Finite Group Databasebeta

← #44507885

Subgroups — #44507885

Order 30848.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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×C42×D241C211yesmaximal, 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×D241—21no—
9C22×C4×D241C2211yescharacteristic
10C2×#16838754C2211yescharacteristic
11#21440623—21no—
12#21440618C412yescomplemented
13#21440613C412yescomplemented
14#21440610—21no—
15C4×C22⋊D241—22no—
16#21440601C2211yescharacteristic
17C2×C4×Dic241—21no—
18C2×C4×Dic241C2211yescharacteristic
19C42×D241—22no—
20C42×D241—22no—
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—24no—
32C2×C4×D241—28no—
33C2×C4×D241—21no—
34C2×C4×D241—21no—
35C2×C4×D241—21no—
36C2×C4×D241—21no—
37C2×C4×D241C2×C412yes—
38C2×C4×D241D412yes—
39#16838754—21no—
40#16838754—21no—
41C2×#14515349—21no—
42C4⋊Dic241C2×C412yescomplemented
43#16838749—22no—
44C22⋊Dic241—22no—
45C22⋊Dic241—21no—
46#16838747—22no—
47C4×Dic241—24no—
48C4×Dic241—21no—
49C4×Dic241—21no—
50C4×Dic241D412yescomplemented
51#41×C241—21no—
52#41×C241—21no—
53#41×C241—21no—
54#41×C241—21no—
55C2×Q8×C241C2×C411yescharacteristic, complemented
56C2×D4×C241—21no—
57C2×D4×C241C2×C411yescharacteristic, complemented
58C22×C4×C241—21no—
59C22×C4×C241—21no—
60C22×C4×C241C2311yescharacteristic
61M16×C241—21no—
62M16×C241—21no—
63C2×C8×C241—21no—
64C42×C241—21no—
65C42×C241D412yescomplemented
66C22×D241—21no—
67C22×D241—21no—
68C22×D241—24no—
69C22×D241C22⋊C412yes—
70C22⋊D241—44no—
71C2×Dic241—24no—
72C2×Dic241—21no—
73C2×Dic241—22no—
74C2×Dic241—21no—
75C2×Dic241—22no—
76C2×Dic241C22⋊C412yes—
77C4×D241—216no—
78C4×D241—22no—
79C4×D241—22no—
80C4×D241—22no—
81C4×D241—22no—
82#14515349—41no—
83C23×C241—21no—
84C23×C241C2×D411yescharacteristic
85Q8×C241—21no—
86Q8×C241—21no—
87D4×C241—21no—
88D4×C241—21no—
89D4×C241—41no—
90D4×C241—41no—
91C2×C4×C241—24no—
92C2×C4×C241—22no—
93C2×C4×C241—21no—
94C2×C4×C241—41no—
95C2×C4×C241—41no—
96C2×C4×C241C22×C411yescharacteristic
97C2×C4×C241C2×D411yescharacteristic
98C2×C4×C241C2×D411yescharacteristic
99C2×C4×C241C2×D411yescharacteristic
100C2×C4×C241#4111yescharacteristic
101C2×C4×C241#4111yescharacteristic
102C8×C241—41no—
103C22×C241—22no—
104C22×C241—41no—
105C22×C241—42no—
106C22×C241C2×C22⋊C411yescharacteristic
107C22×C241#12011yescharacteristic
108C22×C241#12311yescharacteristic
109C2×D241—24no—
110C2×D241—24no—
111C2×D241—22no—
112C2×D241—22no—
113C2×D241#10414yescomplemented
114C4×C241—24no—
115C4×C241—41no—
116C4×C241C4×D411yescharacteristic
117C4×C241C4×D411yescharacteristic
118C4×C241#12111yescharacteristic
119C4×C241#12111yescharacteristic
120Dic241—24no—
121Dic241—22no—
122Dic241—42no—
123C2×C241—21no—
124C2×C241—21no—
125C2×C241—81no—
126C2×C241#38611yescharacteristic
127C2×C241C2×#10412yes—
128D241—24no—
129C241#189611yescharacteristic, complemented, Sylow
130#1896—2411nomaximal, Sylow
131#525—2411no—
132C22×C42—2411no—
133C2×#104—2411no—
134C2×#104D24111yescharacteristic, complemented
135#407—2411no—
136#339—2411no—
137#339—2411no—
138C2×#41C2×D24111yescharacteristic
139C23×C4—4821no—
140C23×C4—2411no—
141C2×M16—2411no—
142C2×M16C2×D24111yescharacteristic
143#123—4821no—
144C22⋊Q8—2412no—
145#121—2412no—
146#120—4821no—
147C4×D4—4822no—
148#117—2411no—
149C2×C42—4822no—
150C2×C42—4821no—
151C2×C42—4822no—
152C2×C42—2411no—
153C2×C42C2×D24111yescharacteristic
154#104—22no—
155#104—4822no—
156C22⋊C8—4822no—
157C24—2411no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8C4×D24111yescharacteristic, complemented
163C2×D4—21no—
164C2×D4—4822no—
165C2×D4C4×D24111yescharacteristic, complemented
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—4824no—
169C22×C4—4828no—
170C22×C4—4821no—
171C22×C4—4821no—
172C22×C4—4821no—
173C22×C4—4821no—
174C22×C4—4821no—
175C22×C4—2411no—
176C22×C4—2412no—
177C22×C4—2412no—
178C22×C4C22×D24111yescharacteristic
179M16—21no—
180M16—21no—
181M16—4821no—
182M16—4821no—
183C2×C8—21no—
184C2×C8—4821no—
185C4⋊C4—4822no—
186C4⋊C4—2412no—
187C22⋊C4—4822no—
188C22⋊C4—4821no—
189C22⋊C4—4822no—
190C42—21no—
191C42—4824no—
192C42—4821no—
193C42—4821no—
194C42—2412no—
195C42C22⋊D24112yescomplemented
196C23—21no—
197C23—4824no—
198C23—4821no—
199C23—4821no—
200C23—2412no—
201C23D4×D24111yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—9644no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—48216no—
215C2×C4—4822no—
216C2×C4—4824no—
217C2×C4—4821no—
218C2×C4—4822no—
219C2×C4—4821no—
220C2×C4—4822no—
221C2×C4—4822no—
222C2×C4—4822no—
223C2×C4—4822no—
224C2×C4—2412no—
225C2×C4C2×C4×D24111yescharacteristic
226C2×C4D4×D24111yescharacteristic
227C2×C4D4×D24111yescharacteristic
228C2×C4C2×C22⋊D24111yescharacteristic
229C2×C4#1683876911yescharacteristic
230C2×C4#1683877011yescharacteristic
231C8—41no—
232C8—9641no—
233C22—22no—
234C22—41no—
235C22—42no—
236C22—4824no—
237C22—4824no—
238C22—4822no—
239C22—4822no—
240C22—2414no—
241C22C22⋊C4×D24111yescharacteristic
242C22#2144061011yescharacteristic
243C22#2144062411yescharacteristic
244C4—24no—
245C4—41no—
246C4—9642no—
247C4—4824no—
248C4—4822no—
249C4#2144060211yescharacteristic
250C4C4×C22⋊D24111yescharacteristic
251C4#2144061311yescharacteristic
252C4#2144061511yescharacteristic
253C2—21no—
254C2—21no—
255C2—81no—
256C2—4824no—
257C2#2950759311yescharacteristic
258C2#104×D24112yes—
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#1896
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×C42×D241C2semidirect
3. C2×#21440569C2semidirect
4. #29507680C2semidirect
5. #29507478C2semidirect
6. #29507477C2semidirect
7. C2×#104×C241C2semidirect
12. #21440618C4semidirect
13. #21440613C4semidirect
42. C4⋊Dic241C2×C4semidirect
50. C4×Dic241D4semidirect
55. C2×Q8×C241C2×C4semidirect
57. C2×D4×C241C2×C4semidirect
65. C42×C241D4semidirect
113. C2×D241#104semidirect
129. C241#1896semidirect
134. C2×#104D241semidirect
162. C2×Q8C4×D241semidirect
165. C2×D4C4×D241semidirect
195. C42C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295082242
C2×C42×D2412
C2×#214405692
#295076802
#295074782
#295074772
C2×#104×C2412
#1896241