Finite Group Databasebeta

← #25084226

Subgroups — #25084226

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145922C211yesmaximal, characteristic
2#19145818C211yesmaximal, characteristic, complemented
3#19145718C211yesmaximal, characteristic, complemented
4#19143757C211yesmaximal, characteristic, complemented
5#19134136C211yesmaximal, characteristic, complemented
6#19134129C211yesmaximal, characteristic, complemented
7#19134124C211yesmaximal, characteristic, complemented
8#19134119C211yesmaximal, characteristic, complemented
9#19134012C211yesmaximal, characteristic, complemented
10#19134005C211yesmaximal, characteristic, complemented
11#19134000C211yesmaximal, characteristic, complemented
12#19133995C211yesmaximal, characteristic, complemented
13#19133291C211yesmaximal, characteristic, complemented
14C2×#14582647C211yesmaximal, characteristic, complemented
15C43×#1573C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583308—21no—
20#14583304C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583259—21no—
23#14583246C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583230—21no—
26#14583213—21no—
27#14583213—21no—
28#14583213—21no—
29#14583200—21no—
30#14583195C2211yescharacteristic
31#14583195C2211yescharacteristic
32#14583195C2211yescharacteristic
33#14583190C2211yescharacteristic
34#14583190C2211yescharacteristic
35#14583190C2211yescharacteristic
36#14583180—21no—
37#14583180—21no—
38#14583135—21no—
39#14583128—21no—
40#14583115—21no—
41#14583100C2211yescharacteristic
42#14583095C2211yescharacteristic
43#14583029C2211yescharacteristic
44C8×Dic86C2211yescharacteristic
45#14582978C2211yescharacteristic
46#14582967—21no—
47C8×D172C2211yescharacteristic
48(C22⋊D43)⋊C8—21no—
49#14582959—21no—
50#14582924—21no—
51C2×C4⋊(C43⋊C8)C2211yescharacteristic
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C22×Dic86—21no—
69C2×#10621873—21no—
70C2×D344—21no—
71C2×#10621872—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74#13063325—21no—
75#13063325—21no—
76#13063325—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063319—21no—
82#13063317D411yescharacteristic
83#13063313—21no—
84#13063313D411yescharacteristic
85#13063308—21no—
86#13063304D411yescharacteristic
87#13063299—21no—
88#13063299—21no—
89#13063299D411yescharacteristic
90C4×Dic86C2311yescharacteristic
91C4×D172—21no—
92C4×D172—21no—
93C4×D172C2311yescharacteristic
94C4×C22⋊D43—21no—
95#13063282—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063259—21no—
105#13063257—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#13063247—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—
127#13063235—21no—
128C8×Dic43—21no—
129C22×C8×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43D411yescharacteristic
140C22⋊C8×C43D411yescharacteristic
141#97×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—
149C22×Dic43—41no—
150#10621898—82no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—41no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—41no—
161C2×Dic86—82no—
162C2×Dic86C2×D411yescharacteristic
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43#4111yescharacteristic
175C42×C43C2411yescharacteristic
176C22⋊Dic43—21no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197C4×Dic43—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—81no—
201D344—81no—
202#10621873—81no—
203#10621872—81no—
204C8×D43—81no—
205C23×C43#12111yescharacteristic
206C22×D43—21no—
207C22×D43—41no—
208C2×C4×C43—22no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43#12111yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C22⋊D43—42no—
220C22⋊D43—82no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—82no—
228D172—21no—
229D172—21no—
230D172—41no—
231D172—41no—
232D172—41no—
233D172—41no—
234D172—81no—
235C4×D43—41no—
236C4×D43—41no—
237C4×D43—82no—
238Dic86—21no—
239Dic86—21no—
240Dic86—82no—
241Dic86—81no—
242Dic86—81no—
243Dic86—81no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#19591—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43#47212yes—
258C22×C43C2×#12111yescharacteristic
259C2×D43—41no—
260C2×D43—41no—
261C2×D43—41no—
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43#57711yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272C4×C43#57811yescharacteristic
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278Dic43—81no—
279#3247—431no—
280#3238—431no—
281#3226—431no—
282#2994—431no—
283#1698—431no—
284#1697—431no—
285#1696—431no—
286#1695—431no—
287#1678—431no—
288#1677—431no—
289#1676—431no—
290#1675—431no—
291#1573D4311yescharacteristic, complemented
292#1551—431no—
293C2×#333—431no—
294C2×C43—22no—
295C2×C43#304611yescharacteristic
296C2×C43#306311yescharacteristic
297C2×C43C2×#47211yescharacteristic
298D43—81no—
299D43—161no—
300#532—431no—
301C2×C4⋊Q8—431no—
302#529—431no—
303#501—861no—
304#500—431no—
305#500—431no—
306#489—861no—
307#486—431no—
308#486—431no—
309#483—861no—
310#480—861no—
311#480—861no—
312#480—861no—
313#478—861no—
314#477—431no—
315#477—431no—
316#477—431no—
317#476—431no—
318#476—431no—
319#476—431no—
320#474—861no—
321#474—861no—
322#466—861no—
323#465—861no—
324#463—861no—
325#460—431no—
326#459—431no—
327#446—431no—
328C8×Q8—431no—
329#436—431no—
330#435—861no—
331C8×D4—431no—
332C8×D4—861no—
333#433—861no—
334#432C2×D4311yescharacteristic
335#431C2×D4311yescharacteristic
336#424—861no—
337C2×C4⋊C8—431no—
338C2×C4⋊C8C2×D4311yescharacteristic
339#335C2×D4311yescharacteristic
340#335C2×D4311yescharacteristic
341#334C2×D4311yescharacteristic
342#334C2×D4311yescharacteristic
343#333—431no—
344#333—431no—
345#333—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#331—431no—
350#331—431no—
351C43#1959111yescharacteristic, complemented, Sylow
352C2×#41—861no—
353C22×Q8—861no—
354C2×SD16—861no—
355C2×D8—861no—
356C2×M16—861no—
357C22×C8—21no—
358C22×C8—861no—
359C22×C8—861no—
360C4⋊Q8—431no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363C4⋊Q8—861no—
364C4⋊Q8—861no—
365C4⋊Q8—861no—
366#127—431no—
367#126—861no—
368#125—431no—
369#124—431no—
370#124—861no—
371#123—861no—
372C22⋊Q8—431no—
373#121—431no—
374#121—861no—
375#121—861no—
376C4×Q8—431no—
377C4×D4—431no—
378C4×D4—861no—
379C4×D4—861no—
380C4×D4—861no—
381#117—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C42C22×D4311yescharacteristic
385#107—861no—
386#107—861no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8D17211yescharacteristic
402C4⋊C8D17211yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—861no—
408#103—861no—
409#103—861no—
410#102—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—21no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8D17211yescharacteristic
423C22⋊C8D17211yescharacteristic
424#97—21no—
425#97—861no—
426C4×C8—861no—
427C4×C8C22×D4311yescharacteristic
428C4×C8C22×D4311yescharacteristic
429#41—3442no—
430C2×Q8—431no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—3442no—
435C2×Q8—1721no—
436C2×D4—431no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—1721no—
442C22×C4—861no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4C2×D17211yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4#1062190211yescharacteristic
448SD16—3441no—
449D8—3441no—
450M16—3441no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—3441no—
459C2×C8—3441no—
460C2×C8C2×D17211yescharacteristic
461C2×C8C2×D17211yescharacteristic
462C2×C8C2×D17211yescharacteristic
463C2×C8C2×D17211yescharacteristic
464C4⋊C4—431no—
465C4⋊C4—431no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C42—861no—
486C42C2×D17211yescharacteristic
487C42D4×D4311yescharacteristic
488C42#1062190211yescharacteristic
489C42C23×D4311yescharacteristic
490C23—861no—
491C23—1721no—
492C23#1306330011yescharacteristic
493Q8—861no—
494Q8—861no—
495Q8—3441no—
496Q8—3441no—
497Q8—3441no—
498Q8—3442no—
499D4—861no—
500D4—861no—
501D4—3441no—
502D4—3442no—
503D4—1722no—
504D4—1721no—
505D4—1721no—
506D4—1721no—
507D4—1721no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—3442no—
517C2×C4—3442no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4#1306330011yescharacteristic
524C2×C4#1306330011yescharacteristic
525C2×C4#1306330011yescharacteristic
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×D17211yescharacteristic
528C2×C4C2×#1062190211yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—1721no—
538C8—1721no—
539C22—21no—
540C22—21no—
541C22—3441no—
542C22—3441no—
543C22—3441no—
544C22—1721no—
545C22—1721no—
546C22—1721no—
547C22#1458317012yes—
548C22C2×#1306330011yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—3441no—
554C4—3441no—
555C4—3441no—
556C4—1721no—
557C4—1721no—
558C4—1721no—
559C4#1458370911yescharacteristic
560C4#1458371111yescharacteristic
561C4#1458371511yescharacteristic
562C4#1458371611yescharacteristic
563C2—22no—
564C2—3441no—
565C2—6881no—
566C2#1914414711yescharacteristic
567C2#1914428711yescharacteristic
568C2C2×#1458317011yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1573C2
socleC22×C43C2×#121
prime radical#19145922C2
hypercenter#1573D43
hypocenterC43#19591
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #19145818C2semidirect
3. #19145718C2semidirect
4. #19143757C2semidirect
5. #19134136C2semidirect
6. #19134129C2semidirect
7. #19134124C2semidirect
8. #19134119C2semidirect
9. #19134012C2semidirect
10. #19134005C2semidirect
11. #19134000C2semidirect
12. #19133995C2semidirect
13. #19133291C2semidirect
14. C2×#14582647C2semidirect
15. C43×#1573C2semidirect
291. #1573D43semidirect
351. C43#19591semidirect

Maximal subgroups

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

subgroupindex
#191459222
#191458182
#191457182
#191437572
#191341362
#191341292
#191341242
#191341192
#191340122
#191340052
#191340002
#191339952
#191332912
C2×#145826472
C43×#15732
#1959143