Finite Group Databasebeta

← #44506579

Subgroups — #44506579

Order 30848.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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#29508096C211yesmaximal, characteristic, complemented
2#29508012C211yesmaximal, characteristic, complemented
3#29508007C211yesmaximal, characteristic
4#29507466C211yesmaximal, characteristic, complemented
5Q8⋊#14515349C211yesmaximal, characteristic, complemented
6D4⋊#14515349C211yesmaximal, characteristic
7#554×C241C211yesmaximal, characteristic
8C2×#16838760—22no—
9#21440642C2211yescharacteristic
10#21440575—21no—
11#21440573—21no—
12C4⋊#14515349C2211yescharacteristic
13C4⋊#14515349C2211yescharacteristic
14#21440566—21no—
15#21440563—21no—
16C4×#14515349C2211yescharacteristic
17C4⋊Q8×C241C2211yescharacteristic
18#125×C241—21no—
19C22⋊Q8×C241—21no—
20C22⋊Q8×C241—22no—
21C4×Q8×C241C2211yescharacteristic
22C4×D4×C241—21no—
23C4×D4×C241C2211yescharacteristic
24C2×C4⋊C4×C241—21no—
25C2×Dic482—21no—
26#16838760—44no—
27C2×#14515349—21no—
28C2×#14515349—21no—
29C2×#14515349—21no—
30C4⋊Dic241—21no—
31C4⋊Dic241—21no—
32C2×Q8×C241D411yescharacteristic
33C2×Q8×C241D412yes—
34C2×D4×C241D411yescharacteristic
35C22×C4×C241—22no—
36C22×C4×C241—21no—
37C4⋊C4×C241—22no—
38C4⋊C4×C241—22no—
39C4⋊C4×C241—21no—
40C4⋊C4×C241—21no—
41C4⋊C4×C241—21no—
42C4⋊C4×C241D411yescharacteristic
43C4⋊C4×C241D411yescharacteristic
44C22⋊C4×C241—22no—
45C22⋊C4×C241—21no—
46C42×C241—21no—
47C42×C241C2311yescharacteristic
48Dic482—42no—
49C2×Dic241—41no—
50#14515349—22no—
51#14515349—41no—
52#14515349—41no—
53C23×C241—21no—
54Q8×C241—21no—
55Q8×C241—21no—
56Q8×C241—42no—
57D4×C241—21no—
58D4×C241Q1612yescomplemented
59C2×C4×C241—21no—
60C2×C4×C241—21no—
61C2×C4×C241—21no—
62C2×C4×C241—22no—
63C2×C4×C241—41no—
64C2×C4×C241—41no—
65C2×C4×C241—82no—
66C2×C4×C241C2×D411yescharacteristic
67C2×C4×C241C2×D411yescharacteristic
68C2×C4×C241C2×D411yescharacteristic
69C22×C241—22no—
70C22×C241—41no—
71C22×C241—41no—
72C22×C241#12011yescharacteristic
73C4×C241—21no—
74C4×C241—41no—
75C4×C241—41no—
76C4×C241—41no—
77C4×C241—42no—
78C4×C241C2×Q1611yescharacteristic
79C4×C241#13511yescharacteristic
80C4×C241#13711yescharacteristic
81C4×C241#13711yescharacteristic
82Dic241—81no—
83C2×C241—42no—
84C2×C241#45111yescharacteristic
85C2×C241#45211yescharacteristic
86C2×C241#45311yescharacteristic
87C241#163211yescharacteristic, complemented, Sylow
88#1632—2411nomaximal, Sylow
89#554D24111yescharacteristic
90#494—2411no—
91#477—2411no—
92#476—2411no—
93#333—2411no—
94Q8⋊C8—2411no—
95D4⋊C8—2411no—
96C2×Q16—4822no—
97C4⋊Q8—2411no—
98C4⋊Q8C2×D24111yescharacteristic
99#125—21no—
100C22⋊Q8—21no—
101C22⋊Q8—22no—
102C4×Q8C2×D24111yescharacteristic
103C4×D4—21no—
104C4×D4C2×D24111yescharacteristic
105C2×C4⋊C4—21no—
106#107—4821no—
107#106—4821no—
108C4⋊C8—2411no—
109C4⋊C8—2411no—
110#103—4821no—
111#102—4821no—
112C4×C8—2411no—
113C2×Q8—4821no—
114C2×Q8C22⋊D24111yescharacteristic
115C2×Q8C22⋊D24112yes—
116C2×D4C22⋊D24111yescharacteristic
117C22×C4—22no—
118C22×C4—21no—
119Q16—9644no—
120C2×C8—4821no—
121C2×C8—4821no—
122C2×C8—4821no—
123C4⋊C4—22no—
124C4⋊C4—22no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—4821no—
129C4⋊C4—4821no—
130C4⋊C4C22⋊D24111yescharacteristic
131C4⋊C4C22⋊D24111yescharacteristic
132C22⋊C4—22no—
133C22⋊C4—21no—
134C42—21no—
135C42C22×D24111yescharacteristic
136C23—21no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—9642no—
141D4—21no—
142D4#1683876012yescomplemented
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—82no—
150C2×C4—9641no—
151C2×C4C2×C22⋊D24111yescharacteristic
152C2×C4C2×C22⋊D24111yescharacteristic
153C2×C4C2×C22⋊D24111yescharacteristic
154C8—9641no—
155C8—9641no—
156C8—4822no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#2144061111yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—41no—
165C4—42no—
166C4—19281no—
167C4C2×#1683876011yescharacteristic
168C4#2144066211yescharacteristic
169C4#2144067211yescharacteristic
170C4#2144067311yescharacteristic
171C2—42no—
172C2#2950787311yescharacteristic
173C2#2950787911yescharacteristic
174C2#2950788511yescharacteristic
subgroupG/H
centerC22#21440611
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#554×C241C2
socleC22×C241#120
prime radicalC2×D4×C241D4
hypercenter#554D241
hypocenterC241#1632
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #29508096C2semidirect
2. #29508012C2semidirect
4. #29507466C2semidirect
5. Q8⋊#14515349C2semidirect
58. D4×C241Q16semidirect
87. C241#1632semidirect
142. D4#16838760semidirect

Maximal subgroups

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

subgroupindex
#295080962
#295080122
#295080072
#295074662
Q8⋊#145153492
D4⋊#145153492
#554×C2412
#1632241