Finite Group Databasebeta

← #25063154

Subgroups — #25063154

Order 11008.

1066 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#19147890C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
4#19133005C214yesmaximal, complemented
5#19132999C211yesmaximal, characteristic, complemented
6#19132997C211yesmaximal, characteristic, complemented
7#19132994C211yesmaximal, characteristic, complemented
8#19132979C214yesmaximal, complemented
9C43×#1480C211yesmaximal, characteristic, complemented
10C22×C8×D43—21no—
11#14583456C2211yescharacteristic
12#14583454C411yescharacteristic
13#14583454C411yescharacteristic
14#14583447C411yescharacteristic
15#14583447C411yescharacteristic
16#14583431—21no—
17#14583431C2212yes—
18#14583430—21no—
19#14583430C412yes—
20#14583428—21no—
21#14583428—21no—
22#14583409—21no—
23#14583409C412yes—
24#14583406—21no—
25#41×Dic43—21no—
26C4×#10621900—21no—
27C4×#10621900C2212yes—
28C2×C42×D43C2211yescharacteristic
29#14582955—21no—
30#14582953—21no—
31#14582952C2211yescharacteristic
32#14582950C2212yes—
33#14582921—21no—
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×Dic43⋊C8—21no—
36C4⋊C8×D43—21no—
37C4⋊C8×D43—21no—
38C4⋊C8×D43C2212yes—
39C4⋊C8×D43C2212yes—
40#14582861—21no—
41C4×#10621872C2212yes—
42#14582631C2214yescomplemented
43#14582629C2214yescomplemented
44D4⋊(C43⋊C8)C2214yescomplemented
45C43×#532C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C2×C4⋊C8×C43C2211yescharacteristic
48C43×D4⋊C8C2214yescomplemented
49C2×#10621900—21no—
50C2×#10621900C2×C412yes—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621872—22no—
55C22×C43⋊C8—21no—
56C2×C8×D43—22no—
57C2×C8×D43—22no—
58C2×C8×D43—44no—
59#13063325C2×C411yescharacteristic
60#13063325C2×C411yescharacteristic
61#13063318—22no—
62#13063318—22no—
63#13063317—21no—
64#13063316—21no—
65#13063316C2×C412yes—
66#13063312—21no—
67#13063312C2×C412yes—
68#13063307—22no—
69#13063307—22no—
70#13063306—22no—
71#13063305—21no—
72#13063305C2×C412yes—
73#13063304—21no—
74#13063304C2×C412yes—
75#13063301—21no—
76#13063301—21no—
77#13063296—21no—
78#13063296—21no—
79#13063296—21no—
80#13063296C2×C412yes—
81#13063293—22no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84C4×Dic86—21no—
85C4×Dic86C2312yes—
86#13063290—21no—
87#13063290C2×C412yes—
88D4×Dic43—22no—
89D4×Dic43—22no—
90D4×Dic43—21no—
91D4×Dic43—21no—
92D4×Dic43—21no—
93D4×Dic43C2×C412yes—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—22no—
96(C22⋊D43)⋊C4—22no—
97(C22⋊D43)⋊C4—22no—
98#13063284—21no—
99#13063284—22no—
100#13063283—21no—
101#13063283C2×C412yes—
102#13063281—22no—
103#13063281—22no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43C2311yescharacteristic
115C42×D43C2311yescharacteristic
116C4⋊(C43⋊C8)—21no—
117C4⋊(C43⋊C8)—21no—
118C4⋊(C43⋊C8)C2312yes—
119Dic43⋊C8—22no—
120Dic43⋊C8—22no—
121Dic43⋊C8—22no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—22no—
124#13063235—22no—
125C4×C43⋊C8C2312yes—
126C2×#41×C43—21no—
127C22×C8×C43—21no—
128C4⋊Q8×C43C2×C411yescharacteristic
129#127×C43C2×C411yescharacteristic
130#124×C43—21no—
131#121×C43—21no—
132#121×C43C2×C412yes—
133C4×D4×C43—21no—
134C4×D4×C43C2312yes—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2312yes—
139C22⋊C8×C43—21no—
140C4×C8×C43C2312yes—
141C23×D43C22⋊C411yescharacteristic
142#41×C43—42no—
143#41×C43—42no—
144C2×Q8×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—22no—
148C2×D4×C43C22×C412yes—
149C22×C4×C43—22no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43C22⋊C411yescharacteristic
158C22×Dic43C22⋊C411yescharacteristic
159C22×Dic43C22⋊C411yescharacteristic
160#10621900—28no—
161#10621900—44no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—24no—
165C2×C4×D43—42no—
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×D43C22×C411yescharacteristic
173C2×C4×D43C22×C411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178C2×Dic86—21no—
179C2×Dic86C22×C412yes—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C2×C8×C43—42no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C22×C412yes—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C42×C43C22×C411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2411yescharacteristic
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
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—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22×C411yescharacteristic
218C4×Dic43C22×C411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C2×C43⋊C8—22no—
224C2×C43⋊C8—22no—
225C2×C43⋊C8—42no—
226#10621872—44no—
227C8×D43—44no—
228C8×D43—44no—
229C23×C43—22no—
230C23×C43C2×C22⋊C411yescharacteristic
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43C2×C22⋊C411yescharacteristic
235C22×D43C2×C22⋊C411yescharacteristic
236Q8×C43—42no—
237D4×C43—24no—
238D4×C43—42no—
239D4×C43—44no—
240D4×C43—42no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43AGL(1,ℤ/8)12yes—
250C2×C4×C43#13712yes—
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C22⋊D43—44no—
255C22⋊D43—44no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—41no—
261C2×Dic43—44no—
262C2×Dic43—44no—
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—21no—
274C4×D43—21no—
275C4×D43—21no—
276C4×D43—21no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43#13114yes—
283Dic86—24no—
284Dic86—42no—
285C8×C43—42no—
286C8×C43—42no—
287C43⋊C8—42no—
288C43⋊C8—42no—
289#17466—431nomaximal, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43#41712yes—
296C22×C43C22×C22⋊C411yescharacteristic
297C2×D43—28no—
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—21no—
301C2×D43—21no—
302C2×D43#40812yes—
303C2×D43#42112yes—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—42no—
308C4×C43#41712yes—
309C4×C43C2×#13112yes—
310C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
311C4×C43C2×#13711yescharacteristic
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—21no—
317Dic43—42no—
318Dic43—42no—
319Dic43#40812yes—
320#3444—431no—
321#2920—431no—
322C22×C4⋊C8—431no—
323#1483—434no—
324#1481—431no—
325#1481—431no—
326#1480—431no—
327#1480D4311yescharacteristic, complemented
328#1477—434no—
329C2×C43—22no—
330C2×C43—82no—
331C2×C43C2×#40811yescharacteristic
332C2×C43C2×#41711yescharacteristic
333C2×C43C2×#42111yescharacteristic
334D43—22no—
335D43—22no—
336C23×C8—861no—
337#533—431no—
338#533—431no—
339#533—431no—
340#532—431no—
341#532—431no—
342#532C2×D4311yescharacteristic
343#529—432no—
344#529—432no—
345#529—861no—
346#529—861no—
347#529—861no—
348#529—861no—
349#525—432no—
350#525—861no—
351#525—861no—
352C4×#41—432no—
353C4×#41—861no—
354C4×#41—861no—
355C22×C42—431no—
356#432—861no—
357#432—861no—
358#431—431no—
359#431—432no—
360#431C2×D4311yescharacteristic
361#423—861no—
362C2×C4⋊C8—431no—
363C2×C4⋊C8—432no—
364C2×C4⋊C8—432no—
365C2×C4⋊C8—861no—
366C2×C4⋊C8—861no—
367C2×C4⋊C8—861no—
368C2×C4⋊C8C2×D4311yescharacteristic
369#407—861no—
370C4×M16—432no—
371Q8⋊C8—434no—
372Q8⋊C8—434no—
373D4⋊C8—434no—
374D4⋊C8C2×D4314yescomplemented
375C43#1746611yescharacteristic, complemented, Sylow
376C2×#41—21no—
377C2×#41—432no—
378C2×#41—861no—
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—431no—
382C2×M16—862no—
383C22×C8—21no—
384C22×C8—862no—
385C22×C8—862no—
386C22×C8—861no—
387C22×C8—1724no—
388C4⋊Q8—431no—
389C4⋊Q8—431no—
390C4⋊Q8C4×D4311yescharacteristic
391#127C4×D4311yescharacteristic
392#126—862no—
393#126—862no—
394#125—432no—
395#125—861no—
396#125—861no—
397#124—21no—
398#124—432no—
399#124—861no—
400#123—862no—
401#123—862no—
402#123—862no—
403C22⋊Q8—432no—
404C22⋊Q8—432no—
405C22⋊Q8—861no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409#121—21no—
410#121—432no—
411#121—861no—
412#121—861no—
413#121—861no—
414#121C4×D4312yes—
415#120—862no—
416C4×Q8—432no—
417C4×Q8—432no—
418C4×Q8—861no—
419C4×Q8—861no—
420C4×Q8—861no—
421C4×Q8—861no—
422C4×D4—21no—
423C4×D4—432no—
424C4×D4—861no—
425C4×D4—861no—
426C4×D4—861no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4C22×D4312yes—
434#117—432no—
435#117—862no—
436#117—862no—
437#117—862no—
438#117—861no—
439#117—861no—
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—431no—
451C2×C42—862no—
452C2×C42C22×D4311yescharacteristic
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—432no—
456C4⋊C8—862no—
457C4⋊C8—862no—
458C4⋊C8—862no—
459C4⋊C8—861no—
460C4⋊C8—861no—
461C4⋊C8C22×D4312yes—
462C22⋊C8—21no—
463C22⋊C8—862no—
464C22⋊C8—861no—
465#97—862no—
466C4×C8—432no—
467C4×C8C22×D4312yes—
468C24—431no—
469#41—42no—
470#41—42no—
471#41—868no—
472#41—1724no—
473C2×Q8—21no—
474C2×Q8—432no—
475C2×Q8—861no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4C2×C4×D4312yes—
482C22×C4—22no—
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—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—864no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—1722no—
504C22×C4C2×C4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4D4×D4311yescharacteristic
507M16—1724no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—42no—
511C2×C8—862no—
512C2×C8—862no—
513C2×C8—1724no—
514C2×C8—1724no—
515C2×C8—1722no—
516C4⋊C4—21no—
517C4⋊C4—432no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4C2×C4×D4312yes—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—862no—
550C42—862no—
551C42—862no—
552C42C2×C4×D4311yescharacteristic
553C42D4×D4311yescharacteristic
554C42D4×D4311yescharacteristic
555C42C23×D4311yescharacteristic
556C23—22no—
557C23—431no—
558C23—431no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23C22⋊C4×D4311yescharacteristic
563Q8—42no—
564Q8—864no—
565Q8—1722no—
566D4—24no—
567D4—42no—
568D4—44no—
569D4—42no—
570D4—1724no—
571D4—1724no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—431no—
578C2×C4—434no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—431no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1724no—
602C2×C4—1721no—
603C2×C4—1724no—
604C2×C4C22⋊C4×D4311yescharacteristic
605C2×C4C22⋊C4×D4311yescharacteristic
606C2×C4C22⋊C4×D4311yescharacteristic
607C2×C4#1306334912yes—
608C2×C4#1306335412yes—
609C2×C4C22×C4×D4311yescharacteristic
610C2×C4C2×D4×D4311yescharacteristic
611C2×C4C2×D4×D4311yescharacteristic
612C8—42no—
613C8—42no—
614C8—1722no—
615C8—1722no—
616C22—21no—
617C22—21no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—432no—
622C22—432no—
623C22—868no—
624C22—861no—
625C22—861no—
626C22—861no—
627C22—861no—
628C22#1458289712yes—
629C22C2×C22⋊C4×D4311yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—42no—
634C4—432no—
635C4—861no—
636C4—861no—
637C4—861no—
638C4—861no—
639C4—861no—
640C4—1722no—
641C4—1722no—
642C4#1458289712yes—
643C4#131×D4312yes—
644C4C2×#1306334911yescharacteristic
645C4C2×#1306335411yescharacteristic
646C2—22no—
647C2—82no—
648C2—862no—
649C2—862no—
650C2#408×D4311yescharacteristic
651C2C2×#1458289711yescharacteristic
652C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1480C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC42×C43C24
hypercenter#1480D43
hypocenterC43#17466
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. C2×C4⋊C8×D43C2semidirect
4. #19133005C2semidirect
5. #19132999C2semidirect
6. #19132997C2semidirect
7. #19132994C2semidirect
8. #19132979C2semidirect
9. C43×#1480C2semidirect
42. #14582631C22semidirect
43. #14582629C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
48. C43×D4⋊C8C22semidirect
327. #1480D43semidirect
374. D4⋊C8C2×D43semidirect
375. C43#17466semidirect

Maximal subgroups

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

subgroupindex
#191478902
#191432232
C2×C4⋊C8×D432
#191330052
#191329992
#191329972
#191329942
#191329792
C43×#14802
#1746643