Finite Group Databasebeta

← #44486243

Subgroups — #44486243

Order 30592.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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#29504756C212yesmaximal
2#29504571C214yesmaximal, complemented
3#536×C239C211yesmaximal, characteristic
4C2×#16838532—22no—
5#21439879C2214yes—
6#21439877—22no—
7C2×#41×C239C2211yescharacteristic
8C22×Q8×C239C411yescharacteristic
9C4⋊Q8×C239C2212yes—
10#124×C239C412yes—
11#123×C239—22no—
12C22⋊Q8×C239—22no—
13#117×C239C411yescharacteristic
14#16838532—24no—
15#16838532—42no—
16C2×C239⋊C8—42no—
17#41×C239—42no—
18C2×Q8×C239—21no—
19C2×Q8×C239—42no—
20C2×Q8×C239C2×C412yes—
21C2×Q8×C239C2311yescharacteristic
22C2×D4×C239C2×C411yescharacteristic
23C2×D4×C239D412yes—
24C22×C4×C239—21no—
25C22×C4×C239C2×C411yescharacteristic
26C22×C4×C239D412yes—
27C4⋊C4×C239—21no—
28C4⋊C4×C239—24no—
29C22⋊C4×C239—21no—
30C22⋊C4×C239—24no—
31C42×C239C2×C412yes—
32C239⋊C8—44no—
33C23×C239C22⋊C412yes—
34C23×C239C22⋊C411yescharacteristic
35Q8×C239—41no—
36Q8×C239—42no—
37Q8×C239—42no—
38D4×C239—41no—
39D4×C239—42no—
40C2×C4×C239—22no—
41C2×C4×C239—22no—
42C2×C4×C239—22no—
43C2×C4×C239—22no—
44C2×C4×C239—22no—
45C2×C4×C239—42no—
46C2×C4×C239C22⋊C411yescharacteristic
47C2×C4×C239C22×C411yescharacteristic
48C2×C4×C239C2×D412yes—
49C22×C239—21no—
50C22×C239—22no—
51C22×C239—42no—
52C22×C239—41no—
53C22×C239C2×C22⋊C411yescharacteristic
54C4×C239—21no—
55C4×C239—22no—
56C4×C239—42no—
57C4×C239—42no—
58C4×C239#9912yes—
59C2×C239—21no—
60C2×C239—41no—
61C2×C239—42no—
62C2×C239C2×#9911yescharacteristic
63C239#213511yescharacteristic, complemented, Sylow
64#2135—2391nomaximal, Sylow
65#536D23911yescharacteristic
66#413—2392no—
67#356—2394no—
68C2×#41C2×D23911yescharacteristic
69C22×Q8Dic23911yescharacteristic
70C2×M16—4782no—
71C4⋊Q8C2×D23912yes—
72#124Dic23912yes—
73#123—22no—
74C22⋊Q8—22no—
75#117Dic23911yescharacteristic
76#101—2394no—
77#100—4782no—
78#41—42no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8C2×Dic23912yes—
82C2×Q8C22×D23911yescharacteristic
83C2×D4C2×Dic23911yescharacteristic
84C2×D4C22⋊D23912yes—
85C22×C4—21no—
86C22×C4C2×Dic23911yescharacteristic
87C22×C4C22⋊D23912yes—
88M16—9562no—
89M16—4784no—
90C2×C8—9562no—
91C4⋊C4—21no—
92C4⋊C4—24no—
93C22⋊C4—21no—
94C22⋊C4—24no—
95C42C2×Dic23912yes—
96C23C22⋊Dic23912yes—
97C23C22⋊Dic23911yescharacteristic
98Q8—41no—
99Q8—42no—
100Q8—42no—
101D4—41no—
102D4—42no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—42no—
109C2×C4C22⋊Dic23911yescharacteristic
110C2×C4C22×Dic23911yescharacteristic
111C2×C4C2×C22⋊D23912yes—
112C8—9564no—
113C22—21no—
114C22—22no—
115C22—42no—
116C22—41no—
117C22C2×C22⋊Dic23911yescharacteristic
118C4—22no—
119C4—21no—
120C4—42no—
121C4—42no—
122C4#2143987512yes—
123C2—21no—
124C2—41no—
125C2—42no—
126C2C2×#2143987511yescharacteristic
subgroupG/H
centerC2C2×#21439875
commutatorC2×C4×C239C22×C4
FrattiniC2×Q8C22×D239
Fitting#536×C239C2
socleC2×C239C2×#99
prime radicalC2×#41×C239C22
cosocleC2×Q8×C239C23
hypercenter#536D239
hypocenterC239#2135
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #29504571C2semidirect
63. C239#2135semidirect

Maximal subgroups

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

subgroupindex
#295047562
#295045712
#536×C2392
#2135239