Finite Group Databasebeta

← #44483652

Subgroups — #44483652

Order 30592.

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

normal subgroups only

This group has 250 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, complemented
2#29505120C211yesmaximal, characteristic, complemented
3#29504973C211yesmaximal, characteristic, complemented
4#29504968C211yesmaximal, characteristic
5#29504502C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic, complemented
7#332×C239C211yesmaximal, characteristic, complemented
8C2×Q8×D239—21no—
9C2×#16838537—21no—
10C2×D1912—21no—
11#21439959—21no—
12#21439957C2211yescharacteristic
13#21439938—22no—
14#21439936—21no—
15C4×Dic478C2211yescharacteristic
16C4×D956C2211yescharacteristic
17#21439922—21no—
18#21439882—21no—
19#21439882—21no—
20#21439880—22no—
21C4×C239⋊C8C2211yescharacteristic
22C4⋊Q8×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4⋊C8×C239C2211yescharacteristic
25C2×Dic478—22no—
26C2×Dic478D411yescharacteristic
27Q8×D239—42no—
28Q8×D239—42no—
29C2×D956—21no—
30C2×D956—21no—
31C2×D956—21no—
32C2×D956D411yescharacteristic
33C2×C4×D239—22no—
34C2×C4×D239—21no—
35#16838537—42no—
36D1912—42no—
37C2×C239⋊C8—21no—
38C4⋊Dic239D411yescharacteristic
39C4⋊Dic239D411yescharacteristic
40Dic239⋊C4—22no—
41Dic239⋊C4—21no—
42(C2×D239)⋊C4—22no—
43(C2×D239)⋊C4—21no—
44C4×Dic239—21no—
45C2×Q8×C239—21no—
46C2×C8×C239—21no—
47C2×C8×C239—21no—
48C4⋊C4×C239—21no—
49C4⋊C4×C239D412yes—
50C42×C239C2311yescharacteristic
51C22×D239—21no—
52C22×D239—41no—
53Dic478—21no—
54Dic478—44no—
55Dic478D812yescomplemented
56D956—21no—
57D956—42no—
58D956—41no—
59D956—41no—
60D956—41no—
61D956—41no—
62D956SD1612yescomplemented
63C2×Dic239—21no—
64C2×Dic239—21no—
65C2×Dic239—21no—
66C4×D239—44no—
67C4×D239—41no—
68C4×D239—41no—
69C239⋊C8—41no—
70Q8×C239—41no—
71Q8×C239—41no—
72C2×C4×C239—22no—
73C2×C4×C239C2×D411yescharacteristic
74C2×C4×C239C2×D411yescharacteristic
75C2×C4×C239C2×D411yescharacteristic
76C8×C239—41no—
77C8×C239—41no—
78C22×C239#12011yescharacteristic
79C2×D239—22no—
80C2×D239—41no—
81C2×D239—41no—
82C2×D239—81no—
83C2×D239—81no—
84C2×D239—81no—
85C4×C239—21no—
86C4×C239—42no—
87C4×C239C2×D811yescharacteristic
88C4×C239C2×SD1611yescharacteristic
89C4×C239AGL(1,ℤ/8)11yescharacteristic
90C4×C239#13711yescharacteristic
91Dic239—22no—
92Dic239—41no—
93Dic239—41no—
94C2×C239#44711yescharacteristic
95C2×C239#44811yescharacteristic
96C2×C239#45411yescharacteristic
97D239—42no—
98D239—161no—
99C239#162711yescharacteristic, complemented, Sylow
100#1627—2391nomaximal, Sylow
101D4×Q8—2391no—
102#486—2391no—
103#460—2391no—
104#459—2391no—
105#332D23911yescharacteristic, complemented
106Q8⋊C8—2391no—
107D4⋊C8—2391no—
108C22×Q8—4781no—
109C2×SD16—4781no—
110C2×D8—4781no—
111C4⋊Q8—4781no—
112C4⋊Q8C2×D23911yescharacteristic
113#127—2391no—
114C22⋊Q8—4781no—
115C22⋊Q8—4782no—
116C4×Q8—2391no—
117C4×D4—4781no—
118C4×D4—2391no—
119C4⋊C8C2×D23911yescharacteristic
120C4⋊C8C2×D23911yescharacteristic
121#102—4781no—
122#102—4781no—
123#102—4782no—
124C4×C8—2391no—
125C2×Q8—21no—
126C2×Q8—9562no—
127C2×Q8—9562no—
128C2×Q8—4782no—
129C2×Q8—2391no—
130C2×D4—4781no—
131C2×D4—4781no—
132C2×D4—4781no—
133C2×D4—2391no—
134C22×C4—4782no—
135C22×C4—4781no—
136SD16—9562no—
137D8—9562no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—4781no—
141C4⋊C4—21no—
142C4⋊C4—4782no—
143C4⋊C4—4781no—
144C4⋊C4—2391no—
145C4⋊C4—2391no—
146C4⋊C4D95612yes—
147C22⋊C4—4782no—
148C22⋊C4—4781no—
149C42—4781no—
150C42C22×D23911yescharacteristic
151C23—9561no—
152C23—4781no—
153Q8—41no—
154Q8—41no—
155Q8—9564no—
156Q8—4781no—
157Q8—2392no—
158D4—9562no—
159D4—9561no—
160D4—9561no—
161D4—9561no—
162D4—9561no—
163D4—4781no—
164D4—2392no—
165C2×C4—22no—
166C2×C4—9564no—
167C2×C4—9561no—
168C2×C4—9561no—
169C2×C4—4781no—
170C2×C4—4781no—
171C2×C4—4781no—
172C2×C4D4×D23911yescharacteristic
173C2×C4D4×D23911yescharacteristic
174C2×C4C2×D95611yescharacteristic
175C8—41no—
176C8—41no—
177C8—9561no—
178C22—19121no—
179C22—19121no—
180C22—19121no—
181C22—9561no—
182C22—9561no—
183C22—4782no—
184C22#2143993011yescharacteristic
185C4—21no—
186C4—42no—
187C4—9561no—
188C4—9561no—
189C4—4782no—
190C4D8×D23911yescharacteristic
191C4SD16×D23911yescharacteristic
192C4#2143998711yescharacteristic
193C4#2143999211yescharacteristic
194C2—9562no—
195C2—38241no—
196C2#2950490711yescharacteristic
197C2#2950491211yescharacteristic
198C2#2950494711yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#332×C239C2
socleC22×C239#120
prime radical#29504968C2
hypercenter#332D239
hypocenterC239#1627
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #29505437C2semidirect
2. #29505120C2semidirect
3. #29504973C2semidirect
5. #29504502C2semidirect
6. #29504499C2semidirect
7. #332×C239C2semidirect
55. Dic478D8semidirect
62. D956SD16semidirect
99. C239#1627semidirect
105. #332D239semidirect

Maximal subgroups

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

subgroupindex
#295054372
#295051202
#295049732
#295049682
#295045022
#295044992
#332×C2392
#1627239