Finite Group Databasebeta

← #25082037

Subgroups — #25082037

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145530C211yesmaximal, characteristic, complemented
2#19144747C211yesmaximal, characteristic, complemented
3#19144656C211yesmaximal, characteristic, complemented
4#19143703C211yesmaximal, characteristic, complemented
5#19134054C211yesmaximal, characteristic, complemented
6#19134047C211yesmaximal, characteristic, complemented
7#19134012C211yesmaximal, characteristic, complemented
8#19134005C211yesmaximal, characteristic, complemented
9#19133956C211yesmaximal, characteristic, complemented
10#19133951C211yesmaximal, characteristic, complemented
11#19133944C211yesmaximal, characteristic, complemented
12#19133937C211yesmaximal, characteristic, complemented
13#19133291C211yesmaximal, characteristic, complemented
14#19133242C211yesmaximal, characteristic, complemented
15C43×#1572C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583449C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583276C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583224—21no—
24#14583224—21no—
25#14583195C2211yescharacteristic
26#14583190C2211yescharacteristic
27#14583185C2211yescharacteristic
28#14583180C2211yescharacteristic
29#14583115—21no—
30#14583115—21no—
31#14583100C2211yescharacteristic
32#14583100C2211yescharacteristic
33#14583095C2211yescharacteristic
34#14583095C2211yescharacteristic
35#14583046—21no—
36#14583046—21no—
37#14583046—21no—
38#14583046—21no—
39C8×Dic86C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14583012—21no—
42#14583001—21no—
43C4×#10621873—21no—
44C4×D344—21no—
45C8×D172C2211yescharacteristic
46C8×D172C2211yescharacteristic
47(C22⋊D43)⋊C8—21no—
48(C22⋊D43)⋊C8—21no—
49#14582951—21no—
50C2×C4⋊(C43⋊C8)C2211yescharacteristic
51C4⋊C8×D43—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56#14582642C2211yescharacteristic
57#14582642C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898—21no—
69C2×#10621898D411yescharacteristic
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×D344—21no—
75C2×D344—21no—
76C2×D344—21no—
77C2×D344—21no—
78C22×C43⋊C8—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81#13063325C2311yescharacteristic
82#13063325C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063322C2311yescharacteristic
85#13063313—21no—
86#13063313—21no—
87#13063299—21no—
88#13063299—21no—
89#13063299—21no—
90#13063299—21no—
91C4×Dic86D411yescharacteristic
92C4×Dic86C2311yescharacteristic
93C4×D172—21no—
94C4×D172—21no—
95C4×D172—21no—
96C4×D172—21no—
97C4×D172D411yescharacteristic
98C4×D172C2311yescharacteristic
99C4×C22⋊D43—21no—
100C4×C22⋊D43—21no—
101#13063284D411yescharacteristic
102#13063282—21no—
103C42×D43—21no—
104#13063259—21no—
105#13063259—21no—
106#13063257—21no—
107#13063257—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063247—21no—
124#13063247—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×C22⋊D43—41no—
149C2×C22⋊D43—41no—
150#10621898—22no—
151#10621898—22no—
152#10621898—81no—
153#10621898—81no—
154#10621898—82no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—41no—
166C2×C4×D43—41no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86C2×D411yescharacteristic
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43#4111yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4—41no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C2×D411yescharacteristic
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203D344—42no—
204D344—42no—
205D344—81no—
206D344—81no—
207#10621873—42no—
208#10621873—42no—
209#10621873—81no—
210#10621873—81no—
211C8×D43—81no—
212C8×D43—81no—
213C23×C43#12111yescharacteristic
214C22×D43—21no—
215C22×D43—41no—
216C22×D43—41no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—24no—
229C22⋊D43—82no—
230C22⋊D43—82no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236D172—21no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—81no—
246D172—81no—
247D172#13512yes—
248C4×D43—24no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—81no—
252C4×D43—82no—
253C4×D43—82no—
254Dic86—21no—
255Dic86—41no—
256Dic86—41no—
257Dic86—81no—
258Dic86#13512yes—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19412—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43C2×#12111yescharacteristic
274C2×D43—22no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43C2×#13511yescharacteristic
288C4×C43C2×#13511yescharacteristic
289C4×C43#57611yescharacteristic
290C4×C43#57711yescharacteristic
291Dic43—22no—
292Dic43—41no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296#3207—431no—
297#3115—431no—
298#3106—431no—
299#2988—431no—
300#1684—431no—
301#1683—431no—
302#1678—431no—
303#1677—431no—
304#1668—431no—
305#1667—431no—
306#1666—431no—
307#1665—431no—
308#1572D4311yescharacteristic, complemented
309#1551—431no—
310#1540—431no—
311C2×C43—41no—
312C2×C43#304511yescharacteristic
313C2×C43#305011yescharacteristic
314C2×C43#306811yescharacteristic
315D43—42no—
316D43—161no—
317D43—161no—
318#532—431no—
319#532—431no—
320C4×#41—431no—
321#493—431no—
322#492—431no—
323#487—431no—
324#486—431no—
325#482—861no—
326#482—861no—
327#477—431no—
328#476—431no—
329#475—431no—
330#474—431no—
331#463—861no—
332#463—861no—
333#460—431no—
334#460—431no—
335#459—431no—
336#459—431no—
337#449—861no—
338#449—861no—
339#449—861no—
340#449—861no—
341C8×Q8—431no—
342C8×Q8—431no—
343#442—861no—
344#440—861no—
345C4×SD16—861no—
346C4×D8—861no—
347C8×D4—431no—
348C8×D4—431no—
349C8×D4—861no—
350C8×D4—861no—
351#432C2×D4311yescharacteristic
352#431—861no—
353#431C2×D4311yescharacteristic
354#431C2×D4311yescharacteristic
355C2×C4⋊C8—431no—
356C2×C4⋊C8—861no—
357#335C2×D4311yescharacteristic
358#335C2×D4311yescharacteristic
359#334C2×D4311yescharacteristic
360#334C2×D4311yescharacteristic
361#333—431no—
362#333—431no—
363#332—431no—
364#332—431no—
365#331—431no—
366#331—431no—
367#331—431no—
368#331—431no—
369C43#1941211yescharacteristic, complemented, Sylow
370C2×#41—431no—
371C2×#41—861no—
372C2×#41—861no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×D8—861no—
378C2×D8—861no—
379C2×D8—861no—
380C2×D8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C4⋊Q8—431no—
385C4⋊Q8—431no—
386#127—431no—
387#127—431no—
388#124—861no—
389#124—861no—
390#121—861no—
391#121—861no—
392#121—861no—
393#121—861no—
394C4×Q8—431no—
395C4×Q8—431no—
396C4×D4—431no—
397C4×D4—431no—
398C4×D4—861no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4—861no—
402C4×D4—861no—
403C4×D4—861no—
404#117—431no—
405#117—861no—
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408#107—861no—
409#107—861no—
410#106—861no—
411#106—861no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8D17211yescharacteristic
418C4⋊C8D17211yescharacteristic
419C4⋊C8C22×D4311yescharacteristic
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422C4⋊C8C22×D4311yescharacteristic
423#103—861no—
424#103—861no—
425#103—861no—
426#103—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8D17211yescharacteristic
440C22⋊C8D17211yescharacteristic
441#97—21no—
442C4×C8—21no—
443C4×C8—861no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447#41—862no—
448#41—862no—
449#41—3441no—
450#41—3441no—
451#41—3442no—
452C2×Q8—431no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—431no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—1721no—
464C2×D4—1721no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—1721no—
469C22×C4—1721no—
470C22×C4C2×D17211yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4#1062190211yescharacteristic
473SD16—3441no—
474SD16—3441no—
475SD16—1722no—
476SD16—1722no—
477D8—3441no—
478D8—3441no—
479D8—1722no—
480D8—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—3441no—
488C2×C8—3441no—
489C2×C8—3441no—
490C2×C8C2×D17211yescharacteristic
491C2×C8C2×D17211yescharacteristic
492C2×C8C2×D17211yescharacteristic
493C2×C8C2×D17211yescharacteristic
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C22⋊C4—861no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—1721no—
506C22⋊C4—1721no—
507C22⋊C4—1721no—
508C22⋊C4—1721no—
509C42—861no—
510C42—861no—
511C42—861no—
512C42C2×D17211yescharacteristic
513C42D4×D4311yescharacteristic
514C42#1062190211yescharacteristic
515C42C23×D4311yescharacteristic
516C23—861no—
517C23—1721no—
518C23—1721no—
519C23#1306330011yescharacteristic
520Q8—432no—
521Q8—861no—
522Q8—3441no—
523Q8—1721no—
524Q8—1721no—
525D4—432no—
526D4—864no—
527D4—861no—
528D4—3441no—
529D4—3441no—
530D4—3442no—
531D4—3442no—
532D4—1721no—
533D4—1721no—
534D4—1721no—
535D4—1721no—
536D4—1721no—
537D4—1721no—
538D4—1721no—
539D4—1721no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—864no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—3442no—
550C2×C4—3442no—
551C2×C4—3441no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4#1306330011yescharacteristic
557C2×C4#1306330011yescharacteristic
558C2×C4#1306330011yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4C22×D17211yescharacteristic
561C2×C4C2×#1062190211yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—1721no—
571C8—1721no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—862no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22—3441no—
581C22—3441no—
582C22—1721no—
583C22—1721no—
584C22C2×#1306330011yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—862no—
590C4—3441no—
591C4—3441no—
592C4—1721no—
593C4—1721no—
594C4#135×D4311yescharacteristic
595C4#135×D4311yescharacteristic
596C4#1458370411yescharacteristic
597C4#1458371111yescharacteristic
598C2—41no—
599C2—1722no—
600C2—6881no—
601C2—6881no—
602C2#1914413611yescharacteristic
603C2#1914417711yescharacteristic
604C2#1914432411yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1572C2
socleC22×C43C2×#121
hypercenter#1572D43
hypocenterC43#19412
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
1. #19145530C2semidirect
2. #19144747C2semidirect
3. #19144656C2semidirect
4. #19143703C2semidirect
5. #19134054C2semidirect
6. #19134047C2semidirect
7. #19134012C2semidirect
8. #19134005C2semidirect
9. #19133956C2semidirect
10. #19133951C2semidirect
11. #19133944C2semidirect
12. #19133937C2semidirect
13. #19133291C2semidirect
14. #19133242C2semidirect
15. C43×#1572C2semidirect
308. #1572D43semidirect
369. C43#19412semidirect

Maximal subgroups

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

subgroupindex
#191455302
#191447472
#191446562
#191437032
#191340542
#191340472
#191340122
#191340052
#191339562
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C43×#15722
#1941243