Finite Group Databasebeta

← #44505938

Subgroups — #44505938

Order 30848.

284 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 71 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#29508262C211yesmaximal, characteristic
2#29507767C211yesmaximal, characteristic, complemented
3#29507568C211yesmaximal, characteristic, complemented
4#29507452C211yesmaximal, characteristic, complemented
5#29507451C211yesmaximal, characteristic, complemented
6#29507450C211yesmaximal, characteristic, complemented
7#327×C241C211yesmaximal, characteristic, complemented
8C2×#16838769—21no—
9#21440641C411yescharacteristic, complemented
10#21440638C411yescharacteristic, complemented
11#21440628—21no—
12#21440616C2211yescharacteristic
13#21440614—21no—
14D4×Dic241C411yescharacteristic, complemented
15#21440604C411yescharacteristic, complemented
16#21440602—21no—
17C2×#16838749—21no—
18C2×C4×Dic241—21no—
19C2×C4×Dic241C2211yescharacteristic
20#21440571—21no—
21C22⋊#14515349C2211yescharacteristic
22C8×Dic241—21no—
23#21440549C2211yescharacteristic
24#121×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27#16838769—42no—
28#16838769—42no—
29C2×Dic482—21no—
30C2×D964C2×C411yescharacteristic
31C2×C22⋊D241—21no—
32C2×C22⋊D241—21no—
33C2×C22⋊D241—21no—
34C22×Dic241—21no—
35C22×Dic241—21no—
36C22×Dic241D411yescharacteristic
37C22×Dic241D411yescharacteristic
38C2×C4×D241—21no—
39C2×#14515349—21no—
40C4⋊Dic241C2×C411yescharacteristic
41#16838749—24no—
42#16838749—21no—
43C22⋊Dic241—21no—
44#16838747—21no—
45#16838747—21no—
46C4×Dic241—42no—
47C4×Dic241C2×C411yescharacteristic
48C4×Dic241C2×C411yescharacteristic
49C4×Dic241D411yescharacteristic
50C4×Dic241D411yescharacteristic
51C2×D4×C241—21no—
52C2×D4×C241C2×C411yescharacteristic
53C22×C4×C241—21no—
54C22×C4×C241C2311yescharacteristic
55C2×C8×C241—21no—
56C4⋊C4×C241C2×C411yescharacteristic
57C22⋊C4×C241—21no—
58C22×D241—21no—
59Dic482—42no—
60D964—41no—
61C22⋊D241—41no—
62C22⋊D241—41no—
63C22⋊D241—42no—
64C22⋊D241—42no—
65C2×Dic241—22no—
66C2×Dic241—22no—
67C2×Dic241—21no—
68C2×Dic241—41no—
69C2×Dic241—41no—
70C2×Dic241—42no—
71C2×Dic241C22⋊C411yescharacteristic
72C2×Dic241C22⋊C411yescharacteristic
73C2×Dic241C22⋊C411yescharacteristic
74C2×Dic241C22⋊C411yescharacteristic
75C2×Dic241D812yes—
76C2×Dic241SD1612yes—
77C4×D241—42no—
78#14515349—41no—
79C23×C241—21no—
80C23×C241C2×D411yescharacteristic
81D4×C241—41no—
82D4×C241—41no—
83D4×C241—41no—
84C2×C4×C241—22no—
85C2×C4×C241—21no—
86C2×C4×C241—41no—
87C2×C4×C241—41no—
88C2×C4×C241—41no—
89C2×C4×C241C22×C411yescharacteristic
90C2×C4×C241C2×D411yescharacteristic
91C8×C241—41no—
92C22×C241—21no—
93C22×C241—21no—
94C22×C241—41no—
95C22×C241—41no—
96C22×C241—41no—
97C22×C241C2×C22⋊C411yescharacteristic
98C22×C241C2×D811yescharacteristic
99C22×C241C2×SD1611yescharacteristic
100C2×D241—41no—
101C2×D241—41no—
102C2×D241—41no—
103C4×C241—21no—
104C4×C241—21no—
105C4×C241—42no—
106C4×C241—41no—
107Dic241—21no—
108Dic241—42no—
109Dic241—41no—
110Dic241#10212yes—
111Dic241#10212yes—
112Dic241#10412yes—
113C2×C241—21no—
114C2×C241—21no—
115C2×C241—81no—
116C2×C241#41011yescharacteristic
117C2×C241C2×#10211yescharacteristic
118C2×C241C2×#10411yescharacteristic
119D241—81no—
120C241#150211yescharacteristic, complemented, Sylow
121#1502—2411nomaximal, Sylow
122#532—2411no—
123#431—2411no—
124C4×C4⋊C4—2411no—
125#327—2411no—
126#327—2411no—
127#327—2411no—
128#327D24111yescharacteristic, complemented
129C2×#41—4821no—
130C4⋊Q8—2411no—
131#127—2411no—
132#124—4821no—
133#121—4821no—
134#121—2411no—
135#121C2×D24111yescharacteristic
136C4×D4—4821no—
137C4×D4—2411no—
138C4×D4—2411no—
139C2×C4⋊C4—4821no—
140C2×C42—4821no—
141C2×C42—2411no—
142C4⋊C8—4821no—
143C22⋊C8—2411no—
144C22⋊C8C2×D24111yescharacteristic
145C4×C8—4821no—
146#95—2411no—
147#95C2×D24111yescharacteristic
148#41—9642no—
149#41—9642no—
150C2×Q8—4821no—
151C2×D4—21no—
152C2×D4—4821no—
153C2×D4—4821no—
154C2×D4—4821no—
155C2×D4—2411no—
156C2×D4C4×D24111yescharacteristic
157C22×C4—21no—
158C22×C4—4821no—
159C22×C4—4821no—
160C22×C4—4821no—
161C22×C4—2411no—
162C22×C4—2411no—
163C22×C4C22×D24111yescharacteristic
164C2×C8—21no—
165C2×C8—4821no—
166C4⋊C4—4824no—
167C4⋊C4—4821no—
168C4⋊C4—2411no—
169C4⋊C4C4×D24111yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—4821no—
172C22⋊C4—4821no—
173C22⋊C4—4821no—
174C42—9642no—
175C42—2411no—
176C42—2411no—
177C42—2411no—
178C42—2411no—
179C23—21no—
180C23—4821no—
181C23D4×D24111yescharacteristic
182Q8—9642no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—9641no—
187D4—9641no—
188D4—9641no—
189D4—9642no—
190D4—9642no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—9642no—
197C2×C4—9641no—
198C2×C4—9641no—
199C2×C4—9642no—
200C2×C4—4822no—
201C2×C4—4821no—
202C2×C4—4822no—
203C2×C4—2411no—
204C2×C4—2411no—
205C2×C4—2411no—
206C2×C4—2411no—
207C2×C4—2412no—
208C2×C4—2412no—
209C2×C4C2×C4×D24111yescharacteristic
210C2×C4D4×D24111yescharacteristic
211C8—41no—
212C8—9641no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—9641no—
219C22—9641no—
220C22—9641no—
221C22C22⋊C4×D24111yescharacteristic
222C22D8×D24111yescharacteristic
223C22SD16×D24111yescharacteristic
224C4—21no—
225C4—21no—
226C4—42no—
227C4—41no—
228C4—9642no—
229C4—9641no—
230C4—4821no—
231C4—2412no—
232C4—2412no—
233C4—2412no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—19281no—
238C2#2950768911yescharacteristic
239C2#102×D24111yescharacteristic
240C2#104×D24111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#327×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508262C2
cosocleC22×C4×C241C23
hypercenter#327D241
hypocenterC241#1502
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #29507767C2semidirect
3. #29507568C2semidirect
4. #29507452C2semidirect
5. #29507451C2semidirect
6. #29507450C2semidirect
7. #327×C241C2semidirect
9. #21440641C4semidirect
10. #21440638C4semidirect
14. D4×Dic241C4semidirect
15. #21440604C4semidirect
120. C241#1502semidirect
128. #327D241semidirect

Maximal subgroups

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

subgroupindex
#295082622
#295077672
#295075682
#295074522
#295074512
#295074502
#327×C2412
#1502241