Finite Group Databasebeta

← #25099320

Subgroups — #25099320

Order 11008.

1338 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582902C211yesmaximal, characteristic
2C2×#14582902C211yesmaximal, characteristic
3C2×#14582851C211yesmaximal, characteristic, complemented
4#19137076C211yesmaximal, characteristic, complemented
5#390×D43C211yesmaximal, characteristic
6#19135295C211yesmaximal, characteristic, complemented
7#19135292C211yesmaximal, characteristic, complemented
8#19135291C211yesmaximal, characteristic, complemented
9#19135280C211yesmaximal, characteristic, complemented
10#19135279C211yesmaximal, characteristic, complemented
11#19135276C211yesmaximal, characteristic, complemented
12#19135275C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23C2×C22⋊C4×D43—21no—
24C2×C42×D43C2211yescharacteristic
25#14582902—24no—
26#14582902C418yescomplemented
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33#14582851—24no—
34C2×#13063236C2211yescharacteristic, complemented
35C2×C8×Dic43C2211yescharacteristic, complemented
36C2×C8×Dic43C2211yescharacteristic, complemented
37#14582802C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582799—21no—
41#14582799—21no—
42#14582798C2211yescharacteristic, complemented
43#14582797C2211yescharacteristic, complemented
44#14582795C2211yescharacteristic, complemented
45#14582773—21no—
46#14582770—21no—
47C4⋊C4×Dic43—21no—
48#14582750—21no—
49#14582662C2211yescharacteristic, complemented
50#14582662C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic, complemented
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C2×D4×D43—22no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43C2×C414yes—
71C22×C4×D43—21no—
72C22×C4×D43D411yescharacteristic
73C22×C4×D43D411yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C2×#10621872—22no—
76C2×#10621872—22no—
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872C2×C414yes—
80C2×#10621872D414yes—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063283—22no—
84#13063283—22no—
85#13063283—22no—
86#13063283C2×C414yes—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C4⋊C4×D43—22no—
95C4⋊C4×D43—22no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C22⋊C4×D43—44no—
105C22⋊C4×D43—44no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43C2311yescharacteristic
111C42×D43—22no—
112C42×D43—22no—
113#13063247—22no—
114#13063247C2×C414yescomplemented
115#13063246—22no—
116#13063246C2×C414yescomplemented
117#13063245—22no—
118#13063245C2×C414yescomplemented
119#13063236—22no—
120C8×Dic43—22no—
121C8×Dic43—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×D4×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#102×C43—22no—
136#102×C43C2×C414yescomplemented
137#97×C43—22no—
138#95×C43—21no—
139C24×C43—21no—
140C23×D43—21no—
141C23×D43—24no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—42no—
148C23×D43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43C22×C412yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—24no—
162C2×C22⋊D43—42no—
163C2×C22⋊D43—42no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170D4×D43—28no—
171D4×D43—28no—
172D4×D43—44no—
173D4×D43—44no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172C22×C412yes—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×C4×D43—22no—
183C2×C4×D43—22no—
184C2×C4×D43—41no—
185C2×C4×D43—41no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43C22×C412yes—
190C2×C4×D43C2×D412yes—
191C2×C4×D43#4112yes—
192C2×C4×D43#4112yes—
193C2×C4×D43#4112yes—
194C2×C4×D43#4112yes—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43C22×C412yes—
200C2×C8×C43C2×D412yes—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43C22×C412yes—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C42×C43—21no—
211C42×C43—21no—
212C22⋊Dic43—42no—
213C22⋊Dic43—42no—
214(C2×D43)⋊C4—24no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—42no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—42no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—42no—
226C4⋊Dic43C22×C412yes—
227Dic43⋊C4—42no—
228Dic43⋊C4—42no—
229Dic43⋊C4—42no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—24no—
233C4×Dic43—22no—
234C4×Dic43—22no—
235C4×Dic43—42no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8C22×C412yes—
241C2×C43⋊C8C2×D412yes—
242#10621872—28no—
243#10621872—28no—
244C23×C43—22no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43C22×D411yescharacteristic
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—22no—
257C22×D43—48no—
258C22×D43—48no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—48no—
266C22×D43—84no—
267C22×D43—84no—
268C22×D43—84no—
269C22×D43—84no—
270C22×D43C4×D412yes—
271C22×D43#12112yes—
272C22×D43#12412yes—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—41no—
276D4×C43—41no—
277C2×C4×C43—22no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
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×C43C23×C411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C22⋊D43—48no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—22no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43C4×D412yes—
313C2×Dic43#12112yes—
314C2×Dic43#12412yes—
315C2×Dic43AGL(1,ℤ/8)12yes—
316C2×Dic43AGL(1,ℤ/8)12yes—
317D172—22no—
318D172—22no—
319D172—41no—
320D172—41no—
321C4×D43—44no—
322C4×D43—44no—
323C4×D43—84no—
324C4×D43#11714yes—
325C4×D43C4×D414yes—
326C4×D43#12314yes—
327C4×D43#12614yes—
328C8×C43—22no—
329C8×C43—22no—
330C43⋊C8—22no—
331C43⋊C8—22no—
332#21095—431nomaximal, Sylow
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43C2×C4×D411yescharacteristic
341C22×C43C2×#12111yescharacteristic
342C22×C43C2×#12411yescharacteristic
343C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C43#57511yescharacteristic
346C22×C43#57511yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—816no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43#38814yes—
362C4×C43—42no—
363C4×C43—41no—
364C4×C43—41no—
365C4×C43—81no—
366C4×C43—81no—
367C4×C43C2×#11711yescharacteristic
368C4×C43C2×C4×D411yescharacteristic
369C4×C43C2×#12311yescharacteristic
370C4×C43C2×#12611yescharacteristic
371Dic43—22no—
372Dic43—22no—
373Dic43—42no—
374Dic43—81no—
375Dic43—81no—
376Dic43#38814yes—
377C2×#418—431no—
378C2×#418—431no—
379C2×C4×M16—431no—
380#2296—431no—
381C2×#390—431no—
382#1936—431no—
383#1936—431no—
384#1936—431no—
385#1936D4311yescharacteristic, complemented
386#1934—431no—
387#1934—431no—
388#1934—431no—
389#1934—431no—
390#1736—431no—
391#1736—431no—
392C2×C43—82no—
393C2×C43C2×#38811yescharacteristic
394C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
395C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
396C2×C43#305511yescharacteristic
397C2×C43#305511yescharacteristic
398C2×C43#313811yescharacteristic
399C2×C43#314011yescharacteristic
400D43—24no—
401D43—82no—
402C23×D4—431no—
403C22×M16—431no—
404C22×M16—431no—
405C2×#117—431no—
406C2×#117—431no—
407C22×C4⋊C4—431no—
408C22×C22⋊C4—861no—
409C22×C22⋊C4—861no—
410C22×C42—431no—
411#418—438no—
412#418—864no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102C2×D4311yescharacteristic
420C2×#102C2×D4311yescharacteristic
421C4×M16—864no—
422C2×#97—431no—
423C2×#97C2×D4311yescharacteristic, complemented
424C2×C4×C8—431no—
425C2×C4×C8—431no—
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—
438C4×C4⋊C4—861no—
439C4×C4⋊C4—861no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#340C2×D4311yescharacteristic, complemented
447#340C2×D4311yescharacteristic, complemented
448C43#2109511yescharacteristic, complemented, Sylow
449C25—861no—
450C22×D4—434no—
451C22×D4—431no—
452C22×D4—862no—
453C22×D4—862no—
454C22×D4—862no—
455C22×D4—862no—
456C22×D4—862no—
457C22×D4—861no—
458C22×D4C22×D4311yescharacteristic
459C23×C4—431no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—861no—
463C2×M16—434no—
464C2×M16—434no—
465C2×M16—862no—
466C2×M16—862no—
467C2×M16—862no—
468C2×M16—862no—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473#117—434no—
474#117—862no—
475#117—862no—
476#117—862no—
477C2×C4⋊C4—21no—
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—861no—
493C2×C22⋊C4—861no—
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—1724no—
501C2×C22⋊C4—1724no—
502C2×C42—431no—
503C2×C42—431no—
504C2×C42—431no—
505C2×C42—862no—
506C2×C42—862no—
507C2×C42—861no—
508C2×C42—861no—
509C2×C42C22×D4311yescharacteristic
510#102—22no—
511#102—434no—
512#102—434no—
513#102—434no—
514#102—862no—
515#102—862no—
516#102—862no—
517#102C4×D4314yescomplemented
518#97—22no—
519#97—862no—
520C4×C8—862no—
521C4×C8—862no—
522#95—21no—
523#95—861no—
524#95—861no—
525#95—861no—
526C24—21no—
527C24—431no—
528C24—864no—
529C24—861no—
530C24—1722no—
531C24—1722no—
532C24—1722no—
533C24—1722no—
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×D4C2×C4×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—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—1721no—
575C22×C4—1721no—
576C22×C4—1722no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4D4×D4311yescharacteristic
580C22×C4D4×D4311yescharacteristic
581C22×C4C23×D4311yescharacteristic
582M16—868no—
583M16—868no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—432no—
589C2×C8—432no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8C2×C4×D4312yes—
595C2×C8D4×D4312yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—432no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—1722no—
609C4⋊C4—1722no—
610C4⋊C4—1722no—
611C4⋊C4—1722no—
612C4⋊C4C2×C4×D4312yes—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—864no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C42—21no—
624C42—21no—
625C42—862no—
626C42—862no—
627C42—864no—
628C42—861no—
629C42—861no—
630C42—1722no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—432no—
639C23—432no—
640C23—432no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23—861no—
645C23—862no—
646C23—3444no—
647C23—3444no—
648C23—3444no—
649C23—3444no—
650C23—1728no—
651C23—1728no—
652C23—1728no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23—1721no—
659C23C2×D4×D4311yescharacteristic
660D4—22no—
661D4—22no—
662D4—41no—
663D4—41no—
664D4—862no—
665D4—862no—
666D4—1728no—
667D4—1721no—
668D4—1721no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
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—432no—
685C2×C4—432no—
686C2×C4—432no—
687C2×C4—434no—
688C2×C4—434no—
689C2×C4—434no—
690C2×C4—434no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—862no—
698C2×C4—3444no—
699C2×C4—1724no—
700C2×C4—1724no—
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×C4C22×C4×D4311yescharacteristic
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4#41×D4311yescharacteristic
712C2×C4#41×D4311yescharacteristic
713C2×C4#41×D4311yescharacteristic
714C2×C4#41×D4311yescharacteristic
715C8—22no—
716C8—22no—
717C8—862no—
718C8—862no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—434no—
727C22—862no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—862no—
732C22—862no—
733C22—34416no—
734C22—3441no—
735C22—3441no—
736C22—3441no—
737C22—3441no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22C4×D4×D4311yescharacteristic
742C22#121×D4311yescharacteristic
743C22#124×D4311yescharacteristic
744C22AGL(1,ℤ/8)×D4311yescharacteristic
745C22AGL(1,ℤ/8)×D4311yescharacteristic
746C22#1458369511yescharacteristic
747C22#1458369811yescharacteristic
748C4—41no—
749C4—41no—
750C4—42no—
751C4—81no—
752C4—81no—
753C4—434no—
754C4—862no—
755C4—862no—
756C4—3441no—
757C4—3441no—
758C4—1722no—
759C4#117×D4311yescharacteristic
760C4C4×D4×D4311yescharacteristic
761C4#123×D4311yescharacteristic
762C4#126×D4311yescharacteristic
763C2—82no—
764C2—864no—
765C2—3442no—
766C2#388×D4311yescharacteristic
767C2#1914340011yescharacteristic
768C2#1914340611yescharacteristic
769C2#1914420911yescharacteristic
770C2#1914421311yescharacteristic
771C2#1914496811yescharacteristic
772C2#1914498011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1936D43
hypocenterC43#21095
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
3. C2×#14582851C2semidirect
4. #19137076C2semidirect
6. #19135295C2semidirect
7. #19135292C2semidirect
8. #19135291C2semidirect
9. #19135280C2semidirect
10. #19135279C2semidirect
11. #19135276C2semidirect
12. #19135275C2semidirect
13. #19134313C2semidirect
14. #19134313C2semidirect
15. C43×#1936C2semidirect
26. #14582902C4semidirect
34. C2×#13063236C22semidirect
35. C2×C8×Dic43C22semidirect
36. C2×C8×Dic43C22semidirect
42. #14582798C22semidirect
43. #14582797C22semidirect
44. #14582795C22semidirect
49. #14582662C22semidirect
50. #14582662C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
57. C2×#97×C43C22semidirect
59. C43×#389C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
114. #13063247C2×C4semidirect
116. #13063246C2×C4semidirect
118. #13063245C2×C4semidirect
136. #102×C43C2×C4semidirect
385. #1936D43semidirect
423. C2×#97C2×D43semidirect
435. #389C2×D43semidirect
446. #340C2×D43semidirect
447. #340C2×D43semidirect
448. C43#21095semidirect
517. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829022
C2×#145828512
#191370762
#390×D432
#191352952
#191352922
#191352912
#191352802
#191352792
#191352762
#191352752
#191343132
C43×#19362
#2109543