Finite Group Databasebeta

← #34077108

Subgroups — #34077108

Order 19328.

712 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 125 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×#18012709C212yesmaximal, complemented
2#23752141C212yesmaximal, complemented
3#23752130C212yesmaximal, complemented
4#23752129C212yesmaximal, complemented
5#23752127C212yesmaximal, complemented
6#23752122C212yesmaximal, complemented
7#23752121C211yesmaximal, characteristic, complemented
8#23752067C211yesmaximal, characteristic, complemented
9#397×C151C211yesmaximal, characteristic, complemented
10C24×D151C2211yescharacteristic
11C22×D604C2212yes—
12C22×D604C2212yes—
13C22×D604C2211yescharacteristic, complemented
14C22×C22⋊D151C2212yes—
15#18012709—28no—
16C2×Dic151⋊C4C2212yescomplemented
17C2×C22⋊Dic151C2211yescharacteristic
18C2×(C2×D151)⋊C4C2212yes—
19C2×(C2×D151)⋊C4C2212yes—
20C2×(C2×D151)⋊C4C2212yes—
21C2×(C2×D151)⋊C4C2212yes—
22C2×(C2×D151)⋊C4C2212yescomplemented
23C2×(C2×D151)⋊C4C2212yescomplemented
24C2×(C2×D151)⋊C4C2212yescomplemented
25C151⋊#95C2211yescharacteristic, complemented
26C151⋊#95C2212yescomplemented
27C2×C4⋊C4×C151C2211yescharacteristic, complemented
28C2×C22⋊C4×C151C2212yes—
29C2×C22⋊C4×C151C2211yescharacteristic
30#95×C151C2212yescomplemented
31#95×C151C2211yescharacteristic, complemented
32C23×D151—41no—
33C23×D151—42no—
34C23×D151—42no—
35C23×D151—41no—
36C23×D151D414yescomplemented
37C23×D151C2312yes—
38C23×D151C2312yes—
39C2×D604—24no—
40C2×D604—24no—
41C2×D604—42no—
42C2×D604—42no—
43C2×D604—42no—
44C2×D604—42no—
45C2×D604—42no—
46C2×D604—41no—
47C2×C22⋊D151—24no—
48C2×C22⋊D151—42no—
49C2×C22⋊D151—42no—
50C22×Dic151C2312yes—
51C22×Dic151C2312yes—
52Dic151⋊C4—42no—
53C22⋊Dic151—41no—
54(C2×D151)⋊C4—24no—
55(C2×D151)⋊C4—24no—
56(C2×D151)⋊C4—42no—
57(C2×D151)⋊C4—42no—
58(C2×D151)⋊C4—42no—
59(C2×D151)⋊C4—42no—
60(C2×D151)⋊C4—42no—
61C24×C151C2311yescharacteristic
62C22×C4×C151C2311yescharacteristic
63C22×C4×C151C2311yescharacteristic
64C22×C4×C151C2312yes—
65C22×C4×C151C2312yes—
66C4⋊C4×C151—41no—
67C22⋊C4×C151—24no—
68C22⋊C4×C151—41no—
69C22×D151—22no—
70C22×D151—22no—
71C22×D151—22no—
72C22×D151—22no—
73C22×D151—22no—
74C22×D151—22no—
75C22×D151—22no—
76C22×D151—22no—
77C22×D151—22no—
78C22×D151—22no—
79C22×D151—22no—
80C22×D151—22no—
81C22×D151—22no—
82C22×D151—44no—
83C22×D151—48no—
84C22×D151—44no—
85C22×D151—48no—
86C22×D151—44no—
87C22×D151C2×D414yes—
88D604—48no—
89D604—48no—
90D604—44no—
91C22⋊D151—48no—
92C2×Dic151—22no—
93C2×Dic151—22no—
94C2×Dic151—22no—
95C2×Dic151—22no—
96C2×Dic151—22no—
97C2×Dic151—22no—
98C23×C151—21no—
99C23×C151—22no—
100C23×C151—22no—
101C23×C151—21no—
102C23×C151C2×D412yes—
103C23×C151C2411yescharacteristic
104C2×C4×C151—22no—
105C2×C4×C151—22no—
106C2×C4×C151—22no—
107C2×C4×C151—22no—
108C2×C4×C151—22no—
109C2×C4×C151—22no—
110C2×C4×C151—22no—
111C2×C4×C151—21no—
112C2×C4×C151—22no—
113C2×C4×C151—21no—
114C22×C151—24no—
115C22×C151—22no—
116C22×C151—41no—
117C22×C151—42no—
118C22×C151—41no—
119C22×C151C22×D411yescharacteristic
120C22×C151H(5,𝔽2)11yescharacteristic
121C22×C151H(5,𝔽2)11yescharacteristic
122C22×C151H(5,𝔽2)12yes—
123C22×C151H(5,𝔽2)12yes—
124C2×D151—24no—
125C2×D151—24no—
126C2×D151—24no—
127C2×D151—416no—
128C2×D151—42no—
129C2×D151—42no—
130C2×D151—42no—
131C2×D151—42no—
132C2×D151—42no—
133C2×D151—42no—
134C2×D151—42no—
135C2×D151—42no—
136C2×D151—42no—
137C2×D151—42no—
138C2×D151—42no—
139C4×C151—42no—
140C4×C151—42no—
141C4×C151—41no—
142C4×C151—41no—
143Dic151—42no—
144Dic151—42no—
145C2×C151—42no—
146C2×C151#53411yescharacteristic
147C2×C151#53412yes—
148C2×C151#56011yescharacteristic
149C2×C151#56012yes—
150C2×C151H(3,𝔽4)11yescharacteristic
151D151—44no—
152D151—82no—
153C151#281211yescharacteristic, complemented, Sylow
154#2812—1511nomaximal, Sylow
155C2×#120—1512no—
156#397—1512no—
157#397D15111yescharacteristic, complemented
158#394—1512no—
159#394—1512no—
160#394—1512no—
161#392—1511no—
162#392—1512no—
163#379—1511no—
164C25—1511no—
165C22×D4—1512no—
166C22×D4—1512no—
167C22×D4—1512no—
168C22×D4—1511no—
169#120—3028no—
170C2×C4⋊C4—1512no—
171C2×C4⋊C4C2×D15111yescharacteristic, complemented
172C2×C22⋊C4—1512no—
173C2×C22⋊C4—1512no—
174C2×C22⋊C4—1511no—
175C2×C22⋊C4—1512no—
176C2×C22⋊C4—1512no—
177C2×C22⋊C4—1512no—
178C2×C22⋊C4—1512no—
179C2×C22⋊C4—1512no—
180C2×C22⋊C4C2×D15112yes—
181C2×C22⋊C4C2×D15111yescharacteristic
182#95—1511no—
183#95—1512no—
184#95C2×D15112yescomplemented
185#95C2×D15111yescharacteristic, complemented
186C24—6041no—
187C24—6041no—
188C24—6042no—
189C24—6042no—
190C24—1512no—
191C24—1512no—
192C24—1514no—
193C24C22×D15111yescharacteristic
194C2×D4—3024no—
195C2×D4—3024no—
196C2×D4—3024no—
197C2×D4—6041no—
198C2×D4—6042no—
199C2×D4—6042no—
200C2×D4—6042no—
201C2×D4—6042no—
202C2×D4—6042no—
203C2×D4—6042no—
204C2×D4—6042no—
205C22×C4—1512no—
206C22×C4—1512no—
207C22×C4C22×D15111yescharacteristic
208C22×C4C22×D15112yes—
209C22×C4C22×D15112yes—
210C22×C4C22×D15111yescharacteristic
211C4⋊C4—41no—
212C4⋊C4—6042no—
213C22⋊C4—24no—
214C22⋊C4—41no—
215C22⋊C4—3024no—
216C22⋊C4—3024no—
217C22⋊C4—6042no—
218C22⋊C4—6042no—
219C22⋊C4—6042no—
220C22⋊C4—6042no—
221C22⋊C4—6042no—
222C22⋊C4—6041no—
223C23—21no—
224C23—21no—
225C23—22no—
226C23—22no—
227C23—3022no—
228C23—3022no—
229C23—3022no—
230C23—3022no—
231C23—3022no—
232C23—3022no—
233C23—3022no—
234C23—3022no—
235C23—3022no—
236C23—3022no—
237C23—3022no—
238C23—3022no—
239C23—3022no—
240C23—6044no—
241C23—6048no—
242C23—6044no—
243C23—6048no—
244C23—6044no—
245C23—1514no—
246C23D4×D15112yes—
247C23C23×D15111yescharacteristic
248D4—6048no—
249D4—6048no—
250D4—6044no—
251D4—6048no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—3022no—
263C2×C4—3022no—
264C2×C4—3022no—
265C2×C4—3022no—
266C2×C4—3022no—
267C2×C4—3022no—
268C22—22no—
269C22—24no—
270C22—41no—
271C22—42no—
272C22—41no—
273C22—3024no—
274C22—3024no—
275C22—3024no—
276C22—60416no—
277C22—6042no—
278C22—6042no—
279C22—6042no—
280C22—6042no—
281C22—6042no—
282C22—6042no—
283C22—6042no—
284C22—6042no—
285C22—6042no—
286C22—6042no—
287C22—6042no—
288C22C2×D4×D15111yescharacteristic
289C22#1801278411yescharacteristic
290C22#1801278511yescharacteristic
291C22#1801278512yes—
292C22#1801278512yes—
293C4—42no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—6042no—
298C4—6042no—
299C2—42no—
300C2—6044no—
301C2—12082no—
302C2#2375277011yescharacteristic
303C2#2375277312yes—
304C2#2375295211yescharacteristic
305C2#2375295312yes—
306C2#2375295411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#397×C151C2
hypercenter#397D151
hypocenterC151#2812
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#18012709C2semidirect
2. #23752141C2semidirect
3. #23752130C2semidirect
4. #23752129C2semidirect
5. #23752127C2semidirect
6. #23752122C2semidirect
7. #23752121C2semidirect
8. #23752067C2semidirect
9. #397×C151C2semidirect
13. C22×D604C22semidirect
16. C2×Dic151⋊C4C22semidirect
22. C2×(C2×D151)⋊C4C22semidirect
23. C2×(C2×D151)⋊C4C22semidirect
24. C2×(C2×D151)⋊C4C22semidirect
25. C151⋊#95C22semidirect
26. C151⋊#95C22semidirect
27. C2×C4⋊C4×C151C22semidirect
30. #95×C151C22semidirect
31. #95×C151C22semidirect
36. C23×D151D4semidirect
153. C151#2812semidirect
157. #397D151semidirect
171. C2×C4⋊C4C2×D151semidirect
184. #95C2×D151semidirect
185. #95C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127092
#237521412
#237521302
#237521292
#237521272
#237521222
#237521212
#237520672
#397×C1512
#2812151