Finite Group Databasebeta

← #44486233

Subgroups — #44486233

Order 30592.

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

normal subgroups only

This group has 250 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, complemented
2#29504571C212yesmaximal, complemented
3#29504569C212yesmaximal, complemented
4#532×C239C211yesmaximal, characteristic
5C2×#16838532—22no—
6#21439879C2214yes—
7#21439877—22no—
8C2×#41×C239C411yescharacteristic
9C2×#41×C239C2211yescharacteristic
10C4⋊Q8×C239C2211yescharacteristic
11#127×C239C411yescharacteristic
12#124×C239C411yescharacteristic
13#124×C239C2211yescharacteristic
14#121×C239—22no—
15C4×D4×C239—22no—
16C2×C42×C239C411yescharacteristic
17#16838532—24no—
18#16838532—42no—
19C2×C239⋊C8—42no—
20#41×C239—41no—
21#41×C239—41no—
22#41×C239—41no—
23#41×C239—41no—
24C2×Q8×C239C2×C411yescharacteristic
25C2×Q8×C239C2311yescharacteristic
26C2×D4×C239—22no—
27C2×D4×C239—21no—
28C2×D4×C239C2×C411yescharacteristic
29C2×D4×C239C2×C411yescharacteristic
30C2×D4×C239D412yes—
31C22×C4×C239—21no—
32C22×C4×C239—21no—
33C22×C4×C239C2×C411yescharacteristic
34C22×C4×C239D412yes—
35C4⋊C4×C239—22no—
36C22⋊C4×C239—22no—
37C22⋊C4×C239—22no—
38C42×C239—21no—
39C42×C239C2×C411yescharacteristic
40C42×C239C2×C411yescharacteristic
41C239⋊C8—44no—
42C23×C239—21no—
43C23×C239C22⋊C412yes—
44C23×C239C22⋊C411yescharacteristic
45Q8×C239—41no—
46Q8×C239—41no—
47D4×C239—41no—
48D4×C239—42no—
49D4×C239—44no—
50D4×C239—41no—
51D4×C239—42no—
52C2×C4×C239—21no—
53C2×C4×C239—21no—
54C2×C4×C239—21no—
55C2×C4×C239—22no—
56C2×C4×C239—22no—
57C2×C4×C239—21no—
58C2×C4×C239—21no—
59C2×C4×C239—42no—
60C2×C4×C239—41no—
61C2×C4×C239—41no—
62C2×C4×C239C22⋊C411yescharacteristic
63C2×C4×C239C22×C411yescharacteristic
64C2×C4×C239C2×D412yes—
65C22×C239—21no—
66C22×C239—22no—
67C22×C239—41no—
68C22×C239—42no—
69C22×C239—42no—
70C22×C239—41no—
71C22×C239C2×C22⋊C411yescharacteristic
72C4×C239—22no—
73C4×C239—21no—
74C4×C239—22no—
75C4×C239—41no—
76C4×C239—41no—
77C4×C239#9911yescharacteristic
78C4×C239#9911yescharacteristic
79C2×C239—21no—
80C2×C239—41no—
81C2×C239—42no—
82C2×C239—81no—
83C2×C239C2×#9911yescharacteristic
84C239#213211yescharacteristic, complemented, Sylow
85#2132—2391nomaximal, Sylow
86#532D23911yescharacteristic
87#413—2392no—
88#356—2392no—
89#355—2392no—
90C2×#41Dic23911yescharacteristic
91C2×#41C2×D23911yescharacteristic
92C2×M16—4782no—
93C4⋊Q8C2×D23911yescharacteristic
94#127Dic23911yescharacteristic
95#124Dic23911yescharacteristic
96#124C2×D23911yescharacteristic
97#121—22no—
98C4×D4—22no—
99C2×C42Dic23911yescharacteristic
100#101—2394no—
101#100—4782no—
102#41—41no—
103#41—41no—
104#41—41no—
105#41—41no—
106C2×Q8C2×Dic23911yescharacteristic
107C2×Q8C22×D23911yescharacteristic
108C2×D4—22no—
109C2×D4—21no—
110C2×D4C2×Dic23911yescharacteristic
111C2×D4C2×Dic23911yescharacteristic
112C2×D4C22⋊D23912yes—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4C2×Dic23911yescharacteristic
116C22×C4C22⋊D23912yes—
117M16—9562no—
118M16—4784no—
119C2×C8—9562no—
120C4⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C42—21no—
124C42C2×Dic23911yescharacteristic
125C42C2×Dic23911yescharacteristic
126C23—21no—
127C23C22⋊Dic23912yes—
128C23C22⋊Dic23911yescharacteristic
129Q8—41no—
130Q8—41no—
131D4—41no—
132D4—42no—
133D4—41no—
134D4—44no—
135D4—42no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—42no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4C22⋊Dic23911yescharacteristic
147C2×C4C22×Dic23911yescharacteristic
148C2×C4C2×C22⋊D23912yes—
149C8—9564no—
150C22—21no—
151C22—22no—
152C22—41no—
153C22—42no—
154C22—42no—
155C22—41no—
156C22C2×C22⋊Dic23911yescharacteristic
157C4—22no—
158C4—22no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4#2143987511yescharacteristic
163C4#2143987511yescharacteristic
164C2—21no—
165C2—41no—
166C2—42no—
167C2—81no—
168C2C2×#2143987511yescharacteristic
subgroupG/H
centerC4#21439875
commutatorC2×C4×C239C22×C4
FrattiniC2×Q8C22×D239
Fitting, prime radical#532×C239C2
socleC2×C239C2×#99
cosocleC2×Q8×C239C23
hypercenter#532D239
hypocenterC239#2132
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #29504756C2semidirect
2. #29504571C2semidirect
3. #29504569C2semidirect
84. C239#2132semidirect

Maximal subgroups

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

subgroupindex
#295047562
#295045712
#295045692
#532×C2392
#2132239