Finite Group Databasebeta

← #44485491

Subgroups — #44485491

Order 30592.

260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 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#29505329C211yesmaximal, characteristic
2C4×#16838532C211yesmaximal, characteristic
3#29504532C214yesmaximal
4C4×C4⋊C4×C239C211yesmaximal, characteristic
5C2×#16838532C2212yes—
6#21439960C411yescharacteristic, complemented
7#21439960C411yescharacteristic, complemented
8#21439952C412yescomplemented
9#21439939—21no—
10#21439939—21no—
11C4×Dic478—21no—
12C4×Dic478—21no—
13#21439919C2212yes—
14#21439871—21no—
15C4×C239⋊C8—21no—
16C2×C4⋊C4×C239—21no—
17C2×C42×C239C2212yes—
18C2×C42×C239C2211yescharacteristic
19#95×C239—21no—
20C2×Dic478—21no—
21C2×Dic478—21no—
22#16838532—22no—
23#16838532Q814yescomplemented
24C2×C239⋊C8—22no—
25C4⋊Dic239—21no—
26C4⋊Dic239—21no—
27C4⋊Dic239C2×C412yes—
28C4⋊Dic239C2×C412yes—
29Dic239⋊C4—22no—
30Dic239⋊C4—22no—
31C22⋊Dic239—22no—
32C4×Dic239—22no—
33C22×C4×C239—22no—
34C22×C4×C239D411yescharacteristic
35C22×C4×C239D411yescharacteristic
36C22×C4×C239C2311yescharacteristic
37C4⋊C4×C239—24no—
38C42×C239—24no—
39C42×C239C2×C411yescharacteristic
40C42×C239C2×C411yescharacteristic
41C42×C239D411yescharacteristic
42C42×C239D411yescharacteristic
43Dic478—42no—
44Dic478—42no—
45C2×Dic239—22no—
46C2×Dic239—22no—
47C239⋊C8—24no—
48C23×C239C2×D411yescharacteristic
49C2×C4×C239—22no—
50C2×C4×C239—24no—
51C2×C4×C239—41no—
52C2×C4×C239—42no—
53C2×C4×C239—42no—
54C2×C4×C239C22⋊C411yescharacteristic
55C2×C4×C239C22⋊C411yescharacteristic
56C2×C4×C239C22⋊C411yescharacteristic
57C2×C4×C239C22⋊C411yescharacteristic
58C2×C4×C239C22×C411yescharacteristic
59C2×C4×C239C2×D411yescharacteristic
60C2×C4×C239C2×Q812yes—
61C2×C4×C239#4112yes—
62C22×C239—21no—
63C22×C239—21no—
64C22×C239C2×C22⋊C411yescharacteristic
65C22×C239#12411yescharacteristic
66C22×C239C4⋊Q811yescharacteristic
67C4×C239—21no—
68C4×C239—21no—
69C4×C239—21no—
70C4×C239—44no—
71C4×C239#10412yes—
72C4×C239C4×Q812yes—
73C4×C239C22⋊Q812yes—
74Dic239—42no—
75Dic239—42no—
76C2×C239—21no—
77C2×C239—21no—
78C2×C239#39111yescharacteristic
79C2×C239C2×#10411yescharacteristic
80C2×C239#42111yescharacteristic
81C239#198611yescharacteristic, complemented, Sylow
82#1986—2391nomaximal, Sylow
83#533—2391no—
84C4×M16—2391no—
85C4×C4⋊C4D23911yescharacteristic
86#339—2394no—
87C2×M16—2392no—
88C4⋊Q8—2391no—
89C4⋊Q8—2391no—
90#125—2392no—
91C22⋊Q8—4781no—
92C22⋊Q8—4781no—
93C4×Q8—4781no—
94C4×Q8—4781no—
95#117—2392no—
96C2×C4⋊C4—21no—
97C2×C42C2×D23912yes—
98C2×C42C2×D23911yescharacteristic
99#97—4781no—
100C4×C8—4781no—
101#95—21no—
102C2×Q8—4781no—
103C2×Q8—4781no—
104C22×C4—22no—
105C22×C4C22⋊D23911yescharacteristic
106C22×C4C22⋊D23911yescharacteristic
107C22×C4C22×D23911yescharacteristic
108M16—4782no—
109M16—2394no—
110C2×C8—4782no—
111C4⋊C4—24no—
112C4⋊C4—4782no—
113C4⋊C4—4782no—
114C4⋊C4—4781no—
115C4⋊C4—4781no—
116C4⋊C4—2392no—
117C4⋊C4—2392no—
118C22⋊C4—4782no—
119C42—24no—
120C42—4782no—
121C42C4×D23911yescharacteristic
122C42C4×D23911yescharacteristic
123C42D95611yescharacteristic
124C42D95611yescharacteristic
125C23C2×C22⋊D23911yescharacteristic
126Q8—9562no—
127Q8—9562no—
128C2×C4—22no—
129C2×C4—24no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—4782no—
134C2×C4—4782no—
135C2×C4(C2×D239)⋊C411yescharacteristic
136C2×C4(C2×D239)⋊C411yescharacteristic
137C2×C4(C2×D239)⋊C411yescharacteristic
138C2×C4(C2×D239)⋊C411yescharacteristic
139C2×C4C2×C4×D23911yescharacteristic
140C2×C4C2×D95611yescharacteristic
141C2×C4Q8×D23912yes—
142C2×C4#1683854712yes—
143C8—4784no—
144C22—21no—
145C22—21no—
146C22C2×(C2×D239)⋊C411yescharacteristic
147C22#2143994711yescharacteristic
148C22#2143995811yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—44no—
153C4—9562no—
154C4—9562no—
155C4#2143988812yes—
156C4#2143992512yes—
157C4#2143994012yes—
158C2—21no—
159C2—21no—
160C2#2950467711yescharacteristic
161C2C2×#2143988811yescharacteristic
162C2#2950479011yescharacteristic
subgroupG/H
centerC2×C4C2×D956
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
FittingC4×C4⋊C4×C239C2
socleC22×C239C2×C22⋊C4
prime radicalC23×C239C2×D4
cosocleC22×C4×C239C23
hypercenterC4×C4⋊C4D239
hypocenterC239#1986
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #21439960C4semidirect
7. #21439960C4semidirect
8. #21439952C4semidirect
23. #16838532Q8semidirect
81. C239#1986semidirect

Maximal subgroups

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

subgroupindex
#295053292
C4×#168385322
#295045322
C4×C4⋊C4×C2392
#1986239