Finite Group Databasebeta

← #44484931

Subgroups — #44484931

Order 30592.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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#29505318C211yesmaximal, characteristic
2#29504788C212yesmaximal, complemented
3#29504746C211yesmaximal, characteristic, complemented
4#29504533C212yesmaximal, complemented
5#568×C239C211yesmaximal, characteristic, complemented
6C2×#16838548C2211yescharacteristic
7#21439958C411yescharacteristic, complemented
8#21439956C411yescharacteristic, complemented
9#21439949C411yescharacteristic, complemented
10#21439947C411yescharacteristic, complemented
11#21439932—22no—
12C4×C22⋊D239—22no—
13#21439919C2212yes—
14C2×C4×Dic239C2211yescharacteristic
15#21439886—24no—
16#21439875—22no—
17C2×#41×C239C2211yescharacteristic
18#131×C239—24no—
19C2×M16×C239—22no—
20C2×M16×C239C2212yes—
21#16838548—22no—
22#16838548—22no—
23C2×Dic478C2×C411yescharacteristic
24C2×D956C2×C411yescharacteristic
25C2×C22⋊D239—22no—
26C2×C22⋊D239—21no—
27C22×Dic239—21no—
28C2×C4×D239—21no—
29C4⋊Dic239—22no—
30Dic239⋊C4—22no—
31C22⋊Dic239—22no—
32C22⋊Dic239—22no—
33(C2×D239)⋊C4—22no—
34C4×Dic239—21no—
35C4×Dic239—22no—
36C4×Dic239C2×C411yescharacteristic
37C4×Dic239C2×C411yescharacteristic
38#41×C239—22no—
39#41×C239—22no—
40C2×Q8×C239C2×C411yescharacteristic
41C2×D4×C239C2×C411yescharacteristic
42C2×D4×C239D412yes—
43C22×C4×C239D412yes—
44C22×C4×C239C2311yescharacteristic
45M16×C239—24no—
46M16×C239—22no—
47M16×C239D414yescomplemented
48C2×C8×C239—24no—
49C2×C8×C239—22no—
50C22×D239—21no—
51Dic478—22no—
52D956—22no—
53C22⋊D239—44no—
54C22⋊D239—42no—
55C2×Dic239—21no—
56C2×Dic239—21no—
57C2×Dic239—21no—
58C2×Dic239—42no—
59C2×Dic239—42no—
60C4×D239—41no—
61C4×D239—41no—
62C23×C239C22⋊C412yes—
63C23×C239C2×D411yescharacteristic
64Q8×C239—22no—
65D4×C239—24no—
66D4×C239—22no—
67C2×C4×C239—22no—
68C2×C4×C239—22no—
69C2×C4×C239C22⋊C412yes—
70C2×C4×C239C22×C411yescharacteristic
71C2×C4×C239C2×D412yes—
72C2×C4×C239C2×D411yescharacteristic
73C2×C4×C239#4112yes—
74C8×C239—24no—
75C22×C239—22no—
76C22×C239—41no—
77C22×C239—42no—
78C22×C239C2×C22⋊C411yescharacteristic
79C22×C239#12112yes—
80C2×D239—42no—
81C2×D239—41no—
82C4×C239—22no—
83C4×C239C4×D412yes—
84C4×C239#12011yescharacteristic
85C4×C239#12311yescharacteristic
86Dic239—22no—
87Dic239—41no—
88Dic239—41no—
89Dic239—82no—
90C2×C239—21no—
91C2×C239—22no—
92C2×C239—42no—
93C2×C239#38611yescharacteristic
94D239—81no—
95C239#188411yescharacteristic, complemented, Sylow
96#1884—2391nomaximal, Sylow
97#568D23911yescharacteristic, complemented
98#532—2391no—
99#421—2392no—
100#410—2391no—
101#339—2392no—
102C2×#41—2391no—
103C2×#41C2×D23911yescharacteristic
104#131—24no—
105C2×M16—22no—
106C2×M16C2×D23912yes—
107C4⋊Q8—2391no—
108#127—2391no—
109#124—2391no—
110#124—2391no—
111#121—4782no—
112C4×D4—4782no—
113#117—2392no—
114C2×C42—2391no—
115#104—4784no—
116#99—4782no—
117#41—22no—
118#41—22no—
119#41—4782no—
120#41—4782no—
121C2×Q8—2391no—
122C2×Q8C4×D23911yescharacteristic
123C2×D4—4782no—
124C2×D4—4781no—
125C2×D4—2391no—
126C2×D4C4×D23911yescharacteristic
127C2×D4D95612yes—
128C22×C4—4781no—
129C22×C4—4781no—
130C22×C4C22⋊D23912yes—
131C22×C4C22×D23911yescharacteristic
132M16—24no—
133M16—22no—
134M16C22⋊D23914yescomplemented
135C2×C8—24no—
136C2×C8—22no—
137C4⋊C4—4782no—
138C4⋊C4—4782no—
139C22⋊C4—4782no—
140C22⋊C4—4782no—
141C22⋊C4—4782no—
142C42—4782no—
143C42—4781no—
144C42—2391no—
145C42—2391no—
146C23—4781no—
147C23(C2×D239)⋊C412yes—
148C23C2×D95611yescharacteristic
149Q8—22no—
150Q8—4782no—
151D4—24no—
152D4—22no—
153D4—9562no—
154D4—9564no—
155D4—4782no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—9562no—
159C2×C4—9562no—
160C2×C4—9561no—
161C2×C4—9561no—
162C2×C4—4781no—
163C2×C4—4781no—
164C2×C4—4781no—
165C2×C4(C2×D239)⋊C412yes—
166C2×C4C2×C4×D23911yescharacteristic
167C2×C4C2×C22⋊D23912yes—
168C2×C4C2×C22⋊D23911yescharacteristic
169C2×C4#1683854812yes—
170C8—24no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—9562no—
175C22—9561no—
176C22C2×(C2×D239)⋊C411yescharacteristic
177C22#2143993412yes—
178C4—22no—
179C4—19122no—
180C4—9561no—
181C4—9561no—
182C4—4782no—
183C4C4×C22⋊D23912yes—
184C4#2143992911yescharacteristic
185C4#2143994311yescharacteristic
186C2—22no—
187C2—21no—
188C2—42no—
189C2—19121no—
190C2#2950465111yescharacteristic
subgroupG/H
centerC4#21439929
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#568×C239C2
socleC2×C239#386
prime radical#29505318C2
cosocleC22×C4×C239C23
hypercenter#568D239
hypocenterC239#1884
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #29504788C2semidirect
3. #29504746C2semidirect
4. #29504533C2semidirect
5. #568×C239C2semidirect
7. #21439958C4semidirect
8. #21439956C4semidirect
9. #21439949C4semidirect
10. #21439947C4semidirect
47. M16×C239D4semidirect
95. C239#1884semidirect
97. #568D239semidirect
134. M16C22⋊D239semidirect

Maximal subgroups

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

subgroupindex
#295053182
#295047882
#295047462
#295045332
#568×C2392
#1884239