Finite Group Databasebeta

← #508×D151 #34082224

Subgroups — #508×D151 #34082224

Order 19328.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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#23752645C211yesmaximal, characteristic, complemented
3#23752644C211yesmaximal, characteristic, complemented
4#23752643C212yesmaximal, complemented
5#23752642C212yesmaximal, complemented
6#23752641C211yesmaximal, characteristic, complemented
7Q32×D151C211yesmaximal, characteristic, complemented
8SD32×D151C212yesmaximal, complemented
9D16×D151C211yesmaximal, characteristic, complemented
10C2×C16×D151C211yesmaximal, characteristic, complemented
11#508×C151C211yesmaximal, characteristic, complemented
12#41×D151—22no—
13#18012762C2212yescomplemented
14#18012761C2212yescomplemented
15#18012760—22no—
16#18012759—22no—
17#18012758C2212yescomplemented
18Q16×D151C2212yes—
19SD16×D151—22no—
20D8×D151C2212yes—
21C2×C8×D151C2211yescharacteristic
22Dic1208C2211yescharacteristic, complemented
23#18012685C2212yescomplemented
24#18012684C2212yescomplemented
25#18012683C2212yescomplemented
26#18012682C2212yescomplemented
27D2416C2211yescharacteristic, complemented
28#18012680C2212yescomplemented
29C2×C151⋊C16C2211yescharacteristic, complemented
30C16×D151C2211yescharacteristic
31C16×D151C2211yescharacteristic
32C16×D151C2211yescharacteristic, complemented
33C16×D151C2211yescharacteristic, complemented
34#135×C151C2212yescomplemented
35Q32×C151C2211yescharacteristic, complemented
36SD32×C151C2212yescomplemented
37D16×C151C2211yescharacteristic, complemented
38C2×C16×C151C2211yescharacteristic, complemented
39#14559005—22no—
40#14559004—22no—
41#14559004—42no—
42#14559003—22no—
43#14559003—42no—
44Q8×D151—22no—
45D4×D151—22no—
46D4×D151—42no—
47C2×C4×D151—42no—
48C2×C4×D151D411yescharacteristic
49Dic604C2312yes—
50#14558994—22no—
51#14558993—22no—
52#14558992—22no—
53#14558991—22no—
54D1208C2312yes—
55#14558989—22no—
56C2×C151⋊C8D411yescharacteristic
57C8×D151D411yescharacteristic
58C8×D151D411yescharacteristic
59C8×D151C2311yescharacteristic
60C8×D151C2311yescharacteristic
61C151⋊C16C2311yescharacteristic
62C151⋊C16C2311yescharacteristic
63#41×C151—22no—
64Q16×C151C2312yes—
65SD16×C151—22no—
66D8×C151C2312yes—
67C2×C8×C151C2311yescharacteristic
68C16×C151C2311yescharacteristic
69C16×C151C2311yescharacteristic
70C22×D151—42no—
71C22×D151D811yescharacteristic
72Dic302—22no—
73Dic302—42no—
74D604—22no—
75D604—42no—
76C22⋊D151—42no—
77C22⋊D151—42no—
78C22⋊D151—42no—
79C2×Dic151—42no—
80C2×Dic151D811yescharacteristic
81C4×D151—42no—
82C4×D151—42no—
83C4×D151—42no—
84C4×D151D811yescharacteristic
85C4×D151D811yescharacteristic
86C4×D151C2×D411yescharacteristic
87C4×D151C2×D411yescharacteristic
88C151⋊C8C2×D411yescharacteristic
89C151⋊C8C2×D411yescharacteristic
90Q8×C151—22no—
91D4×C151—22no—
92D4×C151—42no—
93C2×C4×C151—42no—
94C2×C4×C151C2×D411yescharacteristic
95C8×C151C2×D411yescharacteristic
96C8×C151C2411yescharacteristic
97C22×C151—42no—
98C22×C151C2×D811yescharacteristic
99C2×D151—22no—
100C2×D151—42no—
101C2×D151—84no—
102C2×D151C2×D811yescharacteristic
103C2×D151C2×D811yescharacteristic
104C4×C151—42no—
105C4×C151C2×D811yescharacteristic
106C4×C151C22×D411yescharacteristic
107Dic151—42no—
108Dic151C2×D811yescharacteristic
109Dic151C2×D811yescharacteristic
110C2×C151—21no—
111C2×C151—82no—
112C2×C151C22×D811yescharacteristic
113D151—21no—
114D151—82no—
115D151#50812yesdirect product factor
116C151C2×#50811yescharacteristic, complemented, Sylow
117C2×#508—1511nomaximal, Sylow
118C2×#135—1512no—
119#508—1512no—
120#508—1511no—
121#508—1512no—
122#508—1511no—
123#508—1511no—
124#508D15111yescharacteristic, direct product factor
125C2×Q32—1511no—
126C2×SD32—1512no—
127C2×D16—1511no—
128C22×C16—1511no—
129C2×#41—3022no—
130#135—3022no—
131#135—3022no—
132#135—1512no—
133#135—1512no—
134#135—1512no—
135#135C2×D15112yescomplemented
136C2×Q16—1512no—
137C2×SD16—3022no—
138C2×D8—1512no—
139C22×C8—1511no—
140Q32—1512no—
141Q32—1511no—
142Q32C2×D15111yescharacteristic, complemented
143SD32—1512no—
144SD32—1512no—
145SD32—1512no—
146SD32C2×D15112yescomplemented
147D16—1512no—
148D16—1511no—
149D16C2×D15111yescharacteristic, complemented
150C2×C16—1511no—
151C2×C16—1511no—
152C2×C16—1511no—
153C2×C16—1511no—
154C2×C16—1511no—
155C2×C16C2×D15111yescharacteristic, complemented
156#41—22no—
157#41—3022no—
158#41—3022no—
159#41—3022no—
160#41—6042no—
161#41—6042no—
162C2×Q8—3022no—
163C2×D4—3022no—
164C2×D4—6042no—
165C22×C4—6042no—
166C22×C4—1511no—
167Q16—3022no—
168Q16—1512no—
169Q16C22×D15112yes—
170SD16—22no—
171SD16—3022no—
172SD16—3022no—
173SD16—3022no—
174D8—3022no—
175D8—1512no—
176D8C22×D15112yes—
177C2×C8—1511no—
178C2×C8—1511no—
179C2×C8—1511no—
180C2×C8—1511no—
181C2×C8—1511no—
182C2×C8C22×D15111yescharacteristic
183C16—1511no—
184C16—1511no—
185C16C22×D15111yescharacteristic
186C16C22×D15111yescharacteristic
187C23—6042no—
188C23—1511no—
189Q8—22no—
190Q8—3022no—
191Q8—6042no—
192D4—22no—
193D4—42no—
194D4—3022no—
195D4—6042no—
196D4—6042no—
197D4—6042no—
198D4—6042no—
199C2×C4—42no—
200C2×C4—6042no—
201C2×C4—6042no—
202C2×C4—6042no—
203C2×C4—6042no—
204C2×C4—1511no—
205C2×C4—1511no—
206C2×C4—1511no—
207C2×C4—1511no—
208C2×C4—1511no—
209C2×C4D4×D15111yescharacteristic
210C8—1511no—
211C8—1511no—
212C8D4×D15111yescharacteristic
213C8C23×D15111yescharacteristic
214C22—42no—
215C22—3022no—
216C22—6042no—
217C22—1511no—
218C22—1511no—
219C22—12084no—
220C22D8×D15111yescharacteristic
221C4—42no—
222C4—6042no—
223C4—1511no—
224C4—1511no—
225C4D8×D15111yescharacteristic
226C4C2×D4×D15111yescharacteristic
227C2—21no—
228C2—82no—
229C2—3021no—
230C2—1512no—
231C2—12082no—
232C2C2×D8×D15111yescharacteristic
subgroupG/H
centerC4D8×D151
commutator, cosocleC8×C151C24
FrattiniC8C23×D151
Fitting#508×C151C2
socleC2×C151C22×D8
hypercenter#508D151
hypocenterC151C2×#508
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. #23752645C2semidirect
3. #23752644C2semidirect
4. #23752643C2semidirect
5. #23752642C2semidirect
6. #23752641C2semidirect
7. Q32×D151C2semidirect
8. SD32×D151C2semidirect
9. D16×D151C2semidirect
10. C2×C16×D151C2semidirect
11. #508×C151C2semidirect
13. #18012762C22semidirect
14. #18012761C22semidirect
17. #18012758C22semidirect
22. Dic1208C22semidirect
23. #18012685C22semidirect
24. #18012684C22semidirect
25. #18012683C22semidirect
26. #18012682C22semidirect
27. D2416C22semidirect
28. #18012680C22semidirect
29. C2×C151⋊C16C22semidirect
32. C16×D151C22semidirect
33. C16×D151C22semidirect
34. #135×C151C22semidirect
35. Q32×C151C22semidirect
36. SD32×C151C22semidirect
37. D16×C151C22semidirect
38. C2×C16×C151C22semidirect
115. D151#508direct (N × H)
116. C151C2×#508semidirect
124. #508D151direct (N × H)
135. #135C2×D151semidirect
142. Q32C2×D151semidirect
146. SD32C2×D151semidirect
149. D16C2×D151semidirect
155. 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
#237526452
#237526442
#237526432
#237526422
#237526412
Q32×D1512
SD32×D1512
D16×D1512
C2×C16×D1512
#508×C1512
C2×#508151