Finite Group Databasebeta

← #28376174

Subgroups — #28376174

Order 13952.

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#20295839C211yesmaximal, characteristic, complemented
2#20295827C211yesmaximal, characteristic, complemented
3#20295467C211yesmaximal, characteristic, complemented
4#20295465C212yesmaximal, complemented
5#20295463C212yesmaximal, complemented
6#20295462C211yesmaximal, characteristic, complemented
7#20295458C211yesmaximal, characteristic, complemented
8#20295457C212yesmaximal, complemented
9SD32×D109C212yesmaximal, complemented
10#20295442C211yesmaximal, characteristic, complemented
11C2×SD32×C109C211yesmaximal, characteristic, complemented
12#16812747—21no—
13#16812744—21no—
14#16812731—22no—
15#16812730—21no—
16#16812725—21no—
17#16812723—22no—
18#16812722C2212yescomplemented
19#16812721C2211yescharacteristic
20#16812721C2211yescharacteristic, complemented
21#16812718C2212yes—
22Q16×D109C2212yescomplemented
23D8×D109C2212yes—
24#16812705C2211yescharacteristic
25Dic872C2211yescharacteristic, complemented
26#16812645C2212yescomplemented
27#16812644C2211yescharacteristic, complemented
28#16812644C2211yescharacteristic, complemented
29#16812643C2212yescomplemented
30#16812642C2212yescomplemented
31D1744C2211yescharacteristic, complemented
32#16812640C2212yescomplemented
33#16812639C2211yescharacteristic, complemented
34#16812638C2212yescomplemented
35C16×D109C2212yescomplemented
36C2×Q16×C109C2211yescharacteristic, complemented
37C2×D8×C109C2211yescharacteristic
38SD32×C109C2212yescomplemented
39SD32×C109C2212yescomplemented
40C2×C16×C109C2211yescharacteristic, complemented
41#13182030—22no—
42#13182030—41no—
43#13182029—21no—
44#13182029—21no—
45#13182029—42no—
46#13182029D411yescharacteristic
47#13182028—22no—
48#13182028—41no—
49Q8×D109—22no—
50Q8×D109—41no—
51C2×C22⋊D109—42no—
52D4×D109—22no—
53D4×D109—41no—
54Dic436C2311yescharacteristic
55Dic436C2311yescharacteristic
56#13182019—22no—
57#13182018—21no—
58#13182018—21no—
59#13182017—22no—
60#13182016—22no—
61D872C2311yescharacteristic
62D872C2311yescharacteristic
63#13182014—22no—
64#13182013D411yescharacteristic
65#13182012D412yes—
66C8×D109C2312yes—
67#13182004C2312yes—
68C2×Q8×C109—21no—
69C2×D4×C109—21no—
70Q16×C109—21no—
71Q16×C109C2312yes—
72D8×C109—21no—
73D8×C109C2312yes—
74C2×C8×C109C2311yescharacteristic
75C16×C109C2311yescharacteristic
76C16×C109C2311yescharacteristic
77C23×C109—41no—
78C22×D109—42no—
79Q8×C109—22no—
80Q8×C109—41no—
81D4×C109—22no—
82D4×C109—41no—
83C2×C4×C109—41no—
84C2×C4×C109C2×D411yescharacteristic
85C22⋊D109—41no—
86C22⋊D109—41no—
87C22⋊D109—42no—
88C22⋊D109—42no—
89C22⋊D109D812yes—
90C2×Dic109—42no—
91D436—21no—
92D436—21no—
93D436—42no—
94D436D811yescharacteristic
95C4×D109—42no—
96C4×D109—41no—
97C4×D109—41no—
98C4×D109—42no—
99C4×D109C2×D412yes—
100Dic218—21no—
101Dic218—21no—
102Dic218—42no—
103Dic218D811yescharacteristic
104C8×C109C2×D411yescharacteristic
105C8×C109C2411yescharacteristic
106#11724784C2×D412yes—
107C22×C109—42no—
108C22×C109—161no—
109C22×C109C2×D811yescharacteristic
110C2×D109—41no—
111C2×D109—41no—
112C2×D109—162no—
113C2×D109C2×D812yes—
114C4×C109—42no—
115C4×C109C2×D811yescharacteristic
116C4×C109C22×D411yescharacteristic
117Dic109—41no—
118Dic109—41no—
119Dic109C2×D812yes—
120C2×C109—21no—
121C2×C109—82no—
122C2×C109C22×D811yescharacteristic
123D109—22no—
124D109—81no—
125D109—81no—
126#3416—1091nomaximal, Sylow
127C109#341611yescharacteristic, complemented, Sylow
128#578—1091no—
129#576—1091no—
130#510—1091no—
131#510—1092no—
132#509—1091no—
133#509—1092no—
134#508—1092no—
135#508—1091no—
136C2×SD32—1092no—
137C2×SD32D10911yescharacteristic, complemented
138#504—1091no—
1392−1+4—2181no—
140H(5,𝔽2)—2181no—
141#137—2182no—
142#137—2181no—
143AGL(1,ℤ/8)—2182no—
144AGL(1,ℤ/8)—2181no—
145#135—1092no—
146#135—1092no—
147#135—1091no—
148#135—1091no—
149C2×Q16—1092no—
150C2×Q16C2×D10911yescharacteristic, complemented
151C2×D8—1092no—
152C2×D8C2×D10911yescharacteristic
153#131—1091no—
154Q32—1092no—
155Q32—1091no—
156SD32—1092no—
157SD32—1092no—
158SD32—1091no—
159SD32—1091no—
160SD32C2×D10912yescomplemented
161SD32C2×D10912yescomplemented
162D16—1092no—
163D16—1091no—
164M32—1091no—
165M32—1092no—
166C2×C16—1092no—
167C2×C16C2×D10911yescharacteristic, complemented
168#41—1091no—
169#41—4362no—
170#41—4361no—
171#41—4361no—
172#41—2182no—
173#41—2182no—
174#41—2181no—
175#41—2181no—
176C2×Q8—21no—
177C2×Q8—4361no—
178C2×Q8—2182no—
179C2×D4—21no—
180C2×D4—4361no—
181C2×D4—4362no—
182C2×D4—2182no—
183Q16—21no—
184Q16—1091no—
185Q16—1091no—
186Q16—2182no—
187Q16C22×D10912yes—
188SD16—2182no—
189SD16—2182no—
190SD16—2181no—
191SD16—2181no—
192D8—21no—
193D8—1091no—
194D8—1091no—
195D8—2182no—
196D8C22×D10912yes—
197M16—1091no—
198M16—1092no—
199C2×C8—1092no—
200C2×C8C22×D10911yescharacteristic
201C16—1092no—
202C16C22×D10911yescharacteristic
203C16C22×D10911yescharacteristic
204C23—41no—
205C23—4362no—
206Q8—22no—
207Q8—41no—
208Q8—1091no—
209Q8—4362no—
210Q8—2181no—
211Q8—2181no—
212D4—22no—
213D4—41no—
214D4—1092no—
215D4—1091no—
216D4—4362no—
217D4—4362no—
218D4—4362no—
219D4—4361no—
220D4—4361no—
221D4—2181no—
222D4—2181no—
223C2×C4—41no—
224C2×C4—1092no—
225C2×C4—4362no—
226C2×C4—4362no—
227C2×C4—4362no—
228C2×C4—4361no—
229C2×C4—4361no—
230C2×C4D4×D10911yescharacteristic
231C8—1092no—
232C8D4×D10911yescharacteristic
233C8C23×D10911yescharacteristic
234C22—42no—
235C22—161no—
236C22—1092no—
237C22—4361no—
238C22—4361no—
239C22—17442no—
240C22D8×D10911yescharacteristic
241C4—42no—
242C4—1092no—
243C4—4361no—
244C4—4361no—
245C4D8×D10911yescharacteristic
246C4C2×D4×D10911yescharacteristic
247C2—21no—
248C2—82no—
249C2—8721no—
250C2—8721no—
251C2—2182no—
252C2C2×D8×D10911yescharacteristic
subgroupG/H
centerC2C2×D8×D109
commutator, cosocleC8×C109C24
FrattiniC8C23×D109
FittingC2×SD32×C109C2
socleC2×C109C22×D8
hypercenterC2×SD32D109
hypocenterC109#3416
LCSG ▷ C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #20295839C2semidirect
2. #20295827C2semidirect
3. #20295467C2semidirect
4. #20295465C2semidirect
5. #20295463C2semidirect
6. #20295462C2semidirect
7. #20295458C2semidirect
8. #20295457C2semidirect
9. SD32×D109C2semidirect
10. #20295442C2semidirect
11. C2×SD32×C109C2semidirect
18. #16812722C22semidirect
20. #16812721C22semidirect
22. Q16×D109C22semidirect
25. Dic872C22semidirect
26. #16812645C22semidirect
27. #16812644C22semidirect
28. #16812644C22semidirect
29. #16812643C22semidirect
30. #16812642C22semidirect
31. D1744C22semidirect
32. #16812640C22semidirect
33. #16812639C22semidirect
34. #16812638C22semidirect
35. C16×D109C22semidirect
36. C2×Q16×C109C22semidirect
38. SD32×C109C22semidirect
39. SD32×C109C22semidirect
40. C2×C16×C109C22semidirect
127. C109#3416semidirect
137. C2×SD32D109semidirect
150. C2×Q16C2×D109semidirect
160. SD32C2×D109semidirect
161. SD32C2×D109semidirect
167. C2×C16C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202958392
#202958272
#202954672
#202954652
#202954632
#202954622
#202954582
#202954572
SD32×D1092
#202954422
C2×SD32×C1092
#3416109