Finite Group Databasebeta

← #34092493

Subgroups — #34092493

Order 19904.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19097316C211yesmaximal, characteristic, complemented
2#41×D311C211yesmaximal, characteristic, complemented
3#23755740C212yesmaximal, complemented
4#23755739C211yesmaximal, characteristic, complemented
5#23755736C211yesmaximal, characteristic, complemented
6#23755735C212yesmaximal, complemented
7#23755733C211yesmaximal, characteristic, complemented
8#23755731C212yesmaximal, complemented
9#23755729C212yesmaximal, complemented
10M16×D311C211yesmaximal, characteristic, complemented
11#137×C311C211yesmaximal, characteristic, complemented
12#19097316—21no—
13#19097316—21no—
14#19097316C2212yes—
15#19097316C2212yescomplemented
16#19097316C2211yescharacteristic, complemented
17#19097315—21no—
18#19097315C2211yescharacteristic
19#19097314—21no—
20#19097314C2211yescharacteristic, complemented
21Q8×D311C2211yescharacteristic, complemented
22C2×D1244—21no—
23C2×D1244C2211yescharacteristic, complemented
24D4×D311—21no—
25D4×D311C2211yescharacteristic, complemented
26C2×C4×D311—21no—
27C2×C4×D311—21no—
28C2×C4×D311C2211yescharacteristic
29#19097305C2212yescomplemented
30#19097304C2212yescomplemented
31#19097302C2212yescomplemented
32#19097302C2212yescomplemented
33D2488C2212yescomplemented
34#19097300C2212yescomplemented
35#19097299C2211yescharacteristic, complemented
36#19097298C2212yescomplemented
37C8×D311C2212yescomplemented
38#41×C311C2211yescharacteristic
39C2×Q8×C311C2211yescharacteristic, complemented
40Q16×C311C2212yescomplemented
41SD16×C311C2212yescomplemented
42M16×C311C2211yescharacteristic, complemented
43C22×D311—21no—
44C22×D311—21no—
45C22×D311D411yescharacteristic
46Dic622—21no—
47Dic622C2311yescharacteristic
48D1244—21no—
49D1244—22no—
50D1244—22no—
51D1244—21no—
52D1244C2312yes—
53D1244C2311yescharacteristic
54C22⋊D311—21no—
55C22⋊D311—21no—
56C22⋊D311—21no—
57C2×Dic311—21no—
58C2×Dic311D411yescharacteristic
59C4×D311—21no—
60C4×D311—21no—
61C4×D311—21no—
62C4×D311—22no—
63C4×D311—22no—
64C4×D311D411yescharacteristic
65C4×D311D411yescharacteristic
66C4×D311C2311yescharacteristic
67C4×D311C2311yescharacteristic
68C311⋊C8C2312yes—
69Q8×C311—21no—
70Q8×C311C2312yes—
71Q8×C311C2311yescharacteristic
72D4×C311—21no—
73D4×C311C2311yescharacteristic
74C2×C4×C311—21no—
75C2×C4×C311—21no—
76C2×C4×C311C2311yescharacteristic
77C8×C311C2312yes—
78C22×C311—21no—
79C22×C311C2×D411yescharacteristic
80C2×D311—21no—
81C2×D311—22no—
82C2×D311—41no—
83C2×D311—42no—
84C2×D311—42no—
85C2×D311C2×D411yescharacteristic
86C2×D311C2×D411yescharacteristic
87C4×C311—21no—
88C4×C311—22no—
89C4×C311C2×D411yescharacteristic
90C4×C311C2411yescharacteristic
91Dic311—21no—
92Dic311C2×D411yescharacteristic
93Dic311C2×D411yescharacteristic
94C2×C311—21no—
95C2×C311—41no—
96C2×C311C22×D411yescharacteristic
97D311—21no—
98D311—21no—
99D311—41no—
100D311—42no—
101C311#57511yescharacteristic, complemented, Sylow
102#575—3111nomaximal, Sylow
103C2×#41—3111no—
104C2×#41—3111no—
105#137—3111no—
106#137—3112no—
107#137D31111yescharacteristic, complemented
108AGL(1,ℤ/8)—3111no—
109AGL(1,ℤ/8)—3112no—
110AGL(1,ℤ/8)—3111no—
111#135—3112no—
112#135—3112no—
113C2×M16—3111no—
114#41—3111no—
115#41—3112no—
116#41—3112no—
117#41—3111no—
118#41—3111no—
119#41—6221no—
120#41—6221no—
121#41—6221no—
122#41—6221no—
123#41C2×D31111yescharacteristic
124C2×Q8—3111no—
125C2×Q8C2×D31111yescharacteristic, complemented
126C2×D4—3111no—
127C2×D4—3111no—
128C2×D4—6221no—
129C2×D4—6221no—
130C22×C4—3111no—
131C22×C4—6221no—
132C22×C4—6221no—
133Q16—3112no—
134Q16C2×D31112yescomplemented
135SD16—3112no—
136SD16—3112no—
137SD16—3112no—
138SD16C2×D31112yescomplemented
139D8—3112no—
140D8—3112no—
141M16—3111no—
142M16—3112no—
143M16C2×D31111yescharacteristic, complemented
144C2×C8—3112no—
145C23—3111no—
146C23—6221no—
147C23—6221no—
148Q8—21no—
149Q8—3111no—
150Q8—6221no—
151Q8C22×D31111yescharacteristic
152Q8C22×D31112yes—
153D4—21no—
154D4—3112no—
155D4—3111no—
156D4—6221no—
157D4—6222no—
158D4—6222no—
159D4—6221no—
160D4—6221no—
161D4—6221no—
162D4—6221no—
163D4C22×D31111yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—3111no—
167C2×C4—3111no—
168C2×C4—3111no—
169C2×C4—3111no—
170C2×C4—3111no—
171C2×C4—6221no—
172C2×C4—6222no—
173C2×C4—6222no—
174C2×C4—6221no—
175C2×C4—6221no—
176C2×C4—6221no—
177C2×C4C22×D31111yescharacteristic
178C8—3112no—
179C8C22×D31112yes—
180C22—21no—
181C22—3111no—
182C22—3111no—
183C22—6222no—
184C22—6221no—
185C22—12441no—
186C22—12442no—
187C22—12442no—
188C22D4×D31111yescharacteristic
189C4—21no—
190C4—22no—
191C4—3111no—
192C4—3111no—
193C4—6221no—
194C4D4×D31111yescharacteristic
195C4C23×D31111yescharacteristic
196C2—21no—
197C2—41no—
198C2—6221no—
199C2—6221no—
200C2—12442no—
201C2—12441no—
202C2C2×D4×D31111yescharacteristic
subgroupG/H
centerC2C2×D4×D311
commutator, cosocleC4×C311C24
FrattiniC4C23×D311
Fitting#137×C311C2
socleC2×C311C22×D4
hypercenter#137D311
hypocenterC311#575
LCSG ▷ C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#19097316C2semidirect
2. #41×D311C2semidirect
3. #23755740C2semidirect
4. #23755739C2semidirect
5. #23755736C2semidirect
6. #23755735C2semidirect
7. #23755733C2semidirect
8. #23755731C2semidirect
9. #23755729C2semidirect
10. M16×D311C2semidirect
11. #137×C311C2semidirect
15. #19097316C22semidirect
16. #19097316C22semidirect
20. #19097314C22semidirect
21. Q8×D311C22semidirect
23. C2×D1244C22semidirect
25. D4×D311C22semidirect
29. #19097305C22semidirect
30. #19097304C22semidirect
31. #19097302C22semidirect
32. #19097302C22semidirect
33. D2488C22semidirect
34. #19097300C22semidirect
35. #19097299C22semidirect
36. #19097298C22semidirect
37. C8×D311C22semidirect
39. C2×Q8×C311C22semidirect
40. Q16×C311C22semidirect
41. SD16×C311C22semidirect
42. M16×C311C22semidirect
101. C311#575semidirect
107. #137D311semidirect
125. C2×Q8C2×D311semidirect
134. Q16C2×D311semidirect
138. SD16C2×D311semidirect
143. M16C2×D311semidirect

Maximal subgroups

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

subgroupindex
C2×#190973162
#41×D3112
#237557402
#237557392
#237557362
#237557352
#237557332
#237557312
#237557292
M16×D3112
#137×C3112
#575311