Finite Group Databasebeta

← #44537532

Subgroups — #44537532

Order 31424.

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

normal subgroups only

This group has 258 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
1#30628384C211yesmaximal, characteristic, complemented
2#30628383C211yesmaximal, characteristic, complemented
3#30628369C212yesmaximal, complemented
4#30628367C211yesmaximal, characteristic, complemented
5#30628362C211yesmaximal, characteristic, complemented
6#30628361C212yesmaximal, complemented
7#30628358C212yesmaximal, complemented
8C2×#21463317C211yesmaximal, characteristic, complemented
9SD16×D491C212yesmaximal, complemented
10#30628343C211yesmaximal, characteristic, complemented
11#135×C491C211yesmaximal, characteristic, complemented
12#21463329C2212yes—
13#21463328—21no—
14#21463328—21no—
15#21463328C2211yescharacteristic
16#21463327—22no—
17#21463327C2212yescomplemented
18C2×Dic982—21no—
19C2×Dic982C2211yescharacteristic, complemented
20Q8×D491C2212yescomplemented
21C2×D1964—21no—
22C2×D1964C2211yescharacteristic
23D4×D491—22no—
24D4×D491C2212yes—
25#21463318C2212yescomplemented
26#21463317C2212yescomplemented
27#21463317C2212yescomplemented
28#21463316C2212yescomplemented
29#21463315C2212yescomplemented
30#21463313C2212yescomplemented
31#21463312C2211yescharacteristic, complemented
32#21463311C2212yescomplemented
33C8×D491C2212yescomplemented
34#41×C491C2211yescharacteristic
35#41×C491C2211yescharacteristic, complemented
36Q16×C491C2211yescharacteristic, complemented
37SD16×C491C2211yescharacteristic, complemented
38SD16×C491C2211yescharacteristic, complemented
39D8×C491C2211yescharacteristic, complemented
40C2×C8×C491C2211yescharacteristic, complemented
41C22×D491—21no—
42C22×D491—22no—
43Dic982—21no—
44Dic982—22no—
45Dic982D411yescharacteristic
46Dic982C2312yes—
47D1964—22no—
48D1964—21no—
49D1964D411yescharacteristic
50D1964C2312yes—
51C22⋊D491—22no—
52C22⋊D491—22no—
53C22⋊D491D412yes—
54C2×Dic491—21no—
55C2×Dic491—22no—
56C4×D491—22no—
57C4×D491—22no—
58C4×D491C2312yes—
59C491⋊C8C2312yes—
60Q8×C491C2311yescharacteristic
61Q8×C491C2311yescharacteristic
62D4×C491—21no—
63D4×C491—21no—
64D4×C491C2311yescharacteristic
65D4×C491C2311yescharacteristic
66C2×C4×C491—21no—
67C2×C4×C491—21no—
68C2×C4×C491C2311yescharacteristic
69C8×C491C2311yescharacteristic
70C8×C491C2311yescharacteristic
71C22×C491—21no—
72C22×C491—21no—
73C22×C491C2×D411yescharacteristic
74C2×D491—22no—
75C2×D491—82no—
76C2×D491—81no—
77C2×D491C2×D412yes—
78C4×C491—21no—
79C4×C491—21no—
80C4×C491C2×D411yescharacteristic
81C4×C491C2411yescharacteristic
82Dic491—22no—
83Dic491C2×D412yes—
84C2×C491—21no—
85C2×C491—41no—
86C2×C491—41no—
87C2×C491C22×D411yescharacteristic
88D491—22no—
89D491—42no—
90C491#57711yescharacteristic, complemented, Sylow
91#577—4911nomaximal, Sylow
922−1+4—4911no—
93H(5,𝔽2)—4911no—
94#137—4911no—
95#137—4912no—
96AGL(1,ℤ/8)—4911no—
97AGL(1,ℤ/8)—4912no—
98#135—4912no—
99#135D49111yescharacteristic, complemented
100C2×SD16—4912no—
101C2×SD16—4911no—
102#131—4911no—
103#41—9821no—
104#41—9821no—
105#41—9822no—
106#41—4912no—
107#41—4912no—
108#41—4911no—
109#41C2×D49111yescharacteristic
110#41C2×D49111yescharacteristic, complemented
111C2×Q8—9821no—
112C2×Q8—4912no—
113C2×Q8—4911no—
114C2×D4—9821no—
115C2×D4—9822no—
116C2×D4—4912no—
117C2×D4—4911no—
118Q16—4912no—
119Q16C2×D49111yescharacteristic, complemented
120SD16—4912no—
121SD16—4912no—
122SD16—4912no—
123SD16—4912no—
124SD16C2×D49111yescharacteristic, complemented
125SD16C2×D49111yescharacteristic, complemented
126D8—4912no—
127D8C2×D49111yescharacteristic, complemented
128M16—4911no—
129M16—4912no—
130C2×C8—4912no—
131C2×C8C2×D49111yescharacteristic, complemented
132C23—9822no—
133C23—9821no—
134Q8—9822no—
135Q8—9821no—
136Q8—4912no—
137Q8—4911no—
138Q8C22×D49111yescharacteristic
139Q8C22×D49111yescharacteristic
140D4—21no—
141D4—21no—
142D4—9822no—
143D4—9822no—
144D4—9822no—
145D4—9821no—
146D4—4912no—
147D4—4911no—
148D4—4912no—
149D4C22×D49111yescharacteristic
150D4C22×D49111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—9822no—
154C2×C4—9822no—
155C2×C4—9821no—
156C2×C4—9822no—
157C2×C4—4912no—
158C2×C4C22×D49111yescharacteristic
159C8—4912no—
160C8C22×D49111yescharacteristic
161C8C22×D49111yescharacteristic
162C22—21no—
163C22—21no—
164C22—39281no—
165C22—39282no—
166C22—9822no—
167C22—4912no—
168C22D4×D49111yescharacteristic
169C4—21no—
170C4—21no—
171C4—9822no—
172C4—4912no—
173C4D4×D49111yescharacteristic
174C4C23×D49111yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—19642no—
179C2—9822no—
180C2C2×D4×D49111yescharacteristic
subgroupG/H
centerC2C2×D4×D491
commutator, cosocleC4×C491C24
FrattiniC4C23×D491
Fitting#135×C491C2
socleC2×C491C22×D4
hypercenter#135D491
hypocenterC491#577
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #30628384C2semidirect
2. #30628383C2semidirect
3. #30628369C2semidirect
4. #30628367C2semidirect
5. #30628362C2semidirect
6. #30628361C2semidirect
7. #30628358C2semidirect
8. C2×#21463317C2semidirect
9. SD16×D491C2semidirect
10. #30628343C2semidirect
11. #135×C491C2semidirect
17. #21463327C22semidirect
19. C2×Dic982C22semidirect
20. Q8×D491C22semidirect
25. #21463318C22semidirect
26. #21463317C22semidirect
27. #21463317C22semidirect
28. #21463316C22semidirect
29. #21463315C22semidirect
30. #21463313C22semidirect
31. #21463312C22semidirect
32. #21463311C22semidirect
33. C8×D491C22semidirect
35. #41×C491C22semidirect
36. Q16×C491C22semidirect
37. SD16×C491C22semidirect
38. SD16×C491C22semidirect
39. D8×C491C22semidirect
40. C2×C8×C491C22semidirect
90. C491#577semidirect
99. #135D491semidirect
110. #41C2×D491semidirect
119. Q16C2×D491semidirect
124. SD16C2×D491semidirect
125. SD16C2×D491semidirect
127. D8C2×D491semidirect
131. C2×C8C2×D491semidirect

Maximal subgroups

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

subgroupindex
#306283842
#306283832
#306283692
#306283672
#306283622
#306283612
#306283582
C2×#214633172
SD16×D4912
#306283432
#135×C4912
#577491