Finite Group Databasebeta

← #44483679

Subgroups — #44483679

Order 30592.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#29505483C211yesmaximal, characteristic
2#29505064C211yesmaximal, characteristic, complemented
3#29505059C211yesmaximal, characteristic
4#29504521C211yesmaximal, characteristic, complemented
5#29504504C211yesmaximal, characteristic, complemented
6#29504501C211yesmaximal, characteristic
7#494×C239C211yesmaximal, characteristic, complemented
8#21439951—21no—
9#21439940—21no—
10#21439936—22no—
11C4×Dic478C2211yescharacteristic
12C4×D956C2211yescharacteristic
13#21439922—21no—
14C4⋊C4×D239—21no—
15#21439893—21no—
16#21439891—21no—
17C4⋊(C239⋊C8)C2211yescharacteristic
18C4⋊(C239⋊C8)C2211yescharacteristic
19#21439883—21no—
20#21439880—21no—
21C2×Q16×C239—22no—
22C4⋊Q8×C239C2211yescharacteristic
23C4⋊Q8×C239C2211yescharacteristic
24C4×C8×C239C2211yescharacteristic
25C2×Dic478D411yescharacteristic
26C2×D956D411yescharacteristic
27C2×C4×D239—22no—
28C2×C4×D239—21no—
29C2×C239⋊C8—21no—
30C2×C239⋊C8—21no—
31C4⋊Dic239—22no—
32C4⋊Dic239D411yescharacteristic
33C4⋊Dic239D411yescharacteristic
34Dic239⋊C4—22no—
35Dic239⋊C4—21no—
36(C2×D239)⋊C4—22no—
37(C2×D239)⋊C4—21no—
38C4×Dic239—21no—
39C2×Q8×C239—21no—
40C2×Q8×C239D412yes—
41Q16×C239—44no—
42C2×C8×C239—21no—
43C4⋊C4×C239—21no—
44C4⋊C4×C239—21no—
45C4⋊C4×C239—21no—
46C4⋊C4×C239—21no—
47C42×C239C2311yescharacteristic
48C22×D239—21no—
49Dic478—21no—
50Dic478—21no—
51D956—21no—
52D956Q1612yescomplemented
53C2×Dic239—21no—
54C2×Dic239—21no—
55C2×Dic239—21no—
56C4×D239—41no—
57C4×D239—41no—
58C4×D239—82no—
59C239⋊C8—41no—
60C239⋊C8—41no—
61Q8×C239—42no—
62Q8×C239—42no—
63C2×C4×C239—22no—
64C2×C4×C239—41no—
65C2×C4×C239C2×D411yescharacteristic
66C2×C4×C239C2×D411yescharacteristic
67C2×C4×C239C2×D411yescharacteristic
68C8×C239—22no—
69C22×C239#12011yescharacteristic
70C2×D239—22no—
71C2×D239—41no—
72C2×D239—41no—
73C4×C239—21no—
74C4×C239—42no—
75C4×C239—81no—
76C4×C239C2×Q1611yescharacteristic
77C4×C239#13511yescharacteristic
78C4×C239#13711yescharacteristic
79C4×C239#13711yescharacteristic
80Dic239—41no—
81Dic239—41no—
82Dic239—41no—
83C2×C239#45111yescharacteristic
84C2×C239#45211yescharacteristic
85C2×C239#45311yescharacteristic
86D239—42no—
87C239#163211yescharacteristic, complemented, Sylow
88#1632—2391nomaximal, Sylow
89#554—2391no—
90#494D23911yescharacteristic, complemented
91#477—2391no—
92#476—2391no—
93#333—2391no—
94Q8⋊C8—2391no—
95D4⋊C8—2391no—
96C2×Q16—22no—
97C4⋊Q8C2×D23911yescharacteristic
98C4⋊Q8C2×D23911yescharacteristic
99#125—4781no—
100C22⋊Q8—4781no—
101C22⋊Q8—4782no—
102C4×Q8—2391no—
103C4×D4—4781no—
104C4×D4—2391no—
105C2×C4⋊C4—4781no—
106#107—4781no—
107#106—4781no—
108C4⋊C8—2391no—
109C4⋊C8—2391no—
110#103—4781no—
111#102—4781no—
112C4×C8C2×D23911yescharacteristic
113C2×Q8—21no—
114C2×Q8—2391no—
115C2×Q8C22⋊D23912yes—
116C2×D4—2391no—
117C22×C4—4782no—
118C22×C4—4781no—
119Q16—44no—
120C2×C8—21no—
121C2×C8—4781no—
122C2×C8—4781no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—4782no—
128C4⋊C4—4782no—
129C4⋊C4—4781no—
130C4⋊C4—2391no—
131C4⋊C4—2391no—
132C22⋊C4—4782no—
133C22⋊C4—4781no—
134C42—4781no—
135C42C22×D23911yescharacteristic
136C23—4781no—
137Q8—42no—
138Q8—42no—
139Q8—4781no—
140Q8—4781no—
141D4—4781no—
142D4—2392no—
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—19122no—
146C2×C4—9561no—
147C2×C4—9561no—
148C2×C4—4781no—
149C2×C4—4781no—
150C2×C4—4781no—
151C2×C4D4×D23911yescharacteristic
152C2×C4D4×D23911yescharacteristic
153C2×C4C2×C22⋊D23911yescharacteristic
154C8—22no—
155C8—9561no—
156C8—9561no—
157C22—9561no—
158C22—9561no—
159C22—4782no—
160C22#2143992811yescharacteristic
161C4—21no—
162C4—42no—
163C4—81no—
164C4—9561no—
165C4—9561no—
166C4—9561no—
167C4Q16×D23911yescharacteristic
168C4#2143998311yescharacteristic
169C4#2143999211yescharacteristic
170C4#2143999211yescharacteristic
171C2—9562no—
172C2#2950492611yescharacteristic
173C2#2950493311yescharacteristic
174C2#2950493911yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#494×C239C2
socleC22×C239#120
prime radicalC2×D956D4
hypercenter#494D239
hypocenterC239#1632
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #29505064C2semidirect
4. #29504521C2semidirect
5. #29504504C2semidirect
7. #494×C239C2semidirect
52. D956Q16semidirect
87. C239#1632semidirect
90. #494D239semidirect

Maximal subgroups

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

subgroupindex
#295054832
#295050642
#295050592
#295045212
#295045042
#295045012
#494×C2392
#1632239