Finite Group Databasebeta

← #25064290

Subgroups — #25064290

Order 11008.

930 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148347C211yesmaximal, characteristic
2#19143253C211yesmaximal, characteristic, complemented
3#19133170C212yesmaximal, complemented
4#19133166C211yesmaximal, characteristic, complemented
5#19133145C212yesmaximal, complemented
6#19133136C211yesmaximal, characteristic
7#19133118C212yesmaximal, complemented
8#19133114C211yesmaximal, characteristic, complemented
9#19133093C212yesmaximal, complemented
10#19133084C211yesmaximal, characteristic
11C43×#2347C211yesmaximal, characteristic, complemented
12#14583617—21no—
13#14583604—21no—
14#14583588—21no—
15#14583584—21no—
16#14583582—22no—
17#14583575—22no—
18#14583527C411yescharacteristic, complemented
19#14583520C412yescomplemented
20#14583511C412yescomplemented
21#14583475C411yescharacteristic, complemented
22#14583456C2212yes—
23#14583433C2212yes—
24#14583410C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26#14583379C411yescharacteristic, complemented
27#14583376C411yescharacteristic, complemented
28#14582960—22no—
29#14582956C2212yes—
30#14582952C2212yes—
31#14582926—21no—
32#14582863C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582855—21no—
35#14582635C2211yescharacteristic
36#14582635C2211yescharacteristic
37#14582635C2212yes—
38#14582635C2212yes—
39#14582635C2212yes—
40#14582635C2212yes—
41#14582635C2212yes—
42#14582632C2211yescharacteristic
43#14582632C2211yescharacteristic
44#14582632C2212yes—
45C2×#117×C43C2211yescharacteristic
46C43×#389—21no—
47C43×#388—22no—
48C43×#383C2212yes—
49C43×#380C2211yescharacteristic
50C4×C4⋊C4×C43—21no—
51C4×C4⋊C4×C43C2212yes—
52C4×C22⋊C4×C43C2211yescharacteristic
53C2×#10621898C2×C411yescharacteristic
54C22×Dic86C2×C411yescharacteristic
55C2×#10621877—21no—
56C22×C43⋊C8—21no—
57#13063325C2×C412yes—
58#13063325C2×C412yes—
59#13063324—21no—
60#13063320—22no—
61#13063319—22no—
62#13063318—22no—
63#13063318—22no—
64#13063317—22no—
65#13063317C2×C412yes—
66#13063316—21no—
67#13063315—22no—
68#13063315—22no—
69#13063313C2×C412yes—
70#13063311—22no—
71#13063309—22no—
72#13063308—22no—
73#13063308—21no—
74#13063307—22no—
75#13063305—21no—
76#13063305—21no—
77#13063304—22no—
78#13063304—21no—
79#13063304—21no—
80#13063304C2×C412yes—
81#13063304C2×C411yescharacteristic
82#13063304C2312yes—
83#13063304C2311yescharacteristic
84#13063303—22no—
85#13063302—22no—
86#13063299C2×C411yescharacteristic
87#13063299C2311yescharacteristic
88#13063294—21no—
89C4×Dic86—22no—
90C4×Dic86C2×C412yes—
91C4×Dic86C2×C412yes—
92C4×Dic86C2×C412yes—
93#13063290—21no—
94#13063290—21no—
95C4×D172C2×C412yes—
96C4×C22⋊D43—22no—
97C4×C22⋊D43—21no—
98C4×C22⋊D43—21no—
99(C22⋊D43)⋊C4—22no—
100#13063284—22no—
101#13063284C2×C411yescharacteristic
102#13063283—21no—
103#13063282—22no—
104#13063281—22no—
105C2×C4⋊Dic43C2×C411yescharacteristic
106C2×Dic43⋊C4—21no—
107C4⋊C4×D43—21no—
108C2×C22⋊Dic43—21no—
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
119#117×C43C2×C411yescharacteristic
120#117×C43C2×C411yescharacteristic
121#117×C43C2×C412yes—
122#117×C43D412yes—
123#117×C43D411yescharacteristic
124#117×C43D411yescharacteristic
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—22no—
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43D412yes—
132C2×C42×C43—21no—
133C2×C42×C43—22no—
134C2×C42×C43C2312yes—
135#95×C43—22no—
136#95×C43—22no—
137#95×C43C2311yescharacteristic
138#95×C43C2311yescharacteristic
139#95×C43C2312yes—
140C24×C43C2×D411yescharacteristic
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43—42no—
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—21no—
154C2×C22⋊D43—21no—
155C2×C22⋊D43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158#10621898—42no—
159C2×D172C22×C411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—22no—
162C2×Dic86—21no—
163C2×Dic86—22no—
164C2×Dic86—42no—
165C2×Dic86C22×C412yes—
166C2×Dic86C22×C411yescharacteristic
167C4⋊C4×C43—42no—
168C4⋊C4×C43—44no—
169C4⋊C4×C43C22⋊C411yescharacteristic
170C4⋊C4×C43C22⋊C411yescharacteristic
171C4⋊C4×C43C22⋊C412yes—
172C4⋊C4×C43C22⋊C411yescharacteristic
173C4⋊C4×C43C22⋊C411yescharacteristic
174C4⋊C4×C43C22⋊C412yes—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—81no—
177C22⋊C4×C43C22⋊C412yes—
178C22⋊C4×C43C22⋊C412yes—
179C22⋊C4×C43C22⋊C412yes—
180C22⋊C4×C43C22⋊C412yes—
181C42×C43—42no—
182C42×C43—82no—
183C42×C43C22×C412yes—
184C42×C43C22×C412yes—
185C42×C43C2×D412yes—
186C42×C43C2×D412yes—
187C22⋊Dic43—22no—
188C22⋊Dic43—21no—
189C22⋊Dic43—21no—
190C22⋊Dic43—22no—
191C22⋊Dic43—21no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43C22×C412yes—
202C4⋊Dic43C22×C411yescharacteristic
203C4⋊Dic43C22×C411yescharacteristic
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—21no—
211Dic43⋊C4—22no—
212Dic43⋊C4—21no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—22no—
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×C43C22×D411yescharacteristic
229C22×D43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—41no—
248C2×C4×C43C2×C22⋊C412yes—
249C2×C4×C43C2×C22⋊C412yes—
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C412yes—
252C2×C4×C43C2×C22⋊C412yes—
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C22⋊D43—42no—
257C22⋊D43—41no—
258C22⋊D43—41no—
259C22⋊D43—81no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—42no—
266C2×Dic43—81no—
267D172—41no—
268C4×D43—42no—
269C4×D43—82no—
270Dic86—42no—
271Dic86—42no—
272Dic86—41no—
273Dic86—82no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—42no—
277#17612—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×C43#57711yescharacteristic
290C22×C43#57811yescharacteristic
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—22no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—22no—
301C4×C43—42no—
302C4×C43—82no—
303C4×C43—81no—
304C4×C43#41012yes—
305Dic43—42no—
306Dic43—41no—
307Dic43—41no—
308Dic43—41no—
309Dic43—42no—
310#3495—431no—
311#2924—431no—
312#2347D4311yescharacteristic, complemented
313#1521—432no—
314#1520—431no—
315#1515—432no—
316#1513—431no—
317#1509—432no—
318#1508—431no—
319#1503—432no—
320#1501—431no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43—41no—
324C2×C43—41no—
325C2×C43C2×#41011yescharacteristic
326C2×C43#289811yescharacteristic
327C2×C43#290111yescharacteristic
328D43—81no—
329#556—861no—
330#554—861no—
331#552—862no—
332#552—861no—
333#552—861no—
334#551—862no—
335#544—431no—
336#542—432no—
337#541—432no—
338#536—431no—
339#533—432no—
340#529—432no—
341#525—431no—
342C2×C22⋊Q8—431no—
343#520—431no—
344#519—431no—
345C2×#117C2×D4311yescharacteristic
346#433—862no—
347#432—432no—
348#431—432no—
349#424—861no—
350#407—431no—
351C2×C22⋊C8—431no—
352#405—861no—
353#389—21no—
354#388—22no—
355#383C2×D4312yes—
356#380C2×D4311yescharacteristic
357C4×C4⋊C4—21no—
358C4×C4⋊C4C2×D4312yes—
359C4×C22⋊C4C2×D4311yescharacteristic
360#328—431no—
361#328—431no—
362#328—432no—
363#328—432no—
364#328—432no—
365#328—432no—
366#328—432no—
367#327—431no—
368#327—431no—
369#327—432no—
370C43#1761211yescharacteristic, complemented, Sylow
371C2×#41—431no—
372C22×Q8—431no—
373C23×C4C22×D4311yescharacteristic
374C2×M16—861no—
375C22×C8—861no—
376C4⋊Q8—432no—
377C4⋊Q8—432no—
378C4⋊Q8—861no—
379#126—862no—
380#126—862no—
381#126—862no—
382#126—862no—
383#125—432no—
384#125—862no—
385#125—862no—
386#125—861no—
387#125—862no—
388#124—432no—
389#124—862no—
390#123—861no—
391#123—862no—
392#123—862no—
393#123—862no—
394C22⋊Q8—432no—
395C22⋊Q8—431no—
396C22⋊Q8—432no—
397C22⋊Q8—431no—
398C22⋊Q8—861no—
399C22⋊Q8—861no—
400C22⋊Q8—862no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405#121—431no—
406#121—431no—
407#120—861no—
408C4×Q8—432no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—861no—
412C4×Q8—861no—
413C4×Q8—862no—
414C4×D4—432no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—862no—
418C4×D4—862no—
419#117—431no—
420#117—862no—
421#117—861no—
422#117—862no—
423#117—862no—
424#117C4×D4311yescharacteristic
425#117C4×D4311yescharacteristic
426#117C4×D4312yes—
427#117D17211yescharacteristic
428#117D17212yes—
429#117D17211yescharacteristic
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4C22⋊D4311yescharacteristic
436C2×C4⋊C4C22⋊D4311yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4C22⋊D4312yes—
441C2×C42—21no—
442C2×C42—22no—
443C2×C42C22×D4312yes—
444C4⋊C8—862no—
445C4⋊C8—862no—
446C22⋊C8—431no—
447C22⋊C8—431no—
448C22⋊C8—432no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451#97—862no—
452C4×C8—862no—
453#95—22no—
454#95—22no—
455#95C22×D4311yescharacteristic
456#95C22×D4311yescharacteristic
457#95C22×D4312yes—
458C24C2×C22⋊D4311yescharacteristic
459#41—1722no—
460C2×Q8—432no—
461C2×Q8—431no—
462C2×Q8—862no—
463C2×Q8—861no—
464C2×Q8—1722no—
465C2×D4—431no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—42no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—862no—
476C22×C4—861no—
477C22×C4C2×C4×D4311yescharacteristic
478C22×C4C2×C4×D4311yescharacteristic
479C22×C4C2×D17211yescharacteristic
480C22×C4C2×D17211yescharacteristic
481C22×C4C2×C22⋊D4312yes—
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4312yes—
484C22×C4C23×D4311yescharacteristic
485M16—1722no—
486C2×C8—861no—
487C2×C8—862no—
488C2×C8—861no—
489C2×C8—1722no—
490C4⋊C4—42no—
491C4⋊C4—44no—
492C4⋊C4—432no—
493C4⋊C4—431no—
494C4⋊C4—431no—
495C4⋊C4—861no—
496C4⋊C4—862no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—861no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—861no—
508C4⋊C4(C2×D43)⋊C411yescharacteristic
509C4⋊C4(C2×D43)⋊C411yescharacteristic
510C4⋊C4(C2×D43)⋊C412yes—
511C4⋊C4(C2×D43)⋊C411yescharacteristic
512C4⋊C4(C2×D43)⋊C411yescharacteristic
513C4⋊C4(C2×D43)⋊C412yes—
514C22⋊C4—42no—
515C22⋊C4—81no—
516C22⋊C4—862no—
517C22⋊C4—861no—
518C22⋊C4—861no—
519C22⋊C4—862no—
520C22⋊C4—861no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—861no—
524C22⋊C4—862no—
525C22⋊C4—861no—
526C22⋊C4(C2×D43)⋊C412yes—
527C22⋊C4(C2×D43)⋊C412yes—
528C22⋊C4(C2×D43)⋊C412yes—
529C22⋊C4(C2×D43)⋊C412yes—
530C42—42no—
531C42—82no—
532C42—861no—
533C42—862no—
534C42—862no—
535C42—862no—
536C42C2×C4×D4312yes—
537C42C2×C4×D4312yes—
538C42C2×D17212yes—
539C42C2×D17212yes—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—861no—
545C23C2×(C2×D43)⋊C411yescharacteristic
546C23C2×(C2×D43)⋊C411yescharacteristic
547C23C22×C22⋊D4311yescharacteristic
548Q8—3442no—
549Q8—1722no—
550Q8—1721no—
551Q8—1722no—
552D4—3441no—
553D4—1721no—
554D4—1722no—
555D4—1721no—
556D4—1721no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—862no—
578C2×C4—861no—
579C2×C4—862no—
580C2×C4—3442no—
581C2×C4—3441no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4C2×(C2×D43)⋊C412yes—
585C2×C4C2×(C2×D43)⋊C412yes—
586C2×C4C2×(C2×D43)⋊C412yes—
587C2×C4C2×(C2×D43)⋊C412yes—
588C2×C4C2×(C2×D43)⋊C411yescharacteristic
589C2×C4C2×(C2×D43)⋊C411yescharacteristic
590C2×C4C22×C4×D4311yescharacteristic
591C2×C4C22×D17211yescharacteristic
592C8—1721no—
593C8—1721no—
594C8—1722no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—81no—
604C22—81no—
605C22—1721no—
606C22—1721no—
607C22—1721no—
608C22C22×(C2×D43)⋊C411yescharacteristic
609C22#1458371011yescharacteristic
610C22#1458371411yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—22no—
615C4—22no—
616C4—22no—
617C4—22no—
618C4—42no—
619C4—82no—
620C4—81no—
621C4—1721no—
622C4—1722no—
623C4—1721no—
624C4—1722no—
625C4—1721no—
626C4#1458287212yes—
627C2—21no—
628C2—21no—
629C2—41no—
630C2—41no—
631C2—3441no—
632C2C2×#1458287211yescharacteristic
633C2#1914312511yescharacteristic
634C2#1914314311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2347C2
socleC22×C43C22×C22⋊C4
prime radical#14583410C22
cosocleC22×C4×C43C24
hypercenter#2347D43
hypocenterC43#17612
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #19143253C2semidirect
3. #19133170C2semidirect
4. #19133166C2semidirect
5. #19133145C2semidirect
7. #19133118C2semidirect
8. #19133114C2semidirect
9. #19133093C2semidirect
11. C43×#2347C2semidirect
18. #14583527C4semidirect
19. #14583520C4semidirect
20. #14583511C4semidirect
21. #14583475C4semidirect
26. #14583379C4semidirect
27. #14583376C4semidirect
312. #2347D43semidirect
370. C43#17612semidirect

Maximal subgroups

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

subgroupindex
#191483472
#191432532
#191331702
#191331662
#191331452
#191331362
#191331182
#191331142
#191330932
#191330842
C43×#23472
#1761243