Finite Group Databasebeta

← #34080801

Subgroups — #34080801

Order 19328.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×SD16×D151C212yesmaximal, complemented
2Q8×D604C211yesmaximal, characteristic, complemented
3#23752847C211yesmaximal, characteristic
4#23752584C211yesmaximal, characteristic, complemented
5#23752440C212yesmaximal, complemented
6#23752418C211yesmaximal, characteristic, complemented
7#23752364C212yesmaximal, complemented
8#23752349C212yesmaximal, complemented
9C4×#14558991C211yesmaximal, characteristic, complemented
10#23752277C211yesmaximal, characteristic, complemented
11#460×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151C2212yescomplemented
13C2×D4×D151—21no—
14C2×D4×D151C2212yes—
15C2×#14558993C2212yes—
16C2×#14558992C2212yescomplemented
17C2×#14558992C2212yescomplemented
18C2×#14558991C2211yescharacteristic
19SD16×D151—28no—
20C2×C8×D151C2212yescomplemented
21#18012739—21no—
22#18012739C2211yescharacteristic, complemented
23#18012719—22no—
24#18012719C2212yescomplemented
25#18012710—21no—
26#18012710C2212yes—
27#18012707—22no—
28C4×D604—21no—
29C4×D604C2211yescharacteristic
30C4×D604C2211yescharacteristic
31#18012670C2211yescharacteristic, complemented
32#18012664C2212yescomplemented
33#18012663C2211yescharacteristic, complemented
34#18012659C2211yescharacteristic
35(C2×D151)⋊C8C2212yescomplemented
36C4×C151⋊C8C2211yescharacteristic, complemented
37C2×SD16×C151C2212yescomplemented
38#127×C151C2211yescharacteristic
39C4×Q8×C151C2211yescharacteristic, complemented
40C4⋊C8×C151C2211yescharacteristic, complemented
41#102×C151C2212yescomplemented
42C23×D151—22no—
43C2×Dic302—22no—
44C2×Dic302C2312yes—
45Q8×D151—24no—
46Q8×D151—42no—
47C2×D604D411yescharacteristic
48C2×D604C2311yescharacteristic
49C2×C22⋊D151—22no—
50C2×C22⋊D151—22no—
51D4×D151—24no—
52D4×D151—42no—
53D4×D151—44no—
54C2×C4×D151—22no—
55C2×C4×D151—21no—
56C2×C4×D151C2312yes—
57#14558993—24no—
58#14558992—24no—
59#14558992—42no—
60#14558991D414yescomplemented
61C2×C151⋊C8C2311yescharacteristic
62C2×C151⋊C8C2311yescharacteristic
63C8×D151—24no—
64C4⋊Dic151—22no—
65C4⋊Dic151—21no—
66C4⋊Dic151—21no—
67C4⋊Dic151D411yescharacteristic
68C4⋊Dic151C2311yescharacteristic
69C22⋊Dic151—22no—
70(C2×D151)⋊C4—22no—
71(C2×D151)⋊C4—21no—
72(C2×D151)⋊C4D412yes—
73C2×Q8×C151C2311yescharacteristic
74C2×D4×C151—21no—
75C2×D4×C151—21no—
76C2×D4×C151C2312yes—
77SD16×C151—24no—
78C2×C8×C151C2312yes—
79C4⋊C4×C151—21no—
80C4⋊C4×C151C2311yescharacteristic
81C42×C151—21no—
82C42×C151C2311yescharacteristic
83C22×D151—21no—
84C22×D151—44no—
85C22×D151—44no—
86C22×D151—82no—
87C22×D151C2×D412yes—
88Dic302—22no—
89Dic302—22no—
90Dic302—44no—
91D604—21no—
92D604SD1614yescomplemented
93D604C2×D412yes—
94C22⋊D151—44no—
95C22⋊D151—44no—
96C2×Dic151—21no—
97C2×Dic151—22no—
98C2×Dic151C2×D412yes—
99C4×D151—22no—
100C4×D151—22no—
101C4×D151—44no—
102C4×D151—42no—
103C151⋊C8—21no—
104C151⋊C8C2×D412yescomplemented
105C23×C151—22no—
106Q8×C151—21no—
107Q8×C151C2×D412yescomplemented
108D4×C151—22no—
109D4×C151—22no—
110D4×C151—42no—
111D4×C151—81no—
112C2×C4×C151—21no—
113C2×C4×C151—21no—
114C2×C4×C151C2×D411yescharacteristic
115C2×C4×C151C2×D411yescharacteristic
116C2×C4×C151C2411yescharacteristic
117C8×C151—22no—
118C22×C151—42no—
119C22×C151—42no—
120C22×C151—42no—
121C22×C151C22×D411yescharacteristic
122C2×D151—22no—
123C2×D151—22no—
124C2×D151—22no—
125C2×D151—41no—
126C2×D151—41no—
127C2×D151—88no—
128C2×D151C2×SD1614yescomplemented
129C4×C151—22no—
130C4×C151—21no—
131C4×C151—41no—
132C4×C151C2×SD1612yescomplemented
133C4×C151C22×D411yescharacteristic
134C4×C151H(5,𝔽2)11yescharacteristic
135Dic151—22no—
136Dic151—42no—
137Dic151—41no—
138C2×C151—82no—
139C2×C151D4211yescharacteristic
140C2×C151C22×SD1611yescharacteristic
141C2×C151#57711yescharacteristic
142D151—24no—
143D151—42no—
144C151D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1511nomaximal, Sylow
146C22×SD16—1512no—
147D4×Q8—1511no—
148D42—1511no—
149#492—1511no—
150#465—1512no—
151#461—1511no—
152#460D15111yescharacteristic, complemented
153#450—1512no—
154#448—1512no—
155C4×SD16—1511no—
156C8×D4—1511no—
157C22×Q8—1512no—
158C22×D4—3021no—
159C22×D4—1512no—
160C2×SD16—3028no—
161C2×SD16—1512no—
162C2×SD16—1512no—
163C2×SD16—1511no—
164C2×SD16—1512no—
165C2×SD16C2×D15112yescomplemented
166C22×C8—1512no—
167C4⋊Q8—3021no—
168C4⋊Q8—1511no—
169#127C2×D15111yescharacteristic
170C22⋊Q8—3022no—
171C22⋊Q8—1512no—
172#121—3021no—
173#121—1512no—
174#120—3022no—
175C4×Q8C2×D15111yescharacteristic, complemented
176C4×D4—3021no—
177C4×D4—1511no—
178C4×D4—1511no—
179#106—1511no—
180C4⋊C8C2×D15111yescharacteristic, complemented
181#103—1511no—
182#103—1512no—
183#102—1511no—
184#102C2×D15112yescomplemented
185C22⋊C8—1512no—
186C4×C8—1511no—
187C24—3022no—
188C2×Q8—3022no—
189C2×Q8—3024no—
190C2×Q8—6042no—
191C2×Q8—1512no—
192C2×Q8C22×D15111yescharacteristic
193C2×D4—21no—
194C2×D4—21no—
195C2×D4—3024no—
196C2×D4—3022no—
197C2×D4—3022no—
198C2×D4—6042no—
199C2×D4—6044no—
200C2×D4—1511no—
201C2×D4—1511no—
202C2×D4C22×D15112yes—
203C22×C4—3022no—
204C22×C4—3021no—
205C22×C4—1512no—
206SD16—24no—
207SD16—3024no—
208SD16—3024no—
209SD16—6042no—
210SD16—1514no—
211C2×C8—3024no—
212C2×C8—1511no—
213C2×C8—1511no—
214C2×C8C22×D15112yes—
215C4⋊C4—21no—
216C4⋊C4—3022no—
217C4⋊C4—3021no—
218C4⋊C4—3021no—
219C4⋊C4—1511no—
220C4⋊C4—1511no—
221C4⋊C4C22×D15111yescharacteristic
222C22⋊C4—3022no—
223C22⋊C4—3022no—
224C22⋊C4—3021no—
225C22⋊C4—1512no—
226C42—21no—
227C42C22×D15111yescharacteristic
228C23—22no—
229C23—3021no—
230C23—6044no—
231C23—6044no—
232C23—1512no—
233C23—12082no—
234Q8—21no—
235Q8—3022no—
236Q8—3022no—
237Q8—6044no—
238Q8D4×D15112yescomplemented
239D4—22no—
240D4—22no—
241D4—42no—
242D4—81no—
243D4—3021no—
244D4—6044no—
245D4—6044no—
246D4—1514no—
247D4—1512no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—3022no—
251C2×C4—3022no—
252C2×C4—3021no—
253C2×C4—3022no—
254C2×C4—6044no—
255C2×C4—6042no—
256C2×C4—1512no—
257C2×C4D4×D15111yescharacteristic
258C2×C4D4×D15111yescharacteristic
259C2×C4C23×D15111yescharacteristic
260C8—22no—
261C8—3021no—
262C8—1512no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—3022no—
267C22—3022no—
268C22—3022no—
269C22—6041no—
270C22—6041no—
271C22—1514no—
272C22—12088no—
273C22C2×D4×D15111yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—3022no—
278C4—6041no—
279C4—6042no—
280C4SD16×D15112yescomplemented
281C4C2×D4×D15111yescharacteristic
282C4#1801278511yescharacteristic
283C2—82no—
284C2—3024no—
285C2—6042no—
286C2#2375284611yescharacteristic
287C2C2×SD16×D15111yescharacteristic
288C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#460×C151C2
socleC22×C151C22×D4
prime radical#23752847C2
hypercenter#460D151
hypocenterC151D4×SD16
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D151C2semidirect
2. Q8×D604C2semidirect
4. #23752584C2semidirect
5. #23752440C2semidirect
6. #23752418C2semidirect
7. #23752364C2semidirect
8. #23752349C2semidirect
9. C4×#14558991C2semidirect
10. #23752277C2semidirect
11. #460×C151C2semidirect
12. C2×Q8×D151C22semidirect
16. C2×#14558992C22semidirect
17. C2×#14558992C22semidirect
20. C2×C8×D151C22semidirect
22. #18012739C22semidirect
24. #18012719C22semidirect
31. #18012670C22semidirect
32. #18012664C22semidirect
33. #18012663C22semidirect
35. (C2×D151)⋊C8C22semidirect
36. C4×C151⋊C8C22semidirect
37. C2×SD16×C151C22semidirect
39. C4×Q8×C151C22semidirect
40. C4⋊C8×C151C22semidirect
41. #102×C151C22semidirect
60. #14558991D4semidirect
92. D604SD16semidirect
104. C151⋊C8C2×D4semidirect
107. Q8×C151C2×D4semidirect
128. C2×D151C2×SD16semidirect
132. C4×C151C2×SD16semidirect
144. C151D4×SD16semidirect
152. #460D151semidirect
165. C2×SD16C2×D151semidirect
175. C4×Q8C2×D151semidirect
180. C4⋊C8C2×D151semidirect
184. #102C2×D151semidirect
238. Q8D4×D151semidirect
280. C4SD16×D151semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1512
Q8×D6042
#237528472
#237525842
#237524402
#237524182
#237523642
#237523492
C4×#145589912
#237522772
#460×C1512
D4×SD16151