Finite Group Databasebeta

← #44482915

Subgroups — #44482915

Order 30592.

214 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#21439954C211yesmaximal, characteristic
2#29504829C211yesmaximal, characteristic, complemented
3#29504497C212yesmaximal, complemented
4#29504495C212yesmaximal
5#431×C239C211yesmaximal, characteristic, complemented
6#21439954—21no—
7#21439954—21no—
8#21439954—21no—
9#21439954—21no—
10C2×Dic239⋊C4C411yescharacteristic
11C2×Dic239⋊C4C411yescharacteristic
12C2×Dic239⋊C4C2211yescharacteristic
13C2×(C2×D239)⋊C4C411yescharacteristic
14C2×(C2×D239)⋊C4C411yescharacteristic
15C2×(C2×D239)⋊C4C2211yescharacteristic
16C4⋊(C239⋊C8)—21no—
17C22⋊(C239⋊C8)C2212yes—
18#21439871—21no—
19C2×C42×C239C2211yescharacteristic
20C4⋊C8×C239—21no—
21C22⋊C8×C239C2212yes—
22C4×C8×C239—21no—
23C23×D239C2×C411yescharacteristic
24C22×Dic239C2×C411yescharacteristic
25C22×Dic239C2×C411yescharacteristic
26C22×Dic239C2×C411yescharacteristic
27C2×C239⋊C8—22no—
28Dic239⋊C4—21no—
29Dic239⋊C4—21no—
30Dic239⋊C4—21no—
31Dic239⋊C4—21no—
32Dic239⋊C4—21no—
33Dic239⋊C4—21no—
34(C2×D239)⋊C4—21no—
35(C2×D239)⋊C4—21no—
36(C2×D239)⋊C4—21no—
37(C2×D239)⋊C4—21no—
38(C2×D239)⋊C4—21no—
39(C2×D239)⋊C4—21no—
40C22×C4×C239C2×C411yescharacteristic
41C22×C4×C239C2×C411yescharacteristic
42C22×C4×C239C2311yescharacteristic
43C2×C8×C239—22no—
44C42×C239D411yescharacteristic
45C42×C239D411yescharacteristic
46C42×C239D411yescharacteristic
47C42×C239D411yescharacteristic
48C22×D239—21no—
49C22×D239—22no—
50C22×D239—41no—
51C22×D239—41no—
52C2×Dic239—21no—
53C2×Dic239—21no—
54C2×Dic239—21no—
55C2×Dic239—22no—
56C2×Dic239—41no—
57C2×Dic239—41no—
58C239⋊C8—42no—
59C23×C239C22×C411yescharacteristic
60C2×C4×C239—22no—
61C2×C4×C239—41no—
62C2×C4×C239—41no—
63C2×C4×C239C22⋊C411yescharacteristic
64C2×C4×C239C22⋊C411yescharacteristic
65C2×C4×C239C22⋊C411yescharacteristic
66C2×C4×C239C22⋊C411yescharacteristic
67C2×C4×C239C2×D411yescharacteristic
68C2×C4×C239C2×D411yescharacteristic
69C8×C239—42no—
70C22×C239—21no—
71C22×C239—21no—
72C22×C239C2×C22⋊C411yescharacteristic
73C22×C239#13112yes—
74C2×D239—41no—
75C2×D239—41no—
76C2×D239—41no—
77C2×D239—82no—
78C4×C239—21no—
79C4×C239—21no—
80C4×C239—21no—
81C4×C239—21no—
82C4×C239—21no—
83C4×C239—21no—
84Dic239—41no—
85Dic239—41no—
86Dic239—41no—
87C2×C239—22no—
88C2×C239#40811yescharacteristic
89C2×C239#41011yescharacteristic
90C2×C239#41311yescharacteristic
91D239—81no—
92C239#147311yescharacteristic, complemented, Sylow
93#1473—2391nomaximal, Sylow
94C2×#126—2391no—
95#432—2391no—
96#431D23911yescharacteristic, complemented
97#324—2392no—
98#323—2392no—
99#126—4781no—
100#126—4781no—
101#126—4781no—
102#126—4781no—
103C2×C4⋊C4—2391no—
104C2×C4⋊C4—2391no—
105C2×C4⋊C4—2391no—
106C2×C22⋊C4—2391no—
107C2×C22⋊C4—2391no—
108C2×C22⋊C4—2391no—
109C2×C42C2×D23911yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—4781no—
112C22⋊C8—2392no—
113C22⋊C8C2×D23912yes—
114#97—4781no—
115C4×C8—21no—
116C24—2391no—
117C22×C4—2391no—
118C22×C4—2391no—
119C22×C4—2391no—
120C22×C4C4×D23911yescharacteristic
121C22×C4C4×D23911yescharacteristic
122C22×C4C22×D23911yescharacteristic
123C2×C8—22no—
124C2×C8—4782no—
125C4⋊C4—4781no—
126C4⋊C4—4781no—
127C4⋊C4—4781no—
128C4⋊C4—4781no—
129C4⋊C4—4781no—
130C4⋊C4—4781no—
131C22⋊C4—4781no—
132C22⋊C4—4781no—
133C22⋊C4—4781no—
134C22⋊C4—4781no—
135C22⋊C4—4781no—
136C22⋊C4—4781no—
137C42C22⋊D23911yescharacteristic
138C42C22⋊D23911yescharacteristic
139C42D95611yescharacteristic
140C42D95611yescharacteristic
141C23—9561no—
142C23—9561no—
143C23—4782no—
144C23—4781no—
145C23C2×C4×D23911yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—9561no—
150C2×C4—9561no—
151C2×C4—4781no—
152C2×C4—4781no—
153C2×C4—4781no—
154C2×C4—4782no—
155C2×C4(C2×D239)⋊C411yescharacteristic
156C2×C4(C2×D239)⋊C411yescharacteristic
157C2×C4(C2×D239)⋊C411yescharacteristic
158C2×C4(C2×D239)⋊C411yescharacteristic
159C2×C4C2×C22⋊D23911yescharacteristic
160C2×C4C2×D95611yescharacteristic
161C8—42no—
162C8—9562no—
163C22—21no—
164C22—21no—
165C22—19122no—
166C22—9561no—
167C22—9561no—
168C22—9561no—
169C22C2×(C2×D239)⋊C411yescharacteristic
170C22#2143996612yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—9561no—
178C4—9561no—
179C4—9561no—
180C2—22no—
181C2—19121no—
182C2#2950473811yescharacteristic
183C2#2950474511yescharacteristic
184C2#2950475411yescharacteristic
subgroupG/H
centerC22C2×(C2×D239)⋊C4
commutatorC23×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#431×C239C2
socleC22×C239C2×C22⋊C4
prime radicalC23×D239C2×C4
cosocleC22×C4×C239C23
hypercenter#431D239
hypocenterC239#1473
LCSG ▷ C23×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #29504829C2semidirect
3. #29504497C2semidirect
5. #431×C239C2semidirect
92. C239#1473semidirect
96. #431D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399542
#295048292
#295044972
#295044952
#431×C2392
#1473239