Finite Group Databasebeta

← #23774453

Subgroups — #23774453

Order 10112.

420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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#19099169C211yesmaximal, characteristic, complemented
2#19099131C211yesmaximal, characteristic, complemented
3#19098953C211yesmaximal, characteristic, complemented
4#19098940C211yesmaximal, characteristic, complemented
5#19098929C211yesmaximal, characteristic, complemented
6#19098781C212yesmaximal, complemented
7#19098757C212yesmaximal, complemented
8#19098711C212yesmaximal, complemented
9#19098698C212yesmaximal, complemented
10#19098622C211yesmaximal, characteristic, complemented
11#488×C79C211yesmaximal, characteristic, complemented
12C2×#11929625C2211yescharacteristic
13C2×D4×D79C2211yescharacteristic
14C2×#11929611C2212yescomplemented
15C2×D632C2212yes—
16C2×D632C2212yescomplemented
17C2×#11929609C2212yes—
18#14579158C2211yescharacteristic
19#14579158C2211yescharacteristic, complemented
20#14579157C2211yescharacteristic
21#14579150C2211yescharacteristic
22#14579146—22no—
23#14579136—22no—
24#14579136C2212yes—
25#14579134—22no—
26#14579131—22no—
27#14579123C2212yescomplemented
28#14579118C2211yescharacteristic
29Dic79⋊C8C2212yescomplemented
30#14579081C2212yes—
31#14579081C2212yescomplemented
32(C2×D79)⋊C8C2212yes—
33#14579072C2211yescharacteristic, complemented
34#125×C79C2211yescharacteristic, complemented
35#124×C79C2211yescharacteristic
36#103×C79C2212yescomplemented
37#102×C79C2212yes—
38C4×C8×C79C2211yescharacteristic, complemented
39C23×D79—21no—
40#11929625—42no—
41C2×D316—21no—
42C2×D316—22no—
43C2×D316—22no—
44C2×D316—22no—
45C2×D316C2311yescharacteristic
46C2×D316C2311yescharacteristic
47C2×D316C2312yes—
48C2×C22⋊D79—21no—
49C2×C22⋊D79—22no—
50D4×D79—42no—
51C2×C4×D79—21no—
52C2×C4×D79—22no—
53C2×C4×D79C2311yescharacteristic
54#11929611—42no—
55D632—42no—
56D632—42no—
57#11929609—42no—
58C2×C79⋊C8C2312yes—
59Dic79⋊C4D412yes—
60(C2×D79)⋊C4—22no—
61(C2×D79)⋊C4—22no—
62(C2×D79)⋊C4—22no—
63(C2×D79)⋊C4D412yes—
64C4×Dic79C2311yescharacteristic
65C2×Q8×C79C2311yescharacteristic
66C2×D4×C79C2311yescharacteristic
67C2×C8×C79C2312yes—
68C4⋊C4×C79—22no—
69C4⋊C4×C79C2312yes—
70C22⋊C4×C79—22no—
71C42×C79C2311yescharacteristic
72C23×C79—21no—
73C22×D79—22no—
74C22×D79—21no—
75C22×D79—21no—
76C22×D79—42no—
77C22×D79—82no—
78C22×D79C2×D411yescharacteristic
79Q8×C79—22no—
80D4×C79—22no—
81C2×C4×C79—21no—
82C2×C4×C79—22no—
83C2×C4×C79C2×D412yes—
84C2×C4×C79C2411yescharacteristic
85C22⋊D79—42no—
86C22⋊D79—82no—
87C2×Dic79C2×D412yes—
88C2×Dic79C2×D411yescharacteristic
89D316—22no—
90D316—22no—
91D316—22no—
92D316—22no—
93D316—42no—
94D316—82no—
95D316—82no—
96D316—82no—
97C4×D79—22no—
98C4×D79—42no—
99C4×D79—82no—
100C8×C79—22no—
101C79⋊C8—22no—
102C22×C79—41no—
103C22×C79—42no—
104C22×C79C22×D411yescharacteristic
105C2×D79—21no—
106C2×D79—22no—
107C2×D79—41no—
108C2×D79—41no—
109C2×D79—42no—
110C2×D79—42no—
111C2×D79—42no—
112C2×D79—42no—
113C2×D79—42no—
114C2×D79—84no—
115C4×C79—22no—
116C4×C79—41no—
117C4×C79—42no—
118C4×C79H(5,𝔽2)12yes—
119Dic79—21no—
120Dic79—22no—
121C2×C79—81no—
122C2×C79#53511yescharacteristic
123C2×C79#57612yes—
124D79—41no—
125D79—81no—
126D79—82no—
127D79—81no—
128#3220—791nomaximal, Sylow
129C79#322011yescharacteristic, complemented, Sylow
130#540—791no—
131#535—791no—
132#496—791no—
133#493—791no—
134#490—791no—
135#488D7911yescharacteristic, complemented
136#463—792no—
137#459—792no—
138#449—792no—
139#447—792no—
140#433—791no—
141C2×#41—791no—
142C22×D4—791no—
143C2×SD16—792no—
144C2×D8—792no—
145C2×D8—792no—
146C2×D8—792no—
147#127—791no—
148#127—791no—
149#127—791no—
150#125C2×D7911yescharacteristic, complemented
151#124—791no—
152#124C2×D7911yescharacteristic
153#123—1582no—
154#121—792no—
155#121—1582no—
156#121—1582no—
157#120—1582no—
158C4×D4—792no—
159#117—791no—
160C4⋊C8—792no—
161#103C2×D7912yescomplemented
162#102—792no—
163#102—792no—
164#102C2×D7912yes—
165C22⋊C8—792no—
166#97—791no—
167C4×C8C2×D7911yescharacteristic, complemented
168C24—1581no—
169#41—3162no—
170C2×Q8C22×D7911yescharacteristic
171C2×D4—3162no—
172C2×D4—791no—
173C2×D4—791no—
174C2×D4—792no—
175C2×D4—1581no—
176C2×D4—1582no—
177C2×D4—1581no—
178C2×D4—1582no—
179C2×D4—1582no—
180C2×D4—1582no—
181C2×D4C22×D7911yescharacteristic
182C22×C4—791no—
183C22×C4—1581no—
184C22×C4—1582no—
185SD16—3162no—
186D8—3162no—
187D8—3162no—
188D8—3162no—
189C2×C8—792no—
190C2×C8C22×D7912yes—
191C4⋊C4—22no—
192C4⋊C4—792no—
193C4⋊C4C22×D7912yes—
194C22⋊C4—22no—
195C22⋊C4—792no—
196C22⋊C4—1582no—
197C22⋊C4—1582no—
198C22⋊C4—1582no—
199C42—791no—
200C42C22×D7911yescharacteristic
201C23—21no—
202C23—3162no—
203C23—791no—
204C23—6322no—
205C23—1582no—
206C23—1581no—
207C23—1581no—
208Q8—22no—
209D4—22no—
210D4—3162no—
211D4—3162no—
212D4—6322no—
213D4—6322no—
214D4—6322no—
215D4—6322no—
216D4—1582no—
217D4—1582no—
218D4—1582no—
219D4—1582no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—3162no—
223C2×C4—792no—
224C2×C4—791no—
225C2×C4—6322no—
226C2×C4—1582no—
227C2×C4D4×D7912yes—
228C2×C4C23×D7911yescharacteristic
229C8—22no—
230C8—1582no—
231C22—42no—
232C22—41no—
233C22—3162no—
234C22—3162no—
235C22—3162no—
236C22—3162no—
237C22—3161no—
238C22—3161no—
239C22—3162no—
240C22—6324no—
241C22—1582no—
242C22—1581no—
243C22C2×D4×D7911yescharacteristic
244C4—22no—
245C4—42no—
246C4—41no—
247C4—1582no—
248C4—1581no—
249C4#1457920712yes—
250C2—81no—
251C2—3161no—
252C2—6321no—
253C2—6322no—
254C2—6321no—
255C2#1909913111yescharacteristic
256C2#1909936512yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#488×C79C2
socleC22×C79C22×D4
hypercenter#488D79
hypocenterC79#3220
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #19099169C2semidirect
2. #19099131C2semidirect
3. #19098953C2semidirect
4. #19098940C2semidirect
5. #19098929C2semidirect
6. #19098781C2semidirect
7. #19098757C2semidirect
8. #19098711C2semidirect
9. #19098698C2semidirect
10. #19098622C2semidirect
11. #488×C79C2semidirect
14. C2×#11929611C22semidirect
16. C2×D632C22semidirect
19. #14579158C22semidirect
27. #14579123C22semidirect
29. Dic79⋊C8C22semidirect
31. #14579081C22semidirect
33. #14579072C22semidirect
34. #125×C79C22semidirect
36. #103×C79C22semidirect
38. C4×C8×C79C22semidirect
129. C79#3220semidirect
135. #488D79semidirect
150. #125C2×D79semidirect
161. #103C2×D79semidirect
167. C4×C8C2×D79semidirect