Finite Group Databasebeta

← #508×D103 #27208258

Subgroups — #508×D103 #27208258

Order 13184.

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×D103C212yesmaximal, complemented
2#20268224C211yesmaximal, characteristic, complemented
3#20268223C211yesmaximal, characteristic, complemented
4#20268222C212yesmaximal, complemented
5#20268221C212yesmaximal, complemented
6#20268220C211yesmaximal, characteristic, complemented
7Q32×D103C211yesmaximal, characteristic, complemented
8SD32×D103C212yesmaximal, complemented
9D16×D103C211yesmaximal, characteristic, complemented
10C2×C16×D103C211yesmaximal, characteristic, complemented
11#508×C103C211yesmaximal, characteristic, complemented
12#41×D103—22no—
13#15693044C2212yescomplemented
14#15693043C2212yescomplemented
15#15693042—22no—
16#15693041—22no—
17#15693040C2212yescomplemented
18Q16×D103C2212yes—
19SD16×D103—22no—
20D8×D103C2212yes—
21C2×C8×D103C2211yescharacteristic
22Dic824C2211yescharacteristic, complemented
23#15692967C2212yescomplemented
24#15692966C2212yescomplemented
25#15692965C2212yescomplemented
26#15692964C2212yescomplemented
27D1648C2211yescharacteristic, complemented
28#15692962C2212yescomplemented
29C2×C103⋊C16C2211yescharacteristic, complemented
30C16×D103C2211yescharacteristic
31C16×D103C2211yescharacteristic
32C16×D103C2211yescharacteristic, complemented
33C16×D103C2211yescharacteristic, complemented
34#135×C103C2212yescomplemented
35Q32×C103C2211yescharacteristic, complemented
36SD32×C103C2212yescomplemented
37D16×C103C2211yescharacteristic, complemented
38C2×C16×C103C2211yescharacteristic, complemented
39#13110106—22no—
40#13110105—22no—
41#13110105—42no—
42#13110104—22no—
43#13110104—42no—
44Q8×D103—22no—
45D4×D103—22no—
46D4×D103—42no—
47C2×C4×D103—42no—
48C2×C4×D103D411yescharacteristic
49Dic412C2312yes—
50#13110095—22no—
51#13110094—22no—
52#13110093—22no—
53#13110092—22no—
54D824C2312yes—
55#13110090—22no—
56C2×C103⋊C8D411yescharacteristic
57C8×D103D411yescharacteristic
58C8×D103D411yescharacteristic
59C8×D103C2311yescharacteristic
60C8×D103C2311yescharacteristic
61C103⋊C16C2311yescharacteristic
62C103⋊C16C2311yescharacteristic
63#41×C103—22no—
64Q16×C103C2312yes—
65SD16×C103—22no—
66D8×C103C2312yes—
67C2×C8×C103C2311yescharacteristic
68C16×C103C2311yescharacteristic
69C16×C103C2311yescharacteristic
70C22×D103—42no—
71C22×D103D811yescharacteristic
72Q8×C103—22no—
73D4×C103—22no—
74D4×C103—42no—
75C2×C4×C103—42no—
76C2×C4×C103C2×D411yescharacteristic
77C22⋊D103—42no—
78C22⋊D103—42no—
79C22⋊D103—42no—
80C2×Dic103—42no—
81C2×Dic103D811yescharacteristic
82D412—22no—
83D412—42no—
84C4×D103—42no—
85C4×D103—42no—
86C4×D103—42no—
87C4×D103D811yescharacteristic
88C4×D103D811yescharacteristic
89C4×D103C2×D411yescharacteristic
90C4×D103C2×D411yescharacteristic
91Dic206—22no—
92Dic206—42no—
93C8×C103C2×D411yescharacteristic
94C8×C103C2411yescharacteristic
95C103⋊C8C2×D411yescharacteristic
96C103⋊C8C2×D411yescharacteristic
97C22×C103—42no—
98C22×C103C2×D811yescharacteristic
99C2×D103—22no—
100C2×D103—42no—
101C2×D103—84no—
102C2×D103C2×D811yescharacteristic
103C2×D103C2×D811yescharacteristic
104C4×C103—42no—
105C4×C103C2×D811yescharacteristic
106C4×C103C22×D411yescharacteristic
107Dic103—42no—
108Dic103C2×D811yescharacteristic
109Dic103C2×D811yescharacteristic
110C2×C103—21no—
111C2×C103—82no—
112C2×C103C22×D811yescharacteristic
113D103—21no—
114D103—82no—
115D103#50812yesdirect product factor
116C2×#508—1031nomaximal, Sylow
117C103C2×#50811yescharacteristic, complemented, Sylow
118C2×#135—1032no—
119#508—1032no—
120#508—1031no—
121#508—1032no—
122#508—1031no—
123#508—1031no—
124#508D10311yescharacteristic, direct product factor
125C2×Q32—1031no—
126C2×SD32—1032no—
127C2×D16—1031no—
128C22×C16—1031no—
129C2×#41—2062no—
130#135—1032no—
131#135—1032no—
132#135—1032no—
133#135—2062no—
134#135—2062no—
135#135C2×D10312yescomplemented
136C2×Q16—1032no—
137C2×SD16—2062no—
138C2×D8—1032no—
139C22×C8—1031no—
140Q32—1032no—
141Q32—1031no—
142Q32C2×D10311yescharacteristic, complemented
143SD32—1032no—
144SD32—1032no—
145SD32—1032no—
146SD32C2×D10312yescomplemented
147D16—1032no—
148D16—1031no—
149D16C2×D10311yescharacteristic, complemented
150C2×C16—1031no—
151C2×C16—1031no—
152C2×C16—1031no—
153C2×C16—1031no—
154C2×C16—1031no—
155C2×C16C2×D10311yescharacteristic, complemented
156#41—22no—
157#41—4122no—
158#41—4122no—
159#41—2062no—
160#41—2062no—
161#41—2062no—
162C2×Q8—2062no—
163C2×D4—4122no—
164C2×D4—2062no—
165C22×C4—1031no—
166C22×C4—4122no—
167Q16—1032no—
168Q16—2062no—
169Q16C22×D10312yes—
170SD16—22no—
171SD16—2062no—
172SD16—2062no—
173SD16—2062no—
174D8—1032no—
175D8—2062no—
176D8C22×D10312yes—
177C2×C8—1031no—
178C2×C8—1031no—
179C2×C8—1031no—
180C2×C8—1031no—
181C2×C8—1031no—
182C2×C8C22×D10311yescharacteristic
183C16—1031no—
184C16—1031no—
185C16C22×D10311yescharacteristic
186C16C22×D10311yescharacteristic
187C23—1031no—
188C23—4122no—
189Q8—22no—
190Q8—4122no—
191Q8—2062no—
192D4—22no—
193D4—42no—
194D4—4122no—
195D4—4122no—
196D4—4122no—
197D4—4122no—
198D4—2062no—
199C2×C4—42no—
200C2×C4—1031no—
201C2×C4—1031no—
202C2×C4—1031no—
203C2×C4—1031no—
204C2×C4—1031no—
205C2×C4—4122no—
206C2×C4—4122no—
207C2×C4—4122no—
208C2×C4—4122no—
209C2×C4D4×D10311yescharacteristic
210C8—1031no—
211C8—1031no—
212C8D4×D10311yescharacteristic
213C8C23×D10311yescharacteristic
214C22—42no—
215C22—8244no—
216C22—1031no—
217C22—1031no—
218C22—4122no—
219C22—2062no—
220C22D8×D10311yescharacteristic
221C4—42no—
222C4—1031no—
223C4—1031no—
224C4—4122no—
225C4D8×D10311yescharacteristic
226C4C2×D4×D10311yescharacteristic
227C2—21no—
228C2—82no—
229C2—8242no—
230C2—1032no—
231C2—2061no—
232C2C2×D8×D10311yescharacteristic
subgroupG/H
centerC4D8×D103
commutator, cosocleC8×C103C24
FrattiniC8C23×D103
Fitting#508×C103C2
socleC2×C103C22×D8
hypercenter#508D103
hypocenterC103C2×#508
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D103C2semidirect
2. #20268224C2semidirect
3. #20268223C2semidirect
4. #20268222C2semidirect
5. #20268221C2semidirect
6. #20268220C2semidirect
7. Q32×D103C2semidirect
8. SD32×D103C2semidirect
9. D16×D103C2semidirect
10. C2×C16×D103C2semidirect
11. #508×C103C2semidirect
13. #15693044C22semidirect
14. #15693043C22semidirect
17. #15693040C22semidirect
22. Dic824C22semidirect
23. #15692967C22semidirect
24. #15692966C22semidirect
25. #15692965C22semidirect
26. #15692964C22semidirect
27. D1648C22semidirect
28. #15692962C22semidirect
29. C2×C103⋊C16C22semidirect
32. C16×D103C22semidirect
33. C16×D103C22semidirect
34. #135×C103C22semidirect
35. Q32×C103C22semidirect
36. SD32×C103C22semidirect
37. D16×C103C22semidirect
38. C2×C16×C103C22semidirect
115. D103#508direct (N × H)
117. C103C2×#508semidirect
124. #508D103direct (N × H)
135. #135C2×D103semidirect
142. Q32C2×D103semidirect
146. SD32C2×D103semidirect
149. D16C2×D103semidirect
155. C2×C16C2×D103semidirect

Maximal subgroups

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

subgroupindex
#135×D1032
#202682242
#202682232
#202682222
#202682212
#202682202
Q32×D1032
SD32×D1032
D16×D1032
C2×C16×D1032
#508×C1032
C2×#508103