Finite Group Databasebeta

← #34079037

Subgroups — #34079037

Order 19328.

458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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×C4⋊C4×D151C211yesmaximal, characteristic, complemented
3#23752545C211yesmaximal, characteristic, complemented
4#23752541C212yesmaximal, complemented
5#23752531C211yesmaximal, characteristic, complemented
6#23752530C211yesmaximal, characteristic, complemented
7#23752527C212yesmaximal, complemented
8#23752253C212yesmaximal, complemented
9#23752212C212yesmaximal, complemented
10#23752174C211yesmaximal, characteristic, complemented
11#484×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic
13C22×C4×D151—21no—
14C22×C4×D151C2211yescharacteristic
15C2×#14558987C2212yes—
16#18012724—21no—
17#18012715C2211yescharacteristic
18#18012714C2211yescharacteristic
19#18012713C2211yescharacteristic
20#18012709—21no—
21#18012701—21no—
22(C22⋊D151)⋊C4—21no—
23#18012697C2211yescharacteristic
24C2×C4⋊Dic151C2211yescharacteristic
25C2×Dic151⋊C4—21no—
26C4⋊C4×D151—21no—
27C4⋊C4×D151—21no—
28C4⋊C4×D151C2212yes—
29C4⋊C4×D151C2212yes—
30#18012672C2212yescomplemented
31#18012671C2212yescomplemented
32#18012670C2212yescomplemented
33#18012663C2212yescomplemented
34#18012661C2212yescomplemented
35#18012659C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic
37(C2×D151)⋊C8C2212yes—
38C22⋊Q8×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic
40#107×C151C2212yescomplemented
41#103×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151D411yescharacteristic
44#14559005—24no—
45C2×D604—21no—
46C2×D604—21no—
47C2×D604C2311yescharacteristic
48C2×C22⋊D151—21no—
49C22×Dic151—21no—
50C22×Dic151D411yescharacteristic
51C2×C4×D151—24no—
52C2×C4×D151—22no—
53C2×C4×D151—22no—
54C2×C4×D151—21no—
55C2×C4×D151—44no—
56C2×C4×D151D411yescharacteristic
57C2×C4×D151D411yescharacteristic
58C2×C4×D151C2311yescharacteristic
59C2×C4×D151C2311yescharacteristic
60#14558987—24no—
61C2×C151⋊C8C2312yes—
62C4⋊Dic151—21no—
63C4⋊Dic151C2312yes—
64C4⋊Dic151C2311yescharacteristic
65Dic151⋊C4—22no—
66Dic151⋊C4—22no—
67Dic151⋊C4—21no—
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×C151C2311yescharacteristic
74C22×C4×C151—21no—
75C22×C4×C151C2311yescharacteristic
76C2×C8×C151C2312yes—
77C4⋊C4×C151—21no—
78C4⋊C4×C151—21no—
79C4⋊C4×C151C2311yescharacteristic
80C4⋊C4×C151C2312yes—
81C22⋊C4×C151—21no—
82C22×D151—22no—
83C22×D151—22no—
84C22×D151—22no—
85C22×D151—21no—
86C22×D151C2×D411yescharacteristic
87C22×D151C2×D411yescharacteristic
88D604—22no—
89D604—42no—
90D604—42no—
91C22⋊D151—42no—
92C2×Dic151—22no—
93C2×Dic151—21no—
94C2×Dic151—22no—
95C2×Dic151—42no—
96C2×Dic151C2×D411yescharacteristic
97C2×Dic151C2×D411yescharacteristic
98C4×D151—22no—
99C4×D151—22no—
100C4×D151—22no—
101C4×D151—44no—
102C4×D151—44no—
103C4×D151—42no—
104C4×D151#4114yes—
105C151⋊C8—22no—
106C23×C151C2×D411yescharacteristic
107Q8×C151—22no—
108C2×C4×C151—22no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—22no—
112C2×C4×C151—42no—
113C2×C4×C151C2×D411yescharacteristic
114C2×C4×C151C2411yescharacteristic
115C8×C151—22no—
116C22×C151—21no—
117C22×C151—21no—
118C22×C151#13712yes—
119C22×C151C22×D411yescharacteristic
120C2×D151—28no—
121C2×D151—21no—
122C2×D151—21no—
123C2×D151—21no—
124C2×D151—21no—
125C2×D151—41no—
126C2×D151—41no—
127C2×D151—41no—
128C2×D151#12312yes—
129C2×D151AGL(1,ℤ/8)12yes—
130C4×C151—21no—
131C4×C151—41no—
132C4×C151—42no—
133C4×C151—41no—
134C4×C151C2×#4112yes—
135Dic151—21no—
136Dic151—42no—
137Dic151—41no—
138Dic151#12312yes—
139C2×C151—22no—
140C2×C151C2×#12311yescharacteristic
141C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
142C2×C151C2×#13711yescharacteristic
143D151—22no—
144D151—22no—
145D151—81no—
146C151#309211yescharacteristic, complemented, Sylow
147#3092—1511nomaximal, Sylow
148#525—1511no—
149C22×C4⋊C4—1511no—
150#484—1511no—
151#484D15111yescharacteristic, complemented
152#483—1512no—
153#481—1511no—
154#481—1511no—
155#480—1512no—
156#428—1512no—
157#417—1512no—
158#407—1511no—
159C2×#41—1511no—
160C23×C4—3021no—
161C23×C4—1511no—
162C2×M16—1512no—
163#123—3021no—
164C22⋊Q8—1511no—
165C22⋊Q8C2×D15111yescharacteristic
166#121—1511no—
167#121—1511no—
168#120—3021no—
169C4×D4—3021no—
170C4×D4—3021no—
171#117—1511no—
172C2×C4⋊C4—3021no—
173C2×C4⋊C4—3021no—
174C2×C4⋊C4—3021no—
175C2×C4⋊C4—1511no—
176C2×C4⋊C4—1512no—
177C2×C4⋊C4—1512no—
178C2×C4⋊C4C2×D15111yescharacteristic
179#107—1512no—
180#107C2×D15112yescomplemented
181#106—1512no—
182#106—1512no—
183#103—1512no—
184#103C2×D15112yescomplemented
185#102—1512no—
186#102—1512no—
187C22⋊C8—1511no—
188C22⋊C8—1512no—
189C22⋊C8C2×D15111yescharacteristic
190C24—1511no—
191#41—3024no—
192C2×Q8C22×D15111yescharacteristic
193C2×D4—3021no—
194C2×D4—3021no—
195C2×D4—3021no—
196C2×D4—1511no—
197C22×C4—21no—
198C22×C4—3024no—
199C22×C4—3022no—
200C22×C4—3022no—
201C22×C4—3021no—
202C22×C4—3021no—
203C22×C4—6044no—
204C22×C4—1511no—
205C22×C4—1511no—
206C22×C4—1511no—
207C22×C4—1511no—
208C22×C4—1511no—
209C22×C4C22×D15111yescharacteristic
210M16—3024no—
211C2×C8—1512no—
212C2×C8C22×D15112yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—3022no—
216C4⋊C4—3022no—
217C4⋊C4—3021no—
218C4⋊C4—3021no—
219C4⋊C4—1512no—
220C4⋊C4—1511no—
221C4⋊C4C22×D15112yes—
222C4⋊C4C22×D15111yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—3021no—
225C22⋊C4—3021no—
226C22⋊C4—3021no—
227C22⋊C4—3021no—
228C42—3021no—
229C23—3022no—
230C23—3022no—
231C23—3022no—
232C23—3021no—
233C23—1511no—
234C23—1511no—
235C23D4×D15111yescharacteristic
236Q8—22no—
237D4—3022no—
238D4—6042no—
239D4—6042no—
240D4—6042no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—3022no—
247C2×C4—3022no—
248C2×C4—3022no—
249C2×C4—3022no—
250C2×C4—3021no—
251C2×C4—3022no—
252C2×C4—6044no—
253C2×C4—6044no—
254C2×C4—6042no—
255C2×C4—6042no—
256C2×C4—1511no—
257C2×C4—1511no—
258C2×C4—1514no—
259C2×C4D4×D15111yescharacteristic
260C2×C4C23×D15111yescharacteristic
261C8—22no—
262C8—3022no—
263C22—21no—
264C22—21no—
265C22—3028no—
266C22—3021no—
267C22—3021no—
268C22—3021no—
269C22—3021no—
270C22—6041no—
271C22—6041no—
272C22—6041no—
273C22—1512no—
274C22—1512no—
275C22#1801277112yes—
276C22C2×D4×D15111yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—41no—
281C4—3021no—
282C4—6042no—
283C4—6041no—
284C4—1512no—
285C4#41×D15112yes—
286C2—22no—
287C2—3022no—
288C2—3022no—
289C2—12081no—
290C2#123×D15111yescharacteristic
291C2AGL(1,ℤ/8)×D15111yescharacteristic
292C2C2×#1801277111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#484×C151C2
socleC22×C151C22×D4
prime radical#23752725C2
hypercenter#484D151
hypocenterC151#3092
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D151C2semidirect
3. #23752545C2semidirect
4. #23752541C2semidirect
5. #23752531C2semidirect
6. #23752530C2semidirect
7. #23752527C2semidirect
8. #23752253C2semidirect
9. #23752212C2semidirect
10. #23752174C2semidirect
11. #484×C151C2semidirect
30. #18012672C22semidirect
31. #18012671C22semidirect
32. #18012670C22semidirect
33. #18012663C22semidirect
34. #18012661C22semidirect
35. #18012659C22semidirect
40. #107×C151C22semidirect
41. #103×C151C22semidirect
146. C151#3092semidirect
151. #484D151semidirect
180. #107C2×D151semidirect
184. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
C2×C4⋊C4×D1512
#237525452
#237525412
#237525312
#237525302
#237525272
#237522532
#237522122
#237521742
#484×C1512
#3092151