Finite Group Databasebeta

← #28371881

Subgroups — #28371881

Order 13952.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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
1C2×D8×D109C211yesmaximal, characteristic
2#20295498C212yesmaximal, complemented
3#20295139C211yesmaximal, characteristic, complemented
4#20295138C211yesmaximal, characteristic, complemented
5#20295137C211yesmaximal, characteristic, complemented
6C4×#13182014C212yesmaximal, complemented
7#20295106C212yesmaximal, complemented
8#20295061C211yesmaximal, characteristic, complemented
9#20295029C212yesmaximal, complemented
10#20294983C211yesmaximal, characteristic, complemented
11#442×C109C211yesmaximal, characteristic, complemented
12C2×D4×D109C2212yes—
13C2×D872C2211yescharacteristic
14C2×#13182014C2212yes—
15D8×D109C418yescomplemented
16C2×#13182012C2211yescharacteristic
17C2×C8×D109C2211yescharacteristic
18C4×D436C2212yescomplemented
19D4×Dic109C2212yescomplemented
20#16812661C2212yescomplemented
21C4×C22⋊D109—22no—
22#16812659—22no—
23#16812657C2212yes—
24#16812656C2211yescharacteristic
25C2×#13182006—22no—
26C22⋊C4×D109—22no—
27#16812632C2212yescomplemented
28#16812631C2211yescharacteristic, complemented
29#16812621C2212yescomplemented
30#16812620C2212yescomplemented
31#16812619C2212yescomplemented
32#16812609C2211yescharacteristic, complemented
33C4×#11724784C2211yescharacteristic, complemented
34C8×Dic109C2211yescharacteristic, complemented
35C2×D8×C109C2211yescharacteristic
36C4×D4×C109C2212yescomplemented
37#106×C109C2211yescharacteristic, complemented
38#102×C109C2212yescomplemented
39#97×C109C2211yescharacteristic, complemented
40C23×D109—22no—
41C2×D436C2312yes—
42C2×C22⋊D109—22no—
43D4×D109—24no—
44D4×D109C2×C418yescomplemented
45C22×Dic109—22no—
46C2×C4×D109—22no—
47C2×C4×D109—22no—
48C2×C4×D109C2311yescharacteristic
49D872C2×C414yescomplemented
50#13182014C2×C418yescomplemented
51#13182012—22no—
52C2×#11724784C2311yescharacteristic
53C2×#11724784C2311yescharacteristic
54C8×D109C2×C414yescomplemented
55C4⋊Dic109C2312yes—
56#13182008D412yes—
57C22⋊Dic109—22no—
58#13182006—22no—
59#13182006—22no—
60#13182006—22no—
61#13182006D412yes—
62C4×Dic109—22no—
63C4×Dic109C2311yescharacteristic
64C2×D4×C109C2312yes—
65C22×C4×C109—22no—
66D8×C109C2×C414yescomplemented
67C2×C8×C109C2311yescharacteristic
68C2×C8×C109C2311yescharacteristic
69C4⋊C4×C109C2312yes—
70C22⋊C4×C109—22no—
71C42×C109C2311yescharacteristic
72C23×C109—22no—
73C22×D109—22no—
74C22×D109—28no—
75C22×D109—82no—
76C22×D109—82no—
77C22×D109C2×D411yescharacteristic
78D4×C109—22no—
79D4×C109C22×C414yes—
80C2×C4×C109—22no—
81C2×C4×C109—82no—
82C2×C4×C109C2×D412yes—
83C2×C4×C109C2411yescharacteristic
84C22⋊D109—28no—
85C2×Dic109—22no—
86C2×Dic109—82no—
87C2×Dic109C2×D412yes—
88C2×Dic109C2×D411yescharacteristic
89D436—22no—
90D436C22×C414yes—
91C4×D109—82no—
92C4×D109—82no—
93C4×D109C22×C412yes—
94C4×D109#4112yes—
95C8×C109—21no—
96C8×C109C22×C412yes—
97#11724784—21no—
98#11724784C22×C412yes—
99C22×C109—24no—
100C22×C109—42no—
101C22×C109—42no—
102C22×C109C22×D411yescharacteristic
103C2×D109—22no—
104C2×D109—24no—
105C2×D109—42no—
106C2×D109—42no—
107C2×D109—88no—
108C2×D109C4×D412yes—
109C4×C109—22no—
110C4×C109—42no—
111C4×C109C23×C411yescharacteristic
112C4×C109C2×#4111yescharacteristic
113Dic109—22no—
114Dic109—42no—
115Dic109C4×D412yes—
116C2×C109—44no—
117C2×C109C2×C4×D411yescharacteristic
118C2×C109#57612yes—
119D109—22no—
120D109—44no—
121#2948—1091nomaximal, Sylow
122C109#294811yescharacteristic, complemented, Sylow
123C22×D8—1091no—
124#518—1092no—
125#442—1091no—
126#442—1091no—
127#442—1091no—
128#442D10911yescharacteristic, complemented
129C4×D8—1092no—
130C4×D8—1092no—
131#427—1091no—
132#418—1092no—
133#405—1091no—
134C22×D4—1092no—
135C2×D8—1092no—
136C2×D8—1098no—
137C2×D8—1091no—
138C2×D8C2×D10911yescharacteristic
139C2×M16—1091no—
140C22×C8—1091no—
141C4×D4—1092no—
142C4×D4—1092no—
143C4×D4—1092no—
144C4×D4—2182no—
145C4×D4—2182no—
146C4×D4C2×D10912yescomplemented
147#117—1091no—
148#117—1092no—
149C2×C22⋊C4—2182no—
150C2×C22⋊C4—2182no—
151#107—1092no—
152#106—1091no—
153#106C2×D10911yescharacteristic, complemented
154#102—1092no—
155#102—1092no—
156#102—1092no—
157#102C2×D10912yescomplemented
158#97—1091no—
159#97C2×D10911yescharacteristic, complemented
160C4×C8—1091no—
161C4×C8—1091no—
162C24—2182no—
163C2×D4—1098no—
164C2×D4—1092no—
165C2×D4—2184no—
166C2×D4—2182no—
167C2×D4C22×D10912yes—
168C22×C4—22no—
169C22×C4—1091no—
170C22×C4—2182no—
171C22×C4—2182no—
172C22×C4—2182no—
173D8—1098no—
174D8—1094no—
175D8C4×D10914yescomplemented
176M16—2182no—
177C2×C8—1091no—
178C2×C8—1094no—
179C2×C8—1091no—
180C2×C8C22×D10911yescharacteristic
181C2×C8C22×D10911yescharacteristic
182C4⋊C4—1092no—
183C4⋊C4—1092no—
184C4⋊C4C22×D10912yes—
185C22⋊C4—22no—
186C22⋊C4—1092no—
187C22⋊C4—2182no—
188C22⋊C4—2182no—
189C22⋊C4—2182no—
190C22⋊C4—2182no—
191C42—1091no—
192C42—2182no—
193C42C22×D10911yescharacteristic
194C23—22no—
195C23—8722no—
196C23—8722no—
197C23—1091no—
198C23—2188no—
199C23—2182no—
200D4—22no—
201D4—1094no—
202D4—2188no—
203D4—2182no—
204D4C2×C4×D10914yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—8722no—
208C2×C4—8722no—
209C2×C4—8722no—
210C2×C4—1091no—
211C2×C4—1092no—
212C2×C4—1092no—
213C2×C4—1092no—
214C2×C4—2182no—
215C2×C4D4×D10912yes—
216C2×C4C23×D10911yescharacteristic
217C8—21no—
218C8—1092no—
219C8—2181no—
220C8C2×C4×D10912yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—8728no—
225C22—1092no—
226C22—4362no—
227C22—4362no—
228C22—2184no—
229C22—2182no—
230C22C2×D4×D10911yescharacteristic
231C4—22no—
232C4—42no—
233C4—1092no—
234C4—4362no—
235C4—2182no—
236C4C22×C4×D10911yescharacteristic
237C4#41×D10911yescharacteristic
238C2—44no—
239C2—4364no—
240C2—2182no—
241C2C4×D4×D10911yescharacteristic
242C2#2029583012yes—
subgroupG/H
centerC22C2×D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
Fitting#442×C109C2
socleC22×C109C22×D4
prime radicalC2×D8×D109C2
cosocleC2×C4×C109C24
hypercenter#442D109
hypocenterC109#2948
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #20295498C2semidirect
3. #20295139C2semidirect
4. #20295138C2semidirect
5. #20295137C2semidirect
6. C4×#13182014C2semidirect
7. #20295106C2semidirect
8. #20295061C2semidirect
9. #20295029C2semidirect
10. #20294983C2semidirect
11. #442×C109C2semidirect
15. D8×D109C4semidirect
18. C4×D436C22semidirect
19. D4×Dic109C22semidirect
20. #16812661C22semidirect
27. #16812632C22semidirect
28. #16812631C22semidirect
29. #16812621C22semidirect
30. #16812620C22semidirect
31. #16812619C22semidirect
32. #16812609C22semidirect
33. C4×#11724784C22semidirect
34. C8×Dic109C22semidirect
36. C4×D4×C109C22semidirect
37. #106×C109C22semidirect
38. #102×C109C22semidirect
39. #97×C109C22semidirect
44. D4×D109C2×C4semidirect
49. D872C2×C4semidirect
50. #13182014C2×C4semidirect
54. C8×D109C2×C4semidirect
66. D8×C109C2×C4semidirect
122. C109#2948semidirect
128. #442D109semidirect
146. C4×D4C2×D109semidirect
153. #106C2×D109semidirect
157. #102C2×D109semidirect
159. #97C2×D109semidirect
175. D8C4×D109semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1092
#202954982
#202951392
#202951382
#202951372
C4×#131820142
#202951062
#202950612
#202950292
#202949832
#442×C1092
#2948109