Finite Group Databasebeta

← #27208290

Subgroups — #27208290

Order 13184.

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

normal subgroups only

This group has 360 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#20268605C211yesmaximal, characteristic, complemented
2#20268592C211yesmaximal, characteristic, complemented
3#20268234C211yesmaximal, characteristic, complemented
4#20268230C212yesmaximal, complemented
5#20268225C212yesmaximal, complemented
6#20268221C211yesmaximal, characteristic, complemented
7#20268220C212yesmaximal, complemented
8C2×#15692965C211yesmaximal, characteristic, complemented
9SD32×D103C212yesmaximal, complemented
10#20268209C211yesmaximal, characteristic, complemented
11#509×C103C211yesmaximal, characteristic, complemented
12#15693068—21no—
13#15693066—21no—
14#15693051—21no—
15#15693050—22no—
16#15693047—21no—
17#15693045—22no—
18#15693043C2211yescharacteristic
19#15693040C2212yes—
20#15693040C2212yescomplemented
21C2×Dic412C2211yescharacteristic, complemented
22Q16×D103C2212yescomplemented
23D8×D103C2212yes—
24#15693027C2211yescharacteristic
25Dic824C2212yescomplemented
26#15692967C2211yescharacteristic, complemented
27#15692966C2212yescomplemented
28#15692965C2212yescomplemented
29#15692965C2212yescomplemented
30#15692965C2211yescharacteristic, complemented
31#15692964C2211yescharacteristic, complemented
32#15692962C2211yescharacteristic, complemented
33#15692960C2212yescomplemented
34C2×C103⋊C16C2211yescharacteristic, complemented
35C16×D103C2212yescomplemented
36#135×C103C2211yescharacteristic, complemented
37C2×D8×C103C2211yescharacteristic
38SD32×C103C2212yescomplemented
39D16×C103C2212yescomplemented
40M32×C103C2211yescharacteristic, complemented
41#13110105—21no—
42#13110105—41no—
43#13110105D411yescharacteristic
44#13110104—22no—
45#13110104—22no—
46#13110104—42no—
47#13110104—41no—
48C2×Dic206—21no—
49C2×Dic206—41no—
50Q8×D103—22no—
51C2×C22⋊D103—42no—
52D4×D103—22no—
53D4×D103—41no—
54Dic412—21no—
55Dic412C2312yes—
56Dic412C2311yescharacteristic
57#13110095—22no—
58#13110094—21no—
59#13110093—22no—
60#13110093—22no—
61D824C2311yescharacteristic
62#13110090—22no—
63#13110089D411yescharacteristic
64#13110088D412yes—
65C8×D103C2312yes—
66C103⋊C16C2311yescharacteristic
67C103⋊C16C2311yescharacteristic
68#41×C103—21no—
69C2×D4×C103—21no—
70Q16×C103C2311yescharacteristic
71SD16×C103—21no—
72D8×C103—21no—
73D8×C103C2311yescharacteristic
74D8×C103C2312yes—
75C2×C8×C103C2311yescharacteristic
76C16×C103C2312yes—
77C23×C103—41no—
78C22×D103—42no—
79Q8×C103—21no—
80D4×C103—22no—
81D4×C103—21no—
82D4×C103—41no—
83D4×C103—41no—
84C2×C4×C103—41no—
85C2×C4×C103C2×D411yescharacteristic
86C22⋊D103—41no—
87C22⋊D103—42no—
88C22⋊D103—42no—
89C22⋊D103—42no—
90C22⋊D103D812yes—
91C2×Dic103—41no—
92C2×Dic103—42no—
93C2×Dic103—42no—
94D412—21no—
95D412D811yescharacteristic
96C4×D103—42no—
97C4×D103—41no—
98C4×D103C2×D412yes—
99Dic206—21no—
100Dic206—22no—
101Dic206—41no—
102Dic206—42no—
103Dic206D811yescharacteristic
104C8×C103C2×D411yescharacteristic
105C8×C103C2411yescharacteristic
106C103⋊C8C2×D412yes—
107C22×C103—41no—
108C22×C103—42no—
109C22×C103—161no—
110C22×C103C2×D811yescharacteristic
111C2×D103—41no—
112C2×D103—162no—
113C2×D103C2×D812yes—
114C4×C103—41no—
115C4×C103C2×D811yescharacteristic
116C4×C103C22×D411yescharacteristic
117Dic103—42no—
118Dic103—41no—
119Dic103C2×D812yes—
120C2×C103—21no—
121C2×C103—82no—
122C2×C103—81no—
123C2×C103C22×D811yescharacteristic
124D103—22no—
125D103—81no—
126#3416—1031nomaximal, Sylow
127C103#341611yescharacteristic, complemented, Sylow
128#578—1031no—
129#576—1031no—
130#510—1032no—
131#510—1031no—
132#509—1032no—
133#509D10311yescharacteristic, complemented
134#508—1031no—
135#508—1032no—
136C2×SD32—1031no—
137C2×SD32—1032no—
138#504—1031no—
1392−1+4—2061no—
140H(5,𝔽2)—2061no—
141#137—2062no—
142#137—2061no—
143AGL(1,ℤ/8)—2062no—
144AGL(1,ℤ/8)—2061no—
145#135—1032no—
146#135—1032no—
147#135—1031no—
148#135C2×D10311yescharacteristic, complemented
149C2×Q16—1032no—
150C2×Q16—1031no—
151C2×D8—1032no—
152C2×D8C2×D10311yescharacteristic
153#131—1031no—
154Q32—1031no—
155Q32—1032no—
156SD32—1031no—
157SD32—1032no—
158SD32—1032no—
159SD32—1031no—
160SD32—1032no—
161SD32C2×D10312yescomplemented
162D16—1031no—
163D16C2×D10312yescomplemented
164M32—1032no—
165M32C2×D10311yescharacteristic, complemented
166C2×C16—1031no—
167C2×C16—1032no—
168#41—21no—
169#41—1031no—
170#41—4121no—
171#41—4122no—
172#41—4121no—
173#41—2062no—
174#41—2062no—
175#41—2061no—
176C2×Q8—4121no—
177C2×Q8—2062no—
178C2×Q8—2061no—
179C2×D4—21no—
180C2×D4—4121no—
181C2×D4—4122no—
182C2×D4—2062no—
183Q16—1032no—
184Q16—1031no—
185Q16—2062no—
186Q16—2061no—
187Q16C22×D10311yescharacteristic
188SD16—21no—
189SD16—2062no—
190SD16—2062no—
191SD16—2061no—
192D8—21no—
193D8—1031no—
194D8—2062no—
195D8C22×D10311yescharacteristic
196D8C22×D10312yes—
197M16—1031no—
198M16—1032no—
199C2×C8—1032no—
200C2×C8C22×D10311yescharacteristic
201C16—1031no—
202C16—1031no—
203C16C22×D10312yes—
204C23—41no—
205C23—4122no—
206Q8—21no—
207Q8—1031no—
208Q8—4122no—
209Q8—4121no—
210Q8—2061no—
211Q8—2062no—
212D4—22no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—1032no—
217D4—1031no—
218D4—4122no—
219D4—4122no—
220D4—4122no—
221D4—4121no—
222D4—2061no—
223C2×C4—41no—
224C2×C4—1032no—
225C2×C4—4122no—
226C2×C4—4122no—
227C2×C4—4122no—
228C2×C4—4121no—
229C2×C4—4121no—
230C2×C4D4×D10311yescharacteristic
231C8—1032no—
232C8D4×D10311yescharacteristic
233C8C23×D10311yescharacteristic
234C22—41no—
235C22—42no—
236C22—161no—
237C22—1032no—
238C22—16482no—
239C22—4121no—
240C22D8×D10311yescharacteristic
241C4—41no—
242C4—1032no—
243C4—4121no—
244C4—4122no—
245C4D8×D10311yescharacteristic
246C4C2×D4×D10311yescharacteristic
247C2—21no—
248C2—82no—
249C2—81no—
250C2—8241no—
251C2—2062no—
252C2C2×D8×D10311yescharacteristic
subgroupG/H
centerC2C2×D8×D103
commutator, cosocleC8×C103C24
FrattiniC8C23×D103
Fitting#509×C103C2
socleC2×C103C22×D8
hypercenter#509D103
hypocenterC103#3416
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #20268605C2semidirect
2. #20268592C2semidirect
3. #20268234C2semidirect
4. #20268230C2semidirect
5. #20268225C2semidirect
6. #20268221C2semidirect
7. #20268220C2semidirect
8. C2×#15692965C2semidirect
9. SD32×D103C2semidirect
10. #20268209C2semidirect
11. #509×C103C2semidirect
20. #15693040C22semidirect
21. C2×Dic412C22semidirect
22. Q16×D103C22semidirect
25. Dic824C22semidirect
26. #15692967C22semidirect
27. #15692966C22semidirect
28. #15692965C22semidirect
29. #15692965C22semidirect
30. #15692965C22semidirect
31. #15692964C22semidirect
32. #15692962C22semidirect
33. #15692960C22semidirect
34. C2×C103⋊C16C22semidirect
35. C16×D103C22semidirect
36. #135×C103C22semidirect
38. SD32×C103C22semidirect
39. D16×C103C22semidirect
40. M32×C103C22semidirect
127. C103#3416semidirect
133. #509D103semidirect
148. #135C2×D103semidirect
161. SD32C2×D103semidirect
163. D16C2×D103semidirect
165. M32C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202686052
#202685922
#202682342
#202682302
#202682252
#202682212
#202682202
C2×#156929652
SD32×D1032
#202682092
#509×C1032
#3416103