Finite Group Databasebeta

← #25064056

Subgroups — #25064056

Order 11008.

1086 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#19143225C211yesmaximal, characteristic, complemented
3#382×D43C211yesmaximal, characteristic, complemented
4#19133157C212yesmaximal, complemented
5#19133153C212yesmaximal, complemented
6#19133134C211yesmaximal, characteristic, complemented
7#19133133C211yesmaximal, characteristic, complemented
8#19133131C211yesmaximal, characteristic, complemented
9#19133098C212yesmaximal, complemented
10#19133096C212yesmaximal, complemented
11C43×#1512C211yesmaximal, 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×C4⋊C4×D43—21no—
34C2×C42×D43C2211yescharacteristic
35#14582956C2211yescharacteristic
36#14582954—21no—
37#14582951—21no—
38#14582949C2212yes—
39#14582921—21no—
40#14582861C2212yes—
41#14582851—21no—
42#14582765C2211yescharacteristic
43#14582764—21no—
44#14582763—21no—
45#14582763C2212yes—
46#95×D43—21no—
47#95×D43C2212yes—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#529C2211yescharacteristic
55C43×#432C2211yescharacteristic
56C43×#382C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621900—21no—
62C2×#10621900C2×C411yescharacteristic
63C22×C4×D43—22no—
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C2×#10621872—22no—
68#13063324C2×C411yescharacteristic, complemented
69#13063324C2×C411yescharacteristic, complemented
70#13063323C2×C411yescharacteristic, complemented
71#13063321C2×C411yescharacteristic, complemented
72#13063320—21no—
73#13063319—21no—
74#13063318—21no—
75#13063317C2×C411yescharacteristic, complemented
76#13063315—21no—
77#13063315—21no—
78#13063313C2×C411yescharacteristic, complemented
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#13063304C2311yescharacteristic
88#13063303—21no—
89#13063303—21no—
90#13063303—21no—
91#13063302—21no—
92#13063301C2×C411yescharacteristic
93#13063300C2×C411yescharacteristic
94#13063299C2311yescharacteristic
95#13063298—21no—
96#13063298—21no—
97#13063298—21no—
98#13063297—21no—
99#13063296C2×C411yescharacteristic
100#13063295—21no—
101#13063293—21no—
102Q8×Dic43C2×C411yescharacteristic, complemented
103C4×Dic86—21no—
104C4×Dic86C2×C411yescharacteristic, complemented
105#13063290—21no—
106#13063290—21no—
107#13063290—21no—
108#13063290C2×C411yescharacteristic, complemented
109C4×D172—21no—
110C4×D172C2×C411yescharacteristic, complemented
111D4×Dic43—21no—
112D4×Dic43C2×C411yescharacteristic, complemented
113#13063287—21no—
114#13063287—21no—
115#13063287—21no—
116#13063287C2×C411yescharacteristic, complemented
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×Dic43⋊C4—22no—
138C4⋊C4×D43—44no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43C2311yescharacteristic
143C42×D43—21no—
144C42×D43C2×C411yescharacteristic
145C42×D43C2×C411yescharacteristic
146C42×D43C2×C411yescharacteristic
147C42×D43C2×C411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43D411yescharacteristic
151C42×D43D411yescharacteristic
152C4⋊(C43⋊C8)—21no—
153Dic43⋊C8—22no—
154C22⋊(C43⋊C8)C2312yes—
155(C2×D43)⋊C8—22no—
156#13063236—21no—
157C8×Dic43—22no—
158C43⋊#95—21no—
159C43⋊#95—22no—
160C43⋊#95—22no—
161C43⋊#95C2312yes—
162#126×C43—21no—
163#125×C43C2×C411yescharacteristic, complemented
164#124×C43C2×C411yescharacteristic, complemented
165#123×C43—21no—
166C22⋊Q8×C43C2311yescharacteristic
167#121×C43C2311yescharacteristic
168C4×Q8×C43C2×C411yescharacteristic, complemented
169C4×D4×C43—21no—
170C4×D4×C43C2×C411yescharacteristic, complemented
171#117×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43—21no—
175C22⋊C8×C43C2312yes—
176#97×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—42no—
202#10621900—42no—
203#10621898—44no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172C22×C411yescharacteristic
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43—44no—
215C2×C4×D43—44no—
216C2×C4×D43—44no—
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×D43C22⋊C411yescharacteristic
225C2×C4×D43C22×C411yescharacteristic
226C2×C4×D43C22×C411yescharacteristic
227C2×C4×D43C2×D411yescharacteristic
228C2×C4×D43C2×D411yescharacteristic
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86C22×C411yescharacteristic
232C2×C8×C43—22no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—42no—
238C4⋊C4×C43C22×C411yescharacteristic
239C4⋊C4×C43C22×C411yescharacteristic
240C22⋊C4×C43—21no—
241C22⋊C4×C43—21no—
242C22⋊C4×C43—21no—
243C22⋊C4×C43—21no—
244C22⋊C4×C43—21no—
245C42×C43—21no—
246C42×C43C22×C411yescharacteristic
247C42×C43C22×C411yescharacteristic
248C42×C43C2×D411yescharacteristic
249C42×C43C2×D411yescharacteristic
250C22⋊Dic43—21no—
251C22⋊Dic43—21no—
252C22⋊Dic43—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—
262(C2×D43)⋊C4—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—42no—
266C4⋊Dic43C22×C411yescharacteristic
267C4⋊Dic43C22×C411yescharacteristic
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—
277Dic43⋊C4—21no—
278Dic43⋊C4—44no—
279C4×Dic43—21no—
280C4×Dic43—21no—
281C4×Dic43—21no—
282C4×Dic43—21no—
283C4×Dic43—21no—
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
296C2×C43⋊C8—22no—
297#10621872—44no—
298C23×C43—21no—
299C23×C43C22×D411yescharacteristic
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—21no—
305C22×D43C2×C22⋊C411yescharacteristic
306C22×D43C2×C22⋊C411yescharacteristic
307Q8×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C2×C4×C43C2×C22⋊C411yescharacteristic
325C2×C4×C43C2×C22⋊C411yescharacteristic
326C2×C4×C43C23×C411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C22⋊D43—42no—
329C22⋊D43—41no—
330C22⋊D43—41no—
331C22⋊D43—42no—
332C22⋊D43—42no—
333C22⋊D43—42no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43C2×C22⋊C411yescharacteristic
345C2×Dic43C2×C22⋊C411yescharacteristic
346C2×Dic43C2×C22⋊C411yescharacteristic
347C2×Dic43C2×C22⋊C411yescharacteristic
348C2×Dic43C2×C22⋊C411yescharacteristic
349C2×Dic43C2×C22⋊C411yescharacteristic
350C2×Dic43AGL(1,ℤ/8)12yes—
351C2×Dic43#13712yes—
352D172—41no—
353D172—42no—
354D172—42no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—41no—
364C4×D43—41no—
365C4×D43—41no—
366C4×D43—41no—
367C4×D43—42no—
368C4×D43—42no—
369C4×D43—42no—
370C4×D43—88no—
371Dic86—42no—
372Dic86—42no—
373Dic86—41no—
374C8×C43—42no—
375C43⋊C8—42no—
376#17588—431nomaximal, Sylow
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43C22×C22⋊C411yescharacteristic
383C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C43C2×#13711yescharacteristic
385C2×D43—24no—
386C2×D43—24no—
387C2×D43—21no—
388C2×D43—21no—
389C2×D43—21no—
390C2×D43—21no—
391C2×D43—41no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43#41012yes—
395C2×D43#42112yes—
396C4×C43—21no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—41no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43—82no—
406Dic43—21no—
407Dic43—21no—
408Dic43—21no—
409Dic43—21no—
410Dic43—41no—
411Dic43—41no—
412Dic43—41no—
413Dic43—82no—
414Dic43#41712yes—
415Dic43#41712yes—
416#3444—431no—
417#2920—431no—
418C2×#382—431no—
419#1518—432no—
420#1517—432no—
421#1512—431no—
422#1512—431no—
423#1512—431no—
424#1512D4311yescharacteristic, complemented
425#1504—432no—
426#1504—432no—
427C2×C43—21no—
428C2×C43—21no—
429C2×C43—81no—
430C2×C43C2×#41011yescharacteristic
431C2×C43C2×#41711yescharacteristic
432C2×C43C2×#42111yescharacteristic
433D43—22no—
434D43—22no—
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—
458C22×C4⋊C4—861no—
459C22×C42—431no—
460#432—431no—
461#432—861no—
462#432C2×D4311yescharacteristic
463#431—432no—
464#431—861no—
465#423—861no—
466#407—432no—
467C4×M16—861no—
468#382—431no—
469#382—432no—
470#382—861no—
471#382—861no—
472#382C2×D4311yescharacteristic
473C2×#95—432no—
474C2×#95—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#1758811yescharacteristic, complemented, Sylow
484C2×#41—431no—
485C2×#41—431no—
486C2×#41—861no—
487C2×#41—861no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—431no—
491C23×C4—862no—
492C2×M16—862no—
493C4⋊Q8—431no—
494C4⋊Q8—431no—
495C4⋊Q8—431no—
496#127—431no—
497#126—21no—
498#126—861no—
499#126—861no—
500#126—861no—
501#125—431no—
502#125—861no—
503#125—861no—
504#125C4×D4311yescharacteristic, complemented
505#124—431no—
506#124—861no—
507#124—861no—
508#124C4×D4311yescharacteristic, complemented
509#123—21no—
510#123—861no—
511#123—861no—
512#123—861no—
513#123—861no—
514#123—861no—
515C22⋊Q8—431no—
516C22⋊Q8—431no—
517C22⋊Q8—431no—
518C22⋊Q8—861no—
519C22⋊Q8—861no—
520C22⋊Q8—861no—
521C22⋊Q8—861no—
522C22⋊Q8C22×D4311yescharacteristic
523#121—431no—
524#121—431no—
525#121—431no—
526#121—861no—
527#121—861no—
528#121—861no—
529#121—861no—
530#121C22×D4311yescharacteristic
531#120—861no—
532#120—861no—
533C4×Q8—431no—
534C4×Q8—431no—
535C4×Q8—431no—
536C4×Q8—861no—
537C4×Q8—861no—
538C4×Q8—861no—
539C4×Q8—861no—
540C4×Q8C4×D4311yescharacteristic, complemented
541C4×D4—21no—
542C4×D4—431no—
543C4×D4—431no—
544C4×D4—431no—
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×D4—861no—
560C4×D4C4×D4311yescharacteristic, complemented
561#117—21no—
562#117—431no—
563#117—431no—
564#117—861no—
565#117—861no—
566#117—861no—
567#117—861no—
568#117—861no—
569#117—861no—
570#117—861no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—862no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—1724no—
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×C42C22×D4311yescharacteristic
589C4⋊C8—21no—
590C4⋊C8—862no—
591C4⋊C8—861no—
592C22⋊C8—432no—
593C22⋊C8—862no—
594C22⋊C8C22×D4312yes—
595#97—21no—
596#97—861no—
597C4×C8—862no—
598#95—21no—
599#95—432no—
600#95—862no—
601#95—862no—
602#95—861no—
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—21no—
625C22×C4—22no—
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—862no—
642C22×C4—862no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—862no—
649C22×C4—1722no—
650C22×C4—1722no—
651C22×C4—1724no—
652C22×C4—1724no—
653C22×C4—1724no—
654C22×C4D4×D4311yescharacteristic
655C22×C4D4×D4311yescharacteristic
656C22×C4C23×D4311yescharacteristic
657M16—1724no—
658C2×C8—22no—
659C2×C8—862no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—42no—
665C4⋊C4—431no—
666C4⋊C4—431no—
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—861no—
679C4⋊C4—1722no—
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—861no—
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—
701C42—21no—
702C42—431no—
703C42—431no—
704C42—431no—
705C42—431no—
706C42—431no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—861no—
715C42—861no—
716C42—861no—
717C42—861no—
718C42—861no—
719C42C2×C4×D4311yescharacteristic
720C42C2×C4×D4311yescharacteristic
721C42D4×D4311yescharacteristic
722C42D4×D4311yescharacteristic
723C23—21no—
724C23—431no—
725C23—431no—
726C23—862no—
727C23—862no—
728C23—861no—
729C23—861no—
730C23—861no—
731C23C2×D4×D4311yescharacteristic
732Q8—41no—
733Q8—1721no—
734Q8—1722no—
735Q8—1722no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—1721no—
740D4—1722no—
741D4—1722no—
742D4—1722no—
743D4—1722no—
744D4—1722no—
745D4—1722no—
746D4—1721no—
747D4—1721no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—431no—
760C2×C4—431no—
761C2×C4—432no—
762C2×C4—432no—
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—862no—
774C2×C4—862no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—861no—
778C2×C4—3448no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1722no—
784C2×C4—1722no—
785C2×C4—1722no—
786C2×C4—1722no—
787C2×C4—1721no—
788C2×C4—1721no—
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—432no—
808C22—864no—
809C22—864no—
810C22—861no—
811C22—861no—
812C22—861no—
813C22—861no—
814C22—1721no—
815C22—1721no—
816C22—1721no—
817C22C2×C22⋊C4×D4311yescharacteristic
818C22AGL(1,ℤ/8)×D4311yescharacteristic
819C22#137×D4311yescharacteristic
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—82no—
830C4—432no—
831C4—432no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—861no—
836C4—3442no—
837C4—1721no—
838C4—1721no—
839C4—1721no—
840C2—21no—
841C2—21no—
842C2—81no—
843C2—862no—
844C2—862no—
845C2—3441no—
846C2#410×D4311yescharacteristic
847C2#417×D4311yescharacteristic
848C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1512C2
socleC22×C43C22×C22⋊C4
prime radical#19147889C2
cosocleC22×C4×C43C24
hypercenter#1512D43
hypocenterC43#17588
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. #382×D43C2semidirect
4. #19133157C2semidirect
5. #19133153C2semidirect
6. #19133134C2semidirect
7. #19133133C2semidirect
8. #19133131C2semidirect
9. #19133098C2semidirect
10. #19133096C2semidirect
11. C43×#1512C2semidirect
12. #14583455C4semidirect
13. #14583453C4semidirect
15. #14583448C4semidirect
16. #14583446C4semidirect
18. #14583434C4semidirect
22. #14583428C4semidirect
29. C4×#10621902C4semidirect
32. C4×#10621900C4semidirect
68. #13063324C2×C4semidirect
69. #13063324C2×C4semidirect
70. #13063323C2×C4semidirect
71. #13063321C2×C4semidirect
75. #13063317C2×C4semidirect
78. #13063313C2×C4semidirect
102. Q8×Dic43C2×C4semidirect
104. C4×Dic86C2×C4semidirect
108. #13063290C2×C4semidirect
110. C4×D172C2×C4semidirect
112. D4×Dic43C2×C4semidirect
116. #13063287C2×C4semidirect
163. #125×C43C2×C4semidirect
164. #124×C43C2×C4semidirect
168. C4×Q8×C43C2×C4semidirect
170. C4×D4×C43C2×C4semidirect
424. #1512D43semidirect
483. C43#17588semidirect
504. #125C4×D43semidirect
508. #124C4×D43semidirect
540. C4×Q8C4×D43semidirect
560. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191478892
#191432252
#382×D432
#191331572
#191331532
#191331342
#191331332
#191331312
#191330982
#191330962
C43×#15122
#1758843