Finite Group Databasebeta

← #25063807

Subgroups — #25063807

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148646C211yesmaximal, characteristic
2#19143632C211yesmaximal, characteristic, complemented
3#19136955C211yesmaximal, characteristic, complemented
4#19133113C212yesmaximal, complemented
5#19133108C211yesmaximal, characteristic, complemented
6#19133096C212yesmaximal, complemented
7#19133093C211yesmaximal, characteristic, complemented
8#19133083C212yesmaximal, complemented
9#19133081C211yesmaximal, characteristic, complemented
10#328×D43C212yesmaximal, complemented
11C43×#1509C211yesmaximal, characteristic, complemented
12#14583622C411yescharacteristic, complemented
13#14583606—21no—
14#14583587C412yescomplemented
15#14583572—22no—
16Q8×D172C411yescharacteristic, complemented
17#14583557C412yescomplemented
18#14583554C411yescharacteristic, complemented
19#14583553C411yescharacteristic, complemented
20#14583545—21no—
21#14583520—21no—
22#14583490—22no—
23#14583456C2211yescharacteristic
24#14583409C2212yes—
25C22⋊Q8×D43C2212yes—
26#14583379—21no—
27C2×C4×D172C2211yescharacteristic
28C2×#13063287—21no—
29#14582976—21no—
30#14582972—22no—
31#14582964—21no—
32#14582952C2211yescharacteristic
33#14582861C2212yes—
34C22⋊C8×D43C2212yes—
35C4⋊C4×Dic43—21no—
36C4×(C2×D43)⋊C4—22no—
37#14582746C2212yes—
38#14582745C2211yescharacteristic
39#95×D43C2212yes—
40#14582637C2212yes—
41#14582637C2212yes—
42#14582636C2211yescharacteristic
43#14582636C2211yescharacteristic
44#14582635C2212yes—
45#14582635C2212yes—
46#14582633C2211yescharacteristic
47#14582633C2211yescharacteristic
48C43×#529C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C43×#328C2212yes—
52C43×#327C2212yes—
53C2×#10621898—21no—
54C2×#10621900C2×C412yescomplemented
55C2×Q8×D43C2×C412yescomplemented
56C22×D172D411yescharacteristic
57C22×C4×D43—22no—
58C22×C4×D43C2312yes—
59C2×#10621872—22no—
60C2×C8×D43—22no—
61#13063325—21no—
62#13063325C2×C411yescharacteristic, complemented
63#13063325C2×C411yescharacteristic, complemented
64#13063320—22no—
65#13063320—22no—
66#13063317—21no—
67#13063316—22no—
68#13063313—21no—
69#13063311—22no—
70#13063310—22no—
71#13063309—22no—
72#13063307—22no—
73#13063307—22no—
74#13063305—22no—
75#13063305C2×C412yescomplemented
76#13063305C2×C412yescomplemented
77#13063304—21no—
78#13063304—21no—
79#13063304C2312yes—
80#13063303—22no—
81#13063302—22no—
82#13063302—22no—
83#13063301C2×C412yescomplemented
84#13063299—21no—
85#13063298—22no—
86#13063296C2×C412yescomplemented
87#13063293—22no—
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×Dic86C2×C412yescomplemented
91C4×D172—21no—
92C4×D172C2×C411yescharacteristic
93C4×D172C2×C411yescharacteristic
94C4×D172C2×C412yes—
95C4×D172D411yescharacteristic
96C4×D172D412yes—
97C4×D172D411yescharacteristic
98D4×Dic43—22no—
99#13063287—28no—
100(C22⋊D43)⋊C4—22no—
101(C22⋊D43)⋊C4—22no—
102#13063284—21no—
103#13063283—22no—
104#13063283C2×C412yescomplemented
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43D411yescharacteristic
107C4⋊C4×D43—22no—
108C4⋊C4×D43C2×C412yescomplemented
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4D412yes—
111C22⋊C4×D43—22no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—22no—
114C4⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)C2311yescharacteristic
116C22⋊(C43⋊C8)C2311yescharacteristic
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119C4×C43⋊C8—21no—
120C43⋊#95—21no—
121C43⋊#95—22no—
122C43⋊#95C2311yescharacteristic
123C43⋊#95C2311yescharacteristic
124#126×C43—21no—
125#125×C43C2×C411yescharacteristic, complemented
126#124×C43C2×C411yescharacteristic, complemented
127#123×C43—21no—
128C22⋊Q8×C43C2311yescharacteristic
129#121×C43C2311yescharacteristic
130C4×Q8×C43C2×C411yescharacteristic, complemented
131C4×D4×C43—21no—
132C4×D4×C43C2×C411yescharacteristic, complemented
133#117×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139#97×C43—21no—
140#95×C43C2312yes—
141C23×D43C2×D412yes—
142C2×Q8×C43C22×C411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43C22×C411yescharacteristic
145C22×C4×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C22×Dic43—22no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D412yes—
156Q8×D43—82no—
157#10621900—82no—
158#10621898—44no—
159C2×D172—24no—
160C2×D172C22⋊C412yes—
161C2×D172C22⋊C411yescharacteristic
162C2×D172C22⋊C411yescharacteristic
163C2×C4×D43—28no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—82no—
167C2×C4×D43—82no—
168C2×C4×D43—82no—
169C2×C4×D43C22×C412yes—
170C2×C4×D43C22×C412yes—
171C2×C4×D43C2×D412yes—
172C2×C4×D43C2×D412yes—
173C2×Dic86—21no—
174C2×Dic86—22no—
175C2×Dic86C22×C412yes—
176C2×C8×C43—22no—
177C4⋊C4×C43—24no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43C22×C411yescharacteristic
183C4⋊C4×C43C22×C411yescharacteristic
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C42×C43—21no—
190C42×C43—81no—
191C42×C43C22×C411yescharacteristic
192C42×C43C22×C411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197(C2×D43)⋊C4—28no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4C22⋊C412yes—
203(C2×D43)⋊C4C22⋊C412yes—
204(C2×D43)⋊C4C22⋊C412yes—
205(C2×D43)⋊C4C22⋊C412yes—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—22no—
210C4⋊Dic43—22no—
211C4⋊Dic43C22⋊C411yescharacteristic
212C4⋊Dic43C22⋊C412yes—
213C4⋊Dic43C22⋊C411yescharacteristic
214C4⋊Dic43C22×C412yes—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219C4×Dic43—24no—
220C4×Dic43—22no—
221C4×Dic43—22no—
222C4×Dic43—82no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225#10621872—82no—
226C8×D43—82no—
227C23×C43—21no—
228C23×C43C22×D411yescharacteristic
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—24no—
232C22×D43—42no—
233C22×D43C2×C22⋊C412yes—
234C22×D43C2×C22⋊C412yes—
235Q8×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—24no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C22⋊D43—44no—
257C22⋊D43—82no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—42no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—82no—
268C2×Dic43C2×C22⋊C412yes—
269C2×Dic43C2×C22⋊C412yes—
270D172—24no—
271D172—22no—
272D172#10414yes—
273C4×D43—42no—
274C4×D43—42no—
275C4×D43—42no—
276C4×D43—42no—
277C4×D43—44no—
278C4×D43—82no—
279C4×D43—88no—
280Dic86—42no—
281Dic86—42no—
282Dic86—82no—
283C8×C43—42no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#17548—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43C22×C22⋊C411yescharacteristic
293C22×C43#57711yescharacteristic
294C22×C43#57811yescharacteristic
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—44no—
301C2×D43—44no—
302C2×D43C2×#10414yes—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—44no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43C2×#10412yes—
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316Dic43—42no—
317Dic43—42no—
318Dic43—42no—
319#3520—431no—
320#2974—431no—
321#2275—431no—
322#1509D4311yescharacteristic, complemented
323#1508—432no—
324#1506—431no—
325#1504—432no—
326#1503—431no—
327#1501—432no—
328#1500—431no—
329C2×#328—432no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—81no—
333C2×C43#288311yescharacteristic
334C2×C43#289811yescharacteristic
335C2×C43C22×#10411yescharacteristic
336D43—24no—
337D43—42no—
338#556—431no—
339#554—861no—
340#552—432no—
341#551—862no—
342D4×Q8—431no—
343#548—432no—
344#547—431no—
345#547—431no—
346#546—861no—
347#542—861no—
348#539—862no—
349#533—431no—
350#529C2×D4311yescharacteristic
351#525—432no—
352C2×C22⋊Q8—432no—
353#520—861no—
354C2×C4×D4—431no—
355C2×C4×D4—861no—
356#436—861no—
357#435—862no—
358C8×D4—861no—
359#432C2×D4311yescharacteristic
360#431—431no—
361#407—432no—
362C2×C22⋊C8—432no—
363C4×C4⋊C4—861no—
364C4×C4⋊C4C2×D4311yescharacteristic
365C4×C22⋊C4—432no—
366C4×C22⋊C4—862no—
367#376—431no—
368C2×#95—432no—
369#328—431no—
370#328—431no—
371#328—432no—
372#328—432no—
373#328—432no—
374#328—432no—
375#328C2×D4312yes—
376#327—431no—
377#327—431no—
378#327C2×D4312yes—
379C43#1754811yescharacteristic, complemented, Sylow
380C2×#41—432no—
381C2×#41—861no—
382C22×Q8—432no—
383C22×D4—431no—
384C23×C4—432no—
385C23×C4—862no—
386C2×M16—862no—
387C22×C8—862no—
388C4⋊Q8—431no—
389C4⋊Q8—431no—
390C4⋊Q8—861no—
391#126—21no—
392#126—862no—
393#126—862no—
394#125—862no—
395#125—861no—
396#125C4×D4311yescharacteristic, complemented
397#124—861no—
398#124—862no—
399#124C4×D4311yescharacteristic, complemented
400#123—21no—
401#123—862no—
402#123—862no—
403#123—862no—
404#123—862no—
405C22⋊Q8—432no—
406C22⋊Q8—432no—
407C22⋊Q8—432no—
408C22⋊Q8—432no—
409C22⋊Q8—862no—
410C22⋊Q8—862no—
411C22⋊Q8—862no—
412C22⋊Q8—862no—
413C22⋊Q8—861no—
414C22⋊Q8—861no—
415C22⋊Q8C22×D4311yescharacteristic
416#121—432no—
417#121—862no—
418#121—861no—
419#121C22×D4311yescharacteristic
420#120—862no—
421C4×Q8—432no—
422C4×Q8—861no—
423C4×Q8—861no—
424C4×Q8C4×D4311yescharacteristic, complemented
425C4×D4—21no—
426C4×D4—431no—
427C4×D4—431no—
428C4×D4—432no—
429C4×D4—431no—
430C4×D4—432no—
431C4×D4—431no—
432C4×D4—861no—
433C4×D4—862no—
434C4×D4—862no—
435C4×D4—868no—
436C4×D4—862no—
437C4×D4C4×D4311yescharacteristic, complemented
438#117—21no—
439#117—432no—
440#117—862no—
441#117—861no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—432no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4—861no—
447C2×C22⋊C4—432no—
448C2×C22⋊C4—862no—
449C2×C22⋊C4—862no—
450C2×C42—21no—
451C2×C42—861no—
452C2×C42—862no—
453C2×C42C22×D4311yescharacteristic
454C4⋊C8—21no—
455C4⋊C8—861no—
456C22⋊C8—431no—
457C22⋊C8—431no—
458C22⋊C8—862no—
459C22⋊C8—862no—
460C22⋊C8C22×D4312yes—
461#97—21no—
462C4×C8—861no—
463#95—431no—
464#95—431no—
465#95—862no—
466#95—861no—
467#95C22×D4312yes—
468C24—432no—
469#41—3442no—
470#41—1724no—
471C2×Q8—432no—
472C2×Q8—862no—
473C2×Q8—861no—
474C2×Q8—3442no—
475C2×Q8C2×C4×D4311yescharacteristic
476C2×D4—21no—
477C2×D4—431no—
478C2×D4—432no—
479C2×D4—431no—
480C2×D4—864no—
481C2×D4—862no—
482C2×D4—862no—
483C2×D4C2×C4×D4311yescharacteristic
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—862no—
492C22×C4—868no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—3442no—
498C22×C4—3442no—
499C22×C4—3442no—
500C22×C4D4×D4311yescharacteristic
501C22×C4D4×D4311yescharacteristic
502C22×C4C23×D4311yescharacteristic
503M16—3442no—
504C2×C8—22no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—3442no—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—431no—
514C4⋊C4—432no—
515C4⋊C4—431no—
516C4⋊C4—432no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4C2×C4×D4311yescharacteristic
527C4⋊C4C2×C4×D4311yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—432no—
534C22⋊C4—432no—
535C22⋊C4—432no—
536C22⋊C4—432no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—868no—
542C22⋊C4—862no—
543C22⋊C4—862no—
544C42—21no—
545C42—81no—
546C42—862no—
547C42—864no—
548C42—862no—
549C42—3442no—
550C42C2×C4×D4311yescharacteristic
551C42C2×C4×D4311yescharacteristic
552C42D4×D4311yescharacteristic
553C42D4×D4311yescharacteristic
554C23—21no—
555C23—432no—
556C23—432no—
557C23—864no—
558C23—862no—
559C23—862no—
560C23—1722no—
561C23C2×D4×D4311yescharacteristic
562Q8—41no—
563Q8—3442no—
564Q8—1722no—
565Q8—1722no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—434no—
570D4—864no—
571D4—862no—
572D4—3442no—
573D4—1724no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—3442no—
592C2×C4—3448no—
593C2×C4—3442no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1724no—
599C2×C4—1722no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4C22⋊C4×D4311yescharacteristic
605C2×C4C22⋊C4×D4311yescharacteristic
606C2×C4C22⋊C4×D4311yescharacteristic
607C2×C4C22⋊C4×D4311yescharacteristic
608C2×C4C22×C4×D4311yescharacteristic
609C2×C4C2×D4×D4311yescharacteristic
610C8—42no—
611C8—1721no—
612C8—1721no—
613C22—21no—
614C22—21no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—434no—
619C22—862no—
620C22—862no—
621C22—862no—
622C22—862no—
623C22—862no—
624C22—1724no—
625C22—1724no—
626C22C2×C22⋊C4×D4311yescharacteristic
627C22#1458370911yescharacteristic
628C22#1458371511yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—44no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—862no—
639C4—862no—
640C4—1722no—
641C4—1722no—
642C4—1722no—
643C4—1722no—
644C4#104×D4312yes—
645C2—21no—
646C2—21no—
647C2—81no—
648C2—864no—
649C2—1722no—
650C2#1914305411yescharacteristic
651C2#1914312611yescharacteristic
652C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#19148646C2
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17548
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. #19143632C2semidirect
3. #19136955C2semidirect
4. #19133113C2semidirect
5. #19133108C2semidirect
6. #19133096C2semidirect
7. #19133093C2semidirect
8. #19133083C2semidirect
9. #19133081C2semidirect
10. #328×D43C2semidirect
11. C43×#1509C2semidirect
12. #14583622C4semidirect
14. #14583587C4semidirect
16. Q8×D172C4semidirect
17. #14583557C4semidirect
18. #14583554C4semidirect
19. #14583553C4semidirect
54. C2×#10621900C2×C4semidirect
55. C2×Q8×D43C2×C4semidirect
62. #13063325C2×C4semidirect
63. #13063325C2×C4semidirect
75. #13063305C2×C4semidirect
76. #13063305C2×C4semidirect
83. #13063301C2×C4semidirect
86. #13063296C2×C4semidirect
90. C4×Dic86C2×C4semidirect
104. #13063283C2×C4semidirect
108. C4⋊C4×D43C2×C4semidirect
125. #125×C43C2×C4semidirect
126. #124×C43C2×C4semidirect
130. C4×Q8×C43C2×C4semidirect
132. C4×D4×C43C2×C4semidirect
322. #1509D43semidirect
379. C43#17548semidirect
396. #125C4×D43semidirect
399. #124C4×D43semidirect
424. C4×Q8C4×D43semidirect
437. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486462
#191436322
#191369552
#191331132
#191331082
#191330962
#191330932
#191330832
#191330812
#328×D432
C43×#15092
#1754843