Finite Group Databasebeta

← #34078484

Subgroups — #34078484

Order 19328.

736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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#23753048C211yesmaximal, characteristic, complemented
2C2×#18012767C212yesmaximal, complemented
3#23752776C211yesmaximal, characteristic, complemented
4#23752387C214yesmaximal, complemented
5#23752382C214yesmaximal, complemented
6#23752228C212yesmaximal, complemented
7#413×C151C211yesmaximal, characteristic, complemented
8#18012787C2212yescomplemented
9#18012786—22no—
10#18012785—22no—
11#18012784—22no—
12#18012784C2212yescomplemented
13C2×#14559004—22no—
14C2×#14559004C2212yes—
15#41×D151—24no—
16C22×D604C2211yescharacteristic, complemented
17#18012767—24no—
18#18012767C2218yescomplemented
19C2×#14558993—22no—
20C2×D1208—22no—
21#18012735C2212yescomplemented
22#18012728C2212yescomplemented
23#18012713—22no—
24#18012707—22no—
25#18012698C2211yescharacteristic, complemented
26#18012665C2218yescomplemented
27C2×#41×C151C2211yescharacteristic
28C2×M16×C151C2212yescomplemented
29#101×C151C2212yescomplemented
30#100×C151C2212yescomplemented
31C23×D151—21no—
32#14559005—24no—
33#14559004—24no—
34#14559004—24no—
35#14559004—22no—
36#14559004—24no—
37#14559004—22no—
38#14559004D414yescomplemented
39#14559004C2314yes—
40#14559003—28no—
41#14559003—24no—
42C2×Dic302—22no—
43C2×Dic302D412yescomplemented
44Q8×D151—24no—
45C2×D604—22no—
46C2×D604—22no—
47C2×D604—22no—
48C2×D604—21no—
49C2×D604D412yescomplemented
50C2×D604C2312yes—
51C2×C22⋊D151—24no—
52C2×C22⋊D151—22no—
53C2×C22⋊D151—24no—
54D4×D151—28no—
55D4×D151—24no—
56C2×C4×D151—24no—
57C2×C4×D151—22no—
58#14558993—28no—
59D1208—28no—
60C4⋊Dic151—21no—
61C22⋊Dic151—21no—
62(C2×D151)⋊C4—24no—
63C4×Dic151C2312yes—
64#41×C151—22no—
65#41×C151—22no—
66C2×Q8×C151C2311yescharacteristic
67C2×D4×C151D412yes—
68C2×D4×C151C2311yescharacteristic
69C22×C4×C151D412yes—
70C22×C4×C151C2311yescharacteristic
71M16×C151—22no—
72M16×C151C2314yes—
73C2×C8×C151—22no—
74C22×D151—24no—
75C22×D151—22no—
76C22×D151—22no—
77C22×D151—42no—
78C22×D151—82no—
79Dic302—24no—
80Dic302—22no—
81Dic302C2×D414yes—
82D604—24no—
83D604—22no—
84D604—24no—
85D604—41no—
86D604—41no—
87D604C2×D414yes—
88C22⋊D151—28no—
89C22⋊D151—24no—
90C22⋊D151—24no—
91C22⋊D151—84no—
92C2×Dic151—24no—
93C2×Dic151—22no—
94C2×Dic151—22no—
95C4×D151—28no—
96C4×D151—24no—
97C4×D151—24no—
98C23×C151C2×D412yes—
99C23×C151C2×D411yescharacteristic
100Q8×C151—22no—
101D4×C151—24no—
102D4×C151—22no—
103C2×C4×C151—22no—
104C2×C4×C151—22no—
105C2×C4×C151C2×D412yes—
106C2×C4×C151C2×D412yes—
107C2×C4×C151C2×D412yes—
108C2×C4×C151C2×D411yescharacteristic
109C2×C4×C151C2411yescharacteristic
110C8×C151—24no—
111C22×C151—22no—
112C22×C151—41no—
113C22×C151—42no—
114C22×C151#12012yes—
115C22×C151C22×D411yescharacteristic
116C2×D151—24no—
117C2×D151—44no—
118C2×D151—42no—
119C2×D151—82no—
120C2×D151—84no—
121C2×D151—84no—
122C4×C151—22no—
123C4×C151#12011yescharacteristic
124C4×C151#12011yescharacteristic
125C4×C151C22×D412yes—
126Dic151—24no—
127Dic151—42no—
128C2×C151—21no—
129C2×C151—22no—
130C2×C151—42no—
131C2×C151C2×#12011yescharacteristic
132D151—44no—
133D151—82no—
134C151#302111yescharacteristic, complemented, Sylow
135#3021—1511nomaximal, Sylow
136#585—1511no—
137C2×AGL(1,ℤ/8)—1512no—
138#535—1511no—
139#454—1514no—
140#453—1514no—
141#421—1512no—
142#413D15111yescharacteristic, complemented
1432−1+4—3022no—
1442−1+4—1512no—
145H(5,𝔽2)—3022no—
146H(5,𝔽2)—3022no—
147H(5,𝔽2)—1512no—
148C2×#41—3024no—
149C2×#41—3022no—
150C2×#41—1512no—
151C2×#41C2×D15111yescharacteristic
152C22×D4—1511no—
153AGL(1,ℤ/8)—3024no—
154AGL(1,ℤ/8)—1518no—
155C2×SD16—3022no—
156C2×D8—3022no—
157C2×M16C2×D15112yescomplemented
158#127—1512no—
159#124—1512no—
160#121—3022no—
161#120—3022no—
162#117—1511no—
163#104—1518no—
164#101C2×D15112yescomplemented
165#100C2×D15112yescomplemented
166C24—3021no—
167#41—22no—
168#41—22no—
169#41—3024no—
170#41—3024no—
171#41—3028no—
172#41—3024no—
173#41—3024no—
174#41—3022no—
175#41—3022no—
176#41—3024no—
177#41—1514no—
178#41—1514no—
179C2×Q8—3022no—
180C2×Q8—3024no—
181C2×Q8—1512no—
182C2×Q8C22×D15111yescharacteristic
183C2×D4—3022no—
184C2×D4—3028no—
185C2×D4—3024no—
186C2×D4—3024no—
187C2×D4—3022no—
188C2×D4—3024no—
189C2×D4—3022no—
190C2×D4—3022no—
191C2×D4—3021no—
192C2×D4—1512no—
193C2×D4—1512no—
194C2×D4D60412yes—
195C2×D4C22×D15111yescharacteristic
196C22×C4—3024no—
197C22×C4—3022no—
198C22×C4D60412yes—
199C22×C4C22×D15111yescharacteristic
200SD16—3028no—
201D8—3028no—
202M16—22no—
203M16C22×D15114yes—
204C2×C8—22no—
205C4⋊C4—3021no—
206C22⋊C4—3021no—
207C22⋊C4—3024no—
208C42—1512no—
209C23—3024no—
210C23—3022no—
211C23—3022no—
212C23—6042no—
213C23—12082no—
214C23C2×D60412yes—
215C23C2×D60411yescharacteristic
216Q8—22no—
217Q8—3024no—
218Q8—3022no—
219Q8—1514no—
220D4—24no—
221D4—22no—
222D4—3024no—
223D4—3028no—
224D4—3024no—
225D4—3024no—
226D4—3022no—
227D4—3024no—
228D4—6041no—
229D4—6041no—
230D4—1514no—
231D4—12084no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—3028no—
235C2×C4—3024no—
236C2×C4—3022no—
237C2×C4—3024no—
238C2×C4—3024no—
239C2×C4—3022no—
240C2×C4D4×D15112yes—
241C2×C4D4×D15112yes—
242C2×C4C2×D60412yes—
243C2×C4C2×D60411yescharacteristic
244C2×C4C23×D15111yescharacteristic
245C8—24no—
246C22—22no—
247C22—41no—
248C22—42no—
249C22—3024no—
250C22—6044no—
251C22—6042no—
252C22—12082no—
253C22—12084no—
254C22—12084no—
255C22#1801270912yes—
256C22C22×D60411yescharacteristic
257C4—22no—
258C4—3024no—
259C4—6042no—
260C4#1801270911yescharacteristic
261C4#1801270911yescharacteristic
262C4C2×D4×D15112yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—6044no—
267C2—12082no—
268C2C2×#1801270911yescharacteristic
subgroupG/H
centerC2C2×#18012709
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#413×C151C2
socleC2×C151C2×#120
hypercenter#413D151
hypocenterC151#3021
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #23753048C2semidirect
2. C2×#18012767C2semidirect
3. #23752776C2semidirect
4. #23752387C2semidirect
5. #23752382C2semidirect
6. #23752228C2semidirect
7. #413×C151C2semidirect
8. #18012787C22semidirect
12. #18012784C22semidirect
16. C22×D604C22semidirect
18. #18012767C22semidirect
21. #18012735C22semidirect
22. #18012728C22semidirect
25. #18012698C22semidirect
26. #18012665C22semidirect
28. C2×M16×C151C22semidirect
29. #101×C151C22semidirect
30. #100×C151C22semidirect
38. #14559004D4semidirect
43. C2×Dic302D4semidirect
49. C2×D604D4semidirect
134. C151#3021semidirect
142. #413D151semidirect
157. C2×M16C2×D151semidirect
164. #101C2×D151semidirect
165. #100C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530482
C2×#180127672
#237527762
#237523872
#237523822
#237522282
#413×C1512
#3021151