Finite Group Databasebeta

← #25062580

Subgroups — #25062580

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583435C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3C2×#14582949C211yesmaximal, characteristic, complemented
4#19132963C214yesmaximal, complemented
5#19132959C211yesmaximal, characteristic, complemented
6#19132956C211yesmaximal, characteristic
7#19132954C211yesmaximal, characteristic
8#19132908C214yesmaximal, complemented
9C43×#1472C211yesmaximal, characteristic, complemented
10#14583435—21no—
11#14583435—21no—
12#14583435—21no—
13#14583435—21no—
14#14583435—21no—
15#14583435—21no—
16#14583435—21no—
17#14583435—21no—
18C2×#13063320C2212yes—
19C2×#13063316C411yescharacteristic
20C2×#13063314C411yescharacteristic
21C2×#13063309C412yes—
22C2×#13063299C2211yescharacteristic
23C2×Q8×Dic43C411yescharacteristic
24C2×#13063287C411yescharacteristic
25C2×(C22⋊D43)⋊C4C412yes—
26C2×#13063283C2212yes—
27C22×C4×Dic43C2211yescharacteristic
28#14582953—21no—
29#14582953C2212yes—
30#14582949—21no—
31#14582949—21no—
32#14582949—21no—
33#14582949C2212yes—
34#14582949C2212yes—
35#14582949C2212yes—
36#14582922—21no—
37C2×Dic43⋊C8—21no—
38#14582863C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40M16×Dic43—21no—
41C2×C8×Dic43—21no—
42#14582625C2214yes—
43#14582622C2214yes—
44#14582622C2214yes—
45C2×C22⋊Q8×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#324C2214yes—
49C22×D172C2×C411yescharacteristic
50C22×C22⋊D43C2×C412yes—
51C23×Dic43C2×C411yescharacteristic
52C23×Dic43C2×C411yescharacteristic
53C22×C4×D43C2×C412yes—
54C2×#10621877—21no—
55C22×C43⋊C8—21no—
56#13063320—22no—
57#13063320—22no—
58#13063320—22no—
59#13063320—22no—
60#13063316—21no—
61#13063316—21no—
62#13063316—21no—
63#13063316—21no—
64#13063314—21no—
65#13063314—21no—
66#13063314—21no—
67#13063314—21no—
68#13063309—22no—
69#13063309—22no—
70#13063309—22no—
71#13063309—22no—
72#13063299—21no—
73#13063299—21no—
74#13063299—21no—
75#13063299—21no—
76Q8×Dic43—21no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80#13063287—21no—
81#13063287—21no—
82#13063287—21no—
83#13063287—21no—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86(C22⋊D43)⋊C4—22no—
87(C22⋊D43)⋊C4—22no—
88#13063283—22no—
89#13063283—22no—
90#13063283—22no—
91#13063283—22no—
92C2×C4⋊Dic43C2×C412yes—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43C2×C412yes—
95C2×Dic43⋊C4C2×C412yes—
96C2×(C2×D43)⋊C4C2×C412yes—
97C2×(C2×D43)⋊C4C2×C412yes—
98C2×(C2×D43)⋊C4C2×C412yes—
99C2×(C2×D43)⋊C4C2312yes—
100C2×C4×Dic43C2×C412yes—
101C2×C4×Dic43C2×C411yescharacteristic
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119C22⋊(C43⋊C8)C2312yes—
120C22⋊(C43⋊C8)C2312yes—
121#13063235—22no—
122C8×Dic43—22no—
123C8×Dic43—22no—
124C8×Dic43—22no—
125C22×Q8×C43C2×C411yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43—21no—
128C22×C8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C4⋊C4×C43C2312yes—
135C2×C22⋊C4×C43C2×C412yes—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139C22⋊C8×C43C2312yes—
140C24×C43C22×C411yescharacteristic
141C23×D43C22×C412yes—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43C22×C412yes—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—44no—
157C22×Dic43—24no—
158C22×Dic43—42no—
159C22×Dic43C22⋊C411yescharacteristic
160C22×Dic43C22⋊C411yescharacteristic
161C22×Dic43C22⋊C411yescharacteristic
162C22×Dic43C22⋊C411yescharacteristic
163C22×Dic43C22⋊C411yescharacteristic
164C22×Dic43C22⋊C411yescharacteristic
165C22×Dic43C22⋊C411yescharacteristic
166C22×Dic43C22⋊C411yescharacteristic
167C22×Dic43C22×C411yescharacteristic
168C22×Dic43C22×C412yes—
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C22×Dic43C22×C411yescharacteristic
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—42no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—28no—
178M16×C43—42no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43—42no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204C4×Dic43—22no—
205C4×Dic43—22no—
206C4×Dic43C22⋊C411yescharacteristic
207C4×Dic43C22⋊C411yescharacteristic
208C4×Dic43C22⋊C411yescharacteristic
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222#10621877—42no—
223C2×C43⋊C8—22no—
224C2×C43⋊C8—22no—
225C2×C43⋊C8—42no—
226C23×C43—22no—
227C23×C43—22no—
228C23×C43—41no—
229C23×C43C2×C22⋊C411yescharacteristic
230C23×C43C2×C22⋊C411yescharacteristic
231C23×C43C23×C411yescharacteristic
232C22×D43—22no—
233C22×D43—24no—
234C22×D43—42no—
235C22×D43—42no—
236Q8×C43—42no—
237Q8×C43—42no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—24no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C22⋊D43—44no—
253C22⋊D43—44no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—42no—
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43#13114yes—
276D172—42no—
277D172—42no—
278C4×D43—44no—
279C4×D43—44no—
280C8×C43—42no—
281C8×C43—42no—
282C43⋊C8—42no—
283C43⋊C8—42no—
284#17380—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—44no—
293C22×C43#41312yes—
294C22×C43C22×C22⋊C411yescharacteristic
295C22×C43C2×#13112yes—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—84no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—42no—
304C4×C43—42no—
305C4×C43#41012yes—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—42no—
313Dic43#40812yes—
314Dic43#40812yes—
315C2×#529—431no—
316#2920—431no—
317C2×#431—431no—
318#1473—434no—
319#1472—431no—
320#1472D4311yescharacteristic, complemented
321#1471—431no—
322#1471—431no—
323#1458—434no—
324C2×C43—22no—
325C2×C43—22no—
326C2×C43—41no—
327C2×C43C2×#40811yescharacteristic
328C2×C43C2×#41011yescharacteristic
329C2×C43C2×#41311yescharacteristic
330D43—82no—
331#529—861no—
332#529—861no—
333#529—861no—
334#529—861no—
335#529—861no—
336#529—861no—
337#529—861no—
338#529—861no—
339C2×#126—432no—
340C2×#125—431no—
341C2×#124—431no—
342C2×#123—432no—
343C2×C22⋊Q8C2×D4311yescharacteristic
344C2×#121—431no—
345C2×C4×Q8—431no—
346C2×C4×D4—431no—
347C2×C4×D4—432no—
348C2×#117—432no—
349C22×C42—431no—
350#432—432no—
351#432—861no—
352#431—432no—
353#431—432no—
354#431—432no—
355#431—861no—
356#431—861no—
357#431—861no—
358#423—861no—
359C2×C4⋊C8—861no—
360#407—431no—
361#407C2×D4311yescharacteristic
362C2×C22⋊C8—431no—
363C2×C22⋊C8C2×D4311yescharacteristic
364C4×M16—861no—
365C2×C4×C8—861no—
366#324—434no—
367#324C2×D4314yes—
368#323—434no—
369#323—434no—
370C43#1738011yescharacteristic, complemented, Sylow
371C22×Q8C4×D4311yescharacteristic
372C22×D4—432no—
373C22×D4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—432no—
377C23×C4C22×D4311yescharacteristic
378C2×M16—21no—
379C2×M16—861no—
380C22×C8—21no—
381C22×C8—861no—
382#126—862no—
383#126—862no—
384#126—862no—
385#126—862no—
386#125—861no—
387#125—861no—
388#125—861no—
389#125—861no—
390#124—861no—
391#124—861no—
392#124—861no—
393#124—861no—
394#123—862no—
395#123—862no—
396#123—862no—
397#123—862no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402#121—861no—
403#121—861no—
404#121—861no—
405#121—861no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×Q8—861no—
409C4×Q8—861no—
410C4×D4—861no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4—861no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—862no—
418#117—862no—
419#117—862no—
420#117—862no—
421#117—862no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—432no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—432no—
426C2×C4⋊C4C4×D4311yescharacteristic
427C2×C4⋊C4C22×D4312yes—
428C2×C22⋊C4—432no—
429C2×C22⋊C4—432no—
430C2×C22⋊C4—432no—
431C2×C22⋊C4—432no—
432C2×C22⋊C4C4×D4312yes—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—432no—
446C4⋊C8—862no—
447C4⋊C8—862no—
448C4⋊C8—862no—
449C4⋊C8—862no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—432no—
453C22⋊C8—432no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456C22⋊C8C22×D4312yes—
457C22⋊C8C22×D4312yes—
458#97—862no—
459C4×C8—862no—
460C4×C8—862no—
461C4×C8—862no—
462C24—432no—
463C24C2×C4×D4311yescharacteristic
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—42no—
467C2×D4—862no—
468C2×D4—862no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—1722no—
472C2×D4—1724no—
473C22×C4—42no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—432no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—868no—
490C22×C4—864no—
491C22×C4—1722no—
492C22×C4C2×C4×D4312yes—
493C22×C4C2×C4×D4311yescharacteristic
494C22×C4C2×C4×D4312yes—
495C22×C4D4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500M16—42no—
501M16—1722no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—42no—
505C2×C8—862no—
506C2×C8—862no—
507C2×C8—1722no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—862no—
547C42—862no—
548C23—22no—
549C23—22no—
550C23—41no—
551C23—864no—
552C23—862no—
553C23—1722no—
554C23—1722no—
555C23C22⋊C4×D4311yescharacteristic
556C23C22⋊C4×D4311yescharacteristic
557C23C22×C4×D4311yescharacteristic
558Q8—42no—
559Q8—42no—
560D4—1722no—
561D4—1724no—
562D4—1724no—
563D4—1722no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—434no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—1724no—
592C2×C4—1724no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1722no—
598C2×C4C22⋊C4×D4311yescharacteristic
599C2×C4C22⋊C4×D4311yescharacteristic
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C8—42no—
603C8—42no—
604C8—1722no—
605C8—1722no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—44no—
614C22—3444no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22#1458288212yes—
619C22C2×C22⋊C4×D4311yescharacteristic
620C22#131×D4312yes—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—42no—
625C4—42no—
626C4—432no—
627C4—432no—
628C4—861no—
629C4—861no—
630C4—861no—
631C4—861no—
632C4—861no—
633C4—861no—
634C4—1722no—
635C4#1458287112yes—
636C2—22no—
637C2—22no—
638C2—41no—
639C2—3442no—
640C2#408×D4311yescharacteristic
641C2C2×#1458287111yescharacteristic
642C2C2×#1458288211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1472C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenter#1472D43
hypocenterC43#17380
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. C2×#14582949C2semidirect
4. #19132963C2semidirect
5. #19132959C2semidirect
8. #19132908C2semidirect
9. C43×#1472C2semidirect
320. #1472D43semidirect
370. C43#17380semidirect

Maximal subgroups

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

subgroupindex
C2×#145834352
#191432242
C2×#145829492
#191329632
#191329592
#191329562
#191329542
#191329082
C43×#14722
#1738043