Finite Group Databasebeta

← #44484776

Subgroups — #44484776

Order 30592.

302 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 97 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#29505255C211yesmaximal, characteristic
2#29504814C211yesmaximal, characteristic, complemented
3#29504773C211yesmaximal, characteristic
4#29504642C211yesmaximal, characteristic, complemented
5#29504540C211yesmaximal, characteristic, complemented
6#29504532C211yesmaximal, characteristic, complemented
7C2×#104×C239C211yesmaximal, characteristic
8C2×#16838532C2211yescharacteristic
9Q8×Dic239—21no—
10D4×Dic239—22no—
11D4×Dic239—21no—
12#21439919—21no—
13#21439919C2211yescharacteristic
14C2×C4⋊Dic239—21no—
15C2×C4⋊Dic239—22no—
16C2×C4⋊Dic239C2211yescharacteristic
17C2×C4⋊Dic239C2211yescharacteristic
18#21439894—21no—
19#21439892—21no—
20#21439884—21no—
21#21439881—21no—
22C2×#41×C239C2211yescharacteristic
23C2×M16×C239C2211yescharacteristic
24C2×C42×C239C2211yescharacteristic
25#104×C239C414yescomplemented
26C22×Dic239—22no—
27C22×Dic239—21no—
28C22×Dic239D412yes—
29#16838532—21no—
30#16838532—21no—
31C2×C239⋊C8—21no—
32C4⋊Dic239—22no—
33C4⋊Dic239—21no—
34C4⋊Dic239—21no—
35C4⋊Dic239—21no—
36C4⋊Dic239—21no—
37C4⋊Dic239—44no—
38C4⋊Dic239D411yescharacteristic
39C4⋊Dic239D411yescharacteristic
40C22⋊Dic239—22no—
41C22⋊Dic239—21no—
42C4×Dic239—22no—
43C4×Dic239—21no—
44#41×C239—21no—
45#41×C239—21no—
46#41×C239C2×C412yes—
47#41×C239Q812yes—
48C2×Q8×C239D411yescharacteristic
49C2×D4×C239—21no—
50C2×D4×C239D411yescharacteristic
51C22×C4×C239—21no—
52C22×C4×C239—21no—
53C22×C4×C239C2311yescharacteristic
54M16×C239—21no—
55M16×C239C2×C412yescomplemented
56C2×C8×C239—21no—
57C42×C239—21no—
58C42×C239C2×C412yescomplemented
59C2×Dic239—21no—
60C2×Dic239—22no—
61C2×Dic239—21no—
62C2×Dic239—42no—
63C2×Dic239—42no—
64C2×Dic239—41no—
65C2×Dic239—82no—
66C239⋊C8—41no—
67C23×C239—21no—
68C23×C239C2×D411yescharacteristic
69Q8×C239—21no—
70Q8×C239C4⋊C412yescomplemented
71D4×C239—22no—
72D4×C239—22no—
73D4×C239—21no—
74D4×C239C4⋊C412yescomplemented
75C2×C4×C239—22no—
76C2×C4×C239—22no—
77C2×C4×C239—22no—
78C2×C4×C239—21no—
79C2×C4×C239—22no—
80C2×C4×C239—22no—
81C2×C4×C239C22×C411yescharacteristic
82C2×C4×C239C2×D411yescharacteristic
83C2×C4×C239C2×D411yescharacteristic
84C2×C4×C239C2×Q811yescharacteristic
85C2×C4×C239#4111yescharacteristic
86C2×C4×C239#4111yescharacteristic
87C8×C239—22no—
88C22×C239—21no—
89C22×C239—21no—
90C22×C239—22no—
91C22×C239—41no—
92C22×C239—41no—
93C22×C239C4×D411yescharacteristic
94C22×C239#12011yescharacteristic
95C22×C239C22⋊Q811yescharacteristic
96C4×C239—24no—
97C4×C239—22no—
98C4×C239C2×C4⋊C411yescharacteristic
99C4×C239C4×D411yescharacteristic
100C4×C239C22⋊Q811yescharacteristic
101C4×C239#12311yescharacteristic
102Dic239—42no—
103Dic239—41no—
104Dic239—41no—
105Dic239—81no—
106C2×C239—21no—
107C2×C239—21no—
108C2×C239—42no—
109C2×C239#38511yescharacteristic
110C2×C239#45311yescharacteristic
111C2×C239#45611yescharacteristic
112C239#185911yescharacteristic, complemented, Sylow
113#1859—2391nomaximal, Sylow
114#520—2391no—
115#428—2391no—
116C2×#104D23911yescharacteristic
117#417—2391no—
118#384—2391no—
119#343—2391no—
120#339—2391no—
121C2×#41C2×D23911yescharacteristic
122C2×M16—2391no—
123C2×M16C2×D23911yescharacteristic
124C4×Q8—4781no—
125C4×D4—4781no—
126C4×D4—4782no—
127#117—4781no—
128#117—2391no—
129C2×C4⋊C4—4782no—
130C2×C4⋊C4—4781no—
131C2×C4⋊C4—2391no—
132C2×C4⋊C4—2391no—
133C2×C42C2×D23911yescharacteristic
134#107—4781no—
135#106—4781no—
136#104Dic23914yescomplemented
137#103—4781no—
138#102—4781no—
139#41—21no—
140#41—21no—
141#41C2×Dic23912yes—
142#41Dic47812yes—
143C2×Q8D95611yescharacteristic
144C2×D4—21no—
145C2×D4D95611yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—4782no—
149C22×C4—4781no—
150C22×C4—2392no—
151C22×C4C22×D23911yescharacteristic
152M16—21no—
153M16—4781no—
154M16—4781no—
155M16C2×Dic23912yescomplemented
156C2×C8—21no—
157C2×C8—4781no—
158C4⋊C4—9564no—
159C4⋊C4—4782no—
160C4⋊C4—4781no—
161C4⋊C4—4781no—
162C4⋊C4—4781no—
163C4⋊C4—4781no—
164C4⋊C4—2391no—
165C4⋊C4—2391no—
166C22⋊C4—4782no—
167C22⋊C4—4781no—
168C42—21no—
169C42—4782no—
170C42—4781no—
171C42C2×Dic23912yescomplemented
172C23—21no—
173C23D4×D23911yescharacteristic
174Q8—21no—
175Q8C4⋊Dic23912yescomplemented
176D4—22no—
177D4—22no—
178D4—21no—
179D4C4⋊Dic23912yescomplemented
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—19122no—
187C2×C4—9562no—
188C2×C4—9561no—
189C2×C4—9562no—
190C2×C4—4781no—
191C2×C4—4782no—
192C2×C4—4781no—
193C2×C4C22×Dic23911yescharacteristic
194C2×C4D4×D23911yescharacteristic
195C2×C4C2×D95611yescharacteristic
196C2×C4C2×Dic47811yescharacteristic
197C2×C4#1683854711yescharacteristic
198C2×C4#1683854711yescharacteristic
199C8—22no—
200C8—9561no—
201C22—21no—
202C22—21no—
203C22—22no—
204C22—41no—
205C22—41no—
206C22D4×Dic23911yescharacteristic
207C22#2143993011yescharacteristic
208C22#2143993711yescharacteristic
209C4—24no—
210C4—22no—
211C4—19121no—
212C4—9561no—
213C4—9562no—
214C4—9561no—
215C4C2×C4⋊Dic23911yescharacteristic
216C4D4×Dic23911yescharacteristic
217C4#2143993711yescharacteristic
218C4#2143994411yescharacteristic
219C2—21no—
220C2—21no—
221C2—42no—
222C2#2950464711yescharacteristic
223C2#2950494111yescharacteristic
224C2#2950495611yescharacteristic
subgroupG/H
centerC22#21439930
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
FittingC2×#104×C239C2
socleC22×C239#120
prime radicalC2×#41×C239C22
cosocleC22×C4×C239C23
hypercenterC2×#104D239
hypocenterC239#1859
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #29504814C2semidirect
4. #29504642C2semidirect
5. #29504540C2semidirect
6. #29504532C2semidirect
25. #104×C239C4semidirect
55. M16×C239C2×C4semidirect
58. C42×C239C2×C4semidirect
70. Q8×C239C4⋊C4semidirect
74. D4×C239C4⋊C4semidirect
112. C239#1859semidirect
136. #104Dic239semidirect
155. M16C2×Dic239semidirect
171. C42C2×Dic239semidirect
175. Q8C4⋊Dic239semidirect
179. D4C4⋊Dic239semidirect

Maximal subgroups

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

subgroupindex
#295052552
#295048142
#295047732
#295046422
#295045402
#295045322
C2×#104×C2392
#1859239