Finite Group Databasebeta

← #25063151

Subgroups — #25063151

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583436C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3#431×D43C211yesmaximal, characteristic, complemented
4#19133007C214yesmaximal, complemented
5#19133002C214yesmaximal, complemented
6#19132990C211yesmaximal, characteristic, complemented
7#19132987C211yesmaximal, characteristic, complemented
8#19132985C211yesmaximal, characteristic, complemented
9C43×#1479C211yesmaximal, characteristic, complemented
10#14583436—21no—
11#14583436—21no—
12#14583436—21no—
13#14583436—21no—
14#14583436C412yes—
15#14583436C412yes—
16#14583436C2212yes—
17#14583436C2212yes—
18C2×#13063320—21no—
19C2×#13063316C411yescharacteristic
20C2×#13063314C411yescharacteristic
21C2×#13063310—21no—
22C2×#13063301C411yescharacteristic
23C2×#13063300C411yescharacteristic
24C2×C4×D172—21no—
25C2×C4×D172C2211yescharacteristic
26C2×#13063282—21no—
27C2×C42×D43C2211yescharacteristic
28#14582955—21no—
29#14582953—21no—
30#14582952C2211yescharacteristic
31#14582952C2211yescharacteristic
32#14582951C2212yescomplemented
33#14582950—21no—
34#14582950C2212yescomplemented
35#14582949—21no—
36#14582921—21no—
37C4⋊C8×D43C2212yescomplemented
38#14582861—21no—
39C22⋊C8×D43—21no—
40C4×#10621872C2212yescomplemented
41C4×C8×D43—21no—
42Q8⋊(C43⋊C8)C2214yescomplemented
43#14582628C2214yescomplemented
44#14582626C2214yescomplemented
45C2×C4×Q8×C43C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#431C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C22×D172—21no—
50C22×D172C2×C411yescharacteristic
51C22×C4×D43—21no—
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C2×#10621872—22no—
56C2×C8×D43—22no—
57#13063320—22no—
58#13063320—22no—
59#13063320—22no—
60#13063320—22no—
61#13063316—21no—
62#13063316—21no—
63#13063316C2×C412yes—
64#13063316C2×C412yes—
65#13063314—21no—
66#13063314—21no—
67#13063314C2×C412yes—
68#13063314C2×C412yes—
69#13063310—22no—
70#13063310—22no—
71#13063310—22no—
72#13063310—22no—
73#13063301—21no—
74#13063301—21no—
75#13063301C2×C412yes—
76#13063301C2×C412yes—
77#13063300—21no—
78#13063300—21no—
79#13063300C2×C412yes—
80#13063300C2×C412yes—
81C4×D172—22no—
82C4×D172—22no—
83C4×D172—22no—
84C4×D172—22no—
85C4×D172—21no—
86C4×D172—21no—
87C4×D172C2×C412yes—
88C4×D172C2312yes—
89#13063282—22no—
90#13063282—22no—
91#13063282—22no—
92#13063282—22no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C42×D43C2×C411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43C2311yescharacteristic
112C42×D43C2311yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)C2312yes—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063235—22no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2312yes—
124C8×Dic43—22no—
125C22×Q8×C43C2×C411yescharacteristic
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2×C412yes—
129C4×Q8×C43C2312yes—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2312yes—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43—21no—
141C23×D43C22⋊C411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—22no—
144C2×Q8×C43—22no—
145C2×Q8×C43C22×C412yes—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C22⋊C411yescharacteristic
154C22×Dic43C22⋊C411yescharacteristic
155C2×D172—21no—
156C2×D172—22no—
157C2×D172—22no—
158C2×D172—22no—
159C2×D172—22no—
160C2×D172—44no—
161C2×D172C22×C412yes—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—44no—
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22×C411yescharacteristic
176C2×C4×D43C22×C411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178C2×C4×D43C2×D411yescharacteristic
179C2×C4×D43C2×D411yescharacteristic
180C2×C4×D43C2×D411yescharacteristic
181C2×C8×C43—22no—
182C2×C8×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43C22×C412yes—
187C42×C43—22no—
188C42×C43—22no—
189C42×C43C22×C411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2411yescharacteristic
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43—22no—
206C4⋊Dic43C22×C412yes—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—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—
225#10621872—44no—
226C8×D43—44no—
227C23×C43C2×C22⋊C411yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—41no—
232C22×D43—42no—
233C22×D43—42no—
234C22×D43—42no—
235C22×D43C2×C22⋊C411yescharacteristic
236C22×D43C2×C22⋊C411yescharacteristic
237Q8×C43—22no—
238Q8×C43—22no—
239Q8×C43—42no—
240C2×C4×C43—22no—
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×C43#13112yes—
250C2×C4×C43#13112yes—
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—42no—
259C2×Dic43C2×C22⋊C411yescharacteristic
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265D172—22no—
266D172—22no—
267D172—44no—
268D172—44no—
269D172—42no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—21no—
273C4×D43—21no—
274C4×D43—21no—
275C4×D43—21no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—22no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—41no—
284C4×D43—44no—
285C4×D43—44no—
286C8×C43—42no—
287C8×C43—42no—
288C43⋊C8—42no—
289C43⋊C8—42no—
290#17465—431nomaximal, Sylow
291C22×C43—21no—
292C22×C43—21no—
293C22×C43#40812yes—
294C22×C43C22×C22⋊C411yescharacteristic
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—44no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—84no—
305C2×D43#42112yes—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43#40812yes—
312C4×C43C2×#13111yescharacteristic
313C4×C43C2×#13111yescharacteristic
314C4×C43#57512yes—
315Dic43—21no—
316Dic43—21no—
317Dic43—21no—
318Dic43—21no—
319Dic43—21no—
320Dic43—21no—
321Dic43—42no—
322C2×#529—431no—
323#2920—431no—
324C2×#431—431no—
325#1483—434no—
326#1482—434no—
327#1479—431no—
328#1479D4311yescharacteristic, complemented
329#1478—431no—
330#1478—431no—
331C2×C43—22no—
332C2×C43C2×#40811yescharacteristic
333C2×C43#289611yescharacteristic
334C2×C43C2×#42111yescharacteristic
335D43—22no—
336D43—41no—
337D43—82no—
338#529—432no—
339#529—432no—
340#529—432no—
341#529—432no—
342#529—861no—
343#529—861no—
344#529—861no—
345#529—861no—
346C2×#126—861no—
347C2×#125—431no—
348C2×#124—431no—
349C2×#123—861no—
350C2×C22⋊Q8—431no—
351C2×#121—431no—
352C2×C4×Q8C2×D4311yescharacteristic
353C2×C4×D4—431no—
354C2×C4×D4—861no—
355C2×#117—861no—
356C22×C42—431no—
357#432—861no—
358#432—861no—
359#431—431no—
360#431—432no—
361#431—431no—
362#431—432no—
363#431—861no—
364#431—861no—
365#431C2×D4311yescharacteristic
366#431C2×D4311yescharacteristic
367#423—861no—
368C2×C4⋊C8—432no—
369#407—861no—
370C2×C22⋊C8—861no—
371C4×M16—432no—
372C2×C4×C8—861no—
373Q8⋊C8—434no—
374Q8⋊C8C2×D4314yescomplemented
375D4⋊C8—434no—
376D4⋊C8—434no—
377C43#1746511yescharacteristic, complemented, Sylow
378C22×Q8C4×D4311yescharacteristic
379C22×D4—431no—
380C22×D4—861no—
381C23×C4—431no—
382C23×C4—431no—
383C23×C4—431no—
384C23×C4—861no—
385C2×M16—862no—
386C22×C8—862no—
387#126—862no—
388#126—862no—
389#126—862no—
390#126—862no—
391#125—432no—
392#125—432no—
393#125—861no—
394#125—861no—
395#124—432no—
396#124—432no—
397#124—861no—
398#124—861no—
399#123—862no—
400#123—862no—
401#123—862no—
402#123—862no—
403C22⋊Q8—432no—
404C22⋊Q8—432no—
405C22⋊Q8—861no—
406C22⋊Q8—861no—
407#121—432no—
408#121—432no—
409#121—861no—
410#121—861no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8C4×D4312yes—
414C4×Q8C22×D4312yes—
415C4×D4—432no—
416C4×D4—432no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—861no—
422C4×D4—861no—
423#117—862no—
424#117—862no—
425#117—862no—
426#117—862no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C4×D4311yescharacteristic
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C42—21no—
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×C42C22×D4311yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—432no—
453C4⋊C8—862no—
454C4⋊C8—862no—
455C4⋊C8—861no—
456C4⋊C8C22×D4312yes—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—862no—
460C22⋊C8—862no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463#97—862no—
464C4×C8—21no—
465C4×C8—432no—
466C4×C8—862no—
467C4×C8—861no—
468C4×C8C22×D4312yes—
469C24—431no—
470C24—861no—
471C2×Q8—21no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8C2×C4×D4312yes—
475C2×D4—432no—
476C2×D4—862no—
477C2×D4—862no—
478C2×D4—861no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—1724no—
482C22×C4—21no—
483C22×C4—21no—
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—431no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—861no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—1722no—
505C22×C4—1724no—
506C22×C4—1722no—
507C22×C4C2×C4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510M16—1724no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—862no—
514C2×C8—862no—
515C2×C8—1724no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—432no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—861no—
527C4⋊C4C2×C4×D4312yes—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C42—22no—
539C42—22no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42C2×C4×D4311yescharacteristic
553C42D4×D4311yescharacteristic
554C42D4×D4311yescharacteristic
555C42C23×D4311yescharacteristic
556C23—431no—
557C23—431no—
558C23—862no—
559C23—862no—
560C23—862no—
561C23—1721no—
562C23—1722no—
563C23—1722no—
564C23—1722no—
565C23C22⋊C4×D4311yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—42no—
569D4—862no—
570D4—862no—
571D4—1724no—
572D4—1724no—
573D4—1722no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—431no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—431no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1724no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1722no—
606C2×C4—1724no—
607C2×C4C22⋊C4×D4311yescharacteristic
608C2×C4C22⋊C4×D4311yescharacteristic
609C2×C4C22⋊C4×D4311yescharacteristic
610C2×C4#1306333112yes—
611C2×C4#1306333312yes—
612C2×C4C22×C4×D4311yescharacteristic
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4C2×D4×D4311yescharacteristic
615C8—42no—
616C8—42no—
617C8—1722no—
618C8—1722no—
619C22—21no—
620C22—21no—
621C22—432no—
622C22—861no—
623C22—861no—
624C22—861no—
625C22—861no—
626C22—861no—
627C22—3444no—
628C22—1724no—
629C22—1722no—
630C22—1722no—
631C22—1722no—
632C22#1458286412yes—
633C22C2×C22⋊C4×D4311yescharacteristic
634C4—21no—
635C4—21no—
636C4—21no—
637C4—42no—
638C4—42no—
639C4—861no—
640C4—861no—
641C4—861no—
642C4—861no—
643C4—861no—
644C4—861no—
645C4—1722no—
646C4#1458286412yes—
647C4C2×#1306333111yescharacteristic
648C4C2×#1306333311yescharacteristic
649C4#1458369812yes—
650C2—22no—
651C2—862no—
652C2—3442no—
653C2—1721no—
654C2C2×#1458286411yescharacteristic
655C2#1914311311yescharacteristic
656C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1479C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063300C4
cosocleC42×C43C24
hypercenter#1479D43
hypocenterC43#17465
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. #431×D43C2semidirect
4. #19133007C2semidirect
5. #19133002C2semidirect
6. #19132990C2semidirect
7. #19132987C2semidirect
8. #19132985C2semidirect
9. C43×#1479C2semidirect
32. #14582951C22semidirect
34. #14582950C22semidirect
37. C4⋊C8×D43C22semidirect
40. C4×#10621872C22semidirect
42. Q8⋊(C43⋊C8)C22semidirect
43. #14582628C22semidirect
44. #14582626C22semidirect
48. C43×Q8⋊C8C22semidirect
328. #1479D43semidirect
374. Q8⋊C8C2×D43semidirect
377. C43#17465semidirect

Maximal subgroups

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

subgroupindex
C2×#145834362
#191432232
#431×D432
#191330072
#191330022
#191329902
#191329872
#191329852
C43×#14792
#1746543