Finite Group Databasebeta

← #34078633

Subgroups — #34078633

Order 19328.

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

normal subgroups only

This group has 490 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
1C22×#14558991C211yesmaximal, characteristic, complemented
2#23752776C211yesmaximal, characteristic
3#23752690C211yesmaximal, characteristic, complemented
4#23752436C214yesmaximal, complemented
5#23752410C214yesmaximal, complemented
6#23752240C211yesmaximal, characteristic, complemented
7#23752218C211yesmaximal, characteristic, complemented
8#23752208C211yesmaximal, characteristic, complemented
9C2×#137×C151C211yesmaximal, characteristic, complemented
10C22×D604C2211yescharacteristic
11C2×#14558991—24no—
12C2×#14558991C2214yes—
13C22×C151⋊C8C2211yescharacteristic
14#18012735C2212yes—
15#18012728C2212yes—
16#18012713—22no—
17#18012707—22no—
18Q8×Dic151—22no—
19Q8×Dic151C2214yescomplemented
20#18012698—22no—
21#18012698C2211yescharacteristic
22#18012698C2211yescharacteristic
23Dic151⋊C8C2214yescomplemented
24#18012663C2212yescomplemented
25#18012661C2214yes—
26#18012660C2212yescomplemented
27C2×#41×C151C2211yescharacteristic
28C22×Q8×C151C2211yescharacteristic
29#137×C151—24no—
30C2×Q16×C151C2212yescomplemented
31C2×SD16×C151C2212yescomplemented
32C2×M16×C151C2211yescharacteristic
33C23×D151—21no—
34C2×D604—22no—
35C2×D604—21no—
36C2×D604—22no—
37C2×D604C2312yes—
38C2×C22⋊D151—24no—
39#14558991—28no—
40C2×C151⋊C8—22no—
41C2×C151⋊C8C2312yes—
42C4⋊Dic151—24no—
43C4⋊Dic151D412yes—
44C4⋊Dic151C2312yes—
45C22⋊Dic151—21no—
46C22⋊Dic151D412yes—
47(C2×D151)⋊C4—24no—
48C4×Dic151—24no—
49C4×Dic151—21no—
50C4×Dic151C2312yes—
51#41×C151—22no—
52#41×C151—22no—
53C2×Q8×C151—21no—
54C2×Q8×C151—22no—
55C2×Q8×C151D414yescomplemented
56C2×Q8×C151C2311yescharacteristic
57C2×Q8×C151C2312yes—
58C2×D4×C151—21no—
59C2×D4×C151C2311yescharacteristic
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151C2311yescharacteristic
63Q16×C151—24no—
64SD16×C151—24no—
65M16×C151—22no—
66C2×C8×C151C2312yes—
67C22×D151—22no—
68C22×D151—42no—
69C22×D151—82no—
70D604—22no—
71D604—22no—
72D604—42no—
73C22⋊D151—84no—
74C2×Dic151—22no—
75C2×Dic151C2×D414yes—
76C151⋊C8—22no—
77C23×C151—21no—
78C23×C151C2×D411yescharacteristic
79Q8×C151—24no—
80Q8×C151—22no—
81Q8×C151—21no—
82Q8×C151—21no—
83Q8×C151C2×D414yes—
84D4×C151—21no—
85D4×C151—21no—
86D4×C151—42no—
87C2×C4×C151—24no—
88C2×C4×C151—22no—
89C2×C4×C151—21no—
90C2×C4×C151—42no—
91C2×C4×C151C2×D411yescharacteristic
92C2×C4×C151C2×D412yes—
93C2×C4×C151#4112yes—
94C2×C4×C151C2411yescharacteristic
95C8×C151—22no—
96C22×C151—22no—
97C22×C151—41no—
98C22×C151—42no—
99C22×C151#12112yes—
100C22×C151C22×D411yescharacteristic
101C2×D151—42no—
102C2×D151—44no—
103C2×D151—84no—
104C4×C151—24no—
105C4×C151—41no—
106C4×C151#12112yes—
107C4×C151C22×D411yescharacteristic
108C4×C151C2×#4111yescharacteristic
109Dic151—24no—
110Dic151—42no—
111C2×C151—22no—
112C2×C151—81no—
113C2×C151C2×#12111yescharacteristic
114C2×C151#57712yes—
115D151—82no—
116C151#304311yescharacteristic, complemented, Sylow
117#3043—1511nomaximal, Sylow
118C2×#137D15111yescharacteristic, complemented
119C22×SD16—1511no—
120#535—1511no—
121#519—1511no—
122#464—1514no—
123#460—1514no—
124#424—1511no—
125#418—1511no—
126#416—1511no—
127C2×#41C2×D15111yescharacteristic
128C22×Q8C2×D15111yescharacteristic
129C22×D4—1511no—
130#137—24no—
131C2×Q16C2×D15112yescomplemented
132C2×SD16—3024no—
133C2×SD16—1514no—
134C2×SD16C2×D15112yescomplemented
135C2×M16C2×D15111yescharacteristic
136C22×C8—1511no—
137#127—1512no—
138#124—1512no—
139#121—3022no—
140#120—3022no—
141C4×Q8—3022no—
142C4×Q8—1514no—
143#117—3022no—
144#117—1511no—
145#117—1511no—
146C4⋊C8—1514no—
147#103—1512no—
148#102—1512no—
149#102—1514no—
150C24—3021no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8C22⋊D15114yescomplemented
156C2×Q8C22×D15111yescharacteristic
157C2×Q8C22×D15112yes—
158C2×D4—21no—
159C2×D4—3024no—
160C2×D4—3021no—
161C2×D4—3022no—
162C2×D4—3022no—
163C2×D4—1512no—
164C2×D4C22×D15111yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C22×D15111yescharacteristic
168Q16—24no—
169SD16—24no—
170SD16—3028no—
171M16—22no—
172C2×C8—3022no—
173C2×C8—1512no—
174C2×C8C22×D15112yes—
175C4⋊C4—3024no—
176C4⋊C4—1512no—
177C4⋊C4—1512no—
178C22⋊C4—3024no—
179C22⋊C4—3021no—
180C22⋊C4—1512no—
181C42—3024no—
182C42—3021no—
183C42—1512no—
184C23—21no—
185C23—3022no—
186C23—6042no—
187C23—12082no—
188C23D4×D15111yescharacteristic
189Q8—24no—
190Q8—22no—
191Q8—21no—
192Q8—21no—
193Q8C2×C22⋊D15114yes—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—3022no—
198D4—3022no—
199D4—6042no—
200D4—12084no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—3022no—
206C2×C4—1514no—
207C2×C4D4×D15111yescharacteristic
208C2×C4C2×C22⋊D15112yes—
209C2×C4#1455900312yes—
210C2×C4C23×D15111yescharacteristic
211C8—22no—
212C8—3022no—
213C22—22no—
214C22—42no—
215C22—41no—
216C22—6044no—
217C22—6042no—
218C22—12084no—
219C22#1801271112yes—
220C22C2×D4×D15111yescharacteristic
221C4—24no—
222C4—41no—
223C4—3024no—
224C4—6042no—
225C4#1801271112yes—
226C4C22×C22⋊D15111yescharacteristic
227C4C2×#1455900311yescharacteristic
228C2—22no—
229C2—81no—
230C2—12082no—
231C2C2×#1801271111yescharacteristic
232C2#2375302112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#137×C151C2
socleC22×C151C22×D4
prime radical#23752776C2
hypercenterC2×#137D151
hypocenterC151#3043
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#14558991C2semidirect
3. #23752690C2semidirect
4. #23752436C2semidirect
5. #23752410C2semidirect
6. #23752240C2semidirect
7. #23752218C2semidirect
8. #23752208C2semidirect
9. C2×#137×C151C2semidirect
19. Q8×Dic151C22semidirect
23. Dic151⋊C8C22semidirect
24. #18012663C22semidirect
26. #18012660C22semidirect
30. C2×Q16×C151C22semidirect
31. C2×SD16×C151C22semidirect
55. C2×Q8×C151D4semidirect
116. C151#3043semidirect
118. C2×#137D151semidirect
131. C2×Q16C2×D151semidirect
134. C2×SD16C2×D151semidirect
155. C2×Q8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C22×#145589912
#237527762
#237526902
#237524362
#237524102
#237522402
#237522182
#237522082
C2×#137×C1512
#3043151