Finite Group Databasebeta

← #25063899

Subgroups — #25063899

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3#19136997C211yesmaximal, characteristic, complemented
4#19133139C211yesmaximal, characteristic, complemented
5#19133138C211yesmaximal, characteristic, complemented
6#19133136C211yesmaximal, characteristic, complemented
7#19133132C212yesmaximal, complemented
8#19133130C212yesmaximal, complemented
9#19133092C212yesmaximal, complemented
10#19133088C212yesmaximal, complemented
11C43×#1513C211yesmaximal, 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—
33C2×#13063281—21no—
34C22×C4×Dic43C2211yescharacteristic
35#14582953—21no—
36#14582953C2212yes—
37#14582949—21no—
38#14582949C2212yes—
39#14582922—21no—
40#14582863C2211yescharacteristic
41M16×Dic43—21no—
42#14582768—21no—
43#14582763C2212yes—
44#14582759C2211yescharacteristic
45#14582757—21no—
46C4⋊C4×Dic43—21no—
47#14582750C2212yes—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#525C2211yescharacteristic
55C43×#407C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621898C2×C411yescharacteristic
60C2×#10621900—21no—
61C2×#10621900—21no—
62C23×Dic43D411yescharacteristic
63C23×Dic43D411yescharacteristic
64C2×#10621877—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—
134#13063281—44no—
135C2×C4⋊Dic43—21no—
136C2×Dic43⋊C4—22no—
137C2×Dic43⋊C4—22no—
138C2×C22⋊Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—22no—
141C2×C4×Dic43C2×C411yescharacteristic
142C2×C4×Dic43C2×C411yescharacteristic
143C2×C4×Dic43C2×C411yescharacteristic
144C2×C4×Dic43C2×C411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43D411yescharacteristic
150C2×C4×Dic43D411yescharacteristic
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153C42×D43—21no—
154Dic43⋊C8—22no—
155Dic43⋊C8—22no—
156C22⋊(C43⋊C8)—21no—
157C22⋊(C43⋊C8)C2312yes—
158#13063235—22no—
159C8×Dic43—22no—
160C43⋊#95—22no—
161C43⋊#95C2312yes—
162C2×#41×C43C2×C411yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C2×M16×C43—21no—
165#123×C43—21no—
166C22⋊Q8×C43C2×C411yescharacteristic
167C22⋊Q8×C43C2311yescharacteristic
168#121×C43C2×C411yescharacteristic
169#121×C43C2311yescharacteristic
170#120×C43—21no—
171C4×D4×C43—21no—
172C4×D4×C43—21no—
173#117×C43C2×C411yescharacteristic
174C2×C4⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C22⋊C8×C43—21no—
177C22⋊C8×C43C2312yes—
178#95×C43C2312yes—
179C24×C43C2×D411yescharacteristic
180#41×C43—42no—
181C2×Q8×C43C22×C411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43C22×C411yescharacteristic
186C22×C4×C43—21no—
187C22×C4×C43—22no—
188C22×C4×C43—42no—
189C22×C4×C43C22×C411yescharacteristic
190C22×C4×C43C22×C411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—21no—
196C2×C22⋊D43—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—22no—
205C22×Dic43—42no—
206C22×Dic43C22⋊C411yescharacteristic
207C22×Dic43C22⋊C411yescharacteristic
208C22×Dic43C22⋊C411yescharacteristic
209C22×Dic43C22⋊C411yescharacteristic
210C22×Dic43C22⋊C411yescharacteristic
211C22×Dic43C22⋊C411yescharacteristic
212C22×Dic43C22⋊C411yescharacteristic
213C22×Dic43C22⋊C411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218#10621900—44no—
219#10621900—42no—
220#10621900—42no—
221#10621898—42no—
222C2×D172C22×C411yescharacteristic
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86C22×C411yescharacteristic
229M16×C43—42no—
230C2×C8×C43—22no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—42no—
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—
241C22⋊C4×C43—42no—
242C42×C43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—42no—
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⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—42no—
262C4⋊Dic43C22×C411yescharacteristic
263C4⋊Dic43C22×C411yescharacteristic
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—
274Dic43⋊C4—44no—
275Dic43⋊C4—44no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C4×Dic43—21no—
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×Dic43C22×C411yescharacteristic
293C4×Dic43C22×C411yescharacteristic
294C4×Dic43C2×D411yescharacteristic
295C4×Dic43C2×D411yescharacteristic
296C4×Dic43C2×D411yescharacteristic
297C4×Dic43C2×D411yescharacteristic
298#10621877—42no—
299C2×C43⋊C8—22no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43C2×C22⋊C411yescharacteristic
306C23×C43C2×C22⋊C411yescharacteristic
307C23×C43C22×D411yescharacteristic
308C22×D43—21no—
309Q8×C43—41no—
310D4×C43—41no—
311D4×C43—42no—
312D4×C43—42no—
313D4×C43—41no—
314D4×C43—41no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43C2×C22⋊C411yescharacteristic
329C2×C4×C43C2×C22⋊C411yescharacteristic
330C2×C4×C43C23×C411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C22⋊D43—42no—
333C22⋊D43—42no—
334C22⋊D43—41no—
335C22⋊D43—41no—
336C22⋊D43—42no—
337C22⋊D43—42no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43—42no—
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362C2×Dic43C2×C22⋊C411yescharacteristic
363C2×Dic43C2×C22⋊C411yescharacteristic
364C2×Dic43C2×C22⋊C411yescharacteristic
365C2×Dic43C2×C22⋊C411yescharacteristic
366C2×Dic43AGL(1,ℤ/8)12yes—
367C2×Dic43#13712yes—
368D172—41no—
369C4×D43—42no—
370C4×D43—42no—
371C4×D43—42no—
372Dic86—42no—
373Dic86—42no—
374Dic86—41no—
375C8×C43—42no—
376C43⋊C8—42no—
377#17563—431nomaximal, Sylow
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—21no—
385C22×C43—21no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43C22×C22⋊C411yescharacteristic
392C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C43C2×#13711yescharacteristic
394C2×D43—41no—
395C2×D43—41no—
396C2×D43—41no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—41no—
403C4×C43—82no—
404C4×C43#41012yes—
405Dic43—21no—
406Dic43—21no—
407Dic43—21no—
408Dic43—21no—
409Dic43—21no—
410Dic43—41no—
411Dic43—41no—
412Dic43—41no—
413Dic43—82no—
414Dic43#41712yes—
415Dic43#41712yes—
416Dic43#42112yes—
417#3444—431no—
418#2920—431no—
419#2285—431no—
420#1513—431no—
421#1513—431no—
422#1513—431no—
423#1513D4311yescharacteristic, complemented
424#1512—432no—
425#1512—432no—
426#1503—432no—
427#1502—432no—
428C2×C43—21no—
429C2×C43—21no—
430C2×C43—41no—
431C2×C43—41no—
432C2×C43—81no—
433C2×C43C2×#41011yescharacteristic
434C2×C43C2×#41711yescharacteristic
435C2×C43C2×#42111yescharacteristic
436D43—81no—
437#533—431no—
438#533—431no—
439#533—431no—
440#532—431no—
441#532—431no—
442#532—431no—
443#529—431no—
444#529—431no—
445#529—431no—
446#529—431no—
447#529—861no—
448#529—861no—
449#529—861no—
450#529—861no—
451#525—431no—
452#525—861no—
453#525—861no—
454#525C2×D4311yescharacteristic
455C4×#41—431no—
456C4×#41—431no—
457C4×#41—861no—
458C4×#41—861no—
459C2×#117—861no—
460C22×C42—431no—
461#432—432no—
462#432—861no—
463#431—432no—
464#431—861no—
465#423—861no—
466#407—431no—
467#407C2×D4311yescharacteristic
468C4×M16—861no—
469#384—861no—
470#382—432no—
471#380—431no—
472#380—861no—
473#380C2×D4311yescharacteristic
474C4×C4⋊C4—432no—
475C4×C4⋊C4—861no—
476#328—432no—
477#328—432no—
478#328—432no—
479#328C2×D4312yes—
480#327—432no—
481#327—432no—
482#327—432no—
483#327C2×D4312yes—
484C43#1756311yescharacteristic, complemented, Sylow
485C2×#41—431no—
486C2×#41—861no—
487C2×#41—861no—
488C2×#41C4×D4311yescharacteristic
489C23×C4—431no—
490C23×C4—431no—
491C23×C4C22×D4311yescharacteristic
492C2×M16—21no—
493C2×M16—861no—
494C4⋊Q8—431no—
495C4⋊Q8—431no—
496C4⋊Q8—431no—
497#127—431no—
498#126—861no—
499#126—861no—
500#126—861no—
501#126—861no—
502#125—431no—
503#125—431no—
504#125—861no—
505#125—861no—
506#124—431no—
507#124—431no—
508#124—861no—
509#124—861no—
510#123—21no—
511#123—861no—
512#123—861no—
513#123—861no—
514#123—861no—
515#123—861no—
516C22⋊Q8—431no—
517C22⋊Q8—431no—
518C22⋊Q8—861no—
519C22⋊Q8—861no—
520C22⋊Q8—861no—
521C22⋊Q8—861no—
522C22⋊Q8C4×D4311yescharacteristic
523C22⋊Q8C22×D4311yescharacteristic
524#121—431no—
525#121—431no—
526#121—861no—
527#121—861no—
528#121—861no—
529#121—861no—
530#121C4×D4311yescharacteristic
531#121C22×D4311yescharacteristic
532#120—21no—
533#120—861no—
534C4×Q8—431no—
535C4×Q8—431no—
536C4×Q8—431no—
537C4×Q8—431no—
538C4×Q8—861no—
539C4×Q8—861no—
540C4×Q8—861no—
541C4×Q8—861no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—431no—
545C4×D4—431no—
546C4×D4—431no—
547C4×D4—431no—
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×D4—861no—
560C4×D4—861no—
561C4×D4—861no—
562#117—431no—
563#117—861no—
564#117—861no—
565#117—861no—
566#117—861no—
567#117—861no—
568#117—861no—
569#117—861no—
570#117—861no—
571#117—1724no—
572#117C4×D4311yescharacteristic
573C2×C4⋊C4—21no—
574C2×C4⋊C4—862no—
575C2×C4⋊C4—862no—
576C2×C4⋊C4—861no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—861no—
579C2×C42—431no—
580C2×C42—431no—
581C2×C42—431no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—431no—
587C2×C42—431no—
588C2×C42—431no—
589C2×C42—431no—
590C2×C42—431no—
591C2×C42—861no—
592C2×C42—861no—
593C2×C42—862no—
594C4⋊C8—862no—
595C4⋊C8—862no—
596C22⋊C8—21no—
597C22⋊C8—432no—
598C22⋊C8—861no—
599C22⋊C8C22×D4312yes—
600#97—862no—
601C4×C8—862no—
602#95—432no—
603#95—862no—
604#95C22×D4312yes—
605C24D4×D4311yescharacteristic
606#41—42no—
607#41—1722no—
608#41—1722no—
609#41—1722no—
610#41—1724no—
611C2×Q8—431no—
612C2×Q8—861no—
613C2×Q8—861no—
614C2×Q8C2×C4×D4311yescharacteristic
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—431no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4C2×C4×D4311yescharacteristic
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—42no—
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—861no—
641C22×C4—861no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—862no—
648C22×C4—1722no—
649C22×C4C2×C4×D4311yescharacteristic
650C22×C4C2×C4×D4311yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4D4×D4311yescharacteristic
654C22×C4C23×D4311yescharacteristic
655M16—42no—
656M16—1722no—
657C2×C8—22no—
658C2×C8—862no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
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—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—1722no—
679C4⋊C4—1724no—
680C4⋊C4—1724no—
681C4⋊C4C2×C4×D4311yescharacteristic
682C4⋊C4C2×C4×D4311yescharacteristic
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—42no—
689C22⋊C4—861no—
690C22⋊C4—861no—
691C22⋊C4—861no—
692C22⋊C4—861no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C22⋊C4—861no—
697C22⋊C4—861no—
698C22⋊C4—861no—
699C22⋊C4—861no—
700C22⋊C4—861no—
701C22⋊C4—861no—
702C22⋊C4—1722no—
703C42—21no—
704C42—431no—
705C42—431no—
706C42—431no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—431no—
715C42—431no—
716C42—431no—
717C42—431no—
718C42—431no—
719C42—431no—
720C42—861no—
721C42—861no—
722C42—861no—
723C42—861no—
724C42—861no—
725C42—1724no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—41no—
730C23—41no—
731C23—861no—
732C23C22⋊C4×D4311yescharacteristic
733C23C22⋊C4×D4311yescharacteristic
734C23C2×D4×D4311yescharacteristic
735Q8—41no—
736Q8—1721no—
737Q8—1722no—
738Q8—1722no—
739D4—41no—
740D4—42no—
741D4—42no—
742D4—41no—
743D4—41no—
744D4—1721no—
745D4—1722no—
746D4—1722no—
747D4—1722no—
748D4—1722no—
749D4—1721no—
750D4—1721no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—431no—
765C2×C4—431no—
766C2×C4—431no—
767C2×C4—432no—
768C2×C4—432no—
769C2×C4—431no—
770C2×C4—431no—
771C2×C4—431no—
772C2×C4—431no—
773C2×C4—431no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—1722no—
787C2×C4—1722no—
788C2×C4—1722no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1722no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4—1722no—
796C2×C4—1722no—
797C2×C4C22⋊C4×D4311yescharacteristic
798C2×C4C22⋊C4×D4311yescharacteristic
799C2×C4C22×C4×D4311yescharacteristic
800C2×C4C2×D4×D4311yescharacteristic
801C8—42no—
802C8—1722no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—1721no—
817C22—1721no—
818C22—1721no—
819C22C2×C22⋊C4×D4311yescharacteristic
820C22AGL(1,ℤ/8)×D4311yescharacteristic
821C22#137×D4311yescharacteristic
822C4—21no—
823C4—21no—
824C4—21no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—432no—
830C4—432no—
831C4—432no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—861no—
836C4—861no—
837C4—3442no—
838C4—1721no—
839C4—1721no—
840C4—1721no—
841C4#1458287112yes—
842C2—21no—
843C2—21no—
844C2—41no—
845C2—41no—
846C2—81no—
847C2—3441no—
848C2C2×#1458287111yescharacteristic
849C2#417×D4311yescharacteristic
850C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1513C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1513D43
hypocenterC43#17563
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. #19136997C2semidirect
4. #19133139C2semidirect
5. #19133138C2semidirect
6. #19133136C2semidirect
7. #19133132C2semidirect
8. #19133130C2semidirect
9. #19133092C2semidirect
10. #19133088C2semidirect
11. C43×#1513C2semidirect
12. #14583452C4semidirect
13. #14583451C4semidirect
15. #14583445C4semidirect
16. #14583444C4semidirect
18. #14583435C4semidirect
20. #14583430C4semidirect
29. #41×Dic43C4semidirect
30. #14583367C4semidirect
423. #1513D43semidirect
484. C43#17563semidirect

Maximal subgroups

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

subgroupindex
#191478872
#191432242
#191369972
#191331392
#191331382
#191331362
#191331322
#191331302
#191330922
#191330882
C43×#15132
#1756343