Finite Group Databasebeta

← #44506675

Subgroups — #44506675

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#29508432C211yesmaximal, characteristic
2#29508068C211yesmaximal, characteristic, complemented
3#29507998C211yesmaximal, characteristic, complemented
4#29507922C211yesmaximal, characteristic, complemented
5#29507465C211yesmaximal, characteristic, complemented
6#29507446C211yesmaximal, characteristic, complemented
7D4⋊C8×C241C211yesmaximal, characteristic, complemented
8C2×#16838758—21no—
9#21440642C2211yescharacteristic
10#21440642C2211yescharacteristic
11#21440628—22no—
12#21440616—21no—
13#21440613—21no—
14C4×D964C2211yescharacteristic
15#21440601—21no—
16#21440600—21no—
17#21440576—21no—
18C4⋊#14515349C2211yescharacteristic
19#21440567—22no—
20#21440565—21no—
21#21440564—21no—
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4×C8×C241C2211yescharacteristic
25C2×Dic482—21no—
26C2×Dic482D412yes—
27C2×D964D411yescharacteristic
28C2×C22⋊D241—22no—
29C2×C4×D241—21no—
30#16838758—42no—
31C2×#14515349—21no—
32C4⋊Dic241—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241D411yescharacteristic
37C22⋊Dic241—22no—
38#16838747—22no—
39#16838747—21no—
40C4×Dic241—22no—
41C2×D4×C241D411yescharacteristic
42C22×C4×C241—21no—
43C2×C8×C241—21no—
44C2×C8×C241—21no—
45C4⋊C4×C241D411yescharacteristic
46C22⋊C4×C241—21no—
47C42×C241C2311yescharacteristic
48C22×D241—21no—
49Dic482—42no—
50Dic482—41no—
51Dic482—41no—
52D964—21no—
53D964—21no—
54C22⋊D241—82no—
55C2×Dic241—21no—
56C2×Dic241—22no—
57C2×Dic241—41no—
58C4×D241—41no—
59C4×D241—41no—
60#14515349—41no—
61C23×C241—21no—
62D4×C241—21no—
63D4×C241—21no—
64C2×C4×C241—21no—
65C2×C4×C241—41no—
66C2×C4×C241—41no—
67C2×C4×C241C2×D411yescharacteristic
68C2×C4×C241C2×D411yescharacteristic
69C2×C4×C241C2×D411yescharacteristic
70C8×C241—41no—
71C8×C241—41no—
72C22×C241—41no—
73C22×C241—41no—
74C22×C241—41no—
75C22×C241#12011yescharacteristic
76C2×D241—41no—
77C2×D241—41no—
78C2×D241—41no—
79C4×C241—21no—
80C4×C241—41no—
81C4×C241#13511yescharacteristic
82C4×C241#13511yescharacteristic
83C4×C241AGL(1,ℤ/8)11yescharacteristic
84C4×C241#13711yescharacteristic
85Dic241—41no—
86Dic241—42no—
87Dic241—81no—
88C2×C241—81no—
89C2×C241#44911yescharacteristic
90C2×C241#45211yescharacteristic
91C2×C241#45511yescharacteristic
92D241—81no—
93C241#164611yescharacteristic, complemented, Sylow
94#1646—2411nomaximal, Sylow
95#555—2411no—
96#487—2411no—
97#474—2411no—
98#461—2411no—
99#333—2411no—
100D4⋊C8—2411no—
101D4⋊C8D24111yescharacteristic, complemented
102C2×SD16—4821no—
103C4⋊Q8—2411no—
104C4⋊Q8—2411no—
105#124—4822no—
106#121—4821no—
107#121—4821no—
108C4×D4—2411no—
109C4×D4C2×D24111yescharacteristic
110#117—4821no—
111#117—4821no—
112#107—4821no—
113C4⋊C8—2411no—
114C4⋊C8C2×D24111yescharacteristic
115#103—4822no—
116#103—4821no—
117#102—4821no—
118C4×C8C2×D24111yescharacteristic
119C2×Q8—4821no—
120C2×Q8—2412no—
121C2×D4—4822no—
122C2×D4—2411no—
123C2×D4D96411yescharacteristic
124C22×C4—21no—
125C22×C4—4821no—
126SD16—9642no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—4821no—
130C4⋊C4—4821no—
131C4⋊C4—4821no—
132C4⋊C4—4821no—
133C4⋊C4—4821no—
134C4⋊C4—2411no—
135C4⋊C4D96411yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—4822no—
138C22⋊C4—4822no—
139C22⋊C4—4821no—
140C42—4822no—
141C42C22×D24111yescharacteristic
142C23—21no—
143C23—4821no—
144Q8—9642no—
145Q8—9641no—
146Q8—9641no—
147D4—21no—
148D4—21no—
149D4—19282no—
150D4—4821no—
151D4—4821no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—9641no—
156C2×C4—9641no—
157C2×C4—9641no—
158C2×C4—4821no—
159C2×C4—4822no—
160C2×C4D4×D24111yescharacteristic
161C2×C4D4×D24111yescharacteristic
162C2×C4C2×D96411yescharacteristic
163C8—41no—
164C8—41no—
165C8—9641no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—9641no—
170C22—9641no—
171C22—9641no—
172C22#2144061211yescharacteristic
173C4—21no—
174C4—41no—
175C4—19281no—
176C4—9641no—
177C4—9642no—
178C4#2144066111yescharacteristic
179C4#2144066411yescharacteristic
180C4#2144067011yescharacteristic
181C4#2144067111yescharacteristic
182C2—81no—
183C2—19281no—
184C2#2950786411yescharacteristic
185C2#2950788011yescharacteristic
186C2#2950789611yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
FittingD4⋊C8×C241C2
socleC22×C241#120
prime radical#29508432C2
hypercenterD4⋊C8D241
hypocenterC241#1646
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #29508068C2semidirect
3. #29507998C2semidirect
4. #29507922C2semidirect
5. #29507465C2semidirect
6. #29507446C2semidirect
7. D4⋊C8×C241C2semidirect
93. C241#1646semidirect
101. D4⋊C8D241semidirect

Maximal subgroups

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

subgroupindex
#295084322
#295080682
#295079982
#295079222
#295074652
#295074462
D4⋊C8×C2412
#1646241