Finite Group Databasebeta

← #34078386

Subgroups — #34078386

Order 19328.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012785C211yesmaximal, characteristic
2C22×#14558991C211yesmaximal, characteristic, complemented
3#23752786C211yesmaximal, characteristic, complemented
4#23752373C214yesmaximal, complemented
5#23752361C214yesmaximal, complemented
6#23752218C211yesmaximal, characteristic, complemented
7#23752208C211yesmaximal, characteristic, complemented
8#23752180C211yesmaximal, characteristic, complemented
9C2×#137×C151C211yesmaximal, characteristic, complemented
10#18012785—24no—
11#18012785—24no—
12C2×#14559005C2212yes—
13C2×#14559004—21no—
14C2×#14559004C2211yescharacteristic
15C22×D604—21no—
16C22×D604C2211yescharacteristic
17C2×D4×D151—22no—
18C2×D4×D151C2212yes—
19C2×#14558991—24no—
20C2×#14558991C2214yescomplemented
21C22×C151⋊C8C2211yescharacteristic, complemented
22#18012737—21no—
23#18012728—21no—
24#18012722—22no—
25#18012715C2214yescomplemented
26#18012698C2211yescharacteristic, complemented
27#18012663C2212yescomplemented
28#18012661C2214yescomplemented
29#18012660C2212yescomplemented
30(C2×D151)⋊C8C2214yescomplemented
31C2×#41×C151C2211yescharacteristic
32C22×Q8×C151C2211yescharacteristic, complemented
33#137×C151—24no—
34C2×Q16×C151C2212yescomplemented
35C2×SD16×C151C2212yescomplemented
36C2×M16×C151C2211yescharacteristic, complemented
37C23×D151—22no—
38C23×D151—21no—
39#14559005—24no—
40#14559005—24no—
41#14559004—28no—
42#14559004—22no—
43#14559004—22no—
44C2×Dic302D411yescharacteristic
45C2×D604—28no—
46C2×D604—22no—
47C2×D604—21no—
48C2×D604—22no—
49C2×D604D411yescharacteristic
50C2×D604D414yes—
51C2×D604C2312yes—
52C2×C22⋊D151—22no—
53C2×C22⋊D151D412yes—
54D4×D151—216no—
55D4×D151—24no—
56D4×D151—24no—
57C2×C4×D151—22no—
58C2×C4×D151C2312yes—
59#14558991—28no—
60C2×C151⋊C8—22no—
61C2×C151⋊C8C2312yes—
62C4⋊Dic151C2312yes—
63Dic151⋊C4—24no—
64C22⋊Dic151—21no—
65(C2×D151)⋊C4—24no—
66C4×Dic151—21no—
67#41×C151—22no—
68#41×C151D414yes—
69C2×Q8×C151—21no—
70C2×Q8×C151—22no—
71C2×Q8×C151—22no—
72C2×Q8×C151C2312yes—
73C2×Q8×C151C2311yescharacteristic
74C2×D4×C151—21no—
75C2×D4×C151C2311yescharacteristic
76C22×C4×C151—21no—
77C22×C4×C151—21no—
78C22×C4×C151C2311yescharacteristic
79Q16×C151—24no—
80SD16×C151—24no—
81M16×C151—22no—
82C2×C8×C151C2312yes—
83C22×D151—22no—
84C22×D151—28no—
85C22×D151—24no—
86C22×D151—84no—
87C22×D151—82no—
88C22×D151C2×D412yes—
89Dic302—22no—
90D604—28no—
91D604—22no—
92D604—24no—
93D604—22no—
94D604C2×D414yes—
95C22⋊D151—28no—
96C22⋊D151—24no—
97C2×Dic151—22no—
98C2×Dic151C2×D412yes—
99C4×D151—28no—
100C4×D151—22no—
101C4×D151—22no—
102C151⋊C8—22no—
103C23×C151—21no—
104C23×C151C2×D411yescharacteristic
105Q8×C151—21no—
106Q8×C151—22no—
107Q8×C151—22no—
108Q8×C151—42no—
109Q8×C151C2×D412yes—
110D4×C151—24no—
111D4×C151—21no—
112D4×C151C2×D412yes—
113C2×C4×C151—21no—
114C2×C4×C151—24no—
115C2×C4×C151—22no—
116C2×C4×C151—42no—
117C2×C4×C151C2×D411yescharacteristic
118C2×C4×C151C2×D412yes—
119C2×C4×C151C2×D412yes—
120C2×C4×C151C2411yescharacteristic
121C8×C151—22no—
122C22×C151—22no—
123C22×C151—22no—
124C22×C151—42no—
125C22×C151#12012yes—
126C22×C151C22×D411yescharacteristic
127C2×D151—22no—
128C2×D151—24no—
129C2×D151—24no—
130C2×D151—44no—
131C2×D151—84no—
132C2×D151—88no—
133C4×C151—22no—
134C4×C151—42no—
135C4×C151#12012yes—
136C4×C151C22×D411yescharacteristic
137C4×C151C22×D411yescharacteristic
138Dic151—22no—
139Dic151—42no—
140C2×C151—22no—
141C2×C151—42no—
142C2×C151C2×#12011yescharacteristic
143C2×C151#57712yes—
144D151—42no—
145D151—44no—
146C151#300911yescharacteristic, complemented, Sylow
147#3009—1511nomaximal, Sylow
148C2×H(5,𝔽2)—1511no—
149C2×#137D15111yescharacteristic, complemented
150C22×SD16—1511no—
151#536—1511no—
152#452—1514no—
153#450—1514no—
154#418—1511no—
155#416—1511no—
156#408—1511no—
157H(5,𝔽2)—3024no—
158H(5,𝔽2)—3024no—
159C2×#41—3021no—
160C2×#41—1512no—
161C2×#41—1511no—
162C2×#41C2×D15111yescharacteristic
163C22×Q8C2×D15111yescharacteristic, complemented
164C22×D4—3021no—
165C22×D4—3022no—
166C22×D4—1512no—
167C22×D4—1511no—
168#137—24no—
169C2×Q16C2×D15112yescomplemented
170C2×SD16—3024no—
171C2×SD16—1514no—
172C2×SD16C2×D15112yescomplemented
173C2×M16C2×D15111yescharacteristic, complemented
174C22×C8—1511no—
175C4⋊Q8—3021no—
176#124—3021no—
177#123—3022no—
178C22⋊Q8—1514no—
179#117—1511no—
180#103—1512no—
181#102—1512no—
182#102—1514no—
183C22⋊C8—1514no—
184C24—3022no—
185C24—3021no—
186#41—22no—
187#41—3028no—
188#41—3024no—
189#41—3024no—
190#41—3022no—
191#41—3022no—
192#41C22⋊D15114yes—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—1511no—
197C2×Q8C22×D15112yes—
198C2×Q8C22×D15111yescharacteristic
199C2×D4—21no—
200C2×D4—3028no—
201C2×D4—3022no—
202C2×D4—30216no—
203C2×D4—3024no—
204C2×D4—3024no—
205C2×D4—3022no—
206C2×D4—3021no—
207C2×D4—3022no—
208C2×D4—1512no—
209C2×D4—1511no—
210C2×D4—1514no—
211C2×D4—1512no—
212C2×D4C22×D15111yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—3022no—
216C22×C4—1512no—
217C22×C4C22×D15111yescharacteristic
218Q16—24no—
219SD16—24no—
220SD16—3028no—
221M16—22no—
222C2×C8—3022no—
223C2×C8—1512no—
224C2×C8C22×D15112yes—
225C4⋊C4—3024no—
226C4⋊C4—1512no—
227C22⋊C4—3024no—
228C22⋊C4—3021no—
229C42—3021no—
230C23—21no—
231C23—3028no—
232C23—3022no—
233C23—3024no—
234C23—1512no—
235C23—12082no—
236C23—12084no—
237C23D4×D15111yescharacteristic
238Q8—21no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—3022no—
243Q8C2×C22⋊D15112yes—
244D4—24no—
245D4—21no—
246D4—3028no—
247D4—3028no—
248D4—3024no—
249D4—3022no—
250D4—3024no—
251D4—3022no—
252D4—1514no—
253D4C2×C22⋊D15112yes—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—3028no—
259C2×C4—3022no—
260C2×C4—3022no—
261C2×C4—3022no—
262C2×C4—1512no—
263C2×C4D4×D15111yescharacteristic
264C2×C4D4×D15112yes—
265C2×C4C2×C22⋊D15112yes—
266C2×C4C23×D15111yescharacteristic
267C8—22no—
268C8—3022no—
269C22—22no—
270C22—22no—
271C22—42no—
272C22—3024no—
273C22—3022no—
274C22—3024no—
275C22—6044no—
276C22—12084no—
277C22—12088no—
278C22#1801270712yes—
279C22C2×D4×D15111yescharacteristic
280C4—22no—
281C4—42no—
282C4—3022no—
283C4—6042no—
284C4#1801270712yes—
285C4C2×D4×D15111yescharacteristic
286C4C22×C22⋊D15111yescharacteristic
287C2—22no—
288C2—42no—
289C2—6042no—
290C2—6044no—
291C2C2×#1801270711yescharacteristic
292C2#2375302112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#137×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012785C2
hypercenterC2×#137D151
hypocenterC151#3009
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C22×#14558991C2semidirect
3. #23752786C2semidirect
4. #23752373C2semidirect
5. #23752361C2semidirect
6. #23752218C2semidirect
7. #23752208C2semidirect
8. #23752180C2semidirect
9. C2×#137×C151C2semidirect
20. C2×#14558991C22semidirect
21. C22×C151⋊C8C22semidirect
25. #18012715C22semidirect
26. #18012698C22semidirect
27. #18012663C22semidirect
28. #18012661C22semidirect
29. #18012660C22semidirect
30. (C2×D151)⋊C8C22semidirect
32. C22×Q8×C151C22semidirect
34. C2×Q16×C151C22semidirect
35. C2×SD16×C151C22semidirect
36. C2×M16×C151C22semidirect
146. C151#3009semidirect
149. C2×#137D151semidirect
163. C22×Q8C2×D151semidirect
169. C2×Q16C2×D151semidirect
172. C2×SD16C2×D151semidirect
173. C2×M16C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127852
C22×#145589912
#237527862
#237523732
#237523612
#237522182
#237522082
#237521802
C2×#137×C1512
#3009151