Finite Group Databasebeta

← #37526614

Subgroups — #37526614

Order 22976.

146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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#26040062C211yesmaximal, characteristic, complemented
2#26040041C211yesmaximal, characteristic, complemented
3#26040002C211yesmaximal, characteristic, complemented
4#26039942C211yesmaximal, characteristic, complemented
5#26039941C211yesmaximal, characteristic, complemented
6#26039933C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C359C211yesmaximal, characteristic, complemented
8#19153341—21no—
9#19153341C2211yescharacteristic
10#19153340—22no—
11#19153340—21no—
12C2×Dic718—21no—
13C2×Dic718C2211yescharacteristic
14Q8×D359—21no—
15#19153329—21no—
16#19153326—21no—
17#19153325C2211yescharacteristic
18C22⋊Dic359—22no—
19C4×Dic359C2211yescharacteristic
20#41×C359C2211yescharacteristic
21C2×D4×C359C2211yescharacteristic
22SD16×C359—21no—
23D8×C359—21no—
24M16×C359C2211yescharacteristic
25Dic718—22no—
26Dic718—21no—
27Dic718—21no—
28Dic718D411yescharacteristic
29D1436D411yescharacteristic
30C22⋊D359—22no—
31C22⋊D359—21no—
32C2×Dic359—22no—
33C2×Dic359—21no—
34C2×Dic359D412yes—
35C4×D359—22no—
36C4×D359—21no—
37C359⋊C8—21no—
38C23×C359—21no—
39Q8×C359D411yescharacteristic
40D4×C359—21no—
41D4×C359—21no—
42D4×C359—21no—
43D4×C359D411yescharacteristic
44C2×C4×C359—21no—
45C2×C4×C359C2311yescharacteristic
46C8×C359—21no—
47C22×C359—21no—
48C22×C359—42no—
49C22×C359—41no—
50C22×C359C2×D411yescharacteristic
51C2×D359—21no—
52C4×C359—21no—
53C4×C359C2×D411yescharacteristic
54C4×C359C2×D411yescharacteristic
55Dic359—21no—
56Dic359—22no—
57Dic359—41no—
58C2×C359—21no—
59C2×C359—41no—
60C2×C359—81no—
61C2×C359#12011yescharacteristic
62D359—41no—
63C359#45411yescharacteristic, complemented, Sylow
64#454—3591nomaximal, Sylow
652−1+4—3591no—
66AGL(1,ℤ/8)—3591no—
67AGL(1,ℤ/8)D35911yescharacteristic, complemented
68#124—3591no—
69#104—3591no—
70#104—3591no—
71#101—3591no—
72#41—3591no—
73#41—7181no—
74#41—7182no—
75#41—7181no—
76#41C2×D35911yescharacteristic
77C2×Q8—3591no—
78C2×Q8—7181no—
79C2×Q8—7181no—
80C2×D4C2×D35911yescharacteristic
81SD16—21no—
82SD16—7181no—
83D8—21no—
84D8—7181no—
85M16—3591no—
86M16C2×D35911yescharacteristic
87C22⋊C4—7182no—
88C42—3591no—
89C23—21no—
90Q8—3591no—
91Q8—7182no—
92Q8—7181no—
93Q8—7181no—
94Q8C22⋊D35911yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—3591no—
99D4—7182no—
100D4—7181no—
101D4C22⋊D35911yescharacteristic
102C2×C4—21no—
103C2×C4—3592no—
104C2×C4—7182no—
105C2×C4—7181no—
106C2×C4—7182no—
107C2×C4—7181no—
108C2×C4C22×D35911yescharacteristic
109C8—21no—
110C8—7181no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—7181no—
115C22D4×D35911yescharacteristic
116C4—21no—
117C4—14361no—
118C4—7182no—
119C4—7181no—
120C4D4×D35911yescharacteristic
121C4C2×C22⋊D35911yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—14361no—
126C2#2603998311yescharacteristic
subgroupG/H
centerC2#26039983
commutator, cosocleC2×C4×C359C23
FrattiniC2×C4C22×D359
FittingAGL(1,ℤ/8)×C359C2
socleC2×C359#120
hypercenterAGL(1,ℤ/8)D359
hypocenterC359#454
LCSG ▷ C2×C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #26040062C2semidirect
2. #26040041C2semidirect
3. #26040002C2semidirect
4. #26039942C2semidirect
5. #26039941C2semidirect
6. #26039933C2semidirect
7. AGL(1,ℤ/8)×C359C2semidirect
63. C359#454semidirect
67. AGL(1,ℤ/8)D359semidirect

Maximal subgroups

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

subgroupindex
#260400622
#260400412
#260400022
#260399422
#260399412
#260399332
AGL(1,ℤ/8)×C3592
#454359