Finite Group Databasebeta

← #37526617

Subgroups — #37526617

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#26040043C211yesmaximal, characteristic, complemented
3#26040040C211yesmaximal, characteristic, complemented
4#26040003C211yesmaximal, characteristic, complemented
5#26039943C211yesmaximal, characteristic, complemented
6#26039933C211yesmaximal, characteristic, complemented
7#104×C359C211yesmaximal, characteristic, complemented
8#19153341—21no—
9#19153341C2211yescharacteristic
10#19153340—22no—
11#19153340—21no—
12C2×Dic718—21no—
13C2×Dic718C2211yescharacteristic
14Q8×D359—21no—
15C2×D1436C2211yescharacteristic
16#19153330—21no—
17#19153328—21no—
18D2872—21no—
19#19153326—21no—
20#19153325C2211yescharacteristic
21(C2×D359)⋊C4—22no—
22#41×C359C2211yescharacteristic
23M16×C359C2211yescharacteristic
24C42×C359C2211yescharacteristic
25C22×D359—21no—
26Dic718—22no—
27Dic718—21no—
28Dic718—21no—
29Dic718D411yescharacteristic
30D1436—21no—
31D1436—21no—
32D1436D411yescharacteristic
33C22⋊D359—22no—
34C22⋊D359—21no—
35C2×Dic359—22no—
36C2×Dic359D412yes—
37C4×D359—22no—
38C4×D359—21no—
39C359⋊C8—21no—
40Q8×C359D411yescharacteristic
41D4×C359—21no—
42D4×C359D411yescharacteristic
43C2×C4×C359—21no—
44C2×C4×C359—21no—
45C2×C4×C359C2311yescharacteristic
46C8×C359—21no—
47C22×C359—21no—
48C22×C359C2×D411yescharacteristic
49C2×D359—21no—
50C2×D359—42no—
51C2×D359—41no—
52C4×C359—21no—
53C4×C359—41no—
54C4×C359C2×D411yescharacteristic
55C4×C359C2×D411yescharacteristic
56Dic359—21no—
57Dic359—22no—
58C2×C359—21no—
59C2×C359—41no—
60C2×C359#12011yescharacteristic
61D359—41no—
62D359—81no—
63C359#45411yescharacteristic, complemented, Sylow
64#454—3591nomaximal, Sylow
652−1+4—3591no—
66AGL(1,ℤ/8)—3591no—
67AGL(1,ℤ/8)—3591no—
68#124—3591no—
69#104—3591no—
70#104D35911yescharacteristic, complemented
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×D4—3591no—
81SD16—7181no—
82SD16—7181no—
83D8—7181no—
84D8—7181no—
85M16—3591no—
86M16C2×D35911yescharacteristic
87C22⋊C4—7182no—
88C42C2×D35911yescharacteristic
89C23—7181no—
90Q8—3591no—
91Q8—7182no—
92Q8—7181no—
93Q8—7181no—
94Q8D143611yescharacteristic
95D4—21no—
96D4—3591no—
97D4—7182no—
98D4—7181no—
99D4—7181no—
100D4—7181no—
101D4D143611yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—3592no—
105C2×C4—7182no—
106C2×C4—7182no—
107C2×C4—7181no—
108C2×C4C22×D35911yescharacteristic
109C8—21no—
110C8—7181no—
111C22—21no—
112C22—14362no—
113C22—14361no—
114C22—7181no—
115C22D4×D35911yescharacteristic
116C4—21no—
117C4—41no—
118C4—7182no—
119C4—7181no—
120C4D4×D35911yescharacteristic
121C4C2×D143611yescharacteristic
122C2—21no—
123C2—41no—
124C2—28721no—
125C2—14361no—
126C2#2603998511yescharacteristic
subgroupG/H
centerC2#26039985
commutator, cosocleC2×C4×C359C23
FrattiniC2×C4C22×D359
Fitting#104×C359C2
socleC2×C359#120
hypercenter#104D359
hypocenterC359#454
LCSG ▷ C2×C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #26040062C2semidirect
2. #26040043C2semidirect
3. #26040040C2semidirect
4. #26040003C2semidirect
5. #26039943C2semidirect
6. #26039933C2semidirect
7. #104×C359C2semidirect
63. C359#454semidirect
70. #104D359semidirect

Maximal subgroups

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

subgroupindex
#260400622
#260400432
#260400402
#260400032
#260399432
#260399332
#104×C3592
#454359