Finite Group Databasebeta

← #399×D79 #23766646

Subgroups — #399×D79 #23766646

Order 10112.

908 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 203 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×C4⋊C4×D79C213yesmaximal, complemented
2C2×C22⋊C4×D79C213yesmaximal
3#19098500C211yesmaximal, characteristic, complemented
4#19098499C213yesmaximal, complemented
5#19098498C213yesmaximal, complemented
6#95×D79C211yesmaximal, characteristic, complemented
7#399×C79C211yesmaximal, characteristic, complemented
8C24×D79C2211yescharacteristic
9C22×C4×D79C2213yes—
10C22×C4×D79C2213yes—
11C2×C4⋊Dic79C2213yescomplemented
12C2×Dic79⋊C4C2216yescomplemented
13C4⋊C4×D79—212no—
14C2×C22⋊Dic79C2213yes—
15C2×(C2×D79)⋊C4C2213yes—
16C2×(C2×D79)⋊C4C2213yes—
17C22⋊C4×D79—212no—
18C79⋊#95C2213yescomplemented
19C2×C4⋊C4×C79C2213yescomplemented
20C2×C22⋊C4×C79C2213yes—
21#95×C79C2211yescharacteristic, complemented
22C23×D79—26no—
23C23×D79—26no—
24C23×D79Q814yes—
25C23×D79C2311yescharacteristic
26C23×D79C2311yescharacteristic
27C22×Dic79C2313yes—
28C22×Dic79C2313yes—
29C2×C4×D79—26no—
30C2×C4×D79—212no—
31C2×C4×D79—212no—
32C2×C4×D79D4112yes—
33C4⋊Dic79—26no—
34Dic79⋊C4—212no—
35C22⋊Dic79—26no—
36(C2×D79)⋊C4—26no—
37(C2×D79)⋊C4—26no—
38C24×C79C2311yescharacteristic
39C22×C4×C79C2313yes—
40C22×C4×C79C2313yes—
41C4⋊C4×C79—26no—
42C22⋊C4×C79—26no—
43C23×C79—23no—
44C23×C79—23no—
45C23×C79C2×Q812yes—
46C23×C79C2411yescharacteristic
47C22×D79—23no—
48C22×D79—23no—
49C22×D79—224no—
50C22×D79—412no—
51C22×D79—44no—
52C22×D79C2×D416yes—
53C22×D79C2×Q812yes—
54C22×D79C2×Q812yes—
55C22×D79#4116yes—
56C2×C4×C79—26no—
57C2×C4×C79—23no—
58C2×C4×C79—26no—
59C2×C4×C79C2×D416yes—
60C2×Dic79—26no—
61C2×Dic79—23no—
62C2×Dic79—26no—
63C2×Dic79C2×D416yes—
64C4×D79—224no—
65C4×D79—412no—
66C22×C79—26no—
67C22×C79—43no—
68C22×C79—41no—
69C22×C79C22×D413yes—
70C22×C79C22×Q811yescharacteristic
71C22×C79C2×#4113yes—
72C2×D79—26no—
73C2×D79—43no—
74C2×D79—41no—
75C2×D79—416no—
76C2×D79C22⋊Q8112yes—
77C2×D79#123112yes—
78C2×D79#12714yes—
79C4×C79—26no—
80C4×C79—43no—
81Dic79—26no—
82Dic79—43no—
83C2×C79—42no—
84C2×C79C2×C22⋊Q813yes—
85C2×C79C2×#12313yes—
86C2×C79C2×#12711yescharacteristic
87D79—42no—
88D79#39918yesdirect product factor
89C2×#399—791nomaximal, Sylow
90C79C2×#39911yescharacteristic, complemented, Sylow
91C22×C4⋊C4—793no—
92C22×C22⋊C4—793no—
93#399—793no—
94#399—793no—
95#399—791no—
96#399D7911yescharacteristic, direct product factor
97C2×#95—791no—
98C25—791no—
99C23×C4—793no—
100C23×C4—793no—
101C2×C4⋊C4—796no—
102C2×C4⋊C4—793no—
103C2×C4⋊C4—15812no—
104C2×C4⋊C4C2×D7913yescomplemented
105C2×C22⋊C4—793no—
106C2×C22⋊C4—793no—
107C2×C22⋊C4—793no—
108C2×C22⋊C4—15812no—
109C2×C22⋊C4C2×D7913yes—
110#95—793no—
111#95C2×D7911yescharacteristic, complemented
112C24—791no—
113C24—794no—
114C24—791no—
115C24—1586no—
116C24—1586no—
117C24C22×D7911yescharacteristic
118C22×C4—793no—
119C22×C4—7912no—
120C22×C4—793no—
121C22×C4—1586no—
122C22×C4—15812no—
123C22×C4—15812no—
124C22×C4C22×D7913yes—
125C22×C4C22×D7913yes—
126C4⋊C4—26no—
127C4⋊C4—15812no—
128C4⋊C4—1586no—
129C22⋊C4—26no—
130C22⋊C4—1586no—
131C22⋊C4—1586no—
132C22⋊C4—1586no—
133C23—23no—
134C23—23no—
135C23—31612no—
136C23—3164no—
137C23—792no—
138C23—796no—
139C23—796no—
140C23—792no—
141C23—15824no—
142C23—1583no—
143C23—1583no—
144C23Q8×D7912yes—
145C23C23×D7911yescharacteristic
146C2×C4—26no—
147C2×C4—23no—
148C2×C4—26no—
149C2×C4—31612no—
150C2×C4—796no—
151C2×C4—15824no—
152C2×C4—1583no—
153C2×C4—1586no—
154C2×C4—1586no—
155C2×C4D4×D7916yes—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—31616no—
160C22—3163no—
161C22—3161no—
162C22—7912no—
163C22—7912no—
164C22—794no—
165C22—1586no—
166C22C2×D4×D7913yes—
167C22C2×Q8×D7911yescharacteristic
168C22#41×D7913yes—
169C4—26no—
170C4—43no—
171C4—3163no—
172C4—1586no—
173C2—42no—
174C2—3162no—
175C2—798no—
176C2C22⋊Q8×D7913yes—
177C2#123×D7913yes—
178C2#127×D7911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#399×C79C2
prime radicalC24×D79C22
hypercenter#399D79
hypocenterC79C2×#399
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D79C2semidirect
3. #19098500C2semidirect
4. #19098499C2semidirect
5. #19098498C2semidirect
6. #95×D79C2semidirect
7. #399×C79C2semidirect
11. C2×C4⋊Dic79C22semidirect
12. C2×Dic79⋊C4C22semidirect
18. C79⋊#95C22semidirect
19. C2×C4⋊C4×C79C22semidirect
21. #95×C79C22semidirect
88. D79#399direct (N × H)
90. C79C2×#399semidirect
96. #399D79direct (N × H)
104. C2×C4⋊C4C2×D79semidirect
111. #95C2×D79semidirect