4311yescharacteristic
705C2×C4C2×Q8×D4311yescharacteristic
706C2×C4#41×D4311yescharacteristic
707C2×C4#41×D4311yescharacteristic
708C2×C4#41×D4311yescharacteristic
709C8—22no—
710C8—41no—
711C8—862no—
712C8—1721no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—434no—
721C22—862no—
722C22—862no—
723C22—862no—
724C22—862no—
725C22—862no—
726C22—862no—
727C22—34416no—
728C22—3441no—
729C22—3441no—
730C22—3441no—
731C22—3441no—
732C22—1722no—
733C22—1722no—
734C22—1722no—
735C22#121×D4311yescharacteristic
736C22#121×D4311yescharacteristic
737C22C22⋊Q8×D4311yescharacteristic
738C22#1458370011yescharacteristic
739C22#1458370111yescharacteristic
740C22#1458370811yescharacteristic
741C22#1458370911yescharacteristic
742C4—41no—
743C4—41no—
744C4—42no—
745C4—81no—
746C4—81no—
747C4—434no—
748C4—3441no—
749C4—3441no—
750C4—1721no—
751C4—1721no—
752C4—1722no—
753C4#121×D4311yescharacteristic
754C4C22⋊Q8×D4311yescharacteristic
755C4C22⋊Q8×D4311yescharacteristic
756C4#126×D4311yescharacteristic
757C2—82no—
758C2—864no—
759C2—3442no—
760C2#396×D4311yescharacteristic
761C2#1914412911yescharacteristic
762C2#1914413711yescharacteristic
763C2#1914423211yescharacteristic
764C2#1914423811yescharacteristic
765C2#1914441911yescharacteristic
766C2#1914442311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2067C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
hypercenter#2067D43
hypocenterC43#23612
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2067

Complements

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

NH ≅ G/Ntype
1. C2×#14582936C2semidirect
2. C2×#14582924C2semidirect
5. #19137217C2semidirect
7. #19135982C2semidirect
8. #19135981C2semidirect
9. #19135978C2semidirect
10. #19135970C2semidirect
11. #19135969C2semidirect
12. #19135966C2semidirect
13. #19135965C2semidirect
14. #19134313C2semidirect
15. C43×#2067C2semidirect
24. C2×#13063259C22semidirect
25. C2×#13063256C22semidirect
26. C2×#13063256C22semidirect
28. C2×C4⋊(C43⋊C8)C22semidirect
29. C2×Dic43⋊C8C22semidirect
30. C2×Dic43⋊C8C22semidirect
44. #14582798C22semidirect
45. #14582797C22semidirect
46. #14582795C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
56. C2×#107×C43C22semidirect
57. C2×C4⋊C8×C43C22semidirect
61. C43×#389C22semidirect
62. C43×#340C22semidirect
383. #2067D43semidirect
408. C2×#107C2×D43semidirect
415. C2×C4⋊C8C2×D43semidirect
435. #389C2×D43semidirect
445. #340C2×D43semidirect
446. C43#23612semidirect

Maximal subgroups

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

subgroupindex
C2×#145829362
C2×#145829242
C2×#145829022
C2×#102×D432
#191372172
#191371742
#191359822
#191359812
#191359782
#191359702
#191359692
#191359662
#191359652
#191343132
C43×#20672
#2361243