Finite Group Databasebeta

← #25063129

Subgroups — #25063129

Order 11008.

1096 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2#431×D43C211yesmaximal, characteristic, complemented
3C2×C4×#10621872C211yesmaximal, characteristic, complemented
4#19133014C212yesmaximal, complemented
5#19133010C212yesmaximal, complemented
6#19133007C212yesmaximal, complemented
7#19133005C212yesmaximal, complemented
8#19132978C211yesmaximal, characteristic, complemented
9#19132977C211yesmaximal, characteristic, complemented
10#19132975C211yesmaximal, characteristic, complemented
11C43×#1476C211yesmaximal, characteristic, complemented
12C22×#10621872—21no—
13#14583453C411yescharacteristic
14#14583453C2211yescharacteristic
15#14583452C411yescharacteristic
16#14583446C411yescharacteristic
17#14583446C2211yescharacteristic
18#14583445C411yescharacteristic
19#14583436C411yescharacteristic
20#14583436C2211yescharacteristic
21#14583431C411yescharacteristic
22#14583431C2211yescharacteristic
23#14583429—21no—
24#14583429—21no—
25#14583427—21no—
26#14583427—21no—
27#14583411C411yescharacteristic
28#14583408—21no—
29#14583408—21no—
30#14583406C411yescharacteristic
31C4×#10621898—21no—
32C4×#10621898—21no—
33C4×#10621898C2211yescharacteristic
34C2×C42×D43C2211yescharacteristic
35#14582952C2211yescharacteristic
36#14582951C2212yes—
37#14582950—21no—
38#14582949—21no—
39C4⋊C8×D43C2212yes—
40C22⋊C8×D43—21no—
41C4×#10621872—21no—
42C4×#10621872—21no—
43C4×#10621872C2212yes—
44C4×#10621872C2212yes—
45C2×#13063235—21no—
46C2×C4×C43⋊C8C2211yescharacteristic
47C4×C8×D43—21no—
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C4×#41×C43C2211yescharacteristic
55C43×#431C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2×C411yescharacteristic
62C22×C4×D43C2×C411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C2×#10621872—28no—
66C2×#10621872—22no—
67C2×#10621872—22no—
68C22×C43⋊C8—21no—
69C2×C8×D43—22no—
70#13063324C2×C411yescharacteristic
71#13063324C2×C411yescharacteristic
72#13063323C2×C411yescharacteristic
73#13063321C2×C411yescharacteristic
74#13063320—21no—
75#13063320—21no—
76#13063318—21no—
77#13063318—21no—
78#13063316C2×C411yescharacteristic
79#13063316C2×C411yescharacteristic
80#13063315—21no—
81#13063315—21no—
82#13063314C2×C411yescharacteristic
83#13063312C2×C411yescharacteristic
84#13063311—21no—
85#13063311—21no—
86#13063310—21no—
87#13063310—21no—
88#13063309—21no—
89#13063307—21no—
90#13063307—21no—
91#13063306—21no—
92#13063305C2×C411yescharacteristic
93#13063305C2×C411yescharacteristic
94#13063303—21no—
95#13063303—21no—
96#13063302—21no—
97#13063302—21no—
98#13063301C2×C411yescharacteristic
99#13063301C2×C411yescharacteristic
100#13063300C2×C411yescharacteristic
101#13063300C2×C411yescharacteristic
102#13063298—21no—
103#13063298—21no—
104#13063297—21no—
105#13063297—21no—
106#13063296C2×C411yescharacteristic
107#13063296C2×C411yescharacteristic
108#13063295—21no—
109#13063293—21no—
110C4×Dic86—21no—
111C4×Dic86—21no—
112C4×Dic86—21no—
113C4×Dic86—21no—
114C4×Dic86C2×C411yescharacteristic
115C4×Dic86C2311yescharacteristic
116C4×D172—21no—
117C4×D172—21no—
118C4×D172—21no—
119C4×D172—21no—
120C4×D172C2×C411yescharacteristic
121C4×D172C2311yescharacteristic
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129C4×C22⋊D43—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132#13063284—21no—
133#13063284—21no—
134#13063284C2×C411yescharacteristic
135#13063282—21no—
136#13063282—21no—
137#13063282—21no—
138#13063282—21no—
139#13063282—21no—
140C2×C4×Dic43C2×C411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C42×D43—21no—
144C42×D43C2×C411yescharacteristic
145C42×D43C2×C411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43C2311yescharacteristic
151C42×D43C2311yescharacteristic
152C4⋊(C43⋊C8)C2312yes—
153Dic43⋊C8—22no—
154C22⋊(C43⋊C8)—21no—
155(C2×D43)⋊C8—22no—
156#13063235—22no—
157#13063235—22no—
158C4×C43⋊C8—21no—
159C4×C43⋊C8—21no—
160C4×C43⋊C8C2312yes—
161C8×Dic43—22no—
162C2×#41×C43C2×C411yescharacteristic
163C22×C8×C43—21no—
164C4×Q8×C43C2×C411yescharacteristic
165C4×Q8×C43C2311yescharacteristic
166C4×D4×C43—21no—
167C4×D4×C43—21no—
168C4×D4×C43C2×C411yescharacteristic
169C4×D4×C43C2311yescharacteristic
170#117×C43—21no—
171#117×C43C2×C411yescharacteristic
172C2×C42×C43—21no—
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43C2312yes—
175C22⋊C8×C43—21no—
176C4×C8×C43—21no—
177C4×C8×C43—21no—
178C4×C8×C43C2312yes—
179C23×D43C22⋊C411yescharacteristic
180#41×C43—22no—
181#41×C43—22no—
182C2×Q8×C43C22×C411yescharacteristic
183C2×D4×C43—21no—
184C2×D4×C43C22×C411yescharacteristic
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—21no—
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C22×Dic43C22⋊C411yescharacteristic
197C22×Dic43C22⋊C411yescharacteristic
198C22×Dic43C22⋊C411yescharacteristic
199#10621898—22no—
200#10621898—22no—
201#10621898—44no—
202#10621898—44no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172C22×C411yescharacteristic
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—24no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—42no—
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×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×C4×D43C2×D411yescharacteristic
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86C22×C411yescharacteristic
228C2×C8×C43—24no—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43C22×C411yescharacteristic
234C4⋊C4×C43C22×C411yescharacteristic
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C42×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43C22×C411yescharacteristic
242C42×C43C2×D411yescharacteristic
243C42×C43C2×D411yescharacteristic
244C42×C43C2411yescharacteristic
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249C22⋊Dic43—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—
259(C2×D43)⋊C4—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43C22×C411yescharacteristic
265C4⋊Dic43C22×C411yescharacteristic
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—21no—
275Dic43⋊C4—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22×C411yescharacteristic
286C4×Dic43C22×C411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290C4×Dic43C2×D411yescharacteristic
291C2×C43⋊C8—24no—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—22no—
294#10621872—28no—
295#10621872—28no—
296C8×D43—44no—
297C23×C43—21no—
298C23×C43C2×C22⋊C411yescharacteristic
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—21no—
302C22×D43—41no—
303C22×D43C2×C22⋊C411yescharacteristic
304C22×D43C2×C22⋊C411yescharacteristic
305Q8×C43—21no—
306Q8×C43—21no—
307D4×C43—21no—
308D4×C43—21no—
309D4×C43—42no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43#13112yes—
322C2×C4×C43#13112yes—
323C2×C4×C43C23×C411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C22⋊D43—42no—
327C22⋊D43—42no—
328C22⋊D43—42no—
329C22⋊D43—42no—
330C22⋊D43—42no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—41no—
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342C2×Dic43C2×C22⋊C411yescharacteristic
343D172—21no—
344D172—21no—
345D172—42no—
346D172—42no—
347C4×D43—22no—
348C4×D43—21no—
349C4×D43—21no—
350C4×D43—21no—
351C4×D43—21no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—41no—
359C4×D43—41no—
360C4×D43—42no—
361C4×D43—42no—
362C4×D43—42no—
363C4×D43#10414yes—
364Dic86—21no—
365Dic86—21no—
366Dic86—42no—
367Dic86—42no—
368C8×C43—24no—
369C8×C43—42no—
370C43⋊C8—24no—
371C43⋊C8—42no—
372#17462—431nomaximal, Sylow
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43#40812yes—
379C22×C43C22×C22⋊C411yescharacteristic
380C2×D43—21no—
381C2×D43—21no—
382C2×D43—21no—
383C2×D43—21no—
384C2×D43—21no—
385C2×D43—44no—
386C2×D43—41no—
387C2×D43—41no—
388C2×D43—41no—
389C2×D43C2×#10412yes—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—41no—
393C4×C43—41no—
394C4×C43—41no—
395C4×C43#40812yes—
396C4×C43C2×#10412yes—
397C4×C43C2×#13111yescharacteristic
398C4×C43C2×#13111yescharacteristic
399C4×C43#57512yes—
400Dic43—21no—
401Dic43—21no—
402Dic43—21no—
403Dic43—21no—
404Dic43—21no—
405Dic43—41no—
406Dic43—41no—
407Dic43—41no—
408Dic43C2×#10412yes—
409#3444—431no—
410C2×#431—431no—
411C2×C4×M16—431no—
412#1485—432no—
413#1484—432no—
414#1483—432no—
415#1483—432no—
416#1476—431no—
417#1476—431no—
418#1476—431no—
419#1476D4311yescharacteristic, complemented
420C2×C43—22no—
421C2×C43—81no—
422C2×C43C2×#40811yescharacteristic
423C2×C43#289611yescharacteristic
424C2×C43C22×#10411yescharacteristic
425D43—22no—
426D43—41no—
427D43—81no—
428C22×M16—861no—
429#533—431no—
430#533—431no—
431#533—431no—
432#532—431no—
433#532—431no—
434#532—431no—
435#529—431no—
436#529—431no—
437#529—431no—
438#529—431no—
439#529—861no—
440#529—861no—
441#529—861no—
442#529—861no—
443#525—431no—
444#525—431no—
445#525—861no—
446#525—861no—
447C4×#41—431no—
448C4×#41—861no—
449C4×#41—861no—
450C4×#41C2×D4311yescharacteristic
451C22×C42—431no—
452#431—431no—
453#431—432no—
454#431—861no—
455#431—861no—
456#431C2×D4311yescharacteristic
457C2×C4⋊C8—432no—
458C2×C22⋊C8—861no—
459C4×M16—432no—
460C4×M16—432no—
461C4×M16—861no—
462C4×M16—861no—
463C2×#97—861no—
464C2×C4×C8—431no—
465C2×C4×C8—861no—
466C2×C4×C8C2×D4311yescharacteristic
467Q8⋊C8—432no—
468Q8⋊C8—432no—
469Q8⋊C8—432no—
470Q8⋊C8C2×D4312yescomplemented
471D4⋊C8—432no—
472D4⋊C8—432no—
473D4⋊C8—432no—
474D4⋊C8C2×D4312yescomplemented
475C43#1746211yescharacteristic, complemented, Sylow
476C2×#41—431no—
477C2×#41—861no—
478C2×#41—861no—
479C2×#41C4×D4311yescharacteristic
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—431no—
483C2×M16—862no—
484C2×M16—862no—
485C2×M16—868no—
486C22×C8—21no—
487C22×C8—862no—
488C22×C8—861no—
489C4⋊Q8—431no—
490C4⋊Q8—431no—
491C4⋊Q8—431no—
492#127—431no—
493#126—861no—
494#126—861no—
495#126—861no—
496#126—861no—
497#125—431no—
498#125—431no—
499#125—861no—
500#125—861no—
501#124—431no—
502#124—431no—
503#124—861no—
504#124—861no—
505#123—861no—
506#123—861no—
507#123—861no—
508#123—861no—
509#123—861no—
510#123—861no—
511C22⋊Q8—431no—
512C22⋊Q8—431no—
513C22⋊Q8—431no—
514C22⋊Q8—431no—
515C22⋊Q8—861no—
516C22⋊Q8—861no—
517C22⋊Q8—861no—
518C22⋊Q8—861no—
519#121—431no—
520#121—431no—
521#121—431no—
522#121—431no—
523#121—861no—
524#121—861no—
525#121—861no—
526#121—861no—
527#120—861no—
528#120—861no—
529C4×Q8—431no—
530C4×Q8—431no—
531C4×Q8—861no—
532C4×Q8—861no—
533C4×Q8—861no—
534C4×Q8—861no—
535C4×Q8C4×D4311yescharacteristic
536C4×Q8C22×D4311yescharacteristic
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—431no—
540C4×D4—431no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
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×D4C4×D4311yescharacteristic
556C4×D4C22×D4311yescharacteristic
557#117—21no—
558#117—431no—
559#117—861no—
560#117—861no—
561#117—861no—
562#117—861no—
563#117—861no—
564#117—861no—
565#117—861no—
566#117C4×D4311yescharacteristic
567C2×C42—21no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—431no—
574C2×C42—431no—
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—861no—
580C2×C42C22×D4311yescharacteristic
581C4⋊C8—432no—
582C4⋊C8—862no—
583C4⋊C8C22×D4312yes—
584C22⋊C8—21no—
585C22⋊C8—862no—
586C22⋊C8—861no—
587#97—862no—
588#97—862no—
589C4×C8—21no—
590C4×C8—21no—
591C4×C8—432no—
592C4×C8—862no—
593C4×C8—861no—
594C4×C8—861no—
595C4×C8C22×D4312yes—
596C24—431no—
597#41—22no—
598#41—22no—
599#41—862no—
600#41—862no—
601#41—1724no—
602#41—1724no—
603C2×Q8—431no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×Q8C2×C4×D4311yescharacteristic
607C2×D4—21no—
608C2×D4—431no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4C2×C4×D4311yescharacteristic
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
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—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—864no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—1722no—
642C22×C4C2×C4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4D4×D4311yescharacteristic
645M16—868no—
646M16—868no—
647C2×C8—24no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—864no—
651C2×C8—862no—
652C2×C8—862no—
653C2×C8—1724no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—431no—
657C4⋊C4—431no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
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⋊C4C2×C4×D4311yescharacteristic
673C4⋊C4C2×C4×D4311yescharacteristic
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C22⋊C4—861no—
687C22⋊C4—861no—
688C22⋊C4—861no—
689C22⋊C4—861no—
690C22⋊C4—861no—
691C22⋊C4—861no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—431no—
701C42—431no—
702C42—431no—
703C42—431no—
704C42—431no—
705C42—431no—
706C42—431no—
707C42—861no—
708C42—861no—
709C42—861no—
710C42C2×C4×D4311yescharacteristic
711C42D4×D4311yescharacteristic
712C42D4×D4311yescharacteristic
713C42C23×D4311yescharacteristic
714C23—21no—
715C23—431no—
716C23—431no—
717C23—862no—
718C23—862no—
719C23—861no—
720C23—1721no—
721C23C22⋊C4×D4311yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—861no—
725Q8—861no—
726Q8—1722no—
727Q8—1722no—
728D4—21no—
729D4—21no—
730D4—42no—
731D4—861no—
732D4—861no—
733D4—1722no—
734D4—1722no—
735D4—1722no—
736D4—1722no—
737D4—1722no—
738D4—1722no—
739D4—1722no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—431no—
749C2×C4—434no—
750C2×C4—431no—
751C2×C4—431no—
752C2×C4—431no—
753C2×C4—431no—
754C2×C4—431no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—861no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—861no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1722no—
775C2×C4—1722no—
776C2×C4—1722no—
777C2×C4C22⋊C4×D4311yescharacteristic
778C2×C4C22⋊C4×D4311yescharacteristic
779C2×C4C22⋊C4×D4311yescharacteristic
780C2×C4#1306333112yes—
781C2×C4#1306333312yes—
782C2×C4C22×C4×D4311yescharacteristic
783C2×C4C2×D4×D4311yescharacteristic
784C2×C4C2×D4×D4311yescharacteristic
785C8—24no—
786C8—42no—
787C8—864no—
788C8—1722no—
789C22—21no—
790C22—21no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—432no—
795C22—861no—
796C22—861no—
797C22—861no—
798C22—861no—
799C22—861no—
800C22—1724no—
801C22—1721no—
802C22—1721no—
803C22—1721no—
804C22#1458286412yes—
805C22C2×C22⋊C4×D4311yescharacteristic
806C4—21no—
807C4—21no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—432no—
812C4—861no—
813C4—861no—
814C4—861no—
815C4—861no—
816C4—861no—
817C4—1721no—
818C4—1721no—
819C4—1721no—
820C4#1458286412yes—
821C4#104×D4312yes—
822C4C2×#1306333111yescharacteristic
823C4C2×#1306333311yescharacteristic
824C4#1458369612yes—
825C2—22no—
826C2—81no—
827C2—862no—
828C2—3441no—
829C2—1721no—
830C2C2×#1458286411yescharacteristic
831C2#1914311011yescharacteristic
832C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC42D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1476C2
socleC22×C43C22×C22⋊C4
prime radical#19147888C2
cosocleC42×C43C24
hypercenter#1476D43
hypocenterC43#17462
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #431×D43C2semidirect
3. C2×C4×#10621872C2semidirect
4. #19133014C2semidirect
5. #19133010C2semidirect
6. #19133007C2semidirect
7. #19133005C2semidirect
8. #19132978C2semidirect
9. #19132977C2semidirect
10. #19132975C2semidirect
11. C43×#1476C2semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
419. #1476D43semidirect
470. Q8⋊C8C2×D43semidirect
474. D4⋊C8C2×D43semidirect
475. C43#17462semidirect

Maximal subgroups

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

subgroupindex
#191478882
#431×D432
C2×C4×#106218722
#191330142
#191330102
#191330072
#191330052
#191329782
#191329772
#191329752
C43×#14762
#1746243