Finite Group Databasebeta

← #38763318

Subgroups — #38763318

Order 25408.

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×#20263730C211yesmaximal, characteristic, complemented
2#41×D397C211yesmaximal, characteristic, complemented
3#27163129C211yesmaximal, characteristic, complemented
4#27163126C211yesmaximal, characteristic, complemented
5#27163125C212yesmaximal, complemented
6#27163122C211yesmaximal, characteristic, complemented
7#27163120C212yesmaximal, complemented
8#27163117C212yesmaximal, complemented
9#27163115C212yesmaximal, complemented
10M16×D397C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C397C211yesmaximal, characteristic, complemented
12#20263732C2211yescharacteristic, complemented
13#20263731—21no—
14#20263731C2211yescharacteristic
15#20263730—21no—
16#20263730—21no—
17#20263730—21no—
18#20263730C2212yes—
19#20263730C2211yescharacteristic, complemented
20#20263730C2212yescomplemented
21C2×Dic794C2211yescharacteristic, complemented
22Q8×D397C2211yescharacteristic, complemented
23C2×C22⋊D397—21no—
24D4×D397—21no—
25D4×D397C2211yescharacteristic, complemented
26C22×Dic397—21no—
27C2×C4×D397—21no—
28C2×C4×D397C2211yescharacteristic
29Dic1588C2212yescomplemented
30#20263721C2212yescomplemented
31#20263720C2212yescomplemented
32#20263719C2212yescomplemented
33#20263719C2212yescomplemented
34#20263716C2212yescomplemented
35#20263715C2211yescharacteristic, complemented
36#20263714C2212yescomplemented
37C8×D397C2212yescomplemented
38#41×C397C2211yescharacteristic
39C2×D4×C397C2211yescharacteristic, complemented
40SD16×C397C2212yescomplemented
41D8×C397C2212yescomplemented
42M16×C397C2211yescharacteristic, complemented
43C22×D397—21no—
44C22×D397D411yescharacteristic
45Dic794—21no—
46Dic794—21no—
47Dic794C2311yescharacteristic
48Dic794C2312yes—
49D1588—21no—
50D1588C2311yescharacteristic
51C22⋊D397—21no—
52C22⋊D397—21no—
53C22⋊D397—22no—
54C22⋊D397—22no—
55C22⋊D397—21no—
56C2×Dic397—21no—
57C2×Dic397—21no—
58C2×Dic397—22no—
59C2×Dic397—22no—
60C2×Dic397D411yescharacteristic
61C4×D397—21no—
62C4×D397—21no—
63C4×D397—21no—
64C4×D397D411yescharacteristic
65C4×D397D411yescharacteristic
66C4×D397C2311yescharacteristic
67C4×D397C2311yescharacteristic
68#15691787C2312yes—
69C23×C397—21no—
70Q8×C397C2311yescharacteristic
71D4×C397—21no—
72D4×C397—21no—
73D4×C397C2311yescharacteristic
74D4×C397C2312yes—
75C2×C4×C397—21no—
76C2×C4×C397C2311yescharacteristic
77C8×C397C2312yes—
78C22×C397—21no—
79C22×C397—22no—
80C22×C397—42no—
81C22×C397C2×D411yescharacteristic
82C2×D397—21no—
83C2×D397—41no—
84C2×D397—42no—
85C2×D397C2×D411yescharacteristic
86C2×D397C2×D411yescharacteristic
87C4×C397—21no—
88C4×C397C2×D411yescharacteristic
89C4×C397C2411yescharacteristic
90Dic397—21no—
91Dic397—22no—
92Dic397C2×D411yescharacteristic
93Dic397C2×D411yescharacteristic
94C2×C397—21no—
95C2×C397—41no—
96C2×C397—42no—
97C2×C397C22×D411yescharacteristic
98D397—21no—
99D397—21no—
100D397—41no—
101C397#57511yescharacteristic, complemented, Sylow
102#575—3971nomaximal, Sylow
103C2×#41—3971no—
104C2×#41—3971no—
105#137—3971no—
106#137—3972no—
107#137—3971no—
108AGL(1,ℤ/8)—3971no—
109AGL(1,ℤ/8)—3972no—
110AGL(1,ℤ/8)D39711yescharacteristic, complemented
111#135—3972no—
112#135—3972no—
113C2×M16—3971no—
114#41—7941no—
115#41—7941no—
116#41—7941no—
117#41—7941no—
118#41—3971no—
119#41—3972no—
120#41—3972no—
121#41—3971no—
122#41—3971no—
123#41C2×D39711yescharacteristic
124C2×Q8—3971no—
125C2×Q8—3971no—
126C2×D4—7941no—
127C2×D4—7941no—
128C2×D4—3971no—
129C2×D4C2×D39711yescharacteristic, complemented
130C22×C4—7941no—
131C22×C4—7941no—
132C22×C4—3971no—
133Q16—3972no—
134Q16—3972no—
135SD16—3972no—
136SD16—3972no—
137SD16—3972no—
138SD16C2×D39712yescomplemented
139D8—3972no—
140D8C2×D39712yescomplemented
141M16—3971no—
142M16—3972no—
143M16C2×D39711yescharacteristic, complemented
144C2×C8—3972no—
145C23—21no—
146C23—7941no—
147C23—3971no—
148Q8—7941no—
149Q8—7941no—
150Q8—3971no—
151Q8—3972no—
152Q8C22×D39711yescharacteristic
153D4—21no—
154D4—21no—
155D4—7941no—
156D4—7941no—
157D4—7942no—
158D4—7942no—
159D4—7941no—
160D4—7941no—
161D4—3971no—
162D4C22×D39712yes—
163D4C22×D39711yescharacteristic
164C2×C4—21no—
165C2×C4—7941no—
166C2×C4—7941no—
167C2×C4—7941no—
168C2×C4—7941no—
169C2×C4—7942no—
170C2×C4—7942no—
171C2×C4—7941no—
172C2×C4—3971no—
173C2×C4—3971no—
174C2×C4—3971no—
175C2×C4—3971no—
176C2×C4—3971no—
177C2×C4C22×D39711yescharacteristic
178C8—3972no—
179C8C22×D39712yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—7941no—
184C22—15881no—
185C22—15882no—
186C22—3971no—
187C22—3971no—
188C22D4×D39711yescharacteristic
189C4—21no—
190C4—7941no—
191C4—7942no—
192C4—3971no—
193C4—3971no—
194C4D4×D39711yescharacteristic
195C4C23×D39711yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—7941no—
200C2—7941no—
201C2—15881no—
202C2C2×D4×D39711yescharacteristic
subgroupG/H
centerC2C2×D4×D397
commutator, cosocleC4×C397C24
FrattiniC4C23×D397
FittingAGL(1,ℤ/8)×C397C2
socleC2×C397C22×D4
hypercenterAGL(1,ℤ/8)D397
hypocenterC397#575
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#20263730C2semidirect
2. #41×D397C2semidirect
3. #27163129C2semidirect
4. #27163126C2semidirect
5. #27163125C2semidirect
6. #27163122C2semidirect
7. #27163120C2semidirect
8. #27163117C2semidirect
9. #27163115C2semidirect
10. M16×D397C2semidirect
11. AGL(1,ℤ/8)×C397C2semidirect
12. #20263732C22semidirect
19. #20263730C22semidirect
20. #20263730C22semidirect
21. C2×Dic794C22semidirect
22. Q8×D397C22semidirect
25. D4×D397C22semidirect
29. Dic1588C22semidirect
30. #20263721C22semidirect
31. #20263720C22semidirect
32. #20263719C22semidirect
33. #20263719C22semidirect
34. #20263716C22semidirect
35. #20263715C22semidirect
36. #20263714C22semidirect
37. C8×D397C22semidirect
39. C2×D4×C397C22semidirect
40. SD16×C397C22semidirect
41. D8×C397C22semidirect
42. M16×C397C22semidirect
101. C397#575semidirect
110. AGL(1,ℤ/8)D397semidirect
129. C2×D4C2×D397semidirect
138. SD16C2×D397semidirect
140. D8C2×D397semidirect
143. M16C2×D397semidirect

Maximal subgroups

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

subgroupindex
C2×#202637302
#41×D3972
#271631292
#271631262
#271631252
#271631222
#271631202
#271631172
#271631152
M16×D3972
AGL(1,ℤ/8)×C3972
#575397