Finite Group Databasebeta

← #44483701

Subgroups — #44483701

Order 30592.

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

normal subgroups only

This group has 234 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
2#29505123C211yesmaximal, characteristic, complemented
3#29505063C211yesmaximal, characteristic, complemented
4#29505062C211yesmaximal, characteristic, complemented
5#29504517C211yesmaximal, characteristic, complemented
6#29504501C211yesmaximal, characteristic, complemented
7D4⋊C8×C239C211yesmaximal, characteristic, complemented
8C2×#16838547—21no—
9#21439960C2211yescharacteristic
10#21439960C2211yescharacteristic
11#21439944—22no—
12#21439940—21no—
13#21439934—21no—
14C4×D956C2211yescharacteristic
15C2×C4⋊Dic239—21no—
16#21439892—21no—
17#21439891—21no—
18C4⋊(C239⋊C8)C2211yescharacteristic
19#21439885—22no—
20#21439882—21no—
21#21439881—21no—
22C4×D4×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4×C8×C239C2211yescharacteristic
25#16838547—42no—
26#16838547—42no—
27C2×Dic478—21no—
28C2×Dic478—21no—
29C2×D956D411yescharacteristic
30C2×C22⋊D239—22no—
31C22×Dic239—22no—
32C2×C4×D239—21no—
33C2×C239⋊C8—21no—
34C4⋊Dic239—22no—
35C4⋊Dic239—21no—
36C4⋊Dic239—21no—
37C4⋊Dic239—21no—
38C4⋊Dic239D412yes—
39C4⋊Dic239D411yescharacteristic
40(C2×D239)⋊C4—22no—
41(C2×D239)⋊C4—21no—
42C2×D4×C239D411yescharacteristic
43C22×C4×C239—21no—
44C2×C8×C239—21no—
45C2×C8×C239—21no—
46C4⋊C4×C239D411yescharacteristic
47C22⋊C4×C239—21no—
48C42×C239C2311yescharacteristic
49C22×D239—21no—
50Dic478—41no—
51Dic478—41no—
52Dic478—42no—
53D956—21no—
54D956—21no—
55C22⋊D239—44no—
56C2×Dic239—21no—
57C2×Dic239—22no—
58C2×Dic239—44no—
59C2×Dic239—41no—
60C4×D239—41no—
61C4×D239—41no—
62C239⋊C8—41no—
63C23×C239—21no—
64D4×C239—21no—
65D4×C239SD1612yes—
66C2×C4×C239—21no—
67C2×C4×C239—41no—
68C2×C4×C239—41no—
69C2×C4×C239C2×D411yescharacteristic
70C2×C4×C239C2×D411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C8×C239—41no—
73C8×C239—41no—
74C22×C239—22no—
75C22×C239—41no—
76C22×C239—41no—
77C22×C239#12011yescharacteristic
78C2×D239—41no—
79C2×D239—41no—
80C2×D239—41no—
81C4×C239—21no—
82C4×C239—41no—
83C4×C239C2×SD1611yescharacteristic
84C4×C239#13511yescharacteristic
85C4×C239AGL(1,ℤ/8)11yescharacteristic
86C4×C239#13711yescharacteristic
87Dic239—41no—
88Dic239—42no—
89Dic239—81no—
90C2×C239—42no—
91C2×C239#45011yescharacteristic
92C2×C239#45211yescharacteristic
93C2×C239#45411yescharacteristic
94D239—81no—
95C239#163511yescharacteristic, complemented, Sylow
96#1635—2391nomaximal, Sylow
97#547—2391no—
98#487—2391no—
99#476—2391no—
100#476—2391no—
101#332—2391no—
102D4⋊C8—2391no—
103D4⋊C8D23911yescharacteristic, complemented
104C2×#41—4781no—
105C4⋊Q8—2391no—
106C4⋊Q8—2391no—
107#123—4782no—
108C22⋊Q8—4781no—
109#121—4781no—
110C4×D4—2391no—
111C4×D4C2×D23911yescharacteristic
112C2×C4⋊C4—4781no—
113#106—4781no—
114#106—4781no—
115C4⋊C8—2391no—
116C4⋊C8C2×D23911yescharacteristic
117#103—4782no—
118#102—4781no—
119#102—4781no—
120C4×C8C2×D23911yescharacteristic
121#41—9562no—
122#41—9562no—
123C2×Q8—4781no—
124C2×Q8—4781no—
125C2×D4—4782no—
126C2×D4—2391no—
127C2×D4D95611yescharacteristic
128C22×C4—21no—
129C22×C4—4782no—
130C22×C4—4781no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—4781no—
134C4⋊C4—4782no—
135C4⋊C4—4781no—
136C4⋊C4—4781no—
137C4⋊C4—4781no—
138C4⋊C4—2392no—
139C4⋊C4—2391no—
140C4⋊C4D95611yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—4782no—
143C22⋊C4—4781no—
144C42C22×D23911yescharacteristic
145C23—21no—
146C23—4781no—
147Q8—9562no—
148Q8—9561no—
149Q8—9561no—
150D4—21no—
151D4—9564no—
152D4—4781no—
153D4—4781no—
154D4#1683853712yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—9561no—
159C2×C4—9564no—
160C2×C4—9561no—
161C2×C4—9561no—
162C2×C4—4781no—
163C2×C4—4782no—
164C2×C4D4×D23911yescharacteristic
165C2×C4D4×D23911yescharacteristic
166C2×C4C2×D95611yescharacteristic
167C8—41no—
168C8—41no—
169C8—9561no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—9561no—
174C22—9561no—
175C22—9561no—
176C22#2143993011yescharacteristic
177C4—21no—
178C4—41no—
179C4—19121no—
180C4—9561no—
181C4—9562no—
182C4C2×#1683853711yescharacteristic
183C4#2143997911yescharacteristic
184C4#2143998811yescharacteristic
185C4#2143998911yescharacteristic
186C2—42no—
187C2—19121no—
188C2#2950492511yescharacteristic
189C2#2950493511yescharacteristic
190C2#2950494611yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
FittingD4⋊C8×C239C2
socleC22×C239#120
prime radical#29505426C2
hypercenterD4⋊C8D239
hypocenterC239#1635
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #29505123C2semidirect
3. #29505063C2semidirect
4. #29505062C2semidirect
5. #29504517C2semidirect
6. #29504501C2semidirect
7. D4⋊C8×C239C2semidirect
95. C239#1635semidirect
103. D4⋊C8D239semidirect

Maximal subgroups

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

subgroupindex
#295054262
#295051232
#295050632
#295050622
#295045172
#295045012
D4⋊C8×C2392
#1635239