Finite Group Databasebeta

← #34036310

Subgroups — #34036310

Order 18752.

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

normal subgroups only

This group has 142 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#22627671C211yesmaximal, characteristic
2#22627655C211yesmaximal, characteristic, complemented
3#22627622C211yesmaximal, characteristic, complemented
4#22627551C211yesmaximal, characteristic, complemented
5#22627550C211yesmaximal, characteristic, complemented
6#22627542C211yesmaximal, characteristic, complemented
7#137×C293C211yesmaximal, characteristic, complemented
8#17989802—21no—
9#17989802C2211yescharacteristic
10#17989801—22no—
11#17989801—21no—
12C2×Dic586—21no—
13C2×Dic586C2211yescharacteristic
14Q8×D293—21no—
15#17989792—21no—
16#17989789—21no—
17#17989786C2211yescharacteristic
18#17989781—22no—
19C4×Dic293C2211yescharacteristic
20#41×C293C2211yescharacteristic
21C2×Q8×C293C2211yescharacteristic
22Q16×C293—21no—
23SD16×C293—21no—
24M16×C293C2211yescharacteristic
25Dic586—22no—
26Dic586—21no—
27Dic586—21no—
28Dic586D411yescharacteristic
29D1172D411yescharacteristic
30C22⋊D293—22no—
31C22⋊D293—21no—
32C2×Dic293—22no—
33C2×Dic293—21no—
34C2×Dic293D412yes—
35C4×D293—22no—
36C4×D293—21no—
37#14556873—21no—
38Q8×C293—21no—
39Q8×C293—21no—
40Q8×C293D411yescharacteristic
41D4×C293—21no—
42D4×C293D411yescharacteristic
43C2×C4×C293—21no—
44C2×C4×C293—21no—
45C2×C4×C293C2311yescharacteristic
46C8×C293—21no—
47C22×C293—21no—
48C22×C293C2×D411yescharacteristic
49C2×D293—21no—
50C4×C293—21no—
51C4×C293—41no—
52C4×C293C2×D411yescharacteristic
53C4×C293C2×D411yescharacteristic
54Dic293—22no—
55Dic293—21no—
56Dic293—22no—
57C2×C293—21no—
58C2×C293—41no—
59C2×C293#12011yescharacteristic
60D293—41no—
61C293#45611yescharacteristic, complemented, Sylow
62#456—2931nomaximal, Sylow
632−1+4—2931no—
64#137—2931no—
65#137D29311yescharacteristic, complemented
66C4⋊Q8—2931no—
67#104—2931no—
68#104—2931no—
69#101—2931no—
70#41—2931no—
71#41—5861no—
72#41—5862no—
73#41—5861no—
74#41C2×D29311yescharacteristic
75C2×Q8—2931no—
76C2×Q8—5861no—
77C2×Q8—5861no—
78C2×Q8C2×D29311yescharacteristic
79Q16—21no—
80Q16—5861no—
81SD16—21no—
82SD16—5861no—
83M16—2931no—
84M16C2×D29311yescharacteristic
85C4⋊C4—5862no—
86C42—2931no—
87Q8—21no—
88Q8—21no—
89Q8—2931no—
90Q8—5862no—
91Q8—5861no—
92Q8—5861no—
93Q8C22⋊D29311yescharacteristic
94D4—21no—
95D4—2931no—
96D4—5862no—
97D4—5861no—
98D4C22⋊D29311yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—2932no—
102C2×C4—5862no—
103C2×C4—5862no—
104C2×C4—5861no—
105C2×C4—5861no—
106C2×C4C22×D29311yescharacteristic
107C8—21no—
108C8—5861no—
109C22—21no—
110C22—5861no—
111C22D4×D29311yescharacteristic
112C4—21no—
113C4—41no—
114C4—5862no—
115C4—5862no—
116C4—5861no—
117C4D4×D29311yescharacteristic
118C4C2×C22⋊D29311yescharacteristic
119C2—21no—
120C2—41no—
121C2—11721no—
122C2#2262759211yescharacteristic
subgroupG/H
centerC2#22627592
commutator, cosocleC2×C4×C293C23
FrattiniC2×C4C22×D293
Fitting#137×C293C2
socleC2×C293#120
prime radical#22627671C2
hypercenter#137D293
hypocenterC293#456
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #22627655C2semidirect
3. #22627622C2semidirect
4. #22627551C2semidirect
5. #22627550C2semidirect
6. #22627542C2semidirect
7. #137×C293C2semidirect
61. C293#456semidirect
65. #137D293semidirect

Maximal subgroups

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

subgroupindex
#226276712
#226276552
#226276222
#226275512
#226275502
#226275422
#137×C2932
#456293