Finite Group Databasebeta

← #49132803

Subgroups — #49132803

Order 36224.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583637C211yesmaximal, characteristic, complemented
2C2×#22583631C211yesmaximal, characteristic, complemented
3#31827137C211yesmaximal, characteristic, complemented
4#31827110C211yesmaximal, characteristic, complemented
5#31826854C211yesmaximal, characteristic, complemented
6#31826712C211yesmaximal, characteristic, complemented
7#31826702C211yesmaximal, characteristic, complemented
8#31826687C211yesmaximal, characteristic, complemented
9#31826660C211yesmaximal, characteristic, complemented
10#31826630C211yesmaximal, characteristic, complemented
11#31826613C211yesmaximal, characteristic, complemented
12#31826611C211yesmaximal, characteristic, complemented
13#31826600C211yesmaximal, characteristic, complemented
14#31826538C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985393C2211yescharacteristic, complemented
18C2×#17985391C2211yescharacteristic
19C2×D4×D283C2211yescharacteristic
20#22583637—24no—
21#22583631—24no—
22C2×#17985382C2211yescharacteristic, complemented
23C2×#17985381C2211yescharacteristic, complemented
24C2×#17985381C2211yescharacteristic, complemented
25C2×#17985379C2211yescharacteristic
26C2×D2264C2211yescharacteristic
27C2×D2264C2211yescharacteristic
28C2×#17985377C2211yescharacteristic
29C2×#17985377C2211yescharacteristic
30C2×#17985375C2211yescharacteristic
31C2×C8×D283C2211yescharacteristic, complemented
32#22583607—21no—
33#22583607C2211yescharacteristic, complemented
34#22583598C2211yescharacteristic
35#22583594—21no—
36#22583590C2211yescharacteristic
37#22583585—21no—
38#22583585—21no—
39#22583585C2211yescharacteristic
40#22583585C2211yescharacteristic
41#22583585C2211yescharacteristic, complemented
42#22583584—21no—
43#22583580—21no—
44C4×D1132—21no—
45C4×D1132C2211yescharacteristic
46C2×(C2×D283)⋊C4—21no—
47C4⋊(C283⋊C8)C2211yescharacteristic, complemented
48#22583533C2211yescharacteristic, complemented
49#22583530C2211yescharacteristic
50#22583530C2211yescharacteristic, complemented
51#22583530C2211yescharacteristic, complemented
52(C2×D283)⋊C8C2211yescharacteristic
53(C2×D283)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic, complemented
56C4×D4×C283C2211yescharacteristic
57#107×C283C2211yescharacteristic, complemented
58#103×C283C2211yescharacteristic, complemented
59#102×C283C2211yescharacteristic
60#97×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62#17985393—22no—
63#17985393—22no—
64#17985393—41no—
65#17985393—41no—
66#17985391—22no—
67#17985391—41no—
68C2×Dic566C2311yescharacteristic
69C2×D1132—21no—
70C2×D1132—21no—
71C2×D1132—21no—
72C2×D1132—21no—
73C2×D1132—21no—
74C2×D1132—21no—
75C2×D1132—21no—
76C2×D1132D411yescharacteristic
77C2×D1132C2311yescharacteristic
78C2×D1132C2311yescharacteristic
79C2×D1132C2311yescharacteristic
80C2×C22⋊D283—21no—
81C2×C22⋊D283—21no—
82D4×D283—22no—
83D4×D283—41no—
84C22×Dic283—21no—
85C2×C4×D283—21no—
86C2×C4×D283—21no—
87C2×C4×D283C2311yescharacteristic
88C2×C4×D283C2311yescharacteristic
89#17985382—22no—
90#17985381—22no—
91#17985381—41no—
92#17985379—22no—
93D2264—22no—
94D2264—41no—
95#17985377—22no—
96#17985377—22no—
97#17985375—22no—
98C2×C283⋊C8C2311yescharacteristic
99C2×C283⋊C8C2311yescharacteristic
100C8×D283—22no—
101C4⋊Dic283—21no—
102C4⋊Dic283D411yescharacteristic
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4—21no—
107(C2×D283)⋊C4—21no—
108(C2×D283)⋊C4—21no—
109(C2×D283)⋊C4D411yescharacteristic
110(C2×D283)⋊C4D411yescharacteristic
111C2×Q8×C283C2311yescharacteristic
112C2×D4×C283C2311yescharacteristic
113C22×C4×C283—21no—
114SD16×C283D414yescomplemented
115C2×C8×C283C2311yescharacteristic
116C2×C8×C283C2311yescharacteristic
117C4⋊C4×C283—21no—
118C4⋊C4×C283C2311yescharacteristic
119C4⋊C4×C283C2311yescharacteristic
120C22⋊C4×C283—21no—
121C42×C283—21no—
122C42×C283C2311yescharacteristic
123C22×D283—21no—
124C22×D283—21no—
125C22×D283—21no—
126C22×D283—42no—
127C22×D283—42no—
128C22×D283—81no—
129C22×D283C2×D411yescharacteristic
130C22×D283C2×D411yescharacteristic
131Dic566—21no—
132Dic566—21no—
133D1132—21no—
134D1132—21no—
135D1132—21no—
136D1132—21no—
137D1132—21no—
138D1132—21no—
139D1132—41no—
140D1132—42no—
141D1132—42no—
142D1132—42no—
143D1132—81no—
144D1132—81no—
145D1132—81no—
146D1132—81no—
147C22⋊D283—42no—
148C22⋊D283—42no—
149C2×Dic283—21no—
150C2×Dic283—42no—
151C2×Dic283C2×D411yescharacteristic
152C2×Dic283C2×D411yescharacteristic
153C4×D283—21no—
154C4×D283—21no—
155C4×D283—21no—
156C4×D283—21no—
157C4×D283—42no—
158C4×D283—42no—
159C283⋊C8—21no—
160C283⋊C8—21no—
161C23×C283—21no—
162Q8×C283—21no—
163Q8×C283C2×D412yes—
164D4×C283—21no—
165D4×C283C2×D412yes—
166C2×C4×C283—21no—
167C2×C4×C283—21no—
168C2×C4×C283—21no—
169C2×C4×C283—81no—
170C2×C4×C283C2×D411yescharacteristic
171C2×C4×C283C2×D411yescharacteristic
172C2×C4×C283C2411yescharacteristic
173C8×C283—21no—
174C8×C283C2×D412yes—
175C22×C283—22no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283C22×D411yescharacteristic
179C2×D283—21no—
180C2×D283—21no—
181C2×D283—21no—
182C2×D283—21no—
183C2×D283—21no—
184C2×D283—21no—
185C2×D283—41no—
186C2×D283—41no—
187C2×D283—41no—
188C2×D283—41no—
189C2×D283—41no—
190C2×D283—41no—
191C2×D283—41no—
192C2×D283—41no—
193C2×D283—41no—
194C2×D283—84no—
195C4×C283—22no—
196C4×C283—21no—
197C4×C283—21no—
198C4×C283—41no—
199C4×C283—41no—
200C4×C283C22×D411yescharacteristic
201C4×C283H(5,𝔽2)11yescharacteristic
202Dic283—21no—
203Dic283—21no—
204Dic283—41no—
205C2×C283—42no—
206C2×C283D4211yescharacteristic
207C2×C283#57511yescharacteristic
208C2×C283#57611yescharacteristic
209D283—41no—
210D283—41no—
211D283—81no—
212D283—81no—
213D283—81no—
214C283#326811yescharacteristic, complemented, Sylow
215#3268—2831nomaximal, Sylow
216C2×AGL(1,ℤ/8)—2831no—
217C2×#135—2831no—
218#550—2831no—
219#546—2831no—
220#496—2831no—
221#468—2831no—
222#466—2831no—
223#464—2831no—
224#459—2831no—
225#452—2831no—
226#449—2831no—
227#449—2831no—
228#447—2831no—
229#440D28311yescharacteristic, complemented
230#435—2831no—
231C2×#41—2831no—
232C2×#41—2831no—
233C2×#41—2831no—
234C22×D4—2831no—
235AGL(1,ℤ/8)—5664no—
236#135—5664no—
237C2×Q16—2831no—
238C2×SD16—2831no—
239C2×SD16—2831no—
240C2×SD16—2831no—
241C2×SD16C2×D28311yescharacteristic
242C2×D8—2831no—
243C2×D8—2831no—
244C2×D8—2831no—
245C2×D8—2831no—
246C2×M16—2831no—
247C22×C8—2831no—
248#127—2831no—
249#127—5661no—
250#124—2831no—
251#123—5661no—
252C22⋊Q8—2831no—
253#121—2831no—
254#121—2831no—
255#121—2831no—
256#121—5661no—
257#121—5661no—
258#121—5661no—
259#120—5661no—
260C4×Q8C2×D28311yescharacteristic, complemented
261C4×D4—2831no—
262C4×D4—5661no—
263C4×D4C2×D28311yescharacteristic
264C2×C22⋊C4—5661no—
265#107C2×D28311yescharacteristic, complemented
266C4⋊C8—2831no—
267#103—2831no—
268#103C2×D28311yescharacteristic, complemented
269#102—2831no—
270#102—2831no—
271#102—2831no—
272#102C2×D28311yescharacteristic
273C22⋊C8—2831no—
274C22⋊C8—2831no—
275#97C2×D28311yescharacteristic, complemented
276C24—5661no—
277#41—5662no—
278#41—5662no—
279#41—5662no—
280#41—11321no—
281#41—11321no—
282#41—11321no—
283C2×Q8—2831no—
284C2×Q8C22×D28311yescharacteristic
285C2×D4—2831no—
286C2×D4—2831no—
287C2×D4—2831no—
288C2×D4—2831no—
289C2×D4—5661no—
290C2×D4—5661no—
291C2×D4—5661no—
292C2×D4—5661no—
293C2×D4—5661no—
294C2×D4—5661no—
295C2×D4—5662no—
296C2×D4—5661no—
297C2×D4—5661no—
298C2×D4—5661no—
299C2×D4—11321no—
300C2×D4C22×D28311yescharacteristic
301C22×C4—21no—
302C22×C4—2831no—
303C22×C4—2831no—
304C22×C4—5661no—
305C22×C4—5661no—
306C22×C4—5661no—
307Q16—5662no—
308SD16—5662no—
309SD16—5662no—
310SD16—11321no—
311SD16D113214yescomplemented
312D8—5662no—
313D8—5662no—
314D8—5662no—
315D8—11321no—
316M16—5662no—
317C2×C8—2831no—
318C2×C8—2831no—
319C2×C8—5662no—
320C2×C8C22×D28311yescharacteristic
321C2×C8C22×D28311yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—2831no—
324C4⋊C4—5661no—
325C4⋊C4C22×D28311yescharacteristic
326C4⋊C4C22×D28311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—2831no—
329C22⋊C4—2831no—
330C22⋊C4—5661no—
331C22⋊C4—5661no—
332C22⋊C4—5661no—
333C22⋊C4—5661no—
334C22⋊C4—5661no—
335C22⋊C4—5661no—
336C42—21no—
337C42C22×D28311yescharacteristic
338C23—21no—
339C23—2831no—
340C23—2831no—
341C23—5661no—
342C23—5661no—
343C23—5661no—
344C23—11322no—
345C23—11322no—
346C23—22641no—
347Q8—21no—
348Q8—5661no—
349Q8—5661no—
350Q8C2×D113212yes—
351D4—21no—
352D4—5661no—
353D4—5661no—
354D4—5661no—
355D4—5661no—
356D4—5661no—
357D4—5661no—
358D4—11321no—
359D4—11322no—
360D4—11322no—
361D4—11322no—
362D4—11322no—
363D4—11322no—
364D4—22641no—
365D4—22641no—
366D4—22641no—
367D4—22641no—
368D4C2×D113212yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—2831no—
374C2×C4—2831no—
375C2×C4—5661no—
376C2×C4—5661no—
377C2×C4—5661no—
378C2×C4—5661no—
379C2×C4—5661no—
380C2×C4—11322no—
381C2×C4—11322no—
382C2×C4—11322no—
383C2×C4D4×D28311yescharacteristic
384C2×C4D4×D28311yescharacteristic
385C2×C4C23×D28311yescharacteristic
386C8—21no—
387C8—5661no—
388C8—5661no—
389C8C2×D113212yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—5661no—
394C22—5661no—
395C22—5661no—
396C22—5661no—
397C22—5661no—
398C22—5661no—
399C22—11321no—
400C22—11321no—
401C22—11321no—
402C22—11321no—
403C22—11321no—
404C22—11321no—
405C22—11321no—
406C22—11321no—
407C22—11321no—
408C22—22644no—
409C22C2×D4×D28311yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—5661no—
416C4—5661no—
417C4—11321no—
418C4C22×D113211yescharacteristic
419C4#2258365611yescharacteristic
420C2—42no—
421C2—11321no—
422C2—11321no—
423C2—22641no—
424C2—22641no—
425C2—22641no—
426C2D4×D113211yescharacteristic
427C2#3182726411yescharacteristic
428C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
hypercenter#440D283
hypocenterC283#3268
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. C2×#22583631C2semidirect
3. #31827137C2semidirect
4. #31827110C2semidirect
5. #31826854C2semidirect
6. #31826712C2semidirect
7. #31826702C2semidirect
8. #31826687C2semidirect
9. #31826660C2semidirect
10. #31826630C2semidirect
11. #31826613C2semidirect
12. #31826611C2semidirect
13. #31826600C2semidirect
14. #31826538C2semidirect
15. #440×C283C2semidirect
17. C2×#17985393C22semidirect
22. C2×#17985382C22semidirect
23. C2×#17985381C22semidirect
24. C2×#17985381C22semidirect
31. C2×C8×D283C22semidirect
33. #22583607C22semidirect
41. #22583585C22semidirect
47. C4⋊(C283⋊C8)C22semidirect
48. #22583533C22semidirect
50. #22583530C22semidirect
51. #22583530C22semidirect
53. (C2×D283)⋊C8C22semidirect
55. C4×Q8×C283C22semidirect
57. #107×C283C22semidirect
58. #103×C283C22semidirect
60. #97×C283C22semidirect
114. SD16×C283D4semidirect
214. C283#3268semidirect
229. #440D283semidirect
260. C4×Q8C2×D283semidirect
265. #107C2×D283semidirect
268. #103C2×D283semidirect
275. #97C2×D283semidirect
311. SD16D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
C2×#225836312
#318271372
#318271102
#318268542
#318267122
#318267022
#318266872
#318266602
#318266302
#318266132
#318266112
#318266002
#318265382
#440×C2832
#3268283