Finite Group Databasebeta

← #25063704

Subgroups — #25063704

Order 11008.

1128 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2#431×D43C211yesmaximal, characteristic, complemented
3#19136934C211yesmaximal, characteristic, complemented
4#19133092C212yesmaximal, complemented
5#19133088C212yesmaximal, complemented
6#19133085C212yesmaximal, complemented
7#19133083C212yesmaximal, complemented
8#19133082C211yesmaximal, characteristic, complemented
9#19133081C211yesmaximal, characteristic, complemented
10#19133079C211yesmaximal, characteristic, complemented
11C43×#1500C211yesmaximal, characteristic, complemented
12#14583455C411yescharacteristic, complemented
13#14583453C411yescharacteristic, complemented
14#14583451C2211yescharacteristic
15#14583448C411yescharacteristic, complemented
16#14583446C411yescharacteristic, complemented
17#14583444C2211yescharacteristic
18#14583434C411yescharacteristic, complemented
19#14583433C2211yescharacteristic
20#14583432—21no—
21#14583432—21no—
22#14583428C411yescharacteristic, complemented
23#14583427—21no—
24#14583426—21no—
25#14583412C2211yescharacteristic
26#14583409C2211yescharacteristic
27#14583408—21no—
28#14583407—21no—
29C4×#10621902C411yescharacteristic, complemented
30#14583367—21no—
31C4×#10621900—21no—
32C4×#10621900C411yescharacteristic, complemented
33C2×#13063282—21no—
34C2×C42×D43C2211yescharacteristic
35#14582952C2211yescharacteristic
36#14582951—21no—
37#14582950—21no—
38#14582949C2212yes—
39C4⋊C8×D43—21no—
40C22⋊C8×D43C2212yes—
41C4×C8×D43—21no—
42#14582750—21no—
43#14582750C2212yes—
44#14582746—21no—
45#14582746C2212yes—
46#14582745C2211yescharacteristic
47C42×Dic43—21no—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#529C2211yescharacteristic
55C43×#431C2211yescharacteristic
56C43×#376C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621900—21no—
62C2×#10621900C2×C411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×C8×D43—22no—
67#13063324C2×C411yescharacteristic
68#13063324C2×C411yescharacteristic
69#13063323C2×C411yescharacteristic
70#13063321C2×C411yescharacteristic
71#13063320—21no—
72#13063319—21no—
73#13063318—21no—
74#13063317C2×C411yescharacteristic
75#13063315—21no—
76#13063315—21no—
77#13063313C2×C411yescharacteristic
78#13063311—21no—
79#13063311—21no—
80#13063310—21no—
81#13063310—21no—
82#13063308—21no—
83#13063307—21no—
84#13063307—21no—
85#13063305C2×C411yescharacteristic
86#13063304C2311yescharacteristic
87#13063303—21no—
88#13063303—21no—
89#13063303—21no—
90#13063302—21no—
91#13063301C2×C411yescharacteristic
92#13063300C2×C411yescharacteristic
93#13063299C2311yescharacteristic
94#13063298—21no—
95#13063298—21no—
96#13063298—21no—
97#13063297—21no—
98#13063296C2×C411yescharacteristic
99#13063295—21no—
100#13063293—21no—
101Q8×Dic43C2×C411yescharacteristic
102C4×Dic86—21no—
103C4×Dic86C2×C411yescharacteristic
104#13063290—21no—
105#13063290—21no—
106#13063290—21no—
107#13063290C2×C411yescharacteristic
108C4×D172—21no—
109C4×D172C2×C411yescharacteristic
110D4×Dic43—21no—
111D4×Dic43C2×C411yescharacteristic
112#13063287—21no—
113#13063287—21no—
114#13063287—21no—
115#13063287C2×C411yescharacteristic
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(C22⋊D43)⋊C4—21no—
126#13063283—21no—
127#13063283—21no—
128#13063283C2×C411yescharacteristic
129#13063283C2×C411yescharacteristic
130#13063282—28no—
131#13063282—21no—
132#13063282—21no—
133#13063281—21no—
134#13063281—21no—
135#13063281—21no—
136C2×Dic43⋊C4—22no—
137C2×(C2×D43)⋊C4—22no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—22no—
141C2×C4×Dic43—22no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145C42×D43—21no—
146C42×D43C2×C411yescharacteristic
147C42×D43C2×C411yescharacteristic
148C42×D43C2×C411yescharacteristic
149C42×D43C2×C411yescharacteristic
150C42×D43D411yescharacteristic
151C42×D43D411yescharacteristic
152C42×D43D411yescharacteristic
153C42×D43D411yescharacteristic
154C4⋊(C43⋊C8)—21no—
155Dic43⋊C8—22no—
156C22⋊(C43⋊C8)C2312yes—
157(C2×D43)⋊C8—22no—
158C4×C43⋊C8—21no—
159C8×Dic43—22no—
160C43⋊#95—21no—
161C43⋊#95C2312yes—
162#126×C43—21no—
163#125×C43C2×C411yescharacteristic
164#124×C43C2×C411yescharacteristic
165#123×C43—21no—
166C22⋊Q8×C43C2311yescharacteristic
167#121×C43C2311yescharacteristic
168C4×Q8×C43C2×C411yescharacteristic
169C4×D4×C43—21no—
170C4×D4×C43C2×C411yescharacteristic
171#117×C43—21no—
172C2×C42×C43—21no—
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43—21no—
175C22⋊C8×C43C2312yes—
176C4×C8×C43—21no—
177#95×C43—21no—
178#95×C43C2312yes—
179C23×D43C2×D411yescharacteristic
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43—22no—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
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×Dic43—22no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199#10621902—42no—
200#10621900—42no—
201#10621900—44no—
202#10621898—44no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172C22×C411yescharacteristic
206C2×C4×D43—24no—
207C2×C4×D43—24no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—42no—
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×D43C22⋊C411yescharacteristic
220C2×C4×D43C22×C411yescharacteristic
221C2×C4×D43C22×C411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86C22×C411yescharacteristic
227C2×C8×C43—22no—
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—24no—
240C42×C43—21no—
241C42×C43C22×C411yescharacteristic
242C42×C43C22×C411yescharacteristic
243C42×C43C2×D411yescharacteristic
244C42×C43C2×D411yescharacteristic
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248(C2×D43)⋊C4—28no—
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—28no—
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—
273Dic43⋊C4—21no—
274C4×Dic43—24no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C4×Dic43—44no—
281C4×Dic43—44no—
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22⋊C411yescharacteristic
287C4×Dic43C22⋊C411yescharacteristic
288C4×Dic43C22⋊C411yescharacteristic
289C4×Dic43C22⋊C411yescharacteristic
290C4×Dic43C22×C411yescharacteristic
291C4×Dic43C22×C411yescharacteristic
292C4×Dic43C2×D411yescharacteristic
293C4×Dic43C2×D411yescharacteristic
294C2×C43⋊C8—22no—
295C8×D43—44no—
296C23×C43—21no—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—21no—
301C22×D43—41no—
302C22×D43C2×C22⋊C411yescharacteristic
303C22×D43C2×C22⋊C411yescharacteristic
304Q8×C43—41no—
305D4×C43—41no—
306D4×C43—42no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—41no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C23×C411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—42no—
326C22⋊D43—42no—
327C22⋊D43—42no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—24no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342C2×Dic43C2×C22⋊C411yescharacteristic
343C2×Dic43C2×C22⋊C411yescharacteristic
344C2×Dic43#13514yes—
345D172—41no—
346D172—42no—
347D172—42no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—41no—
358C4×D43—41no—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—42no—
362C4×D43#10414yes—
363Dic86—42no—
364Dic86—42no—
365Dic86—41no—
366C8×C43—42no—
367C43⋊C8—42no—
368#17533—431nomaximal, Sylow
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43C22×C22⋊C411yescharacteristic
375C22×C43C2×#13512yes—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—21no—
380C2×D43—21no—
381C2×D43—44no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43C2×#10412yes—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—21no—
391C4×C43—44no—
392C4×C43—41no—
393C4×C43—41no—
394C4×C43—41no—
395C4×C43C2×#10412yes—
396Dic43—21no—
397Dic43—21no—
398Dic43—44no—
399Dic43—41no—
400Dic43—41no—
401Dic43—41no—
402Dic43#41012yes—
403Dic43#41612yes—
404Dic43#41612yes—
405Dic43C2×#10412yes—
406#3444—431no—
407C2×#431—431no—
408C4×#117—431no—
409#1503—432no—
410#1502—432no—
411#1501—432no—
412#1501—432no—
413#1500—431no—
414#1500—431no—
415#1500—431no—
416#1500D4311yescharacteristic, complemented
417C2×C43—22no—
418C2×C43—81no—
419C2×C43C2×#41011yescharacteristic
420C2×C43C2×#41611yescharacteristic
421C2×C43C22×#10411yescharacteristic
422D43—22no—
423D43—41no—
424D43—81no—
425#533—431no—
426#533—431no—
427#533—431no—
428#532—431no—
429#532—431no—
430#532—431no—
431#529—431no—
432#529—431no—
433#529—431no—
434#529—861no—
435#529—861no—
436#529—861no—
437#529—861no—
438#529C2×D4311yescharacteristic
439#525—431no—
440#525—431no—
441#525—861no—
442#525—861no—
443C4×#41—431no—
444C4×#41—431no—
445C4×#41—861no—
446C4×#41—861no—
447C2×#117—861no—
448C22×C42—431no—
449#431—431no—
450#431—432no—
451#431—861no—
452#431—861no—
453#431C2×D4311yescharacteristic
454C2×C4⋊C8—861no—
455C2×C22⋊C8—432no—
456C2×C4×C8—861no—
457C4×C4⋊C4—432no—
458C4×C4⋊C4—861no—
459C4×C22⋊C4—432no—
460C4×C22⋊C4—861no—
461#376—431no—
462#376C2×D4311yescharacteristic
463C43—861no—
464#328—432no—
465#328—432no—
466#328—432no—
467#328C2×D4312yes—
468#327—432no—
469#327—432no—
470#327—432no—
471#327C2×D4312yes—
472C43#1753311yescharacteristic, complemented, Sylow
473C2×#41—431no—
474C2×#41—431no—
475C2×#41—861no—
476C2×#41—861no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—431no—
480C22×C8—862no—
481C4⋊Q8—431no—
482C4⋊Q8—431no—
483C4⋊Q8—431no—
484#127—431no—
485#126—21no—
486#126—861no—
487#126—861no—
488#126—861no—
489#125—431no—
490#125—861no—
491#125—861no—
492#125C4×D4311yescharacteristic
493#124—431no—
494#124—861no—
495#124—861no—
496#124C4×D4311yescharacteristic
497#123—21no—
498#123—861no—
499#123—861no—
500#123—861no—
501#123—861no—
502#123—861no—
503C22⋊Q8—431no—
504C22⋊Q8—431no—
505C22⋊Q8—431no—
506C22⋊Q8—861no—
507C22⋊Q8—861no—
508C22⋊Q8—861no—
509C22⋊Q8—861no—
510C22⋊Q8C22×D4311yescharacteristic
511#121—431no—
512#121—431no—
513#121—431no—
514#121—861no—
515#121—861no—
516#121—861no—
517#121—861no—
518#121C22×D4311yescharacteristic
519#120—861no—
520#120—861no—
521C4×Q8—431no—
522C4×Q8—431no—
523C4×Q8—431no—
524C4×Q8—861no—
525C4×Q8—861no—
526C4×Q8—861no—
527C4×Q8—861no—
528C4×Q8C4×D4311yescharacteristic
529C4×D4—21no—
530C4×D4—431no—
531C4×D4—431no—
532C4×D4—431no—
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×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
544C4×D4—861no—
545C4×D4—861no—
546C4×D4—861no—
547C4×D4—861no—
548C4×D4C4×D4311yescharacteristic
549#117—21no—
550#117—431no—
551#117—431no—
552#117—861no—
553#117—868no—
554#117—861no—
555#117—861no—
556#117—861no—
557#117—861no—
558#117—861no—
559#117—861no—
560C2×C4⋊C4—862no—
561C2×C22⋊C4—862no—
562C2×C42—21no—
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—431no—
574C2×C42—861no—
575C2×C42—861no—
576C2×C42—861no—
577C2×C42—862no—
578C2×C42—862no—
579C2×C42C22×D4311yescharacteristic
580C4⋊C8—21no—
581C4⋊C8—862no—
582C4⋊C8—861no—
583C22⋊C8—432no—
584C22⋊C8—862no—
585C22⋊C8C22×D4312yes—
586C4×C8—21no—
587C4×C8—862no—
588C4×C8—861no—
589#95—21no—
590#95—432no—
591#95—861no—
592#95C22×D4312yes—
593C24—431no—
594#41—1724no—
595#41—1724no—
596#41—1722no—
597#41—1722no—
598C2×Q8—431no—
599C2×Q8—861no—
600C2×Q8—861no—
601C2×Q8C2×C4×D4311yescharacteristic
602C2×D4—21no—
603C2×D4—431no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4C2×C4×D4311yescharacteristic
612C22×C4—22no—
613C22×C4—21no—
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—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—864no—
630C22×C4—864no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—862no—
636C22×C4—861no—
637C22×C4—1722no—
638C22×C4D4×D4311yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4C23×D4311yescharacteristic
641C2×C8—22no—
642C2×C8—862no—
643C2×C8—1724no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—431no—
649C4⋊C4—431no—
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—868no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4C2×C4×D4311yescharacteristic
664C4⋊C4C2×C4×D4311yescharacteristic
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—861no—
671C22⋊C4—861no—
672C22⋊C4—861no—
673C22⋊C4—861no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—868no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C42—24no—
685C42—21no—
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—861no—
699C42—861no—
700C42—861no—
701C42—861no—
702C42—864no—
703C42—861no—
704C42—1724no—
705C42—1724no—
706C42C2×C4×D4311yescharacteristic
707C42C2×C4×D4311yescharacteristic
708C42D4×D4311yescharacteristic
709C42D4×D4311yescharacteristic
710C23—21no—
711C23—431no—
712C23—431no—
713C23—862no—
714C23—862no—
715C23—861no—
716C23—1721no—
717C23C2×D4×D4311yescharacteristic
718Q8—41no—
719Q8—1721no—
720Q8—1722no—
721Q8—1722no—
722D4—41no—
723D4—42no—
724D4—1721no—
725D4—1722no—
726D4—1722no—
727D4—1722no—
728D4—1722no—
729D4—1722no—
730D4—1722no—
731D4—1722no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—431no—
743C2×C4—431no—
744C2×C4—431no—
745C2×C4—431no—
746C2×C4—434no—
747C2×C4—434no—
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—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—864no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4—1722no—
774C2×C4C22⋊C4×D4311yescharacteristic
775C2×C4C22⋊C4×D4311yescharacteristic
776C2×C4C22⋊C4×D4311yescharacteristic
777C2×C4C22⋊C4×D4311yescharacteristic
778C2×C4C22×C4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C8—42no—
781C8—1722no—
782C22—21no—
783C22—21no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—432no—
788C22—861no—
789C22—861no—
790C22—861no—
791C22—861no—
792C22—861no—
793C22—1724no—
794C22—1721no—
795C22—1721no—
796C22—1721no—
797C22C2×C22⋊C4×D4311yescharacteristic
798C22#135×D4312yes—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—44no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—432no—
809C4—432no—
810C4—432no—
811C4—432no—
812C4—861no—
813C4—861no—
814C4—1724no—
815C4—1721no—
816C4—1721no—
817C4—1721no—
818C4#104×D4312yes—
819C2—22no—
820C2—81no—
821C2—862no—
822C2—3441no—
823C2—1721no—
824C2#410×D4311yescharacteristic
825C2#416×D4311yescharacteristic
826C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1500C2
socleC22×C43C22×C22⋊C4
prime radical#19147889C2
cosocleC22×C4×C43C24
hypercenter#1500D43
hypocenterC43#17533
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #431×D43C2semidirect
3. #19136934C2semidirect
4. #19133092C2semidirect
5. #19133088C2semidirect
6. #19133085C2semidirect
7. #19133083C2semidirect
8. #19133082C2semidirect
9. #19133081C2semidirect
10. #19133079C2semidirect
11. C43×#1500C2semidirect
12. #14583455C4semidirect
13. #14583453C4semidirect
15. #14583448C4semidirect
16. #14583446C4semidirect
18. #14583434C4semidirect
22. #14583428C4semidirect
29. C4×#10621902C4semidirect
32. C4×#10621900C4semidirect
416. #1500D43semidirect
472. C43#17533semidirect

Maximal subgroups

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

subgroupindex
#191478892
#431×D432
#191369342
#191330922
#191330882
#191330852
#191330832
#191330822
#191330812
#191330792
C43×#15002
#1753343