Finite Group Databasebeta

← #44484950

Subgroups — #44484950

Order 30592.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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×#21439948C211yesmaximal, characteristic
2#29505249C211yesmaximal, characteristic, complemented
3#29504778C211yesmaximal, characteristic
4#29504776C211yesmaximal, characteristic
5C2×#21439878C211yesmaximal, characteristic, complemented
6#29504532C211yesmaximal, characteristic, complemented
7#339×C239C211yesmaximal, characteristic, complemented
8C22×Dic478C2211yescharacteristic
9C22×D956C2211yescharacteristic
10C2×#16838532C2211yescharacteristic
11#21439948—22no—
12#21439948C414yescomplemented
13C4×Dic478—22no—
14#21439925—22no—
15#21439919C2211yescharacteristic
16#21439916—22no—
17C2×(C2×D239)⋊C4—22no—
18#21439882—22no—
19#21439880—22no—
20#21439878—22no—
21C2×M16×C239C2211yescharacteristic
22#117×C239C2211yescharacteristic
23C2×C42×C239C2211yescharacteristic
24C23×D239—21no—
25C2×Dic478—21no—
26C2×Dic478—21no—
27C2×Dic478—21no—
28C2×Dic478—21no—
29C2×Dic478C2×C412yes—
30C2×Dic478D412yes—
31C2×D956—21no—
32C2×D956—21no—
33C2×D956—21no—
34C2×D956—21no—
35C2×D956—21no—
36C2×D956C2×C412yes—
37C22×Dic239D412yes—
38#16838532—21no—
39#16838532—21no—
40C2×C239⋊C8—21no—
41C4⋊Dic239D412yes—
42Dic239⋊C4—24no—
43C22⋊Dic239—21no—
44(C2×D239)⋊C4—28no—
45C4×Dic239—24no—
46C4×Dic239—21no—
47C22×C4×C239—21no—
48C22×C4×C239C2311yescharacteristic
49M16×C239—21no—
50M16×C239—21no—
51C2×C8×C239—21no—
52C4⋊C4×C239D412yes—
53C22⋊C4×C239—21no—
54C42×C239—21no—
55C42×C239—21no—
56C42×C239C2×C412yes—
57C22×D239—22no—
58C22×D239—44no—
59C22×D239—41no—
60C22×D239—41no—
61Dic478—22no—
62Dic478—22no—
63Dic478—22no—
64Dic478—22no—
65D956—22no—
66D956—22no—
67D956—41no—
68D956—41no—
69C2×Dic239—22no—
70C2×Dic239—22no—
71C2×Dic239—22no—
72C2×Dic239C22⋊C414yes—
73C239⋊C8—41no—
74C23×C239C2×D411yescharacteristic
75C2×C4×C239—22no—
76C2×C4×C239—22no—
77C2×C4×C239—42no—
78C2×C4×C239C22×C411yescharacteristic
79C2×C4×C239C2×D411yescharacteristic
80C2×C4×C239C2×D411yescharacteristic
81C2×C4×C239C2×D411yescharacteristic
82C2×C4×C239#4111yescharacteristic
83C2×C4×C239#4111yescharacteristic
84C8×C239—41no—
85C22×C239—22no—
86C22×C239C2×C22⋊C411yescharacteristic
87C22×C239#12011yescharacteristic
88C22×C239#12311yescharacteristic
89C2×D239—44no—
90C2×D239—42no—
91C2×D239—82no—
92C2×D239—82no—
93C4×C239—42no—
94C4×C239—42no—
95C4×C239C4×D411yescharacteristic
96C4×C239C4×D411yescharacteristic
97C4×C239#12111yescharacteristic
98C4×C239#12111yescharacteristic
99Dic239—24no—
100Dic239—42no—
101C2×C239—21no—
102C2×C239—21no—
103C2×C239#38611yescharacteristic
104C2×C239#45412yes—
105D239—82no—
106C239#188811yescharacteristic, complemented, Sylow
107#1888—2391nomaximal, Sylow
108C2×#124—2391no—
109#519—2391no—
110#418—2391no—
111#418—2391no—
112C2×#101—2391no—
113#339—2391no—
114#339D23911yescharacteristic, complemented
115C22×Q8—2391no—
116C22×D4—2391no—
117C2×M16—2391no—
118C2×M16C2×D23911yescharacteristic
119#124—4782no—
120#124—2394no—
121C4×Q8—4782no—
122C4×Q8—4782no—
123#117—4782no—
124#117—2391no—
125#117C2×D23911yescharacteristic
126C2×C22⋊C4—4782no—
127C2×C42C2×D23911yescharacteristic
128#102—4782no—
129#102—4782no—
130#101—4782no—
131C24—4781no—
132C2×Q8—4781no—
133C2×Q8—4781no—
134C2×Q8—4781no—
135C2×Q8—4781no—
136C2×Q8—2392no—
137C2×Q8—2392no—
138C2×D4—4781no—
139C2×D4—4781no—
140C2×D4—4781no—
141C2×D4—4781no—
142C2×D4—4781no—
143C2×D4—2392no—
144C22×C4—21no—
145C22×C4—2392no—
146C22×C4C22×D23911yescharacteristic
147M16—21no—
148M16—21no—
149M16—4781no—
150M16—4781no—
151C2×C8—21no—
152C2×C8—4781no—
153C4⋊C4—4784no—
154C4⋊C4—2392no—
155C4⋊C4D95612yes—
156C22⋊C4—21no—
157C22⋊C4—4788no—
158C22⋊C4—4781no—
159C42—21no—
160C42—21no—
161C42—4784no—
162C42—4781no—
163C42C4×D23912yes—
164C23—9564no—
165C23—9561no—
166C23—9561no—
167C23—4782no—
168C23D4×D23911yescharacteristic
169Q8—4782no—
170Q8—4782no—
171Q8—4782no—
172Q8—4782no—
173D4—9561no—
174D4—9561no—
175D4—4782no—
176D4—4782no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—4782no—
181C2×C4—4782no—
182C2×C4—4782no—
183C2×C4—2394no—
184C2×C4C2×C4×D23911yescharacteristic
185C2×C4D4×D23911yescharacteristic
186C2×C4D4×D23911yescharacteristic
187C2×C4C2×D95611yescharacteristic
188C2×C4#1683854811yescharacteristic
189C2×C4#1683854911yescharacteristic
190C8—41no—
191C8—9561no—
192C22—22no—
193C22—19122no—
194C22—19122no—
195C22—9564no—
196C22—9562no—
197C22C22⋊C4×D23911yescharacteristic
198C22#2143993011yescharacteristic
199C22#2143994511yescharacteristic
200C4—42no—
201C4—42no—
202C4—9562no—
203C4—4784no—
204C4#2143992211yescharacteristic
205C4C4×D95611yescharacteristic
206C4#2143993311yescharacteristic
207C4#2143993511yescharacteristic
208C2—21no—
209C2—21no—
210C2—19122no—
211C2#2950465011yescharacteristic
212C2#2950494612yes—
subgroupG/H
centerC22#21439930
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#339×C239C2
socleC22×C239#120
prime radicalC22×D956C22
cosocleC22×C4×C239C23
hypercenter#339D239
hypocenterC239#1888
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #29505249C2semidirect
5. C2×#21439878C2semidirect
6. #29504532C2semidirect
7. #339×C239C2semidirect
12. #21439948C4semidirect
106. C239#1888semidirect
114. #339D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399482
#295052492
#295047782
#295047762
C2×#214398782
#295045322
#339×C2392
#1888239