Finite Group Databasebeta

← #25251281

Subgroups — #25251281

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145128C211yesmaximal, characteristic, complemented
2#19143442C211yesmaximal, characteristic
3#19136754C211yesmaximal, characteristic, complemented
4#19136753C211yesmaximal, characteristic, complemented
5#19136752C211yesmaximal, characteristic, complemented
6#19136751C211yesmaximal, characteristic, complemented
7#19136741C211yesmaximal, characteristic, complemented
8#19136730C211yesmaximal, characteristic, complemented
9#19136729C211yesmaximal, characteristic, complemented
10#19136382C211yesmaximal, characteristic, complemented
11#19136378C211yesmaximal, characteristic, complemented
12#19136352C211yesmaximal, characteristic, complemented
13#19136309C211yesmaximal, characteristic
14#357×D43C211yesmaximal, characteristic
15C43×#2226C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583526—21no—
18#14583371—21no—
19C2×#13063264C2211yescharacteristic
20C2×C16×D43C2211yescharacteristic
21#14583307—21no—
22#14583305—21no—
23#14583303C2211yescharacteristic, complemented
24#14583301C2211yescharacteristic, complemented
25#14583300C2211yescharacteristic, complemented
26#14583009—21no—
27#14583008—21no—
28C4×D344C2211yescharacteristic
29D8×Dic43C2211yescharacteristic
30#14582981C2211yescharacteristic
31#14582940—21no—
32#14582936C2211yescharacteristic
33#14582936C2211yescharacteristic
34#107×D43C2211yescharacteristic
35#14582902—21no—
36#14582853C2211yescharacteristic
37#14582727C2211yescharacteristic, complemented
38#14582726C2211yescharacteristic, complemented
39#14582725C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41#14582724C2211yescharacteristic, complemented
42#14582724C2211yescharacteristic, complemented
43C4⋊(C43⋊C16)C2211yescharacteristic, complemented
44Dic43⋊C16C2211yescharacteristic, complemented
45Dic43⋊C16C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582700C2211yescharacteristic
49#14582700C2211yescharacteristic
50#14582699C2211yescharacteristic
51#14582699C2211yescharacteristic
52C43×#500C2211yescharacteristic, complemented
53C4×D8×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic, complemented
55C43×#367C2211yescharacteristic, complemented
56C43×C4⋊C16C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×D4×D43—21no—
60C2×D344C2311yescharacteristic
61C2×#10621882—21no—
62D8×D43—22no—
63D8×D43Q814yescomplemented
64C2×#10621872D411yescharacteristic
65C2×C8×D43C2311yescharacteristic
66#13063324—21no—
67#13063323—41no—
68#13063317—21no—
69#13063316—21no—
70#13063315—41no—
71#13063303—41no—
72#13063301—41no—
73C4×D172—21no—
74D4×Dic43—21no—
75#13063287—21no—
76C4×C22⋊D43—41no—
77(C22⋊D43)⋊C4—41no—
78#13063283—21no—
79#13063283—21no—
80#13063282D411yescharacteristic
81C4⋊C4×D43—21no—
82C2×(C2×D43)⋊C4—41no—
83C22⋊C4×D43—41no—
84#13063264—22no—
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87C16×D43—22no—
88#13063259C2311yescharacteristic
89#13063259C2311yescharacteristic
90#13063259C2311yescharacteristic
91#13063258—21no—
92#13063258—21no—
93#13063257—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97#13063247—21no—
98#13063246—21no—
99#13063245—21no—
100#13063236D411yescharacteristic
101#13063235D411yescharacteristic
102C8×Dic43C2311yescharacteristic
103C2×D8×C43C2311yescharacteristic
104C4⋊Q8×C43—21no—
105C4×D4×C43—21no—
106C2×C16×C43C2311yescharacteristic
107C2×C16×C43C2311yescharacteristic
108#107×C43—21no—
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#102×C43—21no—
113C4×C8×C43C2311yescharacteristic
114C23×D43—41no—
115C2×Q8×C43—41no—
116C2×D4×C43—21no—
117C22×C4×C43—41no—
118C2×C22⋊D43—41no—
119C22×Dic43—41no—
120D4×D43—24no—
121D4×D43—42no—
122C2×D172—21no—
123C2×C4×D43—41no—
124C2×C4×D43—41no—
125C2×C4×D43—41no—
126C2×C4×D43C2×D411yescharacteristic
127C2×Dic86—41no—
128D8×C43—21no—
129D8×C43C2×Q812yes—
130C2×C8×C43C2×D411yescharacteristic
131C2×C8×C43C2411yescharacteristic
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—41no—
136C22⋊C4×C43—41no—
137C42×C43C2×D411yescharacteristic
138C22⋊Dic43—41no—
139#10621882—24no—
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4D811yescharacteristic
145(C2×D43)⋊C4D811yescharacteristic
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4D811yescharacteristic
156Dic43⋊C4D811yescharacteristic
157C4×Dic43—41no—
158C4×Dic43—41no—
159C4×Dic43C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162D344—21no—
163D344C2×Q812yes—
164#10621872—22no—
165C8×D43C2×Q812yes—
166C8×D43#4112yes—
167C16×C43—21no—
168C16×C43—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C23×C43—41no—
172C22×D43—41no—
173C22×D43—44no—
174C22×D43—161no—
175C22×D43—161no—
176C22×D43C2×D811yescharacteristic
177Q8×C43—161no—
178D4×C43—22no—
179D4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—161no—
184C2×C4×C43C2×D811yescharacteristic
185C2×C4×C43C2×D811yescharacteristic
186C2×C4×C43C22×D411yescharacteristic
187C22⋊D43—44no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—161no—
192C2×Dic43C2×D811yescharacteristic
193C2×Dic43C2×D811yescharacteristic
194C2×Dic43C2×D811yescharacteristic
195D172—22no—
196D172—41no—
197C4×D43—161no—
198C4×D43—161no—
199C4×D43—161no—
200C4×D43C22⋊Q812yes—
201C4×D43#13712yes—
202Dic86—161no—
203C8×C43—21no—
204C8×C43C22×Q811yescharacteristic
205C8×C43C2×#4111yescharacteristic
206C43⋊C8—21no—
207C43⋊C8C22⋊Q812yes—
208#33631—431nomaximal, Sylow
209C22×C43—42no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43C22×D811yescharacteristic
213C2×D43—21no—
214C2×D43—21no—
215C2×D43—42no—
216C2×D43—81no—
217C2×D43—81no—
218C2×D43—164no—
219C2×D43#47412yes—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—81no—
223C4×C43—81no—
224C4×C43—81no—
225C4×C43C2×C22⋊Q811yescharacteristic
226C4×C43C2×#13711yescharacteristic
227Dic43—21no—
228Dic43—21no—
229Dic43—81no—
230Dic43—81no—
231Dic43—81no—
232Dic43#47412yes—
233#3164—431no—
234#2948—431no—
235#2228—431no—
236#2228—431no—
237#2228—431no—
238#2228—431no—
239#2226—431no—
240#2226D4311yescharacteristic, complemented
241#2224—431no—
242#2224—431no—
243#2159—431no—
244#2158—431no—
245#2151—431no—
246#2140—431no—
247C2×#357—431no—
248C2×C43—82no—
249C2×C43C2×#47411yescharacteristic
250C2×C43#341511yescharacteristic
251C2×C43#341611yescharacteristic
252D43—22no—
253D43—82no—
254C22×D8—431no—
255#544—861no—
256#518—861no—
257C2×M32—431no—
258C22×C16—431no—
259#501—861no—
260#501—861no—
261#500—431no—
262#500C2×D4311yescharacteristic, complemented
263#499—431no—
264#499—431no—
265#442—861no—
266#442—861no—
267C4×D8—431no—
268C4×D8—431no—
269C4×D8—431no—
270C4×D8C2×D4311yescharacteristic
271#428—861no—
272#427—431no—
273#427—431no—
274C2×#107—431no—
275#418—861no—
276#405—431no—
277#367—431no—
278#367—431no—
279#367C2×D4311yescharacteristic, complemented
280#367C2×D4311yescharacteristic, complemented
281#366—431no—
282#366—431no—
283#366—431no—
284#366—431no—
285C4⋊C16—431no—
286C4⋊C16—431no—
287C4⋊C16—431no—
288C4⋊C16C2×D4311yescharacteristic, complemented
289#357—431no—
290#357—431no—
291#357—431no—
292#357—431no—
293#357—431no—
294#357—431no—
295#357C2×D4311yescharacteristic
296#357C2×D4311yescharacteristic
297C43#3363111yescharacteristic, complemented, Sylow
298C22×D4—861no—
299C2×D8—434no—
300C2×D8—431no—
301C2×D8—862no—
302C2×D8—861no—
303C2×D8C22×D4311yescharacteristic
304C2×M16—431no—
305C22×C8—431no—
306C4⋊Q8—21no—
307C4⋊Q8—861no—
308C4⋊Q8—1721no—
309#125—861no—
310#125—861no—
311#125—1721no—
312C22⋊Q8—1721no—
313C22⋊Q8—1721no—
314C4×D4—21no—
315C4×D4—861no—
316C4×D4—861no—
317C4×D4—861no—
318C4×D4—1721no—
319C4×D4—1721no—
320#117—431no—
321#117—861no—
322#117—861no—
323C2×C4⋊C4—861no—
324C2×C22⋊C4—1721no—
325C2×C22⋊C4—1721no—
326M32—862no—
327C2×C16—431no—
328C2×C16—431no—
329C2×C16—862no—
330C2×C16C22×D4311yescharacteristic
331C2×C16C22×D4311yescharacteristic
332#107—21no—
333#107—431no—
334#107—431no—
335#107—431no—
336#107—861no—
337#107—861no—
338#107C22×D4311yescharacteristic
339#107C22×D4311yescharacteristic
340#107C22×D4311yescharacteristic
341#106—861no—
342#106—861no—
343#106—861no—
344#106—861no—
345#102—21no—
346#102—861no—
347#102—861no—
348#102—861no—
349#97—431no—
350#97—431no—
351C4×C8—431no—
352C4×C8C22×D4311yescharacteristic
353C24—1721no—
354C2×Q8—41no—
355C2×Q8—1721no—
356C2×D4—21no—
357C2×D4—864no—
358C2×D4—861no—
359C2×D4—1722no—
360C2×D4—1721no—
361C22×C4—41no—
362C22×C4—431no—
363C22×C4—1721no—
364C22×C4—1721no—
365C22×C4—1721no—
366C22×C4—1721no—
367D8—21no—
368D8—432no—
369D8—864no—
370D8—861no—
371D8Q8×D4312yes—
372M16—862no—
373C2×C8—431no—
374C2×C8—432no—
375C2×C8—432no—
376C2×C8—431no—
377C2×C8D4×D4311yescharacteristic
378C2×C8C23×D4311yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—431no—
384C4⋊C4—431no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4—861no—
388C4⋊C4—1721no—
389C4⋊C4—1721no—
390C4⋊C4—1721no—
391C4⋊C4—1721no—
392C4⋊C4—1721no—
393C4⋊C4—1721no—
394C22⋊C4—41no—
395C22⋊C4—431no—
396C22⋊C4—431no—
397C22⋊C4—1721no—
398C22⋊C4—1721no—
399C22⋊C4—1721no—
400C22⋊C4—1721no—
401C22⋊C4—1721no—
402C42—431no—
403C42—1721no—
404C42—1721no—
405C42D4×D4311yescharacteristic
406C16—21no—
407C16—21no—
408C16—861no—
409C16—861no—
410C23—41no—
411C23—431no—
412C23—1724no—
413C23—1721no—
414C23—6881no—
415C23—6881no—
416Q8—161no—
417Q8—6881no—
418D4—22no—
419D4—41no—
420D4—862no—
421D4—1724no—
422D4—1721no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—431no—
428C2×C4—432no—
429C2×C4—432no—
430C2×C4—431no—
431C2×C4—431no—
432C2×C4—1721no—
433C2×C4—1721no—
434C2×C4—1721no—
435C2×C4—6881no—
436C2×C4—6881no—
437C2×C4—6881no—
438C2×C4—6881no—
439C2×C4D8×D4311yescharacteristic
440C2×C4D8×D4311yescharacteristic
441C2×C4C2×D4×D4311yescharacteristic
442C8—21no—
443C8—432no—
444C8—861no—
445C8C2×Q8×D4311yescharacteristic
446C8#41×D4311yescharacteristic
447C22—42no—
448C22—81no—
449C22—81no—
450C22—432no—
451C22—861no—
452C22—861no—
453C22—3441no—
454C22—3441no—
455C22—1722no—
456C22—6884no—
457C22C2×D8×D4311yescharacteristic
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—432no—
464C4—861no—
465C4—861no—
466C4—3441no—
467C4—3441no—
468C4—3441no—
469C4C22⋊Q8×D4311yescharacteristic
470C4#137×D4311yescharacteristic
471C2—82no—
472C2—862no—
473C2—3442no—
474C2#474×D4311yescharacteristic
475C2#1914773511yescharacteristic
476C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2226C2
socleC22×C43C22×D8
prime radicalC2×D8×D43C22
hypercenter#2226D43
hypocenterC43#33631
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #19145128C2semidirect
3. #19136754C2semidirect
4. #19136753C2semidirect
5. #19136752C2semidirect
6. #19136751C2semidirect
7. #19136741C2semidirect
8. #19136730C2semidirect
9. #19136729C2semidirect
10. #19136382C2semidirect
11. #19136378C2semidirect
12. #19136352C2semidirect
15. C43×#2226C2semidirect
23. #14583303C22semidirect
24. #14583301C22semidirect
25. #14583300C22semidirect
37. #14582727C22semidirect
38. #14582726C22semidirect
39. #14582725C22semidirect
40. #14582724C22semidirect
41. #14582724C22semidirect
42. #14582724C22semidirect
43. C4⋊(C43⋊C16)C22semidirect
44. Dic43⋊C16C22semidirect
45. Dic43⋊C16C22semidirect
52. C43×#500C22semidirect
54. C43×#367C22semidirect
55. C43×#367C22semidirect
56. C43×C4⋊C16C22semidirect
63. D8×D43Q8semidirect
240. #2226D43semidirect
262. #500C2×D43semidirect
279. #367C2×D43semidirect
280. #367C2×D43semidirect
288. C4⋊C16C2×D43semidirect
297. C43#33631semidirect

Maximal subgroups

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

subgroupindex
#191451282
#191434422
#191367542
#191367532
#191367522
#191367512
#191367412
#191367302
#191367292
#191363822
#191363782
#191363522
#191363092
#357×D432
C43×#22262
#3363143