Finite Group Databasebeta

← #44506670

Subgroups — #44506670

Order 30848.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#29508433C211yesmaximal, characteristic
2#29507994C211yesmaximal, characteristic, complemented
3#29507919C211yesmaximal, characteristic, complemented
4#29507466C211yesmaximal, characteristic, complemented
5#29507446C211yesmaximal, characteristic, complemented
6#29507446C211yesmaximal, characteristic, complemented
7#487×C241C211yesmaximal, characteristic, complemented
8C2×#16838757—21no—
9#21440631—22no—
10#21440617—21no—
11#21440617—21no—
12C4×D964C2211yescharacteristic
13C4×D964C2211yescharacteristic
14#21440600—21no—
15#21440600—21no—
16#21440575—21no—
17C4⋊#14515349C2211yescharacteristic
18C4⋊#14515349C2211yescharacteristic
19#21440566—21no—
20#21440562—21no—
21C4⋊Q8×C241C2211yescharacteristic
22C4⋊Q8×C241C2211yescharacteristic
23#103×C241—22no—
24C4×C8×C241C2211yescharacteristic
25C2×D964—22no—
26C2×D964D411yescharacteristic
27C2×D964D411yescharacteristic
28C2×C4×D241—21no—
29C2×C4×D241—21no—
30#16838757—42no—
31C2×#14515349—21no—
32C2×#14515349—21no—
33C4⋊Dic241D411yescharacteristic
34C4⋊Dic241D411yescharacteristic
35#16838747—22no—
36#16838747—22no—
37#16838747—21no—
38#16838747—21no—
39C4×Dic241—22no—
40C2×Q8×C241—21no—
41C2×Q8×C241D412yes—
42C2×C8×C241—21no—
43C4⋊C4×C241—21no—
44C4⋊C4×C241—21no—
45C4⋊C4×C241—21no—
46C4⋊C4×C241—21no—
47C42×C241C2311yescharacteristic
48C22×D241—21no—
49C22×D241—21no—
50D964—21no—
51D964—21no—
52D964—21no—
53D964—21no—
54D964—82no—
55C2×Dic241—21no—
56C2×Dic241—21no—
57C4×D241—41no—
58C4×D241—41no—
59C4×D241—41no—
60C4×D241—41no—
61#14515349—41no—
62#14515349—41no—
63Q8×C241—42no—
64Q8×C241—41no—
65Q8×C241—41no—
66C2×C4×C241—22no—
67C2×C4×C241—41no—
68C2×C4×C241C2×D411yescharacteristic
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C8×C241—41no—
72C22×C241#12011yescharacteristic
73C2×D241—41no—
74C2×D241—41no—
75C2×D241—41no—
76C2×D241—41no—
77C2×D241—41no—
78C2×D241—41no—
79C4×C241—21no—
80C4×C241—42no—
81C4×C241—81no—
82C4×C241#13511yescharacteristic
83C4×C241#13511yescharacteristic
84C4×C241AGL(1,ℤ/8)11yescharacteristic
85C4×C241#13711yescharacteristic
86Dic241—41no—
87Dic241—41no—
88C2×C241#44911yescharacteristic
89C2×C241#45211yescharacteristic
90C2×C241#45511yescharacteristic
91D241—81no—
92D241—81no—
93C241#164611yescharacteristic, complemented, Sylow
94#1646—2411nomaximal, Sylow
95#555—2411no—
96#487D24111yescharacteristic, complemented
97#474—2411no—
98#461—2411no—
99#333—2411no—
100D4⋊C8—2411no—
101D4⋊C8—2411no—
102C2×SD16—4821no—
103C4⋊Q8C2×D24111yescharacteristic
104C4⋊Q8C2×D24111yescharacteristic
105#124—4822no—
106#121—4821no—
107#121—4821no—
108C4×D4—2411no—
109C4×D4—2411no—
110#117—4821no—
111#117—4821no—
112#107—4821no—
113C4⋊C8—2411no—
114C4⋊C8—2411no—
115#103—22no—
116#103—4821no—
117#102—4821no—
118C4×C8C2×D24111yescharacteristic
119C2×Q8—21no—
120C2×Q8C22⋊D24112yes—
121C2×D4—4822no—
122C2×D4—2411no—
123C2×D4—2411no—
124C22×C4—4821no—
125C22×C4—4821no—
126SD16—9642no—
127C2×C8—21no—
128C2×C8—4821no—
129C2×C8—4821no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2411no—
135C4⋊C4—2411no—
136C22⋊C4—4822no—
137C22⋊C4—4822no—
138C22⋊C4—4821no—
139C22⋊C4—4821no—
140C42—4822no—
141C42C22×D24111yescharacteristic
142C23—4821no—
143C23—4821no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—19282no—
148D4—4821no—
149D4—4821no—
150D4—4821no—
151D4—4821no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—9641no—
155C2×C4—9641no—
156C2×C4—9641no—
157C2×C4—9641no—
158C2×C4—4821no—
159C2×C4—4821no—
160C2×C4D4×D24111yescharacteristic
161C2×C4D4×D24111yescharacteristic
162C2×C4C2×C22⋊D24111yescharacteristic
163C8—41no—
164C8—9641no—
165C8—9641no—
166C22—9641no—
167C22—9641no—
168C22—9641no—
169C22—9641no—
170C22—9641no—
171C22—9641no—
172C22#2144061011yescharacteristic
173C4—21no—
174C4—42no—
175C4—81no—
176C4—9641no—
177C4—9641no—
178C4#2144066311yescharacteristic
179C4#2144066511yescharacteristic
180C4#2144066911yescharacteristic
181C4#2144067411yescharacteristic
182C2—19281no—
183C2—19281no—
184C2#2950786111yescharacteristic
185C2#2950787811yescharacteristic
186C2#2950789411yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#487×C241C2
socleC22×C241#120
prime radical#29508433C2
hypercenter#487D241
hypocenterC241#1646
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #29507994C2semidirect
3. #29507919C2semidirect
4. #29507466C2semidirect
5. #29507446C2semidirect
6. #29507446C2semidirect
7. #487×C241C2semidirect
93. C241#1646semidirect
96. #487D241semidirect

Maximal subgroups

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

subgroupindex
#295084332
#295079942
#295079192
#295074662
#295074462
#487×C2412
#1646241