Finite Group Databasebeta

← #44483042

Subgroups — #44483042

Order 30592.

284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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#29505322C211yesmaximal, characteristic
2#29504825C211yesmaximal, characteristic, complemented
3#29504505C214yesmaximal, complemented
4C4×C4⋊C4×C239C211yesmaximal, characteristic, complemented
5C2×#16838548—21no—
6#21439960C411yescharacteristic, complemented
7#21439957C411yescharacteristic, complemented
8#21439948—21no—
9#21439934—21no—
10#21439934C2212yes—
11C4×D956—21no—
12C4×D956C412yescomplemented
13C4⋊(C239⋊C8)—21no—
14C22⋊(C239⋊C8)C2212yes—
15C4×C239⋊C8—21no—
16C2×C4⋊C4×C239—21no—
17C2×C42×C239—21no—
18C2×C42×C239C2211yescharacteristic
19#95×C239C2212yes—
20#16838548—42no—
21#16838548—42no—
22C2×Dic478—21no—
23C2×D956—21no—
24C2×D956—21no—
25C2×D956C2×C412yes—
26C2×C22⋊D239—22no—
27C2×C4×D239—22no—
28C2×C239⋊C8—22no—
29C4⋊Dic239—21no—
30C4⋊Dic239C2×C412yes—
31(C2×D239)⋊C4—22no—
32(C2×D239)⋊C4—22no—
33C22×C4×C239—22no—
34C22×C4×C239D411yescharacteristic
35C22×C4×C239D411yescharacteristic
36C22×C4×C239C2311yescharacteristic
37C4⋊C4×C239—24no—
38C42×C239—42no—
39C42×C239C2×C411yescharacteristic
40C42×C239C2×C411yescharacteristic
41C42×C239D411yescharacteristic
42C42×C239D411yescharacteristic
43C22×D239—22no—
44Dic478—42no—
45D956—42no—
46D956—42no—
47D956—42no—
48C22⋊D239—42no—
49C22⋊D239—42no—
50C2×Dic239—22no—
51C4×D239—44no—
52C239⋊C8—42no—
53C23×C239C2×D411yescharacteristic
54C2×C4×C239—22no—
55C2×C4×C239—24no—
56C2×C4×C239—41no—
57C2×C4×C239—42no—
58C2×C4×C239—42no—
59C2×C4×C239C22⋊C411yescharacteristic
60C2×C4×C239C22⋊C411yescharacteristic
61C2×C4×C239C22⋊C411yescharacteristic
62C2×C4×C239C22⋊C411yescharacteristic
63C2×C4×C239D812yes—
64C2×C4×C239SD1612yes—
65C2×C4×C239C22×C411yescharacteristic
66C2×C4×C239C2×D411yescharacteristic
67C22×C239—21no—
68C22×C239—21no—
69C22×C239C2×C22⋊C411yescharacteristic
70C22×C239C2×D811yescharacteristic
71C22×C239C2×SD1611yescharacteristic
72C2×D239—42no—
73C2×D239—42no—
74C2×D239—42no—
75C4×C239—21no—
76C4×C239—21no—
77C4×C239—21no—
78C4×C239—44no—
79C4×C239#10212yes—
80C4×C239#10212yes—
81C4×C239#10412yes—
82Dic239—42no—
83C2×C239—21no—
84C2×C239—21no—
85C2×C239#41011yescharacteristic
86C2×C239C2×#10211yescharacteristic
87C2×C239C2×#10411yescharacteristic
88D239—82no—
89C239#150211yescharacteristic, complemented, Sylow
90#1502—2391nomaximal, Sylow
91#532—2391no—
92#431—2391no—
93C4×C4⋊C4D23911yescharacteristic, complemented
94#327—2394no—
95C2×#41—4781no—
96C4⋊Q8—2391no—
97#127—2391no—
98#124—4781no—
99#121—4781no—
100#121—2392no—
101C4×D4—4781no—
102C4×D4—2392no—
103C2×C4⋊C4—21no—
104C2×C42—21no—
105C2×C42C2×D23911yescharacteristic
106C4⋊C8—4781no—
107C22⋊C8—2392no—
108C4×C8—4781no—
109#95C2×D23912yes—
110#41—9562no—
111#41—9562no—
112C2×Q8—4781no—
113C2×D4—4782no—
114C2×D4—4781no—
115C2×D4—4781no—
116C2×D4—2392no—
117C22×C4—22no—
118C22×C4—4782no—
119C22×C4C22⋊D23911yescharacteristic
120C22×C4C22⋊D23911yescharacteristic
121C22×C4C22×D23911yescharacteristic
122C2×C8—4782no—
123C4⋊C4—24no—
124C4⋊C4—4781no—
125C4⋊C4—2392no—
126C22⋊C4—4782no—
127C22⋊C4—4782no—
128C42—42no—
129C42C4×D23911yescharacteristic
130C42C4×D23911yescharacteristic
131C42D95611yescharacteristic
132C42D95611yescharacteristic
133C23—4782no—
134C23C2×C22⋊D23911yescharacteristic
135Q8—9562no—
136D4—9562no—
137D4—9562no—
138D4—9562no—
139D4—9562no—
140D4—9562no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—41no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—9564no—
147C2×C4—4782no—
148C2×C4(C2×D239)⋊C411yescharacteristic
149C2×C4(C2×D239)⋊C411yescharacteristic
150C2×C4(C2×D239)⋊C411yescharacteristic
151C2×C4(C2×D239)⋊C411yescharacteristic
152C2×C4#1683853312yes—
153C2×C4#1683853512yes—
154C2×C4C2×C4×D23911yescharacteristic
155C2×C4C2×D95611yescharacteristic
156C8—9562no—
157C22—21no—
158C22—21no—
159C22—9562no—
160C22—9562no—
161C22—9562no—
162C22C2×(C2×D239)⋊C411yescharacteristic
163C22C2×#1683853311yescharacteristic
164C22C2×#1683853511yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—44no—
169C4—9562no—
170C4#2143988012yes—
171C4#2143988012yes—
172C4#2143988812yes—
173C2—21no—
174C2—21no—
175C2—19122no—
176C2#2950474511yescharacteristic
177C2C2×#2143988011yescharacteristic
178C2C2×#2143988811yescharacteristic
subgroupG/H
centerC2×C4(C2×D239)⋊C4
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
FittingC4×C4⋊C4×C239C2
socleC22×C239C2×C22⋊C4
prime radical#29505322C2
cosocleC22×C4×C239C23
hypercenterC4×C4⋊C4D239
hypocenterC239#1502
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #29504825C2semidirect
3. #29504505C2semidirect
4. C4×C4⋊C4×C239C2semidirect
6. #21439960C4semidirect
7. #21439957C4semidirect
12. C4×D956C4semidirect
89. C239#1502semidirect
93. C4×C4⋊C4D239semidirect

Maximal subgroups

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

subgroupindex
#295053222
#295048252
#295045052
C4×C4⋊C4×C2392
#1502239