Finite Group Databasebeta

← #34079574

Subgroups — #34079574

Order 19328.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#18012770C212yesmaximal, complemented
2C2×#18012765C212yesmaximal, complemented
3#23752762C211yesmaximal, characteristic, complemented
4#23752607C212yesmaximal, complemented
5#23752602C212yesmaximal, complemented
6#23752594C214yesmaximal, complemented
7C4×#14558988C211yesmaximal, characteristic, complemented
8C2×#124×C151C211yesmaximal, characteristic, complemented
9C2×#14559004C2212yes—
10#18012770—28no—
11#18012765—28no—
12C2×#14558994C2214yescomplemented
13C2×#14558992C2214yes—
14C2×#14558991C2214yescomplemented
15C2×#14558989C2214yes—
16C2×#14558988C2212yes—
17#18012739C2211yescharacteristic, complemented
18#18012736C2211yescharacteristic, complemented
19#18012727C2212yescomplemented
20#18012713—22no—
21C4×D604—22no—
22#18012650C2212yescomplemented
23C4×C151⋊C8C2212yescomplemented
24C22×Q8×C151C2211yescharacteristic
25C22×D4×C151C2211yescharacteristic
26#124×C151—22no—
27#124×C151C2212yes—
28#124×C151C2212yes—
29C2×C22⋊C4×C151—22no—
30C2×C42×C151C2211yescharacteristic
31#14559004—24no—
32#14559004—24no—
33C2×Dic302C2312yes—
34C2×D604—22no—
35C2×D604C2312yes—
36C2×C22⋊D151—22no—
37C2×C4×D151—22no—
38#14558994—28no—
39#14558992—28no—
40#14558991—28no—
41#14558989—28no—
42#14558988D418yescomplemented
43C2×C151⋊C8C2314yes—
44C4⋊Dic151—22no—
45(C2×D151)⋊C4—24no—
46C24×C151—21no—
47C2×Q8×C151—21no—
48C2×Q8×C151—24no—
49C2×Q8×C151C2312yes—
50C2×D4×C151—24no—
51C2×D4×C151—21no—
52C2×D4×C151C2312yes—
53C22×C4×C151—21no—
54C22×C4×C151D412yes—
55C22×C4×C151C2311yescharacteristic
56C22⋊C4×C151—24no—
57C22⋊C4×C151—24no—
58C42×C151D412yes—
59C42×C151C2311yescharacteristic
60C42×C151C2311yescharacteristic
61C22×D151—22no—
62Dic302—22no—
63Dic302—22no—
64D604—22no—
65D604—22no—
66D604—44no—
67C22⋊D151—44no—
68C2×Dic151—22no—
69C4×D151—44no—
70C151⋊C8C2×D418yes—
71C23×C151—22no—
72C23×C151—44no—
73C23×C151—42no—
74C23×C151C2×D411yescharacteristic
75Q8×C151—24no—
76Q8×C151—42no—
77D4×C151—24no—
78D4×C151—42no—
79C2×C4×C151—22no—
80C2×C4×C151—42no—
81C2×C4×C151—42no—
82C2×C4×C151C2×D414yes—
83C2×C4×C151C2×D412yes—
84C2×C4×C151C2×D412yes—
85C2×C4×C151C2×D411yescharacteristic
86C2×C4×C151C2411yescharacteristic
87C22×C151—22no—
88C22×C151—42no—
89C22×C151—44no—
90C22×C151—84no—
91C22×C151#12712yes—
92C22×C151C22×D411yescharacteristic
93C2×D151—42no—
94C2×D151—44no—
95C4×C151—22no—
96C4×C151—22no—
97C4×C151—42no—
98C4×C151#12712yes—
99C4×C151C22×D412yes—
100Dic151—42no—
101C2×C151—22no—
102C2×C151—82no—
103C2×C151C2×#12711yescharacteristic
104C2×C151#57512yes—
105D151—82no—
106C151#315311yescharacteristic, complemented, Sylow
107#3153—1511nomaximal, Sylow
108C2×#137—1512no—
109C2×AGL(1,ℤ/8)—1512no—
110#532—1511no—
111C2×#124D15111yescharacteristic, complemented
112#497—1512no—
113#496—1512no—
114#495—1514no—
115C4×M16—1511no—
116C2×#41—1512no—
117C22×Q8C2×D15111yescharacteristic
118C22×D4C2×D15111yescharacteristic
119#137—3028no—
120AGL(1,ℤ/8)—3028no—
121C2×Q16—1514no—
122C2×SD16—1514no—
123C2×SD16—1514no—
124C2×D8—1514no—
125C2×M16—1512no—
126C4⋊Q8—1511no—
127#127—1511no—
128#124—22no—
129#124—1512no—
130#124C2×D15112yes—
131#124C2×D15112yes—
132#121—3022no—
133C4×D4—3022no—
134C2×C22⋊C4—22no—
135C2×C42C2×D15111yescharacteristic
136#97—1512no—
137C4×C8—1512no—
138C24—21no—
139#41—3024no—
140#41—3024no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—1512no—
144C2×Q8C22×D15112yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—3022no—
148C2×D4—3022no—
149C2×D4—1512no—
150C2×D4C22×D15112yes—
151C22×C4—21no—
152C22×C4—3022no—
153C22×C4C22⋊D15112yes—
154C22×C4C22×D15111yescharacteristic
155Q16—3028no—
156SD16—3028no—
157SD16—3028no—
158D8—3028no—
159M16—1518no—
160C2×C8—1514no—
161C4⋊C4—3022no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—3024no—
165C42C22⋊D15112yes—
166C42C22×D15111yescharacteristic
167C42C22×D15111yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—3022no—
172C23C2×C22⋊D15111yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—3022no—
176Q8—3022no—
177D4—24no—
178D4—42no—
179D4—3022no—
180D4—3022no—
181D4—6044no—
182D4—6044no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—3022no—
187C2×C4—6044no—
188C2×C4D4×D15114yes—
189C2×C4C2×C22⋊D15112yes—
190C2×C4C2×C22⋊D15112yes—
191C2×C4C2×C22⋊D15111yescharacteristic
192C2×C4C23×D15111yescharacteristic
193C8—1518no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—6042no—
199C22—6044no—
200C22#1801273512yes—
201C22C22×C22⋊D15111yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—6042no—
206C4#1801273512yes—
207C4C2×D4×D15112yes—
208C2—22no—
209C2—82no—
210C2—12082no—
211C2C2×#1801273511yescharacteristic
212C2#2375301012yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#124×C151C2
socleC22×C151C22×D4
hypercenterC2×#124D151
hypocenterC151#3153
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#18012770C2semidirect
2. C2×#18012765C2semidirect
3. #23752762C2semidirect
4. #23752607C2semidirect
5. #23752602C2semidirect
6. #23752594C2semidirect
7. C4×#14558988C2semidirect
8. C2×#124×C151C2semidirect
12. C2×#14558994C22semidirect
14. C2×#14558991C22semidirect
17. #18012739C22semidirect
18. #18012736C22semidirect
19. #18012727C22semidirect
22. #18012650C22semidirect
23. C4×C151⋊C8C22semidirect
42. #14558988D4semidirect
106. C151#3153semidirect
111. C2×#124D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127702
C2×#180127652
#237527622
#237526072
#237526022
#237525942
C4×#145589882
C2×#124×C1512
#3153151