Finite Group Databasebeta

← #44506708

Subgroups — #44506708

Order 30848.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#29508113C211yesmaximal, characteristic, complemented
2#29508002C211yesmaximal, characteristic, complemented
3#29507922C211yesmaximal, characteristic
4#29507463C211yesmaximal, characteristic, complemented
5Q8⋊#14515349C211yesmaximal, characteristic, complemented
6D4⋊#14515349C211yesmaximal, characteristic
7D4×Q8×C241C211yesmaximal, characteristic
8C2×#16838758—21no—
9#21440642C2211yescharacteristic
10#21440573—22no—
11#21440573—21no—
12C4⋊#14515349C2211yescharacteristic
13C4⋊#14515349C2211yescharacteristic
14#21440566—21no—
15#21440565—21no—
16C4×#14515349C2211yescharacteristic
17C22×Q8×C241—21no—
18C4⋊Q8×C241—21no—
19C4⋊Q8×C241C2211yescharacteristic
20C22⋊Q8×C241—21no—
21C22⋊Q8×C241—22no—
22C4×Q8×C241C2211yescharacteristic
23C4×D4×C241—21no—
24C4×D4×C241C2211yescharacteristic
25C2×Dic482—21no—
26#16838758—42no—
27C2×#14515349—21no—
28C2×#14515349—21no—
29C2×#14515349—21no—
30C4⋊Dic241—21no—
31C4⋊Dic241—21no—
32C2×Q8×C241—22no—
33C2×Q8×C241—21no—
34C2×Q8×C241—42no—
35C2×Q8×C241—42no—
36C2×Q8×C241D411yescharacteristic
37C2×D4×C241D411yescharacteristic
38C22×C4×C241—22no—
39C22×C4×C241—21no—
40C4⋊C4×C241—22no—
41C4⋊C4×C241—21no—
42C4⋊C4×C241—21no—
43C4⋊C4×C241D411yescharacteristic
44C4⋊C4×C241D411yescharacteristic
45C4⋊C4×C241D412yes—
46C22⋊C4×C241—22no—
47C22⋊C4×C241—21no—
48C42×C241—21no—
49C42×C241C2311yescharacteristic
50Dic482—41no—
51Dic482—41no—
52C2×Dic241—41no—
53#14515349—22no—
54#14515349—41no—
55#14515349—41no—
56C23×C241—21no—
57Q8×C241—21no—
58Q8×C241—44no—
59Q8×C241—41no—
60Q8×C241—41no—
61Q8×C241SD1612yescomplemented
62D4×C241—21no—
63D4×C241SD1612yes—
64C2×C4×C241—21no—
65C2×C4×C241—21no—
66C2×C4×C241—22no—
67C2×C4×C241—21no—
68C2×C4×C241—44no—
69C2×C4×C241—41no—
70C2×C4×C241—41no—
71C2×C4×C241C2×D411yescharacteristic
72C2×C4×C241C2×D411yescharacteristic
73C2×C4×C241C2×D411yescharacteristic
74C22×C241—22no—
75C22×C241—41no—
76C22×C241—41no—
77C22×C241#12011yescharacteristic
78C4×C241—22no—
79C4×C241—21no—
80C4×C241—42no—
81C4×C241—41no—
82C4×C241—41no—
83C4×C241C2×SD1611yescharacteristic
84C4×C241C2×SD1611yescharacteristic
85C4×C241AGL(1,ℤ/8)11yescharacteristic
86C4×C241#13711yescharacteristic
87Dic241—81no—
88C2×C241—42no—
89C2×C241#44811yescharacteristic
90C2×C241#45011yescharacteristic
91C2×C241#45611yescharacteristic
92C241#165111yescharacteristic, complemented, Sylow
93#1651—2411nomaximal, Sylow
94D4×Q8D24111yescharacteristic
95#498—2411no—
96#475—2411no—
97#461—2411no—
98#332—2411no—
99Q8⋊C8—2411no—
100D4⋊C8—2411no—
101C22×Q8—21no—
102C2×SD16—4821no—
103C4⋊Q8—21no—
104C4⋊Q8—2411no—
105C4⋊Q8C2×D24111yescharacteristic
106C22⋊Q8—21no—
107C22⋊Q8—22no—
108C4×Q8C2×D24111yescharacteristic
109C4×D4—21no—
110C4×D4C2×D24111yescharacteristic
111#106—4821no—
112#106—4822no—
113C4⋊C8—2411no—
114C4⋊C8—2411no—
115#103—4821no—
116#103—4821no—
117C4×C8—2411no—
118C2×Q8—22no—
119C2×Q8—21no—
120C2×Q8—42no—
121C2×Q8—42no—
122C2×Q8—4821no—
123C2×Q8C22⋊D24111yescharacteristic
124C2×D4C22⋊D24111yescharacteristic
125C22×C4—22no—
126C22×C4—21no—
127SD16—9642no—
128C2×C8—4821no—
129C2×C8—4821no—
130C2×C8—4821no—
131C4⋊C4—22no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—4821no—
135C4⋊C4—4821no—
136C4⋊C4C22⋊D24111yescharacteristic
137C4⋊C4C22⋊D24111yescharacteristic
138C4⋊C4C22⋊D24112yes—
139C22⋊C4—22no—
140C22⋊C4—21no—
141C42—21no—
142C42C22×D24111yescharacteristic
143C23—21no—
144Q8—21no—
145Q8—44no—
146Q8—41no—
147Q8—41no—
148Q8—9641no—
149Q8—9641no—
150Q8#1683875812yescomplemented
151D4—21no—
152D4#1683875712yes—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—44no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—9641no—
161C2×C4C2×C22⋊D24111yescharacteristic
162C2×C4C2×C22⋊D24111yescharacteristic
163C2×C4C2×C22⋊D24111yescharacteristic
164C8—9641no—
165C8—9641no—
166C8—4822no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2144061111yescharacteristic
171C4—22no—
172C4—21no—
173C4—42no—
174C4—41no—
175C4—41no—
176C4—19281no—
177C4C2×#1683875711yescharacteristic
178C4C2×#1683875811yescharacteristic
179C4#2144066811yescharacteristic
180C4#2144067311yescharacteristic
181C2—42no—
182C2#2950785611yescharacteristic
183C2#2950786811yescharacteristic
184C2#2950790011yescharacteristic
subgroupG/H
centerC22#21440611
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
FittingD4×Q8×C241C2
socleC22×C241#120
prime radicalC2×D4×C241D4
hypercenterD4×Q8D241
hypocenterC241#1651
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #29508113C2semidirect
2. #29508002C2semidirect
4. #29507463C2semidirect
5. Q8⋊#14515349C2semidirect
61. Q8×C241SD16semidirect
92. C241#1651semidirect
150. Q8#16838758semidirect

Maximal subgroups

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

subgroupindex
#295081132
#295080022
#295079222
#295074632
Q8⋊#145153492
D4⋊#145153492
D4×Q8×C2412
#1651241