Finite Group Databasebeta

← #36370322

Subgroups — #36370322

Order 22144.

528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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#26012558C212yesmaximal, complemented
2#26012532C214yesmaximal, complemented
3D8×#10621924C214yesmaximal, complemented
4#26012501C211yesmaximal, characteristic, complemented
5#26012483C212yesmaximal, complemented
6#26012454C211yesmaximal, characteristic, complemented
7C2×D8×D173C211yesmaximal, characteristic
8D173⋊M16C2211yescharacteristic
9D4×#10621924—24no—
10D4×#10621924C2218yescomplemented
11#19149758C2212yes—
12#19149758C2211yescharacteristic
13C2×C22⋊#10621924—24no—
14#19149748C2212yescomplemented
15#19149747C2212yescomplemented
16#19149741C2218yescomplemented
17#19149733C2212yescomplemented
18C8×#10621924C2212yescomplemented
19C2×D4×D173C2212yes—
20C2×D1384C411yescharacteristic, complemented
21C2×#14583811C412yescomplemented
22D8×D173C412yescomplemented
23D8×D173C412yescomplemented
24D8×D173C2212yes—
25D8×D173C2212yes—
26C2×C8×D173C2211yescharacteristic
27C2×D8×C173C411yescharacteristic, complemented
28C22×#10621924—28no—
29#14583836—21no—
30#14583835—21no—
31D173⋊C8C2312yes—
32C4⋊#10621924D412yes—
33C4⋊#10621924C2314yes—
34C22⋊#10621924—28no—
35C22⋊#10621924—22no—
36C22⋊#10621924D412yes—
37C4×#10621924—22no—
38C4×#10621924C2312yes—
39C23×D173—22no—
40C2×D692C2×C412yescomplemented
41C2×C22⋊D173—22no—
42D4×D173—22no—
43D4×D173—22no—
44D4×D173C2×C414yescomplemented
45D4×D173C2314yes—
46C2×C4×D173C2311yescharacteristic
47D1384C2×C412yescomplemented
48D1384C2×C412yescomplemented
49#14583811C2×C414yescomplemented
50#14583811C2×C414yescomplemented
51C2×#13063436C2×C411yescharacteristic, complemented
52C8×D173C2×C411yescharacteristic, complemented
53C8×D173C2×C411yescharacteristic, complemented
54C8×D173C2311yescharacteristic
55C8×D173C2311yescharacteristic
56C2×D4×C173C2×C412yescomplemented
57D8×C173C2×C412yescomplemented
58D8×C173C2×C412yescomplemented
59C2×C8×C173C2×C411yescharacteristic, complemented
60C2×#10621924—24no—
61C2×#10621924—88no—
62C2×#10621924C2×D414yes—
63#13063443—22no—
64C22×D173—22no—
65C22×D173—24no—
66C22×D173—24no—
67C22×D173—84no—
68C22×D173C2×D411yescharacteristic
69D692—22no—
70D692C22×C414yes—
71C22⋊D173—24no—
72C22⋊D173—24no—
73C2×Dic173#4111yescharacteristic
74C4×D173C22×C411yescharacteristic
75C4×D173C2×D411yescharacteristic
76C4×D173#4111yescharacteristic
77C4×D173C2411yescharacteristic
78#13063436C22×C411yescharacteristic
79#13063436C22×C411yescharacteristic
80C23×C173—22no—
81D4×C173—22no—
82D4×C173C22×C414yes—
83C2×C4×C173C22×C411yescharacteristic
84C8×C173C22×C411yescharacteristic
85C8×C173C22×C411yescharacteristic
86C22×C173—24no—
87C22×C173—82no—
88C22×C173C4×D411yescharacteristic
89C2×D173—22no—
90C2×D173—24no—
91C2×D173—48no—
92C2×D173—84no—
93C2×D173—82no—
94C2×D173C4×D411yescharacteristic
95C2×D173C22×D411yescharacteristic
96#10621924—24no—
97#10621924—44no—
98C4×C173C4×D411yescharacteristic
99C4×C173C23×C411yescharacteristic
100Dic173C4×D411yescharacteristic
101Dic173C2×#4111yescharacteristic
102C2×C173—21no—
103C2×C173—44no—
104C2×C173C2×C4×D411yescharacteristic
105D173—21no—
106D173—44no—
107D173#57612yes—
108C173#294811yescharacteristic, complemented, Sylow
109#2948—1731nomaximal, Sylow
110C22×D8—1731no—
111#518—1732no—
112#442—1734no—
113C4×D8—1734no—
114#427—1731no—
115#418—1732no—
116#405—1731no—
117C22×D4—1732no—
118C2×D8—1732no—
119C2×D8—1732no—
120C2×D8—1732no—
121C2×D8—1732no—
122C2×D8—1732no—
123C2×D8—1731no—
124C2×D8#1062192411yescharacteristic, complemented
125C2×M16—1731no—
126C22×C8—1731no—
127C4×D4—3464no—
128C4×D4—1738no—
129#117—1732no—
130#117—1731no—
131C2×C22⋊C4—3464no—
132#107—1732no—
133#106—1732no—
134#102—1738no—
135#97—1732no—
136C4×C8—1732no—
137C24—3462no—
138C2×D4—3462no—
139C2×D4—3462no—
140C2×D4—3462no—
141C2×D4—1734no—
142C2×D4—1734no—
143C2×D4—1732no—
144C2×D4C2×#1062192412yescomplemented
145C22×C4—3468no—
146C22×C4—1731no—
147D8—1734no—
148D8—1734no—
149D8—1732no—
150D8—1732no—
151D8C2×#1062192412yescomplemented
152D8C2×#1062192412yescomplemented
153M16—3461no—
154M16—3461no—
155C2×C8—1732no—
156C2×C8—1731no—
157C2×C8—1731no—
158C2×C8—1731no—
159C2×C8—1731no—
160C2×C8—1731no—
161C2×C8C2×#1062192411yescharacteristic, complemented
162C4⋊C4—1734no—
163C4⋊C4—1732no—
164C22⋊C4—3462no—
165C22⋊C4—3468no—
166C22⋊C4—1732no—
167C42—3462no—
168C42—1732no—
169C23—22no—
170C23—3464no—
171C23—3464no—
172C23—3462no—
173C23—13844no—
174C23—1731no—
175D4—22no—
176D4—3464no—
177D4—3464no—
178D4—3462no—
179D4—1734no—
180D4C22×#1062192414yes—
181C2×C4—3464no—
182C2×C4—13848no—
183C2×C4—1734no—
184C2×C4—1731no—
185C2×C4—1731no—
186C2×C4—1731no—
187C2×C4—1731no—
188C2×C4—1731no—
189C2×C4C22×#1062192411yescharacteristic
190C8—3462no—
191C8—1731no—
192C8—1731no—
193C8C22×#1062192411yescharacteristic
194C8C22×#1062192411yescharacteristic
195C22—24no—
196C22—82no—
197C22—3462no—
198C22—3464no—
199C22—13842no—
200C22—13844no—
201C22—1731no—
202C22—1731no—
203C22—6928no—
204C22D4×#1062192411yescharacteristic
205C4—3464no—
206C4—1731no—
207C4—1731no—
208C4—6924no—
209C4D4×#1062192411yescharacteristic
210C4C23×#1062192411yescharacteristic
211C2—21no—
212C2—44no—
213C2—3461no—
214C2—1732no—
215C2—6924no—
216C2C2×D4×#1062192411yescharacteristic
subgroupG/H
centerC2C2×D4×#10621924
commutatorC4×C173C23×C4
FrattiniC4C23×#10621924
FittingC2×D8×C173C4
socleC2×C173C2×C4×D4
prime radicalC2×D8×D173C2
cosocleC4×D173C24
hypercenterC2×D8#10621924
hypocenterC173#2948
LCSG ▷ C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #26012558C2semidirect
2. #26012532C2semidirect
3. D8×#10621924C2semidirect
4. #26012501C2semidirect
5. #26012483C2semidirect
6. #26012454C2semidirect
10. D4×#10621924C22semidirect
14. #19149748C22semidirect
15. #19149747C22semidirect
16. #19149741C22semidirect
17. #19149733C22semidirect
18. C8×#10621924C22semidirect
20. C2×D1384C4semidirect
21. C2×#14583811C4semidirect
22. D8×D173C4semidirect
23. D8×D173C4semidirect
27. C2×D8×C173C4semidirect
40. C2×D692C2×C4semidirect
44. D4×D173C2×C4semidirect
47. D1384C2×C4semidirect
48. D1384C2×C4semidirect
49. #14583811C2×C4semidirect
50. #14583811C2×C4semidirect
51. C2×#13063436C2×C4semidirect
52. C8×D173C2×C4semidirect
53. C8×D173C2×C4semidirect
56. C2×D4×C173C2×C4semidirect
57. D8×C173C2×C4semidirect
58. D8×C173C2×C4semidirect
59. C2×C8×C173C2×C4semidirect
108. C173#2948semidirect
124. C2×D8#10621924semidirect
144. C2×D4C2×#10621924semidirect
151. D8C2×#10621924semidirect
152. D8C2×#10621924semidirect
161. C2×C8C2×#10621924semidirect

Maximal subgroups

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

subgroupindex
#260125582
#260125322
D8×#106219242
#260125012
#260124832
#260124542
C2×D8×D1732
#2948173