Finite Group Databasebeta

← #137×D433 #42122601

Subgroups — #137×D433 #42122601

Order 27712.

258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 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#41×D433C211yesmaximal, characteristic
2C2×Q8×D433C211yesmaximal, characteristic, complemented
3#28357253C211yesmaximal, characteristic, complemented
4#28357252C212yesmaximal, complemented
5#28357251C211yesmaximal, characteristic, complemented
6#28357250C211yesmaximal, characteristic, complemented
7#28357249C212yesmaximal, complemented
8Q16×D433C212yesmaximal, complemented
9SD16×D433C212yesmaximal, complemented
10M16×D433C211yesmaximal, characteristic, complemented
11#137×C433C211yesmaximal, characteristic, complemented
12#20294098C2211yescharacteristic
13#20294097—21no—
14#20294097C2211yescharacteristic
15#20294096—21no—
16#20294096C2211yescharacteristic
17C2×Dic866—21no—
18C2×Dic866C2211yescharacteristic, complemented
19Q8×D433—21no—
20Q8×D433—21no—
21Q8×D433C2212yes—
22Q8×D433C2211yescharacteristic
23Q8×D433C2212yescomplemented
24D4×D433—21no—
25D4×D433C2211yescharacteristic
26C2×C4×D433—21no—
27C2×C4×D433—21no—
28C2×C4×D433C2211yescharacteristic
29Dic1732C2212yescomplemented
30#20294087C2212yescomplemented
31#20294087C2212yescomplemented
32#20294086C2212yescomplemented
33#20294085C2212yescomplemented
34#20294084C2212yescomplemented
35#20294081C2211yescharacteristic, complemented
36#20294080C2212yescomplemented
37C8×D433C2212yes—
38#41×C433C2211yescharacteristic
39C2×Q8×C433C2211yescharacteristic, complemented
40Q16×C433C2212yescomplemented
41SD16×C433C2212yescomplemented
42M16×C433C2211yescharacteristic, complemented
43C22×D433—21no—
44C22×D433D411yescharacteristic
45Dic866—21no—
46Dic866—22no—
47Dic866—22no—
48Dic866—21no—
49Dic866C2312yes—
50Dic866C2311yescharacteristic
51D1732—21no—
52D1732C2311yescharacteristic
53C22⋊D433—21no—
54C22⋊D433—21no—
55C22⋊D433—21no—
56C2×Dic433—21no—
57C2×Dic433—21no—
58C2×Dic433D411yescharacteristic
59C4×D433—21no—
60C4×D433—22no—
61C4×D433—22no—
62C4×D433—21no—
63C4×D433—21no—
64C4×D433D411yescharacteristic
65C4×D433D411yescharacteristic
66C4×D433C2311yescharacteristic
67C4×D433C2311yescharacteristic
68#16812358C2312yes—
69Q8×C433—21no—
70Q8×C433C2312yes—
71Q8×C433C2311yescharacteristic
72D4×C433—21no—
73D4×C433C2311yescharacteristic
74C2×C4×C433—21no—
75C2×C4×C433—21no—
76C2×C4×C433C2311yescharacteristic
77C8×C433C2312yes—
78C22×C433—21no—
79C22×C433C2×D411yescharacteristic
80C2×D433—22no—
81C2×D433—21no—
82C2×D433—42no—
83C2×D433C2×D411yescharacteristic
84C2×D433C2×D411yescharacteristic
85C4×C433—21no—
86C4×C433—22no—
87C4×C433C2×D411yescharacteristic
88C4×C433C2411yescharacteristic
89Dic433—21no—
90Dic433—22no—
91Dic433C2×D411yescharacteristic
92Dic433C2×D411yescharacteristic
93C2×C433—21no—
94C2×C433—41no—
95C2×C433C22×D411yescharacteristic
96D433—21no—
97D433—41no—
98D433#13712yesdirect product factor
99C433C2×#13711yescharacteristic, complemented, Sylow
100C2×#137—4331nomaximal, Sylow
101C2×#41—4331no—
102C22×Q8—4331no—
103#137—4331no—
104#137—4331no—
105#137—4332no—
106#137—4332no—
107#137—4331no—
108#137D43311yescharacteristic, direct product factor
109C2×Q16—4332no—
110C2×SD16—4332no—
111C2×M16—4331no—
112#41—8661no—
113#41—8661no—
114#41—4331no—
115#41—4331no—
116#41—4331no—
117#41C2×D43311yescharacteristic
118C2×Q8—8661no—
119C2×Q8—8661no—
120C2×Q8—8661no—
121C2×Q8—4332no—
122C2×Q8—4331no—
123C2×Q8—4332no—
124C2×Q8—4331no—
125C2×Q8C2×D43311yescharacteristic, complemented
126C2×D4—8661no—
127C2×D4—4331no—
128C22×C4—8661no—
129C22×C4—8661no—
130C22×C4—4331no—
131Q16—4332no—
132Q16—4332no—
133Q16—4332no—
134Q16C2×D43312yescomplemented
135SD16—4332no—
136SD16—4332no—
137SD16—4332no—
138SD16C2×D43312yescomplemented
139M16—4331no—
140M16—4332no—
141M16C2×D43311yescharacteristic, complemented
142C2×C8—4332no—
143C23—8661no—
144C23—4331no—
145Q8—21no—
146Q8—8662no—
147Q8—8662no—
148Q8—8661no—
149Q8—8661no—
150Q8—4332no—
151Q8—4331no—
152Q8C22×D43312yes—
153Q8C22×D43311yescharacteristic
154D4—21no—
155D4—8661no—
156D4—8661no—
157D4—8661no—
158D4—8661no—
159D4—4331no—
160D4C22×D43311yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—8661no—
164C2×C4—8662no—
165C2×C4—8662no—
166C2×C4—8661no—
167C2×C4—8661no—
168C2×C4—8661no—
169C2×C4—8661no—
170C2×C4—4331no—
171C2×C4—4331no—
172C2×C4—4331no—
173C2×C4—4331no—
174C2×C4—4331no—
175C2×C4C22×D43311yescharacteristic
176C8—4332no—
177C8C22×D43312yes—
178C22—21no—
179C22—8662no—
180C22—8661no—
181C22—4331no—
182C22—4331no—
183C22—17322no—
184C22D4×D43311yescharacteristic
185C4—21no—
186C4—22no—
187C4—8661no—
188C4—8662no—
189C4—4331no—
190C4—4331no—
191C4D4×D43311yescharacteristic
192C4C23×D43311yescharacteristic
193C2—21no—
194C2—41no—
195C2—8661no—
196C2—4332no—
197C2—17321no—
198C2C2×D4×D43311yescharacteristic
subgroupG/H
centerC2C2×D4×D433
commutator, cosocleC4×C433C24
FrattiniC4C23×D433
Fitting#137×C433C2
socleC2×C433C22×D4
prime radical#41×D433C2
hypercenter#137D433
hypocenterC433C2×#137
LCSG ▷ C4×C433 ▷ C2×C433 ▷ C433
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. C2×Q8×D433C2semidirect
3. #28357253C2semidirect
4. #28357252C2semidirect
5. #28357251C2semidirect
6. #28357250C2semidirect
7. #28357249C2semidirect
8. Q16×D433C2semidirect
9. SD16×D433C2semidirect
10. M16×D433C2semidirect
11. #137×C433C2semidirect
18. C2×Dic866C22semidirect
23. Q8×D433C22semidirect
29. Dic1732C22semidirect
30. #20294087C22semidirect
31. #20294087C22semidirect
32. #20294086C22semidirect
33. #20294085C22semidirect
34. #20294084C22semidirect
35. #20294081C22semidirect
36. #20294080C22semidirect
39. C2×Q8×C433C22semidirect
40. Q16×C433C22semidirect
41. SD16×C433C22semidirect
42. M16×C433C22semidirect
98. D433#137direct (N × H)
99. C433C2×#137semidirect
108. #137D433direct (N × H)
125. C2×Q8C2×D433semidirect
134. Q16C2×D433semidirect
138. SD16C2×D433semidirect
141. M16C2×D433semidirect

Maximal subgroups

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

subgroupindex
#41×D4332
C2×Q8×D4332
#283572532
#283572522
#283572512
#283572502
#283572492
Q16×D4332
SD16×D4332
M16×D4332
#137×C4332
C2×#137433