Finite Group Databasebeta

← #442×D79 #23772189

Subgroups — #442×D79 #23772189

Order 10112.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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×D79C211yesmaximal, characteristic
2C4×D4×D79C212yesmaximal, complemented
3#19098676C211yesmaximal, characteristic, complemented
4#19098675C211yesmaximal, characteristic, complemented
5#19098674C211yesmaximal, characteristic, complemented
6#19098673C212yesmaximal, complemented
7#19098672C212yesmaximal, complemented
8#106×D79C211yesmaximal, characteristic, complemented
9#102×D79C212yesmaximal, complemented
10#97×D79C211yesmaximal, characteristic, complemented
11#442×C79C211yesmaximal, characteristic, complemented
12C2×D4×D79C2212yes—
13C22×C4×D79—22no—
14C2×D632C2211yescharacteristic
15C2×#11929609C2212yes—
16D8×D79C418yescomplemented
17C2×C8×D79C2211yescharacteristic
18C2×C8×D79C2211yescharacteristic
19C4×D316C2212yescomplemented
20D4×Dic79C2212yescomplemented
21#14579123C2212yescomplemented
22C4×C22⋊D79—22no—
23(C22⋊D79)⋊C4—22no—
24C4⋊C4×D79C2212yes—
25C22⋊C4×D79—22no—
26C42×D79C2211yescharacteristic
27#14579093C2211yescharacteristic, complemented
28#14579092C2212yescomplemented
29#14579083C2212yescomplemented
30#14579082C2212yescomplemented
31#14579081C2212yescomplemented
32#14579072C2211yescharacteristic, complemented
33#14579071C2211yescharacteristic, complemented
34#14579071C2211yescharacteristic, complemented
35C2×D8×C79C2211yescharacteristic
36C4×D4×C79C2212yescomplemented
37#106×C79C2211yescharacteristic, complemented
38#102×C79C2212yescomplemented
39#97×C79C2211yescharacteristic, complemented
40C23×D79—22no—
41C2×D316C2312yes—
42C2×C22⋊D79—22no—
43D4×D79—24no—
44D4×D79C2×C418yescomplemented
45C22×Dic79—22no—
46C2×C4×D79—22no—
47C2×C4×D79—22no—
48C2×C4×D79—22no—
49C2×C4×D79—48no—
50C2×C4×D79D412yes—
51C2×C4×D79C2311yescharacteristic
52D632C2×C414yescomplemented
53#11929609C2×C418yescomplemented
54C2×C79⋊C8C2311yescharacteristic
55C2×C79⋊C8C2311yescharacteristic
56C8×D79—22no—
57C8×D79C2×C414yescomplemented
58C4⋊Dic79C2312yes—
59Dic79⋊C4—22no—
60C22⋊Dic79—22no—
61(C2×D79)⋊C4—22no—
62(C2×D79)⋊C4—22no—
63C4×Dic79D412yes—
64C4×Dic79C2311yescharacteristic
65C2×D4×C79C2312yes—
66C22×C4×C79—22no—
67D8×C79C2×C414yescomplemented
68C2×C8×C79C2311yescharacteristic
69C2×C8×C79C2311yescharacteristic
70C4⋊C4×C79C2312yes—
71C22⋊C4×C79—22no—
72C42×C79C2311yescharacteristic
73C23×C79—22no—
74C22×D79—22no—
75C22×D79—28no—
76C22×D79—44no—
77C22×D79—44no—
78C22×D79C2×D411yescharacteristic
79D4×C79—22no—
80D4×C79C22×C414yescomplemented
81C2×C4×C79—22no—
82C2×C4×C79—44no—
83C2×C4×C79C2×D412yes—
84C2×C4×C79C2411yescharacteristic
85C22⋊D79—28no—
86C2×Dic79—22no—
87C2×Dic79—44no—
88C2×Dic79C2×D412yes—
89C2×Dic79C2×D411yescharacteristic
90D316—22no—
91D316C22×C414yescomplemented
92C4×D79—24no—
93C4×D79—44no—
94C4×D79—44no—
95C4×D79—44no—
96C4×D79C22×C412yes—
97C4×D79#4112yes—
98C8×C79—21no—
99C8×C79C22×C412yescomplemented
100C79⋊C8—21no—
101C79⋊C8C22×C412yescomplemented
102C22×C79—24no—
103C22×C79—42no—
104C22×C79—42no—
105C22×C79C22×D411yescharacteristic
106C2×D79—24no—
107C2×D79—42no—
108C2×D79—42no—
109C2×D79—416no—
110C2×D79C4×D412yes—
111C2×D79AGL(1,ℤ/8)14yes—
112C4×C79—22no—
113C4×C79—42no—
114C4×C79C23×C411yescharacteristic
115C4×C79C2×#4111yescharacteristic
116Dic79—22no—
117Dic79—42no—
118Dic79C4×D412yes—
119C2×C79—44no—
120C2×C79C2×C4×D411yescharacteristic
121C2×C79C2×AGL(1,ℤ/8)12yes—
122D79—44no—
123D79#44214yesdirect product factor
124C2×#442—791nomaximal, Sylow
125C79C2×#44211yescharacteristic, complemented, Sylow
126C22×D8—791no—
127C2×C4×D4—792no—
128#442—791no—
129#442—792no—
130#442—791no—
131#442—792no—
132#442—791no—
133#442D7911yescharacteristic, direct product factor
134C2×#106—791no—
135C2×#102—792no—
136C2×#97—791no—
137C22×D4—792no—
138C23×C4—1582no—
139C2×D8—792no—
140C2×D8—798no—
141C2×D8—791no—
142C2×D8C2×D7911yescharacteristic
143C22×C8—791no—
144C22×C8—791no—
145C4×D4—792no—
146C4×D4—792no—
147C4×D4—792no—
148C4×D4—1582no—
149C4×D4—1582no—
150C4×D4C2×D7912yescomplemented
151C2×C4⋊C4—792no—
152C2×C22⋊C4—1582no—
153C2×C42—791no—
154#106—791no—
155#106—792no—
156#106C2×D7911yescharacteristic, complemented
157#102—792no—
158#102—792no—
159#102—792no—
160#102C2×D7912yescomplemented
161#97—791no—
162#97—791no—
163#97—791no—
164#97C2×D7911yescharacteristic, complemented
165C24—1582no—
166C2×D4—798no—
167C2×D4—792no—
168C2×D4—1584no—
169C2×D4—1582no—
170C2×D4C22×D7912yes—
171C22×C4—22no—
172C22×C4—3168no—
173C22×C4—791no—
174C22×C4—792no—
175C22×C4—1582no—
176C22×C4—1582no—
177C22×C4—1582no—
178C22×C4—1582no—
179D8—798no—
180D8—794no—
181D8C4×D7914yescomplemented
182C2×C8—791no—
183C2×C8—794no—
184C2×C8—791no—
185C2×C8—1582no—
186C2×C8C22×D7911yescharacteristic
187C2×C8C22×D7911yescharacteristic
188C4⋊C4—792no—
189C4⋊C4—1582no—
190C4⋊C4C22×D7912yes—
191C22⋊C4—22no—
192C22⋊C4—1582no—
193C22⋊C4—1582no—
194C22⋊C4—1582no—
195C42—792no—
196C42—791no—
197C42C22×D7911yescharacteristic
198C23—22no—
199C23—3164no—
200C23—3164no—
201C23—791no—
202C23—1588no—
203C23—1582no—
204D4—22no—
205D4—794no—
206D4—1588no—
207D4—1582no—
208D4C2×C4×D7914yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—3164no—
212C2×C4—3164no—
213C2×C4—3164no—
214C2×C4—3164no—
215C2×C4—791no—
216C2×C4—792no—
217C2×C4—792no—
218C2×C4—792no—
219C2×C4—1584no—
220C2×C4—1582no—
221C2×C4D4×D7912yes—
222C2×C4C23×D7911yescharacteristic
223C8—21no—
224C8—792no—
225C8—1581no—
226C8C2×C4×D7912yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—31616no—
231C22—3162no—
232C22—3162no—
233C22—792no—
234C22—794no—
235C22—1584no—
236C22C2×D4×D7911yescharacteristic
237C4—22no—
238C4—42no—
239C4—3162no—
240C4—792no—
241C4—1582no—
242C4C22×C4×D7911yescharacteristic
243C4#41×D7911yescharacteristic
244C2—44no—
245C2—3164no—
246C2—794no—
247C2C4×D4×D7911yescharacteristic
248C2AGL(1,ℤ/8)×D7912yes—
subgroupG/H
centerC22C2×D4×D79
commutatorC4×C79C23×C4
FrattiniC2×C4C23×D79
Fitting#442×C79C2
socleC22×C79C22×D4
prime radicalC2×D8×D79C2
cosocleC2×C4×C79C24
hypercenter#442D79
hypocenterC79C2×#442
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D79C2semidirect
3. #19098676C2semidirect
4. #19098675C2semidirect
5. #19098674C2semidirect
6. #19098673C2semidirect
7. #19098672C2semidirect
8. #106×D79C2semidirect
9. #102×D79C2semidirect
10. #97×D79C2semidirect
11. #442×C79C2semidirect
16. D8×D79C4semidirect
19. C4×D316C22semidirect
20. D4×Dic79C22semidirect
21. #14579123C22semidirect
27. #14579093C22semidirect
28. #14579092C22semidirect
29. #14579083C22semidirect
30. #14579082C22semidirect
31. #14579081C22semidirect
32. #14579072C22semidirect
33. #14579071C22semidirect
34. #14579071C22semidirect
36. C4×D4×C79C22semidirect
37. #106×C79C22semidirect
38. #102×C79C22semidirect
39. #97×C79C22semidirect
44. D4×D79C2×C4semidirect
52. D632C2×C4semidirect
53. #11929609C2×C4semidirect
57. C8×D79C2×C4semidirect
67. D8×C79C2×C4semidirect
80. D4×C79C22×C4semidirect
91. D316C22×C4semidirect
99. C8×C79C22×C4semidirect
101. C79⋊C8C22×C4semidirect
123. D79#442direct (N × H)
125. C79C2×#442semidirect
133. #442D79direct (N × H)
150. C4×D4C2×D79semidirect
156. #106C2×D79semidirect
160. #102C2×D79semidirect
164. #97C2×D79semidirect
181. D8C4×D79semidirect
208. D4C2×C4×D79semidirect
226. C8C2×C4×D79semidirect