Finite Group Databasebeta

← #44483267

Subgroups — #44483267

Order 30592.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#29505320C211yesmaximal, characteristic
2#29504828C211yesmaximal, characteristic, complemented
3#29504794C211yesmaximal, characteristic, complemented
4#29504519C211yesmaximal, characteristic, complemented
5#29504517C211yesmaximal, characteristic, complemented
6#29504516C211yesmaximal, characteristic, complemented
7#331×C239C211yesmaximal, characteristic, complemented
8C2×#16838547—21no—
9C2×#16838531—21no—
10#21439960C2211yescharacteristic
11#21439947—21no—
12#21439931—21no—
13#21439931C412yes—
14D4×Dic239—21no—
15D4×Dic239C412yes—
16C42×D239C2211yescharacteristic
17C4⋊(C239⋊C8)C2211yescharacteristic
18C4⋊(C239⋊C8)C2211yescharacteristic
19Dic239⋊C8—21no—
20(C2×D239)⋊C8—21no—
21#21439870—21no—
22#127×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4⋊C8×C239C2211yescharacteristic
25#16838547—42no—
26#16838547—42no—
27C2×Dic478—21no—
28C2×C22⋊D239—22no—
29C22×Dic239—22no—
30C2×C4×D239C2×C411yescharacteristic
31C2×C4×D239D411yescharacteristic
32C2×C4×D239D411yescharacteristic
33#16838531—42no—
34C2×C239⋊C8—21no—
35C2×C239⋊C8—21no—
36C4⋊Dic239—21no—
37C4⋊Dic239C2×C412yes—
38C22⋊Dic239—22no—
39C22⋊Dic239—22no—
40C4×Dic239C2×C411yescharacteristic
41C4×Dic239D411yescharacteristic
42C4×Dic239D411yescharacteristic
43C2×D4×C239—21no—
44C2×D4×C239—21no—
45C2×D4×C239C2×C412yes—
46C2×C8×C239—21no—
47C2×C8×C239—21no—
48C42×C239C2311yescharacteristic
49C22×D239C22⋊C411yescharacteristic
50Dic478—41no—
51Dic478—41no—
52C22⋊D239—44no—
53C2×Dic239—22no—
54C2×Dic239—44no—
55C2×Dic239C22⋊C411yescharacteristic
56C2×Dic239C22⋊C411yescharacteristic
57C2×Dic239C22⋊C411yescharacteristic
58C4×D239—21no—
59C4×D239—21no—
60C4×D239—21no—
61C4×D239—21no—
62C4×D239—41no—
63C239⋊C8—41no—
64C239⋊C8—41no—
65C23×C239—22no—
66D4×C239—42no—
67D4×C239—41no—
68D4×C239—41no—
69D4×C239—41no—
70D4×C239—41no—
71C2×C4×C239C22×C411yescharacteristic
72C2×C4×C239C2×D411yescharacteristic
73C2×C4×C239C2×D411yescharacteristic
74C8×C239—41no—
75C8×C239—41no—
76C22×C239—42no—
77C22×C239—42no—
78C22×C239—42no—
79C22×C239C2×C22⋊C411yescharacteristic
80C2×D239—21no—
81C2×D239—21no—
82C2×D239—21no—
83C4×C239—21no—
84C4×C239AGL(1,ℤ/8)11yescharacteristic
85C4×C239AGL(1,ℤ/8)11yescharacteristic
86C4×C239AGL(1,ℤ/8)11yescharacteristic
87C4×C239#13711yescharacteristic
88Dic239—21no—
89Dic239—21no—
90Dic239—21no—
91Dic239—42no—
92C2×C239—82no—
93C2×C239#41311yescharacteristic
94C2×C239#41711yescharacteristic
95C2×C239#41811yescharacteristic
96D239—41no—
97C239#155711yescharacteristic, complemented, Sylow
98#1557—2391nomaximal, Sylow
99#532—2391no—
100#432—2391no—
101#423—2391no—
102#332—2391no—
103#332—2391no—
104#331—2391no—
105#331D23911yescharacteristic, complemented
106C2×#41—4781no—
107C2×M16—4781no—
108C4⋊Q8—2391no—
109#127C2×D23911yescharacteristic
110#124—4781no—
111#121—4781no—
112#121—2392no—
113C4×D4—4781no—
114C4×D4—2392no—
115C2×C42—2391no—
116C4⋊C8—4781no—
117C4⋊C8—2391no—
118C4⋊C8—2391no—
119C4⋊C8C2×D23911yescharacteristic
120C4⋊C8C2×D23911yescharacteristic
121C22⋊C8—4781no—
122#97—4781no—
123#41—9562no—
124#41—9562no—
125C2×Q8—4781no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—4782no—
129C2×D4C4×D23912yes—
130C22×C4—4782no—
131C22×C4—2391no—
132C22×C4—2391no—
133C22×C4—2391no—
134M16—9562no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—4781no—
138C2×C8—4781no—
139C4⋊C4—4781no—
140C4⋊C4—2392no—
141C22⋊C4—4782no—
142C22⋊C4—4782no—
143C42—2391no—
144C42—2391no—
145C42—2391no—
146C42C22×D23911yescharacteristic
147C23—22no—
148C23—2391no—
149Q8—9561no—
150Q8—9561no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—9564no—
157C2×C4—9561no—
158C2×C4—9564no—
159C2×C4—4782no—
160C2×C4—4781no—
161C2×C4—4781no—
162C2×C4—4781no—
163C2×C4—4781no—
164C2×C4—2391no—
165C2×C4—2391no—
166C2×C4—2391no—
167C2×C4C2×C4×D23911yescharacteristic
168C2×C4D4×D23911yescharacteristic
169C2×C4D4×D23911yescharacteristic
170C8—41no—
171C8—41no—
172C8—9561no—
173C8—9561no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—4781no—
178C22—4781no—
179C22—4781no—
180C22C22⋊C4×D23911yescharacteristic
181C4—21no—
182C4—9562no—
183C4—4781no—
184C4—4781no—
185C4—4781no—
186C4#2143998411yescharacteristic
187C4#2143998411yescharacteristic
188C4#2143998711yescharacteristic
189C4#2143998911yescharacteristic
190C2—82no—
191C2—9561no—
192C2#2950475311yescharacteristic
193C2#2950477011yescharacteristic
194C2#2950477511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
Fitting#331×C239C2
socleC22×C239C2×C22⋊C4
prime radical#29505320C2
cosocleC42×C239C23
hypercenter#331D239
hypocenterC239#1557
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #29504828C2semidirect
3. #29504794C2semidirect
4. #29504519C2semidirect
5. #29504517C2semidirect
6. #29504516C2semidirect
7. #331×C239C2semidirect
97. C239#1557semidirect
105. #331D239semidirect

Maximal subgroups

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

subgroupindex
#295053202
#295048282
#295047942
#295045192
#295045172
#295045162
#331×C2392
#1557239