Finite Group Databasebeta

← #44507890

Subgroups — #44507890

Order 30848.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#29508224C211yesmaximal, characteristic
2C2×#21440599C211yesmaximal, characteristic, complemented
3C2×#21440569C211yesmaximal, characteristic, complemented
4#29507680C211yesmaximal, characteristic, complemented
5#29507478C211yesmaximal, characteristic, complemented
6#29507477C211yesmaximal, characteristic, complemented
7C2×#104×C241C211yesmaximal, characteristic, complemented
8C22×C4×D241C2211yescharacteristic
9C2×#16838754C2211yescharacteristic
10#21440623—21no—
11#21440618C412yescomplemented
12#21440613C412yescomplemented
13#21440610—21no—
14C4×C22⋊D241—22no—
15#21440601C2211yescharacteristic
16#21440599—22no—
17#21440599—22no—
18C2×#16838749—21no—
19C2×#16838747—21no—
20C2×C4×Dic241C2211yescharacteristic
21#21440569—22no—
22#21440554—22no—
23C2×#41×C241C2211yescharacteristic
24C2×M16×C241C2211yescharacteristic
25C2×C42×C241C2211yescharacteristic
26#104×C241—22no—
27C23×D241D411yescharacteristic
28C2×C22⋊D241—22no—
29C22×Dic241—21no—
30C22×Dic241D411yescharacteristic
31C2×C4×D241—21no—
32C2×C4×D241—21no—
33C2×C4×D241—21no—
34C2×C4×D241—21no—
35C2×C4×D241C2×C412yes—
36C2×C4×D241D412yes—
37#16838754—21no—
38#16838754—21no—
39C2×#14515349—21no—
40C4⋊Dic241C2×C412yes—
41#16838749—24no—
42#16838749—22no—
43C22⋊Dic241—22no—
44C22⋊Dic241—21no—
45#16838747—24no—
46#16838747—22no—
47C4×Dic241—21no—
48C4×Dic241—21no—
49C4×Dic241D412yescomplemented
50#41×C241—21no—
51#41×C241—21no—
52#41×C241—21no—
53#41×C241—21no—
54C2×Q8×C241C2×C411yescharacteristic
55C2×D4×C241—21no—
56C2×D4×C241C2×C411yescharacteristic
57C22×C4×C241—21no—
58C22×C4×C241—21no—
59C22×C4×C241C2311yescharacteristic
60M16×C241—21no—
61M16×C241—21no—
62C2×C8×C241—21no—
63C42×C241—21no—
64C42×C241D412yescomplemented
65C22×D241—21no—
66C22×D241—21no—
67C22×D241—42no—
68C22×D241C22⋊C412yes—
69C22⋊D241—44no—
70C2×Dic241—21no—
71C2×Dic241—21no—
72C2×Dic241—22no—
73C2×Dic241—22no—
74C2×Dic241—42no—
75C2×Dic241C22⋊C412yes—
76C4×D241—22no—
77C4×D241—22no—
78C4×D241—22no—
79C4×D241—22no—
80#14515349—41no—
81C23×C241—21no—
82C23×C241C2×D411yescharacteristic
83Q8×C241—21no—
84Q8×C241—21no—
85D4×C241—21no—
86D4×C241—21no—
87D4×C241—41no—
88D4×C241—41no—
89C2×C4×C241—21no—
90C2×C4×C241—22no—
91C2×C4×C241—42no—
92C2×C4×C241—41no—
93C2×C4×C241—41no—
94C2×C4×C241C22×C411yescharacteristic
95C2×C4×C241C2×D411yescharacteristic
96C2×C4×C241C2×D411yescharacteristic
97C2×C4×C241C2×D411yescharacteristic
98C2×C4×C241#4111yescharacteristic
99C2×C4×C241#4111yescharacteristic
100C8×C241—41no—
101C22×C241—22no—
102C22×C241—41no—
103C22×C241—42no—
104C22×C241C2×C22⋊C411yescharacteristic
105C22×C241#12011yescharacteristic
106C22×C241#12311yescharacteristic
107C2×D241—22no—
108C2×D241—22no—
109C2×D241—22no—
110C2×D241—42no—
111C2×D241—42no—
112C4×C241—42no—
113C4×C241—41no—
114C4×C241C4×D411yescharacteristic
115C4×C241C4×D411yescharacteristic
116C4×C241#12111yescharacteristic
117C4×C241#12111yescharacteristic
118Dic241—22no—
119Dic241—42no—
120Dic241—42no—
121C2×C241—21no—
122C2×C241—21no—
123C2×C241—81no—
124C2×C241#38611yescharacteristic
125C2×C241#42112yes—
126D241—42no—
127C241#189711yescharacteristic, complemented, Sylow
128#1897—2411nomaximal, Sylow
129#525—2411no—
130C2×#117—2411no—
131C2×#104—2411no—
132C2×#104D24111yescharacteristic, complemented
133#407—2411no—
134#339—2411no—
135#339—2411no—
136C2×#41C2×D24111yescharacteristic
137C23×C4—2411no—
138C2×M16—2411no—
139C2×M16C2×D24111yescharacteristic
140#123—4821no—
141C22⋊Q8—2412no—
142#121—2412no—
143#120—4821no—
144C4×D4—4822no—
145#117—4822no—
146#117—4822no—
147#117—2411no—
148C2×C4⋊C4—4821no—
149C2×C22⋊C4—4821no—
150C2×C42—2411no—
151C2×C42C2×D24111yescharacteristic
152#104—22no—
153#104—4822no—
154C22⋊C8—4822no—
155C24—2411no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160C2×Q8C4×D24111yescharacteristic
161C2×D4—21no—
162C2×D4—4822no—
163C2×D4C4×D24111yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—4821no—
167C22×C4—4821no—
168C22×C4—4821no—
169C22×C4—4821no—
170C22×C4—4821no—
171C22×C4—2411no—
172C22×C4—2412no—
173C22×C4—2412no—
174C22×C4C22×D24111yescharacteristic
175M16—21no—
176M16—21no—
177M16—4821no—
178M16—4821no—
179C2×C8—21no—
180C2×C8—4821no—
181C4⋊C4—4824no—
182C4⋊C4—4822no—
183C4⋊C4—2412no—
184C22⋊C4—4824no—
185C22⋊C4—4822no—
186C22⋊C4—4821no—
187C22⋊C4—4822no—
188C42—21no—
189C42—4821no—
190C42—4821no—
191C42—2412no—
192C42C22⋊D24112yescomplemented
193C23—21no—
194C23—9642no—
195C23—4821no—
196C23—4821no—
197C23—2412no—
198C23D4×D24111yescharacteristic
199Q8—21no—
200Q8—21no—
201D4—21no—
202D4—21no—
203D4—41no—
204D4—41no—
205D4—9644no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—9642no—
212C2×C4—4822no—
213C2×C4—4822no—
214C2×C4—4821no—
215C2×C4—4821no—
216C2×C4—4822no—
217C2×C4—4822no—
218C2×C4—4822no—
219C2×C4—4822no—
220C2×C4—2412no—
221C2×C4C2×C4×D24111yescharacteristic
222C2×C4D4×D24111yescharacteristic
223C2×C4D4×D24111yescharacteristic
224C2×C4C2×C22⋊D24111yescharacteristic
225C2×C4#1683876911yescharacteristic
226C2×C4#1683877011yescharacteristic
227C8—41no—
228C8—9641no—
229C22—22no—
230C22—41no—
231C22—42no—
232C22—9642no—
233C22—9642no—
234C22—4822no—
235C22—4822no—
236C22—4822no—
237C22C22⋊C4×D24111yescharacteristic
238C22#2144061011yescharacteristic
239C22#2144062411yescharacteristic
240C4—42no—
241C4—41no—
242C4—9642no—
243C4—9642no—
244C4—4822no—
245C4#2144060211yescharacteristic
246C4C4×C22⋊D24111yescharacteristic
247C4#2144061311yescharacteristic
248C4#2144061511yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—9642no—
253C2#2950759311yescharacteristic
254C2#2950773212yes—
subgroupG/H
centerC2×C4D4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
FittingC2×#104×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508224C2
cosocleC22×C4×C241C23
hypercenterC2×#104D241
hypocenterC241#1897
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#21440599C2semidirect
3. C2×#21440569C2semidirect
4. #29507680C2semidirect
5. #29507478C2semidirect
6. #29507477C2semidirect
7. C2×#104×C241C2semidirect
11. #21440618C4semidirect
12. #21440613C4semidirect
49. C4×Dic241D4semidirect
64. C42×C241D4semidirect
127. C241#1897semidirect
132. C2×#104D241semidirect
192. C42C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295082242
C2×#214405992
C2×#214405692
#295076802
#295074782
#295074772
C2×#104×C2412
#1897241