Finite Group Databasebeta

← #44483708

Subgroups — #44483708

Order 30592.

188 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 55 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#29505500C211yesmaximal, characteristic
2#29505123C211yesmaximal, characteristic
3#29505068C211yesmaximal, characteristic
4#29505067C211yesmaximal, characteristic
5#29504517C211yesmaximal, characteristic
6#29504504C211yesmaximal, characteristic
7Q8⋊C8×C239C211yesmaximal, characteristic
8#21439960C2211yescharacteristic
9#21439960C2211yescharacteristic
10#21439958—21no—
11#21439952—21no—
12#21439950—22no—
13C4×Dic478—21no—
14C4×Dic478C2211yescharacteristic
15#21439925—21no—
16#21439894—21no—
17#21439893—21no—
18C4⋊(C239⋊C8)C2211yescharacteristic
19#21439885—21no—
20#21439885—22no—
21#21439884—21no—
22C4×Q8×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4×C8×C239C2211yescharacteristic
25C2×Dic478—21no—
26C2×Dic478—21no—
27C2×Dic478D411yescharacteristic
28C2×C239⋊C8—21no—
29C4⋊Dic239—21no—
30C4⋊Dic239—21no—
31C4⋊Dic239—21no—
32C4⋊Dic239D412yes—
33C4⋊Dic239D411yescharacteristic
34Dic239⋊C4—22no—
35Dic239⋊C4—22no—
36Dic239⋊C4—22no—
37Dic239⋊C4—21no—
38C4×Dic239—22no—
39C4×Dic239—21no—
40C2×Q8×C239D411yescharacteristic
41C2×C8×C239—21no—
42C2×C8×C239—21no—
43C4⋊C4×C239—21no—
44C4⋊C4×C239D411yescharacteristic
45C42×C239—21no—
46C42×C239C2311yescharacteristic
47Dic478—21no—
48Dic478—41no—
49Dic478—41no—
50Dic478—42no—
51Dic478Q1612yes—
52C2×Dic239—21no—
53C2×Dic239—21no—
54C2×Dic239—22no—
55C2×Dic239—41no—
56C239⋊C8—41no—
57Q8×C239—21no—
58Q8×C239—21no—
59C2×C4×C239—21no—
60C2×C4×C239—21no—
61C2×C4×C239C2×D411yescharacteristic
62C2×C4×C239C2×D411yescharacteristic
63C2×C4×C239C2×D411yescharacteristic
64C8×C239—41no—
65C8×C239—41no—
66C22×C239#12011yescharacteristic
67C4×C239—21no—
68C4×C239—41no—
69C4×C239—41no—
70C4×C239C2×Q1611yescharacteristic
71C4×C239#13511yescharacteristic
72C4×C239#13711yescharacteristic
73C4×C239#13711yescharacteristic
74Dic239—22no—
75Dic239—42no—
76Dic239—41no—
77Dic239—81no—
78C2×C239#45111yescharacteristic
79C2×C239#45211yescharacteristic
80C2×C239#45411yescharacteristic
81C239#163611yescharacteristic, complemented, Sylow
82#1636—2391nomaximal, Sylow
83#557—2391no—
84#487—2391no—
85#477—2391no—
86#477—2391no—
87#332—2391no—
88Q8⋊C8—2391no—
89Q8⋊C8D23911yescharacteristic
90C4⋊Q8—4781no—
91C4⋊Q8—2391no—
92C4⋊Q8—2391no—
93#125—4781no—
94#125—4782no—
95C4×Q8—4781no—
96C4×Q8—4781no—
97C4×Q8—2391no—
98C4×Q8C2×D23911yescharacteristic
99#107—4781no—
100#107—4781no—
101C4⋊C8—2391no—
102C4⋊C8C2×D23911yescharacteristic
103#103—4781no—
104#103—4781no—
105#103—4782no—
106C4×C8C2×D23911yescharacteristic
107C2×Q8—4781no—
108C2×Q8—4781no—
109C2×Q8—2391no—
110C2×Q8D95611yescharacteristic
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—4781no—
114C4⋊C4—21no—
115C4⋊C4—4782no—
116C4⋊C4—4782no—
117C4⋊C4—4782no—
118C4⋊C4—4781no—
119C4⋊C4—4781no—
120C4⋊C4—4781no—
121C4⋊C4—4781no—
122C4⋊C4—2392no—
123C4⋊C4—2391no—
124C4⋊C4D95611yescharacteristic
125C42—21no—
126C42—4782no—
127C42—4781no—
128C42C22×D23911yescharacteristic
129Q8—21no—
130Q8—21no—
131Q8—9562no—
132Q8—9561no—
133Q8—9561no—
134Q8—4781no—
135Q8—2392no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—9561no—
139C2×C4—4781no—
140C2×C4—4782no—
141C2×C4—4781no—
142C2×C4D4×D23911yescharacteristic
143C2×C4D4×D23911yescharacteristic
144C2×C4C2×D95611yescharacteristic
145C8—41no—
146C8—41no—
147C8—9561no—
148C22#2143993011yescharacteristic
149C4—21no—
150C4—41no—
151C4—41no—
152C4—19121no—
153C4—9562no—
154C4—9561no—
155C4—4782no—
156C4Q16×D23911yescharacteristic
157C4#2143998211yescharacteristic
158C4#2143998911yescharacteristic
159C4#2143999311yescharacteristic
160C2#2950492911yescharacteristic
161C2#2950493611yescharacteristic
162C2#2950494611yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
FittingQ8⋊C8×C239C2
socle, prime radicalC22×C239#120
hypercenterQ8⋊C8D239
hypocenterC239#1636
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
81. C239#1636semidirect

Maximal subgroups

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

subgroupindex
#295055002
#295051232
#295050682
#295050672
#295045172
#295045042
Q8⋊C8×C2392
#1636239