Finite Group Databasebeta

← #44506707

Subgroups — #44506707

Order 30848.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×D964C211yesmaximal, characteristic
2#29508113C211yesmaximal, characteristic, complemented
3#29507919C211yesmaximal, characteristic
4#29507464C211yesmaximal, characteristic, complemented
5Q8⋊#14515349C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic
7#475×C241C211yesmaximal, characteristic, complemented
8C2×Q8×D241—21no—
9C2×#16838757—21no—
10#21440642—21no—
11#21440642C2211yescharacteristic
12#21440622—22no—
13#21440622—21no—
14C4×D964—21no—
15C4×D964C2211yescharacteristic
16#21440573—22no—
17C4⋊#14515349C2211yescharacteristic
18#21440566—21no—
19C4×#14515349C2211yescharacteristic
20C4⋊Q8×C241C2211yescharacteristic
21C4×Q8×C241C2211yescharacteristic
22#106×C241—21no—
23C4⋊C8×C241C2211yescharacteristic
24#103×C241—21no—
25C2×Dic482—22no—
26C2×Dic482—21no—
27Q8×D241—42no—
28Q8×D241—42no—
29C2×D964D411yescharacteristic
30C2×C4×D241—22no—
31C2×C4×D241—21no—
32#16838757—42no—
33C2×#14515349—21no—
34C2×#14515349—21no—
35C4⋊Dic241—22no—
36C4⋊Dic241—21no—
37C4⋊Dic241D411yescharacteristic
38C4⋊Dic241D412yes—
39#16838747—22no—
40#16838747—21no—
41C2×Q8×C241—21no—
42C2×Q8×C241D411yescharacteristic
43C2×C8×C241—21no—
44C4⋊C4×C241—21no—
45C4⋊C4×C241—21no—
46C4⋊C4×C241—21no—
47C4⋊C4×C241D411yescharacteristic
48C42×C241—21no—
49C42×C241C2311yescharacteristic
50C22×D241—21no—
51Dic482—44no—
52Dic482—41no—
53Dic482—41no—
54D964—21no—
55D964SD1612yes—
56C2×Dic241—22no—
57C2×Dic241—21no—
58C4×D241—44no—
59C4×D241—41no—
60C4×D241—41no—
61#14515349—22no—
62#14515349—41no—
63Q8×C241—21no—
64Q8×C241—41no—
65Q8×C241—41no—
66Q8×C241SD1612yescomplemented
67C2×C4×C241—21no—
68C2×C4×C241—21no—
69C2×C4×C241—41no—
70C2×C4×C241C2×D411yescharacteristic
71C2×C4×C241C2×D411yescharacteristic
72C2×C4×C241C2×D411yescharacteristic
73C8×C241—41no—
74C22×C241#12011yescharacteristic
75C2×D241—22no—
76C2×D241—41no—
77C2×D241—41no—
78C4×C241—22no—
79C4×C241—21no—
80C4×C241—41no—
81C4×C241—81no—
82C4×C241C2×SD1611yescharacteristic
83C4×C241C2×SD1611yescharacteristic
84C4×C241AGL(1,ℤ/8)11yescharacteristic
85C4×C241#13711yescharacteristic
86Dic241—42no—
87Dic241—41no—
88C2×C241#44811yescharacteristic
89C2×C241#45011yescharacteristic
90C2×C241#45611yescharacteristic
91D241—42no—
92C241#165111yescharacteristic, complemented, Sylow
93#1651—2411nomaximal, Sylow
94D4×Q8—2411no—
95#498—2411no—
96#475D24111yescharacteristic, complemented
97#461—2411no—
98#332—2411no—
99Q8⋊C8—2411no—
100D4⋊C8—2411no—
101C22×Q8—4821no—
102C2×SD16—4821no—
103C4⋊Q8—4821no—
104C4⋊Q8—2411no—
105C4⋊Q8C2×D24111yescharacteristic
106C22⋊Q8—4822no—
107C22⋊Q8—4821no—
108C4×Q8C2×D24111yescharacteristic
109C4×D4—4821no—
110C4×D4—2411no—
111#106—21no—
112#106—4822no—
113C4⋊C8—2411no—
114C4⋊C8C2×D24111yescharacteristic
115#103—21no—
116#103—4821no—
117C4×C8—2411no—
118C2×Q8—21no—
119C2×Q8—9642no—
120C2×Q8—9642no—
121C2×Q8—4822no—
122C2×Q8—4821no—
123C2×Q8C22⋊D24111yescharacteristic
124C2×D4—2411no—
125C22×C4—4822no—
126C22×C4—4821no—
127SD16—9642no—
128C2×C8—21no—
129C2×C8—4821no—
130C2×C8—4821no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—4822no—
135C4⋊C4—4821no—
136C4⋊C4—2411no—
137C4⋊C4—2412no—
138C4⋊C4C22⋊D24111yescharacteristic
139C22⋊C4—4822no—
140C22⋊C4—4821no—
141C42—21no—
142C42C22×D24111yescharacteristic
143C23—4821no—
144Q8—21no—
145Q8—41no—
146Q8—41no—
147Q8—9644no—
148Q8—9641no—
149Q8—9641no—
150Q8#1683875712yescomplemented
151D4—4821no—
152D4—2412no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—9644no—
157C2×C4—9641no—
158C2×C4—9641no—
159C2×C4—4822no—
160C2×C4—4821no—
161C2×C4D4×D24111yescharacteristic
162C2×C4D4×D24111yescharacteristic
163C2×C4C2×C22⋊D24111yescharacteristic
164C8—41no—
165C8—9641no—
166C8—4822no—
167C22—9641no—
168C22—9641no—
169C22—4822no—
170C22#2144061011yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—81no—
175C4—9642no—
176C4—9641no—
177C4SD16×D24111yescharacteristic
178C4C2×#1683875711yescharacteristic
179C4#2144066711yescharacteristic
180C4#2144067111yescharacteristic
181C2—9642no—
182C2#2950785411yescharacteristic
183C2#2950786711yescharacteristic
184C2#2950789811yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#475×C241C2
socleC22×C241#120
prime radicalC2×D964D4
hypercenter#475D241
hypocenterC241#1651
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #29508113C2semidirect
4. #29507464C2semidirect
5. Q8⋊#14515349C2semidirect
7. #475×C241C2semidirect
66. Q8×C241SD16semidirect
92. C241#1651semidirect
96. #475D241semidirect
150. Q8#16838757semidirect

Maximal subgroups

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

subgroupindex
Q8×D9642
#295081132
#295079192
#295074642
Q8⋊#145153492
#295074442
#475×C2412
#1651241