Finite Group Databasebeta

← #23772977

Subgroups — #23772977

Order 10112.

520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C22×C8×D79C211yesmaximal, characteristic, complemented
2#19099070C212yesmaximal, complemented
3#19098801C212yesmaximal, complemented
4#19098796C212yesmaximal, complemented
5#19098789C214yesmaximal, complemented
6#19098601C211yesmaximal, characteristic, complemented
7#19098559C212yesmaximal, complemented
8C2×#135×C79C211yesmaximal, characteristic, complemented
9C22×C4×D79C2211yescharacteristic
10C22×C79⋊C8C2211yescharacteristic
11C2×C8×D79—24no—
12C2×C8×D79C2212yes—
13C2×C8×D79C2212yes—
14#14579142—22no—
15#14579137C2214yes—
16#14579132C2214yes—
17#14579129—22no—
18C4×C22⋊D79—24no—
19#14579120C2212yes—
20#14579095C2212yescomplemented
21#14579093C2212yescomplemented
22#14579085C2214yescomplemented
23#14579082C2214yescomplemented
24C2×#41×C79C2212yes—
25#135×C79—24no—
26C2×Q16×C79C2211yescharacteristic, complemented
27C2×SD16×C79C2212yescomplemented
28C2×D8×C79C2211yescharacteristic, complemented
29C22×C8×C79C2211yescharacteristic
30C23×D79D411yescharacteristic
31C2×C22⋊D79—24no—
32C22×Dic79D411yescharacteristic
33C2×C4×D79—22no—
34C2×C4×D79—22no—
35C2×C4×D79D412yes—
36C2×C4×D79C2312yes—
37C2×C79⋊C8—22no—
38C2×C79⋊C8C2312yes—
39C8×D79—24no—
40C8×D79—24no—
41C4⋊Dic79C2314yes—
42Dic79⋊C4—24no—
43C22⋊Dic79—24no—
44C22⋊Dic79—22no—
45(C2×D79)⋊C4—24no—
46C4×Dic79—22no—
47#41×C79—24no—
48#41×C79—24no—
49C2×Q8×C79C2312yes—
50C2×D4×C79—22no—
51C2×D4×C79C2312yes—
52C22×C4×C79—22no—
53C22×C4×C79C2311yescharacteristic
54Q16×C79—22no—
55SD16×C79—24no—
56D8×C79—22no—
57C2×C8×C79D414yescomplemented
58C2×C8×C79C2311yescharacteristic
59C2×C8×C79C2311yescharacteristic
60C23×C79—22no—
61C23×C79C2×D411yescharacteristic
62C22×D79—22no—
63C22×D79—24no—
64C22×D79C2×D412yes—
65Q8×C79—22no—
66Q8×C79—22no—
67D4×C79—22no—
68D4×C79—22no—
69D4×C79—44no—
70C2×C4×C79—22no—
71C2×C4×C79—44no—
72C2×C4×C79C2×D411yescharacteristic
73C2×C4×C79C2×D412yes—
74C2×C4×C79#4112yes—
75C2×C4×C79C2411yescharacteristic
76C22⋊D79—48no—
77C2×Dic79—22no—
78C2×Dic79—24no—
79C2×Dic79C2×D412yes—
80C4×D79—24no—
81C4×D79—22no—
82C4×D79—22no—
83C8×C79C2×D412yes—
84C8×C79C2×D412yes—
85C79⋊C8—22no—
86C22×C79—22no—
87C22×C79—42no—
88C22×C79—44no—
89C22×C79#12112yes—
90C22×C79C22×D411yescharacteristic
91C2×D79—28no—
92C2×D79—22no—
93C2×D79—22no—
94C2×D79#13514yescomplemented
95C4×C79—42no—
96C4×C79#12112yes—
97C4×C79C22×D411yescharacteristic
98C4×C79C2×#4111yescharacteristic
99Dic79—22no—
100Dic79—44no—
101C2×C79—22no—
102C2×C79—82no—
103C2×C79C2×#12111yescharacteristic
104C2×C79C2×#13512yes—
105D79—24no—
106#3050—791nomaximal, Sylow
107C79#305011yescharacteristic, complemented, Sylow
108C2×#135D7911yescharacteristic, complemented
109C23×C8—791no—
110#525—792no—
111#467—792no—
112#466—792no—
113#465—794no—
114#427—791no—
115#416—792no—
116C2×#41C2×D7912yes—
117C23×C4—791no—
118#135—24no—
119C2×Q16C2×D7911yescharacteristic, complemented
120C2×SD16C2×D7912yescomplemented
121C2×D8C2×D7911yescharacteristic, complemented
122C22×C8—791no—
123C22×C8—792no—
124C22×C8—792no—
125C22×C8—1584no—
126C22×C8C2×D7911yescharacteristic
127#123—1582no—
128C22⋊Q8—794no—
129#121—794no—
130#120—1582no—
131C4×D4—1584no—
132#117—792no—
133#107—792no—
134#106—792no—
135#103—794no—
136#102—794no—
137C24—791no—
138#41—24no—
139#41—24no—
140C2×Q8C22×D7912yes—
141C2×D4—22no—
142C2×D4—1584no—
143C2×D4C22×D7912yes—
144C22×C4—22no—
145C22×C4—791no—
146C22×C4—792no—
147C22×C4—792no—
148C22×C4—1582no—
149C22×C4—1582no—
150C22×C4C22×D7911yescharacteristic
151Q16—22no—
152SD16—24no—
153D8—22no—
154C2×C8—792no—
155C2×C8—1582no—
156C2×C8—1584no—
157C2×C8—1584no—
158C2×C8C22⋊D7914yescomplemented
159C2×C8C22×D7911yescharacteristic
160C2×C8C22×D7911yescharacteristic
161C4⋊C4—794no—
162C4⋊C4—1584no—
163C22⋊C4—1584no—
164C22⋊C4—1584no—
165C22⋊C4—1582no—
166C42—1582no—
167C23—22no—
168C23—792no—
169C23—1584no—
170C23—1582no—
171C23D4×D7911yescharacteristic
172Q8—22no—
173Q8—22no—
174D4—22no—
175D4—22no—
176D4—44no—
177D4—3168no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—792no—
181C2×C4—1584no—
182C2×C4—1582no—
183C2×C4—1582no—
184C2×C4—1584no—
185C2×C4—1582no—
186C2×C4D4×D7911yescharacteristic
187C2×C4C2×C22⋊D7912yes—
188C2×C4#1192962312yes—
189C2×C4C23×D7911yescharacteristic
190C8—1582no—
191C8C2×C22⋊D7912yes—
192C8C2×C22⋊D7912yes—
193C22—22no—
194C22—42no—
195C22—44no—
196C22—794no—
197C22—1588no—
198C22—1582no—
199C22—1582no—
200C22#1457913212yes—
201C22C2×D4×D7911yescharacteristic
202C4—42no—
203C4—3164no—
204C4—1582no—
205C4#1457913212yes—
206C4C22×C22⋊D7911yescharacteristic
207C4C2×#1192962311yescharacteristic
208C2—22no—
209C2—82no—
210C2—1584no—
211C2C2×#1457913211yescharacteristic
212C2#135×D7912yes—
subgroupG/H
centerC2×C4D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×#135×C79C2
socleC22×C79C22×D4
hypercenterC2×#135D79
hypocenterC79#3050
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×C8×D79C2semidirect
2. #19099070C2semidirect
3. #19098801C2semidirect
4. #19098796C2semidirect
5. #19098789C2semidirect
6. #19098601C2semidirect
7. #19098559C2semidirect
8. C2×#135×C79C2semidirect
20. #14579095C22semidirect
21. #14579093C22semidirect
22. #14579085C22semidirect
23. #14579082C22semidirect
26. C2×Q16×C79C22semidirect
27. C2×SD16×C79C22semidirect
28. C2×D8×C79C22semidirect
57. C2×C8×C79D4semidirect
94. C2×D79#135semidirect
107. C79#3050semidirect
108. C2×#135D79semidirect
119. C2×Q16C2×D79semidirect
120. C2×SD16C2×D79semidirect
121. C2×D8C2×D79semidirect
158. C2×C8C22⋊D79semidirect