Finite Group Databasebeta

← #23773644

Subgroups — #23773644

Order 10112.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#19099168C211yesmaximal, characteristic, complemented
2#19099037C211yesmaximal, characteristic, complemented
3#19098888C212yesmaximal, complemented
4#19098864C212yesmaximal, complemented
5#19098759C212yesmaximal, complemented
6#19098699C212yesmaximal, complemented
7#19098676C212yesmaximal, complemented
8C4×D632C212yesmaximal, complemented
9#433×C79C211yesmaximal, characteristic, complemented
10C22×D316C2211yescharacteristic
11C2×D632C2212yes—
12C2×D632C2212yes—
13#14579158C2211yescharacteristic, complemented
14#14579153C2211yescharacteristic, complemented
15#14579146—22no—
16#14579135C2212yes—
17#14579134—22no—
18C4×D316C2212yes—
19C4×D316C2212yes—
20C4×D316C2212yescomplemented
21#14579123—22no—
22#14579120C2211yescharacteristic
23C22⋊C4×D79—22no—
24#14579095C2212yescomplemented
25#14579093C2212yescomplemented
26#14579083C2212yes—
27#14579083C2212yes—
28#14579083C2212yescomplemented
29#14579083C2212yescomplemented
30#117×C79C2211yescharacteristic
31C4⋊C8×C79C2212yescomplemented
32C22⋊C8×C79C2212yes—
33#97×C79C2211yescharacteristic, complemented
34C4×C8×C79C2211yescharacteristic, complemented
35C23×D79—21no—
36C2×D316—24no—
37C2×D316—21no—
38C2×D316—22no—
39C2×D316C2312yes—
40C2×D316C2312yes—
41C2×C22⋊D79—22no—
42C2×C4×D79—22no—
43C2×C4×D79—22no—
44C2×C4×D79—22no—
45D632—24no—
46D632—24no—
47C4⋊Dic79C2312yes—
48C4⋊Dic79C2312yes—
49Dic79⋊C4—22no—
50C22⋊Dic79—21no—
51(C2×D79)⋊C4—22no—
52(C2×D79)⋊C4—22no—
53(C2×D79)⋊C4—22no—
54(C2×D79)⋊C4—22no—
55C4×Dic79—21no—
56C22×C4×C79C2311yescharacteristic
57C2×C8×C79C2312yes—
58C2×C8×C79C2312yes—
59C4⋊C4×C79D412yes—
60C22⋊C4×C79D412yes—
61C42×C79C2311yescharacteristic
62C42×C79C2311yescharacteristic
63C23×C79C2×D411yescharacteristic
64C22×D79—22no—
65C22×D79—24no—
66C22×D79—22no—
67C22×D79—82no—
68C2×C4×C79—22no—
69C2×C4×C79C2×D411yescharacteristic
70C2×C4×C79C2×D412yes—
71C2×C4×C79C2×D412yes—
72C2×C4×C79C2411yescharacteristic
73C22⋊D79—82no—
74C2×Dic79—22no—
75C2×Dic79—22no—
76D316—24no—
77D316—22no—
78D316—22no—
79D316—22no—
80D316—82no—
81D316#4114yes—
82C4×D79—82no—
83C4×D79—82no—
84C4×D79—82no—
85C8×C79—22no—
86C8×C79—22no—
87C22×C79—21no—
88C22×C79—22no—
89C22×C79C22×D411yescharacteristic
90C2×D79—24no—
91C2×D79—42no—
92C2×D79—42no—
93C2×D79—42no—
94C2×D79—42no—
95C2×D79—42no—
96C2×D79—84no—
97C4×C79—21no—
98C4×C79—22no—
99C4×C79—22no—
100C4×C79C2×#4112yes—
101Dic79—42no—
102Dic79—42no—
103C2×C79—41no—
104C2×C79#52511yescharacteristic
105C2×C79#57612yes—
106D79—44no—
107D79—82no—
108#3122—791nomaximal, Sylow
109C79#312211yescharacteristic, complemented, Sylow
110#540—791no—
111#518—791no—
112#482—792no—
113#478—792no—
114#459—792no—
115#447—792no—
116#442—792no—
117C4×D8—792no—
118#433D7911yescharacteristic, complemented
119C22×D4—791no—
120C2×D8—792no—
121C2×D8—792no—
122#127—791no—
123#125—791no—
124#123—1582no—
125#121—792no—
126#121—1582no—
127C4×D4—792no—
128C4×D4—792no—
129C4×D4—792no—
130C4×D4—1582no—
131#117—791no—
132#117C2×D7911yescharacteristic
133C2×C22⋊C4—1582no—
134#107—792no—
135#106—792no—
136C4⋊C8C2×D7912yescomplemented
137#102—792no—
138#102—792no—
139#102—792no—
140#102—792no—
141C22⋊C8C2×D7912yes—
142#97C2×D7911yescharacteristic, complemented
143C4×C8C2×D7911yescharacteristic, complemented
144C24—1581no—
145C2×D4—792no—
146C2×D4—792no—
147C2×D4—1584no—
148C2×D4—1582no—
149C2×D4—1582no—
150C2×D4—1581no—
151C22×C4—1582no—
152C22×C4—1582no—
153C22×C4—1582no—
154C22×C4C22×D7911yescharacteristic
155D8—1584no—
156D8—1584no—
157C2×C8C22×D7912yes—
158C2×C8C22×D7912yes—
159C4⋊C4—792no—
160C4⋊C4—792no—
161C4⋊C4—1582no—
162C4⋊C4D31612yes—
163C22⋊C4—1581no—
164C22⋊C4—1582no—
165C22⋊C4—1582no—
166C22⋊C4—1582no—
167C22⋊C4—1582no—
168C22⋊C4D31612yes—
169C42—1581no—
170C42C22×D7911yescharacteristic
171C42C22×D7911yescharacteristic
172C23—6322no—
173C23—1584no—
174C23—1582no—
175C23—1582no—
176C23C2×D31611yescharacteristic
177D4—794no—
178D4—6322no—
179D4—6322no—
180D4—1584no—
181D4—1582no—
182D4—1582no—
183D4—1582no—
184C2×C4—22no—
185C2×C4—6322no—
186C2×C4—6322no—
187C2×C4—6322no—
188C2×C4—1582no—
189C2×C4—1582no—
190C2×C4C2×D31611yescharacteristic
191C2×C4C2×D31612yes—
192C2×C4C2×D31612yes—
193C2×C4C23×D7911yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—3162no—
199C22—3162no—
200C22—3162no—
201C22—3162no—
202C22—3162no—
203C22—6324no—
204C22—1584no—
205C22C22×D31611yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—3162no—
210C4—3162no—
211C4#41×D7912yes—
212C2—41no—
213C2—3164no—
214C2—6322no—
215C2#1909907511yescharacteristic
216C2#1909936812yes—
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#433×C79C2
socleC22×C79C22×D4
hypercenter#433D79
hypocenterC79#3122
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #19099168C2semidirect
2. #19099037C2semidirect
3. #19098888C2semidirect
4. #19098864C2semidirect
5. #19098759C2semidirect
6. #19098699C2semidirect
7. #19098676C2semidirect
8. C4×D632C2semidirect
9. #433×C79C2semidirect
13. #14579158C22semidirect
14. #14579153C22semidirect
20. C4×D316C22semidirect
24. #14579095C22semidirect
25. #14579093C22semidirect
28. #14579083C22semidirect
29. #14579083C22semidirect
31. C4⋊C8×C79C22semidirect
33. #97×C79C22semidirect
34. C4×C8×C79C22semidirect
109. C79#3122semidirect
118. #433D79semidirect
136. C4⋊C8C2×D79semidirect
142. #97C2×D79semidirect
143. C4×C8C2×D79semidirect