Finite Group Databasebeta

← #44483717

Subgroups — #44483717

Order 30592.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#29505496C211yesmaximal, characteristic
2#29505064C211yesmaximal, characteristic, complemented
3#29505059C211yesmaximal, characteristic
4#29504518C211yesmaximal, characteristic, complemented
5#29504504C211yesmaximal, characteristic, complemented
6#29504501C211yesmaximal, characteristic
7#487×C239C211yesmaximal, characteristic, complemented
8#21439955—22no—
9#21439949—21no—
10#21439940—21no—
11Q8×Dic239—21no—
12C4×Dic478C2211yescharacteristic
13C4×D956C2211yescharacteristic
14#21439918—21no—
15#21439893—21no—
16#21439891—21no—
17C4⋊(C239⋊C8)C2211yescharacteristic
18C4⋊(C239⋊C8)C2211yescharacteristic
19#21439883—21no—
20#21439880—21no—
21C4⋊Q8×C239C2211yescharacteristic
22C4⋊Q8×C239C2211yescharacteristic
23#103×C239—22no—
24C4×C8×C239C2211yescharacteristic
25C2×Dic478D411yescharacteristic
26C2×D956D411yescharacteristic
27C2×C4×D239—21no—
28C2×C239⋊C8—21no—
29C2×C239⋊C8—21no—
30C4⋊Dic239—22no—
31C4⋊Dic239D411yescharacteristic
32C4⋊Dic239D411yescharacteristic
33Dic239⋊C4—21no—
34(C2×D239)⋊C4—22no—
35(C2×D239)⋊C4—22no—
36(C2×D239)⋊C4—21no—
37C4×Dic239—22no—
38C4×Dic239—21no—
39C2×Q8×C239—21no—
40C2×Q8×C239—21no—
41C2×C8×C239—21no—
42C4⋊C4×C239—21no—
43C4⋊C4×C239—21no—
44C4⋊C4×C239—21no—
45C4⋊C4×C239D412yes—
46C42×C239C2311yescharacteristic
47C22×D239—21no—
48Dic478—21no—
49Dic478—21no—
50D956—21no—
51D956—21no—
52C2×Dic239—21no—
53C2×Dic239—21no—
54C2×Dic239—21no—
55C4×D239—41no—
56C4×D239—41no—
57C239⋊C8—41no—
58C239⋊C8—41no—
59Q8×C239—42no—
60Q8×C239—41no—
61Q8×C239—41no—
62C2×C4×C239—22no—
63C2×C4×C239—41no—
64C2×C4×C239C2×D411yescharacteristic
65C2×C4×C239C2×D411yescharacteristic
66C2×C4×C239C2×D411yescharacteristic
67C8×C239—41no—
68C22×C239#12011yescharacteristic
69C2×D239—41no—
70C2×D239—41no—
71C2×D239—41no—
72C4×C239—21no—
73C4×C239—42no—
74C4×C239—81no—
75C4×C239#13511yescharacteristic
76C4×C239#13511yescharacteristic
77C4×C239#13711yescharacteristic
78C4×C239#13711yescharacteristic
79Dic239—41no—
80Dic239—41no—
81Dic239—41no—
82C2×C239#45211yescharacteristic
83C2×C239#45211yescharacteristic
84C2×C239#45411yescharacteristic
85D239—81no—
86C239#163811yescharacteristic, complemented, Sylow
87#1638—2391nomaximal, Sylow
88#556—2391no—
89#487D23911yescharacteristic, complemented
90#477—2391no—
91#476—2391no—
92#332—2391no—
93Q8⋊C8—2391no—
94D4⋊C8—2391no—
95C4⋊Q8C2×D23911yescharacteristic
96C4⋊Q8C2×D23911yescharacteristic
97#126—4782no—
98#124—4781no—
99C22⋊Q8—4781no—
100C4×Q8—4781no—
101C4×Q8—2391no—
102C4×D4—2391no—
103#117—4781no—
104#107—4781no—
105#106—4781no—
106C4⋊C8—2391no—
107C4⋊C8—2391no—
108#103—22no—
109#103—4781no—
110#102—4781no—
111C4×C8C2×D23911yescharacteristic
112C2×Q8—21no—
113C2×Q8—21no—
114C2×Q8—2391no—
115C2×D4—2391no—
116C22×C4—4781no—
117C2×C8—21no—
118C2×C8—4781no—
119C2×C8—4781no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—4782no—
124C4⋊C4—4781no—
125C4⋊C4—2391no—
126C4⋊C4—2391no—
127C4⋊C4C22⋊D23912yes—
128C22⋊C4—4782no—
129C22⋊C4—4782no—
130C22⋊C4—4781no—
131C42—4782no—
132C42—4781no—
133C42C22×D23911yescharacteristic
134C23—4781no—
135Q8—42no—
136Q8—41no—
137Q8—41no—
138Q8—4781no—
139Q8—4781no—
140D4—4781no—
141D4—4781no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—9561no—
145C2×C4—9561no—
146C2×C4—4781no—
147C2×C4—4781no—
148C2×C4—4781no—
149C2×C4D4×D23911yescharacteristic
150C2×C4D4×D23911yescharacteristic
151C2×C4C2×C22⋊D23911yescharacteristic
152C8—41no—
153C8—9561no—
154C8—9561no—
155C22—9561no—
156C22—9561no—
157C22—9561no—
158C22#2143992811yescharacteristic
159C4—21no—
160C4—42no—
161C4—81no—
162C4—9561no—
163C4—9561no—
164C4—9561no—
165C4#2143998111yescharacteristic
166C4#2143998311yescharacteristic
167C4#2143998911yescharacteristic
168C4#2143999211yescharacteristic
169C2—19121no—
170C2#2950493111yescharacteristic
171C2#2950493311yescharacteristic
172C2#2950494411yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#487×C239C2
socleC22×C239#120
prime radicalC2×D956D4
hypercenter#487D239
hypocenterC239#1638
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #29505064C2semidirect
4. #29504518C2semidirect
5. #29504504C2semidirect
7. #487×C239C2semidirect
86. C239#1638semidirect
89. #487D239semidirect

Maximal subgroups

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

subgroupindex
#295054962
#295050642
#295050592
#295045182
#295045042
#295045012
#487×C2392
#1638239