Finite Group Databasebeta

← #25063763

Subgroups — #25063763

Order 11008.

1108 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2#432×D43C211yesmaximal, characteristic, complemented
3C4×#13063283C211yesmaximal, characteristic, complemented
4#19133121C211yesmaximal, characteristic, complemented
5#19133120C211yesmaximal, characteristic, complemented
6#19133118C211yesmaximal, characteristic, complemented
7#19133105C212yesmaximal, complemented
8#19133101C212yesmaximal, complemented
9#19133085C212yesmaximal, complemented
10#19133083C212yesmaximal, complemented
11C43×#1509C211yesmaximal, 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×#13063283—21no—
34C2×C42×D43C2211yescharacteristic
35#14582956C2211yescharacteristic
36#14582955—21no—
37#14582954—21no—
38#14582953C2212yes—
39C4⋊C8×D43—21no—
40C22⋊C8×D43C2212yes—
41#97×D43—21no—
42C4⋊C4×Dic43—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4—21no—
45#14582746C2212yes—
46#14582744C2212yes—
47C42×Dic43—21no—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#529C2211yescharacteristic
55C43×#432C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
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—28no—
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×(C2×D43)⋊C4—22no—
138C2×C4×Dic43—22no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
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—
158#13063236—21no—
159#13063235—22no—
160C43⋊#95—22no—
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×C4⋊C4×C43—21no—
173C2×C42×C43—21no—
174C2×C42×C43C2311yescharacteristic
175C4⋊C8×C43—21no—
176C22⋊C8×C43C2312yes—
177#97×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—42no—
202#10621900—42no—
203#10621898—44no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172C22×C411yescharacteristic
207C2×C4×D43—24no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—41no—
212C2×C4×D43—41no—
213C2×C4×D43—42no—
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×D43C22×C411yescharacteristic
223C2×C4×D43C22×C411yescharacteristic
224C2×C4×D43C2×D411yescharacteristic
225C2×C4×D43C2×D411yescharacteristic
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86C22×C411yescharacteristic
229C2×C8×C43—22no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C22×C411yescharacteristic
236C4⋊C4×C43C22×C411yescharacteristic
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C22⋊C4×C43—21no—
242C42×C43—21no—
243C42×C43—42no—
244C42×C43C22×C411yescharacteristic
245C42×C43C22×C411yescharacteristic
246C42×C43C2×D411yescharacteristic
247C42×C43C2×D411yescharacteristic
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—21no—
251(C2×D43)⋊C4—28no—
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—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—21no—
261(C2×D43)⋊C4—21no—
262C4⋊Dic43—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43C22×C411yescharacteristic
266C4⋊Dic43C22×C411yescharacteristic
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277C4×Dic43—28no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C4×Dic43—21no—
281C4×Dic43—21no—
282C4×Dic43—21no—
283C4×Dic43—44no—
284C4×Dic43—42no—
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22⋊C411yescharacteristic
287C4×Dic43C22⋊C411yescharacteristic
288C4×Dic43C22⋊C411yescharacteristic
289C4×Dic43C22⋊C411yescharacteristic
290C4×Dic43C22⋊C411yescharacteristic
291C4×Dic43C22⋊C411yescharacteristic
292C4×Dic43C22⋊C411yescharacteristic
293C4×Dic43C22×C411yescharacteristic
294C4×Dic43C22×C411yescharacteristic
295C4×Dic43C2×D411yescharacteristic
296C4×Dic43C2×D411yescharacteristic
297C2×C43⋊C8—22no—
298C8×D43—44no—
299C23×C43—21no—
300C23×C43C22×D411yescharacteristic
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—22no—
304C22×D43—21no—
305C22×D43—41no—
306C22×D43C2×C22⋊C411yescharacteristic
307C22×D43C2×C22⋊C411yescharacteristic
308Q8×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—22no—
315C2×C4×C43—24no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—41no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C2×C4×C43C2×C22⋊C411yescharacteristic
325C2×C4×C43C2×C22⋊C411yescharacteristic
326C2×C4×C43C2×C22⋊C411yescharacteristic
327C2×C4×C43C23×C411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C22⋊D43—42no—
330C22⋊D43—42no—
331C22⋊D43—41no—
332C22⋊D43—41no—
333C22⋊D43—42no—
334C22⋊D43—42no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—24no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43C2×C22⋊C411yescharacteristic
348C2×Dic43C2×C22⋊C411yescharacteristic
349C2×Dic43C2×C22⋊C411yescharacteristic
350C2×Dic43C2×C22⋊C411yescharacteristic
351C2×Dic43C2×C22⋊C411yescharacteristic
352C2×Dic43C2×C22⋊C411yescharacteristic
353D172—41no—
354D172—42no—
355D172—42no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—41no—
362C4×D43—41no—
363C4×D43—41no—
364C4×D43—41no—
365C4×D43—41no—
366C4×D43—41no—
367C4×D43—42no—
368C4×D43—42no—
369C4×D43—42no—
370C4×D43#10414yes—
371Dic86—42no—
372Dic86—42no—
373Dic86—41no—
374C8×C43—42no—
375C43⋊C8—42no—
376#17543—431nomaximal, Sylow
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43C22×C22⋊C411yescharacteristic
383C22×C43#57511yescharacteristic
384C22×C43#57511yescharacteristic
385C2×D43—21no—
386C2×D43—21no—
387C2×D43—21no—
388C2×D43—21no—
389C2×D43—21no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43C2×#10412yes—
396C4×C43—21no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—44no—
402C4×C43—41no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43C2×#10412yes—
406Dic43—21no—
407Dic43—21no—
408Dic43—21no—
409Dic43—21no—
410Dic43—44no—
411Dic43—41no—
412Dic43—41no—
413Dic43—41no—
414Dic43#41012yes—
415Dic43C2×#10412yes—
416#3444—431no—
417C2×#432—431no—
418C4×#117—431no—
419#1509—431no—
420#1509—431no—
421#1509—431no—
422#1509D4311yescharacteristic, complemented
423#1506—432no—
424#1505—432no—
425#1501—432no—
426#1501—432no—
427C2×C43—21no—
428C2×C43—21no—
429C2×C43—81no—
430C2×C43C2×#41011yescharacteristic
431C2×C43#289611yescharacteristic
432C2×C43C22×#10411yescharacteristic
433D43—22no—
434D43—41no—
435D43—81no—
436#533—431no—
437#533—431no—
438#533—431no—
439#532—431no—
440#532—431no—
441#532—431no—
442#529—431no—
443#529—431no—
444#529—431no—
445#529—861no—
446#529—861no—
447#529—861no—
448#529—861no—
449#529C2×D4311yescharacteristic
450#525—431no—
451#525—431no—
452#525—861no—
453#525—861no—
454C4×#41—431no—
455C4×#41—431no—
456C4×#41—861no—
457C4×#41—861no—
458C2×#117—861no—
459C22×C42—431no—
460#432—431no—
461#432—432no—
462#432—861no—
463#432—861no—
464#432C2×D4311yescharacteristic
465C2×C4⋊C8—861no—
466C2×C22⋊C8—432no—
467C2×#97—861no—
468C4×C4⋊C4—431no—
469C4×C4⋊C4—861no—
470C4×C4⋊C4C2×D4311yescharacteristic
471C4×C22⋊C4—432no—
472C4×C22⋊C4—861no—
473#376—432no—
474C43—861no—
475#328—432no—
476#328—432no—
477#328—432no—
478#328C2×D4312yes—
479#327—432no—
480#327—432no—
481#327—432no—
482#327C2×D4312yes—
483C43#1754311yescharacteristic, complemented, Sylow
484C2×#41—431no—
485C2×#41—431no—
486C2×#41—861no—
487C2×#41—861no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—431no—
491C22×C8—862no—
492C4⋊Q8—431no—
493C4⋊Q8—431no—
494C4⋊Q8—431no—
495#127—431no—
496#126—21no—
497#126—861no—
498#126—861no—
499#126—861no—
500#125—431no—
501#125—861no—
502#125—861no—
503#125C4×D4311yescharacteristic
504#124—431no—
505#124—861no—
506#124—861no—
507#124C4×D4311yescharacteristic
508#123—21no—
509#123—861no—
510#123—861no—
511#123—861no—
512#123—861no—
513#123—861no—
514C22⋊Q8—431no—
515C22⋊Q8—431no—
516C22⋊Q8—431no—
517C22⋊Q8—861no—
518C22⋊Q8—861no—
519C22⋊Q8—861no—
520C22⋊Q8—861no—
521C22⋊Q8C22×D4311yescharacteristic
522#121—431no—
523#121—431no—
524#121—431no—
525#121—861no—
526#121—861no—
527#121—861no—
528#121—861no—
529#121C22×D4311yescharacteristic
530#120—861no—
531#120—861no—
532C4×Q8—431no—
533C4×Q8—431no—
534C4×Q8—431no—
535C4×Q8—861no—
536C4×Q8—861no—
537C4×Q8—861no—
538C4×Q8—861no—
539C4×Q8C4×D4311yescharacteristic
540C4×D4—21no—
541C4×D4—431no—
542C4×D4—431no—
543C4×D4—431no—
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×D4—861no—
554C4×D4—861no—
555C4×D4—861no—
556C4×D4—861no—
557C4×D4—861no—
558C4×D4—861no—
559C4×D4C4×D4311yescharacteristic
560#117—21no—
561#117—431no—
562#117—431no—
563#117—861no—
564#117—861no—
565#117—861no—
566#117—861no—
567#117—861no—
568#117—861no—
569#117—868no—
570#117—861no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—861no—
573C2×C22⋊C4—862no—
574C2×C42—21no—
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—431no—
581C2×C42—431no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—861no—
587C2×C42—861no—
588C2×C42—862no—
589C2×C42—862no—
590C2×C42—861no—
591C2×C42C22×D4311yescharacteristic
592C4⋊C8—21no—
593C4⋊C8—862no—
594C4⋊C8—861no—
595C22⋊C8—432no—
596C22⋊C8—862no—
597C22⋊C8C22×D4312yes—
598#97—21no—
599#97—862no—
600#97—861no—
601#95—432no—
602#95—862no—
603#95C22×D4312yes—
604C24—431no—
605#41—1724no—
606#41—1722no—
607#41—1722no—
608#41—1722no—
609#41—1722no—
610C2×Q8—431no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8C2×C4×D4311yescharacteristic
614C2×D4—21no—
615C2×D4—431no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4C2×C4×D4311yescharacteristic
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—864no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—862no—
647C22×C4—861no—
648C22×C4—1721no—
649C22×C4—1721no—
650C22×C4—1722no—
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4C23×D4311yescharacteristic
654C2×C8—22no—
655C2×C8—862no—
656C2×C8—1724no—
657C4⋊C4—24no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—431no—
663C4⋊C4—431no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—861no—
672C4⋊C4—864no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4C2×C4×D4311yescharacteristic
678C4⋊C4C2×C4×D4311yescharacteristic
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C22⋊C4—861no—
687C22⋊C4—861no—
688C22⋊C4—861no—
689C22⋊C4—861no—
690C22⋊C4—868no—
691C22⋊C4—861no—
692C22⋊C4—861no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C22⋊C4—861no—
697C22⋊C4—861no—
698C42—21no—
699C42—42no—
700C42—431no—
701C42—431no—
702C42—431no—
703C42—431no—
704C42—431no—
705C42—431no—
706C42—431no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—861no—
713C42—861no—
714C42—861no—
715C42—861no—
716C42—868no—
717C42—861no—
718C42—1722no—
719C42—1724no—
720C42C2×C4×D4311yescharacteristic
721C42C2×C4×D4311yescharacteristic
722C42D4×D4311yescharacteristic
723C42D4×D4311yescharacteristic
724C23—21no—
725C23—431no—
726C23—431no—
727C23—862no—
728C23—861no—
729C23—861no—
730C23—861no—
731C23—1721no—
732C23C2×D4×D4311yescharacteristic
733Q8—41no—
734Q8—1721no—
735Q8—1722no—
736Q8—1722no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—1721no—
741D4—1722no—
742D4—1722no—
743D4—1722no—
744D4—1722no—
745D4—1722no—
746D4—1722no—
747D4—1721no—
748D4—1721no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—431no—
761C2×C4—431no—
762C2×C4—434no—
763C2×C4—431no—
764C2×C4—431no—
765C2×C4—431no—
766C2×C4—431no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—861no—
774C2×C4—861no—
775C2×C4—862no—
776C2×C4—864no—
777C2×C4—861no—
778C2×C4—861no—
779C2×C4—861no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1722no—
787C2×C4—1722no—
788C2×C4—1722no—
789C2×C4—1722no—
790C2×C4—1722no—
791C2×C4—1722no—
792C2×C4—1722no—
793C2×C4C22⋊C4×D4311yescharacteristic
794C2×C4C22⋊C4×D4311yescharacteristic
795C2×C4C22⋊C4×D4311yescharacteristic
796C2×C4C22⋊C4×D4311yescharacteristic
797C2×C4C22×C4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C8—42no—
800C8—1722no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—432no—
807C22—861no—
808C22—861no—
809C22—861no—
810C22—861no—
811C22—861no—
812C22—1722no—
813C22—1722no—
814C22—1721no—
815C22—1721no—
816C22—1721no—
817C22C2×C22⋊C4×D4311yescharacteristic
818C22#1458369511yescharacteristic
819C22#1458369811yescharacteristic
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—44no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—432no—
830C4—432no—
831C4—861no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—1724no—
836C4—1721no—
837C4—1721no—
838C4—1721no—
839C4#104×D4312yes—
840C2—21no—
841C2—21no—
842C2—81no—
843C2—862no—
844C2—3441no—
845C2—1721no—
846C2#410×D4311yescharacteristic
847C2#1914311111yescharacteristic
848C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#19147889C2
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17543
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #432×D43C2semidirect
3. C4×#13063283C2semidirect
4. #19133121C2semidirect
5. #19133120C2semidirect
6. #19133118C2semidirect
7. #19133105C2semidirect
8. #19133101C2semidirect
9. #19133085C2semidirect
10. #19133083C2semidirect
11. C43×#1509C2semidirect
12. #14583455C4semidirect
13. #14583453C4semidirect
15. #14583448C4semidirect
16. #14583446C4semidirect
18. #14583434C4semidirect
22. #14583428C4semidirect
29. C4×#10621902C4semidirect
32. C4×#10621900C4semidirect
422. #1509D43semidirect
483. C43#17543semidirect

Maximal subgroups

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

subgroupindex
#191478892
#432×D432
C4×#130632832
#191331212
#191331202
#191331182
#191331052
#191331012
#191330852
#191330832
C43×#15092
#1754343