Finite Group Databasebeta

← #34082243

Subgroups — #34082243

Order 19328.

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

normal subgroups only

This group has 364 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#135×D151C212yesmaximal, complemented
2#23752654C212yesmaximal, complemented
3#23752651C212yesmaximal, complemented
4#23752649C212yesmaximal, complemented
5#23752646C212yesmaximal, complemented
6#23752644C211yesmaximal, characteristic, complemented
7#23752642C212yesmaximal, complemented
8C2×#18012678C211yesmaximal, characteristic, complemented
9#508×C151C211yesmaximal, characteristic, complemented
10#41×D151—22no—
11#18012762C2212yes—
12#18012761C2212yescomplemented
13#18012760—22no—
14#18012759—22no—
15#18012758C2212yes—
16Q16×D151C2212yescomplemented
17SD16×D151—22no—
18D8×D151C2212yescomplemented
19C2×C8×D151C2211yescharacteristic
20Dic1208C2211yescharacteristic, complemented
21#18012685C2212yescomplemented
22#18012684C2212yescomplemented
23#18012683C2212yescomplemented
24#18012682C2212yescomplemented
25D2416C2211yescharacteristic, complemented
26#18012680C2212yescomplemented
27#18012678C2212yescomplemented
28#18012678C2212yescomplemented
29C2×C151⋊C16C2211yescharacteristic, complemented
30#135×C151C2212yescomplemented
31Q32×C151C2211yescharacteristic, complemented
32SD32×C151C2212yescomplemented
33D16×C151C2211yescharacteristic, complemented
34C2×C16×C151C2211yescharacteristic, complemented
35#14559005—22no—
36#14559004—22no—
37#14559004—42no—
38#14559003—22no—
39#14559003—42no—
40Q8×D151—22no—
41D4×D151—22no—
42D4×D151—42no—
43C2×C4×D151—42no—
44C2×C4×D151D411yescharacteristic
45Dic604C2312yes—
46#14558994—22no—
47#14558993—22no—
48#14558992—22no—
49#14558991—22no—
50D1208C2312yes—
51#14558989—22no—
52C2×C151⋊C8D411yescharacteristic
53C8×D151D412yes—
54C8×D151C2312yes—
55C151⋊C16C2312yes—
56#41×C151—22no—
57Q16×C151C2312yes—
58SD16×C151—22no—
59D8×C151C2312yes—
60C2×C8×C151C2311yescharacteristic
61C16×C151C2311yescharacteristic
62C16×C151C2311yescharacteristic
63C22×D151—42no—
64C22×D151D811yescharacteristic
65Dic302—22no—
66Dic302—42no—
67D604—22no—
68D604—42no—
69C22⋊D151—42no—
70C22⋊D151—42no—
71C22⋊D151—42no—
72C2×Dic151—42no—
73C2×Dic151D811yescharacteristic
74C4×D151—42no—
75C4×D151—42no—
76C4×D151—42no—
77C4×D151D812yes—
78C4×D151C2×D412yes—
79C151⋊C8C2×D412yes—
80Q8×C151—22no—
81D4×C151—22no—
82D4×C151—42no—
83C2×C4×C151—42no—
84C2×C4×C151C2×D411yescharacteristic
85C8×C151C2×D411yescharacteristic
86C8×C151C2411yescharacteristic
87C22×C151—42no—
88C22×C151C2×D811yescharacteristic
89C2×D151—41no—
90C2×D151—42no—
91C2×D151—84no—
92C2×D151C2×D812yes—
93C4×C151—42no—
94C4×C151C2×D811yescharacteristic
95C4×C151C22×D411yescharacteristic
96Dic151—42no—
97Dic151C2×D812yes—
98C2×C151—21no—
99C2×C151—82no—
100C2×C151C22×D811yescharacteristic
101D151—22no—
102D151—82no—
103C151#341411yescharacteristic, complemented, Sylow
104#3414—1511nomaximal, Sylow
105C2×#135—1512no—
106#510—1512no—
107#510—1512no—
108#509—1512no—
109#509—1512no—
110#508—1512no—
111#508—1511no—
112#508D15111yescharacteristic, complemented
113C2×M32—1511no—
114C2×#41—3022no—
115#135—3022no—
116#135—3022no—
117#135—1512no—
118#135—1512no—
119#135—1512no—
120#135C2×D15112yescomplemented
121C2×Q16—1512no—
122C2×SD16—3022no—
123C2×D8—1512no—
124C22×C8—1511no—
125Q32—1512no—
126Q32—1511no—
127Q32C2×D15111yescharacteristic, complemented
128SD32—1512no—
129SD32—1512no—
130SD32—1512no—
131SD32C2×D15112yescomplemented
132D16—1512no—
133D16—1511no—
134D16C2×D15111yescharacteristic, complemented
135M32—1512no—
136M32—1512no—
137C2×C16—1511no—
138C2×C16C2×D15111yescharacteristic, complemented
139#41—22no—
140#41—3022no—
141#41—3022no—
142#41—3022no—
143#41—6042no—
144#41—6042no—
145C2×Q8—3022no—
146C2×D4—3022no—
147C2×D4—6042no—
148C22×C4—6042no—
149C22×C4—1511no—
150Q16—3022no—
151Q16—1512no—
152Q16C22×D15112yes—
153SD16—22no—
154SD16—3022no—
155SD16—3022no—
156SD16—3022no—
157D8—3022no—
158D8—1512no—
159D8C22×D15112yes—
160C2×C8—1511no—
161C2×C8—1512no—
162C2×C8—1512no—
163C2×C8C22×D15111yescharacteristic
164C16—1512no—
165C16C22×D15111yescharacteristic
166C16C22×D15111yescharacteristic
167C23—6042no—
168C23—1511no—
169Q8—22no—
170Q8—3022no—
171Q8—6042no—
172D4—22no—
173D4—42no—
174D4—3022no—
175D4—6042no—
176D4—6042no—
177D4—6042no—
178D4—6042no—
179C2×C4—42no—
180C2×C4—6042no—
181C2×C4—6042no—
182C2×C4—6042no—
183C2×C4—6042no—
184C2×C4—1511no—
185C2×C4—1512no—
186C2×C4—1512no—
187C2×C4D4×D15111yescharacteristic
188C8—1512no—
189C8D4×D15111yescharacteristic
190C8C23×D15111yescharacteristic
191C22—42no—
192C22—6041no—
193C22—6042no—
194C22—1512no—
195C22—12084no—
196C22D8×D15111yescharacteristic
197C4—42no—
198C4—6042no—
199C4—1512no—
200C4D8×D15111yescharacteristic
201C4C2×D4×D15111yescharacteristic
202C2—21no—
203C2—82no—
204C2—3022no—
205C2—12082no—
206C2C2×D8×D15111yescharacteristic
subgroupG/H
centerC4D8×D151
commutator, cosocleC8×C151C24
FrattiniC8C23×D151
Fitting#508×C151C2
socleC2×C151C22×D8
hypercenter#508D151
hypocenterC151#3414
LCSG ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D151C2semidirect
2. #23752654C2semidirect
3. #23752651C2semidirect
4. #23752649C2semidirect
5. #23752646C2semidirect
6. #23752644C2semidirect
7. #23752642C2semidirect
8. C2×#18012678C2semidirect
9. #508×C151C2semidirect
12. #18012761C22semidirect
16. Q16×D151C22semidirect
18. D8×D151C22semidirect
20. Dic1208C22semidirect
21. #18012685C22semidirect
22. #18012684C22semidirect
23. #18012683C22semidirect
24. #18012682C22semidirect
25. D2416C22semidirect
26. #18012680C22semidirect
27. #18012678C22semidirect
28. #18012678C22semidirect
29. C2×C151⋊C16C22semidirect
30. #135×C151C22semidirect
31. Q32×C151C22semidirect
32. SD32×C151C22semidirect
33. D16×C151C22semidirect
34. C2×C16×C151C22semidirect
103. C151#3414semidirect
112. #508D151semidirect
120. #135C2×D151semidirect
127. Q32C2×D151semidirect
131. SD32C2×D151semidirect
134. D16C2×D151semidirect
138. C2×C16C2×D151semidirect

Maximal subgroups

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

subgroupindex
#135×D1512
#237526542
#237526512
#237526492
#237526462
#237526442
#237526422
C2×#180126782
#508×C1512
#3414151