Finite Group Databasebeta

← #34079157

Subgroups — #34079157

Order 19328.

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

normal subgroups only

This group has 454 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
1#23752746C211yesmaximal, characteristic, complemented
2#23752547C211yesmaximal, characteristic, complemented
3#23752530C211yesmaximal, characteristic, complemented
4#23752512C212yesmaximal, complemented
5#23752427C212yesmaximal, complemented
6#23752363C211yesmaximal, characteristic, complemented
7#23752346C211yesmaximal, characteristic
8C4×#14558992C212yesmaximal, complemented
9C4×#14558989C212yesmaximal, complemented
10#23752265C211yesmaximal, characteristic, complemented
11C2×C4×D4×C151C211yesmaximal, characteristic, complemented
12C2×#14558992C2212yes—
13C2×#14558989C2212yes—
14#18012733—21no—
15#18012731C2211yescharacteristic, complemented
16#18012727C2211yescharacteristic, complemented
17#18012722—21no—
18#18012718C2211yescharacteristic
19#18012713C2211yescharacteristic
20C4×Dic302C2211yescharacteristic, complemented
21C4×D604C2211yescharacteristic, complemented
22C4×C22⋊D151—21no—
23#18012696—21no—
24#18012672C2212yescomplemented
25#18012670C2212yescomplemented
26C4⋊(C151⋊C8)C2212yescomplemented
27#18012662C2212yescomplemented
28#18012660C2212yes—
29#18012660C2212yes—
30#18012659C2212yescomplemented
31C22⋊(C151⋊C8)C2211yescharacteristic
32C22⋊(C151⋊C8)C2211yescharacteristic
33C4×C151⋊C8C2212yescomplemented
34C22×D4×C151C2211yescharacteristic
35C23×C4×C151—21no—
36C4×D4×C151—21no—
37C4×D4×C151—21no—
38C4×D4×C151C2212yes—
39C4×D4×C151C2212yes—
40C2×C4⋊C4×C151C2211yescharacteristic
41C2×C22⋊C4×C151—21no—
42C2×C42×C151C2211yescharacteristic
43C2×Dic302C2311yescharacteristic
44C2×D604C2311yescharacteristic
45C2×C22⋊D151—21no—
46C2×C4×D151—21no—
47#14558992—24no—
48#14558989—24no—
49C2×C151⋊C8C2312yes—
50C2×C151⋊C8C2312yes—
51C4⋊Dic151C2311yescharacteristic
52C4⋊Dic151C2311yescharacteristic
53Dic151⋊C4—21no—
54Dic151⋊C4—21no—
55Dic151⋊C4—21no—
56Dic151⋊C4—21no—
57C22⋊Dic151—21no—
58(C2×D151)⋊C4—21no—
59(C2×D151)⋊C4—21no—
60(C2×D151)⋊C4—21no—
61(C2×D151)⋊C4—21no—
62C4×Dic151—21no—
63C24×C151—21no—
64C2×D4×C151—24no—
65C2×D4×C151—21no—
66C2×D4×C151C2312yes—
67C22×C4×C151—21no—
68C22×C4×C151—22no—
69C22×C4×C151—22no—
70C22×C4×C151—44no—
71C22×C4×C151D411yescharacteristic
72C22×C4×C151D411yescharacteristic
73C22×C4×C151C2311yescharacteristic
74C4⋊C4×C151—21no—
75C4⋊C4×C151C2312yes—
76C22⋊C4×C151—22no—
77C22⋊C4×C151—22no—
78C42×C151D411yescharacteristic
79C42×C151D411yescharacteristic
80C42×C151C2311yescharacteristic
81C42×C151C2311yescharacteristic
82C22×D151—21no—
83Dic302—22no—
84D604—22no—
85C22⋊D151—42no—
86C2×Dic151—21no—
87C2×Dic151—21no—
88C2×Dic151—21no—
89C4×D151—42no—
90C151⋊C8—22no—
91C151⋊C8—22no—
92C23×C151—24no—
93C23×C151—22no—
94C23×C151—42no—
95C23×C151—42no—
96C23×C151C2×D411yescharacteristic
97D4×C151—24no—
98D4×C151—22no—
99D4×C151#4114yes—
100C2×C4×C151—22no—
101C2×C4×C151—22no—
102C2×C4×C151—22no—
103C2×C4×C151—22no—
104C2×C4×C151—44no—
105C2×C4×C151—42no—
106C2×C4×C151—44no—
107C2×C4×C151C2×D411yescharacteristic
108C2×C4×C151C2×D411yescharacteristic
109C2×C4×C151C2×D411yescharacteristic
110C2×C4×C151C2×D411yescharacteristic
111C2×C4×C151C2×D411yescharacteristic
112C2×C4×C151C2411yescharacteristic
113C22×C151—21no—
114C22×C151—21no—
115C22×C151—24no—
116C22×C151—48no—
117C22×C151—42no—
118C22×C151—42no—
119C22×C151#13512yes—
120C22×C151C22×D411yescharacteristic
121C2×D151—41no—
122C2×D151—41no—
123C2×D151—41no—
124C4×C151—21no—
125C4×C151—21no—
126C4×C151—21no—
127C4×C151—21no—
128C4×C151—42no—
129C4×C151AGL(1,ℤ/8)12yes—
130C4×C151C2×#4112yes—
131Dic151—41no—
132Dic151—41no—
133Dic151—41no—
134C2×C151—22no—
135C2×C151—44no—
136C2×C151#52511yescharacteristic
137C2×C151C2×#13511yescharacteristic
138C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
139D151—81no—
140C151#310511yescharacteristic, complemented, Sylow
141#3105—1511nomaximal, Sylow
142#529—1511no—
143C2×C4×D4D15111yescharacteristic, complemented
144#484—1511no—
145#481—1511no—
146#478—1512no—
147#463—1512no—
148#450—1511no—
149#447—1511no—
150C4×SD16—1512no—
151C4×D8—1512no—
152#431—1511no—
153C22×D4C2×D15111yescharacteristic
154C23×C4—21no—
155C2×SD16—1512no—
156C2×D8—1512no—
157#126—3021no—
158#125—1511no—
159#124—1511no—
160#123—3021no—
161C22⋊Q8—1511no—
162#121—1511no—
163C4×Q8—1511no—
164C4×D4—21no—
165C4×D4—21no—
166C4×D4—3021no—
167C4×D4—1511no—
168C4×D4C2×D15112yes—
169C4×D4C2×D15112yes—
170#117—3021no—
171C2×C4⋊C4C2×D15111yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C2×D15111yescharacteristic
174#107—1512no—
175#106—1512no—
176C4⋊C8—1512no—
177#103—1512no—
178#102—1512no—
179#102—1512no—
180#102—1512no—
181C22⋊C8—1511no—
182C22⋊C8—1511no—
183C4×C8—1512no—
184C24—21no—
185C2×Q8—1511no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—3021no—
189C2×D4—1511no—
190C2×D4C22×D15112yes—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—3021no—
196C22×C4C22⋊D15111yescharacteristic
197C22×C4C22⋊D15111yescharacteristic
198C22×C4C22×D15111yescharacteristic
199SD16—3024no—
200D8—3024no—
201C2×C8—1512no—
202C2×C8—1512no—
203C4⋊C4—21no—
204C4⋊C4—3021no—
205C4⋊C4—3021no—
206C4⋊C4—3021no—
207C4⋊C4—3021no—
208C4⋊C4—1511no—
209C4⋊C4—1511no—
210C4⋊C4C22×D15112yes—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—3021no—
214C22⋊C4—3021no—
215C22⋊C4—3021no—
216C22⋊C4—3021no—
217C22⋊C4—3021no—
218C42—3021no—
219C42C22⋊D15111yescharacteristic
220C42C22⋊D15111yescharacteristic
221C42C22×D15111yescharacteristic
222C42C22×D15111yescharacteristic
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—3021no—
228C23C2×C22⋊D15111yescharacteristic
229Q8—3022no—
230D4—24no—
231D4—22no—
232D4—3022no—
233D4—6042no—
234D4#1455900414yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—44no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—3021no—
243C2×C4—3021no—
244C2×C4—3021no—
245C2×C4—6042no—
246C2×C4C2×C22⋊D15111yescharacteristic
247C2×C4C2×C22⋊D15111yescharacteristic
248C2×C4C2×C22⋊D15111yescharacteristic
249C2×C4C2×C22⋊D15111yescharacteristic
250C2×C4C2×C22⋊D15111yescharacteristic
251C2×C4C23×D15111yescharacteristic
252C8—3022no—
253C8—3022no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—6041no—
261C22—6041no—
262C22—6041no—
263C22#1801275912yes—
264C22C22×C22⋊D15111yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—42no—
270C4—6041no—
271C4—6041no—
272C4—6041no—
273C4#1801276512yes—
274C4C2×#1455900412yes—
275C2—22no—
276C2—44no—
277C2—12081no—
278C2#2375272311yescharacteristic
279C2C2×#1801275911yescharacteristic
280C2C2×#1801276511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×C4×D4×C151C2
socleC22×C151C22×D4
prime radical#23752346C2
hypercenterC2×C4×D4D151
hypocenterC151#3105
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #23752746C2semidirect
2. #23752547C2semidirect
3. #23752530C2semidirect
4. #23752512C2semidirect
5. #23752427C2semidirect
6. #23752363C2semidirect
8. C4×#14558992C2semidirect
9. C4×#14558989C2semidirect
10. #23752265C2semidirect
11. C2×C4×D4×C151C2semidirect
15. #18012731C22semidirect
16. #18012727C22semidirect
20. C4×Dic302C22semidirect
21. C4×D604C22semidirect
24. #18012672C22semidirect
25. #18012670C22semidirect
26. C4⋊(C151⋊C8)C22semidirect
27. #18012662C22semidirect
30. #18012659C22semidirect
33. C4×C151⋊C8C22semidirect
140. C151#3105semidirect
143. C2×C4×D4D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237525472
#237525302
#237525122
#237524272
#237523632
#237523462
C4×#145589922
C4×#145589892
#237522652
C2×C4×D4×C1512
#3105151