Finite Group Databasebeta

← #44483812

Subgroups — #44483812

Order 30592.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#29505437C211yesmaximal, characteristic
2#29505168C211yesmaximal, characteristic, complemented
3#29505058C211yesmaximal, characteristic, complemented
4#29504978C211yesmaximal, characteristic
5#29504502C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic
7#332×C239C211yesmaximal, characteristic, complemented
8C2×Q8×D239—21no—
9C2×#16838537—21no—
10#21439960C2211yescharacteristic
11#21439959—21no—
12#21439938—22no—
13#21439936—21no—
14C4×Dic478C2211yescharacteristic
15C4×D956C2211yescharacteristic
16#21439922—21no—
17#21439892—21no—
18#21439891—22no—
19#21439885—21no—
20#21439885—21no—
21C4×C239⋊C8C2211yescharacteristic
22C4⋊Q8×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4⋊C8×C239C2211yescharacteristic
25C2×Dic478—22no—
26C2×Dic478—21no—
27C2×Dic478D411yescharacteristic
28Q8×D239—42no—
29Q8×D239—42no—
30C2×D956D411yescharacteristic
31C2×C4×D239—22no—
32C2×C4×D239—21no—
33#16838537—42no—
34C2×C239⋊C8—21no—
35C4⋊Dic239—21no—
36C4⋊Dic239—21no—
37C4⋊Dic239D411yescharacteristic
38C4⋊Dic239D411yescharacteristic
39Dic239⋊C4—22no—
40Dic239⋊C4—21no—
41(C2×D239)⋊C4—22no—
42(C2×D239)⋊C4—21no—
43C4×Dic239—21no—
44C2×Q8×C239—21no—
45C2×C8×C239—21no—
46C2×C8×C239—21no—
47C4⋊C4×C239—21no—
48C4⋊C4×C239D412yes—
49C42×C239C2311yescharacteristic
50C22×D239—21no—
51Dic478—21no—
52Dic478—44no—
53Dic478—41no—
54Dic478—41no—
55Dic478SD1612yescomplemented
56D956—21no—
57D956SD1612yes—
58C2×Dic239—21no—
59C2×Dic239—21no—
60C2×Dic239—21no—
61C2×Dic239—41no—
62C4×D239—44no—
63C4×D239—41no—
64C4×D239—41no—
65C239⋊C8—22no—
66Q8×C239—41no—
67Q8×C239—41no—
68C2×C4×C239—22no—
69C2×C4×C239C2×D411yescharacteristic
70C2×C4×C239C2×D411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C8×C239—41no—
73C8×C239—41no—
74C22×C239#12011yescharacteristic
75C2×D239—22no—
76C2×D239—41no—
77C2×D239—41no—
78C4×C239—21no—
79C4×C239—42no—
80C4×C239C2×SD1611yescharacteristic
81C4×C239C2×SD1611yescharacteristic
82C4×C239AGL(1,ℤ/8)11yescharacteristic
83C4×C239#13711yescharacteristic
84Dic239—22no—
85Dic239—41no—
86Dic239—41no—
87Dic239—81no—
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#475—2391no—
97#461—2391no—
98#332D23911yescharacteristic, complemented
99Q8⋊C8—2391no—
100D4⋊C8—2391no—
101C22×Q8—4781no—
102C2×SD16—4781no—
103C4⋊Q8—4781no—
104C4⋊Q8—2391no—
105C4⋊Q8C2×D23911yescharacteristic
106C22⋊Q8—4781no—
107C22⋊Q8—4782no—
108C4×Q8—2391no—
109C4×D4—4781no—
110C4×D4—2391no—
111#106—4781no—
112#106—4782no—
113C4⋊C8C2×D23911yescharacteristic
114C4⋊C8C2×D23911yescharacteristic
115#103—4781no—
116#103—4781no—
117C4×C8—2391no—
118C2×Q8—21no—
119C2×Q8—9562no—
120C2×Q8—9562no—
121C2×Q8—4782no—
122C2×Q8—4781no—
123C2×Q8—2391no—
124C2×D4—2391no—
125C22×C4—4782no—
126C22×C4—4781no—
127SD16—9562no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—4781no—
131C4⋊C4—21no—
132C4⋊C4—4782no—
133C4⋊C4—4781no—
134C4⋊C4—4781no—
135C4⋊C4—4781no—
136C4⋊C4—2391no—
137C4⋊C4—2391no—
138C4⋊C4D95612yes—
139C22⋊C4—4782no—
140C22⋊C4—4781no—
141C42—4781no—
142C42C22×D23911yescharacteristic
143C23—4781no—
144Q8—41no—
145Q8—41no—
146Q8—9564no—
147Q8—9561no—
148Q8—9561no—
149Q8—4781no—
150Q8—2392no—
151D4—4781no—
152D4—2392no—
153C2×C4—22no—
154C2×C4—9564no—
155C2×C4—9561no—
156C2×C4—9561no—
157C2×C4—9561no—
158C2×C4—4781no—
159C2×C4—4781no—
160C2×C4—4781no—
161C2×C4D4×D23911yescharacteristic
162C2×C4D4×D23911yescharacteristic
163C2×C4C2×D95611yescharacteristic
164C8—41no—
165C8—41no—
166C8—4782no—
167C22—9561no—
168C22—9561no—
169C22—4782no—
170C22#2143993011yescharacteristic
171C4—21no—
172C4—42no—
173C4—19121no—
174C4—9561no—
175C4—9561no—
176C4—4782no—
177C4SD16×D23911yescharacteristic
178C4SD16×D23911yescharacteristic
179C4#2143998411yescharacteristic
180C4#2143999211yescharacteristic
181C2—9562no—
182C2#2950491211yescharacteristic
183C2#2950492411yescharacteristic
184C2#2950495711yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#332×C239C2
socleC22×C239#120
prime radicalC2×D956D4
hypercenter#332D239
hypocenterC239#1651
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #29505168C2semidirect
3. #29505058C2semidirect
5. #29504502C2semidirect
7. #332×C239C2semidirect
55. Dic478SD16semidirect
92. C239#1651semidirect
98. #332D239semidirect

Maximal subgroups

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

subgroupindex
#295054372
#295051682
#295050582
#295049782
#295045022
#295044992
#332×C2392
#1651239