Finite Group Databasebeta

← #34079894

Subgroups — #34079894

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#23752725C211yesmaximal, characteristic
2C2×#18012715C211yesmaximal, characteristic, complemented
3#23752552C212yesmaximal, complemented
4#23752540C211yesmaximal, characteristic, complemented
5#23752526C211yesmaximal, characteristic, complemented
6#23752450C212yesmaximal, complemented
7#23752444C212yesmaximal, complemented
8#23752373C212yesmaximal, complemented
9#23752351C211yesmaximal, characteristic, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#451×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic
13C22×C4×D151C2211yescharacteristic
14C2×#14558991C2212yescomplemented
15C2×C8×D151C2212yes—
16#18012724—21no—
17#18012715—21no—
18#18012715—21no—
19#18012715C2211yescharacteristic
20#18012715C2212yes—
21#18012715C2212yes—
22#18012714C2211yescharacteristic
23#18012713C2211yescharacteristic
24#18012709—21no—
25#18012701—21no—
26(C22⋊D151)⋊C4—21no—
27#18012697C2211yescharacteristic
28C2×C4⋊Dic151C2211yescharacteristic
29C2×Dic151⋊C4—21no—
30C2×(C2×D151)⋊C4—21no—
31#18012673C2212yescomplemented
32#18012670C2212yescomplemented
33#18012663C2212yescomplemented
34#18012663C2212yescomplemented
35#18012661C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic
37(C2×D151)⋊C8C2212yes—
38C22×Q8×C151C2211yescharacteristic
39C2×Q16×C151C2212yescomplemented
40C22⋊Q8×C151C2211yescharacteristic
41#103×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151D411yescharacteristic
44#14559005—42no—
45C2×D604—21no—
46C2×D604—21no—
47C2×D604C2311yescharacteristic
48C2×C22⋊D151—21no—
49C22×Dic151—21no—
50C22×Dic151D411yescharacteristic
51C2×C4×D151—21no—
52C2×C4×D151—42no—
53C2×C4×D151D411yescharacteristic
54C2×C4×D151D411yescharacteristic
55C2×C4×D151C2311yescharacteristic
56C2×C4×D151C2311yescharacteristic
57#14558991—42no—
58C2×C151⋊C8C2312yes—
59C8×D151—42no—
60C4⋊Dic151—21no—
61C4⋊Dic151C2311yescharacteristic
62C4⋊Dic151C2312yes—
63Dic151⋊C4—22no—
64Dic151⋊C4—22no—
65Dic151⋊C4—21no—
66(C2×D151)⋊C4—22no—
67(C2×D151)⋊C4—22no—
68(C2×D151)⋊C4—21no—
69(C2×D151)⋊C4—21no—
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×Q8×C151C2311yescharacteristic
77C22×C4×C151—21no—
78C22×C4×C151C2311yescharacteristic
79Q16×C151—42no—
80C2×C8×C151C2312yes—
81C4⋊C4×C151—21no—
82C4⋊C4×C151C2311yescharacteristic
83C22⋊C4×C151—21no—
84C22×D151—22no—
85C22×D151—22no—
86C22×D151—21no—
87C22×D151—41no—
88C22×D151C2×D411yescharacteristic
89C22×D151C2×D411yescharacteristic
90D604—22no—
91D604—42no—
92D604—42no—
93C22⋊D151—42no—
94C2×Dic151—21no—
95C2×Dic151—22no—
96C2×Dic151—41no—
97C2×Dic151—42no—
98C2×Dic151C2×D411yescharacteristic
99C2×Dic151C2×D411yescharacteristic
100C4×D151—22no—
101C4×D151—22no—
102C4×D151—41no—
103C4×D151—41no—
104C4×D151—42no—
105C151⋊C8—22no—
106C23×C151C2×D411yescharacteristic
107Q8×C151—22no—
108Q8×C151—22no—
109Q8×C151—22no—
110Q8×C151—42no—
111C2×C4×C151—22no—
112C2×C4×C151—22no—
113C2×C4×C151—21no—
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#13512yes—
122C22×C151C22×D411yescharacteristic
123C2×D151—21no—
124C2×D151—21no—
125C2×D151—21no—
126C2×D151—21no—
127C2×D151—21no—
128C2×D151—44no—
129C2×D151—41no—
130C2×D151—41no—
131C2×D151—41no—
132C2×D151#13712yes—
133C4×C151—21no—
134C4×C151—42no—
135C4×C151—41no—
136C4×C151—41no—
137C4×C151H(5,𝔽2)12yes—
138Dic151—21no—
139Dic151—21no—
140Dic151—42no—
141Dic151—41no—
142C2×C151—22no—
143C2×C151#53411yescharacteristic
144C2×C151C2×#13511yescharacteristic
145C2×C151C2×#13711yescharacteristic
146D151—22no—
147D151—41no—
148D151—81no—
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#451D15111yescharacteristic, complemented
160#448—1511no—
161C2×C22⋊C8—1511no—
162C2×#41—1511no—
163C22×Q8C2×D15111yescharacteristic
164C23×C4—1511no—
165C2×Q16C2×D15112yescomplemented
166C2×SD16—1512no—
167C22×C8—1512no—
168#123—3021no—
169C22⋊Q8—3021no—
170C22⋊Q8—3021no—
171C22⋊Q8—1512no—
172C22⋊Q8—1512no—
173C22⋊Q8—1511no—
174C22⋊Q8C2×D15111yescharacteristic
175#121—1511no—
176#121—1511no—
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×Q8C22×D15111yescharacteristic
198C2×Q8C22×D15112yes—
199C2×D4—3021no—
200C2×D4—3021no—
201C2×D4—3021no—
202C2×D4—1511no—
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—42no—
214SD16—6042no—
215C2×C8—6042no—
216C2×C8—1512no—
217C2×C8C22×D15112yes—
218C4⋊C4—21no—
219C4⋊C4—3022no—
220C4⋊C4—3022no—
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—3022no—
235C23—3022no—
236C23—3021no—
237C23—6041no—
238C23—1511no—
239C23—1511no—
240C23D4×D15111yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—22no—
244Q8—42no—
245D4—3022no—
246D4—6042no—
247D4—6042no—
248D4—6042no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—3022no—
255C2×C4—3022no—
256C2×C4—3021no—
257C2×C4—3022no—
258C2×C4—6041no—
259C2×C4—6041no—
260C2×C4—6042no—
261C2×C4—6041no—
262C2×C4—6042no—
263C2×C4—1511no—
264C2×C4—1511no—
265C2×C4D4×D15111yescharacteristic
266C2×C4C23×D15111yescharacteristic
267C8—22no—
268C8—3022no—
269C22—21no—
270C22—21no—
271C22—3021no—
272C22—3021no—
273C22—3021no—
274C22—3021no—
275C22—3021no—
276C22—6044no—
277C22—6041no—
278C22—6041no—
279C22—6041no—
280C22—1512no—
281C22#1801276212yes—
282C22C2×D4×D15111yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—41no—
287C4—3021no—
288C4—3021no—
289C4—6042no—
290C4—6041no—
291C4#1801278412yes—
292C2—22no—
293C2—3022no—
294C2—6041no—
295C2—12081no—
296C2#2375277211yescharacteristic
297C2C2×#1801276211yescharacteristic
298C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#451×C151C2
socleC22×C151C22×D4
prime radical#23752725C2
hypercenter#451D151
hypocenterC151#3190
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#18012715C2semidirect
3. #23752552C2semidirect
4. #23752540C2semidirect
5. #23752526C2semidirect
6. #23752450C2semidirect
7. #23752444C2semidirect
8. #23752373C2semidirect
9. #23752351C2semidirect
10. C22⋊C8×D151C2semidirect
11. #451×C151C2semidirect
14. C2×#14558991C22semidirect
31. #18012673C22semidirect
32. #18012670C22semidirect
33. #18012663C22semidirect
34. #18012663C22semidirect
35. #18012661C22semidirect
39. C2×Q16×C151C22semidirect
41. #103×C151C22semidirect
149. C151#3190semidirect
159. #451D151semidirect
165. C2×Q16C2×D151semidirect
188. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
C2×#180127152
#237525522
#237525402
#237525262
#237524502
#237524442
#237523732
#237523512
C22⋊C8×D1512
#451×C1512
#3190151