Finite Group Databasebeta

← #25065143

Subgroups — #25065143

Order 11008.

952 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic
3#432×D43C211yesmaximal, characteristic
4#19133326C211yesmaximal, characteristic, complemented
5#19133325C211yesmaximal, characteristic, complemented
6#19133323C211yesmaximal, characteristic, complemented
7#19133319C212yesmaximal, complemented
8#19133310C212yesmaximal, complemented
9#19133251C212yesmaximal, complemented
10#19133249C212yesmaximal, complemented
11C43×#1559C211yesmaximal, characteristic, complemented
12#14583456C2211yescharacteristic
13#14583455—21no—
14#14583454C2211yescharacteristic
15#14583454C2211yescharacteristic
16#14583453—21no—
17#14583453C412yes—
18#14583452—21no—
19#14583451—21no—
20#14583451C412yes—
21C4⋊Q8×D43C2211yescharacteristic
22C4⋊Q8×D43C2211yescharacteristic
23#125×D43—21no—
24C22⋊Q8×D43—21no—
25C22⋊Q8×D43C412yes—
26C4×Q8×D43—21no—
27C4×Q8×D43C412yes—
28#117×D43—21no—
29C2×C42×D43C2211yescharacteristic
30#14582956C2211yescharacteristic
31#14582955—21no—
32#14582955C2212yes—
33#14582955C2212yes—
34#14582954—21no—
35#14582953—21no—
36#14582951—21no—
37#14582951C2212yes—
38#14582923C2211yescharacteristic
39C4⋊C8×D43C2212yes—
40#14582862—21no—
41C22⋊C8×D43—21no—
42M16×Dic43—21no—
43#97×D43—21no—
44#14582648C2212yescomplemented
45#14582647C2212yescomplemented
46#14582647C2212yescomplemented
47#14582646C2212yescomplemented
48#14582645C2212yescomplemented
49#14582644C2212yescomplemented
50C43×#533C2211yescharacteristic
51C43×#432C2211yescharacteristic
52C43×#423C2211yescharacteristic
53C43×#333C2212yescomplemented
54C43×#332C2212yescomplemented
55C2×Q8×D43—21no—
56C2×Q8×D43C2×C412yes—
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C2×#10621877—21no—
61C2×C8×D43—22no—
62#13063325C2311yescharacteristic
63#13063325C2311yescharacteristic
64#13063324—21no—
65#13063324—21no—
66#13063324—21no—
67#13063324C2×C412yes—
68#13063323—21no—
69#13063323C2×C412yes—
70#13063317—21no—
71#13063316—21no—
72#13063316—21no—
73#13063315—22no—
74#13063315—22no—
75#13063305—21no—
76#13063305C2×C412yes—
77#13063304—21no—
78#13063304C2×C412yes—
79#13063303—22no—
80#13063303—22no—
81#13063302—22no—
82#13063302—22no—
83#13063301—21no—
84#13063301C2×C412yes—
85Q8×Dic43—21no—
86Q8×Dic43C2×C412yes—
87C4×Dic86—21no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86C2×C412yes—
91#13063290—22no—
92#13063290—22no—
93#13063290—21no—
94#13063290C2×C412yes—
95#13063284—21no—
96#13063283—21no—
97#13063283—21no—
98#13063282—22no—
99#13063281—22no—
100C4⋊C4×D43—22no—
101C4⋊C4×D43—22no—
102C4⋊C4×D43—21no—
103C4⋊C4×D43—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43C2×C412yes—
106C22⋊C4×D43—22no—
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C42×D43—22no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43C2311yescharacteristic
118C42×D43C2311yescharacteristic
119C4⋊(C43⋊C8)—21no—
120C4⋊(C43⋊C8)C2312yes—
121C4⋊(C43⋊C8)C2312yes—
122Dic43⋊C8—22no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127#13063236—21no—
128#13063235—22no—
129#13063235—22no—
130C8×Dic43—22no—
131C2×M16×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134#125×C43—21no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43C2×C412yes—
137C4×Q8×C43—21no—
138C4×Q8×C43C2×C412yes—
139#117×C43—21no—
140C2×C42×C43C2311yescharacteristic
141C4⋊C8×C43—21no—
142C4⋊C8×C43C2312yes—
143C4⋊C8×C43C2312yes—
144C22⋊C8×C43—21no—
145#97×C43—21no—
146C23×D43C22⋊C411yescharacteristic
147C2×Q8×C43—21no—
148C2×Q8×C43C22×C412yes—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C22⋊C411yescharacteristic
154C22×Dic43C22⋊C411yescharacteristic
155Q8×D43—42no—
156Q8×D43—42no—
157Q8×D43—44no—
158C2×C4×D43—24no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—42no—
162C2×C4×D43—41no—
163C2×C4×D43—41no—
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22×C411yescharacteristic
171C2×C4×D43C22×C411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×Dic86—21no—
177C2×Dic86—22no—
178C2×Dic86—22no—
179C2×Dic86C22×C412yes—
180M16×C43—42no—
181C2×C8×C43—22no—
182C2×C8×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43C22×C412yes—
189C22⋊C4×C43—22no—
190C42×C43—22no—
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2411yescharacteristic
195C22⋊Dic43—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22×C411yescharacteristic
222C4×Dic43C22×C411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227#10621877—42no—
228C2×C43⋊C8—22no—
229C2×C43⋊C8—22no—
230C8×D43—44no—
231C23×C43C2×C22⋊C411yescharacteristic
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—41no—
235C22×D43C2×C22⋊C411yescharacteristic
236C22×D43C2×C22⋊C411yescharacteristic
237Q8×C43—42no—
238Q8×C43—41no—
239Q8×C43—41no—
240C2×C4×C43—22no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43C2×C22⋊C411yescharacteristic
258C2×Dic43C2×C22⋊C411yescharacteristic
259C2×Dic43C2×C22⋊C411yescharacteristic
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—21no—
268C4×D43—21no—
269C4×D43—21no—
270C4×D43—21no—
271C4×D43—22no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—44no—
277C4×D43—44no—
278C4×D43#13714yes—
279Dic86—44no—
280Dic86—44no—
281Dic86—41no—
282Dic86—41no—
283Dic86—42no—
284C8×C43—42no—
285C8×C43—42no—
286C43⋊C8—42no—
287C43⋊C8—42no—
288#17734—431nomaximal, Sylow
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43C22×C22⋊C411yescharacteristic
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—44no—
298C2×D43#41312yes—
299C2×D43#41912yes—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43—42no—
306C4×C43C2×#13712yes—
307C4×C43#57511yescharacteristic
308C4×C43#57511yescharacteristic
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—21no—
313Dic43—21no—
314Dic43—42no—
315Dic43—42no—
316Dic43#41912yes—
317C2×#533—431no—
318#2920—431no—
319C2×#432—431no—
320#1559—431no—
321#1559—431no—
322#1559—431no—
323#1559D4311yescharacteristic, complemented
324#1558—432no—
325#1556—432no—
326#1542—432no—
327#1542—432no—
328C2×C43—41no—
329C2×C43C2×#41311yescharacteristic
330C2×C43C2×#41911yescharacteristic
331C2×C43#289611yescharacteristic
332D43—22no—
333D43—22no—
334#533—431no—
335#533—431no—
336#533—432no—
337#533—432no—
338#533—431no—
339#533—861no—
340#533—861no—
341#533—861no—
342#533—861no—
343#533C2×D4311yescharacteristic
344C2×C4⋊Q8—431no—
345C2×C4⋊Q8—431no—
346C2×#125—861no—
347C2×C22⋊Q8—432no—
348C2×C22⋊Q8—861no—
349C2×C4×Q8—432no—
350C2×C4×Q8—861no—
351C2×#117—861no—
352C22×C42—431no—
353#432—431no—
354#432—432no—
355#432—432no—
356#432—861no—
357#432—861no—
358#432—861no—
359#432C2×D4311yescharacteristic
360#431—432no—
361#431—861no—
362#423—431no—
363#423C2×D4311yescharacteristic
364C2×C4⋊C8—432no—
365#407—861no—
366C2×C22⋊C8—861no—
367C4×M16—861no—
368C2×#97—861no—
369#333—432no—
370#333—432no—
371#333—432no—
372#333C2×D4312yescomplemented
373#332—432no—
374#332—432no—
375#332—432no—
376#332C2×D4312yescomplemented
377C43#1773411yescharacteristic, complemented, Sylow
378C22×Q8—432no—
379C22×Q8—861no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—431no—
383C2×M16—21no—
384C2×M16—861no—
385C22×C8—862no—
386C4⋊Q8—432no—
387C4⋊Q8—432no—
388C4⋊Q8—431no—
389C4⋊Q8—431no—
390C4⋊Q8—861no—
391C4⋊Q8—861no—
392C4⋊Q8—861no—
393C4⋊Q8—861no—
394C4⋊Q8C22×D4311yescharacteristic
395C4⋊Q8C22×D4311yescharacteristic
396#125—21no—
397#125—862no—
398#125—862no—
399#125—861no—
400#125—861no—
401#125—861no—
402C22⋊Q8—21no—
403C22⋊Q8—432no—
404C22⋊Q8—432no—
405C22⋊Q8—432no—
406C22⋊Q8—862no—
407C22⋊Q8—862no—
408C22⋊Q8—862no—
409C22⋊Q8—862no—
410C22⋊Q8—861no—
411C22⋊Q8—861no—
412C22⋊Q8—861no—
413C22⋊Q8C4×D4312yes—
414C4×Q8—21no—
415C4×Q8—432no—
416C4×Q8—432no—
417C4×Q8—432no—
418C4×Q8—862no—
419C4×Q8—862no—
420C4×Q8—862no—
421C4×Q8—862no—
422C4×Q8—861no—
423C4×Q8—861no—
424C4×Q8—861no—
425C4×Q8C4×D4312yes—
426#117—21no—
427#117—862no—
428#117—862no—
429#117—861no—
430#117—861no—
431#117—861no—
432C2×C4⋊C4—432no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—862no—
436C2×C4⋊C4—862no—
437C2×C4⋊C4—861no—
438C2×C22⋊C4—862no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—862no—
451C2×C42C22×D4311yescharacteristic
452C4⋊C8—21no—
453C4⋊C8—432no—
454C4⋊C8—432no—
455C4⋊C8—862no—
456C4⋊C8—861no—
457C4⋊C8C22×D4312yes—
458C4⋊C8C22×D4312yes—
459C22⋊C8—21no—
460C22⋊C8—862no—
461C22⋊C8—862no—
462C22⋊C8—862no—
463C22⋊C8—861no—
464#97—21no—
465#97—862no—
466#97—862no—
467#97—861no—
468C4×C8—862no—
469C24—431no—
470C2×Q8—21no—
471C2×Q8—432no—
472C2×Q8—862no—
473C2×Q8—862no—
474C2×Q8—861no—
475C2×Q8—1722no—
476C2×Q8—1722no—
477C2×Q8—1724no—
478C2×Q8C2×C4×D4312yes—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—864no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—1721no—
498C22×C4—1721no—
499C22×C4—1722no—
500C22×C4C2×C4×D4311yescharacteristic
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503M16—42no—
504M16—1722no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—862no—
508C2×C8—862no—
509C2×C8—1724no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—432no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4C2×C4×D4312yes—
530C22⋊C4—22no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C42—22no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—862no—
548C42—862no—
549C42—862no—
550C42C2×C4×D4311yescharacteristic
551C42D4×D4311yescharacteristic
552C42D4×D4311yescharacteristic
553C42C23×D4311yescharacteristic
554C23—431no—
555C23—431no—
556C23—862no—
557C23—862no—
558C23—1721no—
559C23C22⋊C4×D4311yescharacteristic
560Q8—42no—
561Q8—41no—
562Q8—41no—
563Q8—1722no—
564Q8—1724no—
565Q8—1724no—
566Q8—1721no—
567Q8—1721no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—431no—
575C2×C4—434no—
576C2×C4—431no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1724no—
598C2×C4—1724no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4C22⋊C4×D4311yescharacteristic
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4C22⋊C4×D4311yescharacteristic
604C2×C4C22×C4×D4311yescharacteristic
605C2×C4C2×D4×D4311yescharacteristic
606C2×C4C2×D4×D4311yescharacteristic
607C8—42no—
608C8—42no—
609C8—1722no—
610C8—1722no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—432no—
615C22—432no—
616C22—861no—
617C22—861no—
618C22—861no—
619C22—861no—
620C22—1724no—
621C22C2×C22⋊C4×D4311yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—42no—
628C4—432no—
629C4—861no—
630C4—861no—
631C4—861no—
632C4—861no—
633C4—861no—
634C4—1722no—
635C4—1722no—
636C4#137×D4312yes—
637C4#1458369511yescharacteristic
638C4#1458369811yescharacteristic
639C2—41no—
640C2—862no—
641C2—862no—
642C2#413×D4311yescharacteristic
643C2#419×D4311yescharacteristic
644C2#1914311111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1559C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1559D43
hypocenterC43#17734
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1559

Complements

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

NH ≅ G/Ntype
4. #19133326C2semidirect
5. #19133325C2semidirect
6. #19133323C2semidirect
7. #19133319C2semidirect
8. #19133310C2semidirect
9. #19133251C2semidirect
10. #19133249C2semidirect
11. C43×#1559C2semidirect
44. #14582648C22semidirect
45. #14582647C22semidirect
46. #14582647C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
53. C43×#333C22semidirect
54. C43×#332C22semidirect
323. #1559D43semidirect
372. #333C2×D43semidirect
376. #332C2×D43semidirect
377. C43#17734semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432272
#432×D432
#191333262
#191333252
#191333232
#191333192
#191333102
#191332512
#191332492
C43×#15592
#1773443