Finite Group Databasebeta

← #25063943

Subgroups — #25063943

Order 11008.

1036 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2C2×#14582949C211yesmaximal, characteristic, complemented
3#19136986C211yesmaximal, characteristic, complemented
4#19133157C212yesmaximal, complemented
5#19133153C212yesmaximal, complemented
6#19133152C211yesmaximal, characteristic, complemented
7#19133151C211yesmaximal, characteristic, complemented
8#19133149C211yesmaximal, characteristic, complemented
9#19133080C212yesmaximal, complemented
10#19133078C212yesmaximal, complemented
11C43×#1516C211yesmaximal, characteristic, complemented
12#14583452C411yescharacteristic, complemented
13#14583451C411yescharacteristic, complemented
14#14583451C2211yescharacteristic
15#14583445C411yescharacteristic, complemented
16#14583444C411yescharacteristic, complemented
17#14583444C2211yescharacteristic
18#14583435C411yescharacteristic, complemented
19#14583435C2211yescharacteristic
20#14583430C411yescharacteristic, complemented
21#14583430C2211yescharacteristic
22#14583429—21no—
23#14583429—21no—
24#14583426—21no—
25#14583426—21no—
26#14583410C2211yescharacteristic
27#14583405—21no—
28#14583405—21no—
29#41×Dic43C411yescharacteristic, complemented
30#14583367C411yescharacteristic, complemented
31C4×#10621900—21no—
32C4×#10621900—21no—
33C22×C4×Dic43C2211yescharacteristic
34#14582949—21no—
35#14582949—21no—
36#14582949C2212yes—
37#14582949C2212yes—
38C2×Dic43⋊C8—21no—
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C8×Dic43—21no—
41#14582766—21no—
42#14582763C2212yes—
43#14582762C2211yescharacteristic
44#14582757—21no—
45#14582750—21no—
46C22⋊C4×Dic43—21no—
47#14582744C2212yes—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#525C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C43×#381C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621898C2×C411yescharacteristic
60C2×#10621900—21no—
61C2×#10621900—21no—
62C23×Dic43D411yescharacteristic
63C23×Dic43D411yescharacteristic
64C22×C43⋊C8—21no—
65#13063324C2×C411yescharacteristic
66#13063324C2×C411yescharacteristic
67#13063323C2×C411yescharacteristic
68#13063321C2×C411yescharacteristic
69#13063320—21no—
70#13063320—21no—
71#13063318—21no—
72#13063318—21no—
73#13063316C2×C411yescharacteristic
74#13063316C2×C411yescharacteristic
75#13063315—21no—
76#13063315—21no—
77#13063314C2×C411yescharacteristic
78#13063312C2×C411yescharacteristic
79#13063311—21no—
80#13063311—21no—
81#13063309—21no—
82#13063309—21no—
83#13063308—21no—
84#13063306—21no—
85#13063306—21no—
86#13063304C2×C411yescharacteristic
87#13063304C2311yescharacteristic
88#13063302—21no—
89#13063302—21no—
90#13063302—21no—
91#13063302—21no—
92#13063299C2×C411yescharacteristic
93#13063299C2311yescharacteristic
94#13063297—21no—
95#13063297—21no—
96#13063297—21no—
97#13063297—21no—
98#13063294—21no—
99Q8×Dic43C2×C411yescharacteristic
100Q8×Dic43C2×C411yescharacteristic
101C4×Dic86—21no—
102C4×Dic86—21no—
103#13063290—21no—
104#13063290—21no—
105#13063290C2×C411yescharacteristic
106#13063290C2×C411yescharacteristic
107D4×Dic43—21no—
108D4×Dic43—21no—
109D4×Dic43—21no—
110D4×Dic43—21no—
111D4×Dic43C2×C411yescharacteristic
112D4×Dic43C2×C411yescharacteristic
113#13063287C2×C411yescharacteristic
114#13063287C2×C411yescharacteristic
115C4×C22⋊D43—21no—
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119(C22⋊D43)⋊C4—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125#13063284—21no—
126#13063284C2×C411yescharacteristic
127#13063283—21no—
128#13063283—21no—
129#13063282—21no—
130#13063281—21no—
131#13063281—21no—
132#13063281—21no—
133#13063281—21no—
134C2×Dic43⋊C4—22no—
135C2×C22⋊Dic43—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43—22no—
138C2×C4×Dic43C2×C411yescharacteristic
139C2×C4×Dic43C2×C411yescharacteristic
140C2×C4×Dic43C2×C411yescharacteristic
141C2×C4×Dic43C2×C411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149C2×C4×Dic43C2311yescharacteristic
150C42×D43—21no—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)—21no—
154C22⋊(C43⋊C8)C2312yes—
155C8×Dic43—22no—
156C8×Dic43—22no—
157C43⋊#95—21no—
158C43⋊#95—22no—
159C43⋊#95—22no—
160C43⋊#95C2312yes—
161C2×#41×C43C2×C411yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C22×C8×C43—21no—
164#123×C43—21no—
165C22⋊Q8×C43C2×C411yescharacteristic
166C22⋊Q8×C43C2311yescharacteristic
167#121×C43C2×C411yescharacteristic
168#121×C43C2311yescharacteristic
169#120×C43—21no—
170C4×D4×C43—21no—
171C4×D4×C43—21no—
172#117×C43C2×C411yescharacteristic
173C2×C22⋊C4×C43—21no—
174C22⋊C8×C43—21no—
175C22⋊C8×C43C2312yes—
176#95×C43—21no—
177#95×C43C2312yes—
178C24×C43C2×D411yescharacteristic
179#41×C43—42no—
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43C22×C411yescharacteristic
185C22×C4×C43—21no—
186C22×C4×C43—22no—
187C22×C4×C43—42no—
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C22×C411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C2×C22⋊D43—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C22×Dic43—24no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—22no—
203C22×Dic43—42no—
204C22×Dic43C22⋊C411yescharacteristic
205C22×Dic43C22⋊C411yescharacteristic
206C22×Dic43C22⋊C411yescharacteristic
207C22×Dic43C22⋊C411yescharacteristic
208C22×Dic43C22⋊C411yescharacteristic
209C22×Dic43C22⋊C411yescharacteristic
210C22×Dic43C22⋊C411yescharacteristic
211C22×Dic43C22⋊C411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216#10621900—44no—
217#10621900—44no—
218#10621898—42no—
219C2×D172C22×C411yescharacteristic
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86C22×C411yescharacteristic
226C2×C8×C43—22no—
227C2×C8×C43—42no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43C22×C411yescharacteristic
231C4⋊C4×C43C22×C411yescharacteristic
232C22⋊C4×C43—21no—
233C22⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—42no—
238C42×C43—21no—
239C22⋊Dic43—21no—
240C22⋊Dic43—21no—
241C22⋊Dic43—21no—
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—42no—
247(C2×D43)⋊C4—21no—
248(C2×D43)⋊C4—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43C22×C411yescharacteristic
258C4⋊Dic43C22×C411yescharacteristic
259Dic43⋊C4—21no—
260Dic43⋊C4—21no—
261Dic43⋊C4—21no—
262Dic43⋊C4—21no—
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—44no—
270C4×Dic43—21no—
271C4×Dic43—21no—
272C4×Dic43—21no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—44no—
276C4×Dic43C22⋊C411yescharacteristic
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22×C411yescharacteristic
285C4×Dic43C22×C411yescharacteristic
286C4×Dic43C22×C411yescharacteristic
287C4×Dic43C22×C411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290C4×Dic43C2×D411yescharacteristic
291C4×Dic43C2×D411yescharacteristic
292C2×C43⋊C8—22no—
293C2×C43⋊C8—42no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—21no—
297C23×C43—41no—
298C23×C43C2×C22⋊C411yescharacteristic
299C23×C43C2×C22⋊C411yescharacteristic
300C23×C43C22×D411yescharacteristic
301C22×D43—21no—
302Q8×C43—41no—
303D4×C43—41no—
304D4×C43—42no—
305D4×C43—42no—
306D4×C43—42no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C2×C22⋊C411yescharacteristic
322C2×C4×C43C23×C411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C22⋊D43—42no—
325C22⋊D43—42no—
326C22⋊D43—42no—
327C22⋊D43—42no—
328C22⋊D43—42no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43C2×C22⋊C411yescharacteristic
349C2×Dic43C2×C22⋊C411yescharacteristic
350C2×Dic43C2×C22⋊C411yescharacteristic
351C2×Dic43C2×C22⋊C411yescharacteristic
352C2×Dic43C2×C22⋊C411yescharacteristic
353C2×Dic43C2×C22⋊C411yescharacteristic
354C2×Dic43C2×C22⋊C411yescharacteristic
355C2×Dic43C2×C22⋊C411yescharacteristic
356C2×Dic43#13514yes—
357D172—41no—
358C4×D43—42no—
359C4×D43—42no—
360C4×D43—42no—
361Dic86—42no—
362Dic86—42no—
363Dic86—41no—
364C8×C43—42no—
365C43⋊C8—42no—
366#17571—431nomaximal, Sylow
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—44no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43#41012yes—
379C22×C43C22×C22⋊C411yescharacteristic
380C22×C43C2×#13512yes—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—41no—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—82no—
392Dic43—21no—
393Dic43—21no—
394Dic43—21no—
395Dic43—21no—
396Dic43—21no—
397Dic43—41no—
398Dic43—41no—
399Dic43—41no—
400Dic43—82no—
401Dic43#41612yes—
402Dic43#41612yes—
403Dic43#42112yes—
404#3444—431no—
405C2×#431—431no—
406#2283—431no—
407#1518—432no—
408#1517—432no—
409#1516—431no—
410#1516—431no—
411#1516—431no—
412#1516D4311yescharacteristic, complemented
413#1500—432no—
414#1500—432no—
415C2×C43—22no—
416C2×C43—22no—
417C2×C43—41no—
418C2×C43—81no—
419C2×C43C2×#41011yescharacteristic
420C2×C43C2×#41611yescharacteristic
421C2×C43C2×#42111yescharacteristic
422D43—81no—
423#533—431no—
424#533—431no—
425#533—431no—
426#532—431no—
427#532—431no—
428#532—431no—
429#529—431no—
430#529—431no—
431#529—431no—
432#529—431no—
433#529—861no—
434#529—861no—
435#529—861no—
436#529—861no—
437#525—431no—
438#525—861no—
439#525—861no—
440#525C2×D4311yescharacteristic
441C4×#41—431no—
442C4×#41—431no—
443C4×#41—861no—
444C4×#41—861no—
445C22×C42—431no—
446#431—432no—
447#431—432no—
448#431—861no—
449#431—861no—
450C2×C4⋊C8—861no—
451C2×C22⋊C8—431no—
452C2×C22⋊C8C2×D4311yescharacteristic
453C2×C4×C8—861no—
454#383—861no—
455#382—432no—
456#381—431no—
457#381C2×D4311yescharacteristic
458#380—861no—
459C4×C4⋊C4—861no—
460C4×C22⋊C4—861no—
461#376—432no—
462#328—432no—
463#328—432no—
464#328—432no—
465#328C2×D4312yes—
466#327—432no—
467#327—432no—
468#327—432no—
469#327C2×D4312yes—
470C43#1757111yescharacteristic, complemented, Sylow
471C2×#41—431no—
472C2×#41—861no—
473C2×#41—861no—
474C2×#41C4×D4311yescharacteristic
475C23×C4—431no—
476C23×C4—431no—
477C23×C4C22×D4311yescharacteristic
478C22×C8—21no—
479C22×C8—861no—
480C4⋊Q8—431no—
481C4⋊Q8—431no—
482C4⋊Q8—431no—
483#127—431no—
484#126—861no—
485#126—861no—
486#126—861no—
487#126—861no—
488#125—431no—
489#125—431no—
490#125—861no—
491#125—861no—
492#124—431no—
493#124—431no—
494#124—861no—
495#124—861no—
496#123—21no—
497#123—861no—
498#123—861no—
499#123—861no—
500#123—861no—
501#123—861no—
502C22⋊Q8—431no—
503C22⋊Q8—431no—
504C22⋊Q8—861no—
505C22⋊Q8—861no—
506C22⋊Q8—861no—
507C22⋊Q8—861no—
508C22⋊Q8C4×D4311yescharacteristic
509C22⋊Q8C22×D4311yescharacteristic
510#121—431no—
511#121—431no—
512#121—861no—
513#121—861no—
514#121—861no—
515#121—861no—
516#121C4×D4311yescharacteristic
517#121C22×D4311yescharacteristic
518#120—21no—
519#120—861no—
520C4×Q8—431no—
521C4×Q8—431no—
522C4×Q8—431no—
523C4×Q8—431no—
524C4×Q8—861no—
525C4×Q8—861no—
526C4×Q8—861no—
527C4×Q8—861no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—431no—
531C4×D4—431no—
532C4×D4—431no—
533C4×D4—431no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4—861no—
537C4×D4—861no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
544C4×D4—861no—
545C4×D4—861no—
546C4×D4—861no—
547C4×D4—861no—
548#117—431no—
549#117—861no—
550#117—861no—
551#117—861no—
552#117—861no—
553#117—861no—
554#117—861no—
555#117—861no—
556#117—861no—
557#117C4×D4311yescharacteristic
558C2×C4⋊C4—862no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—861no—
561C2×C42—431no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—861no—
574C2×C42—861no—
575C2×C42—862no—
576C4⋊C8—862no—
577C4⋊C8—862no—
578C22⋊C8—21no—
579C22⋊C8—432no—
580C22⋊C8—861no—
581C22⋊C8C22×D4312yes—
582C4×C8—862no—
583C4×C8—862no—
584#95—21no—
585#95—432no—
586#95—862no—
587#95—862no—
588#95—861no—
589#95C22×D4312yes—
590C24D4×D4311yescharacteristic
591#41—42no—
592#41—1722no—
593#41—1724no—
594#41—1724no—
595C2×Q8—431no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8C2×C4×D4311yescharacteristic
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—431no—
603C2×D4—861no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4C2×C4×D4311yescharacteristic
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—42no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—864no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—862no—
631C22×C4—1722no—
632C22×C4C2×C4×D4311yescharacteristic
633C22×C4C2×C4×D4311yescharacteristic
634C22×C4D4×D4311yescharacteristic
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638C2×C8—22no—
639C2×C8—42no—
640C2×C8—862no—
641C2×C8—1722no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—431no—
645C4⋊C4—431no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—1724no—
661C4⋊C4C2×C4×D4311yescharacteristic
662C4⋊C4C2×C4×D4311yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—42no—
669C22⋊C4—861no—
670C22⋊C4—861no—
671C22⋊C4—861no—
672C22⋊C4—861no—
673C22⋊C4—861no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—861no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—1722no—
683C42—21no—
684C42—431no—
685C42—431no—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—861no—
701C42—861no—
702C42—861no—
703C42—861no—
704C42—861no—
705C42—1724no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—41no—
710C23—861no—
711C23C22⋊C4×D4311yescharacteristic
712C23C22⋊C4×D4311yescharacteristic
713C23C2×D4×D4311yescharacteristic
714Q8—41no—
715Q8—1721no—
716Q8—1722no—
717Q8—1722no—
718D4—41no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—1721no—
723D4—1722no—
724D4—1722no—
725D4—1722no—
726D4—1722no—
727D4—1722no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—431no—
742C2×C4—431no—
743C2×C4—431no—
744C2×C4—434no—
745C2×C4—431no—
746C2×C4—431no—
747C2×C4—431no—
748C2×C4—431no—
749C2×C4—431no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—861no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4C22⋊C4×D4311yescharacteristic
773C2×C4C22⋊C4×D4311yescharacteristic
774C2×C4C22×C4×D4311yescharacteristic
775C2×C4C2×D4×D4311yescharacteristic
776C8—42no—
777C8—1722no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—44no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—1721no—
790C22—1721no—
791C22—1721no—
792C22#1458287112yes—
793C22C2×C22⋊C4×D4311yescharacteristic
794C22#135×D4312yes—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—82no—
803C4—432no—
804C4—432no—
805C4—432no—
806C4—861no—
807C4—861no—
808C4—861no—
809C4—861no—
810C4—861no—
811C4—3442no—
812C4—1721no—
813C4—1721no—
814C4—1721no—
815C2—22no—
816C2—22no—
817C2—41no—
818C2—81no—
819C2—3441no—
820C2C2×#1458287111yescharacteristic
821C2#416×D4311yescharacteristic
822C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1516C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1516D43
hypocenterC43#17571
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. C2×#14582949C2semidirect
3. #19136986C2semidirect
4. #19133157C2semidirect
5. #19133153C2semidirect
6. #19133152C2semidirect
7. #19133151C2semidirect
8. #19133149C2semidirect
9. #19133080C2semidirect
10. #19133078C2semidirect
11. C43×#1516C2semidirect
12. #14583452C4semidirect
13. #14583451C4semidirect
15. #14583445C4semidirect
16. #14583444C4semidirect
18. #14583435C4semidirect
20. #14583430C4semidirect
29. #41×Dic43C4semidirect
30. #14583367C4semidirect
412. #1516D43semidirect
470. C43#17571semidirect

Maximal subgroups

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

subgroupindex
#191478872
C2×#145829492
#191369862
#191331572
#191331532
#191331522
#191331512
#191331492
#191330802
#191330782
C43×#15162
#1757143