Finite Group Databasebeta

← #25062621

Subgroups — #25062621

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×#14583482C211yesmaximal, characteristic
2#19143621C211yesmaximal, characteristic, complemented
3#19143617C211yesmaximal, characteristic, complemented
4#19132963C212yesmaximal, complemented
5#19132953C212yesmaximal, complemented
6#19132945C212yesmaximal, complemented
7#19132942C212yesmaximal, complemented
8#19132913C211yesmaximal, characteristic, complemented
9C2×#14582622C211yesmaximal, characteristic, complemented
10C2×#14582622C211yesmaximal, characteristic, complemented
11C43×#1459C211yesmaximal, characteristic, complemented
12#14583482—22no—
13#14583482—22no—
14#14583482—22no—
15#14583482—22no—
16C2×#13063320C2211yescharacteristic
17C2×#13063319C411yescharacteristic
18C2×#13063313C411yescharacteristic
19C2×#13063311C2211yescharacteristic
20C2×#13063310C2211yescharacteristic
21C2×#13063308C411yescharacteristic
22C2×#13063302C411yescharacteristic
23C2×#13063299C411yescharacteristic
24C2×#13063298C2211yescharacteristic
25C2×#13063297C411yescharacteristic
26C2×#13063295C411yescharacteristic
27C2×#13063293C411yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
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#14582625C2212yescomplemented
41#14582623C2212yescomplemented
42#14582622C2212yes—
43#14582622C2212yes—
44#14582622C2212yes—
45#14582622C2212yes—
46C2×C4×D4×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C43×#324C2212yescomplemented
50C43×#323C2212yescomplemented
51C24×D43C2×C411yescharacteristic
52C22×Dic86C2×C411yescharacteristic
53C22×D172C2×C411yescharacteristic
54C22×D172C2×C411yescharacteristic
55C22×C22⋊D43C2×C411yescharacteristic
56C22×C22⋊D43C2×C411yescharacteristic
57C22×C22⋊D43C2×C411yescharacteristic
58C22×C22⋊D43C2×C411yescharacteristic
59C23×Dic43C2×C411yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C2×#10621872—22no—
62C22×C43⋊C8—21no—
63C22×C43⋊C8—21no—
64C2×C8×D43—22no—
65#13063320—22no—
66#13063320—22no—
67#13063319—22no—
68#13063319—22no—
69#13063313—22no—
70#13063313—22no—
71#13063311—22no—
72#13063311—22no—
73#13063310—22no—
74#13063310—22no—
75#13063308—22no—
76#13063308—22no—
77#13063302—22no—
78#13063302—22no—
79#13063299—22no—
80#13063299—22no—
81#13063298—22no—
82#13063298—22no—
83#13063297—22no—
84#13063297—22no—
85#13063295—22no—
86#13063295—22no—
87#13063293—22no—
88#13063293—22no—
89C4×C22⋊D43D412yes—
90C4×C22⋊D43D412yes—
91C4×C22⋊D43D412yes—
92C4×C22⋊D43D412yes—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×C22⋊Dic43C2×C411yescharacteristic
99C2×C22⋊Dic43C2×C411yescharacteristic
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2311yescharacteristic
113C2×(C2×D43)⋊C4C2311yescharacteristic
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—
125C22×D4×C43C2×C411yescharacteristic
126C23×C4×C43C2×C411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43—21no—
129C22×C8×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43C2×C411yescharacteristic
136C2×C22⋊C4×C43C2311yescharacteristic
137C2×C42×C43C2×C411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43C2312yes—
141C22⋊C8×C43C2312yes—
142C24×C43C22×C411yescharacteristic
143C24×C43C22×C411yescharacteristic
144C23×D43—21no—
145C23×D43—21no—
146C23×D43—22no—
147C23×D43—22no—
148C23×D43—81no—
149C23×D43—81no—
150C23×D43C22×C411yescharacteristic
151C23×D43C22×C411yescharacteristic
152C23×D43C22×C411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—81no—
160C22×C4×C43—81no—
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2411yescharacteristic
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⋊D43C22⋊C412yes—
179C2×C22⋊D43C22⋊C412yes—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—81no—
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186C22×Dic43C22×C411yescharacteristic
187C22×Dic43C22×C411yescharacteristic
188C2×D172—22no—
189C2×D172—22no—
190C2×D172—81no—
191C2×D172—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—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C42×C43—21no—
208C42×C43—21no—
209C22⋊Dic43—22no—
210C22⋊Dic43C22⋊C412yes—
211C22⋊Dic43C22⋊C412yes—
212(C2×D43)⋊C4—21no—
213(C2×D43)⋊C4—21no—
214(C2×D43)⋊C4—21no—
215(C2×D43)⋊C4—21no—
216(C2×D43)⋊C4—21no—
217(C2×D43)⋊C4—21no—
218(C2×D43)⋊C4—21no—
219(C2×D43)⋊C4—21no—
220(C2×D43)⋊C4—22no—
221(C2×D43)⋊C4—22no—
222(C2×D43)⋊C4—22no—
223(C2×D43)⋊C4—22no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4C22⋊C412yes—
226(C2×D43)⋊C4C22⋊C412yes—
227C4⋊Dic43—22no—
228Dic43⋊C4—22no—
229Dic43⋊C4—22no—
230Dic43⋊C4—22no—
231Dic43⋊C4C22⋊C412yes—
232Dic43⋊C4C22⋊C412yes—
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—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43C2×C22⋊C411yescharacteristic
249C23×C43C2×C22⋊C411yescharacteristic
250C23×C43#13112yes—
251C23×C43#13112yes—
252C23×C43C23×C411yescharacteristic
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—42no—
264C22×D43—42no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—81no—
270C22×D43—81no—
271C22×D43—81no—
272C22×D43—81no—
273C22×D43—84no—
274C22×D43—84no—
275C22×D43C2×C22⋊C412yes—
276D4×C43—42no—
277D4×C43—42no—
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×C43—81no—
292C2×C4×C43—81no—
293C2×C4×C43C2×C22⋊C411yescharacteristic
294C2×C4×C43C2×C22⋊C411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C22⋊D43—24no—
298C22⋊D43—24no—
299C22⋊D43—82no—
300C22⋊D43—82no—
301C22⋊D43—82no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—81no—
311C2×Dic43—81no—
312C2×Dic43C2×C22⋊C412yes—
313C2×Dic43C2×C22⋊C412yes—
314C2×Dic43C2×C22⋊C412yes—
315D172—82no—
316D172—82no—
317C4×D43—42no—
318C4×D43—42no—
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—81no—
337C22×C43—81no—
338C22×C43#40812yes—
339C22×C43#40812yes—
340C22×C43C22×C22⋊C411yescharacteristic
341C22×C43C2×#13111yescharacteristic
342C22×C43C2×#13111yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—81no—
353C2×D43—81no—
354C2×D43—84no—
355C2×D43—84no—
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—
366C4×C43—41no—
367Dic43—22no—
368Dic43—22no—
369Dic43—22no—
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#1459D4311yescharacteristic, complemented
381C2×#323—431no—
382C2×#323—431no—
383C2×C43—21no—
384C2×C43—21no—
385C2×C43—22no—
386C2×C43—22no—
387C2×C43—81no—
388C2×C43C2×#40811yescharacteristic
389C2×C43#288311yescharacteristic
390C2×C43#288811yescharacteristic
391D43—42no—
392D43—81no—
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×D4C2×D4311yescharacteristic
412C22×C22⋊C4—431no—
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#324C2×D4312yescomplemented
427#323—432no—
428#323—432no—
429#323—432no—
430#323—432no—
431#323—432no—
432#323C2×D4312yescomplemented
433C43#1738611yescharacteristic, complemented, Sylow
434C25—431no—
435C22×Q8—431no—
436C22×D4—431no—
437C22×D4—431no—
438C22×D4—431no—
439C22×D4—431no—
440C22×D4—431no—
441C22×D4—431no—
442C22×D4C4×D4311yescharacteristic
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—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—432no—
482C4×D4—432no—
483C4×D4—432no—
484C4×D4—432no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C22⋊C4—431no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—431no—
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—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4C4×D4311yescharacteristic
508C2×C22⋊C4C22×D4311yescharacteristic
509C2×C42—431no—
510C2×C42C4×D4311yescharacteristic
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—431no—
526C24—431no—
527C24—431no—
528C24—861no—
529C24—861no—
530C24—862no—
531C24—862no—
532C24—3441no—
533C24—3441no—
534C24C2×C4×D4311yescharacteristic
535C24C2×C4×D4311yescharacteristic
536C2×Q8—862no—
537C2×Q8—3441no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—432no—
543C2×D4—432no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—862no—
547C2×D4—862no—
548C2×D4—862no—
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—861no—
568C22×C4—861no—
569C22×C4—3441no—
570C22×C4—3441no—
571C22×C4C2×C4×D4311yescharacteristic
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—21no—
591C4⋊C4—21no—
592C4⋊C4—432no—
593C4⋊C4—432no—
594C4⋊C4—862no—
595C4⋊C4—862no—
596C4⋊C4—862no—
597C4⋊C4—862no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—432no—
603C22⋊C4—432no—
604C22⋊C4—432no—
605C22⋊C4—432no—
606C22⋊C4—862no—
607C22⋊C4—862no—
608C22⋊C4—862no—
609C22⋊C4—862no—
610C22⋊C4—862no—
611C22⋊C4—862no—
612C22⋊C4—861no—
613C22⋊C4—861no—
614C22⋊C4—861no—
615C22⋊C4—861no—
616C22⋊C4—861no—
617C22⋊C4—861no—
618C22⋊C4—861no—
619C22⋊C4—861no—
620C42—21no—
621C42—21no—
622C42—432no—
623C42—432no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—432no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—3441no—
641C23—3441no—
642C23—3441no—
643C23—3441no—
644C23—3444no—
645C23—3444no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1722no—
653C23—1722no—
654C23C22⋊C4×D4311yescharacteristic
655C23C22⋊C4×D4311yescharacteristic
656C23#1306333112yes—
657C23#1306333312yes—
658C23C22×C4×D4311yescharacteristic
659Q8—3442no—
660D4—42no—
661D4—42no—
662D4—864no—
663D4—864no—
664D4—3442no—
665D4—3442no—
666D4—3442no—
667D4—3442no—
668D4—3442no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
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—81no—
683C2×C4—81no—
684C2×C4—432no—
685C2×C4—432no—
686C2×C4—432no—
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—81no—
719C22—81no—
720C22—862no—
721C22—862no—
722C22—862no—
723C22—3441no—
724C22—3441no—
725C22—3441no—
726C22—3441no—
727C22—3444no—
728C22—3444no—
729C22—3441no—
730C22—3441no—
731C22—1721no—
732C22—1721no—
733C22—1721no—
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—41no—
749C4—862no—
750C4—862no—
751C4—862no—
752C4—1721no—
753C4—1721no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—22no—
758C2—81no—
759C2—3441no—
760C2—3441no—
761C2—1722no—
762C2C2×#1458286411yescharacteristic
763C2#1914305311yescharacteristic
764C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1459C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583482C2
cosocleC22×C4×C43C24
hypercenter#1459D43
hypocenterC43#17386
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #19143621C2semidirect
3. #19143617C2semidirect
4. #19132963C2semidirect
5. #19132953C2semidirect
6. #19132945C2semidirect
7. #19132942C2semidirect
8. #19132913C2semidirect
9. C2×#14582622C2semidirect
10. C2×#14582622C2semidirect
11. C43×#1459C2semidirect
34. #14582953C22semidirect
35. #14582949C22semidirect
36. #14582861C22semidirect
39. C22⋊C8×D43C22semidirect
40. #14582625C22semidirect
41. #14582623C22semidirect
49. C43×#324C22semidirect
50. C43×#323C22semidirect
380. #1459D43semidirect
426. #324C2×D43semidirect
432. #323C2×D43semidirect
433. C43#17386semidirect

Maximal subgroups

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

subgroupindex
C2×#145834822
#191436212
#191436172
#191329632
#191329532
#191329452
#191329422
#191329132
C2×#145826222
C43×#14592
#1738643