Finite Group Databasebeta

← #44483250

Subgroups — #44483250

Order 30592.

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

normal subgroups only

This group has 242 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#29504824C211yesmaximal, characteristic, complemented
4#29504519C211yesmaximal, characteristic, complemented
5#29504517C211yesmaximal, characteristic, complemented
6#29504516C211yesmaximal, characteristic, complemented
7#331×C239C211yesmaximal, characteristic, complemented
8C2×#16838547—21no—
9#21439960C2211yescharacteristic
10#21439947—21no—
11#21439931—21no—
12#21439931C412yes—
13D4×Dic239—21no—
14D4×Dic239C412yes—
15C42×D239C2211yescharacteristic
16C4⋊(C239⋊C8)C2211yescharacteristic
17C4⋊(C239⋊C8)C2211yescharacteristic
18(C2×D239)⋊C8—21no—
19(C2×D239)⋊C8—21no—
20#21439870—21no—
21C8×Dic239—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
33C2×C239⋊C8—21no—
34C2×C239⋊C8—21no—
35C4⋊Dic239—21no—
36C4⋊Dic239C2×C412yes—
37C22⋊Dic239—22no—
38C22⋊Dic239—22no—
39C4×Dic239C2×C411yescharacteristic
40C4×Dic239D411yescharacteristic
41C4×Dic239D411yescharacteristic
42C2×D4×C239—21no—
43C2×D4×C239—21no—
44C2×D4×C239C2×C412yes—
45C2×C8×C239—21no—
46C2×C8×C239—21no—
47C42×C239C2311yescharacteristic
48C22×D239C22⋊C411yescharacteristic
49Dic478—41no—
50Dic478—41no—
51C22⋊D239—44no—
52C2×Dic239—22no—
53C2×Dic239—44no—
54C2×Dic239C22⋊C411yescharacteristic
55C2×Dic239C22⋊C411yescharacteristic
56C2×Dic239C22⋊C411yescharacteristic
57C4×D239—21no—
58C4×D239—21no—
59C4×D239—21no—
60C4×D239—21no—
61C4×D239—41no—
62C239⋊C8—41no—
63C239⋊C8—41no—
64C23×C239—22no—
65D4×C239—42no—
66D4×C239—41no—
67D4×C239—41no—
68D4×C239—41no—
69D4×C239—41no—
70C2×C4×C239C22×C411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C2×C4×C239C2×D411yescharacteristic
73C8×C239—41no—
74C8×C239—41no—
75C22×C239—42no—
76C22×C239—42no—
77C22×C239—42no—
78C22×C239C2×C22⋊C411yescharacteristic
79C2×D239—21no—
80C2×D239—21no—
81C2×D239—21no—
82C4×C239—21no—
83C4×C239#13511yescharacteristic
84C4×C239#13511yescharacteristic
85C4×C239AGL(1,ℤ/8)11yescharacteristic
86C4×C239AGL(1,ℤ/8)11yescharacteristic
87Dic239—21no—
88Dic239—21no—
89Dic239—21no—
90Dic239—42no—
91C2×C239—82no—
92C2×C239#41311yescharacteristic
93C2×C239#41611yescharacteristic
94C2×C239#41811yescharacteristic
95D239—41no—
96C239#155311yescharacteristic, complemented, Sylow
97#1553—2391nomaximal, Sylow
98#532—2391no—
99#432—2391no—
100#431—2391no—
101#332—2391no—
102#332—2391no—
103#331—2391no—
104#331D23911yescharacteristic, complemented
105C2×#41—4781no—
106C4⋊Q8—2391no—
107#127C2×D23911yescharacteristic
108#124—4781no—
109#121—4781no—
110#121—2392no—
111C4×D4—4781no—
112C4×D4—2392no—
113C2×C42—2391no—
114C4⋊C8—2391no—
115C4⋊C8—2391no—
116C4⋊C8C2×D23911yescharacteristic
117C4⋊C8C2×D23911yescharacteristic
118C22⋊C8—4781no—
119C22⋊C8—4781no—
120#97—4781no—
121C4×C8—4781no—
122#41—9562no—
123#41—9562no—
124C2×Q8—4781no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—4782no—
128C2×D4C4×D23912yes—
129C22×C4—4782no—
130C22×C4—2391no—
131C22×C4—2391no—
132C22×C4—2391no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—4781no—
136C2×C8—4781no—
137C4⋊C4—4781no—
138C4⋊C4—2392no—
139C22⋊C4—4782no—
140C22⋊C4—4782no—
141C42—2391no—
142C42—2391no—
143C42—2391no—
144C42C22×D23911yescharacteristic
145C23—22no—
146C23—2391no—
147Q8—9561no—
148Q8—9561no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—9564no—
155C2×C4—9561no—
156C2×C4—9564no—
157C2×C4—4782no—
158C2×C4—4781no—
159C2×C4—4781no—
160C2×C4—4781no—
161C2×C4—4781no—
162C2×C4—2391no—
163C2×C4—2391no—
164C2×C4—2391no—
165C2×C4C2×C4×D23911yescharacteristic
166C2×C4D4×D23911yescharacteristic
167C2×C4D4×D23911yescharacteristic
168C8—41no—
169C8—41no—
170C8—9561no—
171C8—9561no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—4781no—
176C22—4781no—
177C22—4781no—
178C22C22⋊C4×D23911yescharacteristic
179C4—21no—
180C4—9562no—
181C4—4781no—
182C4—4781no—
183C4—4781no—
184C4#2143997911yescharacteristic
185C4#2143998111yescharacteristic
186C4#2143998411yescharacteristic
187C4#2143998711yescharacteristic
188C2—82no—
189C2—9561no—
190C2#2950475311yescharacteristic
191C2#2950476511yescharacteristic
192C2#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#1553
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. #29504824C2semidirect
4. #29504519C2semidirect
5. #29504517C2semidirect
6. #29504516C2semidirect
7. #331×C239C2semidirect
96. C239#1553semidirect
104. #331D239semidirect

Maximal subgroups

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

subgroupindex
#295053202
#295048282
#295048242
#295045192
#295045172
#295045162
#331×C2392
#1553239