Finite Group Databasebeta

← #44483810

Subgroups — #44483810

Order 30592.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×D956C211yesmaximal, characteristic
2#29505168C211yesmaximal, characteristic, complemented
3#29504974C211yesmaximal, characteristic
4#29504519C211yesmaximal, characteristic, complemented
5Q8⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic
7#475×C239C211yesmaximal, characteristic, complemented
8C2×Q8×D239—21no—
9C2×#16838535—21no—
10#21439960—21no—
11#21439960C2211yescharacteristic
12#21439940—22no—
13#21439940—21no—
14C4×D956—21no—
15C4×D956C2211yescharacteristic
16#21439891—22no—
17C4⋊(C239⋊C8)C2211yescharacteristic
18#21439884—21no—
19C4×C239⋊C8C2211yescharacteristic
20C4⋊Q8×C239C2211yescharacteristic
21C4×Q8×C239C2211yescharacteristic
22#106×C239—21no—
23C4⋊C8×C239C2211yescharacteristic
24#103×C239—21no—
25C2×Dic478—22no—
26C2×Dic478—21no—
27Q8×D239—42no—
28Q8×D239—42no—
29C2×D956D411yescharacteristic
30C2×C4×D239—22no—
31C2×C4×D239—21no—
32#16838535—42no—
33C2×C239⋊C8—21no—
34C2×C239⋊C8—21no—
35C4⋊Dic239—22no—
36C4⋊Dic239—21no—
37C4⋊Dic239D411yescharacteristic
38C4⋊Dic239D412yes—
39(C2×D239)⋊C4—22no—
40(C2×D239)⋊C4—21no—
41C2×Q8×C239—21no—
42C2×Q8×C239D411yescharacteristic
43C2×C8×C239—21no—
44C4⋊C4×C239—21no—
45C4⋊C4×C239—21no—
46C4⋊C4×C239—21no—
47C4⋊C4×C239D411yescharacteristic
48C42×C239—21no—
49C42×C239C2311yescharacteristic
50C22×D239—21no—
51Dic478—44no—
52Dic478—41no—
53Dic478—41no—
54D956—21no—
55D956SD1612yes—
56C2×Dic239—22no—
57C2×Dic239—21no—
58C4×D239—44no—
59C4×D239—41no—
60C4×D239—41no—
61C239⋊C8—22no—
62C239⋊C8—41no—
63Q8×C239—21no—
64Q8×C239—41no—
65Q8×C239—41no—
66Q8×C239SD1612yescomplemented
67C2×C4×C239—21no—
68C2×C4×C239—21no—
69C2×C4×C239—41no—
70C2×C4×C239C2×D411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C2×C4×C239C2×D411yescharacteristic
73C8×C239—41no—
74C22×C239#12011yescharacteristic
75C2×D239—22no—
76C2×D239—41no—
77C2×D239—41no—
78C4×C239—22no—
79C4×C239—21no—
80C4×C239—41no—
81C4×C239—81no—
82C4×C239C2×SD1611yescharacteristic
83C4×C239C2×SD1611yescharacteristic
84C4×C239AGL(1,ℤ/8)11yescharacteristic
85C4×C239#13711yescharacteristic
86Dic239—42no—
87Dic239—41no—
88C2×C239#44811yescharacteristic
89C2×C239#45011yescharacteristic
90C2×C239#45611yescharacteristic
91D239—42no—
92C239#165111yescharacteristic, complemented, Sylow
93#1651—2391nomaximal, Sylow
94D4×Q8—2391no—
95#498—2391no—
96#475D23911yescharacteristic, complemented
97#461—2391no—
98#332—2391no—
99Q8⋊C8—2391no—
100D4⋊C8—2391no—
101C22×Q8—4781no—
102C2×SD16—4781no—
103C4⋊Q8—4781no—
104C4⋊Q8—2391no—
105C4⋊Q8C2×D23911yescharacteristic
106C22⋊Q8—4782no—
107C22⋊Q8—4781no—
108C4×Q8C2×D23911yescharacteristic
109C4×D4—4781no—
110C4×D4—2391no—
111#106—21no—
112#106—4782no—
113C4⋊C8—2391no—
114C4⋊C8C2×D23911yescharacteristic
115#103—21no—
116#103—4781no—
117C4×C8—2391no—
118C2×Q8—21no—
119C2×Q8—9562no—
120C2×Q8—9562no—
121C2×Q8—4782no—
122C2×Q8—4781no—
123C2×Q8C22⋊D23911yescharacteristic
124C2×D4—2391no—
125C22×C4—4782no—
126C22×C4—4781no—
127SD16—9562no—
128C2×C8—21no—
129C2×C8—4781no—
130C2×C8—4781no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—4782no—
135C4⋊C4—4781no—
136C4⋊C4—2391no—
137C4⋊C4—2392no—
138C4⋊C4C22⋊D23911yescharacteristic
139C22⋊C4—4782no—
140C22⋊C4—4781no—
141C42—21no—
142C42C22×D23911yescharacteristic
143C23—4781no—
144Q8—21no—
145Q8—41no—
146Q8—41no—
147Q8—9564no—
148Q8—9561no—
149Q8—9561no—
150Q8#1683853512yescomplemented
151D4—4781no—
152D4—2392no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—9564no—
157C2×C4—9561no—
158C2×C4—9561no—
159C2×C4—4782no—
160C2×C4—4781no—
161C2×C4D4×D23911yescharacteristic
162C2×C4D4×D23911yescharacteristic
163C2×C4C2×C22⋊D23911yescharacteristic
164C8—41no—
165C8—9561no—
166C8—4782no—
167C22—9561no—
168C22—9561no—
169C22—4782no—
170C22#2143992811yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—81no—
175C4—9562no—
176C4—9561no—
177C4SD16×D23911yescharacteristic
178C4C2×#1683853511yescharacteristic
179C4#2143998511yescharacteristic
180C4#2143998911yescharacteristic
181C2—9562no—
182C2#2950490911yescharacteristic
183C2#2950492211yescharacteristic
184C2#2950495311yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#475×C239C2
socleC22×C239#120
prime radicalC2×D956D4
hypercenter#475D239
hypocenterC239#1651
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #29505168C2semidirect
4. #29504519C2semidirect
5. Q8⋊(C239⋊C8)C2semidirect
7. #475×C239C2semidirect
66. Q8×C239SD16semidirect
92. C239#1651semidirect
96. #475D239semidirect
150. Q8#16838535semidirect

Maximal subgroups

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

subgroupindex
Q8×D9562
#295051682
#295049742
#295045192
Q8⋊(C239⋊C8)2
#295044992
#475×C2392
#1651239