Finite Group Databasebeta

← #25251769

Subgroups — #25251769

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145247C211yesmaximal, characteristic, complemented
2#19143446C211yesmaximal, characteristic
3#19136803C211yesmaximal, characteristic, complemented
4#19136755C211yesmaximal, characteristic, complemented
5#19136751C211yesmaximal, characteristic, complemented
6#19136639C211yesmaximal, characteristic, complemented
7#19136639C211yesmaximal, characteristic, complemented
8#19136526C211yesmaximal, characteristic
9#19136523C211yesmaximal, characteristic
10#19136462C211yesmaximal, characteristic, complemented
11#19136458C211yesmaximal, characteristic, complemented
12#19136446C211yesmaximal, characteristic, complemented
13#19136444C211yesmaximal, characteristic, complemented
14#19136399C211yesmaximal, characteristic, complemented
15C43×#2237C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17#14583509—21no—
18#14583373—21no—
19C2×#13063270C2211yescharacteristic
20C2×#13063270C2211yescharacteristic
21C2×#13063268C2211yescharacteristic
22C2×#13063268C2211yescharacteristic
23#14583300C2211yescharacteristic, complemented
24#14583277C2211yescharacteristic, complemented
25#14583266—21no—
26#14583155—21no—
27#14583140C2211yescharacteristic
28#14583010—21no—
29#14583010—21no—
30#14583003—21no—
31Q16×Dic43C2211yescharacteristic, complemented
32#14582993C2211yescharacteristic, complemented
33#14582981C2211yescharacteristic
34#14582981C2211yescharacteristic
35#14582981C2211yescharacteristic
36#14582981C2211yescharacteristic
37#14582903—21no—
38#14582854C2211yescharacteristic
39#14582726C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42Dic43⋊C16C2211yescharacteristic, complemented
43#14582702C2211yescharacteristic, complemented
44#14582702C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic
46#14582701C2211yescharacteristic
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50#14582674C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C43×#467C2211yescharacteristic
53C43×#427C2211yescharacteristic
54C43×#367C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×#358C2211yescharacteristic, complemented
57C43×#358C2211yescharacteristic, complemented
58C43×C22⋊C16C2211yescharacteristic
59C22×D172—21no—
60C2×Dic172C2311yescharacteristic
61C2×#10621885—21no—
62C2×D344—21no—
63C2×D344—22no—
64C2×D344—22no—
65C2×D344C2311yescharacteristic
66C2×D344C2311yescharacteristic
67C2×#10621877D411yescharacteristic
68#13063323—21no—
69#13063318—41no—
70#13063318—41no—
71#13063316—21no—
72#13063316—41no—
73#13063315—41no—
74#13063304—21no—
75Q8×Dic43—21no—
76#13063290—21no—
77C4×D172—41no—
78C4×D172—41no—
79#13063287—21no—
80#13063287—21no—
81#13063287—21no—
82#13063287—21no—
83#13063284D411yescharacteristic
84C22⋊C4×D43—41no—
85C22⋊C4×D43—41no—
86#13063270—22no—
87#13063270—22no—
88#13063268—22no—
89#13063268—22no—
90C2×C43⋊C16C2311yescharacteristic
91C2×C43⋊C16C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063256—21no—
94#13063250—21no—
95#13063249—21no—
96#13063248—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101#13063235D411yescharacteristic
102#13063235D411yescharacteristic
103C8×Dic43C2311yescharacteristic
104C8×Dic43C2311yescharacteristic
105C2×Q16×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22⋊Q8×C43—21no—
108#117×C43—21no—
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#107×C43C2311yescharacteristic
114#106×C43—21no—
115#103×C43—21no—
116C23×D43—41no—
117C2×Q8×C43—21no—
118C22×C4×C43C2×D411yescharacteristic
119C2×D172—24no—
120C2×D172—21no—
121C2×D172—21no—
122C2×D172—42no—
123C2×D172—41no—
124C2×C4×D43—41no—
125C2×C4×D43—41no—
126C2×C4×D43—41no—
127C2×C4×D43—41no—
128C2×Dic86—21no—
129Q16×C43—21no—
130Q16×C43—21no—
131C2×C8×C43—21no—
132C2×C8×C43—21no—
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2411yescharacteristic
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—41no—
139C22⋊C4×C43—41no—
140C22⋊C4×C43—41no—
141C42×C43—41no—
142C22⋊Dic43—41no—
143C22⋊Dic43D811yescharacteristic
144C22⋊Dic43D811yescharacteristic
145#10621885—42no—
146(C2×D43)⋊C4—41no—
147(C2×D43)⋊C4—41no—
148(C2×D43)⋊C4—41no—
149(C2×D43)⋊C4—41no—
150C4⋊Dic43—21no—
151C4⋊Dic43—41no—
152C4⋊Dic43—41no—
153C4⋊Dic43D811yescharacteristic
154C4⋊Dic43D811yescharacteristic
155Dic43⋊C4—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160C4×Dic43—41no—
161C4×Dic43—41no—
162C4×Dic43C2×D411yescharacteristic
163C4×Dic43C2×D411yescharacteristic
164#10621877—41no—
165C2×C43⋊C8C2×D411yescharacteristic
166C2×C43⋊C8C2×D411yescharacteristic
167Dic172—21no—
168Dic172—21no—
169D344—24no—
170D344—21no—
171D344—21no—
172D344#4112yes—
173D344#4112yes—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43C2×D811yescharacteristic
179C22×D43—41no—
180C22×D43—41no—
181C22×D43—44no—
182C22×D43—161no—
183C22×D43—161no—
184Q8×C43—41no—
185Q8×C43—41no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43C2×D811yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43C2×D811yescharacteristic
197C2×Dic43C2×D811yescharacteristic
198C2×Dic43C2×D811yescharacteristic
199C2×Dic43C2×D811yescharacteristic
200D172—22no—
201D172—22no—
202D172—44no—
203D172—41no—
204D172—41no—
205C4×D43—161no—
206C4×D43—161no—
207C4×D43—161no—
208C4×D43—161no—
209Dic86—41no—
210Dic86—41no—
211C8×C43—21no—
212C8×C43C2×#4111yescharacteristic
213C8×C43C2×#4111yescharacteristic
214C43⋊C8—21no—
215C43⋊C8—21no—
216#33683—431nomaximal, Sylow
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—21no—
220C22×C43C22×D811yescharacteristic
221C2×D43—42no—
222C2×D43—42no—
223C2×D43—81no—
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—164no—
228C4×C43—21no—
229C4×C43—81no—
230C4×C43—81no—
231C4×C43—81no—
232C4×C43—81no—
233C4×C43#52511yescharacteristic
234C4×C43#57511yescharacteristic
235Dic43—21no—
236Dic43—21no—
237Dic43—21no—
238Dic43—21no—
239Dic43—81no—
240Dic43—81no—
241#3177—431no—
242#2948—431no—
243#2237—431no—
244#2237D4311yescharacteristic, complemented
245#2228—431no—
246#2228—431no—
247#2208—431no—
248#2208—431no—
249#2187—431no—
250#2187—431no—
251#2175—431no—
252#2175—431no—
253C4×SD32—431no—
254C4×SD32—431no—
255#2164—431no—
256C2×C43—41no—
257C2×C43#310011yescharacteristic
258C2×C43#341611yescharacteristic
259C2×C43#341611yescharacteristic
260D43—82no—
261D43—82no—
262C22×D8—431no—
263#541—861no—
264#518—861no—
265C2×SD32—431no—
266C2×SD32—431no—
267C2×SD32—431no—
268C2×SD32—431no—
269#499—431no—
270#494—431no—
271#491—861no—
272#470—861no—
273#467—431no—
274#467C2×D4311yescharacteristic
275#442—861no—
276#442—861no—
277#441—861no—
278C4×Q16—431no—
279C4×Q16—431no—
280C4×D8—431no—
281C4×D8—431no—
282C4×D8—431no—
283C4×D8—431no—
284#427C2×D4311yescharacteristic
285#418—861no—
286#405—431no—
287#367—431no—
288#367C2×D4311yescharacteristic, complemented
289#366—431no—
290#366C2×D4311yescharacteristic, complemented
291C4⋊C16—431no—
292C4⋊C16—431no—
293#358—431no—
294#358—431no—
295#358C2×D4311yescharacteristic, complemented
296#358C2×D4311yescharacteristic, complemented
297#357—431no—
298#357—431no—
299#357—431no—
300#357—431no—
301C22⋊C16—431no—
302C22⋊C16C2×D4311yescharacteristic
303#346—431no—
304C4×C16—431no—
305C43#3368311yescharacteristic, complemented, Sylow
306C22×D4—861no—
307C2×Q16—431no—
308C2×Q16—861no—
309C2×Q16C22×D4311yescharacteristic
310C2×D8—431no—
311C2×D8—431no—
312C2×D8—862no—
313C2×D8—862no—
314C2×D8—861no—
315C2×M16—431no—
316C22×C8C22×D4311yescharacteristic
317C4⋊Q8—861no—
318#126—1721no—
319#126—1721no—
320#125—861no—
321#125—1721no—
322#125—1721no—
323C22⋊Q8—21no—
324C22⋊Q8—861no—
325C4×Q8—861no—
326C4×Q8—861no—
327C4×D4—861no—
328C4×D4—861no—
329C4×D4—861no—
330C4×D4—861no—
331C4×D4—1721no—
332C4×D4—1721no—
333#117—21no—
334#117—431no—
335C2×C22⋊C4—1721no—
336C2×C22⋊C4—1721no—
337SD32—862no—
338SD32—862no—
339SD32—862no—
340SD32—862no—
341C2×C16—431no—
342C2×C16—431no—
343C2×C16C22×D4311yescharacteristic
344C2×C16C22×D4311yescharacteristic
345#107—431no—
346#107C22×D4311yescharacteristic
347#107C22×D4311yescharacteristic
348#107C22×D4311yescharacteristic
349#106—21no—
350#106—861no—
351#103—21no—
352#103—861no—
353#103—861no—
354#103—861no—
355#102—861no—
356#102—861no—
357#102—861no—
358#102—861no—
359#97—431no—
360#97—431no—
361C4×C8—431no—
362C4×C8—431no—
363C24—1721no—
364C2×Q8—21no—
365C2×Q8—861no—
366C2×D4—864no—
367C2×D4—861no—
368C2×D4—861no—
369C2×D4—1722no—
370C2×D4—1721no—
371C22×C4—1721no—
372C22×C4—1721no—
373C22×C4—1721no—
374C22×C4—1721no—
375C22×C4D4×D4311yescharacteristic
376Q16—21no—
377Q16—21no—
378Q16—861no—
379Q16—861no—
380Q16—1722no—
381D8—432no—
382D8—432no—
383D8—864no—
384D8—861no—
385D8—861no—
386M16—1721no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—431no—
390C2×C8—431no—
391C2×C8D4×D4311yescharacteristic
392C2×C8C23×D4311yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—431no—
398C4⋊C4—431no—
399C4⋊C4—861no—
400C4⋊C4—1721no—
401C4⋊C4—1721no—
402C4⋊C4—1721no—
403C4⋊C4—1721no—
404C4⋊C4—1721no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—431no—
410C22⋊C4—431no—
411C22⋊C4—1721no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C42—41no—
417C42—431no—
418C42—431no—
419C42—1721no—
420C42—1721no—
421C16—21no—
422C16—21no—
423C16—861no—
424C16—861no—
425C23—1724no—
426C23—1721no—
427C23—1721no—
428C23—6881no—
429C23—6881no—
430C23D8×D4311yescharacteristic
431Q8—41no—
432Q8—41no—
433Q8—1721no—
434Q8—1721no—
435D4—862no—
436D4—862no—
437D4—1724no—
438D4—1721no—
439D4—1721no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—431no—
447C2×C4—431no—
448C2×C4—431no—
449C2×C4—431no—
450C2×C4—1721no—
451C2×C4—1721no—
452C2×C4—6881no—
453C2×C4—6881no—
454C2×C4—6881no—
455C2×C4—6881no—
456C2×C4D8×D4311yescharacteristic
457C2×C4C2×D4×D4311yescharacteristic
458C8—21no—
459C8—861no—
460C8—861no—
461C8#41×D4311yescharacteristic
462C8#41×D4311yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—3441no—
467C22—3441no—
468C22—3441no—
469C22—3441no—
470C22—1722no—
471C22—1722no—
472C22—6884no—
473C22C2×D8×D4311yescharacteristic
474C4—21no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4—81no—
479C4—861no—
480C4—861no—
481C4—861no—
482C4—861no—
483C4—3441no—
484C4—3441no—
485C4#1458340711yescharacteristic
486C4#1458369811yescharacteristic
487C2—41no—
488C2—3442no—
489C2—3442no—
490C2#1914459211yescharacteristic
491C2#1914773811yescharacteristic
492C2#1914774011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2237C2
socleC22×C43C22×D8
prime radicalC22×D344C22
hypercenter#2237D43
hypocenterC43#33683
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
1. #19145247C2semidirect
3. #19136803C2semidirect
4. #19136755C2semidirect
5. #19136751C2semidirect
6. #19136639C2semidirect
7. #19136639C2semidirect
10. #19136462C2semidirect
11. #19136458C2semidirect
12. #19136446C2semidirect
13. #19136444C2semidirect
14. #19136399C2semidirect
15. C43×#2237C2semidirect
23. #14583300C22semidirect
24. #14583277C22semidirect
31. Q16×Dic43C22semidirect
32. #14582993C22semidirect
39. #14582726C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582702C22semidirect
44. #14582702C22semidirect
50. #14582674C22semidirect
51. C16×Dic43C22semidirect
54. C43×#367C22semidirect
55. C43×#366C22semidirect
56. C43×#358C22semidirect
57. C43×#358C22semidirect
244. #2237D43semidirect
288. #367C2×D43semidirect
290. #366C2×D43semidirect
295. #358C2×D43semidirect
296. #358C2×D43semidirect
305. C43#33683semidirect

Maximal subgroups

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

subgroupindex
#191452472
#191434462
#191368032
#191367552
#191367512
#191366392
#191365262
#191365232
#191364622
#191364582
#191364462
#191364442
#191363992
C43×#22372
#3368343