Finite Group Databasebeta

← #44483780

Subgroups — #44483780

Order 30592.

240 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 55 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#29505425C211yesmaximal, characteristic
2#29505049C211yesmaximal, characteristic, complemented
3#29504974C211yesmaximal, characteristic, complemented
4#29504518C211yesmaximal, characteristic, complemented
5#29504501C211yesmaximal, characteristic, complemented
6#29504501C211yesmaximal, characteristic, complemented
7#500×C239C211yesmaximal, characteristic, complemented
8C2×#16838549—21no—
9C2×#16838535—21no—
10#21439945—22no—
11#21439936—21no—
12#21439935—21no—
13C4×D956C2211yescharacteristic
14C4×D956C2211yescharacteristic
15C4⋊C4×D239—21no—
16#21439893—21no—
17C4⋊(C239⋊C8)C2211yescharacteristic
18C4⋊(C239⋊C8)C2211yescharacteristic
19#21439884—21no—
20#21439880—21no—
21C4⋊Q8×C239C2211yescharacteristic
22C4⋊Q8×C239C2211yescharacteristic
23#107×C239—22no—
24C4×C8×C239C2211yescharacteristic
25#16838549—42no—
26#16838549—42no—
27C2×D956—22no—
28C2×D956D411yescharacteristic
29C2×D956D411yescharacteristic
30C2×C4×D239—22no—
31C2×C4×D239—21no—
32C2×C4×D239—21no—
33#16838535—42no—
34C2×C239⋊C8—21no—
35C2×C239⋊C8—21no—
36C4⋊Dic239D411yescharacteristic
37C4⋊Dic239D411yescharacteristic
38Dic239⋊C4—22no—
39(C2×D239)⋊C4—22no—
40(C2×D239)⋊C4—21no—
41(C2×D239)⋊C4—21no—
42C2×Q8×C239—21no—
43C2×Q8×C239—21no—
44C2×C8×C239—21no—
45C4⋊C4×C239—21no—
46C4⋊C4×C239—21no—
47C4⋊C4×C239—21no—
48C4⋊C4×C239D412yes—
49C42×C239C2311yescharacteristic
50C22×D239—21no—
51C22×D239—21no—
52D956—21no—
53D956—21no—
54D956—21no—
55D956—44no—
56D956D812yes—
57C2×Dic239—21no—
58C2×Dic239—21no—
59C4×D239—44no—
60C4×D239—41no—
61C4×D239—41no—
62C4×D239—41no—
63C4×D239—41no—
64C239⋊C8—41no—
65C239⋊C8—41no—
66Q8×C239—41no—
67Q8×C239—41no—
68Q8×C239—41no—
69Q8×C239—41no—
70C2×C4×C239—22no—
71C2×C4×C239—41no—
72C2×C4×C239C2×D411yescharacteristic
73C2×C4×C239C2×D411yescharacteristic
74C2×C4×C239C2×D411yescharacteristic
75C8×C239—22no—
76C22×C239#12011yescharacteristic
77C2×D239—22no—
78C2×D239—41no—
79C2×D239—41no—
80C2×D239—41no—
81C2×D239—41no—
82C2×D239—41no—
83C4×C239—21no—
84C4×C239—42no—
85C4×C239—81no—
86C4×C239C2×D811yescharacteristic
87C4×C239#13511yescharacteristic
88C4×C239AGL(1,ℤ/8)11yescharacteristic
89C4×C239#13711yescharacteristic
90Dic239—41no—
91Dic239—41no—
92C2×C239#44711yescharacteristic
93C2×C239#45211yescharacteristic
94C2×C239#45611yescharacteristic
95D239—42no—
96D239—81no—
97C239#164711yescharacteristic, complemented, Sylow
98#1647—2391nomaximal, Sylow
99#547—2391no—
100#500D23911yescharacteristic, complemented
101#474—2391no—
102#461—2391no—
103#332—2391no—
104D4⋊C8—2391no—
105D4⋊C8—2391no—
106C2×#41—4781no—
107C2×SD16—4781no—
108C4⋊Q8C2×D23911yescharacteristic
109C4⋊Q8C2×D23911yescharacteristic
110#123—4782no—
111C22⋊Q8—4781no—
112#121—4781no—
113C4×D4—2391no—
114C4×D4—2391no—
115C2×C4⋊C4—4781no—
116#107—22no—
117#107—4781no—
118C4⋊C8—2391no—
119C4⋊C8—2391no—
120#103—4781no—
121#102—4781no—
122C4×C8C2×D23911yescharacteristic
123#41—9562no—
124#41—9562no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×D4—4782no—
128C2×D4—2391no—
129C2×D4—2391no—
130C22×C4—4782no—
131C22×C4—4781no—
132C22×C4—4781no—
133SD16—9562no—
134C2×C8—21no—
135C2×C8—4781no—
136C2×C8—4781no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—4782no—
141C4⋊C4—2391no—
142C4⋊C4—2391no—
143C4⋊C4C22⋊D23912yes—
144C22⋊C4—4782no—
145C22⋊C4—4781no—
146C22⋊C4—4781no—
147C42C22×D23911yescharacteristic
148C23—4781no—
149C23—4781no—
150Q8—41no—
151Q8—41no—
152Q8—41no—
153Q8—41no—
154D4—9564no—
155D4—4781no—
156D4—4781no—
157D4—4781no—
158D4—2392no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—9564no—
162C2×C4—9561no—
163C2×C4—9561no—
164C2×C4—9561no—
165C2×C4—9561no—
166C2×C4—4781no—
167C2×C4—4781no—
168C2×C4D4×D23911yescharacteristic
169C2×C4D4×D23911yescharacteristic
170C2×C4C2×C22⋊D23911yescharacteristic
171C8—22no—
172C8—9561no—
173C8—9561no—
174C22—9561no—
175C22—9561no—
176C22—9561no—
177C22—9561no—
178C22—9561no—
179C22—4782no—
180C22#2143992811yescharacteristic
181C4—21no—
182C4—42no—
183C4—81no—
184C4—9561no—
185C4—9561no—
186C4D8×D23911yescharacteristic
187C4#2143998311yescharacteristic
188C4#2143998411yescharacteristic
189C4#2143999211yescharacteristic
190C2—19121no—
191C2—9562no—
192C2#2950490411yescharacteristic
193C2#2950493311yescharacteristic
194C2#2950495411yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#500×C239C2
socleC22×C239#120
prime radical#29505425C2
hypercenter#500D239
hypocenterC239#1647
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #29505049C2semidirect
3. #29504974C2semidirect
4. #29504518C2semidirect
5. #29504501C2semidirect
6. #29504501C2semidirect
7. #500×C239C2semidirect
97. C239#1647semidirect
100. #500D239semidirect

Maximal subgroups

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

subgroupindex
#295054252
#295050492
#295049742
#295045182
#295045012
#500×C2392
#1647239