Finite Group Databasebeta

← #25062617

Subgroups — #25062617

Order 11008.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583487C211yesmaximal, characteristic
2#19143621C211yesmaximal, characteristic, complemented
3#19143617C211yesmaximal, characteristic, complemented
4#19132961C212yesmaximal, complemented
5#19132953C212yesmaximal, complemented
6#19132945C212yesmaximal, complemented
7#19132940C212yesmaximal, complemented
8#19132911C211yesmaximal, characteristic, complemented
9#19132911C211yesmaximal, characteristic, complemented
10C2×#14582623C211yesmaximal, characteristic, complemented
11C2×C43×#323C211yesmaximal, characteristic, complemented
12#14583487—22no—
13#14583487—22no—
14#14583487—22no—
15#14583487—22no—
16C2×#13063318C411yescharacteristic
17C2×#13063318C2211yescharacteristic
18C2×#13063311C411yescharacteristic
19C2×#13063311C2211yescharacteristic
20C2×#13063307C411yescharacteristic
21C2×#13063307C2211yescharacteristic
22C2×#13063304C411yescharacteristic
23C2×#13063299C411yescharacteristic
24C2×#13063298C411yescharacteristic
25C2×#13063298C2211yescharacteristic
26C2×#13063294C411yescharacteristic
27C2×#13063294C411yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30#14582970—22no—
31#14582967—22no—
32C8×C22⋊D43—22no—
33(C22⋊D43)⋊C8—22no—
34#14582953C2212yescomplemented
35#14582949C2212yescomplemented
36#14582861C2212yescomplemented
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C22⋊C8×D43C2212yescomplemented
40#14582624C2212yescomplemented
41#14582624C2212yescomplemented
42#14582623C2212yes—
43#14582623C2212yes—
44#14582622C2212yescomplemented
45#14582622C2212yescomplemented
46C22×C22⋊C4×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C43×#323C2212yes—
50C43×#323C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×D172C2×C411yescharacteristic
53C22×C22⋊D43C2×C411yescharacteristic
54C22×C22⋊D43C2×C411yescharacteristic
55C22×C22⋊D43C2×C411yescharacteristic
56C22×C22⋊D43C2×C411yescharacteristic
57C22×C22⋊D43C2×C411yescharacteristic
58C22×C22⋊D43C2×C411yescharacteristic
59C22×C4×D43C2×C411yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C2×#10621872—22no—
62C22×C43⋊C8—21no—
63C22×C43⋊C8—21no—
64C2×C8×D43—22no—
65#13063318—22no—
66#13063318—22no—
67#13063318—22no—
68#13063318—22no—
69#13063311—22no—
70#13063311—22no—
71#13063311—22no—
72#13063311—22no—
73#13063307—22no—
74#13063307—22no—
75#13063307—22no—
76#13063307—22no—
77#13063304—22no—
78#13063304—22no—
79#13063299—22no—
80#13063299—22no—
81#13063298—22no—
82#13063298—22no—
83#13063298—22no—
84#13063298—22no—
85#13063294—22no—
86#13063294—22no—
87#13063294—22no—
88#13063294—22no—
89C4×C22⋊D43—21no—
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92C4×C22⋊D43—21no—
93C4×C22⋊D43D412yes—
94C4×C22⋊D43D412yes—
95C4×C22⋊D43D412yes—
96C4×C22⋊D43D412yes—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2311yescharacteristic
103C2×C22⋊Dic43C2×C411yescharacteristic
104C2×C22⋊Dic43C2×C411yescharacteristic
105C2×C22⋊Dic43C2×C411yescharacteristic
106C2×C22⋊Dic43C2×C411yescharacteristic
107C2×C22⋊Dic43C2×C411yescharacteristic
108C2×C22⋊Dic43C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2311yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119C22⋊(C43⋊C8)C2312yes—
120C22⋊(C43⋊C8)C2312yes—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123#13063235—22no—
124C8×Dic43—22no—
125C25×C43C2×C411yescharacteristic
126C23×C4×C43C2×C411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43—21no—
129C22×C8×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43C2×C411yescharacteristic
135C2×C22⋊C4×C43C2×C411yescharacteristic
136C2×C22⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43C2312yes—
141C22⋊C8×C43C2312yes—
142C24×C43—21no—
143C24×C43—21no—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C22×C411yescharacteristic
149C24×C43C22×C411yescharacteristic
150C24×C43C22×C411yescharacteristic
151C23×D43C22×C411yescharacteristic
152C23×D43C22×C411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—81no—
156C22×C4×C43—81no—
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—21no—
168C2×C22⋊D43—21no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—81no—
176C2×C22⋊D43—81no—
177C2×C22⋊D43—81no—
178C2×C22⋊D43—81no—
179C2×C22⋊D43C22⋊C412yes—
180C2×C22⋊D43C22⋊C412yes—
181C22×Dic43C22×C411yescharacteristic
182C22×Dic43C22×C411yescharacteristic
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186C22×Dic43C22×C411yescharacteristic
187C2×D172—22no—
188C2×D172—81no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—81no—
192C2×C4×D43—81no—
193C2×C4×D43C2×D412yes—
194C2×C4×D43C2×D412yes—
195C2×Dic86—22no—
196C2×Dic86—81no—
197C2×C8×C43—22no—
198C2×C8×C43—22no—
199C2×C8×C43—81no—
200C2×C8×C43—81no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C22⋊Dic43—22no—
210C22⋊Dic43—22no—
211C22⋊Dic43—22no—
212C22⋊Dic43—22no—
213C22⋊Dic43—21no—
214C22⋊Dic43—21no—
215C22⋊Dic43C22⋊C412yes—
216C22⋊Dic43C22⋊C412yes—
217(C2×D43)⋊C4—21no—
218(C2×D43)⋊C4—21no—
219(C2×D43)⋊C4—22no—
220(C2×D43)⋊C4—22no—
221(C2×D43)⋊C4C22⋊C412yes—
222(C2×D43)⋊C4C22⋊C412yes—
223C4⋊Dic43—22no—
224C4⋊Dic43—22no—
225Dic43⋊C4—21no—
226Dic43⋊C4—21no—
227Dic43⋊C4—22no—
228Dic43⋊C4—22no—
229Dic43⋊C4C22⋊C412yes—
230Dic43⋊C4C22⋊C412yes—
231C4×Dic43—21no—
232C4×Dic43—21no—
233C4×Dic43C2×D412yes—
234C4×Dic43C2×D412yes—
235C2×C43⋊C8—22no—
236C2×C43⋊C8—22no—
237C2×C43⋊C8—81no—
238C2×C43⋊C8—81no—
239#10621872—82no—
240C8×D43—82no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—42no—
254C23×C43—42no—
255C23×C43—81no—
256C23×C43—81no—
257C23×C43—81no—
258C23×C43—81no—
259C23×C43—84no—
260C23×C43—84no—
261C23×C43C2×C22⋊C411yescharacteristic
262C23×C43C2×C22⋊C411yescharacteristic
263C23×C43#13112yes—
264C23×C43#13112yes—
265C23×C43C23×C411yescharacteristic
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43C2×C22⋊C412yes—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—81no—
287C2×C4×C43—81no—
288C2×C4×C43C2×C22⋊C411yescharacteristic
289C2×C4×C43C2×C22⋊C411yescharacteristic
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C22⋊D43—24no—
293C22⋊D43—24no—
294C22⋊D43—42no—
295C22⋊D43—42no—
296C22⋊D43—82no—
297C22⋊D43—82no—
298C22⋊D43—82no—
299C22⋊D43—82no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43C2×C22⋊C412yes—
312C2×Dic43C2×C22⋊C412yes—
313C2×Dic43C2×C22⋊C412yes—
314D172—82no—
315C4×D43—42no—
316C4×D43—42no—
317C4×D43—81no—
318C4×D43—81no—
319Dic86—82no—
320C8×C43—42no—
321C8×C43—42no—
322C43⋊C8—42no—
323C43⋊C8—42no—
324#17386—431nomaximal, Sylow
325C22×C43—21no—
326C22×C43—21no—
327C22×C43—21no—
328C22×C43—21no—
329C22×C43—21no—
330C22×C43—21no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—84no—
344C22×C43—84no—
345C22×C43#40812yes—
346C22×C43#40812yes—
347C22×C43C22×C22⋊C411yescharacteristic
348C22×C43C2×#13111yescharacteristic
349C22×C43C2×#13111yescharacteristic
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—41no—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C4×C43—21no—
361C4×C43—21no—
362C4×C43—21no—
363C4×C43—21no—
364C4×C43—41no—
365C4×C43—41no—
366Dic43—22no—
367Dic43—22no—
368Dic43—22no—
369Dic43—41no—
370Dic43—41no—
371Dic43—41no—
372C2×#538—431no—
373#2973—431no—
374#2972—431no—
375#1473—432no—
376#1471—432no—
377#1469—432no—
378#1468—432no—
379#1459—431no—
380#1459—431no—
381C2×#323—431no—
382C2×#323D4311yescharacteristic, complemented
383C2×C43—21no—
384C2×C43—21no—
385C2×C43—22no—
386C2×C43—22no—
387C2×C43—81no—
388C2×C43—81no—
389C2×C43C2×#40811yescharacteristic
390C2×C43#288311yescharacteristic
391C2×C43#288811yescharacteristic
392D43—42no—
393D43—81no—
394#538—862no—
395#538—862no—
396#538—862no—
397#538—862no—
398C2×#126—431no—
399C2×#126—431no—
400C2×#124—431no—
401C2×#124—431no—
402C2×#123—431no—
403C2×#123—431no—
404C2×C22⋊Q8—431no—
405C2×#121—431no—
406C2×#121—431no—
407C2×#121—431no—
408C2×#120—431no—
409C2×#120—431no—
410C2×C4×D4—431no—
411C2×C4×D4—431no—
412C22×C22⋊C4C2×D4311yescharacteristic
413#435—862no—
414#435—862no—
415C8×D4—862no—
416C8×D4—862no—
417#432—432no—
418#431—432no—
419#407—432no—
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422C2×C22⋊C8—432no—
423C2×C22⋊C8C2×D4311yescharacteristic
424C2×C22⋊C8C2×D4311yescharacteristic
425#324—432no—
426#324—432no—
427#323—432no—
428#323—432no—
429#323—432no—
430#323—432no—
431#323C2×D4312yes—
432#323C2×D4312yes—
433C43#1738611yescharacteristic, complemented, Sylow
434C25C4×D4311yescharacteristic
435C22×Q8—431no—
436C22×D4—431no—
437C22×D4—431no—
438C22×D4—431no—
439C22×D4—431no—
440C22×D4—431no—
441C22×D4—431no—
442C22×D4—431no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4C4×D4311yescharacteristic
446C23×C4C22×D4311yescharacteristic
447C2×M16—862no—
448C22×C8—21no—
449C22×C8—21no—
450C22×C8—862no—
451C22×C8—861no—
452C22×C8—861no—
453#126—862no—
454#126—862no—
455#126—862no—
456#126—862no—
457#124—862no—
458#124—862no—
459#124—862no—
460#124—862no—
461#123—862no—
462#123—862no—
463#123—862no—
464#123—862no—
465C22⋊Q8—862no—
466C22⋊Q8—862no—
467#121—862no—
468#121—862no—
469#121—862no—
470#121—862no—
471#121—862no—
472#121—862no—
473#120—862no—
474#120—862no—
475#120—862no—
476#120—862no—
477C4×D4—432no—
478C4×D4—432no—
479C4×D4—432no—
480C4×D4—432no—
481C4×D4—861no—
482C4×D4—861no—
483C4×D4—861no—
484C4×D4—861no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—431no—
497C2×C22⋊C4—431no—
498C2×C22⋊C4—431no—
499C2×C22⋊C4—431no—
500C2×C22⋊C4—431no—
501C2×C22⋊C4—431no—
502C2×C22⋊C4—431no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4C4×D4311yescharacteristic
506C2×C22⋊C4C4×D4311yescharacteristic
507C2×C22⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4C22×D4311yescharacteristic
509C2×C42—431no—
510C2×C42—431no—
511C4⋊C8—862no—
512C4⋊C8—862no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—432no—
516C22⋊C8—432no—
517C22⋊C8—862no—
518C22⋊C8—862no—
519C22⋊C8—861no—
520C22⋊C8—861no—
521C22⋊C8C22×D4312yes—
522C22⋊C8C22×D4312yes—
523#97—862no—
524C4×C8—862no—
525C24—21no—
526C24—21no—
527C24—22no—
528C24—22no—
529C24—81no—
530C24—81no—
531C24—431no—
532C24—431no—
533C24C2×C4×D4311yescharacteristic
534C24C2×C4×D4311yescharacteristic
535C24C2×C4×D4311yescharacteristic
536C2×Q8—862no—
537C2×Q8—3441no—
538C2×D4—432no—
539C2×D4—432no—
540C2×D4—862no—
541C2×D4—862no—
542C2×D4—862no—
543C2×D4—862no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—862no—
547C2×D4—861no—
548C2×D4—861no—
549C2×D4—862no—
550C2×D4—862no—
551C2×D4—3441no—
552C2×D4—3441no—
553C2×D4—3441no—
554C2×D4—3441no—
555C2×D4—3441no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—431no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—3441no—
571C22×C4—3441no—
572C22×C4C2×C4×D4311yescharacteristic
573C22×C4C2×C4×D4311yescharacteristic
574C22×C4C2×C4×D4311yescharacteristic
575C22×C4D4×D4311yescharacteristic
576C22×C4D4×D4311yescharacteristic
577C22×C4D4×D4311yescharacteristic
578C22×C4D4×D4311yescharacteristic
579C22×C4C23×D4311yescharacteristic
580M16—3442no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—81no—
584C2×C8—81no—
585C2×C8—862no—
586C2×C8—862no—
587C2×C8—3442no—
588C2×C8—3441no—
589C2×C8—3441no—
590C4⋊C4—432no—
591C4⋊C4—432no—
592C4⋊C4—862no—
593C4⋊C4—862no—
594C4⋊C4—862no—
595C4⋊C4—862no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—432no—
607C22⋊C4—432no—
608C22⋊C4—432no—
609C22⋊C4—432no—
610C22⋊C4—862no—
611C22⋊C4—862no—
612C22⋊C4—862no—
613C22⋊C4—862no—
614C22⋊C4—862no—
615C22⋊C4—862no—
616C22⋊C4—861no—
617C22⋊C4—861no—
618C22⋊C4—861no—
619C22⋊C4—861no—
620C42—432no—
621C42—432no—
622C42—861no—
623C42—861no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—42no—
637C23—42no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—84no—
643C23—84no—
644C23—432no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23C22⋊C4×D4311yescharacteristic
655C23C22⋊C4×D4311yescharacteristic
656C23#1306333112yes—
657C23#1306333312yes—
658C23C22×C4×D4311yescharacteristic
659Q8—3442no—
660D4—864no—
661D4—864no—
662D4—3442no—
663D4—3442no—
664D4—3442no—
665D4—3442no—
666D4—3442no—
667D4—1722no—
668D4—1722no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—432no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—3441no—
692C2×C4—3441no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4C22⋊C4×D4311yescharacteristic
700C2×C4C22⋊C4×D4311yescharacteristic
701C2×C4C2×D4×D4311yescharacteristic
702C2×C4C2×D4×D4311yescharacteristic
703C8—42no—
704C8—42no—
705C8—1722no—
706C8—1722no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—42no—
714C22—42no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—84no—
726C22—84no—
727C22—862no—
728C22—862no—
729C22—862no—
730C22—3441no—
731C22—3441no—
732C22—3441no—
733C22—3441no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22#1458286412yes—
738C22#1458286412yes—
739C22C2×C22⋊C4×D4311yescharacteristic
740C22C2×#1306333111yescharacteristic
741C22C2×#1306333311yescharacteristic
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—41no—
747C4—41no—
748C4—862no—
749C4—862no—
750C4—862no—
751C4—1721no—
752C4—1721no—
753C4—1721no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—22no—
758C2—81no—
759C2—81no—
760C2—3441no—
761C2—1722no—
762C2C2×#1458286411yescharacteristic
763C2#1914305311yescharacteristic
764C2#1914307111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#323C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583487C2
cosocleC22×C4×C43C24
hypercenterC2×#323D43
hypocenterC43#17386
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #19143621C2semidirect
3. #19143617C2semidirect
4. #19132961C2semidirect
5. #19132953C2semidirect
6. #19132945C2semidirect
7. #19132940C2semidirect
8. #19132911C2semidirect
9. #19132911C2semidirect
10. C2×#14582623C2semidirect
11. C2×C43×#323C2semidirect
34. #14582953C22semidirect
35. #14582949C22semidirect
36. #14582861C22semidirect
39. C22⋊C8×D43C22semidirect
40. #14582624C22semidirect
41. #14582624C22semidirect
44. #14582622C22semidirect
45. #14582622C22semidirect
382. C2×#323D43semidirect
433. C43#17386semidirect

Maximal subgroups

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

subgroupindex
C2×#145834872
#191436212
#191436172
#191329612
#191329532
#191329452
#191329402
#191329112
C2×#145826232
C2×C43×#3232
#1738643