Finite Group Databasebeta

← #25064157

Subgroups — #25064157

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148646C211yesmaximal, characteristic
2#19143629C211yesmaximal, characteristic, complemented
3#19137239C211yesmaximal, characteristic, complemented
4#19133165C212yesmaximal, complemented
5#19133148C212yesmaximal, complemented
6#19133135C212yesmaximal, complemented
7#19133126C212yesmaximal, complemented
8#19133120C211yesmaximal, characteristic, complemented
9#19133106C211yesmaximal, characteristic, complemented
10#19133095C211yesmaximal, characteristic, complemented
11C43×#1500C211yesmaximal, characteristic, complemented
12#14583622C411yescharacteristic, complemented
13#14583606—21no—
14#14583587C412yescomplemented
15#14583572—22no—
16Q8×D172C411yescharacteristic, complemented
17#14583557C412yescomplemented
18#14583554C411yescharacteristic, complemented
19#14583553C411yescharacteristic, complemented
20#14583545—21no—
21#14583520—21no—
22#14583490—22no—
23#14583456C2211yescharacteristic
24#14583409C2212yes—
25C22⋊Q8×D43C2212yes—
26#14583379—21no—
27C2×C4×D172C2211yescharacteristic
28#14582978—21no—
29#14582969—22no—
30C8×D172—21no—
31#14582956C2211yescharacteristic
32#14582861C2212yes—
33C22⋊C8×D43C2212yes—
34#14582801—21no—
35#14582797—21no—
36#14582788—22no—
37#14582761C2212yes—
38#14582758C2212yes—
39C4×C4⋊Dic43C2211yescharacteristic
40#14582637C2212yes—
41#14582637C2212yes—
42#14582636C2212yes—
43#14582635C2212yes—
44#14582635C2212yes—
45#14582633C2212yes—
46C43×#529C2211yescharacteristic
47C43×#431C2211yescharacteristic
48C43×#376C2211yescharacteristic
49C43×#328C2211yescharacteristic
50C43×#328C2211yescharacteristic
51C43×#327C2211yescharacteristic
52C43×#327C2211yescharacteristic
53C2×#10621898—21no—
54C2×#10621900C2×C412yes—
55C2×Q8×D43C2×C412yes—
56C22×D172D411yescharacteristic
57C22×C4×D43C2312yes—
58C2×#10621872—22no—
59C2×C8×D43—22no—
60#13063325—21no—
61#13063325C2×C411yescharacteristic
62#13063325C2×C411yescharacteristic
63#13063320—22no—
64#13063320—22no—
65#13063317—21no—
66#13063316—22no—
67#13063313—21no—
68#13063311—22no—
69#13063310—22no—
70#13063309—22no—
71#13063307—22no—
72#13063307—22no—
73#13063305—22no—
74#13063305C2×C412yes—
75#13063305C2×C412yes—
76#13063304—21no—
77#13063304—21no—
78#13063304C2312yes—
79#13063303—22no—
80#13063302—22no—
81#13063302—22no—
82#13063301C2×C412yes—
83#13063299—21no—
84#13063298—22no—
85#13063296C2×C412yes—
86#13063293—22no—
87C4×Dic86—21no—
88C4×Dic86—21no—
89C4×Dic86C2×C412yes—
90C4×D172—21no—
91C4×D172C2×C411yescharacteristic
92C4×D172C2×C411yescharacteristic
93C4×D172C2×C412yes—
94C4×D172D411yescharacteristic
95C4×D172D411yescharacteristic
96C4×D172D412yes—
97D4×Dic43—22no—
98(C22⋊D43)⋊C4—22no—
99(C22⋊D43)⋊C4—22no—
100#13063284—21no—
101#13063283—22no—
102#13063283C2×C412yes—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43D411yescharacteristic
106C2×Dic43⋊C4—22no—
107C4⋊C4×D43—22no—
108C4⋊C4×D43C2×C412yes—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4D412yes—
112C22⋊C4×D43—22no—
113C2×C4×Dic43—21no—
114C4⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)C2312yes—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118#13063236—21no—
119C43⋊#95—22no—
120C43⋊#95C2312yes—
121#126×C43—21no—
122#125×C43C2×C411yescharacteristic
123#124×C43C2×C411yescharacteristic
124#123×C43—21no—
125C22⋊Q8×C43C2311yescharacteristic
126#121×C43C2311yescharacteristic
127C4×Q8×C43C2×C411yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2×C411yescharacteristic
130#117×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C22⋊C8×C43C2311yescharacteristic
135C22⋊C8×C43C2311yescharacteristic
136C4×C8×C43—21no—
137#95×C43—21no—
138#95×C43C2311yescharacteristic
139#95×C43C2311yescharacteristic
140C23×D43C2×D412yes—
141C2×Q8×C43C22×C411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43C22×C411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43C2×D412yes—
155Q8×D43—82no—
156#10621900—82no—
157#10621898—44no—
158C2×D172—42no—
159C2×D172C22⋊C411yescharacteristic
160C2×D172C22⋊C411yescharacteristic
161C2×D172C22⋊C412yes—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—82no—
165C2×C4×D43C22×C412yes—
166C2×C4×D43C22×C412yes—
167C2×C4×D43C2×D412yes—
168C2×C4×D43C2×D412yes—
169C2×Dic86—21no—
170C2×Dic86—22no—
171C2×Dic86C22×C412yes—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C22×C411yescharacteristic
179C4⋊C4×C43C22×C411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C42×C43—21no—
186C42×C43—42no—
187C42×C43C22×C411yescharacteristic
188C42×C43C22×C411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—82no—
198(C2×D43)⋊C4—82no—
199(C2×D43)⋊C4C22⋊C412yes—
200(C2×D43)⋊C4C22⋊C412yes—
201(C2×D43)⋊C4C22⋊C412yes—
202(C2×D43)⋊C4C22⋊C412yes—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—22no—
207C4⋊Dic43—22no—
208C4⋊Dic43—42no—
209C4⋊Dic43C22⋊C411yescharacteristic
210C4⋊Dic43C22⋊C412yes—
211C4⋊Dic43C22⋊C411yescharacteristic
212C4⋊Dic43C22×C412yes—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—82no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43—81no—
221C2×C43⋊C8—22no—
222#10621872—82no—
223C8×D43—82no—
224C23×C43—21no—
225C23×C43C22×D411yescharacteristic
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—42no—
229C22×D43—42no—
230C22×D43C2×C22⋊C412yes—
231C22×D43C2×C22⋊C412yes—
232Q8×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—42no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C22⋊D43—44no—
257C22⋊D43—82no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—82no—
265C2×Dic43C2×C22⋊C412yes—
266C2×Dic43C2×C22⋊C412yes—
267D172—22no—
268D172—22no—
269D172—42no—
270C4×D43—42no—
271C4×D43—42no—
272C4×D43—42no—
273C4×D43—42no—
274C4×D43—44no—
275C4×D43—82no—
276Dic86—42no—
277Dic86—42no—
278Dic86—82no—
279C8×C43—41no—
280C8×C43—41no—
281C43⋊C8—42no—
282#17600—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43C22×C22⋊C411yescharacteristic
289C22×C43#57711yescharacteristic
290C22×C43#57811yescharacteristic
291C2×D43—22no—
292C2×D43—22no—
293C2×D43—22no—
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—82no—
298C2×D43—82no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43#42112yes—
310Dic43—22no—
311Dic43—22no—
312Dic43—42no—
313Dic43—42no—
314Dic43—82no—
315#3520—431no—
316#2974—431no—
317#2319—431no—
318#1520—432no—
319#1516—432no—
320#1513—432no—
321#1511—432no—
322#1509—431no—
323#1506—431no—
324#1503—431no—
325#1500D4311yescharacteristic, complemented
326C2×C43—21no—
327C2×C43—21no—
328C2×C43—81no—
329C2×C43#288311yescharacteristic
330C2×C43#289811yescharacteristic
331C2×C43C2×#42111yescharacteristic
332D43—42no—
333D43—42no—
334#556—431no—
335#554—861no—
336#552—432no—
337#551—862no—
338D4×Q8—431no—
339#548—432no—
340#547—431no—
341#547—431no—
342#546—861no—
343#542—861no—
344#539—862no—
345#533—431no—
346#529C2×D4311yescharacteristic
347#525—432no—
348C2×C22⋊Q8—432no—
349#520—861no—
350C2×C4×D4—431no—
351#436—861no—
352#435—862no—
353C8×D4—861no—
354#432—431no—
355#431C2×D4311yescharacteristic
356#407—432no—
357C2×C22⋊C8—432no—
358#390—861no—
359#389—861no—
360#388—862no—
361#381—432no—
362#380—432no—
363C4×C4⋊C4—431no—
364#376C2×D4311yescharacteristic
365#328—432no—
366#328—432no—
367#328—432no—
368#328—432no—
369#328—432no—
370#328C2×D4311yescharacteristic
371#328C2×D4311yescharacteristic
372#327—432no—
373#327C2×D4311yescharacteristic
374#327C2×D4311yescharacteristic
375C43#1760011yescharacteristic, complemented, Sylow
376C2×#41—432no—
377C2×#41—861no—
378C22×Q8—432no—
379C22×D4—431no—
380C23×C4—432no—
381C2×M16—862no—
382C22×C8—862no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8—861no—
386#126—21no—
387#126—862no—
388#126—862no—
389#125—862no—
390#125—861no—
391#125C4×D4311yescharacteristic
392#124—861no—
393#124—862no—
394#124C4×D4311yescharacteristic
395#123—21no—
396#123—862no—
397#123—862no—
398#123—862no—
399#123—862no—
400C22⋊Q8—432no—
401C22⋊Q8—432no—
402C22⋊Q8—432no—
403C22⋊Q8—432no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407C22⋊Q8—862no—
408C22⋊Q8—861no—
409C22⋊Q8—861no—
410C22⋊Q8C22×D4311yescharacteristic
411#121—432no—
412#121—862no—
413#121—861no—
414#121C22×D4311yescharacteristic
415#120—862no—
416C4×Q8—432no—
417C4×Q8—861no—
418C4×Q8—861no—
419C4×Q8C4×D4311yescharacteristic
420C4×D4—21no—
421C4×D4—431no—
422C4×D4—431no—
423C4×D4—432no—
424C4×D4—431no—
425C4×D4—432no—
426C4×D4—431no—
427C4×D4—861no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4C4×D4311yescharacteristic
432#117—21no—
433#117—432no—
434#117—862no—
435#117—861no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—432no—
438C2×C4⋊C4—862no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—862no—
441C2×C4⋊C4—861no—
442C2×C22⋊C4—432no—
443C2×C22⋊C4—862no—
444C2×C22⋊C4—862no—
445C2×C22⋊C4—862no—
446C2×C42—21no—
447C2×C42—861no—
448C2×C42C22×D4311yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—861no—
451C22⋊C8—432no—
452C22⋊C8—862no—
453C22⋊C8—862no—
454C22⋊C8C22×D4311yescharacteristic
455C22⋊C8C22×D4311yescharacteristic
456#97—861no—
457C4×C8—21no—
458#95—21no—
459#95—432no—
460#95—862no—
461#95C22×D4311yescharacteristic
462#95C22×D4311yescharacteristic
463C24—432no—
464#41—3442no—
465#41—1724no—
466C2×Q8—432no—
467C2×Q8—862no—
468C2×Q8—861no—
469C2×Q8—3442no—
470C2×Q8C2×C4×D4311yescharacteristic
471C2×D4—21no—
472C2×D4—431no—
473C2×D4—431no—
474C2×D4—432no—
475C2×D4—862no—
476C2×D4—862no—
477C2×D4—1722no—
478C2×D4C2×C4×D4311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—432no—
483C22×C4—432no—
484C22×C4—432no—
485C22×C4—432no—
486C22×C4—432no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—3442no—
492C22×C4D4×D4311yescharacteristic
493C22×C4D4×D4311yescharacteristic
494C22×C4C23×D4311yescharacteristic
495M16—3442no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—862no—
499C2×C8—3442no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—431no—
505C4⋊C4—432no—
506C4⋊C4—431no—
507C4⋊C4—432no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—3442no—
518C4⋊C4—1722no—
519C4⋊C4C2×C4×D4311yescharacteristic
520C4⋊C4C2×C4×D4311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—432no—
527C22⋊C4—432no—
528C22⋊C4—432no—
529C22⋊C4—432no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—3442no—
537C22⋊C4—3442no—
538C42—21no—
539C42—42no—
540C42—862no—
541C42—862no—
542C42—3441no—
543C42C2×C4×D4311yescharacteristic
544C42C2×C4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C23—21no—
548C23—432no—
549C23—432no—
550C23—862no—
551C23—862no—
552C23—1722no—
553C23—1722no—
554C23C2×D4×D4311yescharacteristic
555Q8—41no—
556Q8—3442no—
557Q8—1722no—
558Q8—1722no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—862no—
563D4—862no—
564D4—3442no—
565D4—1722no—
566D4—1724no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—3442no—
586C2×C4—3442no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1724no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C22⋊C4×D4311yescharacteristic
598C2×C4C22⋊C4×D4311yescharacteristic
599C2×C4C22⋊C4×D4311yescharacteristic
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C8—41no—
603C8—41no—
604C8—1722no—
605C22—21no—
606C22—21no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—862no—
611C22—862no—
612C22—862no—
613C22—862no—
614C22—862no—
615C22—862no—
616C22—3442no—
617C22—3442no—
618C22C2×C22⋊C4×D4311yescharacteristic
619C22#1458370611yescharacteristic
620C22#1458371311yescharacteristic
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—81no—
630C4—81no—
631C4—862no—
632C4—862no—
633C4—3442no—
634C4—1722no—
635C4—1722no—
636C4#1458291412yes—
637C2—21no—
638C2—21no—
639C2—81no—
640C2—1722no—
641C2—1722no—
642C2#1914305411yescharacteristic
643C2#1914312411yescharacteristic
644C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1500C2
socleC22×C43C22×C22⋊C4
prime radical#19148646C2
cosocleC22×C4×C43C24
hypercenter#1500D43
hypocenterC43#17600
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #19143629C2semidirect
3. #19137239C2semidirect
4. #19133165C2semidirect
5. #19133148C2semidirect
6. #19133135C2semidirect
7. #19133126C2semidirect
8. #19133120C2semidirect
9. #19133106C2semidirect
10. #19133095C2semidirect
11. C43×#1500C2semidirect
12. #14583622C4semidirect
14. #14583587C4semidirect
16. Q8×D172C4semidirect
17. #14583557C4semidirect
18. #14583554C4semidirect
19. #14583553C4semidirect
325. #1500D43semidirect
375. C43#17600semidirect

Maximal subgroups

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

subgroupindex
#191486462
#191436292
#191372392
#191331652
#191331482
#191331352
#191331262
#191331202
#191331062
#191330952
C43×#15002
#1760043