Finite Group Databasebeta

← #25102333

Subgroups — #25102333

Order 11008.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583371C211yesmaximal, characteristic
2C2×#14583051C211yesmaximal, characteristic
3C2×#14583001C211yesmaximal, characteristic, complemented
4C2×C4×#10621883C211yesmaximal, characteristic, complemented
5#19137278C211yesmaximal, characteristic, complemented
6#19134930C211yesmaximal, characteristic, complemented
7#19134927C211yesmaximal, characteristic, complemented
8#19134906C211yesmaximal, characteristic, complemented
9#19134857C211yesmaximal, characteristic, complemented
10#19134844C211yesmaximal, characteristic, complemented
11#19134797C211yesmaximal, characteristic, complemented
12#19134524C211yesmaximal, characteristic
13C4×#13063245C211yesmaximal, characteristic, complemented
14#19134364C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20#14583371—24no—
21#14583371—24no—
22C2×C4×Dic86C2211yescharacteristic, complemented
23C2×C4×D172C2211yescharacteristic
24C2×D4×Dic43C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063283C2211yescharacteristic
29C2×#13063282C2211yescharacteristic
30C22×(C2×D43)⋊C4—21no—
31C2×C22⋊C4×D43—21no—
32#14583051C418yescomplemented
33#14583001—24no—
34C4×#10621883—24no—
35C2×#13063259C2211yescharacteristic, complemented
36C2×#13063256C2211yescharacteristic, complemented
37C2×#13063250C2211yescharacteristic, complemented
38C2×#13063248C2211yescharacteristic, complemented
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic, complemented
46#14582804C2211yescharacteristic, complemented
47#14582798C2211yescharacteristic, complemented
48#14582797—21no—
49#14582791—21no—
50#14582790—21no—
51#14582784—21no—
52#14582756C2211yescharacteristic
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic, complemented
61C4×C4⋊C4×C43C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×Dic86C2311yescharacteristic
66C22×D172C2311yescharacteristic
67C22×C22⋊D43—21no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—22no—
73C2×D4×D43C2×C414yes—
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C2×#10621873—22no—
79C2×#10621873—22no—
80C2×#10621873C2×C414yescomplemented
81C2×#10621883—22no—
82C2×#10621883—22no—
83C2×#10621883C2×C414yescomplemented
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86#13063305—22no—
87#13063305C2×C414yescomplemented
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×D172—22no—
91C4×D172D414yes—
92D4×Dic43—22no—
93D4×Dic43—22no—
94#13063287—22no—
95#13063287—22no—
96C4×C22⋊D43—28no—
97(C22⋊D43)⋊C4—28no—
98#13063283—22no—
99#13063283—22no—
100#13063282—22no—
101#13063282—22no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4D411yescharacteristic
108C2×Dic43⋊C4D411yescharacteristic
109C2×C22⋊Dic43—21no—
110C2×(C2×D43)⋊C4—28no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×(C2×D43)⋊C4D411yescharacteristic
118C22⋊C4×D43—28no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43C2311yescharacteristic
122#13063259—22no—
123#13063256—22no—
124#13063250—22no—
125#13063248—22no—
126#13063247—22no—
127#13063246—22no—
128#13063245—22no—
129#13063245C2×C414yescomplemented
130(C2×D43)⋊C8—22no—
131(C2×D43)⋊C8C2×C414yescomplemented
132C4×C43⋊C8—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C22×D4×C43C2311yescharacteristic
138C23×C4×C43—21no—
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×D4×C43—22no—
142C4×D4×C43D414yes—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#102×C43—22no—
150#102×C43C2×C414yescomplemented
151#97×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C23×D43—21no—
155C23×D43—24no—
156C23×D43—24no—
157C23×D43—24no—
158C23×D43—81no—
159C23×D43—81no—
160C23×D43—81no—
161C23×D43—81no—
162C23×D43C2×D411yescharacteristic
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43C22×C412yes—
167C2×D4×C43C2×D412yes—
168C2×D4×C43#4112yes—
169C22×C4×C43—24no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—81no—
174C22×C4×C43—81no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2411yescharacteristic
178C2×C22⋊D43—24no—
179C2×C22⋊D43—24no—
180C2×C22⋊D43—24no—
181C22×Dic43—24no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—81no—
186C22×Dic43—81no—
187C22×Dic43C2×D411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190D4×D43—28no—
191D4×D43—28no—
192D4×D43—28no—
193D4×D43—28no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172C22×C412yes—
198C2×D172C2×D412yes—
199C2×D172#4112yes—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—24no—
205C2×C4×D43—24no—
206C2×C4×D43—81no—
207C2×C4×D43—81no—
208C2×C4×D43—81no—
209C2×C4×D43—81no—
210C2×C4×D43C22×C412yes—
211C2×C4×D43#4112yes—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86C22×C412yes—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43C22×C412yes—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43C22×C412yes—
229C4⋊C4×C43C2×D412yes—
230C22⋊C4×C43—24no—
231C42×C43—81no—
232C42×C43C2×D412yes—
233C42×C43C2×D412yes—
234C22⋊Dic43—24no—
235#10621883—28no—
236(C2×D43)⋊C4—24no—
237(C2×D43)⋊C4—24no—
238(C2×D43)⋊C4—22no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—81no—
243C4⋊Dic43—21no—
244C4⋊Dic43—24no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—81no—
248C4⋊Dic43C2×D412yes—
249Dic43⋊C4—22no—
250Dic43⋊C4—22no—
251Dic43⋊C4—42no—
252C4×Dic43—24no—
253C4×Dic43—21no—
254C4×Dic43—21no—
255C4×Dic43—42no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8C22×C412yes—
262#10621873—28no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C22×D411yescharacteristic
271C22×D43—22no—
272C22×D43—21no—
273C22×D43—22no—
274C22×D43—21no—
275C22×D43—22no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—216no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—84no—
286C22×D43—84no—
287C22×D43—84no—
288C22×D43—84no—
289C22×D43—84no—
290C22×D43—84no—
291C22×D43C4×D412yes—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43C4×D414yes—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—84no—
310C2×C4×C43#12012yes—
311C2×C4×C43#12012yes—
312C2×C4×C43C23×C411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C22⋊D43—216no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—22no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—22no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—84no—
337C2×Dic43C4×D412yes—
338D172—22no—
339D172—22no—
340D172—22no—
341D172C4×D414yes—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—84no—
347C4×D43—84no—
348Dic86—22no—
349Dic86—22no—
350Dic86—41no—
351Dic86—41no—
352C8×C43—22no—
353C8×C43—41no—
354C43⋊C8—22no—
355C43⋊C8—41no—
356#21459—431nomaximal, Sylow
357C22×C43—24no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43C2×C4×D411yescharacteristic
365C22×C43C2×#12011yescharacteristic
366C22×C43#52511yescharacteristic
367C22×C43#57611yescharacteristic
368C22×C43#57711yescharacteristic
369C22×C43#57711yescharacteristic
370C22×C43#57711yescharacteristic
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—22no—
374C2×D43—24no—
375C2×D43—41no—
376C2×D43—42no—
377C2×D43—41no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—41no—
382C2×D43—42no—
383C2×D43—41no—
384C2×D43—42no—
385C2×D43—816no—
386C4×C43—22no—
387C4×C43—22no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43—81no—
391C4×C43C2×C4×D411yescharacteristic
392C4×C43C2×C4×D411yescharacteristic
393C4×C43#52511yescharacteristic
394C4×C43#52511yescharacteristic
395Dic43—22no—
396Dic43—41no—
397Dic43—42no—
398Dic43—41no—
399Dic43—42no—
400Dic43—81no—
401C2×#518—431no—
402C2×#450—431no—
403C2×#440—431no—
404C2×C4×SD16—431no—
405#2323—431no—
406#1877—431no—
407#1877—431no—
408#1873—431no—
409#1864—431no—
410#1862—431no—
411#1854—431no—
412#1786—431no—
413#1762D4311yescharacteristic, complemented
414C4×#102—431no—
415#1750—431no—
416C2×C43—44no—
417C2×C43C4×#12011yescharacteristic
418C2×C43#294611yescharacteristic
419C2×C43#294911yescharacteristic
420C2×C43#300911yescharacteristic
421C2×C43#301211yescharacteristic
422C2×C43#311811yescharacteristic
423C2×C43#312311yescharacteristic
424D43—42no—
425D43—44no—
426C23×D4—431no—
427C22×SD16—431no—
428C22×SD16—431no—
429C2×C22⋊Q8—431no—
430#518—864no—
431#518—864no—
432C2×C4×Q8—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×C4×D4C2×D4311yescharacteristic
439C2×#117—431no—
440C2×#117—431no—
441C22×C22⋊C4—861no—
442C22×C22⋊C4—861no—
443#450—438no—
444#440—864no—
445C4×SD16—864no—
446C2×#107—431no—
447C2×#106—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102C2×D4311yescharacteristic
455C2×#102C2×D4311yescharacteristic
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×#97C2×D4311yescharacteristic, complemented
459C2×C4×C8—431no—
460#391—431no—
461#389—431no—
462#389—861no—
463#388—861no—
464#388—861no—
465#387—861no—
466#380—431no—
467C4×C4⋊C4C2×D4311yescharacteristic, complemented
468#340—431no—
469#340—431no—
470#340C2×D4311yescharacteristic, complemented
471#340C2×D4311yescharacteristic, complemented
472#336—431no—
473#336—431no—
474C43#2145911yescharacteristic, complemented, Sylow
475C25—861no—
476C22×Q8—431no—
477C22×D4—434no—
478C22×D4—431no—
479C22×D4—862no—
480C22×D4—861no—
481C22×D4—862no—
482C22×D4—862no—
483C22×D4—862no—
484C22×D4—862no—
485C22×D4C22×D4311yescharacteristic
486C23×C4—21no—
487C23×C4—431no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491C2×SD16—434no—
492C2×SD16—434no—
493C2×SD16—862no—
494C2×SD16—862no—
495C2×SD16—862no—
496C2×SD16—862no—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8C22×D4311yescharacteristic
500C22×C8C22×D4311yescharacteristic
501C22⋊Q8—434no—
502C22⋊Q8—862no—
503C4×Q8—862no—
504C4×Q8—862no—
505C4×D4—22no—
506C4×D4—434no—
507C4×D4—868no—
508C4×D4—862no—
509C4×D4—862no—
510C4×D4—868no—
511C4×D4—862no—
512C4×D4—862no—
513C4×D4—862no—
514C4×D4D17214yes—
515#117—862no—
516#117—862no—
517#117—862no—
518#117—862no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—868no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—868no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C42—21no—
541C2×C42—431no—
542C2×C42—861no—
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545#107—862no—
546#106—862no—
547#103—862no—
548#103—862no—
549#102—22no—
550#102—434no—
551#102—862no—
552#102—862no—
553#102—862no—
554#102C4×D4314yescomplemented
555C22⋊C8—434no—
556C22⋊C8—862no—
557#97—22no—
558C4×C8—862no—
559#95—21no—
560#95—861no—
561#95—861no—
562#95—861no—
563#95—861no—
564C24—21no—
565C24—431no—
566C24—864no—
567C24—864no—
568C24—864no—
569C24—861no—
570C24—3441no—
571C24—3441no—
572C24—3441no—
573C24—3441no—
574C2×Q8—432no—
575C2×Q8—861no—
576C2×Q8—861no—
577C2×Q8—861no—
578C2×Q8—861no—
579C2×Q8—861no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—432no—
584C2×D4—432no—
585C2×D4—432no—
586C2×D4—864no—
587C2×D4—868no—
588C2×D4—868no—
589C2×D4—868no—
590C2×D4—864no—
591C2×D4—864no—
592C2×D4—868no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4C2×C4×D4312yes—
597C2×D4C2×D17212yes—
598C2×D4#1062189812yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—431no—
606C22×C4—432no—
607C22×C4—432no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—864no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—864no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—864no—
619C22×C4—861no—
620C22×C4—3441no—
621C22×C4—3441no—
622C22×C4—3441no—
623C22×C4—3441no—
624C22×C4—3441no—
625C22×C4—3441no—
626C22×C4D4×D4311yescharacteristic
627C22×C4D4×D4311yescharacteristic
628C22×C4C23×D4311yescharacteristic
629SD16—868no—
630SD16—868no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—432no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8C2×C4×D4312yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—432no—
648C4⋊C4—864no—
649C4⋊C4—862no—
650C4⋊C4—862no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—3441no—
655C4⋊C4—1722no—
656C4⋊C4C2×C4×D4312yes—
657C4⋊C4C2×D17212yes—
658C22⋊C4—24no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—862no—
664C22⋊C4—862no—
665C22⋊C4—864no—
666C22⋊C4—3441no—
667C42—81no—
668C42—864no—
669C42—861no—
670C42—861no—
671C42—1722no—
672C42C2×D17212yes—
673C42D4×D4312yes—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—432no—
682C23—8616no—
683C23—862no—
684C23—861no—
685C23—862no—
686C23—861no—
687C23—862no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—3444no—
693C23—3444no—
694C23—3444no—
695C23—3444no—
696C23—3444no—
697C23—3444no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23—1721no—
702C23C2×D4×D4311yescharacteristic
703Q8—862no—
704Q8—862no—
705Q8—1721no—
706Q8—1721no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—434no—
711D4—8616no—
712D4—862no—
713D4—862no—
714D4—862no—
715D4C4×D17214yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—84no—
730C2×C4—432no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—3444no—
746C2×C4—3444no—
747C2×C4—3444no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4#1306329512yes—
756C2×C4#1306329512yes—
757C2×C4C22×C4×D4311yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4C22×D17211yescharacteristic
760C2×C4#41×D4311yescharacteristic
761C2×C4#41×D4311yescharacteristic
762C2×C4C2×#1062189811yescharacteristic
763C8—22no—
764C8—41no—
765C8—862no—
766C8—1721no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—862no—
775C22—862no—
776C22—862no—
777C22—864no—
778C22—34416no—
779C22—1722no—
780C22—1722no—
781C22—1721no—
782C22—1722no—
783C22—1721no—
784C22—1722no—
785C22—1722no—
786C22—1721no—
787C22—1722no—
788C22—1721no—
789C22C4×D4×D4311yescharacteristic
790C22C2×#1306329511yescharacteristic
791C22#1458340811yescharacteristic
792C22#1458370311yescharacteristic
793C22#1458370811yescharacteristic
794C22#1458370911yescharacteristic
795C22#1458370911yescharacteristic
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—81no—
801C4—862no—
802C4—3441no—
803C4—1722no—
804C4—1721no—
805C4—1721no—
806C4—1722no—
807C4C4×D4×D4311yescharacteristic
808C4C2×C4×D17211yescharacteristic
809C4#1458340811yescharacteristic
810C4#1458341111yescharacteristic
811C2—44no—
812C2—1722no—
813C2—1724no—
814C2C4×#1306329511yescharacteristic
815C2#1914342411yescharacteristic
816C2#1914345111yescharacteristic
817C2#1914387311yescharacteristic
818C2#1914390111yescharacteristic
819C2#1914477711yescharacteristic
820C2#1914484611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#21459
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. C2×#14583001C2semidirect
4. C2×C4×#10621883C2semidirect
5. #19137278C2semidirect
6. #19134930C2semidirect
7. #19134927C2semidirect
8. #19134906C2semidirect
9. #19134857C2semidirect
10. #19134844C2semidirect
11. #19134797C2semidirect
13. C4×#13063245C2semidirect
14. #19134364C2semidirect
15. C43×#1762C2semidirect
22. C2×C4×Dic86C22semidirect
32. #14583051C4semidirect
35. C2×#13063259C22semidirect
36. C2×#13063256C22semidirect
37. C2×#13063250C22semidirect
38. C2×#13063248C22semidirect
45. C2×C4×C43⋊C8C22semidirect
46. #14582804C22semidirect
47. #14582798C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
60. C2×#97×C43C22semidirect
61. C4×C4⋊C4×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
80. C2×#10621873C2×C4semidirect
83. C2×#10621883C2×C4semidirect
87. #13063305C2×C4semidirect
129. #13063245C2×C4semidirect
131. (C2×D43)⋊C8C2×C4semidirect
150. #102×C43C2×C4semidirect
413. #1762D43semidirect
458. C2×#97C2×D43semidirect
467. C4×C4⋊C4C2×D43semidirect
470. #340C2×D43semidirect
471. #340C2×D43semidirect
474. C43#21459semidirect
554. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833712
C2×#145830512
C2×#145830012
C2×C4×#106218832
#191372782
#191349302
#191349272
#191349062
#191348572
#191348442
#191347972
#191345242
C4×#130632452
#191343642
C43×#17622
#2145943