Finite Group Databasebeta

← #44483635

Subgroups — #44483635

Order 30592.

256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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#29505426C211yesmaximal, characteristic, complemented
2#29505118C211yesmaximal, characteristic, complemented
3#29504964C211yesmaximal, characteristic, complemented
4#29504519C211yesmaximal, characteristic, complemented
5D4⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic, complemented
7#459×C239C211yesmaximal, characteristic, complemented
8C2×#16838547—21no—
9C2×#16838533—21no—
10#21439960C2211yescharacteristic
11#21439944—22no—
12#21439940—21no—
13#21439934—21no—
14C4×D956C2211yescharacteristic
15C2×C4⋊Dic239—21no—
16C4⋊(C239⋊C8)C2211yescharacteristic
17#21439881—22no—
18#21439881—21no—
19C4×C239⋊C8C2211yescharacteristic
20C2×D8×C239—21no—
21#127×C239C2211yescharacteristic
22C4×D4×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24#102×C239—21no—
25#16838547—42no—
26#16838547—42no—
27C2×Dic478—21no—
28C2×D956D411yescharacteristic
29C2×C22⋊D239—22no—
30C22×Dic239—22no—
31C2×C4×D239—21no—
32#16838533—42no—
33C2×C239⋊C8—21no—
34C2×C239⋊C8—21no—
35C4⋊Dic239—22no—
36C4⋊Dic239—21no—
37C4⋊Dic239D411yescharacteristic
38C4⋊Dic239D412yes—
39(C2×D239)⋊C4—22no—
40(C2×D239)⋊C4—21no—
41C2×D4×C239—21no—
42C2×D4×C239—21no—
43C2×D4×C239—21no—
44C2×D4×C239D411yescharacteristic
45C22×C4×C239—21no—
46D8×C239—42no—
47C2×C8×C239—21no—
48C4⋊C4×C239D411yescharacteristic
49C22⋊C4×C239—21no—
50C42×C239C2311yescharacteristic
51C22×D239—21no—
52Dic478—41no—
53Dic478—41no—
54D956—21no—
55D956—21no—
56C22⋊D239—44no—
57C2×Dic239—21no—
58C2×Dic239—22no—
59C2×Dic239—44no—
60C4×D239—41no—
61C4×D239—41no—
62C239⋊C8—41no—
63C239⋊C8—41no—
64C23×C239—21no—
65C23×C239—41no—
66D4×C239—21no—
67D4×C239—42no—
68D4×C239—41no—
69D4×C239—41no—
70D4×C239—41no—
71D4×C239—41no—
72D4×C239D812yescomplemented
73C2×C4×C239—21no—
74C2×C4×C239—41no—
75C2×C4×C239—41no—
76C2×C4×C239C2×D411yescharacteristic
77C2×C4×C239C2×D411yescharacteristic
78C2×C4×C239C2×D411yescharacteristic
79C8×C239—41no—
80C22×C239—22no—
81C22×C239—41no—
82C22×C239—41no—
83C22×C239—81no—
84C22×C239—81no—
85C22×C239—81no—
86C22×C239#12011yescharacteristic
87C2×D239—41no—
88C2×D239—41no—
89C2×D239—41no—
90C4×C239—21no—
91C4×C239—41no—
92C4×C239C2×D811yescharacteristic
93C4×C239#13511yescharacteristic
94C4×C239AGL(1,ℤ/8)11yescharacteristic
95C4×C239AGL(1,ℤ/8)11yescharacteristic
96Dic239—41no—
97Dic239—42no—
98C2×C239—42no—
99C2×C239—161no—
100C2×C239#44711yescharacteristic
101C2×C239#44911yescharacteristic
102C2×C239#45411yescharacteristic
103D239—81no—
104C239#162511yescharacteristic, complemented, Sylow
105#1625—2391nomaximal, Sylow
106#547—2391no—
107#486—2391no—
108#459—2391no—
109#459D23911yescharacteristic, complemented
110#332—2391no—
111D4⋊C8—2391no—
112D4⋊C8—2391no—
113C2×#41—4781no—
114C2×D8—21no—
115C2×D8—4781no—
116C4⋊Q8—2391no—
117#127C2×D23911yescharacteristic
118#123—4782no—
119C22⋊Q8—4781no—
120#121—4781no—
121C4×D4—2391no—
122C4×D4C2×D23911yescharacteristic
123C2×C4⋊C4—4781no—
124C4⋊C8—2391no—
125C4⋊C8C2×D23911yescharacteristic
126#102—21no—
127#102—4781no—
128#102—4782no—
129C4×C8—2391no—
130#41—9562no—
131#41—9562no—
132C2×Q8—4781no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—4782no—
137C2×D4—2391no—
138C2×D4C22⋊D23911yescharacteristic
139C22×C4—21no—
140C22×C4—4782no—
141C22×C4—4781no—
142D8—42no—
143D8—9562no—
144C2×C8—21no—
145C2×C8—4781no—
146C2×C8—4781no—
147C4⋊C4—4782no—
148C4⋊C4—4781no—
149C4⋊C4—2391no—
150C4⋊C4—2392no—
151C4⋊C4C22⋊D23911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—4782no—
154C22⋊C4—4781no—
155C42C22×D23911yescharacteristic
156C23—21no—
157C23—41no—
158C23—4781no—
159Q8—9561no—
160Q8—9561no—
161D4—21no—
162D4—42no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—9564no—
168D4—4781no—
169D4—4781no—
170D4#1683853312yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—9564no—
175C2×C4—9561no—
176C2×C4—9561no—
177C2×C4—4781no—
178C2×C4—4782no—
179C2×C4D4×D23911yescharacteristic
180C2×C4D4×D23911yescharacteristic
181C2×C4C2×C22⋊D23911yescharacteristic
182C8—41no—
183C8—9561no—
184C8—9561no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—9561no—
192C22—9561no—
193C22—9561no—
194C22#2143992811yescharacteristic
195C4—21no—
196C4—41no—
197C4—9561no—
198C4—9562no—
199C4C2×#1683853311yescharacteristic
200C4#2143997911yescharacteristic
201C4#2143998411yescharacteristic
202C4#2143998511yescharacteristic
203C2—42no—
204C2—161no—
205C2—19121no—
206C2#2950490511yescharacteristic
207C2#2950491411yescharacteristic
208C2#2950494311yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#459×C239C2
socleC22×C239#120
hypercenter#459D239
hypocenterC239#1625
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #29505426C2semidirect
2. #29505118C2semidirect
3. #29504964C2semidirect
4. #29504519C2semidirect
5. D4⋊(C239⋊C8)C2semidirect
6. #29504499C2semidirect
7. #459×C239C2semidirect
72. D4×C239D8semidirect
104. C239#1625semidirect
109. #459D239semidirect
170. D4#16838533semidirect

Maximal subgroups

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

subgroupindex
#295054262
#295051182
#295049642
#295045192
D4⋊(C239⋊C8)2
#295044992
#459×C2392
#1625239