Finite Group Databasebeta

← #44509459

Subgroups — #44509459

Order 30848.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#29508470C211yesmaximal, characteristic, complemented
2#29507908C211yesmaximal, characteristic
3#29507906C211yesmaximal, characteristic
4#29507897C211yesmaximal, characteristic
5#29507511C211yesmaximal, characteristic, complemented
6#29507508C211yesmaximal, characteristic, complemented
7#352×C241C211yesmaximal, characteristic, complemented
8#21440687C2211yescharacteristic
9#21440675—21no—
10#21440641—21no—
11#21440635—21no—
12#21440635—21no—
13#21440632—21no—
14#21440629C2211yescharacteristic
15#21440626—21no—
16#21440625—21no—
17#21440623C2211yescharacteristic
18#21440621—21no—
19#21440619—21no—
20#21440568—21no—
21#21440557C2211yescharacteristic
22#21440556—21no—
23#21440556—21no—
24#123×C241C2211yescharacteristic
25#100×C241C2211yescharacteristic
26#99×C241C2211yescharacteristic
27#16838770—21no—
28#16838769—41no—
29C2×Dic482—21no—
30C2×Dic482D411yescharacteristic
31C2×C22⋊D241—21no—
32C2×C22⋊D241—21no—
33D4×D241—41no—
34C22×Dic241D411yescharacteristic
35Dic964—41no—
36#16838759—41no—
37C4⋊Dic241—21no—
38C4⋊Dic241—21no—
39C4⋊Dic241—41no—
40#16838749—21no—
41#16838749—21no—
42#16838749—21no—
43#16838749—21no—
44#16838749—21no—
45#16838749—41no—
46C22⋊Dic241—21no—
47C22⋊Dic241—21no—
48C22⋊Dic241—21no—
49C22⋊Dic241—21no—
50C22⋊Dic241D411yescharacteristic
51#16838747—41no—
52#16838747—41no—
53C4×Dic241—21no—
54C4×Dic241D411yescharacteristic
55C2×D4×C241C2311yescharacteristic
56C22×C4×C241D411yescharacteristic
57M16×C241—21no—
58C4⋊C4×C241—21no—
59C22⋊C4×C241—21no—
60C22⋊C4×C241—21no—
61C22⋊C4×C241D411yescharacteristic
62C22×D241—21no—
63C22×D241—21no—
64Dic482—21no—
65Dic482—41no—
66Dic482—81no—
67D964—21no—
68C22⋊D241—41no—
69C22⋊D241—41no—
70C22⋊D241—41no—
71C2×Dic241—21no—
72C2×Dic241—21no—
73C2×Dic241—21no—
74C2×Dic241—21no—
75C2×Dic241—21no—
76C2×Dic241—21no—
77C2×Dic241—41no—
78C2×Dic241—41no—
79C4×D241—41no—
80C23×C241C2×D411yescharacteristic
81C23×C241C2×D411yescharacteristic
82D4×C241—41no—
83C2×C4×C241—21no—
84C2×C4×C241—21no—
85C2×C4×C241—41no—
86C2×C4×C241—41no—
87C2×C4×C241C2×D411yescharacteristic
88C8×C241—41no—
89C22×C241—21no—
90C22×C241—21no—
91C22×C241—41no—
92C22×C241—41no—
93C22×C241#12011yescharacteristic
94C2×D241—41no—
95C2×D241—81no—
96C2×D241—81no—
97C4×C241—21no—
98C4×C241—41no—
99C4×C241—41no—
100C4×C241—81no—
101Dic241—41no—
102Dic241—41no—
103Dic241—41no—
104Dic241—41no—
105Dic241—41no—
106Dic241—81no—
107C2×C241—21no—
108C2×C241—41no—
109C2×C241—41no—
110C2×C241B(4,𝔽2)11yescharacteristic
111D241—81no—
112C241#220111yescharacteristic, complemented, Sylow
113#2201—2411nomaximal, Sylow
114#563—2411no—
115#458—2411no—
116#458—2411no—
117#455—2411no—
118#354—2411no—
119#352—2411no—
120#352D24111yescharacteristic, complemented
121H(5,𝔽2)—2411no—
122#137—4821no—
123C4⋊Q8—4821no—
124#126—4821no—
125#126—4821no—
126#125—4821no—
127#124—2411no—
128#123—4821no—
129#123—4821no—
130#123—2411no—
131#123C2×D24111yescharacteristic
132C22⋊Q8—4821no—
133C22⋊Q8—4821no—
134#104—4821no—
135#100C2×D24111yescharacteristic
136#99—4821no—
137#99—4821no—
138#99—2411no—
139#99C2×D24111yescharacteristic
140#41—9641no—
141#41—4821no—
142C2×Q8—4821no—
143C2×Q8—2411no—
144C2×D4—9641no—
145C2×D4—4821no—
146C2×D4—4821no—
147C2×D4C22×D24111yescharacteristic
148C22×C4—2411no—
149C22×C4D96411yescharacteristic
150Q16—9641no—
151SD16—9641no—
152M16—21no—
153C4⋊C4—21no—
154C4⋊C4—9641no—
155C4⋊C4—9641no—
156C4⋊C4—4821no—
157C4⋊C4—4821no—
158C4⋊C4—4821no—
159C4⋊C4—4821no—
160C4⋊C4—4821no—
161C4⋊C4—4821no—
162C4⋊C4—4821no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—9641no—
166C22⋊C4—9641no—
167C22⋊C4—4821no—
168C22⋊C4—4821no—
169C22⋊C4—4821no—
170C22⋊C4—4821no—
171C22⋊C4—2411no—
172C22⋊C4D96411yescharacteristic
173C42—4821no—
174C42—2411no—
175C23—4821no—
176C23—4821no—
177C23D4×D24111yescharacteristic
178C23C2×D96411yescharacteristic
179Q8—19281no—
180Q8—9641no—
181Q8—4821no—
182D4—41no—
183D4—9641no—
184D4—9641no—
185D4—9641no—
186D4—4821no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—9641no—
192C2×C4—9641no—
193C2×C4—9641no—
194C2×C4—4821no—
195C2×C4—4821no—
196C2×C4—4821no—
197C2×C4—4821no—
198C2×C4—4821no—
199C2×C4—4821no—
200C2×C4D4×D24111yescharacteristic
201C8—41no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—19281no—
207C22—19281no—
208C22—9641no—
209C22#2144061211yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—81no—
214C4—19281no—
215C4—9641no—
216C4—9641no—
217C4—9641no—
218C4—9641no—
219C4—9641no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—19281no—
224C2#2950790511yescharacteristic
subgroupG/H
centerC2#29507905
commutator, cosocleC2×D4×C241C23
FrattiniC2×D4C22×D241
Fitting#352×C241C2
socleC2×C241B(4,𝔽2)
prime radical#21440687C22
hypercenter#352D241
hypocenterC241#2201
LCSG ▷ C2×D4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
1. #29508470C2semidirect
5. #29507511C2semidirect
6. #29507508C2semidirect
7. #352×C241C2semidirect
112. C241#2201semidirect
120. #352D241semidirect

Maximal subgroups

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

subgroupindex
#295084702
#295079082
#295079062
#295078972
#295075112
#295075082
#352×C2412
#2201241