Finite Group Databasebeta

← #37511079

Subgroups — #37511079

Order 22912.

150 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 45 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#26038879C211yesmaximal, characteristic
2#26038817C211yesmaximal, characteristic, complemented
3#26038556C211yesmaximal, characteristic
4#26038259C211yesmaximal, characteristic, complemented
5#26038256C211yesmaximal, characteristic, complemented
6#26038255C211yesmaximal, characteristic, complemented
7#510×C179C211yesmaximal, characteristic
8C2×Dic716C2211yescharacteristic
9C2×#15668249—21no—
10#19153120—21no—
11#19153111—21no—
12#19153059—21no—
13#19153057—21no—
14#19153053C2211yescharacteristic
15#19153049C2211yescharacteristic
16#19153040—21no—
17C8×Dic179C2211yescharacteristic
18#135×C179C2211yescharacteristic
19C2×Q16×C179C2211yescharacteristic
20Q32×C179—21no—
21SD32×C179—21no—
22M32×C179C2211yescharacteristic
23C2×Dic358—21no—
24Dic716—21no—
25Dic716—21no—
26#15668249—41no—
27#15668249—41no—
28#15668243—21no—
29#15668243—41no—
30C2×C179⋊C8—41no—
31C2×C179⋊C8D411yescharacteristic
32Dic179⋊C4—42no—
33C4×Dic179D411yescharacteristic
34C179⋊C16—21no—
35#41×C179—21no—
36C2×Q8×C179—21no—
37Q16×C179—21no—
38Q16×C179—21no—
39Q16×C179D411yescharacteristic
40SD16×C179—21no—
41D8×C179D411yescharacteristic
42C2×C8×C179C2311yescharacteristic
43C16×C179—21no—
44Dic358—41no—
45Dic358—41no—
46C2×Dic179—21no—
47C2×Dic179—41no—
48C179⋊C8—41no—
49C179⋊C8D811yescharacteristic
50C179⋊C8D811yescharacteristic
51Q8×C179—21no—
52Q8×C179—41no—
53Q8×C179—41no—
54D4×C179—21no—
55D4×C179—41no—
56C2×C4×C179—41no—
57C2×C4×C179—41no—
58C2×C4×C179C2×D411yescharacteristic
59C8×C179C2×D411yescharacteristic
60C8×C179#4111yescharacteristic
61C22×C179—41no—
62C22×C179AGL(1,ℤ/8)11yescharacteristic
63C4×C179—41no—
64C4×C179—81no—
65C4×C179#12111yescharacteristic
66C4×C179C2×D811yescharacteristic
67Dic179—22no—
68Dic179—81no—
69C2×C179—21no—
70C2×C179—81no—
71C2×C179#45911yescharacteristic
72C179#221411yescharacteristic, complemented, Sylow
73#2214—1791nomaximal, Sylow
74#510—1791no—
75#510D17911yescharacteristic
76#494—1791no—
77#443—1791no—
78#364—1791no—
79#362—1791no—
80#362—1791no—
81#135C2×D17911yescharacteristic
82C2×Q16—3581no—
83C2×Q16—1791no—
84C2×Q16C2×D17911yescharacteristic
85#131—3581no—
86C4⋊Q8—3581no—
87Q32—21no—
88Q32—3581no—
89SD32—21no—
90SD32—3581no—
91M32—1791no—
92M32C2×D17911yescharacteristic
93#108—1791no—
94#104—3581no—
95C4×C8—1791no—
96#41—21no—
97C2×Q8—21no—
98C2×Q8—3581no—
99Q16—21no—
100Q16—21no—
101Q16—3581no—
102Q16—3581no—
103Q16—7161no—
104Q16—7161no—
105Q16C22⋊D17911yescharacteristic
106SD16—21no—
107D8C22⋊D17911yescharacteristic
108M16—3581no—
109M16—7161no—
110C2×C8—1791no—
111C2×C8—7161no—
112C2×C8C22×D17911yescharacteristic
113C4⋊C4—7162no—
114C42—1791no—
115C16—21no—
116C16—3581no—
117Q8—21no—
118Q8—41no—
119Q8—41no—
120Q8—7161no—
121Q8—7161no—
122D4—21no—
123D4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—3581no—
127C2×C4—7161no—
128C2×C4D4×D17911yescharacteristic
129C8—1791no—
130C8—1791no—
131C8—7161no—
132C8C2×C22⋊D17911yescharacteristic
133C8#1566825811yescharacteristic
134C22—41no—
135C22#1915313711yescharacteristic
136C4—41no—
137C4—81no—
138C4—3582no—
139C4—14321no—
140C4#1915308511yescharacteristic
141C4D8×D17911yescharacteristic
142C2—21no—
143C2—81no—
144C2#2603863211yescharacteristic
subgroupG/H
centerC2#26038632
commutator, cosocleC2×C8×C179C23
FrattiniC2×C8C22×D179
Fitting#510×C179C2
socleC2×C179#459
prime radical#135×C179C22
hypercenter#510D179
hypocenterC179#2214
LCSG ▷ C2×C8×C179 ▷ C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #26038817C2semidirect
4. #26038259C2semidirect
5. #26038256C2semidirect
6. #26038255C2semidirect
72. C179#2214semidirect

Maximal subgroups

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

subgroupindex
#260388792
#260388172
#260385562
#260382592
#260382562
#260382552
#510×C1792
#2214179