Finite Group Databasebeta

← #44537531

Subgroups — #44537531

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#30628385C211yesmaximal, characteristic, complemented
2#30628382C211yesmaximal, characteristic, complemented
3#30628368C211yesmaximal, characteristic, complemented
4#30628366C212yesmaximal, complemented
5#30628364C212yesmaximal, complemented
6#30628363C211yesmaximal, characteristic, complemented
7#30628359C211yesmaximal, characteristic, complemented
8#30628358C212yesmaximal, complemented
9SD16×D491C212yesmaximal, complemented
10#30628343C211yesmaximal, characteristic, complemented
11C2×SD16×C491C211yesmaximal, characteristic, complemented
12#21463329—21no—
13#21463329C2212yescomplemented
14#21463328—22no—
15#21463328C2211yescharacteristic
16#21463328C2211yescharacteristic
17#21463328C2211yescharacteristic, complemented
18#21463327—21no—
19#21463327C2212yes—
20Q8×D491—21no—
21Q8×D491C2212yescomplemented
22C2×C22⋊D491—22no—
23D4×D491—21no—
24D4×D491C2212yes—
25Dic1964C2211yescharacteristic, complemented
26#21463318C2212yescomplemented
27#21463317C2211yescharacteristic, complemented
28#21463317C2211yescharacteristic, complemented
29#21463316C2212yescomplemented
30#21463315C2212yescomplemented
31D3928C2211yescharacteristic, complemented
32#21463313C2212yescomplemented
33#21463312C2211yescharacteristic, complemented
34#21463311C2212yescomplemented
35C8×D491C2212yescomplemented
36C2×Q8×C491C2211yescharacteristic, complemented
37C2×D4×C491C2211yescharacteristic
38SD16×C491C2212yescomplemented
39SD16×C491C2212yescomplemented
40C2×C8×C491C2211yescharacteristic, complemented
41C22×D491—22no—
42Dic982—22no—
43Dic982D411yescharacteristic
44Dic982C2311yescharacteristic
45Dic982C2311yescharacteristic
46D1964—22no—
47D1964D411yescharacteristic
48D1964C2311yescharacteristic
49D1964C2311yescharacteristic
50C22⋊D491—21no—
51C22⋊D491—21no—
52C22⋊D491—22no—
53C22⋊D491—22no—
54C22⋊D491D412yes—
55C2×Dic491—22no—
56C4×D491—22no—
57C4×D491—21no—
58C4×D491—21no—
59C4×D491—22no—
60C4×D491C2312yes—
61C491⋊C8C2312yes—
62C23×C491—21no—
63Q8×C491—21no—
64Q8×C491C2312yes—
65D4×C491—21no—
66D4×C491C2312yes—
67C2×C4×C491—21no—
68C2×C4×C491C2311yescharacteristic
69C8×C491C2311yescharacteristic
70C8×C491C2311yescharacteristic
71C22×C491—22no—
72C22×C491—81no—
73C22×C491C2×D411yescharacteristic
74C2×D491—21no—
75C2×D491—21no—
76C2×D491—82no—
77C2×D491C2×D412yes—
78C4×C491—22no—
79C4×C491C2×D411yescharacteristic
80C4×C491C2411yescharacteristic
81Dic491—21no—
82Dic491—21no—
83Dic491C2×D412yes—
84C2×C491—21no—
85C2×C491—42no—
86C2×C491C22×D411yescharacteristic
87D491—22no—
88D491—41no—
89D491—41no—
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#135—4911no—
100C2×SD16—4912no—
101C2×SD16D49111yescharacteristic, complemented
102#131—4911no—
103#41—9822no—
104#41—9821no—
105#41—9821no—
106#41—4912no—
107#41—4912no—
108#41—4911no—
109#41—4911no—
110#41—4911no—
111C2×Q8—9821no—
112C2×Q8—4912no—
113C2×Q8C2×D49111yescharacteristic, complemented
114C2×D4—9821no—
115C2×D4—9822no—
116C2×D4—4912no—
117C2×D4C2×D49111yescharacteristic
118Q16—4912no—
119Q16—4911no—
120SD16—4912no—
121SD16—4912no—
122SD16—4911no—
123SD16—4911no—
124SD16C2×D49112yescomplemented
125SD16C2×D49112yescomplemented
126D8—4912no—
127D8—4911no—
128M16—4911no—
129M16—4912no—
130C2×C8—4912no—
131C2×C8C2×D49111yescharacteristic, complemented
132C23—21no—
133C23—9822no—
134Q8—21no—
135Q8—9822no—
136Q8—4911no—
137Q8—4911no—
138Q8—4911no—
139Q8C22×D49112yes—
140D4—21no—
141D4—9822no—
142D4—9822no—
143D4—9821no—
144D4—9821no—
145D4—9822no—
146D4—4912no—
147D4—4911no—
148D4—4911no—
149D4—4911no—
150D4C22×D49112yes—
151C2×C4—21no—
152C2×C4—9822no—
153C2×C4—9822no—
154C2×C4—9822no—
155C2×C4—9821no—
156C2×C4—9821no—
157C2×C4—4912no—
158C2×C4C22×D49111yescharacteristic
159C8—4912no—
160C8C22×D49111yescharacteristic
161C8C22×D49111yescharacteristic
162C22—22no—
163C22—81no—
164C22—39282no—
165C22—9821no—
166C22—9821no—
167C22—4912no—
168C22D4×D49111yescharacteristic
169C4—22no—
170C4—9821no—
171C4—9821no—
172C4—4912no—
173C4D4×D49111yescharacteristic
174C4C23×D49111yescharacteristic
175C2—21no—
176C2—42no—
177C2—19641no—
178C2—19641no—
179C2—9822no—
180C2C2×D4×D49111yescharacteristic
subgroupG/H
centerC2C2×D4×D491
commutator, cosocleC4×C491C24
FrattiniC4C23×D491
FittingC2×SD16×C491C2
socleC2×C491C22×D4
hypercenterC2×SD16D491
hypocenterC491#577
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #30628385C2semidirect
2. #30628382C2semidirect
3. #30628368C2semidirect
4. #30628366C2semidirect
5. #30628364C2semidirect
6. #30628363C2semidirect
7. #30628359C2semidirect
8. #30628358C2semidirect
9. SD16×D491C2semidirect
10. #30628343C2semidirect
11. C2×SD16×C491C2semidirect
13. #21463329C22semidirect
17. #21463328C22semidirect
21. Q8×D491C22semidirect
25. Dic1964C22semidirect
26. #21463318C22semidirect
27. #21463317C22semidirect
28. #21463317C22semidirect
29. #21463316C22semidirect
30. #21463315C22semidirect
31. D3928C22semidirect
32. #21463313C22semidirect
33. #21463312C22semidirect
34. #21463311C22semidirect
35. C8×D491C22semidirect
36. C2×Q8×C491C22semidirect
38. SD16×C491C22semidirect
39. SD16×C491C22semidirect
40. C2×C8×C491C22semidirect
90. C491#577semidirect
101. C2×SD16D491semidirect
113. C2×Q8C2×D491semidirect
124. SD16C2×D491semidirect
125. SD16C2×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
#306283852
#306283822
#306283682
#306283662
#306283642
#306283632
#306283592
#306283582
SD16×D4912
#306283432
C2×SD16×C4912
#577491