Finite Group Databasebeta

← #34080481

Subgroups — #34080481

Order 19328.

348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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#23752767C211yesmaximal, characteristic, complemented
2#23752749C211yesmaximal, characteristic
3#23752517C212yesmaximal, complemented
4#23752507C211yesmaximal, characteristic, complemented
5#23752503C211yesmaximal, characteristic, complemented
6#23752467C212yesmaximal, complemented
7#23752461C212yesmaximal
8#23752436C212yesmaximal, complemented
9#23752414C211yesmaximal, characteristic, complemented
10#23752234C211yesmaximal, characteristic, complemented
11#462×C151C211yesmaximal, characteristic, complemented
12C2×#14558991C2212yes—
13C2×#14558987C2212yes—
14#18012739C2211yescharacteristic
15#18012734—21no—
16#18012730—21no—
17#18012730C2211yescharacteristic
18#18012728C2211yescharacteristic
19#18012724—21no—
20#18012719—21no—
21#18012715C2212yes—
22#18012715C2211yescharacteristic
23#18012714C2211yescharacteristic
24Q8×Dic151C2212yes—
25#18012704—21no—
26C4×D604—21no—
27C4×D604C2211yescharacteristic
28#18012697—21no—
29#18012696—21no—
30C42×D151C2211yescharacteristic
31#18012672C2212yes—
32#18012671C2212yes—
33C4⋊(C151⋊C8)C2211yescharacteristic
34Dic151⋊C8C2212yes—
35#18012663C2212yes—
36#18012663C2212yes—
37#18012661C2212yes—
38C2×Q16×C151C2212yes—
39C4⋊Q8×C151C2211yescharacteristic
40C4×Q8×C151C2211yescharacteristic
41C4⋊C8×C151C2211yescharacteristic
42#103×C151C2212yes—
43C2×Dic302—21no—
44C2×D604—21no—
45C2×D604C2311yescharacteristic
46C2×C4×D151—21no—
47C2×C4×D151D411yescharacteristic
48C2×C4×D151D411yescharacteristic
49C2×C4×D151C2311yescharacteristic
50#14558991—42no—
51#14558987—42no—
52C2×C151⋊C8C2312yes—
53C4⋊Dic151—21no—
54C4⋊Dic151—22no—
55C4⋊Dic151—21no—
56C4⋊Dic151C2312yes—
57C4⋊Dic151C2311yescharacteristic
58Dic151⋊C4—21no—
59Dic151⋊C4—21no—
60Dic151⋊C4—22no—
61(C2×D151)⋊C4—22no—
62(C2×D151)⋊C4—21no—
63(C2×D151)⋊C4—21no—
64(C2×D151)⋊C4—21no—
65(C2×D151)⋊C4—21no—
66(C2×D151)⋊C4—21no—
67C4×Dic151—22no—
68C4×Dic151D411yescharacteristic
69C4×Dic151D411yescharacteristic
70C4×Dic151C2311yescharacteristic
71C2×Q8×C151C2312yes—
72C2×Q8×C151C2311yescharacteristic
73Q16×C151—42no—
74C2×C8×C151C2312yes—
75C4⋊C4×C151—21no—
76C4⋊C4×C151—21no—
77C4⋊C4×C151—21no—
78C4⋊C4×C151C2311yescharacteristic
79C42×C151—21no—
80C42×C151C2311yescharacteristic
81C22×D151—21no—
82C22×D151C2×D411yescharacteristic
83Dic302—42no—
84D604—21no—
85D604—21no—
86D604—42no—
87C2×Dic151—22no—
88C2×Dic151—21no—
89C2×Dic151C2×D411yescharacteristic
90C2×Dic151C2×D411yescharacteristic
91C2×Dic151C2×D411yescharacteristic
92C4×D151—22no—
93C4×D151—21no—
94C4×D151—21no—
95C4×D151—41no—
96C4×D151—42no—
97C151⋊C8—22no—
98Q8×C151—22no—
99Q8×C151—21no—
100Q8×C151—22no—
101Q8×C151—21no—
102C2×C4×C151—22no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151C2×D411yescharacteristic
106C2×C4×C151C2×D411yescharacteristic
107C2×C4×C151C2411yescharacteristic
108C8×C151—22no—
109C22×C151C22×D411yescharacteristic
110C2×D151—21no—
111C2×D151—21no—
112C2×D151—21no—
113C2×D151—41no—
114C2×D151—41no—
115C2×D151—41no—
116C4×C151—21no—
117C4×C151—42no—
118C4×C151—41no—
119C4×C151—41no—
120C4×C151#13712yes—
121C4×C151H(5,𝔽2)11yescharacteristic
122C4×C1512−1+411yescharacteristic
123Dic151—21no—
124Dic151—21no—
125Dic151—21no—
126Dic151—41no—
127Dic151—42no—
128C2×C151#53711yescharacteristic
129C2×C151C2×#13711yescharacteristic
130C2×C151#57511yescharacteristic
131D151—41no—
132D151—81no—
133C151#325211yescharacteristic, complemented, Sylow
134#3252—1511nomaximal, Sylow
135#533—1511no—
136#529—1511no—
137#479—1512no—
138#477—1511no—
139#476—1511no—
140#470—1512no—
141#468—1512no—
142#464—1512no—
143#462D15111yescharacteristic, complemented
144#461—1511no—
145#423—1511no—
146C2×Q16C2×D15112yes—
147C2×SD16—1512no—
148C2×M16—1512no—
149C4⋊Q8—1511no—
150C4⋊Q8C2×D15111yescharacteristic
151#126—3021no—
152#125—3021no—
153#125—1511no—
154#124—1511no—
155#123—3021no—
156C22⋊Q8—3021no—
157C22⋊Q8—1511no—
158C22⋊Q8—1512no—
159#121—1511no—
160C4×Q8—3021no—
161C4×Q8—1512no—
162C4×Q8C2×D15111yescharacteristic
163C4×D4—3021no—
164C4×D4—1511no—
165#117—3021no—
166#117—3021no—
167C2×C42—1511no—
168#107—1512no—
169#106—1512no—
170C4⋊C8—1512no—
171C4⋊C8—1511no—
172C4⋊C8C2×D15111yescharacteristic
173#103—1512no—
174#103—1512no—
175#103C2×D15112yes—
176#102—1512no—
177C2×Q8—3021no—
178C2×Q8C22×D15111yescharacteristic
179C2×Q8C22×D15112yes—
180C2×D4—3021no—
181C2×D4—1511no—
182C22×C4—3021no—
183C22×C4—1511no—
184C22×C4—1511no—
185C22×C4—1511no—
186Q16—42no—
187SD16—6042no—
188M16—6042no—
189C2×C8—1512no—
190C2×C8C22×D15112yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—3021no—
195C4⋊C4—3021no—
196C4⋊C4—3022no—
197C4⋊C4—3021no—
198C4⋊C4—3022no—
199C4⋊C4—3021no—
200C4⋊C4—1512no—
201C4⋊C4—1511no—
202C4⋊C4C22×D15111yescharacteristic
203C22⋊C4—3022no—
204C22⋊C4—3021no—
205C22⋊C4—3021no—
206C22⋊C4—3021no—
207C22⋊C4—3021no—
208C22⋊C4—3021no—
209C42—21no—
210C42—3022no—
211C42—1511no—
212C42—1511no—
213C42—1511no—
214C42C22×D15111yescharacteristic
215C23—3021no—
216C23—1511no—
217Q8—22no—
218Q8—21no—
219Q8—21no—
220Q8—22no—
221Q8—6042no—
222D4—3021no—
223D4—3021no—
224D4—6042no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—3022no—
229C2×C4—3021no—
230C2×C4—3021no—
231C2×C4—3022no—
232C2×C4—3021no—
233C2×C4—6041no—
234C2×C4—6042no—
235C2×C4—1511no—
236C2×C4—1511no—
237C2×C4—1511no—
238C2×C4D4×D15111yescharacteristic
239C2×C4D4×D15111yescharacteristic
240C2×C4C23×D15111yescharacteristic
241C8—22no—
242C8—3022no—
243C22—3021no—
244C22—3021no—
245C22—3021no—
246C22—6041no—
247C22—6041no—
248C22—6041no—
249C22C2×D4×D15111yescharacteristic
250C4—21no—
251C4—41no—
252C4—41no—
253C4—42no—
254C4—3021no—
255C4—3021no—
256C4—3021no—
257C4—6041no—
258C4—6042no—
259C4#1801277112yes—
260C4#1801278411yescharacteristic
261C4#1801278611yescharacteristic
262C2—6041no—
263C2—12081no—
264C2#2375279111yescharacteristic
265C2C2×#1801277111yescharacteristic
266C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#462×C151C2
socleC22×C151C22×D4
prime radical#18012714C22
hypercenter#462D151
hypocenterC151#3252
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #23752767C2semidirect
3. #23752517C2semidirect
4. #23752507C2semidirect
5. #23752503C2semidirect
6. #23752467C2semidirect
8. #23752436C2semidirect
9. #23752414C2semidirect
10. #23752234C2semidirect
11. #462×C151C2semidirect
133. C151#3252semidirect
143. #462D151semidirect

Maximal subgroups

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

subgroupindex
#237527672
#237527492
#237525172
#237525072
#237525032
#237524672
#237524612
#237524362
#237524142
#237522342
#462×C1512
#3252151