Finite Group Databasebeta

← #34079888

Subgroups — #34079888

Order 19328.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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#23752722C211yesmaximal, characteristic
2C2×#18012715C211yesmaximal, characteristic, complemented
3#23752551C212yesmaximal, complemented
4#23752543C211yesmaximal, characteristic, complemented
5#23752523C211yesmaximal, characteristic, complemented
6#23752452C212yesmaximal, complemented
7#23752438C212yesmaximal, complemented
8#23752371C212yesmaximal, complemented
9#23752368C211yesmaximal, characteristic, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#448×C151C211yesmaximal, characteristic, complemented
12C2×#14559003C2211yescharacteristic
13C22×C4×D151C2211yescharacteristic
14C2×#14558994C2212yescomplemented
15C2×C8×D151C2212yes—
16#18012721—21no—
17#18012719C2211yescharacteristic
18#18012718C2211yescharacteristic
19#18012715—21no—
20#18012715—21no—
21#18012715C2212yes—
22#18012715C2212yes—
23#18012710C2211yescharacteristic
24#18012707—21no—
25D4×Dic151—21no—
26(C22⋊D151)⋊C4—21no—
27#18012697C2211yescharacteristic
28C2×C4⋊Dic151C2211yescharacteristic
29C2×Dic151⋊C4—21no—
30C2×(C2×D151)⋊C4—21no—
31#18012672C2212yescomplemented
32#18012671C2212yescomplemented
33#18012664C2212yescomplemented
34#18012663C2212yescomplemented
35#18012660C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic
37(C2×D151)⋊C8C2212yes—
38C22×Q8×C151C2211yescharacteristic
39C2×SD16×C151C2212yescomplemented
40#121×C151C2211yescharacteristic
41#103×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151D411yescharacteristic
44#14559003—42no—
45C2×Dic302C2311yescharacteristic
46C2×C22⋊D151—21no—
47C2×C22⋊D151—21no—
48C22×Dic151—21no—
49C22×Dic151—21no—
50C22×Dic151D411yescharacteristic
51C2×C4×D151—42no—
52C2×C4×D151D411yescharacteristic
53C2×C4×D151D411yescharacteristic
54C2×C4×D151C2311yescharacteristic
55C2×C4×D151C2311yescharacteristic
56#14558994—42no—
57C2×C151⋊C8C2312yes—
58C8×D151—42no—
59C4⋊Dic151—21no—
60C4⋊Dic151—21no—
61C4⋊Dic151C2312yes—
62C4⋊Dic151C2311yescharacteristic
63Dic151⋊C4—22no—
64Dic151⋊C4—22no—
65Dic151⋊C4—21no—
66C22⋊Dic151—21no—
67C22⋊Dic151—21no—
68(C2×D151)⋊C4—22no—
69(C2×D151)⋊C4—22no—
70(C2×D151)⋊C4—21no—
71(C2×D151)⋊C4—21no—
72C4×Dic151—21no—
73C2×Q8×C151—21no—
74C2×Q8×C151—42no—
75C2×Q8×C151C2312yes—
76C2×D4×C151—21no—
77C2×D4×C151C2311yescharacteristic
78C22×C4×C151—21no—
79C22×C4×C151C2311yescharacteristic
80SD16×C151—42no—
81C2×C8×C151C2312yes—
82C4⋊C4×C151C2311yescharacteristic
83C22⋊C4×C151—21no—
84C22×D151—22no—
85C22×D151—22no—
86C22×D151—41no—
87C22×D151C2×D411yescharacteristic
88C22×D151C2×D411yescharacteristic
89Dic302—22no—
90C22⋊D151—42no—
91C22⋊D151—42no—
92C2×Dic151—21no—
93C2×Dic151—22no—
94C2×Dic151—21no—
95C2×Dic151—41no—
96C2×Dic151—42no—
97C2×Dic151—42no—
98C2×Dic151C2×D411yescharacteristic
99C2×Dic151C2×D411yescharacteristic
100C4×D151—22no—
101C4×D151—22no—
102C4×D151—41no—
103C4×D151—41no—
104C151⋊C8—22no—
105C23×C151—21no—
106C23×C151C2×D411yescharacteristic
107Q8×C151—22no—
108Q8×C151—22no—
109Q8×C151—42no—
110D4×C151—22no—
111D4×C151—42no—
112C2×C4×C151—22no—
113C2×C4×C151—22no—
114C2×C4×C151—21no—
115C2×C4×C151—42no—
116C2×C4×C151C2×D411yescharacteristic
117C2×C4×C151C2411yescharacteristic
118C8×C151—22no—
119C22×C151—21no—
120C22×C151—21no—
121C22×C151—41no—
122C22×C151—41no—
123C22×C151—41no—
124C22×C151#13512yes—
125C22×C151C22×D411yescharacteristic
126C2×D151—21no—
127C2×D151—21no—
128C2×D151—21no—
129C2×D151—21no—
130C2×D151—21no—
131C2×D151—44no—
132C2×D151#13712yes—
133C4×C151—21no—
134C4×C151—42no—
135C4×C151—41no—
136C4×C151H(5,𝔽2)12yes—
137Dic151—21no—
138Dic151—21no—
139Dic151—41no—
140Dic151—42no—
141Dic151—41no—
142C2×C151—22no—
143C2×C151—81no—
144C2×C151#53411yescharacteristic
145C2×C151C2×#13511yescharacteristic
146C2×C151C2×#13711yescharacteristic
147D151—22no—
148D151—41no—
149C151#319011yescharacteristic, complemented, Sylow
150#3190—1511nomaximal, Sylow
151#525—1511no—
152C2×C22⋊Q8—1511no—
153#485—1512no—
154#483—1511no—
155#480—1511no—
156#467—1512no—
157#465—1512no—
158#452—1512no—
159#451—1511no—
160#448D15111yescharacteristic, complemented
161C2×C22⋊C8—1511no—
162C2×#41—1511no—
163C22×Q8C2×D15111yescharacteristic
164C23×C4—1511no—
165C2×Q16—1512no—
166C2×SD16C2×D15112yescomplemented
167C22×C8—1512no—
168#123—3021no—
169C22⋊Q8—3021no—
170C22⋊Q8—3021no—
171C22⋊Q8—1512no—
172C22⋊Q8—1512no—
173C22⋊Q8—1511no—
174C22⋊Q8—1511no—
175#121—1511no—
176#121C2×D15111yescharacteristic
177#120—3021no—
178C4×D4—3021no—
179C4×D4—3021no—
180#117—1511no—
181C2×C4⋊C4—3021no—
182C2×C4⋊C4—1511no—
183C2×C22⋊C4—3021no—
184#107—1512no—
185#106—1512no—
186#103—1512no—
187#103—1512no—
188#103C2×D15112yescomplemented
189#102—1512no—
190C22⋊C8—1511no—
191C22⋊C8—1512no—
192C22⋊C8C2×D15111yescharacteristic
193C24—1511no—
194#41—6042no—
195C2×Q8—21no—
196C2×Q8—42no—
197C2×Q8—1511no—
198C2×Q8C22×D15112yes—
199C2×D4—21no—
200C2×D4—3021no—
201C2×D4—3021no—
202C2×D4C22×D15111yescharacteristic
203C22×C4—21no—
204C22×C4—3021no—
205C22×C4—3021no—
206C22×C4—6042no—
207C22×C4—1511no—
208C22×C4—1511no—
209C22×C4—1511no—
210C22×C4—1511no—
211C22×C4—1511no—
212C22×C4C22×D15111yescharacteristic
213Q16—6042no—
214SD16—42no—
215C2×C8—6042no—
216C2×C8—1512no—
217C2×C8C22×D15112yes—
218C4⋊C4—3022no—
219C4⋊C4—3022no—
220C4⋊C4—3021no—
221C4⋊C4—3021no—
222C4⋊C4—3021no—
223C4⋊C4—1512no—
224C4⋊C4—1511no—
225C4⋊C4C22×D15111yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—3022no—
228C22⋊C4—3022no—
229C22⋊C4—3021no—
230C22⋊C4—3021no—
231C22⋊C4—3021no—
232C22⋊C4—3021no—
233C42—3021no—
234C23—21no—
235C23—3022no—
236C23—3022no—
237C23—6041no—
238C23—1511no—
239C23—1511no—
240C23D4×D15111yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—42no—
244Q8—3022no—
245D4—22no—
246D4—42no—
247D4—6042no—
248D4—6042no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—3022no—
254C2×C4—3022no—
255C2×C4—3021no—
256C2×C4—3022no—
257C2×C4—3021no—
258C2×C4—6041no—
259C2×C4—6041no—
260C2×C4—6041no—
261C2×C4—6042no—
262C2×C4—6042no—
263C2×C4—1511no—
264C2×C4—1511no—
265C2×C4D4×D15111yescharacteristic
266C2×C4C23×D15111yescharacteristic
267C8—22no—
268C8—3022no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—3021no—
275C22—3021no—
276C22—3021no—
277C22—3021no—
278C22—3021no—
279C22—6044no—
280C22—1512no—
281C22#1801276012yes—
282C22C2×D4×D15111yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—3021no—
287C4—3021no—
288C4—6042no—
289C4—6041no—
290C4—6041no—
291C4#1801278412yes—
292C2—22no—
293C2—81no—
294C2—3022no—
295C2—6041no—
296C2#2375277211yescharacteristic
297C2C2×#1801276011yescharacteristic
298C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#448×C151C2
socleC22×C151C22×D4
prime radical#23752722C2
hypercenter#448D151
hypocenterC151#3190
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. C2×#18012715C2semidirect
3. #23752551C2semidirect
4. #23752543C2semidirect
5. #23752523C2semidirect
6. #23752452C2semidirect
7. #23752438C2semidirect
8. #23752371C2semidirect
9. #23752368C2semidirect
10. C22⋊C8×D151C2semidirect
11. #448×C151C2semidirect
14. C2×#14558994C22semidirect
31. #18012672C22semidirect
32. #18012671C22semidirect
33. #18012664C22semidirect
34. #18012663C22semidirect
35. #18012660C22semidirect
39. C2×SD16×C151C22semidirect
41. #103×C151C22semidirect
149. C151#3190semidirect
160. #448D151semidirect
166. C2×SD16C2×D151semidirect
188. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527222
C2×#180127152
#237525512
#237525432
#237525232
#237524522
#237524382
#237523712
#237523682
C22⋊C8×D1512
#448×C1512
#3190151