Finite Group Databasebeta

← #44484582

Subgroups — #44484582

Order 30592.

316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C22×#16838531C211yesmaximal, characteristic
2C2×#21439892C211yesmaximal, characteristic, complemented
3#29504629C212yesmaximal
4#29504534C212yesmaximal, complemented
5C2×#107×C239C211yesmaximal, characteristic, complemented
6C22×C4×D239C2211yescharacteristic
7C2×#16838531—22no—
8C2×#16838531—22no—
9C2×#16838531C414yescomplemented
10C22×C239⋊C8C2211yescharacteristic
11C2×C4⋊Dic239C2212yes—
12C2×(C2×D239)⋊C4—22no—
13#21439892—22no—
14C239⋊#95—22no—
15C22×C8×C239C2211yescharacteristic
16C2×C4⋊C4×C239C2212yes—
17#107×C239—22no—
18C23×D239D411yescharacteristic
19C22×Dic239—22no—
20C22×Dic239D411yescharacteristic
21C2×C4×D239—21no—
22C2×C4×D239—21no—
23C2×C4×D239—21no—
24C2×C4×D239—21no—
25C2×C4×D239C2×C412yes—
26C2×C4×D239Q812yes—
27#16838531—28no—
28C2×C239⋊C8—21no—
29C2×C239⋊C8—21no—
30C2×C239⋊C8C2×C412yes—
31C4⋊Dic239—22no—
32C4⋊Dic239—22no—
33(C2×D239)⋊C4—44no—
34C22×C4×C239—22no—
35C22×C4×C239C2311yescharacteristic
36C2×C8×C239C2×C412yes—
37C2×C8×C239D412yes—
38C2×C8×C239D412yes—
39C4⋊C4×C239—22no—
40C4⋊C4×C239—22no—
41C22×D239—21no—
42C22×D239—21no—
43C22×D239—22no—
44C22×D239—22no—
45C22×D239C4⋊C412yes—
46C2×Dic239—21no—
47C2×Dic239—21no—
48C2×Dic239—42no—
49C2×Dic239—42no—
50C2×Dic239—42no—
51C2×Dic239C4⋊C412yes—
52C4×D239—22no—
53C4×D239—22no—
54C4×D239—22no—
55C4×D239—22no—
56C239⋊C8—22no—
57C23×C239C2×D411yescharacteristic
58C2×C4×C239—42no—
59C2×C4×C239—42no—
60C2×C4×C239—42no—
61C2×C4×C239C22×C411yescharacteristic
62C2×C4×C239C2×D411yescharacteristic
63C2×C4×C239C2×D411yescharacteristic
64C2×C4×C239C2×Q811yescharacteristic
65C2×C4×C239#4111yescharacteristic
66C2×C4×C239#4111yescharacteristic
67C8×C239C22⋊C414yescomplemented
68C22×C239C2×C4⋊C411yescharacteristic
69C22×C239#12111yescharacteristic
70C22×C239#12111yescharacteristic
71C22×C239AGL(1,ℤ/8)12yes—
72C22×C239#13712yes—
73C2×D239—22no—
74C2×D239—24no—
75C2×D239—42no—
76C2×D239—41no—
77C2×D239—41no—
78C4×C239—82no—
79C4×C239C2×C22⋊C411yescharacteristic
80C4×C239#11711yescharacteristic
81C4×C239C22⋊Q811yescharacteristic
82C4×C239C22⋊Q811yescharacteristic
83Dic239—22no—
84Dic239—82no—
85C2×C239#38011yescharacteristic
86C2×C239#42812yes—
87C2×C239#46812yes—
88C2×C239#46911yescharacteristic
89C2×C239#47011yescharacteristic
90D239—42no—
91C239#180911yescharacteristic, complemented, Sylow
92#1809—2391nomaximal, Sylow
93C22×M16—2391no—
94C2×#107D23911yescharacteristic, complemented
95C2×#106—2391no—
96#380—2392no—
97#340—2392no—
98C23×C4—2391no—
99C2×M16—4782no—
100C2×M16—4782no—
101C2×M16—2394no—
102C22×C8—2391no—
103C22×C8C2×D23911yescharacteristic
104C2×C4⋊C4—2392no—
105C2×C4⋊C4C2×D23912yes—
106C2×C22⋊C4—4782no—
107#107—22no—
108#106—4782no—
109#95—4782no—
110C24—2391no—
111C22×C4—22no—
112C22×C4—4782no—
113C22×C4—4781no—
114C22×C4—4781no—
115C22×C4—4781no—
116C22×C4—4781no—
117C22×C4—2391no—
118C22×C4—2392no—
119C22×C4—2392no—
120C22×C4C22×D23911yescharacteristic
121M16—4788no—
122C2×C8—4781no—
123C2×C8—4781no—
124C2×C8—2392no—
125C2×C8C4×D23912yes—
126C2×C8C22⋊D23912yes—
127C2×C8D95612yes—
128C4⋊C4—22no—
129C4⋊C4—22no—
130C4⋊C4—4782no—
131C4⋊C4—4782no—
132C22⋊C4—9564no—
133C23—4781no—
134C23—4781no—
135C23—4782no—
136C23—4782no—
137C23—2392no—
138C23D4×D23911yescharacteristic
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—9562no—
143C2×C4—9562no—
144C2×C4—9562no—
145C2×C4—4781no—
146C2×C4—4781no—
147C2×C4—4782no—
148C2×C4—4782no—
149C2×C4—4782no—
150C2×C4—4782no—
151C2×C4—2392no—
152C2×C4C2×C4×D23911yescharacteristic
153C2×C4C2×C22⋊D23911yescharacteristic
154C2×C4C2×D95611yescharacteristic
155C2×C4Q8×D23911yescharacteristic
156C2×C4#1683854711yescharacteristic
157C2×C4#1683854911yescharacteristic
158C8—4782no—
159C8(C2×D239)⋊C414yescomplemented
160C22—9561no—
161C22—9562no—
162C22—9561no—
163C22—4784no—
164C22—4782no—
165C22C4⋊C4×D23911yescharacteristic
166C22#2143993111yescharacteristic
167C22#2143993511yescharacteristic
168C22#2143998412yes—
169C22#2143999212yes—
170C4—82no—
171C4—19122no—
172C4—4782no—
173C4C2×(C2×D239)⋊C411yescharacteristic
174C4#2143991811yescharacteristic
175C4#2143993611yescharacteristic
176C4#2143994011yescharacteristic
177C2—9562no—
178C2#2950462911yescharacteristic
179C2#2950481312yes—
180C2#2950501912yes—
181C2#2950502211yescharacteristic
182C2#2950502711yescharacteristic
subgroupG/H
centerC23D4×D239
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
FittingC2×#107×C239C2
socleC23×C239C2×D4
prime radicalC23×D239D4
cosocleC22×C4×C239C23
hypercenterC2×#107D239
hypocenterC239#1809
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#21439892C2semidirect
4. #29504534C2semidirect
5. C2×#107×C239C2semidirect
9. C2×#16838531C4semidirect
67. C8×C239C22⋊C4semidirect
91. C239#1809semidirect
94. C2×#107D239semidirect
159. C8(C2×D239)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#168385312
C2×#214398922
#295046292
#295045342
C2×#107×C2392
#1809239