Finite Group Databasebeta

← #34080075

Subgroups — #34080075

Order 19328.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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#23752746C211yesmaximal, characteristic, complemented
2#23752594C212yesmaximal, complemented
3#23752566C212yesmaximal, complemented
4#23752431C212yesmaximal, complemented
5#23752424C212yesmaximal, complemented
6#23752368C211yesmaximal, characteristic, complemented
7#23752363C211yesmaximal, characteristic, complemented
8#23752351C211yesmaximal, characteristic, complemented
9#23752346C211yesmaximal, characteristic
10#23752265C211yesmaximal, characteristic, complemented
11C2×#124×C151C211yesmaximal, characteristic, complemented
12C2×#14558994C2212yescomplemented
13C2×#14558992C2212yes—
14C2×#14558991C2212yescomplemented
15C2×#14558989C2212yes—
16#18012733—21no—
17#18012731C2211yescharacteristic, complemented
18#18012727C2211yescharacteristic, complemented
19#18012722—21no—
20#18012718C2211yescharacteristic
21#18012713C2211yescharacteristic
22C4×Dic302C2211yescharacteristic, complemented
23C4×D604C2211yescharacteristic, complemented
24C4×C22⋊D151—21no—
25#18012696—21no—
26C4⋊(C151⋊C8)C2212yescomplemented
27#18012663C2212yescomplemented
28#18012663C2212yescomplemented
29#18012660C2212yes—
30#18012660C2212yes—
31C22⋊(C151⋊C8)C2211yescharacteristic
32C22⋊(C151⋊C8)C2211yescharacteristic
33C4×C151⋊C8C2212yescomplemented
34C22×Q8×C151C2211yescharacteristic
35C22×D4×C151C2211yescharacteristic
36#124×C151—21no—
37#124×C151—21no—
38#124×C151C2212yes—
39#124×C151C2212yes—
40C2×C22⋊C4×C151—21no—
41C2×C22⋊C4×C151—21no—
42C2×C42×C151C2211yescharacteristic
43C2×Dic302C2311yescharacteristic
44C2×D604C2311yescharacteristic
45C2×C22⋊D151—21no—
46C2×C4×D151—21no—
47#14558994—42no—
48#14558992—42no—
49#14558991—42no—
50#14558989—42no—
51C2×C151⋊C8C2312yes—
52C2×C151⋊C8C2312yes—
53C4⋊Dic151C2311yescharacteristic
54C4⋊Dic151C2311yescharacteristic
55Dic151⋊C4—21no—
56Dic151⋊C4—21no—
57Dic151⋊C4—21no—
58Dic151⋊C4—21no—
59C22⋊Dic151—21no—
60(C2×D151)⋊C4—21no—
61(C2×D151)⋊C4—21no—
62(C2×D151)⋊C4—21no—
63(C2×D151)⋊C4—21no—
64C4×Dic151—21no—
65C24×C151—21no—
66C2×Q8×C151—21no—
67C2×Q8×C151—42no—
68C2×Q8×C151C2312yes—
69C2×D4×C151—21no—
70C2×D4×C151—42no—
71C2×D4×C151C2312yes—
72C22×C4×C151—21no—
73C22×C4×C151D411yescharacteristic
74C22×C4×C151D411yescharacteristic
75C22×C4×C151C2311yescharacteristic
76C22⋊C4×C151—22no—
77C22⋊C4×C151—22no—
78C22⋊C4×C151—22no—
79C22⋊C4×C151—22no—
80C42×C151D411yescharacteristic
81C42×C151D411yescharacteristic
82C42×C151C2311yescharacteristic
83C42×C151C2311yescharacteristic
84C22×D151—21no—
85Dic302—22no—
86D604—22no—
87C22⋊D151—42no—
88C2×Dic151—21no—
89C2×Dic151—21no—
90C2×Dic151—21no—
91C4×D151—42no—
92C151⋊C8—22no—
93C151⋊C8—22no—
94C23×C151—22no—
95C23×C151—42no—
96C23×C151—42no—
97C23×C151—42no—
98C23×C151C2×D411yescharacteristic
99Q8×C151—22no—
100Q8×C151—22no—
101Q8×C151—42no—
102D4×C151—22no—
103D4×C151—22no—
104D4×C151—42no—
105C2×C4×C151—22no—
106C2×C4×C151—22no—
107C2×C4×C151—22no—
108C2×C4×C151—41no—
109C2×C4×C151—42no—
110C2×C4×C151C2×D411yescharacteristic
111C2×C4×C151C2×D411yescharacteristic
112C2×C4×C151C2×D411yescharacteristic
113C2×C4×C151C2×D411yescharacteristic
114C2×C4×C151C2×D411yescharacteristic
115C2×C4×C151C2411yescharacteristic
116C22×C151—21no—
117C22×C151—21no—
118C22×C151—42no—
119C22×C151—42no—
120C22×C151—42no—
121C22×C151—84no—
122C22×C151#13512yes—
123C22×C151C22×D411yescharacteristic
124C2×D151—41no—
125C2×D151—41no—
126C2×D151—41no—
127C4×C151—21no—
128C4×C151—21no—
129C4×C151—21no—
130C4×C151—21no—
131C4×C151—21no—
132C4×C151—42no—
133C4×C151H(5,𝔽2)12yes—
134Dic151—41no—
135Dic151—41no—
136Dic151—41no—
137C2×C151—22no—
138C2×C151—82no—
139C2×C151#53511yescharacteristic
140C2×C151C2×#13511yescharacteristic
141C2×C151#57511yescharacteristic
142D151—81no—
143C151#321111yescharacteristic, complemented, Sylow
144#3211—1511nomaximal, Sylow
145#529—1511no—
146C2×#124D15111yescharacteristic, complemented
147#495—1512no—
148#488—1512no—
149#464—1512no—
150#463—1512no—
151#451—1511no—
152#450—1511no—
153#448—1511no—
154#447—1511no—
155#431—1511no—
156C22×Q8C2×D15111yescharacteristic
157C22×D4C2×D15111yescharacteristic
158C2×Q16—1512no—
159C2×SD16—1512no—
160C2×SD16—1512no—
161C2×D8—1512no—
162#126—3021no—
163#125—1511no—
164#124—21no—
165#124—21no—
166#124—1511no—
167#124C2×D15112yes—
168#124C2×D15112yes—
169#123—3021no—
170C22⋊Q8—1511no—
171#121—1511no—
172C4×Q8—1511no—
173C4×D4—3021no—
174C4×D4—1511no—
175#117—3021no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C42C2×D15111yescharacteristic
179C4⋊C8—1512no—
180#103—1512no—
181#103—1512no—
182#102—1512no—
183#102—1512no—
184C22⋊C8—1511no—
185C22⋊C8—1511no—
186C4×C8—1512no—
187C24—21no—
188C2×Q8—21no—
189C2×Q8—42no—
190C2×Q8—1511no—
191C2×Q8C22×D15112yes—
192C2×D4—21no—
193C2×D4—42no—
194C2×D4—3021no—
195C2×D4—1511no—
196C2×D4C22×D15112yes—
197C22×C4—21no—
198C22×C4—3021no—
199C22×C4C22⋊D15111yescharacteristic
200C22×C4C22⋊D15111yescharacteristic
201C22×C4C22×D15111yescharacteristic
202Q16—6042no—
203SD16—6042no—
204SD16—6042no—
205D8—6042no—
206C2×C8—1512no—
207C2×C8—1512no—
208C4⋊C4—3021no—
209C4⋊C4—3021no—
210C4⋊C4—3021no—
211C4⋊C4—3021no—
212C4⋊C4—1511no—
213C4⋊C4—1511no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—3021no—
219C22⋊C4—3021no—
220C22⋊C4—3021no—
221C22⋊C4—3021no—
222C22⋊C4—3021no—
223C42—3021no—
224C42C22⋊D15111yescharacteristic
225C42C22⋊D15111yescharacteristic
226C42C22×D15111yescharacteristic
227C42C22×D15111yescharacteristic
228C23—22no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—3021no—
233C23C2×C22⋊D15111yescharacteristic
234Q8—22no—
235Q8—22no—
236Q8—42no—
237Q8—3022no—
238D4—22no—
239D4—22no—
240D4—42no—
241D4—3022no—
242D4—6042no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—3021no—
249C2×C4—3021no—
250C2×C4—3021no—
251C2×C4—6042no—
252C2×C4C2×C22⋊D15111yescharacteristic
253C2×C4C2×C22⋊D15111yescharacteristic
254C2×C4C2×C22⋊D15111yescharacteristic
255C2×C4C2×C22⋊D15111yescharacteristic
256C2×C4C2×C22⋊D15111yescharacteristic
257C2×C4C23×D15111yescharacteristic
258C8—3022no—
259C8—3022no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—6041no—
267C22—6041no—
268C22—6041no—
269C22#1801275912yes—
270C22C22×C22⋊D15111yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—42no—
277C4—6041no—
278C4—6041no—
279C4—6041no—
280C4#1801278412yes—
281C2—22no—
282C2—82no—
283C2—12081no—
284C2#2375277911yescharacteristic
285C2C2×#1801275911yescharacteristic
286C2#2375301011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#124×C151C2
socleC22×C151C22×D4
prime radical#23752346C2
hypercenterC2×#124D151
hypocenterC151#3211
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #23752746C2semidirect
2. #23752594C2semidirect
3. #23752566C2semidirect
4. #23752431C2semidirect
5. #23752424C2semidirect
6. #23752368C2semidirect
7. #23752363C2semidirect
8. #23752351C2semidirect
10. #23752265C2semidirect
11. C2×#124×C151C2semidirect
12. C2×#14558994C22semidirect
14. C2×#14558991C22semidirect
17. #18012731C22semidirect
18. #18012727C22semidirect
22. C4×Dic302C22semidirect
23. C4×D604C22semidirect
26. C4⋊(C151⋊C8)C22semidirect
27. #18012663C22semidirect
28. #18012663C22semidirect
33. C4×C151⋊C8C22semidirect
143. C151#3211semidirect
146. C2×#124D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237525942
#237525662
#237524312
#237524242
#237523682
#237523632
#237523512
#237523462
#237522652
C2×#124×C1512
#3211151