Finite Group Databasebeta

← #25062798

Subgroups — #25062798

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583588C211yesmaximal, characteristic
2#19143253C211yesmaximal, characteristic, complemented
3#19132960C211yesmaximal, characteristic, complemented
4#19132958C211yesmaximal, characteristic, complemented
5#19132952C212yesmaximal, complemented
6#19132950C212yesmaximal, complemented
7#19132931C211yesmaximal, characteristic
8#19132927C212yesmaximal, complemented
9#19132911C211yesmaximal, characteristic
10#19132907C212yesmaximal, complemented
11C43×#2924C211yesmaximal, characteristic, complemented
12#14583588—21no—
13#14583588—21no—
14#14583588—22no—
15#14583588—21no—
16#14583588—21no—
17#14583588—22no—
18C2×#13063318C412yes—
19C2×#13063317C2212yes—
20C2×#13063316C411yescharacteristic
21C2×#13063307C412yes—
22C2×#13063305C411yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063290C411yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×#13063282C2212yes—
27C2×C4⋊C4×D43C411yescharacteristic
28#14582960—22no—
29#14582956C2212yes—
30#14582952C2212yes—
31#14582926—21no—
32#14582863C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582855—21no—
35#14582624C2212yes—
36#14582624C2211yescharacteristic
37#14582624C2212yes—
38#14582624C2212yes—
39#14582624C2211yescharacteristic
40#14582624C2212yes—
41#14582624C2212yes—
42#14582622C2212yes—
43#14582622C2211yescharacteristic
44#14582622C2211yescharacteristic
45C2×#117×C43C2211yescharacteristic
46C43×#433—22no—
47C43×#432C2212yes—
48C43×#431C2212yes—
49C43×#424—21no—
50C43×#407C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C43×#405—21no—
53C22×Dic86C2×C411yescharacteristic
54C22×C22⋊D43C2×C411yescharacteristic
55C22×C4×D43C2×C412yes—
56C22×C4×D43C2×C411yescharacteristic
57C2×#10621877—21no—
58C22×C43⋊C8—21no—
59#13063318—22no—
60#13063318—22no—
61#13063318—22no—
62#13063318—22no—
63#13063317—22no—
64#13063317—22no—
65#13063317—22no—
66#13063317—22no—
67#13063316—22no—
68#13063316—21no—
69#13063316—21no—
70#13063307—22no—
71#13063307—22no—
72#13063307—22no—
73#13063307—22no—
74#13063305—22no—
75#13063305—21no—
76#13063305—21no—
77#13063304—21no—
78#13063304—21no—
79#13063304—21no—
80#13063304—21no—
81#13063290—22no—
82#13063290—21no—
83#13063290—21no—
84C4×C22⋊D43—21no—
85C4×C22⋊D43—21no—
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88#13063282—22no—
89#13063282—22no—
90#13063282—22no—
91#13063282—22no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C412yes—
94C2×C4⋊Dic43C2×C412yes—
95C2×Dic43⋊C4C2×C412yes—
96C2×Dic43⋊C4C2×C412yes—
97C2×Dic43⋊C4C2×C412yes—
98C2×Dic43⋊C4C2312yes—
99C2×Dic43⋊C4C2311yescharacteristic
100C4⋊C4×D43—22no—
101C4⋊C4×D43—21no—
102C4⋊C4×D43—21no—
103C2×C22⋊Dic43C2×C411yescharacteristic
104C2×C22⋊Dic43C2×C412yes—
105C2×(C2×D43)⋊C4C2×C412yes—
106C2×(C2×D43)⋊C4C2311yescharacteristic
107C2×C4×Dic43C2×C412yes—
108C2×C4×Dic43C2×C411yescharacteristic
109C4⋊(C43⋊C8)—22no—
110C4⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)C2311yescharacteristic
114C22⋊(C43⋊C8)C2311yescharacteristic
115C22⋊(C43⋊C8)C2312yes—
116#13063236—22no—
117C4×C43⋊C8—22no—
118C23×C4×C43C2311yescharacteristic
119C2×M16×C43—21no—
120C22×C8×C43—21no—
121#117×C43D411yescharacteristic
122#117×C43D411yescharacteristic
123#117×C43D412yes—
124#117×C43D411yescharacteristic
125#117×C43D411yescharacteristic
126#117×C43D412yes—
127C2×C4⋊C4×C43C2×C411yescharacteristic
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C22⋊C4×C43C2×C412yes—
130C2×C42×C43C2312yes—
131C4⋊C8×C43—22no—
132C4⋊C8×C43—22no—
133C22⋊C8×C43—21no—
134C22⋊C8×C43—21no—
135C22⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43C2311yescharacteristic
137C22⋊C8×C43C2312yes—
138#97×C43—22no—
139C4×C8×C43—22no—
140C24×C43C22×C411yescharacteristic
141C23×D43C22×C411yescharacteristic
142C22×C4×C43—42no—
143C22×C4×C43C22×C412yes—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C22×C412yes—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43—41no—
155C22×Dic43C22×C411yescharacteristic
156C22×Dic43C22×C412yes—
157C22×Dic43C22×C411yescharacteristic
158C22×Dic43C22×C412yes—
159C22×Dic43C22×C411yescharacteristic
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—24no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—42no—
170M16×C43—42no—
171C2×C8×C43—21no—
172C2×C8×C43—22no—
173C2×C8×C43—21no—
174C2×C8×C43—42no—
175C4⋊C4×C43C22⋊C412yes—
176C4⋊C4×C43C22⋊C411yescharacteristic
177C4⋊C4×C43C22⋊C411yescharacteristic
178C4⋊C4×C43C22⋊C412yes—
179C4⋊C4×C43C22⋊C411yescharacteristic
180C4⋊C4×C43C22⋊C411yescharacteristic
181C22⋊C4×C43C22⋊C412yes—
182C22⋊C4×C43C22⋊C412yes—
183C22⋊C4×C43C22⋊C412yes—
184C22⋊C4×C43C22⋊C412yes—
185C42×C43C2×D412yes—
186C42×C43C2×D412yes—
187C42×C43C2×D412yes—
188C42×C43C2×D412yes—
189C22⋊Dic43—21no—
190C22⋊Dic43—21no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—21no—
212Dic43⋊C4—21no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217#10621877—42no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—42no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C2×C22⋊C411yescharacteristic
227C23×C43C2×C22⋊C411yescharacteristic
228C23×C43C23×C411yescharacteristic
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43#13112yes—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43C2×C22⋊C412yes—
244C2×C4×C43C2×C22⋊C412yes—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C412yes—
247C2×C4×C43C2×C22⋊C412yes—
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C22⋊D43—42no—
252C22⋊D43—42no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—21no—
262C2×Dic43—42no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C4×D43—44no—
266C4×D43—44no—
267C4×D43—42no—
268C4×D43—42no—
269Dic86—42no—
270Dic86—42no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—42no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—42no—
277#17413—431nomaximal, Sylow
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43C22×C22⋊C411yescharacteristic
289C22×C43C2×#13111yescharacteristic
290C22×C43#56811yescharacteristic
291C2×D43—22no—
292C2×D43—42no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—42no—
296C4×C43—22no—
297C4×C43—22no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43#41012yes—
304Dic43—42no—
305Dic43—41no—
306Dic43—42no—
307Dic43—41no—
308Dic43—41no—
309C2×#552—431no—
310#2924—431no—
311#2924D4311yescharacteristic, complemented
312#1472—431no—
313#1472—431no—
314#1470—432no—
315#1470—432no—
316#1465—431no—
317#1464—432no—
318#1459—431no—
319#1458—432no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43—41no—
323C2×C43—41no—
324C2×C43#288011yescharacteristic
325C2×C43C2×#41011yescharacteristic
326C2×C43#288911yescharacteristic
327D43—42no—
328#552—861no—
329#552—861no—
330#552—862no—
331#552—861no—
332#552—861no—
333#552—862no—
334C2×#126—432no—
335C2×#125—431no—
336C2×#125—432no—
337C2×#123—432no—
338C2×C22⋊Q8—431no—
339C2×C22⋊Q8—431no—
340C2×C4×Q8—431no—
341C2×C4×D4—431no—
342C2×#117—432no—
343C2×#117C2×D4311yescharacteristic
344C22×C4⋊C4—431no—
345#433—22no—
346#433—862no—
347#432—432no—
348#432C2×D4312yes—
349#431—432no—
350#431C2×D4312yes—
351#424—21no—
352#424—861no—
353#407—431no—
354#407C2×D4311yescharacteristic
355C2×C22⋊C8—431no—
356C2×C22⋊C8C2×D4311yescharacteristic
357#405—21no—
358#405—861no—
359#324—432no—
360#324—432no—
361#324—431no—
362#324—431no—
363#324—432no—
364#324—432no—
365#324—432no—
366#323—431no—
367#323—432no—
368#323—431no—
369C43#1741311yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C22×D4—431no—
372C23×C4—432no—
373C23×C4—431no—
374C23×C4C22×D4311yescharacteristic
375C2×M16—21no—
376C2×M16—861no—
377C22×C8—21no—
378C22×C8—861no—
379#126—862no—
380#126—862no—
381#126—862no—
382#126—862no—
383#125—862no—
384#125—861no—
385#125—861no—
386#125—862no—
387#125—862no—
388#125—862no—
389#125—862no—
390#123—862no—
391#123—862no—
392#123—862no—
393#123—862no—
394C22⋊Q8—861no—
395C22⋊Q8—861no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398C22⋊Q8—862no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401C4×Q8—862no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×D4—861no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4—861no—
408#117—862no—
409#117—862no—
410#117—862no—
411#117—862no—
412#117D17211yescharacteristic
413#117D17211yescharacteristic
414#117D17212yes—
415#117C22⋊D4311yescharacteristic
416#117C22⋊D4311yescharacteristic
417#117C22⋊D4312yes—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—432no—
420C2×C4⋊C4—432no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—432no—
424C2×C4⋊C4—432no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C4×D4311yescharacteristic
430C2×C4⋊C4C4×D4311yescharacteristic
431C2×C22⋊C4—431no—
432C2×C22⋊C4—432no—
433C2×C22⋊C4—432no—
434C2×C22⋊C4—431no—
435C2×C22⋊C4C4×D4312yes—
436C2×C42—432no—
437C2×C42—431no—
438C2×C42C22×D4312yes—
439C4⋊C8—22no—
440C4⋊C8—22no—
441C4⋊C8—862no—
442C4⋊C8—862no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—431no—
446C22⋊C8—431no—
447C22⋊C8—432no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C22⋊C8C22×D4311yescharacteristic
451C22⋊C8C22×D4311yescharacteristic
452C22⋊C8C22×D4312yes—
453#97—22no—
454#97—862no—
455C4×C8—22no—
456C4×C8—862no—
457C24—431no—
458C24C2×C4×D4311yescharacteristic
459C2×Q8—861no—
460C2×Q8—861no—
461C2×Q8—1722no—
462C2×D4—862no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—1721no—
466C22×C4—42no—
467C22×C4—431no—
468C22×C4—432no—
469C22×C4—431no—
470C22×C4—432no—
471C22×C4—431no—
472C22×C4—864no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4C2×C4×D4312yes—
480C22×C4C2×C4×D4311yescharacteristic
481C22×C4C2×C4×D4312yes—
482C22×C4C2×D17211yescharacteristic
483C22×C4C2×D17211yescharacteristic
484C22×C4C2×C22⋊D4311yescharacteristic
485C22×C4C2×C22⋊D4311yescharacteristic
486C22×C4C23×D4311yescharacteristic
487M16—42no—
488M16—1722no—
489C2×C8—21no—
490C2×C8—22no—
491C2×C8—21no—
492C2×C8—42no—
493C2×C8—861no—
494C2×C8—862no—
495C2×C8—861no—
496C2×C8—1722no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—862no—
512C4⋊C4—861no—
513C4⋊C4(C2×D43)⋊C412yes—
514C4⋊C4(C2×D43)⋊C411yescharacteristic
515C4⋊C4(C2×D43)⋊C411yescharacteristic
516C4⋊C4(C2×D43)⋊C412yes—
517C4⋊C4(C2×D43)⋊C411yescharacteristic
518C4⋊C4(C2×D43)⋊C411yescharacteristic
519C22⋊C4—861no—
520C22⋊C4—861no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—861no—
526C22⋊C4—861no—
527C22⋊C4(C2×D43)⋊C412yes—
528C22⋊C4(C2×D43)⋊C412yes—
529C22⋊C4(C2×D43)⋊C412yes—
530C22⋊C4(C2×D43)⋊C412yes—
531C42—862no—
532C42—862no—
533C42—861no—
534C42—861no—
535C42C2×D17212yes—
536C42C2×D17212yes—
537C42C2×C22⋊D4312yes—
538C42C2×C22⋊D4312yes—
539C23—21no—
540C23—21no—
541C23—41no—
542C23—41no—
543C23—432no—
544C23—861no—
545C23—861no—
546C23—1721no—
547C23—1721no—
548C23C2×(C2×D43)⋊C411yescharacteristic
549C23C2×(C2×D43)⋊C411yescharacteristic
550C23C22×C4×D4311yescharacteristic
551Q8—1722no—
552Q8—1722no—
553D4—1722no—
554D4—1722no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—861no—
565C2×C4—862no—
566C2×C4—861no—
567C2×C4—862no—
568C2×C4—861no—
569C2×C4—862no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—1724no—
574C2×C4—1724no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1721no—
578C2×C4—1722no—
579C2×C4—1721no—
580C2×C4C2×(C2×D43)⋊C412yes—
581C2×C4C2×(C2×D43)⋊C412yes—
582C2×C4C2×(C2×D43)⋊C411yescharacteristic
583C2×C4C2×(C2×D43)⋊C412yes—
584C2×C4C2×(C2×D43)⋊C412yes—
585C2×C4C2×(C2×D43)⋊C411yescharacteristic
586C2×C4C22×C22⋊D4311yescharacteristic
587C2×C4C22×D17211yescharacteristic
588C8—41no—
589C8—41no—
590C8—42no—
591C8—1721no—
592C8—1721no—
593C8—1722no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—81no—
603C22—81no—
604C22—862no—
605C22—1722no—
606C22—1722no—
607C22—1721no—
608C22—1721no—
609C22C22×(C2×D43)⋊C411yescharacteristic
610C22#131×D4311yescharacteristic
611C22#1458366411yescharacteristic
612C4—22no—
613C4—22no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—22no—
618C4—22no—
619C4—1722no—
620C4—1721no—
621C4—1721no—
622C4—1722no—
623C4—1721no—
624C4#1458287212yes—
625C2—21no—
626C2—21no—
627C2—41no—
628C2—41no—
629C2—1722no—
630C2#1914304211yescharacteristic
631C2C2×#1458287211yescharacteristic
632C2#1914307711yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2924C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#2924D43
hypocenterC43#17413
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #19143253C2semidirect
3. #19132960C2semidirect
4. #19132958C2semidirect
5. #19132952C2semidirect
6. #19132950C2semidirect
8. #19132927C2semidirect
10. #19132907C2semidirect
11. C43×#2924C2semidirect
311. #2924D43semidirect
369. C43#17413semidirect

Maximal subgroups

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

subgroupindex
C2×#145835882
#191432532
#191329602
#191329582
#191329522
#191329502
#191329312
#191329272
#191329112
#191329072
C43×#29242
#1741343