Finite Group Databasebeta

← #34078385

Subgroups — #34078385

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
2C2×#18012770C211yesmaximal, characteristic, complemented
3C22×#14558991C211yesmaximal, characteristic, complemented
4#23752372C214yesmaximal, complemented
5#23752362C214yesmaximal, complemented
6#23752216C211yesmaximal, characteristic, complemented
7#23752206C211yesmaximal, characteristic, complemented
8#23752179C211yesmaximal, characteristic, complemented
9#536×C151C211yesmaximal, characteristic, complemented
10#18012785—24no—
11#18012785—24no—
12C2×#14559005—21no—
13C2×#14559004C2212yes—
14C2×#14559004C2211yescharacteristic
15C22×D604C2212yes—
16C22×D604C2211yescharacteristic
17C2×D4×D151—22no—
18C2×D4×D151—21no—
19#18012770—24no—
20C2×#14558994C2212yescomplemented
21C2×#14558991—24no—
22C2×#14558991C2214yescomplemented
23C2×#14558991C2212yescomplemented
24C2×#14558988C2211yescharacteristic, complemented
25C22×C151⋊C8C2211yescharacteristic, complemented
26#18012662C2212yescomplemented
27#18012659C2212yescomplemented
28#18012659C2214yescomplemented
29C22⋊(C151⋊C8)C2214yescomplemented
30C2×#41×C151C2211yescharacteristic
31C22×Q8×C151C2211yescharacteristic, complemented
32C4⋊Q8×C151—21no—
33#124×C151—21no—
34#123×C151—22no—
35C22⋊Q8×C151C2214yescomplemented
36#117×C151C2211yescharacteristic, complemented
37C23×D151—22no—
38C23×D151—21no—
39#14559005—28no—
40#14559004—24no—
41#14559004—24no—
42#14559004—22no—
43#14559004D414yes—
44C2×Dic302C2311yescharacteristic
45C2×D604—24no—
46C2×D604—24no—
47C2×D604—22no—
48C2×D604—21no—
49C2×D604—22no—
50C2×D604D414yes—
51C2×D604C2311yescharacteristic
52C2×D604C2312yes—
53C2×C22⋊D151—22no—
54C2×C22⋊D151—21no—
55D4×D151—216no—
56D4×D151—28no—
57C2×C4×D151—22no—
58C2×C4×D151—21no—
59#14558994—24no—
60#14558991—28no—
61#14558991—24no—
62#14558988—22no—
63C2×C151⋊C8—22no—
64C2×C151⋊C8C2312yes—
65C2×C151⋊C8C2312yes—
66#41×C151—22no—
67#41×C151—22no—
68C2×Q8×C151—21no—
69C2×Q8×C151—22no—
70C2×Q8×C151—22no—
71C2×Q8×C151D411yescharacteristic
72C2×Q8×C151C2312yes—
73C2×D4×C151D412yes—
74C2×D4×C151D411yescharacteristic
75C22×C4×C151—21no—
76C22×C4×C151C2312yes—
77C22×C4×C151C2311yescharacteristic
78C4⋊C4×C151—24no—
79C4⋊C4×C151C2312yes—
80C22⋊C4×C151—21no—
81C22⋊C4×C151—24no—
82C42×C151—21no—
83C22×D151—22no—
84C22×D151—21no—
85C22×D151—28no—
86C22×D151—24no—
87C22×D151—82no—
88C22×D151—84no—
89Dic302—21no—
90Dic302C2×D412yes—
91D604—28no—
92D604—24no—
93D604—22no—
94D604—21no—
95D604C2×D412yes—
96D604C2×D414yes—
97C22⋊D151—28no—
98C22⋊D151—24no—
99C2×Dic151—21no—
100C4×D151—28no—
101C4×D151—24no—
102C151⋊C8—22no—
103C151⋊C8—22no—
104C23×C151C2×D412yes—
105C23×C151C2×D411yescharacteristic
106Q8×C151—22no—
107Q8×C151—22no—
108Q8×C151—22no—
109Q8×C151—42no—
110D4×C151—24no—
111D4×C151—22no—
112C2×C4×C151—22no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151—22no—
116C2×C4×C151—42no—
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2×D412yes—
119C2×C4×C151C2×D412yes—
120C2×C4×C151C2×D411yescharacteristic
121C2×C4×C151C2411yescharacteristic
122C22×C151—22no—
123C22×C151—22no—
124C22×C151—24no—
125C22×C151#12012yes—
126C22×C151C22×D411yescharacteristic
127C2×D151—24no—
128C2×D151—22no—
129C2×D151—44no—
130C2×D151—42no—
131C2×D151—84no—
132C2×D151—88no—
133C4×C151—22no—
134C4×C151—42no—
135C4×C151—42no—
136C4×C151#12012yes—
137C4×C151C22×D411yescharacteristic
138C4×C151C22×D411yescharacteristic
139Dic151—22no—
140C2×C151—22no—
141C2×C151—42no—
142C2×C151C2×#12011yescharacteristic
143C2×C151#57712yes—
144D151—44no—
145D151—42no—
146C151#300911yescharacteristic, complemented, Sylow
147#3009—1511nomaximal, Sylow
148C2×H(5,𝔽2)—1511no—
149C2×#137—1511no—
150C22×SD16—1511no—
151#536D15111yescharacteristic, complemented
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—3022no—
165C22×D4—3021no—
166C22×D4—1512no—
167C22×D4—1511no—
168#137—3024no—
169C2×Q16—1512no—
170C2×SD16—3024no—
171C2×SD16—1514no—
172C2×SD16—1512no—
173C2×M16—1511no—
174C22×C8—1511no—
175C4⋊Q8—21no—
176#124—21no—
177#123—22no—
178C22⋊Q8C2×D15114yescomplemented
179#117C2×D15111yescharacteristic, complemented
180#103—1512no—
181#102—1512no—
182#102—1514no—
183C22⋊C8—1514no—
184C24—3022no—
185C24—3021no—
186#41—22no—
187#41—22no—
188#41—3024no—
189#41—3024no—
190#41—3028no—
191#41—3022no—
192#41—1514no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—1511no—
197C2×Q8C22⋊D15111yescharacteristic
198C2×Q8C22×D15112yes—
199C2×D4—3024no—
200C2×D4—3024no—
201C2×D4—30216no—
202C2×D4—3028no—
203C2×D4—3022no—
204C2×D4—3021no—
205C2×D4—3022no—
206C2×D4—3022no—
207C2×D4—3021no—
208C2×D4—1514no—
209C2×D4—1511no—
210C2×D4—1512no—
211C2×D4C22⋊D15112yes—
212C2×D4C22⋊D15111yescharacteristic
213C22×C4—21no—
214C22×C4—3022no—
215C22×C4—3021no—
216C22×C4C22×D15112yes—
217C22×C4C22×D15111yescharacteristic
218Q16—3024no—
219SD16—3028no—
220SD16—3024no—
221M16—3022no—
222C2×C8—3022no—
223C2×C8—1512no—
224C2×C8—1512no—
225C4⋊C4—24no—
226C4⋊C4C22×D15112yes—
227C22⋊C4—21no—
228C22⋊C4—24no—
229C42—21no—
230C23—3028no—
231C23—3022no—
232C23—3021no—
233C23—3024no—
234C23—12082no—
235C23—12084no—
236C23C2×C22⋊D15112yes—
237C23C2×C22⋊D15111yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—3021no—
243Q8—1512no—
244D4—24no—
245D4—22no—
246D4—3028no—
247D4—3028no—
248D4—3024no—
249D4—3024no—
250D4—3022no—
251D4—3021no—
252D4—1512no—
253D4—1514no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—3028no—
260C2×C4—3021no—
261C2×C4—3024no—
262C2×C4D4×D15112yes—
263C2×C4D4×D15112yes—
264C2×C4C2×C22⋊D15112yes—
265C2×C4C2×C22⋊D15111yescharacteristic
266C2×C4C23×D15111yescharacteristic
267C8—3022no—
268C8—3022no—
269C22—22no—
270C22—24no—
271C22—22no—
272C22—3024no—
273C22—3022no—
274C22—6044no—
275C22—6042no—
276C22—12084no—
277C22—12088no—
278C22#1801270712yes—
279C22C22×C22⋊D15111yescharacteristic
280C4—22no—
281C4—42no—
282C4—42no—
283C4—3022no—
284C4#1801270712yes—
285C4C2×D4×D15111yescharacteristic
286C4C2×D4×D15111yescharacteristic
287C2—22no—
288C2—42no—
289C2—6044no—
290C2—6042no—
291C2C2×#1801270711yescharacteristic
292C2#2375302012yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#536×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012785C2
hypercenter#536D151
hypocenterC151#3009
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#18012770C2semidirect
3. C22×#14558991C2semidirect
4. #23752372C2semidirect
5. #23752362C2semidirect
6. #23752216C2semidirect
7. #23752206C2semidirect
8. #23752179C2semidirect
9. #536×C151C2semidirect
20. C2×#14558994C22semidirect
22. C2×#14558991C22semidirect
23. C2×#14558991C22semidirect
24. C2×#14558988C22semidirect
25. C22×C151⋊C8C22semidirect
26. #18012662C22semidirect
27. #18012659C22semidirect
28. #18012659C22semidirect
29. C22⋊(C151⋊C8)C22semidirect
31. C22×Q8×C151C22semidirect
35. C22⋊Q8×C151C22semidirect
36. #117×C151C22semidirect
146. C151#3009semidirect
151. #536D151semidirect
163. C22×Q8C2×D151semidirect
178. C22⋊Q8C2×D151semidirect
179. #117C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127852
C2×#180127702
C22×#145589912
#237523722
#237523622
#237522162
#237522062
#237521792
#536×C1512
#3009151