Finite Group Databasebeta

← #25064833

Subgroups — #25064833

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148515C211yesmaximal, characteristic
2#19143612C211yesmaximal, characteristic, complemented
3#19143607C211yesmaximal, characteristic, complemented
4#19133223C212yesmaximal, complemented
5#19133212C212yesmaximal, complemented
6#19133199C212yesmaximal, complemented
7#19133198C211yesmaximal, characteristic, complemented
8#19133198C211yesmaximal, characteristic, complemented
9#19133187C211yesmaximal, characteristic, complemented
10#19133180C212yesmaximal, complemented
11C43×#1536C211yesmaximal, characteristic, complemented
12#14583595—21no—
13#14583595—21no—
14#14583592—22no—
15#14583592—22no—
16#14583589—21no—
17#14583589—21no—
18#14583510C412yes—
19#14583503C412yes—
20#14583477C411yescharacteristic
21#14583477C411yescharacteristic
22#14583428C2212yes—
23#14583428C2212yes—
24C2×#13063317C2211yescharacteristic
25#14583382C411yescharacteristic
26#14583382C411yescharacteristic
27C4×#10621898C2211yescharacteristic
28#14583026—21no—
29#14583023—21no—
30#14582976—21no—
31#14582974—22no—
32#14582973—22no—
33#14582964—21no—
34#14582954C2212yes—
35#14582954C2212yes—
36C4×#10621877C2211yescharacteristic
37C4×#10621877C2211yescharacteristic
38#14582851C2212yes—
39#97×D43C2212yes—
40#14582640C2212yes—
41#14582640C2212yes—
42#14582640C2212yes—
43#14582640C2212yes—
44#14582639C2211yescharacteristic
45#14582639C2211yescharacteristic
46#14582639C2211yescharacteristic
47#14582639C2211yescharacteristic
48C43×#532C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#432C2211yescharacteristic
51C43×#329C2212yes—
52C43×#329C2212yes—
53C2×#10621898C2×C411yescharacteristic
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621872—22no—
57C2×C8×D43—22no—
58#13063320—22no—
59#13063320—22no—
60#13063318—22no—
61#13063318—22no—
62#13063317—21no—
63#13063317—21no—
64#13063317C2×C412yes—
65#13063317C2312yes—
66#13063315—22no—
67#13063315—22no—
68#13063307—22no—
69#13063307—22no—
70#13063306—22no—
71#13063306—22no—
72#13063304—21no—
73#13063304—21no—
74#13063301C2×C412yes—
75#13063301C2×C412yes—
76#13063299—21no—
77#13063299—21no—
78#13063297—22no—
79#13063297—22no—
80#13063297—22no—
81#13063297—22no—
82#13063296C2×C412yes—
83#13063296C2×C412yes—
84Q8×Dic43C2×C412yes—
85Q8×Dic43C2×C412yes—
86C4×Dic86D411yescharacteristic
87C4×Dic86D411yescharacteristic
88C4×D172D411yescharacteristic
89C4×D172D411yescharacteristic
90D4×Dic43—22no—
91D4×Dic43—22no—
92D4×Dic43C2×C412yes—
93D4×Dic43C2×C412yes—
94C4×C22⋊D43D412yes—
95C4×C22⋊D43D412yes—
96(C22⋊D43)⋊C4—22no—
97(C22⋊D43)⋊C4—22no—
98#13063284—21no—
99#13063284—21no—
100#13063284C2×C411yescharacteristic
101#13063282C2×C412yes—
102#13063281—22no—
103#13063281—22no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43C2×C411yescharacteristic
107C2×C4⋊Dic43C2×C411yescharacteristic
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C42×D43C2312yes—
111Dic43⋊C8—22no—
112Dic43⋊C8—22no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8—22no—
115#13063236C2311yescharacteristic
116#13063236C2311yescharacteristic
117#13063236C2311yescharacteristic
118#13063236C2311yescharacteristic
119#13063235—22no—
120C4×C43⋊C8—21no—
121C4×C43⋊C8—21no—
122C8×Dic43—22no—
123C2×#41×C43C2×C411yescharacteristic
124C2×#41×C43C2×C411yescharacteristic
125C4⋊Q8×C43C2×C411yescharacteristic
126#127×C43C2×C411yescharacteristic
127#124×C43C2311yescharacteristic
128#124×C43C2311yescharacteristic
129#121×C43—21no—
130#121×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43C2312yes—
139#97×C43C2312yes—
140#41×C43—42no—
141#41×C43—42no—
142C2×Q8×C43C22×C411yescharacteristic
143C2×Q8×C43C22×C411yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43C22×C411yescharacteristic
149C2×D4×C43C22×C411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43C22⋊C412yes—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162#10621898—42no—
163C2×D172C22⋊C411yescharacteristic
164C2×C4×D43C22×C412yes—
165C2×C4×D43C2×D412yes—
166C2×C4×D43C2×D412yes—
167C2×Dic86C22⋊C411yescharacteristic
168C2×C8×C43—22no—
169C2×C8×C43—22no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C42×C43C22×C411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43C2411yescharacteristic
180C22⋊Dic43—22no—
181C22⋊Dic43—22no—
182C22⋊Dic43—22no—
183C22⋊Dic43—22no—
184C22⋊Dic43C22⋊C412yes—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4C22⋊C412yes—
188(C2×D43)⋊C4C22⋊C412yes—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43C22⋊C411yescharacteristic
194C4⋊Dic43C22⋊C411yescharacteristic
195C4⋊Dic43C22×C412yes—
196C4⋊Dic43C22×C412yes—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4C22⋊C412yes—
204Dic43⋊C4C22⋊C412yes—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43C22×C412yes—
208C4×Dic43C2×D412yes—
209C4×Dic43C2×D412yes—
210#10621877—42no—
211#10621877—42no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216#10621872—44no—
217C8×D43—44no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43C2×C22⋊C411yescharacteristic
221C22×D43C2×C22⋊C412yes—
222Q8×C43—41no—
223Q8×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—42no—
227D4×C43—42no—
228D4×C43—81no—
229D4×C43—81no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43C2×C22⋊C411yescharacteristic
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C22⋊D43—42no—
244C22⋊D43—82no—
245C22⋊D43—82no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—82no—
249C2×Dic43—82no—
250C2×Dic43—81no—
251C2×Dic43—81no—
252C2×Dic43C2×C22⋊C412yes—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255D172—22no—
256C4×D43—42no—
257C4×D43—42no—
258C4×D43—42no—
259Dic86—22no—
260C8×C43—42no—
261C8×C43—42no—
262C43⋊C8—22no—
263C43⋊C8—22no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266#17687—431nomaximal, Sylow
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43C22×C22⋊C411yescharacteristic
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—22no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43#41312yes—
288Dic43—22no—
289Dic43—22no—
290Dic43—22no—
291Dic43—42no—
292Dic43—42no—
293#3512—431no—
294#2971—431no—
295#2970—431no—
296#1536D4311yescharacteristic, complemented
297#1535—432no—
298#1532—432no—
299#1529—432no—
300#1528—431no—
301#1528—431no—
302#1525—431no—
303#1524—432no—
304C2×C43—41no—
305C2×C43—81no—
306C2×C43—81no—
307C2×C43C2×#41311yescharacteristic
308C2×C43#290111yescharacteristic
309C2×C43#290111yescharacteristic
310D43—42no—
311#553—861no—
312#553—861no—
313#553—862no—
314#553—862no—
315#552—861no—
316#552—861no—
317#541—432no—
318#540—432no—
319#537—431no—
320#537—431no—
321#532C2×D4311yescharacteristic
322#529—432no—
323#529—432no—
324C2×#125—431no—
325#520—431no—
326#520—431no—
327C4×#41—431no—
328#446—861no—
329C8×Q8—861no—
330#436—862no—
331#436—861no—
332#435—862no—
333C8×D4—861no—
334#432—432no—
335#432—432no—
336#432C2×D4311yescharacteristic
337#432C2×D4311yescharacteristic
338C4×M16—431no—
339C4×M16—431no—
340C4×M16—432no—
341C2×#97—432no—
342#330—432no—
343#330—432no—
344#330—432no—
345#330—432no—
346#329—431no—
347#329—431no—
348#329—431no—
349#329—431no—
350#329C2×D4312yes—
351#329C2×D4312yes—
352C43#1768711yescharacteristic, complemented, Sylow
353C2×#41—431no—
354C2×#41C4×D4311yescharacteristic
355C2×#41C4×D4311yescharacteristic
356C2×M16—862no—
357C2×M16—861no—
358C2×M16—861no—
359C22×C8—862no—
360C4⋊Q8C4×D4311yescharacteristic
361#127C4×D4311yescharacteristic
362#126—862no—
363#126—862no—
364#126—862no—
365#126—862no—
366#125—432no—
367#125—432no—
368#125—862no—
369#125—862no—
370#125—861no—
371#125—861no—
372#124C22×D4311yescharacteristic
373#124C22×D4311yescharacteristic
374#123—862no—
375#123—862no—
376#123—862no—
377#123—862no—
378C22⋊Q8—432no—
379C22⋊Q8—432no—
380C22⋊Q8—861no—
381C22⋊Q8—861no—
382#121—21no—
383#121—21no—
384#121—432no—
385#121—432no—
386#121—862no—
387#121—862no—
388#121—861no—
389#121—861no—
390#121—862no—
391#121—862no—
392C4×Q8—431no—
393C4×Q8—431no—
394C4×Q8—432no—
395C4×Q8—432no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—432no—
399C4×D4—432no—
400C4×D4—432no—
401C4×D4—432no—
402C4×D4—431no—
403C4×D4—431no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—862no—
407C4×D4—862no—
408#117—431no—
409#117—432no—
410#117—862no—
411#117—862no—
412#117—861no—
413#117—861no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C42—432no—
421C2×C42C22×D4311yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—862no—
425C4⋊C8—862no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—862no—
429C22⋊C8—862no—
430#97—431no—
431#97—431no—
432#97—431no—
433#97—431no—
434#97—862no—
435#97C22×D4312yes—
436#97C22×D4312yes—
437C4×C8—862no—
438C4×C8—861no—
439C4×C8—861no—
440#41—42no—
441#41—42no—
442#41—1722no—
443C2×Q8—431no—
444C2×Q8C2×C4×D4311yescharacteristic
445C2×Q8C2×C4×D4311yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—432no—
451C2×D4—431no—
452C2×D4—862no—
453C2×D4—862no—
454C2×D4C2×C4×D4311yescharacteristic
455C2×D4C2×C4×D4311yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4D4×D4311yescharacteristic
468M16—1724no—
469M16—1722no—
470M16—1722no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—1724no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—431no—
481C4⋊C4—431no—
482C4⋊C4—432no—
483C4⋊C4—432no—
484C4⋊C4—432no—
485C4⋊C4—432no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C4⋊C4—862no—
489C4⋊C4—862no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—432no—
501C22⋊C4—432no—
502C22⋊C4—432no—
503C22⋊C4—862no—
504C22⋊C4—862no—
505C22⋊C4—862no—
506C22⋊C4—862no—
507C22⋊C4—862no—
508C22⋊C4—862no—
509C42—432no—
510C42—432no—
511C42—432no—
512C42—862no—
513C42—862no—
514C42C2×C4×D4311yescharacteristic
515C42D4×D4311yescharacteristic
516C42D4×D4311yescharacteristic
517C42C23×D4311yescharacteristic
518C23—21no—
519C23—21no—
520C23—432no—
521C23C22⋊C4×D4311yescharacteristic
522Q8—41no—
523Q8—41no—
524Q8—862no—
525D4—41no—
526D4—41no—
527D4—42no—
528D4—42no—
529D4—81no—
530D4—81no—
531D4—862no—
532D4—3442no—
533D4—3442no—
534D4—1722no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—3442no—
548C2×C4—3442no—
549C2×C4—3441no—
550C2×C4—3441no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4C22⋊C4×D4311yescharacteristic
555C2×C4C22⋊C4×D4311yescharacteristic
556C2×C4C22⋊C4×D4311yescharacteristic
557C2×C4C22×C4×D4311yescharacteristic
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C8—42no—
561C8—42no—
562C8—862no—
563C8—862no—
564C8—1721no—
565C8—1721no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—862no—
576C22—862no—
577C22—862no—
578C22C2×C22⋊C4×D4311yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—41no—
585C4—41no—
586C4—862no—
587C4—862no—
588C4—862no—
589C4—1722no—
590C4—1722no—
591C4#1458288012yes—
592C2—41no—
593C2—81no—
594C2—81no—
595C2—1722no—
596C2C2×#1458288011yescharacteristic
597C2#1914314111yescharacteristic
598C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1536C2
socleC22×C43C22×C22⋊C4
prime radical#19148515C2
cosocleC42×C43C24
hypercenter#1536D43
hypocenterC43#17687
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1536

Complements

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

NH ≅ G/Ntype
2. #19143612C2semidirect
3. #19143607C2semidirect
4. #19133223C2semidirect
5. #19133212C2semidirect
6. #19133199C2semidirect
7. #19133198C2semidirect
8. #19133198C2semidirect
9. #19133187C2semidirect
10. #19133180C2semidirect
11. C43×#1536C2semidirect
296. #1536D43semidirect
352. C43#17687semidirect

Maximal subgroups

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

subgroupindex
#191485152
#191436122
#191436072
#191332232
#191332122
#191331992
#191331982
#191331872
#191331802
C43×#15362
#1768743