Finite Group Databasebeta

← #44505935

Subgroups — #44505935

Order 30848.

304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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#29508230C211yesmaximal, characteristic
2C22⋊C8×D241C211yesmaximal, characteristic, complemented
3#29507564C211yesmaximal, characteristic, complemented
4#29507454C211yesmaximal, characteristic, complemented
5#29507452C211yesmaximal, characteristic, complemented
6#29507450C211yesmaximal, characteristic, complemented
7#328×C241C211yesmaximal, characteristic, complemented
8C2×#16838771C411yescharacteristic, complemented
9C22×C4×D241C2211yescharacteristic
10C2×C8×D241—21no—
11#21440627—21no—
12#21440618C411yescharacteristic, complemented
13#21440617C411yescharacteristic, complemented
14#21440616C2211yescharacteristic
15#21440612—21no—
16#21440604—21no—
17#21440602—21no—
18#21440600C411yescharacteristic, complemented
19C2×#16838747—21no—
20C2×C4×Dic241—21no—
21C22⋊#14515349C2211yescharacteristic
22#21440554—21no—
23#21440549C2211yescharacteristic
24C22⋊Q8×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27C23×D241D411yescharacteristic
28#16838771—42no—
29C2×D964—21no—
30C2×D964—21no—
31C2×D964C2×C411yescharacteristic
32C2×C22⋊D241—21no—
33C22×Dic241—21no—
34C22×Dic241D411yescharacteristic
35C2×C4×D241—21no—
36C2×C4×D241—42no—
37C2×C4×D241C2×C411yescharacteristic
38C2×C4×D241C2×C411yescharacteristic
39C2×C4×D241D411yescharacteristic
40C2×C4×D241D411yescharacteristic
41C2×#14515349—21no—
42C8×D241—42no—
43C4⋊Dic241C2×C411yescharacteristic
44#16838749—21no—
45#16838747—24no—
46#16838747—21no—
47#16838747—21no—
48#16838747—21no—
49#16838747—21no—
50C4×Dic241—21no—
51C4×Dic241—42no—
52C2×Q8×C241C2×C411yescharacteristic
53C22×C4×C241—21no—
54C22×C4×C241C2311yescharacteristic
55C2×C8×C241—21no—
56C4⋊C4×C241—21no—
57C4⋊C4×C241C2×C411yescharacteristic
58C22⋊C4×C241—21no—
59C22×D241—21no—
60C22×D241—21no—
61C22×D241—22no—
62C22×D241—21no—
63C22×D241—41no—
64C22×D241C22⋊C411yescharacteristic
65C22×D241C22⋊C411yescharacteristic
66D964—41no—
67D964—42no—
68D964—42no—
69C22⋊D241—41no—
70C22⋊D241—41no—
71C2×Dic241—22no—
72C2×Dic241—22no—
73C2×Dic241—21no—
74C2×Dic241—41no—
75C2×Dic241—41no—
76C2×Dic241C22⋊C411yescharacteristic
77C2×Dic241C22⋊C411yescharacteristic
78C4×D241—22no—
79C4×D241—22no—
80C4×D241—41no—
81C4×D241—41no—
82C4×D241—42no—
83#14515349—41no—
84C23×C241C2×D411yescharacteristic
85Q8×C241—41no—
86C2×C4×C241—22no—
87C2×C4×C241—21no—
88C2×C4×C241—21no—
89C2×C4×C241—41no—
90C2×C4×C241—41no—
91C2×C4×C241—41no—
92C2×C4×C241C22×C411yescharacteristic
93C2×C4×C241C2×D411yescharacteristic
94C8×C241—41no—
95C22×C241—21no—
96C22×C241—21no—
97C22×C241C2×C22⋊C411yescharacteristic
98C22×C241#13511yescharacteristic
99C22×C241#13511yescharacteristic
100C2×D241—21no—
101C2×D241—21no—
102C2×D241—21no—
103C2×D241—21no—
104C2×D241—21no—
105C2×D241—42no—
106C2×D241—42no—
107C2×D241—41no—
108C2×D241—41no—
109C2×D241—41no—
110C2×D241#10412yes—
111C4×C241—21no—
112C4×C241—21no—
113C4×C241—42no—
114C4×C241—41no—
115C4×C241—41no—
116Dic241—21no—
117Dic241—42no—
118Dic241—41no—
119Dic241#9912yes—
120C2×C241—21no—
121C2×C241—21no—
122C2×C241C2×#9911yescharacteristic
123C2×C241#41611yescharacteristic
124C2×C241C2×#10411yescharacteristic
125D241—22no—
126D241—41no—
127D241—81no—
128C241#150111yescharacteristic, complemented, Sylow
129#1501—2411nomaximal, Sylow
130#525—2411no—
131C2×C22⋊C8—2411no—
132C4×C22⋊C4—2411no—
133#328—2411no—
134#328D24111yescharacteristic, complemented
135#327—2411no—
136#327—2411no—
137C2×#41—2411no—
138C23×C4—2411no—
139C22×C8—4821no—
140#123—4821no—
141C22⋊Q8—2411no—
142C22⋊Q8C2×D24111yescharacteristic
143#121—2411no—
144#121—2411no—
145#120—4821no—
146C4×D4—4821no—
147C4×D4—4821no—
148#117—2411no—
149C2×C22⋊C4—4821no—
150C2×C42—4821no—
151C22⋊C8—4821no—
152C22⋊C8—2411no—
153C22⋊C8C2×D24111yescharacteristic
154#95—2411no—
155#95C2×D24111yescharacteristic
156C24—2411no—
157#41—9642no—
158C2×Q8C4×D24111yescharacteristic
159C2×D4—4821no—
160C2×D4—4821no—
161C2×D4—4821no—
162C2×D4—2411no—
163C22×C4—21no—
164C22×C4—9642no—
165C22×C4—4821no—
166C22×C4—4821no—
167C22×C4—2411no—
168C22×C4—2411no—
169C22×C4—2411no—
170C22×C4—2411no—
171C22×C4—2411no—
172C22×C4C22×D24111yescharacteristic
173C2×C8—21no—
174C2×C8—9642no—
175C2×C8—4821no—
176C4⋊C4—21no—
177C4⋊C4—4821no—
178C4⋊C4—2411no—
179C4⋊C4C4×D24111yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—4824no—
182C22⋊C4—4821no—
183C22⋊C4—4821no—
184C22⋊C4—4821no—
185C22⋊C4—4821no—
186C42—9642no—
187C42—4821no—
188C23—9641no—
189C23—4822no—
190C23—4821no—
191C23—4821no—
192C23—4821no—
193C23—2411no—
194C23—2411no—
195C23D4×D24111yescharacteristic
196Q8—41no—
197D4—9641no—
198D4—9642no—
199D4—9642no—
200D4—9641no—
201D4—9641no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—9641no—
209C2×C4—9641no—
210C2×C4—9642no—
211C2×C4—9641no—
212C2×C4—9641no—
213C2×C4—4822no—
214C2×C4—4822no—
215C2×C4—4822no—
216C2×C4—4821no—
217C2×C4—4822no—
218C2×C4—2411no—
219C2×C4—2411no—
220C2×C4C2×C4×D24111yescharacteristic
221C2×C4D4×D24111yescharacteristic
222C8—41no—
223C8—9641no—
224C22—21no—
225C22—21no—
226C22—9642no—
227C22—9642no—
228C22—9641no—
229C22—9641no—
230C22—9641no—
231C22—4821no—
232C22—4821no—
233C22—4821no—
234C22—4821no—
235C22—4821no—
236C22—2412no—
237C22C22⋊C4×D24111yescharacteristic
238C22#2144066311yescharacteristic
239C22#2144066511yescharacteristic
240C4—21no—
241C4—21no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—9642no—
246C4—9641no—
247C4—4821no—
248C4—2412no—
249C2—21no—
250C2—21no—
251C2—19281no—
252C2—9641no—
253C2—4822no—
254C2#99×D24111yescharacteristic
255C2#2950771211yescharacteristic
256C2#104×D24111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#328×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508230C2
cosocleC22×C4×C241C23
hypercenter#328D241
hypocenterC241#1501
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D241C2semidirect
3. #29507564C2semidirect
4. #29507454C2semidirect
5. #29507452C2semidirect
6. #29507450C2semidirect
7. #328×C241C2semidirect
8. C2×#16838771C4semidirect
12. #21440618C4semidirect
13. #21440617C4semidirect
18. #21440600C4semidirect
128. C241#1501semidirect
134. #328D241semidirect

Maximal subgroups

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

subgroupindex
#295082302
C22⋊C8×D2412
#295075642
#295074542
#295074522
#295074502
#328×C2412
#1501241