Finite Group Databasebeta

← #469×D109 #28372624

Subgroups — #469×D109 #28372624

Order 13952.

596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 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, complemented
2C2×M16×D109C211yesmaximal, characteristic, complemented
3#121×D109C212yesmaximal, complemented
4#20295280C211yesmaximal, characteristic, complemented
5#20295279C211yesmaximal, characteristic, complemented
6#20295278C212yesmaximal, complemented
7#20295277C212yesmaximal, complemented
8#20295276C211yesmaximal, characteristic, complemented
9#106×D109C211yesmaximal, characteristic, complemented
10#102×D109C212yesmaximal, complemented
11#469×C109C211yesmaximal, characteristic, complemented
12C2×D4×D109—22no—
13C2×D4×D109C2212yes—
14C22×C4×D109C2211yescharacteristic
15C2×D872C2211yescharacteristic, complemented
16C2×#13182014C2212yescomplemented
17D8×D109—24no—
18C2×#13182013C2211yescharacteristic, complemented
19C2×#13182012C2211yescharacteristic, complemented
20C2×#13182012C2211yescharacteristic, complemented
21M16×D109—24no—
22C2×C8×D109C2211yescharacteristic
23C2×C8×D109C2211yescharacteristic
24#16812674C2212yescomplemented
25#16812673C2212yescomplemented
26#16812672—22no—
27#16812671—22no—
28#16812670C2212yescomplemented
29C4⋊C4×D109C2212yes—
30C22⋊C4×D109—22no—
31#16812631C2211yescharacteristic, complemented
32#16812630C2212yescomplemented
33#16812621C2212yescomplemented
34#16812620C2212yescomplemented
35#16812619C2212yescomplemented
36C2×D8×C109C2211yescharacteristic, complemented
37C2×M16×C109C2211yescharacteristic, complemented
38#121×C109C2212yescomplemented
39#106×C109C2211yescharacteristic, complemented
40#102×C109C2212yescomplemented
41C23×D109—22no—
42C23×D109D411yescharacteristic
43C2×D436—22no—
44C2×D436C2312yes—
45C2×C22⋊D109—22no—
46C2×C22⋊D109—22no—
47C2×C22⋊D109—22no—
48D4×D109—24no—
49D4×D109—24no—
50D4×D109—48no—
51C22×Dic109D411yescharacteristic
52C2×C4×D109—22no—
53C2×C4×D109—22no—
54C2×C4×D109—22no—
55C2×C4×D109D411yescharacteristic
56C2×C4×D109D411yescharacteristic
57C2×C4×D109C2311yescharacteristic
58C2×C4×D109C2311yescharacteristic
59D872—22no—
60#13182014—24no—
61#13182013—22no—
62#13182012—22no—
63#13182012—22no—
64C2×#11724784C2311yescharacteristic
65C2×#11724784C2311yescharacteristic
66C8×D109—22no—
67C8×D109D414yescomplemented
68C4⋊Dic109C2312yes—
69#13182008—22no—
70C22⋊Dic109—22no—
71#13182006—22no—
72#13182006—22no—
73C2×D4×C109—22no—
74C2×D4×C109C2312yes—
75C22×C4×C109C2311yescharacteristic
76D8×C109—22no—
77M16×C109—22no—
78C2×C8×C109C2311yescharacteristic
79C2×C8×C109C2311yescharacteristic
80C4⋊C4×C109C2312yes—
81C22⋊C4×C109—22no—
82C23×C109—22no—
83C23×C109C2×D411yescharacteristic
84C22×D109—22no—
85C22×D109—24no—
86C22×D109—22no—
87C22×D109—44no—
88C22×D109—44no—
89C22×D109—44no—
90C22×D109C2×D411yescharacteristic
91C22×D109C2×D411yescharacteristic
92D4×C109—22no—
93D4×C109—22no—
94D4×C109—44no—
95C2×C4×C109—21no—
96C2×C4×C109—21no—
97C2×C4×C109—22no—
98C2×C4×C109C2×D411yescharacteristic
99C2×C4×C109C2411yescharacteristic
100C22⋊D109—44no—
101C22⋊D109—44no—
102C22⋊D109—44no—
103C2×Dic109—22no—
104C2×Dic109—22no—
105C2×Dic109C2×D411yescharacteristic
106C2×Dic109C2×D411yescharacteristic
107D436—22no—
108D436—22no—
109D436—44no—
110C4×D109—22no—
111C4×D109—21no—
112C4×D109—21no—
113C4×D109—22no—
114C4×D109—44no—
115C4×D109C2×D412yes—
116C4×D109#4112yes—
117C8×C109—21no—
118C8×C109C2×D412yescomplemented
119#11724784—21no—
120#11724784C2×D412yescomplemented
121C22×C109—21no—
122C22×C109—22no—
123C22×C109—42no—
124C22×C109—42no—
125C22×C109—42no—
126C22×C109C22×D411yescharacteristic
127C2×D109—21no—
128C2×D109—22no—
129C2×D109—44no—
130C2×D109—42no—
131C2×D109—42no—
132C2×D109—42no—
133C2×D109—88no—
134C2×D109#12112yes—
135C2×D109AGL(1,ℤ/8)14yes—
136C4×C109—21no—
137C4×C109—42no—
138C4×C109C22×D411yescharacteristic
139C4×C109C2×#4111yescharacteristic
140Dic109—21no—
141Dic109—42no—
142Dic109#12112yes—
143C2×C109—41no—
144C2×C109—82no—
145C2×C109C2×#12111yescharacteristic
146C2×C109C2×AGL(1,ℤ/8)12yes—
147D109—41no—
148D109—82no—
149D109#46914yesdirect product factor
150C2×#469—1091nomaximal, Sylow
151C109C2×#46911yescharacteristic, complemented, Sylow
152C22×D8—1091no—
153C22×M16—1091no—
154C2×#121—1092no—
155#469—1091no—
156#469—1091no—
157#469—1092no—
158#469—1091no—
159#469—1092no—
160#469D10911yescharacteristic, direct product factor
161C2×#106—1091no—
162C2×#102—1092no—
163C22×D4—1092no—
164C22×D4—2182no—
165C23×C4—1091no—
166C2×D8—1092no—
167C2×D8—1091no—
168C2×D8—2184no—
169C2×D8C2×D10911yescharacteristic, complemented
170C2×M16—1091no—
171C2×M16—1091no—
172C2×M16—1091no—
173C2×M16—2184no—
174C2×M16C2×D10911yescharacteristic, complemented
175C22×C8—1091no—
176C22×C8—1091no—
177#121—1092no—
178#121—1092no—
179#121—1092no—
180#121—2182no—
181#121—2182no—
182#121C2×D10912yescomplemented
183C2×C4⋊C4—1092no—
184C2×C22⋊C4—2182no—
185#106—1091no—
186#106—1092no—
187#106C2×D10911yescharacteristic, complemented
188#102—1092no—
189#102—1092no—
190#102—1092no—
191#102C2×D10912yescomplemented
192C24—1091no—
193C24—2182no—
194C2×D4—22no—
195C2×D4—1092no—
196C2×D4—4368no—
197C2×D4—2182no—
198C2×D4—2184no—
199C2×D4—2184no—
200C2×D4—2182no—
201C2×D4—2182no—
202C2×D4—2182no—
203C2×D4C22×D10912yes—
204C22×C4—1091no—
205C22×C4—1091no—
206C22×C4—1091no—
207C22×C4—1091no—
208C22×C4—1091no—
209C22×C4—2182no—
210C22×C4—2182no—
211C22×C4—2182no—
212C22×C4C22×D10911yescharacteristic
213D8—22no—
214D8—2184no—
215D8—2182no—
216M16—22no—
217M16—2182no—
218M16—2182no—
219M16—2182no—
220C2×C8—1091no—
221C2×C8—1094no—
222C2×C8—1091no—
223C2×C8—2182no—
224C2×C8C22×D10911yescharacteristic
225C2×C8C22×D10911yescharacteristic
226C4⋊C4—1092no—
227C4⋊C4—2182no—
228C4⋊C4C22×D10912yes—
229C22⋊C4—22no—
230C22⋊C4—2182no—
231C22⋊C4—2182no—
232C22⋊C4—2182no—
233C23—22no—
234C23—1091no—
235C23—1091no—
236C23—4364no—
237C23—4364no—
238C23—4364no—
239C23—2182no—
240C23—2184no—
241C23—2182no—
242C23D4×D10911yescharacteristic
243D4—22no—
244D4—22no—
245D4—44no—
246D4—4364no—
247D4—4364no—
248D4—4364no—
249D4—4364no—
250D4—2182no—
251D4—2182no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—1091no—
256C2×C4—1092no—
257C2×C4—1092no—
258C2×C4—1091no—
259C2×C4—4364no—
260C2×C4—2182no—
261C2×C4—2182no—
262C2×C4—2182no—
263C2×C4—2182no—
264C2×C4—2181no—
265C2×C4—2181no—
266C2×C4D4×D10911yescharacteristic
267C2×C4C23×D10911yescharacteristic
268C8—21no—
269C8—1092no—
270C8—2181no—
271C8D4×D10912yescomplemented
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—8728no—
278C22—1092no—
279C22—1094no—
280C22—4364no—
281C22—4362no—
282C22—4362no—
283C22—4362no—
284C22—2181no—
285C22—2182no—
286C22C2×D4×D10911yescharacteristic
287C4—21no—
288C4—42no—
289C4—1092no—
290C4—4362no—
291C4—2181no—
292C4C2×D4×D10911yescharacteristic
293C4#41×D10911yescharacteristic
294C2—41no—
295C2—82no—
296C2—8722no—
297C2—1094no—
298C2—4361no—
299C2#121×D10911yescharacteristic
300C2AGL(1,ℤ/8)×D10912yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#469×C109C2
socleC22×C109C22×D4
hypercenter#469D109
hypocenterC109C2×#469
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D109C2semidirect
2. C2×M16×D109C2semidirect
3. #121×D109C2semidirect
4. #20295280C2semidirect
5. #20295279C2semidirect
6. #20295278C2semidirect
7. #20295277C2semidirect
8. #20295276C2semidirect
9. #106×D109C2semidirect
10. #102×D109C2semidirect
11. #469×C109C2semidirect
15. C2×D872C22semidirect
16. C2×#13182014C22semidirect
18. C2×#13182013C22semidirect
19. C2×#13182012C22semidirect
20. C2×#13182012C22semidirect
24. #16812674C22semidirect
25. #16812673C22semidirect
28. #16812670C22semidirect
31. #16812631C22semidirect
32. #16812630C22semidirect
33. #16812621C22semidirect
34. #16812620C22semidirect
35. #16812619C22semidirect
36. C2×D8×C109C22semidirect
37. C2×M16×C109C22semidirect
38. #121×C109C22semidirect
39. #106×C109C22semidirect
40. #102×C109C22semidirect
67. C8×D109D4semidirect
118. C8×C109C2×D4semidirect
120. #11724784C2×D4semidirect
149. D109#469direct (N × H)
151. C109C2×#469semidirect
160. #469D109direct (N × H)
169. C2×D8C2×D109semidirect
174. C2×M16C2×D109semidirect
182. #121C2×D109semidirect
187. #106C2×D109semidirect
191. #102C2×D109semidirect
271. C8D4×D109semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1092
C2×M16×D1092
#121×D1092
#202952802
#202952792
#202952782
#202952772
#202952762
#106×D1092
#102×D1092
#469×C1092
C2×#469109