Finite Group Databasebeta

← #34080934

Subgroups — #34080934

Order 19328.

462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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#23752919C211yesmaximal, characteristic, complemented
2#23752558C211yesmaximal, characteristic, complemented
3#23752528C212yesmaximal, complemented
4#23752502C211yesmaximal, characteristic, complemented
5#23752439C212yesmaximal, complemented
6#23752409C211yesmaximal, characteristic, complemented
7#23752363C212yesmaximal, complemented
8C4×#14558992C211yesmaximal, characteristic, complemented
9D4×C151⋊C8C211yesmaximal, characteristic, complemented
10C2×#18012660C212yesmaximal, complemented
11D42×C151C211yesmaximal, characteristic
12C2×#14558992C2211yescharacteristic
13C2×#14558992C2212yescomplemented
14C22×C151⋊C8C2212yescomplemented
15#18012739C2211yescharacteristic, complemented
16#18012730—21no—
17#18012718C2212yescomplemented
18#18012716—22no—
19C4×Dic302C2211yescharacteristic, complemented
20D4×Dic151—21no—
21C2×C4⋊Dic151C2212yescomplemented
22#18012670C2212yescomplemented
23#18012670C2211yescharacteristic, complemented
24C4⋊(C151⋊C8)C2211yescharacteristic, complemented
25#18012662C2211yescharacteristic, complemented
26#18012660C2211yescharacteristic
27#18012660C2212yes—
28#18012660C2212yescomplemented
29#18012660C2212yescomplemented
30#18012660C2212yescomplemented
31C22⋊(C151⋊C8)C2212yescomplemented
32C4×C151⋊C8C2211yescharacteristic, complemented
33C22×D4×C151—21no—
34C22×D4×C151C2212yes—
35#127×C151C2211yescharacteristic
36#121×C151—21no—
37#121×C151C2212yes—
38#120×C151—22no—
39C4×D4×C151C2211yescharacteristic
40C4×D4×C151C2211yescharacteristic
41C2×Dic302—21no—
42C2×Dic302C2311yescharacteristic
43C22×Dic151—22no—
44#14558992—22no—
45#14558992—42no—
46C2×C151⋊C8—42no—
47C2×C151⋊C8C2311yescharacteristic
48C2×C151⋊C8C2312yes—
49C2×C151⋊C8C2311yescharacteristic
50C4⋊Dic151—22no—
51C4⋊Dic151—21no—
52C4⋊Dic151C2311yescharacteristic
53C4⋊Dic151C2312yes—
54Dic151⋊C4—21no—
55Dic151⋊C4—22no—
56C22⋊Dic151—22no—
57C4×Dic151—21no—
58C24×C151—22no—
59C2×D4×C151—24no—
60C2×D4×C151—22no—
61C2×D4×C151—22no—
62C2×D4×C151—21no—
63C2×D4×C151—21no—
64C2×D4×C151—42no—
65C2×D4×C151—44no—
66C2×D4×C151D411yescharacteristic
67C2×D4×C151C2312yes—
68C2×D4×C151C2311yescharacteristic
69C22×C4×C151—21no—
70C22×C4×C151C2312yes—
71C4⋊C4×C151D411yescharacteristic
72C4⋊C4×C151C2311yescharacteristic
73C22⋊C4×C151—21no—
74C22⋊C4×C151—22no—
75C22⋊C4×C151D412yes—
76C42×C151C2311yescharacteristic
77Dic302—21no—
78Dic302—21no—
79Dic302—81no—
80C2×Dic151—21no—
81C2×Dic151—21no—
82C2×Dic151—22no—
83C2×Dic151—82no—
84C151⋊C8—21no—
85C151⋊C8—21no—
86C151⋊C8—22no—
87C23×C151—21no—
88C23×C151—22no—
89C23×C151—44no—
90C23×C151—44no—
91C23×C151—82no—
92C23×C151C2×D412yes—
93D4×C151—22no—
94D4×C151—21no—
95D4×C151—22no—
96D4×C151—44no—
97D4×C151—44no—
98D4×C151—42no—
99D4×C151—81no—
100D4×C151SD1614yescomplemented
101D4×C151#4112yes—
102C2×C4×C151—22no—
103C2×C4×C151—22no—
104C2×C4×C151—21no—
105C2×C4×C151—42no—
106C2×C4×C151C2×D412yes—
107C2×C4×C151C2×D411yescharacteristic
108C2×C4×C151C2×D411yescharacteristic
109C2×C4×C151C2411yescharacteristic
110C22×C151—22no—
111C22×C151—22no—
112C22×C151—22no—
113C22×C151—41no—
114C22×C151—41no—
115C22×C151—42no—
116C22×C151—42no—
117C22×C151—42no—
118C22×C151—88no—
119C22×C151C2×SD1614yes—
120C22×C151C22×D411yescharacteristic
121C4×C151—22no—
122C4×C151—21no—
123C4×C151—41no—
124C4×C151C2×SD1612yes—
125C4×C151C2×#4111yescharacteristic
126C4×C151H(5,𝔽2)11yescharacteristic
127Dic151—41no—
128Dic151—41no—
129Dic151—42no—
130C2×C151—24no—
131C2×C151—42no—
132C2×C151—82no—
133C2×C151#54611yescharacteristic
134C2×C151C22×SD1611yescharacteristic
135C2×C151#57611yescharacteristic
136C151#329511yescharacteristic, complemented, Sylow
137#3295—1511nomaximal, Sylow
138#554—1511no—
139D42D15111yescharacteristic
140#486—1511no—
141#481—1512no—
142#476—1511no—
143#465—1512no—
144#460—1511no—
145#450—1512no—
146C4×SD16—1511no—
147C8×D4—1511no—
148C2×#102—1512no—
149C22×D4—21no—
150C22×D4C2×D15112yes—
151C2×SD16—1511no—
152C2×SD16—1512no—
153C22×C8—1512no—
154C4⋊Q8—1511no—
155#127C2×D15111yescharacteristic
156#125—3021no—
157C22⋊Q8—3022no—
158C22⋊Q8—1512no—
159#121—21no—
160#121C2×D15112yes—
161#120—22no—
162C4×Q8—1511no—
163C4×D4—3021no—
164C4×D4C2×D15111yescharacteristic
165C4×D4C2×D15111yescharacteristic
166C2×C4⋊C4—1512no—
167#106—1511no—
168#106—1512no—
169C4⋊C8—1511no—
170#103—1511no—
171#102—1511no—
172#102—1512no—
173#102—1512no—
174#102—1512no—
175#102—1512no—
176C22⋊C8—1512no—
177C4×C8—1511no—
178C24—22no—
179C2×Q8—3021no—
180C2×Q8—1511no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—42no—
187C2×D4—44no—
188C2×D4C22⋊D15111yescharacteristic
189C2×D4C22×D15112yes—
190C2×D4C22×D15111yescharacteristic
191C22×C4—21no—
192C22×C4—3022no—
193C22×C4C22×D15112yes—
194SD16—3022no—
195SD16—6042no—
196C2×C8—6042no—
197C2×C8—1511no—
198C2×C8—1511no—
199C2×C8—1512no—
200C4⋊C4—3021no—
201C4⋊C4—3022no—
202C4⋊C4—3022no—
203C4⋊C4—3021no—
204C4⋊C4—1511no—
205C4⋊C4—1512no—
206C4⋊C4C22⋊D15111yescharacteristic
207C4⋊C4C22×D15111yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—3022no—
211C22⋊C4C22⋊D15112yes—
212C42—3021no—
213C42C22×D15111yescharacteristic
214C23—21no—
215C23—22no—
216C23—44no—
217C23—44no—
218C23—82no—
219C23C2×C22⋊D15112yes—
220Q8—3021no—
221Q8—3021no—
222Q8—12081no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#1455899214yescomplemented
231D4#1455900312yes—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—3021no—
237C2×C4—3021no—
238C2×C4—3022no—
239C2×C4—12082no—
240C2×C4C2×C22⋊D15111yescharacteristic
241C2×C4C2×C22⋊D15112yes—
242C2×C4C2×C22⋊D15111yescharacteristic
243C2×C4C23×D15111yescharacteristic
244C8—3021no—
245C8—3021no—
246C8—3022no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—88no—
256C22C2×#1455899214yes—
257C22C22×C22⋊D15111yescharacteristic
258C4—21no—
259C4—22no—
260C4—41no—
261C4—6041no—
262C4—6042no—
263C4—6041no—
264C4C2×#1455899212yes—
265C4C2×#1455900311yescharacteristic
266C4#1801278411yescharacteristic
267C2—24no—
268C2—42no—
269C2—82no—
270C2#2375285611yescharacteristic
271C2C22×#1455899211yescharacteristic
272C2#2375301511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting, prime radicalD42×C151C2
socleC22×C151C22×D4
hypercenterD42D151
hypocenterC151#3295
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #23752919C2semidirect
2. #23752558C2semidirect
3. #23752528C2semidirect
4. #23752502C2semidirect
5. #23752439C2semidirect
6. #23752409C2semidirect
7. #23752363C2semidirect
8. C4×#14558992C2semidirect
9. D4×C151⋊C8C2semidirect
10. C2×#18012660C2semidirect
13. C2×#14558992C22semidirect
14. C22×C151⋊C8C22semidirect
15. #18012739C22semidirect
17. #18012718C22semidirect
19. C4×Dic302C22semidirect
21. C2×C4⋊Dic151C22semidirect
22. #18012670C22semidirect
23. #18012670C22semidirect
24. C4⋊(C151⋊C8)C22semidirect
25. #18012662C22semidirect
28. #18012660C22semidirect
29. #18012660C22semidirect
30. #18012660C22semidirect
31. C22⋊(C151⋊C8)C22semidirect
32. C4×C151⋊C8C22semidirect
100. D4×C151SD16semidirect
136. C151#3295semidirect
230. D4#14558992semidirect

Maximal subgroups

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

subgroupindex
#237529192
#237525582
#237525282
#237525022
#237524392
#237524092
#237523632
C4×#145589922
D4×C151⋊C82
C2×#180126602
D42×C1512
#3295151