Finite Group Databasebeta

← #44483137

Subgroups — #44483137

Order 30592.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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#29505306C211yesmaximal, characteristic
2C2×#21439871C211yesmaximal, characteristic, complemented
3#29504513C212yesmaximal, complemented
4#29504511C212yesmaximal, complemented
5C4×M16×C239C211yesmaximal, characteristic, complemented
6C22×C239⋊C8—21no—
7#21439954—21no—
8#21439952C2211yescharacteristic
9#21439948C2211yescharacteristic
10#21439943—21no—
11#21439939C411yescharacteristic
12#21439934C411yescharacteristic
13C4×Dic478C411yescharacteristic
14C4×D956C411yescharacteristic
15C4×C22⋊D239—21no—
16#21439917—21no—
17#21439871—21no—
18#21439871C2212yes—
19C2×M16×C239—21no—
20C2×C42×C239C2211yescharacteristic
21#97×C239C2212yes—
22C4×C8×C239—21no—
23C2×Dic478C2×C411yescharacteristic
24C2×D956C2×C411yescharacteristic
25C2×C22⋊D239—21no—
26C2×C4×D239—21no—
27C2×C239⋊C8—24no—
28C2×C239⋊C8—22no—
29C4⋊Dic239C2×C411yescharacteristic
30C4⋊Dic239C2×C411yescharacteristic
31Dic239⋊C4—21no—
32Dic239⋊C4—21no—
33Dic239⋊C4—21no—
34Dic239⋊C4—21no—
35C22⋊Dic239—21no—
36(C2×D239)⋊C4—21no—
37(C2×D239)⋊C4—21no—
38(C2×D239)⋊C4—21no—
39(C2×D239)⋊C4—21no—
40C4×Dic239—21no—
41C22×C4×C239C2×C411yescharacteristic
42C22×C4×C239D411yescharacteristic
43C22×C4×C239D411yescharacteristic
44M16×C239—24no—
45C2×C8×C239—22no—
46C42×C239C2×C411yescharacteristic
47C42×C239D411yescharacteristic
48C42×C239D411yescharacteristic
49C42×C239C2311yescharacteristic
50C22×D239—21no—
51Dic478—41no—
52D956—41no—
53C22⋊D239—42no—
54C2×Dic239—21no—
55C2×Dic239—21no—
56C2×Dic239—21no—
57C4×D239—42no—
58C239⋊C8—24no—
59C23×C239C22⋊C411yescharacteristic
60C2×C4×C239—22no—
61C2×C4×C239—22no—
62C2×C4×C239—41no—
63C2×C4×C239C22⋊C411yescharacteristic
64C2×C4×C239C22⋊C411yescharacteristic
65C2×C4×C239C22⋊C411yescharacteristic
66C2×C4×C239C22×C411yescharacteristic
67C2×C4×C239C2×D411yescharacteristic
68C2×C4×C239C2×D411yescharacteristic
69C8×C239—24no—
70C22×C239—21no—
71C22×C239—21no—
72C22×C239#10412yes—
73C22×C239C2×C22⋊C411yescharacteristic
74C2×D239—41no—
75C2×D239—41no—
76C2×D239—41no—
77C4×C239—21no—
78C4×C239—21no—
79C4×C239—21no—
80C4×C239—21no—
81C4×C239—21no—
82C4×C239#10412yes—
83Dic239—41no—
84Dic239—41no—
85Dic239—41no—
86C2×C239—22no—
87C2×C239#41311yescharacteristic
88C2×C239C2×#10411yescharacteristic
89C2×C239C2×#10411yescharacteristic
90D239—81no—
91C239#152411yescharacteristic, complemented, Sylow
92#1524—2391nomaximal, Sylow
93#529—2391no—
94C4×M16D23911yescharacteristic, complemented
95C2×#97—2391no—
96#330—2392no—
97#329—2392no—
98C2×M16—21no—
99C22×C8—4781no—
100#126—4781no—
101#125—2391no—
102#124—2391no—
103#123—4781no—
104C22⋊Q8—2391no—
105#121—2391no—
106C4×Q8—2391no—
107C4×D4—4781no—
108C4×D4—2391no—
109#117—4781no—
110C2×C42C2×D23911yescharacteristic
111#97—4781no—
112#97—2392no—
113#97C2×D23912yes—
114C4×C8—21no—
115C2×Q8—2391no—
116C2×D4—4781no—
117C2×D4—2391no—
118C22×C4—4781no—
119C22×C4C4×D23911yescharacteristic
120C22×C4C22⋊D23911yescharacteristic
121C22×C4D95611yescharacteristic
122M16—24no—
123C2×C8—22no—
124C2×C8—4784no—
125C2×C8—4782no—
126C4⋊C4—4781no—
127C4⋊C4—4781no—
128C4⋊C4—4781no—
129C4⋊C4—4781no—
130C4⋊C4—2391no—
131C4⋊C4—2391no—
132C22⋊C4—4781no—
133C22⋊C4—4781no—
134C22⋊C4—4781no—
135C22⋊C4—4781no—
136C22⋊C4—4781no—
137C42—4781no—
138C42C4×D23911yescharacteristic
139C42C22⋊D23911yescharacteristic
140C42D95611yescharacteristic
141C42C22×D23911yescharacteristic
142C23—4781no—
143C23(C2×D239)⋊C411yescharacteristic
144Q8—9561no—
145D4—9561no—
146D4—9562no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—9562no—
151C2×C4—4781no—
152C2×C4—4781no—
153C2×C4—4781no—
154C2×C4(C2×D239)⋊C411yescharacteristic
155C2×C4(C2×D239)⋊C411yescharacteristic
156C2×C4(C2×D239)⋊C411yescharacteristic
157C2×C4C2×C4×D23911yescharacteristic
158C2×C4C2×C22⋊D23911yescharacteristic
159C2×C4C2×D95611yescharacteristic
160C8—24no—
161C8—4784no—
162C22—21no—
163C22—21no—
164C22—9561no—
165C22—9561no—
166C22—9561no—
167C22#2143988812yes—
168C22C2×(C2×D239)⋊C411yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—9561no—
175C4—9561no—
176C4—9561no—
177C4#2143988612yes—
178C2—22no—
179C2—19121no—
180C2#2950475411yescharacteristic
181C2C2×#2143988611yescharacteristic
182C2C2×#2143988811yescharacteristic
subgroupG/H
centerC2×C4(C2×D239)⋊C4
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
FittingC4×M16×C239C2
socleC22×C239C2×C22⋊C4
prime radical#21439934C4
cosocleC42×C239C23
hypercenterC4×M16D239
hypocenterC239#1524
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×#21439871C2semidirect
3. #29504513C2semidirect
4. #29504511C2semidirect
5. C4×M16×C239C2semidirect
91. C239#1524semidirect
94. C4×M16D239semidirect

Maximal subgroups

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

subgroupindex
#295053062
C2×#214398712
#295045132
#295045112
C4×M16×C2392
#1524239