Finite Group Databasebeta

← #25064641

Subgroups — #25064641

Order 11008.

974 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3C2×#14582954C211yesmaximal, characteristic, complemented
4#19133231C212yesmaximal, complemented
5#19133228C212yesmaximal, complemented
6#19133225C212yesmaximal, complemented
7#19133223C212yesmaximal, complemented
8#19133184C211yesmaximal, characteristic, complemented
9#19133183C211yesmaximal, characteristic, complemented
10#19133181C211yesmaximal, characteristic, complemented
11C43×#1524C211yesmaximal, characteristic, complemented
12#14583455C2211yescharacteristic
13#14583453C411yescharacteristic
14#14583451C411yescharacteristic
15#14583448C2211yescharacteristic
16#14583446C411yescharacteristic
17#14583444C411yescharacteristic
18#14583434C2211yescharacteristic
19#14583433C2211yescharacteristic
20#14583432—21no—
21#14583432—21no—
22#14583428C2211yescharacteristic
23#14583427—21no—
24#14583426—21no—
25#14583412C411yescharacteristic
26#14583409C411yescharacteristic
27#14583408—21no—
28#14583407—21no—
29C4×#10621902C411yescharacteristic
30#14583367—21no—
31C4×#10621900—21no—
32C4×#10621900C411yescharacteristic
33C2×C42×D43C2211yescharacteristic
34#14582954—21no—
35#14582954—21no—
36#14582954C2212yes—
37#14582954C2212yes—
38#14582954C2212yes—
39#14582954C2212yes—
40#14582950—21no—
41#14582950—21no—
42#14582922—21no—
43C2×Dic43⋊C8—21no—
44#14582862—21no—
45C2×(C2×D43)⋊C8—21no—
46C4×#10621877C2211yescharacteristic
47C2×#13063236C2211yescharacteristic
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—
67C22×C43⋊C8—21no—
68#13063324C2×C411yescharacteristic
69#13063324C2×C411yescharacteristic
70#13063323C2×C411yescharacteristic
71#13063321C2×C411yescharacteristic
72#13063320—21no—
73#13063319—21no—
74#13063318—21no—
75#13063317C2311yescharacteristic
76#13063315—21no—
77#13063315—21no—
78#13063313C2311yescharacteristic
79#13063311—21no—
80#13063311—21no—
81#13063310—21no—
82#13063310—21no—
83#13063308—21no—
84#13063307—21no—
85#13063307—21no—
86#13063305C2×C411yescharacteristic
87#13063304C2×C411yescharacteristic
88#13063303—21no—
89#13063303—21no—
90#13063303—21no—
91#13063302—21no—
92#13063301C2×C411yescharacteristic
93#13063300C2×C411yescharacteristic
94#13063299C2×C411yescharacteristic
95#13063298—21no—
96#13063298—21no—
97#13063298—21no—
98#13063297—21no—
99#13063296C2×C411yescharacteristic
100#13063295—21no—
101#13063293—21no—
102Q8×Dic43C2×C411yescharacteristic
103C4×Dic86—21no—
104C4×Dic86C2×C411yescharacteristic
105#13063290—21no—
106#13063290—21no—
107#13063290—21no—
108#13063290C2×C411yescharacteristic
109C4×D172—21no—
110C4×D172C2×C411yescharacteristic
111D4×Dic43—21no—
112D4×Dic43C2×C411yescharacteristic
113#13063287—21no—
114#13063287—21no—
115#13063287—21no—
116#13063287C2×C411yescharacteristic
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119C4×C22⋊D43—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(C22⋊D43)⋊C4—21no—
126(C22⋊D43)⋊C4—21no—
127#13063283—21no—
128#13063283—21no—
129#13063283C2×C411yescharacteristic
130#13063283C2×C411yescharacteristic
131#13063282—21no—
132#13063282—21no—
133#13063281—21no—
134#13063281—21no—
135#13063281—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43C2×C411yescharacteristic
138C2×C4×Dic43D411yescharacteristic
139C2×C4×Dic43D411yescharacteristic
140C42×D43—21no—
141C42×D43C2×C411yescharacteristic
142C42×D43C2×C411yescharacteristic
143C42×D43D411yescharacteristic
144C42×D43D411yescharacteristic
145C42×D43D411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43C2311yescharacteristic
148C42×D43C2311yescharacteristic
149Dic43⋊C8—22no—
150Dic43⋊C8—22no—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153(C2×D43)⋊C8—22no—
154(C2×D43)⋊C8—22no—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157#13063236—21no—
158#13063236C2312yes—
159#13063236C2312yes—
160C4×C43⋊C8—21no—
161C2×M16×C43—21no—
162C22×C8×C43—21no—
163#126×C43—21no—
164#125×C43C2311yescharacteristic
165#124×C43C2311yescharacteristic
166#123×C43—21no—
167C22⋊Q8×C43C2×C411yescharacteristic
168#121×C43C2×C411yescharacteristic
169C4×Q8×C43C2×C411yescharacteristic
170C4×D4×C43—21no—
171C4×D4×C43C2×C411yescharacteristic
172#117×C43—21no—
173C2×C42×C43C2311yescharacteristic
174#97×C43—21no—
175#97×C43C2312yes—
176#97×C43C2312yes—
177C4×C8×C43—21no—
178C23×D43C22⋊C411yescharacteristic
179C2×Q8×C43C22×C411yescharacteristic
180C2×D4×C43—21no—
181C2×D4×C43C22×C411yescharacteristic
182C22×C4×C43—21no—
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43C22⋊C411yescharacteristic
194C22×Dic43C22⋊C411yescharacteristic
195C22×Dic43C22⋊C411yescharacteristic
196#10621902—42no—
197#10621900—42no—
198#10621900—44no—
199#10621898—44no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172C22×C411yescharacteristic
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43C22⋊C411yescharacteristic
210C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86C22×C411yescharacteristic
224M16×C43—42no—
225C2×C8×C43—22no—
226C2×C8×C43—22no—
227C2×C8×C43—42no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43C22×C411yescharacteristic
233C4⋊C4×C43C22×C411yescharacteristic
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C42×C43—21no—
240C42×C43C22×C411yescharacteristic
241C42×C43C2×D411yescharacteristic
242C42×C43C2×D411yescharacteristic
243C42×C43C2411yescharacteristic
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
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—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43C22×C411yescharacteristic
260C4⋊Dic43C22×C411yescharacteristic
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—21no—
270Dic43⋊C4—21no—
271C4×Dic43—21no—
272C4×Dic43—21no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
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×Dic43C2×D411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288#10621877—42no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8—42no—
292C23×C43—21no—
293C23×C43C2×C22⋊C411yescharacteristic
294C22×D43—22no—
295C22×D43—21no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43C2×C22⋊C411yescharacteristic
299C22×D43C2×C22⋊C411yescharacteristic
300Q8×C43—41no—
301D4×C43—41no—
302D4×C43—42no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—41no—
309C2×C4×C43—42no—
310C2×C4×C43C2×C22⋊C411yescharacteristic
311C2×C4×C43C2×C22⋊C411yescharacteristic
312C2×C4×C43C2×C22⋊C411yescharacteristic
313C2×C4×C43C23×C411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C22⋊D43—42no—
317C22⋊D43—42no—
318C22⋊D43—42no—
319C22⋊D43—42no—
320C22⋊D43—42no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—41no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43C2×C22⋊C411yescharacteristic
330C2×Dic43C2×C22⋊C411yescharacteristic
331C2×Dic43C2×C22⋊C411yescharacteristic
332C2×Dic43C2×C22⋊C411yescharacteristic
333C2×Dic43C2×C22⋊C411yescharacteristic
334C2×Dic43C2×C22⋊C411yescharacteristic
335D172—41no—
336D172—42no—
337D172—42no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—41no—
343C4×D43—41no—
344C4×D43—41no—
345C4×D43—41no—
346C4×D43—41no—
347C4×D43—41no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—42no—
351C4×D43—42no—
352C4×D43—42no—
353Dic86—42no—
354Dic86—42no—
355Dic86—41no—
356C8×C43—42no—
357C8×C43—42no—
358C43⋊C8—42no—
359C43⋊C8—42no—
360#17662—431nomaximal, Sylow
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43#42112yes—
367C22×C43C22×C22⋊C411yescharacteristic
368C2×D43—21no—
369C2×D43—21no—
370C2×D43—21no—
371C2×D43—21no—
372C2×D43—21no—
373C2×D43—21no—
374C2×D43—44no—
375C2×D43—41no—
376C2×D43—41no—
377C2×D43—41no—
378C4×C43—21no—
379C4×C43—21no—
380C4×C43—21no—
381C4×C43—21no—
382C4×C43—21no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43#42112yes—
387Dic43—21no—
388Dic43—21no—
389Dic43—21no—
390Dic43—21no—
391Dic43—21no—
392Dic43—41no—
393Dic43—41no—
394Dic43—41no—
395Dic43#41312yes—
396#3444—431no—
397#2920—431no—
398C2×#432—431no—
399#1537—432no—
400#1536—432no—
401#1535—432no—
402#1535—432no—
403#1524—431no—
404#1524—431no—
405#1524—431no—
406#1524D4311yescharacteristic, complemented
407C2×C43—22no—
408C2×C43—81no—
409C2×C43C2×#41311yescharacteristic
410C2×C43C2×#42111yescharacteristic
411C2×C43C2×#42111yescharacteristic
412D43—41no—
413D43—41no—
414D43—81no—
415#533—431no—
416#533—431no—
417#533—431no—
418#532—431no—
419#532—431no—
420#532—431no—
421#529—431no—
422#529—431no—
423#529—431no—
424#529—861no—
425#529—861no—
426#529—861no—
427#529—861no—
428#529C2×D4311yescharacteristic
429#525—431no—
430#525—431no—
431#525—861no—
432#525—861no—
433C4×#41—431no—
434C4×#41—431no—
435C4×#41—861no—
436C4×#41—861no—
437C22×C42—431no—
438#432—432no—
439#432—432no—
440#432—432no—
441#432—432no—
442#432—861no—
443#432—861no—
444#431—861no—
445#431—861no—
446#423—861no—
447C2×C4⋊C8—861no—
448#407—861no—
449C2×C22⋊C8—861no—
450C4×M16—431no—
451C4×M16C2×D4311yescharacteristic
452C2×#97—431no—
453C2×#97C2×D4311yescharacteristic
454#330—432no—
455#330—432no—
456#330—432no—
457#330C2×D4312yescomplemented
458#329—432no—
459#329—432no—
460#329—432no—
461#329C2×D4312yescomplemented
462C43#1766211yescharacteristic, complemented, Sylow
463C2×#41—431no—
464C2×#41—431no—
465C2×#41—861no—
466C2×#41—861no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C2×M16—21no—
471C2×M16—861no—
472C22×C8—21no—
473C22×C8—861no—
474C4⋊Q8—431no—
475C4⋊Q8—431no—
476C4⋊Q8—431no—
477#127—431no—
478#126—21no—
479#126—861no—
480#126—861no—
481#126—861no—
482#125—431no—
483#125—861no—
484#125—861no—
485#125C22×D4311yescharacteristic
486#124—431no—
487#124—861no—
488#124—861no—
489#124C22×D4311yescharacteristic
490#123—21no—
491#123—861no—
492#123—861no—
493#123—861no—
494#123—861no—
495#123—861no—
496C22⋊Q8—431no—
497C22⋊Q8—431no—
498C22⋊Q8—431no—
499C22⋊Q8—861no—
500C22⋊Q8—861no—
501C22⋊Q8—861no—
502C22⋊Q8—861no—
503C22⋊Q8C4×D4311yescharacteristic
504#121—431no—
505#121—431no—
506#121—431no—
507#121—861no—
508#121—861no—
509#121—861no—
510#121—861no—
511#121C4×D4311yescharacteristic
512#120—861no—
513#120—861no—
514C4×Q8—431no—
515C4×Q8—431no—
516C4×Q8—431no—
517C4×Q8—861no—
518C4×Q8—861no—
519C4×Q8—861no—
520C4×Q8—861no—
521C4×Q8C4×D4311yescharacteristic
522C4×D4—21no—
523C4×D4—431no—
524C4×D4—431no—
525C4×D4—431no—
526C4×D4—861no—
527C4×D4—861no—
528C4×D4—861no—
529C4×D4—861no—
530C4×D4—861no—
531C4×D4—861no—
532C4×D4—861no—
533C4×D4—861no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4—861no—
537C4×D4—861no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4—861no—
541C4×D4C4×D4311yescharacteristic
542#117—21no—
543#117—431no—
544#117—431no—
545#117—861no—
546#117—861no—
547#117—861no—
548#117—861no—
549#117—861no—
550#117—861no—
551#117—861no—
552C2×C42—431no—
553C2×C42—431no—
554C2×C42—431no—
555C2×C42—431no—
556C2×C42—431no—
557C2×C42—431no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—431no—
563C2×C42—861no—
564C2×C42—861no—
565C2×C42C22×D4311yescharacteristic
566C4⋊C8—862no—
567C4⋊C8—862no—
568C4⋊C8—862no—
569C4⋊C8—862no—
570C22⋊C8—862no—
571C22⋊C8—862no—
572C22⋊C8—862no—
573C22⋊C8—862no—
574#97—21no—
575#97—432no—
576#97—432no—
577#97—861no—
578#97C22×D4312yes—
579#97C22×D4312yes—
580C4×C8—21no—
581C4×C8—861no—
582C24—431no—
583#41—1724no—
584#41—1724no—
585#41—1722no—
586#41—1722no—
587C2×Q8—431no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8C2×C4×D4311yescharacteristic
591C2×D4—21no—
592C2×D4—431no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4—861no—
599C2×D4—861no—
600C2×D4C2×C4×D4311yescharacteristic
601C22×C4—21no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4C2×C4×D4311yescharacteristic
626C22×C4D4×D4311yescharacteristic
627C22×C4D4×D4311yescharacteristic
628M16—42no—
629M16—1722no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—42no—
633C2×C8—862no—
634C2×C8—862no—
635C2×C8—1722no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—431no—
641C4⋊C4—431no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
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⋊C4C2×C4×D4311yescharacteristic
655C4⋊C4C2×C4×D4311yescharacteristic
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—861no—
662C22⋊C4—861no—
663C22⋊C4—861no—
664C22⋊C4—861no—
665C22⋊C4—861no—
666C22⋊C4—861no—
667C22⋊C4—861no—
668C22⋊C4—861no—
669C22⋊C4—861no—
670C22⋊C4—861no—
671C22⋊C4—861no—
672C22⋊C4—861no—
673C22⋊C4—861no—
674C42—21no—
675C42—431no—
676C42—431no—
677C42—431no—
678C42—431no—
679C42—431no—
680C42—431no—
681C42—431no—
682C42—431no—
683C42—431no—
684C42—431no—
685C42—431no—
686C42—431no—
687C42—861no—
688C42—861no—
689C42—861no—
690C42—861no—
691C42—861no—
692C42C2×C4×D4311yescharacteristic
693C42D4×D4311yescharacteristic
694C42D4×D4311yescharacteristic
695C42C23×D4311yescharacteristic
696C23—21no—
697C23—431no—
698C23—431no—
699C23—862no—
700C23—861no—
701C23—1721no—
702C23—1721no—
703C23C22⋊C4×D4311yescharacteristic
704Q8—41no—
705Q8—1721no—
706Q8—1722no—
707Q8—1722no—
708D4—41no—
709D4—42no—
710D4—1721no—
711D4—1722no—
712D4—1722no—
713D4—1722no—
714D4—1722no—
715D4—1722no—
716D4—1722no—
717D4—1722no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—431no—
726C2×C4—431no—
727C2×C4—431no—
728C2×C4—431no—
729C2×C4—431no—
730C2×C4—431no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4—1722no—
751C2×C4—1721no—
752C2×C4—1722no—
753C2×C4—1722no—
754C2×C4C22⋊C4×D4311yescharacteristic
755C2×C4C22⋊C4×D4311yescharacteristic
756C2×C4C22⋊C4×D4311yescharacteristic
757C2×C4C22×C4×D4311yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4C2×D4×D4311yescharacteristic
760C8—42no—
761C8—42no—
762C8—1722no—
763C8—1722no—
764C22—21no—
765C22—21no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—861no—
770C22—861no—
771C22—861no—
772C22—861no—
773C22—861no—
774C22—861no—
775C22—1724no—
776C22—1721no—
777C22—1721no—
778C22—1721no—
779C22#1458291412yes—
780C22C2×C22⋊C4×D4311yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—432no—
790C4—861no—
791C4—861no—
792C4—861no—
793C4—861no—
794C4—861no—
795C4—1721no—
796C4—1721no—
797C4—1721no—
798C4#1458291412yes—
799C2—22no—
800C2—81no—
801C2—3441no—
802C2—1721no—
803C2—1721no—
804C2#413×D4311yescharacteristic
805C2C2×#1458291411yescharacteristic
806C2C2×#1458291411yescharacteristic
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#17662
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. #19143226C2semidirect
3. C2×#14582954C2semidirect
4. #19133231C2semidirect
5. #19133228C2semidirect
6. #19133225C2semidirect
7. #19133223C2semidirect
8. #19133184C2semidirect
9. #19133183C2semidirect
10. #19133181C2semidirect
11. C43×#1524C2semidirect
48. #14582641C22semidirect
49. #14582640C22semidirect
50. #14582640C22semidirect
51. #14582639C22semidirect
52. #14582638C22semidirect
53. #14582638C22semidirect
57. C43×#330C22semidirect
58. C43×#329C22semidirect
406. #1524D43semidirect
457. #330C2×D43semidirect
461. #329C2×D43semidirect
462. C43#17662semidirect

Maximal subgroups

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

subgroupindex
#191478892
#191432262
C2×#145829542
#191332312
#191332282
#191332252
#191332232
#191331842
#191331832
#191331812
C43×#15242
#1766243