Finite Group Databasebeta

← #508×D89 #26033366

Subgroups — #508×D89 #26033366

Order 11392.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#135×D89C212yesmaximal, complemented
2#19152031C211yesmaximal, characteristic, complemented
3#19152030C211yesmaximal, characteristic, complemented
4#19152029C212yesmaximal, complemented
5#19152028C212yesmaximal, complemented
6#19152027C211yesmaximal, characteristic, complemented
7Q32×D89C211yesmaximal, characteristic, complemented
8SD32×D89C212yesmaximal, complemented
9D16×D89C211yesmaximal, characteristic, complemented
10C2×C16×D89C211yesmaximal, characteristic, complemented
11#508×C89C211yesmaximal, characteristic, complemented
12#41×D89—22no—
13#15668035C2212yescomplemented
14#15668034C2212yescomplemented
15#15668033—22no—
16#15668032—22no—
17#15668031C2212yescomplemented
18Q16×D89C2212yes—
19SD16×D89—22no—
20D8×D89C2212yes—
21C2×C8×D89C2211yescharacteristic
22Dic712C2211yescharacteristic, complemented
23#15667958C2212yescomplemented
24#15667957C2212yescomplemented
25#15667956C2212yescomplemented
26#15667955C2212yescomplemented
27D1424C2211yescharacteristic, complemented
28#15667953C2212yescomplemented
29C2×#13083549C2211yescharacteristic, complemented
30C16×D89C2211yescharacteristic
31C16×D89C2211yescharacteristic
32C16×D89C2211yescharacteristic, complemented
33C16×D89C2211yescharacteristic, complemented
34#135×C89C2212yescomplemented
35Q32×C89C2211yescharacteristic, complemented
36SD32×C89C2212yescomplemented
37D16×C89C2211yescharacteristic, complemented
38C2×C16×C89C2211yescharacteristic, complemented
39#13083575—22no—
40#13083574—22no—
41#13083574—42no—
42#13083573—22no—
43#13083573—42no—
44Q8×D89—22no—
45D4×D89—22no—
46D4×D89—42no—
47C2×C4×D89—42no—
48C2×C4×D89D411yescharacteristic
49Dic356C2312yes—
50#13083564—22no—
51#13083563—22no—
52#13083562—22no—
53#13083561—22no—
54D712C2312yes—
55#13083559—22no—
56C2×#10623494D411yescharacteristic
57C8×D89D411yescharacteristic
58C8×D89D411yescharacteristic
59C8×D89C2311yescharacteristic
60C8×D89C2311yescharacteristic
61#13083549C2311yescharacteristic
62#13083549C2311yescharacteristic
63#41×C89—22no—
64Q16×C89C2312yes—
65SD16×C89—22no—
66D8×C89C2312yes—
67C2×C8×C89C2311yescharacteristic
68C16×C89C2311yescharacteristic
69C16×C89C2311yescharacteristic
70C22×D89—42no—
71C22×D89D811yescharacteristic
72Q8×C89—22no—
73D4×C89—22no—
74D4×C89—42no—
75C2×C4×C89—42no—
76C2×C4×C89C2×D411yescharacteristic
77C22⋊D89—42no—
78C22⋊D89—42no—
79C22⋊D89—42no—
80C2×Dic89—42no—
81C2×Dic89D811yescharacteristic
82D356—22no—
83D356—42no—
84C4×D89—42no—
85C4×D89—42no—
86C4×D89—42no—
87C4×D89D811yescharacteristic
88C4×D89D811yescharacteristic
89C4×D89C2×D411yescharacteristic
90C4×D89C2×D411yescharacteristic
91Dic178—22no—
92Dic178—42no—
93C8×C89C2×D411yescharacteristic
94C8×C89C2411yescharacteristic
95#10623494C2×D411yescharacteristic
96#10623494C2×D411yescharacteristic
97C22×C89—42no—
98C22×C89C2×D811yescharacteristic
99C2×D89—22no—
100C2×D89—42no—
101C2×D89—84no—
102C2×D89C2×D811yescharacteristic
103C2×D89C2×D811yescharacteristic
104C4×C89—42no—
105C4×C89C2×D811yescharacteristic
106C4×C89C22×D411yescharacteristic
107Dic89—42no—
108Dic89C2×D811yescharacteristic
109Dic89C2×D811yescharacteristic
110C2×C89—21no—
111C2×C89—82no—
112C2×C89C22×D811yescharacteristic
113D89—21no—
114D89—82no—
115D89#50812yesdirect product factor
116C2×#508—891nomaximal, Sylow
117C89C2×#50811yescharacteristic, complemented, Sylow
118C2×#135—892no—
119#508—892no—
120#508—891no—
121#508—892no—
122#508—891no—
123#508—891no—
124#508D8911yescharacteristic, direct product factor
125C2×Q32—891no—
126C2×SD32—892no—
127C2×D16—891no—
128C22×C16—891no—
129C2×#41—1782no—
130#135—892no—
131#135—892no—
132#135—892no—
133#135—1782no—
134#135—1782no—
135#135C2×D8912yescomplemented
136C2×Q16—892no—
137C2×SD16—1782no—
138C2×D8—892no—
139C22×C8—891no—
140Q32—892no—
141Q32—891no—
142Q32C2×D8911yescharacteristic, complemented
143SD32—892no—
144SD32—892no—
145SD32—892no—
146SD32C2×D8912yescomplemented
147D16—892no—
148D16—891no—
149D16C2×D8911yescharacteristic, complemented
150C2×C16—891no—
151C2×C16—891no—
152C2×C16—891no—
153C2×C16—891no—
154C2×C16—891no—
155C2×C16C2×D8911yescharacteristic, complemented
156#41—22no—
157#41—3562no—
158#41—3562no—
159#41—1782no—
160#41—1782no—
161#41—1782no—
162C2×Q8—1782no—
163C2×D4—3562no—
164C2×D4—1782no—
165C22×C4—891no—
166C22×C4—3562no—
167Q16—892no—
168Q16—1782no—
169Q16C22×D8912yes—
170SD16—22no—
171SD16—1782no—
172SD16—1782no—
173SD16—1782no—
174D8—892no—
175D8—1782no—
176D8C22×D8912yes—
177C2×C8—891no—
178C2×C8—891no—
179C2×C8—891no—
180C2×C8—891no—
181C2×C8—891no—
182C2×C8C22×D8911yescharacteristic
183C16—891no—
184C16—891no—
185C16C22×D8911yescharacteristic
186C16C22×D8911yescharacteristic
187C23—891no—
188C23—3562no—
189Q8—22no—
190Q8—3562no—
191Q8—1782no—
192D4—22no—
193D4—42no—
194D4—3562no—
195D4—3562no—
196D4—3562no—
197D4—3562no—
198D4—1782no—
199C2×C4—42no—
200C2×C4—891no—
201C2×C4—891no—
202C2×C4—891no—
203C2×C4—891no—
204C2×C4—891no—
205C2×C4—3562no—
206C2×C4—3562no—
207C2×C4—3562no—
208C2×C4—3562no—
209C2×C4D4×D8911yescharacteristic
210C8—891no—
211C8—891no—
212C8D4×D8911yescharacteristic
213C8C23×D8911yescharacteristic
214C22—42no—
215C22—891no—
216C22—891no—
217C22—3562no—
218C22—1782no—
219C22—7124no—
220C22D8×D8911yescharacteristic
221C4—42no—
222C4—891no—
223C4—891no—
224C4—3562no—
225C4D8×D8911yescharacteristic
226C4C2×D4×D8911yescharacteristic
227C2—21no—
228C2—82no—
229C2—892no—
230C2—1781no—
231C2—7122no—
232C2C2×D8×D8911yescharacteristic
subgroupG/H
centerC4D8×D89
commutator, cosocleC8×C89C24
FrattiniC8C23×D89
Fitting#508×C89C2
socleC2×C89C22×D8
hypercenter#508D89
hypocenterC89C2×#508
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D89C2semidirect
2. #19152031C2semidirect
3. #19152030C2semidirect
4. #19152029C2semidirect
5. #19152028C2semidirect
6. #19152027C2semidirect
7. Q32×D89C2semidirect
8. SD32×D89C2semidirect
9. D16×D89C2semidirect
10. C2×C16×D89C2semidirect
11. #508×C89C2semidirect
13. #15668035C22semidirect
14. #15668034C22semidirect
17. #15668031C22semidirect
22. Dic712C22semidirect
23. #15667958C22semidirect
24. #15667957C22semidirect
25. #15667956C22semidirect
26. #15667955C22semidirect
27. D1424C22semidirect
28. #15667953C22semidirect
29. C2×#13083549C22semidirect
32. C16×D89C22semidirect
33. C16×D89C22semidirect
34. #135×C89C22semidirect
35. Q32×C89C22semidirect
36. SD32×C89C22semidirect
37. D16×C89C22semidirect
38. C2×C16×C89C22semidirect
115. D89#508direct (N × H)
117. C89C2×#508semidirect
124. #508D89direct (N × H)
135. #135C2×D89semidirect
142. Q32C2×D89semidirect
146. SD32C2×D89semidirect
149. D16C2×D89semidirect
155. C2×C16C2×D89semidirect

Maximal subgroups

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

subgroupindex
#135×D892
#191520312
#191520302
#191520292
#191520282
#191520272
Q32×D892
SD32×D892
D16×D892
C2×C16×D892
#508×C892
C2×#50889