Finite Group Databasebeta

← #25064492

Subgroups — #25064492

Order 11008.

1144 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2C2×#14582851C211yesmaximal, characteristic, complemented
3C4×M16×D43C211yesmaximal, characteristic, complemented
4#19133188C212yesmaximal, complemented
5#19133185C212yesmaximal, complemented
6#19133184C211yesmaximal, characteristic, complemented
7#19133183C211yesmaximal, characteristic, complemented
8#19133182C212yesmaximal, complemented
9#19133181C211yesmaximal, characteristic, complemented
10#19133180C212yesmaximal, complemented
11C43×#1524C211yesmaximal, characteristic, complemented
12C22×#10621872—21no—
13C2×M16×D43—21no—
14#14583455C2211yescharacteristic
15#14583453C411yescharacteristic
16#14583451C411yescharacteristic
17#14583448C2211yescharacteristic
18#14583446C411yescharacteristic
19#14583444C411yescharacteristic
20#14583434C2211yescharacteristic
21#14583433C2211yescharacteristic
22#14583432—21no—
23#14583432—21no—
24#14583428C2211yescharacteristic
25#14583427—21no—
26#14583426—21no—
27#14583412C411yescharacteristic
28#14583409C411yescharacteristic
29#14583408—21no—
30#14583407—21no—
31C4×#10621902C411yescharacteristic
32#14583367—21no—
33C4×#10621900—21no—
34C4×#10621900C411yescharacteristic
35C2×C42×D43C2211yescharacteristic
36C4×#10621877C2211yescharacteristic
37#14582851—21no—
38#14582851—21no—
39#14582851C2212yes—
40#14582851C2212yes—
41#14582851C2212yes—
42M16×Dic43—21no—
43C4×#10621872—21no—
44C2×#13063236C2211yescharacteristic
45#97×D43C2212yes—
46C2×C8×Dic43—21no—
47C4×C8×D43—21no—
48#14582641C2212yescomplemented
49#14582640C2212yescomplemented
50#14582640C2212yescomplemented
51#14582639C2212yescomplemented
52#14582638C2212yescomplemented
53#14582638C2212yescomplemented
54C43×#529C2211yescharacteristic
55C4×M16×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#330C2212yescomplemented
58C43×#329C2212yescomplemented
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621900—21no—
62C2×#10621900C2×C411yescharacteristic
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C2×#10621877—21no—
67C2×#10621872—28no—
68C2×#10621872—22no—
69C2×#10621872—22no—
70C2×#10621872—22no—
71M16×D43—28no—
72C22×C43⋊C8—21no—
73C2×C8×D43—22no—
74#13063324C2×C411yescharacteristic
75#13063324C2×C411yescharacteristic
76#13063323C2×C411yescharacteristic
77#13063321C2×C411yescharacteristic
78#13063320—21no—
79#13063319—21no—
80#13063318—21no—
81#13063317C2311yescharacteristic
82#13063315—21no—
83#13063315—21no—
84#13063313C2311yescharacteristic
85#13063311—21no—
86#13063311—21no—
87#13063310—21no—
88#13063310—21no—
89#13063308—21no—
90#13063307—21no—
91#13063307—21no—
92#13063305C2×C411yescharacteristic
93#13063304C2×C411yescharacteristic
94#13063303—21no—
95#13063303—21no—
96#13063303—21no—
97#13063302—21no—
98#13063301C2×C411yescharacteristic
99#13063300C2×C411yescharacteristic
100#13063299C2×C411yescharacteristic
101#13063298—21no—
102#13063298—21no—
103#13063298—21no—
104#13063297—21no—
105#13063296C2×C411yescharacteristic
106#13063295—21no—
107#13063293—21no—
108Q8×Dic43C2×C411yescharacteristic
109C4×Dic86—21no—
110C4×Dic86C2×C411yescharacteristic
111#13063290—21no—
112#13063290—21no—
113#13063290—21no—
114#13063290C2×C411yescharacteristic
115C4×D172—21no—
116C4×D172C2×C411yescharacteristic
117D4×Dic43—21no—
118D4×Dic43C2×C411yescharacteristic
119#13063287—21no—
120#13063287—21no—
121#13063287—21no—
122#13063287C2×C411yescharacteristic
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126(C22⋊D43)⋊C4—21no—
127(C22⋊D43)⋊C4—21no—
128(C22⋊D43)⋊C4—21no—
129(C22⋊D43)⋊C4—21no—
130(C22⋊D43)⋊C4—21no—
131(C22⋊D43)⋊C4—21no—
132(C22⋊D43)⋊C4—21no—
133#13063283—21no—
134#13063283—21no—
135#13063283C2×C411yescharacteristic
136#13063283C2×C411yescharacteristic
137#13063282—21no—
138#13063282—21no—
139#13063281—21no—
140#13063281—21no—
141#13063281—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43C2×C411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C42×D43—21no—
147C42×D43C2×C411yescharacteristic
148C42×D43C2×C411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43D411yescharacteristic
151C42×D43D411yescharacteristic
152C42×D43D411yescharacteristic
153C42×D43C2311yescharacteristic
154C42×D43C2311yescharacteristic
155#13063236—21no—
156#13063236C2312yes—
157#13063236C2312yes—
158#13063235—22no—
159C4×C43⋊C8—21no—
160C8×Dic43—22no—
161C8×Dic43—22no—
162C8×Dic43—22no—
163C2×M16×C43—21no—
164C22×C8×C43—21no—
165#126×C43—21no—
166#125×C43C2311yescharacteristic
167#124×C43C2311yescharacteristic
168#123×C43—21no—
169C22⋊Q8×C43C2×C411yescharacteristic
170#121×C43C2×C411yescharacteristic
171C4×Q8×C43C2×C411yescharacteristic
172C4×D4×C43—21no—
173C4×D4×C43C2×C411yescharacteristic
174#117×C43—21no—
175C2×C42×C43C2311yescharacteristic
176#97×C43—21no—
177#97×C43C2312yes—
178#97×C43C2312yes—
179C4×C8×C43—21no—
180C23×D43C22⋊C411yescharacteristic
181C2×Q8×C43C22×C411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43C22×C411yescharacteristic
184C22×C4×C43—21no—
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43C22⋊C411yescharacteristic
196C22×Dic43C22⋊C411yescharacteristic
197C22×Dic43C22⋊C411yescharacteristic
198#10621902—42no—
199#10621900—42no—
200#10621900—44no—
201#10621898—44no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172C22×C411yescharacteristic
205C2×C4×D43—24no—
206C2×C4×D43—24no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—42no—
211C2×C4×D43C22⋊C411yescharacteristic
212C2×C4×D43C22⋊C411yescharacteristic
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22⋊C411yescharacteristic
217C2×C4×D43C22×C411yescharacteristic
218C2×C4×D43C22×C411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86C22×C411yescharacteristic
226M16×C43—24no—
227C2×C8×C43—24no—
228C2×C8×C43—22no—
229C2×C8×C43—22no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C22×C411yescharacteristic
235C4⋊C4×C43C22×C411yescharacteristic
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C42×C43—21no—
242C42×C43C22×C411yescharacteristic
243C42×C43C2×D411yescharacteristic
244C42×C43C2×D411yescharacteristic
245C42×C43C2411yescharacteristic
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43C22×C411yescharacteristic
262C4⋊Dic43C22×C411yescharacteristic
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
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×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290#10621877—24no—
291C2×C43⋊C8—24no—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—22no—
294#10621872—28no—
295#10621872—28no—
296#10621872—28no—
297C8×D43—28no—
298C23×C43—21no—
299C23×C43C2×C22⋊C411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—21no—
303C22×D43—41no—
304C22×D43C2×C22⋊C411yescharacteristic
305C22×D43C2×C22⋊C411yescharacteristic
306Q8×C43—41no—
307D4×C43—41no—
308D4×C43—42no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—41no—
315C2×C4×C43—42no—
316C2×C4×C43C2×C22⋊C411yescharacteristic
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C23×C411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C22⋊D43—42no—
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—42no—
326C22⋊D43—42no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43#10414yes—
335C2×Dic43C2×C22⋊C411yescharacteristic
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341D172—41no—
342D172—42no—
343D172—42no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—41no—
354C4×D43—41no—
355C4×D43—42no—
356C4×D43—42no—
357C4×D43—42no—
358C4×D43#10414yes—
359Dic86—42no—
360Dic86—42no—
361Dic86—41no—
362C8×C43—24no—
363C8×C43—24no—
364C43⋊C8—24no—
365C43⋊C8—24no—
366#17638—431nomaximal, Sylow
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43C2×#10412yes—
373C22×C43C22×C22⋊C411yescharacteristic
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—44no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43C2×#10412yes—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43C2×#10412yes—
393Dic43—21no—
394Dic43—21no—
395Dic43—41no—
396Dic43—41no—
397Dic43—41no—
398Dic43#41312yes—
399Dic43C2×#10412yes—
400Dic43C2×#10412yes—
401Dic43C2×#10412yes—
402#3444—431no—
403C2×C4×M16—431no—
404C2×C4×M16—431no—
405#1526—432no—
406#1525—432no—
407#1524—431no—
408#1524—431no—
409#1524—432no—
410#1524—432no—
411#1524—431no—
412#1524D4311yescharacteristic, complemented
413C2×C43—22no—
414C2×C43—81no—
415C2×C43C2×#41311yescharacteristic
416C2×C43C22×#10411yescharacteristic
417C2×C43C22×#10411yescharacteristic
418D43—22no—
419D43—41no—
420D43—81no—
421C22×M16—861no—
422C22×M16—861no—
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—861no—
433#529—861no—
434#529—861no—
435#529—861no—
436#529C2×D4311yescharacteristic
437#525—431no—
438#525—431no—
439#525—861no—
440#525—861no—
441C4×#41—431no—
442C4×#41—431no—
443C4×#41—861no—
444C4×#41—861no—
445C22×C42—431no—
446C4×M16—431no—
447C4×M16—432no—
448C4×M16—432no—
449C4×M16—432no—
450C4×M16—861no—
451C4×M16—861no—
452C4×M16—861no—
453C4×M16—861no—
454C4×M16C2×D4311yescharacteristic
455C2×#97—431no—
456C2×#97—432no—
457C2×#97C2×D4311yescharacteristic
458C2×C4×C8—861no—
459C2×C4×C8—861no—
460#330—432no—
461#330—432no—
462#330—432no—
463#330C2×D4312yescomplemented
464#329—432no—
465#329—432no—
466#329—432no—
467#329C2×D4312yescomplemented
468C43#1763811yescharacteristic, complemented, Sylow
469C2×#41—431no—
470C2×#41—431no—
471C2×#41—861no—
472C2×#41—861no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—431no—
476C2×M16—21no—
477C2×M16—862no—
478C2×M16—862no—
479C2×M16—862no—
480C2×M16—868no—
481C2×M16—868no—
482C2×M16—861no—
483C22×C8—21no—
484C22×C8—862no—
485C22×C8—861no—
486C4⋊Q8—431no—
487C4⋊Q8—431no—
488C4⋊Q8—431no—
489#127—431no—
490#126—21no—
491#126—861no—
492#126—861no—
493#126—861no—
494#125—431no—
495#125—861no—
496#125—861no—
497#125C22×D4311yescharacteristic
498#124—431no—
499#124—861no—
500#124—861no—
501#124C22×D4311yescharacteristic
502#123—21no—
503#123—861no—
504#123—861no—
505#123—861no—
506#123—861no—
507#123—861no—
508C22⋊Q8—431no—
509C22⋊Q8—431no—
510C22⋊Q8—431no—
511C22⋊Q8—861no—
512C22⋊Q8—861no—
513C22⋊Q8—861no—
514C22⋊Q8—861no—
515C22⋊Q8C4×D4311yescharacteristic
516#121—431no—
517#121—431no—
518#121—431no—
519#121—861no—
520#121—861no—
521#121—861no—
522#121—861no—
523#121C4×D4311yescharacteristic
524#120—861no—
525#120—861no—
526C4×Q8—431no—
527C4×Q8—431no—
528C4×Q8—431no—
529C4×Q8—861no—
530C4×Q8—861no—
531C4×Q8—861no—
532C4×Q8—861no—
533C4×Q8C4×D4311yescharacteristic
534C4×D4—21no—
535C4×D4—431no—
536C4×D4—431no—
537C4×D4—431no—
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—
548C4×D4—861no—
549C4×D4—861no—
550C4×D4—861no—
551C4×D4—861no—
552C4×D4—861no—
553C4×D4C4×D4311yescharacteristic
554#117—21no—
555#117—431no—
556#117—431no—
557#117—861no—
558#117—861no—
559#117—861no—
560#117—861no—
561#117—861no—
562#117—861no—
563#117—861no—
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—431no—
574C2×C42—431no—
575C2×C42—861no—
576C2×C42—861no—
577C2×C42C22×D4311yescharacteristic
578#97—21no—
579#97—432no—
580#97—432no—
581#97—862no—
582#97—861no—
583#97C22×D4312yes—
584#97C22×D4312yes—
585C4×C8—21no—
586C4×C8—862no—
587C4×C8—862no—
588C4×C8—862no—
589C4×C8—861no—
590C24—431no—
591#41—1724no—
592#41—1724no—
593#41—1722no—
594#41—1722no—
595C2×Q8—431no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8C2×C4×D4311yescharacteristic
599C2×D4—21no—
600C2×D4—431no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4C2×C4×D4311yescharacteristic
609C22×C4—21no—
610C22×C4—431no—
611C22×C4—431no—
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—431no—
625C22×C4—864no—
626C22×C4—864no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—1722no—
633C22×C4C2×C4×D4311yescharacteristic
634C22×C4D4×D4311yescharacteristic
635C22×C4D4×D4311yescharacteristic
636M16—24no—
637M16—868no—
638M16—868no—
639M16—868no—
640M16—864no—
641C2×C8—24no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—868no—
645C2×C8—864no—
646C2×C8—862no—
647C2×C8—862no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—431no—
653C4⋊C4—431no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4C2×C4×D4311yescharacteristic
667C4⋊C4C2×C4×D4311yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
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—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C42—21no—
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—861no—
700C42—861no—
701C42—861no—
702C42—861no—
703C42—861no—
704C42C2×C4×D4311yescharacteristic
705C42D4×D4311yescharacteristic
706C42D4×D4311yescharacteristic
707C42C23×D4311yescharacteristic
708C23—21no—
709C23—431no—
710C23—431no—
711C23—862no—
712C23—862no—
713C23—861no—
714C23—1721no—
715C23C22⋊C4×D4311yescharacteristic
716Q8—41no—
717Q8—1721no—
718Q8—1722no—
719Q8—1722no—
720D4—41no—
721D4—42no—
722D4—1721no—
723D4—1722no—
724D4—1722no—
725D4—1722no—
726D4—1722no—
727D4—1722no—
728D4—1722no—
729D4—1722no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—431no—
738C2×C4—431no—
739C2×C4—431no—
740C2×C4—431no—
741C2×C4—434no—
742C2×C4—434no—
743C2×C4—431no—
744C2×C4—431no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—861no—
757C2×C4—861no—
758C2×C4—861no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4C22⋊C4×D4311yescharacteristic
767C2×C4C22⋊C4×D4311yescharacteristic
768C2×C4C22⋊C4×D4311yescharacteristic
769C2×C4C22×C4×D4311yescharacteristic
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4C2×D4×D4311yescharacteristic
772C8—24no—
773C8—24no—
774C8—864no—
775C8—864no—
776C22—21no—
777C22—21no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—432no—
782C22—861no—
783C22—861no—
784C22—861no—
785C22—861no—
786C22—861no—
787C22—1724no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22#104×D4312yes—
792C22C2×C22⋊C4×D4311yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—432no—
802C4—432no—
803C4—432no—
804C4—432no—
805C4—861no—
806C4—861no—
807C4—1721no—
808C4—1721no—
809C4—1721no—
810C4#104×D4312yes—
811C2—22no—
812C2—81no—
813C2—862no—
814C2—3441no—
815C2—1721no—
816C2#413×D4311yescharacteristic
817C2C2×#104×D4311yescharacteristic
818C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1524C2
socleC22×C43C22×C22⋊C4
prime radical#19147889C2
cosocleC42×C43C24
hypercenter#1524D43
hypocenterC43#17638
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1524

Complements

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

NH ≅ G/Ntype
2. C2×#14582851C2semidirect
3. C4×M16×D43C2semidirect
4. #19133188C2semidirect
5. #19133185C2semidirect
6. #19133184C2semidirect
7. #19133183C2semidirect
8. #19133182C2semidirect
9. #19133181C2semidirect
10. #19133180C2semidirect
11. C43×#1524C2semidirect
48. #14582641C22semidirect
49. #14582640C22semidirect
50. #14582640C22semidirect
51. #14582639C22semidirect
52. #14582638C22semidirect
53. #14582638C22semidirect
57. C43×#330C22semidirect
58. C43×#329C22semidirect
412. #1524D43semidirect
463. #330C2×D43semidirect
467. #329C2×D43semidirect
468. C43#17638semidirect

Maximal subgroups

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

subgroupindex
#191478892
C2×#145828512
C4×M16×D432
#191331882
#191331852
#191331842
#191331832
#191331822
#191331812
#191331802
C43×#15242
#1763843