Finite Group Databasebeta

← #44509435

Subgroups — #44509435

Order 30848.

258 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 45 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#29507906C211yesmaximal, characteristic, complemented
2#29507903C211yesmaximal, characteristic
3#29507894C211yesmaximal, characteristic, complemented
4#29507512C211yesmaximal, characteristic, complemented
5#29507507C211yesmaximal, characteristic, complemented
6#29507504C211yesmaximal, characteristic, complemented
7#551×C241C211yesmaximal, characteristic, complemented
8#21440687C2211yescharacteristic
9#21440673—21no—
10#21440625—21no—
11#21440611—21no—
12#21440570—21no—
13#21440559C2211yescharacteristic
14#21440557C2211yescharacteristic
15#21440557C2211yescharacteristic
16#21440556—21no—
17#21440556—21no—
18#126×C241—21no—
19#124×C241C2211yescharacteristic
20#123×C241—21no—
21#123×C241C2211yescharacteristic
22C22⋊Q8×C241—21no—
23#120×C241C2211yescharacteristic
24C4×D4×C241—21no—
25#117×C241—21no—
26C2×C22⋊C4×C241—21no—
27#16838770—21no—
28#16838769—41no—
29C2×C22⋊D241—21no—
30C2×C22⋊D241—21no—
31C2×C22⋊D241—41no—
32D4×D241—41no—
33#16838760—41no—
34#16838757—41no—
35#16838754—21no—
36#16838749—41no—
37C22⋊Dic241—21no—
38C22⋊Dic241—21no—
39C22⋊Dic241—41no—
40#16838747—41no—
41C24×C241D411yescharacteristic
42C2×Q8×C241D411yescharacteristic, complemented
43C2×D4×C241—21no—
44C2×D4×C241C2311yescharacteristic
45C22×C4×C241—21no—
46C22×C4×C241—21no—
47C22×C4×C241D411yescharacteristic, complemented
48C4⋊C4×C241—21no—
49C4⋊C4×C241—21no—
50C4⋊C4×C241—21no—
51C4⋊C4×C241—21no—
52C22⋊C4×C241—21no—
53C22⋊C4×C241—21no—
54C22⋊C4×C241—21no—
55C22⋊C4×C241—21no—
56C22⋊C4×C241—21no—
57C22⋊C4×C241—21no—
58C22⋊C4×C241D411yescharacteristic
59C22⋊C4×C241D411yescharacteristic, complemented
60C42×C241—21no—
61C42×C241D411yescharacteristic, complemented
62C22×D241—21no—
63C22×D241—21no—
64Dic482—21no—
65D964—21no—
66C22⋊D241—41no—
67C22⋊D241—41no—
68C22⋊D241—41no—
69C22⋊D241—82no—
70C2×Dic241—21no—
71C2×Dic241—21no—
72C2×Dic241—41no—
73C2×Dic241—41no—
74C4×D241—41no—
75#14515349—41no—
76C23×C241—21no—
77C23×C241—42no—
78C23×C241—41no—
79C23×C241C2×D411yescharacteristic
80C23×C241C2×D411yescharacteristic
81Q8×C241—41no—
82D4×C241—41no—
83D4×C241—42no—
84C2×C4×C241—21no—
85C2×C4×C241—21no—
86C2×C4×C241—21no—
87C2×C4×C241—21no—
88C2×C4×C241—21no—
89C2×C4×C241—42no—
90C2×C4×C241—41no—
91C2×C4×C241—81no—
92C2×C4×C241C2×D411yescharacteristic
93C22×C241—22no—
94C22×C241—21no—
95C22×C241—21no—
96C22×C241—41no—
97C22×C241—41no—
98C22×C241—41no—
99C22×C241—42no—
100C22×C241—41no—
101C22×C241—81no—
102C22×C241#12011yescharacteristic
103C2×D241—41no—
104C2×D241—81no—
105C2×D241—81no—
106C4×C241—21no—
107C4×C241—41no—
108C4×C241—41no—
109C4×C241—41no—
110C4×C241—41no—
111C4×C241—41no—
112Dic241—41no—
113Dic241—81no—
114Dic241—81no—
115C2×C241—21no—
116C2×C241—41no—
117C2×C241—41no—
118C2×C241—42no—
119C2×C241B(4,𝔽2)11yescharacteristic
120D241—81no—
121C241#219711yescharacteristic, complemented, Sylow
122#2197—2411nomaximal, Sylow
123#551D24111yescharacteristic, complemented
124#458—2411no—
125B(4,𝔽2)—2411no—
126#455—2411no—
127#354—2411no—
128#352—2411no—
129AΣL(1,𝔽16)—2411no—
130H(5,𝔽2)—2411no—
131#137—4821no—
132#126—21no—
133#124C2×D24111yescharacteristic
134#123—21no—
135#123—4821no—
136#123C2×D24111yescharacteristic
137C22⋊Q8—21no—
138#120—4821no—
139#120C2×D24111yescharacteristic
140C4×D4—21no—
141#117—21no—
142C2×C22⋊C4—21no—
143#104—4821no—
144#100—2411no—
145#99—4821no—
146#99—4821no—
147#99—2411no—
148#99—2411no—
149C24C22⋊D24111yescharacteristic
150#41—9641no—
151#41—4821no—
152C2×Q8C22⋊D24111yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—9641no—
155C2×D4—9641no—
156C2×D4—4821no—
157C2×D4—4821no—
158C2×D4C22×D24111yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4C22⋊D24111yescharacteristic, complemented
162Q16—9641no—
163SD16—9641no—
164M16—4821no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—9641no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—9641no—
177C22⋊C4—9641no—
178C22⋊C4—4821no—
179C22⋊C4—4821no—
180C22⋊C4C22⋊D24111yescharacteristic
181C22⋊C4C22⋊D24111yescharacteristic, complemented
182C42—21no—
183C42C22⋊D24111yescharacteristic, complemented
184C23—21no—
185C23—41no—
186C23—42no—
187C23—4821no—
188C23—4821no—
189C23C2×C22⋊D24111yescharacteristic
190C23C2×C22⋊D24111yescharacteristic
191Q8—41no—
192Q8—4821no—
193D4—41no—
194D4—42no—
195D4—19282no—
196D4—9641no—
197D4—9641no—
198D4—9641no—
199D4—4821no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—9641no—
209C2×C4—9641no—
210C2×C4—9641no—
211C2×C4—4821no—
212C2×C4—4821no—
213C2×C4C2×C22⋊D24111yescharacteristic
214C8—9641no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22—19281no—
225C22—19281no—
226C22—9641no—
227C22#2144061111yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—19281no—
235C4—19281no—
236C4—9641no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—42no—
241C2—19281no—
242C2#2950790411yescharacteristic
subgroupG/H
centerC2#29507904
commutator, cosocleC2×D4×C241C23
FrattiniC2×D4C22×D241
Fitting#551×C241C2
socleC2×C241B(4,𝔽2)
prime radical#29507903C2
hypercenter#551D241
hypocenterC241#2197
LCSG ▷ C2×D4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #551

Complements

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

NH ≅ G/Ntype
1. #29507906C2semidirect
3. #29507894C2semidirect
4. #29507512C2semidirect
5. #29507507C2semidirect
6. #29507504C2semidirect
7. #551×C241C2semidirect
42. C2×Q8×C241D4semidirect
47. C22×C4×C241D4semidirect
59. C22⋊C4×C241D4semidirect
61. C42×C241D4semidirect
121. C241#2197semidirect
123. #551D241semidirect
152. C2×Q8C22⋊D241semidirect
161. C22×C4C22⋊D241semidirect
181. C22⋊C4C22⋊D241semidirect
183. C42C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295079062
#295079032
#295078942
#295075122
#295075072
#295075042
#551×C2412
#2197241