Finite Group Databasebeta

← #49134396

Subgroups — #49134396

Order 36224.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583633C211yesmaximal, characteristic, complemented
2#135×D283C211yesmaximal, characteristic, complemented
3#31826907C212yesmaximal, complemented
4#31826906C211yesmaximal, characteristic, complemented
5#31826903C211yesmaximal, characteristic, complemented
6#31826902C212yesmaximal, complemented
7#31826900C211yesmaximal, characteristic, complemented
8#31826898C212yesmaximal, complemented
9#31826896C212yesmaximal, complemented
10M32×D283C211yesmaximal, characteristic, complemented
11#510×C283C211yesmaximal, characteristic, complemented
12C2×#17985393—21no—
13#41×D283—21no—
14#22583633—21no—
15#22583633—21no—
16#22583633C2212yes—
17#22583633C2211yescharacteristic, complemented
18#22583633C2212yescomplemented
19#22583632C2211yescharacteristic
20#22583631—21no—
21#22583630—21no—
22#22583629C2211yescharacteristic, complemented
23Q16×D283C2211yescharacteristic, complemented
24C2×#17985379—21no—
25SD16×D283—21no—
26C2×D2264C2211yescharacteristic, complemented
27D8×D283C2211yescharacteristic, complemented
28C2×C8×D283C2211yescharacteristic
29#22583556C2212yescomplemented
30#22583555C2212yescomplemented
31#22583553C2212yescomplemented
32#22583553C2212yescomplemented
33D4528C2212yescomplemented
34#22583551C2212yescomplemented
35#22583550C2211yescharacteristic, complemented
36#22583549C2212yescomplemented
37C16×D283C2212yescomplemented
38#135×C283C2211yescharacteristic
39C2×Q16×C283C2211yescharacteristic, complemented
40Q32×C283C2212yescomplemented
41SD32×C283C2212yescomplemented
42M32×C283C2211yescharacteristic, complemented
43#17985393—21no—
44#17985393—22no—
45#17985393—22no—
46#17985393—41no—
47#17985393—41no—
48#17985392—21no—
49#17985392—41no—
50#17985391—21no—
51#17985391—41no—
52Q8×D283—21no—
53C2×D1132—21no—
54C2×D1132—41no—
55D4×D283—21no—
56D4×D283—41no—
57C2×C4×D283—41no—
58C2×C4×D283—41no—
59C2×C4×D283D411yescharacteristic
60Dic1132C2311yescharacteristic
61#17985382—21no—
62#17985381—21no—
63#17985380—21no—
64#17985379—21no—
65#17985379—22no—
66#17985379—22no—
67D2264—21no—
68D2264C2311yescharacteristic
69D2264C2312yes—
70#17985377—21no—
71C2×C283⋊C8D411yescharacteristic
72C8×D283D411yescharacteristic
73C8×D283D411yescharacteristic
74C8×D283C2311yescharacteristic
75C8×D283C2311yescharacteristic
76C283⋊C16C2312yes—
77#41×C283—21no—
78C2×Q8×C283—21no—
79Q16×C283—21no—
80Q16×C283C2311yescharacteristic
81Q16×C283C2312yes—
82SD16×C283—21no—
83D8×C283C2311yescharacteristic
84C2×C8×C283C2311yescharacteristic
85C16×C283C2312yes—
86C22×D283—41no—
87C22×D283—41no—
88C22×D283D811yescharacteristic
89Dic566—21no—
90Dic566—41no—
91D1132—21no—
92D1132—22no—
93D1132—41no—
94D1132—42no—
95D1132—42no—
96D1132—41no—
97C22⋊D283—41no—
98C22⋊D283—41no—
99C22⋊D283—41no—
100C2×Dic283—41no—
101C2×Dic283D811yescharacteristic
102C4×D283—41no—
103C4×D283—41no—
104C4×D283—41no—
105C4×D283—42no—
106C4×D283—42no—
107C4×D283D811yescharacteristic
108C4×D283D811yescharacteristic
109C4×D283C2×D411yescharacteristic
110C4×D283C2×D411yescharacteristic
111C283⋊C8C2×D411yescharacteristic
112C283⋊C8C2×D411yescharacteristic
113Q8×C283—21no—
114Q8×C283—22no—
115Q8×C283—41no—
116D4×C283—21no—
117D4×C283—41no—
118C2×C4×C283—41no—
119C2×C4×C283—41no—
120C2×C4×C283C2×D411yescharacteristic
121C8×C283C2×D411yescharacteristic
122C8×C283C2411yescharacteristic
123C22×C283—41no—
124C22×C283C2×D811yescharacteristic
125C2×D283—41no—
126C2×D283—41no—
127C2×D283—42no—
128C2×D283—82no—
129C2×D283—82no—
130C2×D283C2×D811yescharacteristic
131C2×D283C2×D811yescharacteristic
132C4×C283—41no—
133C4×C283—42no—
134C4×C283C2×D811yescharacteristic
135C4×C283C22×D411yescharacteristic
136Dic283—41no—
137Dic283C2×D811yescharacteristic
138Dic283C2×D811yescharacteristic
139C2×C283—21no—
140C2×C283—81no—
141C2×C283C22×D811yescharacteristic
142D283—21no—
143D283—21no—
144D283—81no—
145D283—82no—
146C283#341411yescharacteristic, complemented, Sylow
147#3414—2831nomaximal, Sylow
148C2×#135—2831no—
149C2×#135—2831no—
150#510—2831no—
151#510—2832no—
152#510D28311yescharacteristic, complemented
153#509—2831no—
154#509—2832no—
155#509—2831no—
156#508—2832no—
157#508—2832no—
158C2×M32—2831no—
159C2×#41—5661no—
160C2×#41—5661no—
161#135—2832no—
162#135—2831no—
163#135—2832no—
164#135—2831no—
165#135—2831no—
166#135—5661no—
167#135—5661no—
168#135—5661no—
169#135—5661no—
170#135C2×D28311yescharacteristic
171C2×Q16—2831no—
172C2×Q16C2×D28311yescharacteristic, complemented
173C2×SD16—5661no—
174C2×SD16—5661no—
175C2×D8—2831no—
176C2×D8—2831no—
177C22×C8—2831no—
178Q32—2832no—
179Q32C2×D28312yescomplemented
180SD32—2832no—
181SD32—2832no—
182SD32—2832no—
183SD32C2×D28312yescomplemented
184D16—2832no—
185D16—2832no—
186M32—2831no—
187M32—2832no—
188M32C2×D28311yescharacteristic, complemented
189C2×C16—2832no—
190#41—21no—
191#41—5661no—
192#41—5662no—
193#41—5661no—
194#41—5662no—
195#41—5661no—
196#41—11321no—
197#41—11321no—
198#41—11321no—
199#41—11321no—
200C2×Q8—21no—
201C2×Q8—5661no—
202C2×D4—5661no—
203C2×D4—5661no—
204C2×D4—11321no—
205C2×D4—11321no—
206C22×C4—2831no—
207C22×C4—11321no—
208C22×C4—11321no—
209Q16—21no—
210Q16—2831no—
211Q16—5661no—
212Q16C22×D28311yescharacteristic
213Q16C22×D28312yes—
214SD16—21no—
215SD16—5661no—
216SD16—5662no—
217SD16—5661no—
218SD16—5662no—
219SD16—5661no—
220D8—2831no—
221D8—2832no—
222D8—5661no—
223D8—5661no—
224D8C22×D28311yescharacteristic
225C2×C8—2831no—
226C2×C8—2831no—
227C2×C8—2831no—
228C2×C8—2831no—
229C2×C8—2831no—
230C2×C8C22×D28311yescharacteristic
231C16—2832no—
232C16C22×D28312yes—
233C23—2831no—
234C23—11321no—
235C23—11321no—
236Q8—21no—
237Q8—22no—
238Q8—41no—
239Q8—5661no—
240Q8—11321no—
241D4—21no—
242D4—41no—
243D4—5661no—
244D4—5662no—
245D4—11321no—
246D4—11322no—
247D4—11322no—
248D4—11321no—
249D4—11321no—
250D4—11321no—
251D4—11321no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—2831no—
255C2×C4—2831no—
256C2×C4—2831no—
257C2×C4—2831no—
258C2×C4—2831no—
259C2×C4—11321no—
260C2×C4—11322no—
261C2×C4—11322no—
262C2×C4—11321no—
263C2×C4—11321no—
264C2×C4—11321no—
265C2×C4D4×D28311yescharacteristic
266C8—2831no—
267C8—2831no—
268C8D4×D28311yescharacteristic
269C8C23×D28311yescharacteristic
270C22—41no—
271C22—2831no—
272C22—2831no—
273C22—11321no—
274C22—11322no—
275C22—11321no—
276C22—22642no—
277C22—22642no—
278C22D8×D28311yescharacteristic
279C4—41no—
280C4—42no—
281C4—2831no—
282C4—2831no—
283C4—11321no—
284C4D8×D28311yescharacteristic
285C4C2×D4×D28311yescharacteristic
286C2—21no—
287C2—81no—
288C2—5661no—
289C2—5661no—
290C2—22642no—
291C2—22641no—
292C2C2×D8×D28311yescharacteristic
subgroupG/H
centerC2C2×D8×D283
commutator, cosocleC8×C283C24
FrattiniC8C23×D283
Fitting#510×C283C2
socleC2×C283C22×D8
hypercenter#510D283
hypocenterC283#3414
LCSG ▷ C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. C2×#22583633C2semidirect
2. #135×D283C2semidirect
3. #31826907C2semidirect
4. #31826906C2semidirect
5. #31826903C2semidirect
6. #31826902C2semidirect
7. #31826900C2semidirect
8. #31826898C2semidirect
9. #31826896C2semidirect
10. M32×D283C2semidirect
11. #510×C283C2semidirect
17. #22583633C22semidirect
18. #22583633C22semidirect
22. #22583629C22semidirect
23. Q16×D283C22semidirect
26. C2×D2264C22semidirect
27. D8×D283C22semidirect
29. #22583556C22semidirect
30. #22583555C22semidirect
31. #22583553C22semidirect
32. #22583553C22semidirect
33. D4528C22semidirect
34. #22583551C22semidirect
35. #22583550C22semidirect
36. #22583549C22semidirect
37. C16×D283C22semidirect
39. C2×Q16×C283C22semidirect
40. Q32×C283C22semidirect
41. SD32×C283C22semidirect
42. M32×C283C22semidirect
146. C283#3414semidirect
152. #510D283semidirect
172. C2×Q16C2×D283semidirect
179. Q32C2×D283semidirect
183. SD32C2×D283semidirect
188. M32C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836332
#135×D2832
#318269072
#318269062
#318269032
#318269022
#318269002
#318268982
#318268962
M32×D2832
#510×C2832
#3414283