Finite Group Databasebeta

← #44537521

Subgroups — #44537521

Order 31424.

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×#21463327C211yesmaximal, characteristic, complemented
2#41×D491C211yesmaximal, characteristic, complemented
3#30628370C211yesmaximal, characteristic, complemented
4#30628367C211yesmaximal, characteristic, complemented
5#30628366C212yesmaximal, complemented
6#30628363C211yesmaximal, characteristic, complemented
7#30628361C212yesmaximal, complemented
8#30628358C212yesmaximal, complemented
9#30628356C212yesmaximal, complemented
10M16×D491C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C491C211yesmaximal, characteristic, complemented
12#21463329C2211yescharacteristic, complemented
13#21463328—21no—
14#21463328C2211yescharacteristic
15#21463327—21no—
16#21463327—21no—
17#21463327—21no—
18#21463327C2212yes—
19#21463327C2211yescharacteristic, complemented
20#21463327C2212yescomplemented
21C2×Dic982C2211yescharacteristic, complemented
22Q8×D491C2211yescharacteristic, complemented
23C2×C22⋊D491—21no—
24D4×D491—21no—
25D4×D491C2211yescharacteristic, complemented
26C22×Dic491—21no—
27C2×C4×D491—21no—
28C2×C4×D491C2211yescharacteristic
29Dic1964C2212yescomplemented
30#21463318C2212yescomplemented
31#21463317C2212yescomplemented
32#21463316C2212yescomplemented
33#21463316C2212yescomplemented
34#21463313C2212yescomplemented
35#21463312C2211yescharacteristic, complemented
36#21463311C2212yescomplemented
37C8×D491C2212yescomplemented
38#41×C491C2211yescharacteristic
39C2×D4×C491C2211yescharacteristic, complemented
40SD16×C491C2212yescomplemented
41D8×C491C2212yescomplemented
42M16×C491C2211yescharacteristic, complemented
43C22×D491—21no—
44C22×D491D411yescharacteristic
45Dic982—21no—
46Dic982—21no—
47Dic982C2311yescharacteristic
48Dic982C2312yes—
49D1964—21no—
50D1964C2311yescharacteristic
51C22⋊D491—21no—
52C22⋊D491—21no—
53C22⋊D491—22no—
54C22⋊D491—22no—
55C22⋊D491—21no—
56C2×Dic491—21no—
57C2×Dic491—21no—
58C2×Dic491—22no—
59C2×Dic491—22no—
60C2×Dic491D411yescharacteristic
61C4×D491—21no—
62C4×D491—21no—
63C4×D491—21no—
64C4×D491D411yescharacteristic
65C4×D491D411yescharacteristic
66C4×D491C2311yescharacteristic
67C4×D491C2311yescharacteristic
68C491⋊C8C2312yes—
69C23×C491—21no—
70Q8×C491C2311yescharacteristic
71D4×C491—21no—
72D4×C491—21no—
73D4×C491C2312yes—
74D4×C491C2311yescharacteristic
75C2×C4×C491—21no—
76C2×C4×C491C2311yescharacteristic
77C8×C491C2312yes—
78C22×C491—21no—
79C22×C491—22no—
80C22×C491—42no—
81C22×C491C2×D411yescharacteristic
82C2×D491—21no—
83C2×D491—41no—
84C2×D491—42no—
85C2×D491C2×D411yescharacteristic
86C2×D491C2×D411yescharacteristic
87C4×C491—21no—
88C4×C491C2×D411yescharacteristic
89C4×C491C2411yescharacteristic
90Dic491—21no—
91Dic491—22no—
92Dic491C2×D411yescharacteristic
93Dic491C2×D411yescharacteristic
94C2×C491—21no—
95C2×C491—41no—
96C2×C491—42no—
97C2×C491C22×D411yescharacteristic
98D491—21no—
99D491—21no—
100D491—41no—
101C491#57511yescharacteristic, complemented, Sylow
102#575—4911nomaximal, Sylow
103C2×#41—4911no—
104C2×#41—4911no—
105#137—4911no—
106#137—4912no—
107#137—4911no—
108AGL(1,ℤ/8)—4911no—
109AGL(1,ℤ/8)—4912no—
110AGL(1,ℤ/8)D49111yescharacteristic, complemented
111#135—4912no—
112#135—4912no—
113C2×M16—4911no—
114#41—9821no—
115#41—9821no—
116#41—9821no—
117#41—9821no—
118#41—4911no—
119#41—4912no—
120#41—4912no—
121#41—4911no—
122#41—4911no—
123#41C2×D49111yescharacteristic
124C2×Q8—4911no—
125C2×Q8—4911no—
126C2×D4—9821no—
127C2×D4—9821no—
128C2×D4—4911no—
129C2×D4C2×D49111yescharacteristic, complemented
130C22×C4—9821no—
131C22×C4—9821no—
132C22×C4—4911no—
133Q16—4912no—
134Q16—4912no—
135SD16—4912no—
136SD16—4912no—
137SD16—4912no—
138SD16C2×D49112yescomplemented
139D8—4912no—
140D8C2×D49112yescomplemented
141M16—4911no—
142M16—4912no—
143M16C2×D49111yescharacteristic, complemented
144C2×C8—4912no—
145C23—21no—
146C23—9821no—
147C23—4911no—
148Q8—9821no—
149Q8—9821no—
150Q8—4911no—
151Q8—4912no—
152Q8C22×D49111yescharacteristic
153D4—21no—
154D4—21no—
155D4—9821no—
156D4—9821no—
157D4—9822no—
158D4—9822no—
159D4—9821no—
160D4—9821no—
161D4—4911no—
162D4C22×D49112yes—
163D4C22×D49111yescharacteristic
164C2×C4—21no—
165C2×C4—9821no—
166C2×C4—9821no—
167C2×C4—9821no—
168C2×C4—9821no—
169C2×C4—9822no—
170C2×C4—9822no—
171C2×C4—9821no—
172C2×C4—4911no—
173C2×C4—4911no—
174C2×C4—4911no—
175C2×C4—4911no—
176C2×C4—4911no—
177C2×C4C22×D49111yescharacteristic
178C8—4912no—
179C8C22×D49112yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—19641no—
184C22—19642no—
185C22—9821no—
186C22—4911no—
187C22—4911no—
188C22D4×D49111yescharacteristic
189C4—21no—
190C4—9821no—
191C4—9822no—
192C4—4911no—
193C4—4911no—
194C4D4×D49111yescharacteristic
195C4C23×D49111yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—19641no—
200C2—9821no—
201C2—9821no—
202C2C2×D4×D49111yescharacteristic
subgroupG/H
centerC2C2×D4×D491
commutator, cosocleC4×C491C24
FrattiniC4C23×D491
FittingAGL(1,ℤ/8)×C491C2
socleC2×C491C22×D4
hypercenterAGL(1,ℤ/8)D491
hypocenterC491#575
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#21463327C2semidirect
2. #41×D491C2semidirect
3. #30628370C2semidirect
4. #30628367C2semidirect
5. #30628366C2semidirect
6. #30628363C2semidirect
7. #30628361C2semidirect
8. #30628358C2semidirect
9. #30628356C2semidirect
10. M16×D491C2semidirect
11. AGL(1,ℤ/8)×C491C2semidirect
12. #21463329C22semidirect
19. #21463327C22semidirect
20. #21463327C22semidirect
21. C2×Dic982C22semidirect
22. Q8×D491C22semidirect
25. D4×D491C22semidirect
29. Dic1964C22semidirect
30. #21463318C22semidirect
31. #21463317C22semidirect
32. #21463316C22semidirect
33. #21463316C22semidirect
34. #21463313C22semidirect
35. #21463312C22semidirect
36. #21463311C22semidirect
37. C8×D491C22semidirect
39. C2×D4×C491C22semidirect
40. SD16×C491C22semidirect
41. D8×C491C22semidirect
42. M16×C491C22semidirect
101. C491#575semidirect
110. AGL(1,ℤ/8)D491semidirect
129. C2×D4C2×D491semidirect
138. SD16C2×D491semidirect
140. D8C2×D491semidirect
143. M16C2×D491semidirect

Maximal subgroups

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

subgroupindex
C2×#214633272
#41×D4912
#306283702
#306283672
#306283662
#306283632
#306283612
#306283582
#306283562
M16×D4912
AGL(1,ℤ/8)×C4912
#575491