Finite Group Databasebeta

← #399×D61 #21449065

Subgroups — #399×D61 #21449065

Order 7808.

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×D61C213yesmaximal, complemented
2C2×C22⋊C4×D61C213yesmaximal
3#16839699C211yesmaximal, characteristic, complemented
4#16839698C213yesmaximal, complemented
5#16839697C213yesmaximal, complemented
6#95×D61C211yesmaximal, characteristic, complemented
7C61×#399C211yesmaximal, characteristic, complemented
8C24×D61C2211yescharacteristic
9C22×C4×D61C2213yes—
10C22×C4×D61C2213yes—
11C2×C4⋊Dic61C2213yescomplemented
12C2×#11758196C2216yescomplemented
13C4⋊C4×D61—212no—
14C2×C22⋊Dic61C2213yes—
15C2×#11758198C2213yes—
16C2×#11758198C2213yes—
17C22⋊C4×D61—212no—
18#14519684C2213yescomplemented
19C2×C4⋊C4×C61C2213yescomplemented
20C2×C22⋊C4×C61C2213yes—
21#95×C61C2211yescharacteristic, complemented
22C24×C61C2311yescharacteristic
23C23×D61—26no—
24C23×D61—26no—
25C23×D61Q814yes—
26C23×D61C2311yescharacteristic
27C23×D61C2311yescharacteristic
28C22×C4×C61C2313yes—
29C22×C4×C61C2313yes—
30C22×Dic61C2313yes—
31C22×Dic61C2313yes—
32C2×C4×D61—212no—
33C2×C4×D61—26no—
34C2×C4×D61—212no—
35C2×C4×D61D4112yes—
36C4⋊C4×C61—26no—
37C22⋊C4×C61—26no—
38C22⋊Dic61—26no—
39#11758198—26no—
40#11758198—26no—
41C4⋊Dic61—26no—
42#11758196—212no—
43C23×C61—23no—
44C23×C61—23no—
45C23×C61C2×Q812yes—
46C23×C61C2411yescharacteristic
47C22×D61—23no—
48C22×D61—23no—
49C22×D61—224no—
50C22×D61—412no—
51C22×D61—44no—
52C22×D61C2×D416yes—
53C22×D61C2×Q812yes—
54C22×D61C2×Q812yes—
55C22×D61#4116yes—
56C2×C4×C61—26no—
57C2×C4×C61—26no—
58C2×C4×C61—23no—
59C2×C4×C61C2×D416yes—
60C2×Dic61—26no—
61C2×Dic61—26no—
62C2×Dic61—23no—
63C2×Dic61C2×D416yes—
64C4×D61—224no—
65C4×D61—412no—
66C22×C61—26no—
67C22×C61—43no—
68C22×C61—41no—
69C22×C61C22×D413yes—
70C22×C61C22×Q811yescharacteristic
71C22×C61C2×#4113yes—
72C2×D61—26no—
73C2×D61—43no—
74C2×D61—41no—
75C2×D61—416no—
76C2×D61C22⋊Q8112yes—
77C2×D61#123112yes—
78C2×D61#12714yes—
79C4×C61—26no—
80C4×C61—43no—
81Dic61—26no—
82Dic61—43no—
83C2×#399—611nomaximal, Sylow
84C2×C61—42no—
85C2×C61C2×C22⋊Q813yes—
86C2×C61C2×#12313yes—
87C2×C61C2×#12711yescharacteristic
88D61—42no—
89D61#39918yesdirect product factor
90C22×C4⋊C4—613no—
91C22×C22⋊C4—613no—
92#399—613no—
93#399—613no—
94#399—611no—
95#399D6111yescharacteristic, direct product factor
96C2×#95—611no—
97C61C2×#39911yescharacteristic, complemented, Sylow
98C25—611no—
99C23×C4—613no—
100C23×C4—613no—
101C2×C4⋊C4—616no—
102C2×C4⋊C4—613no—
103C2×C4⋊C4—12212no—
104C2×C4⋊C4C2×D6113yescomplemented
105C2×C22⋊C4—613no—
106C2×C22⋊C4—613no—
107C2×C22⋊C4—613no—
108C2×C22⋊C4—12212no—
109C2×C22⋊C4C2×D6113yes—
110#95—613no—
111#95C2×D6111yescharacteristic, complemented
112C24—611no—
113C24—614no—
114C24—611no—
115C24—1226no—
116C24—1226no—
117C24C22×D6111yescharacteristic
118C22×C4—613no—
119C22×C4—6112no—
120C22×C4—613no—
121C22×C4—12212no—
122C22×C4—1226no—
123C22×C4—12212no—
124C22×C4C22×D6113yes—
125C22×C4C22×D6113yes—
126C4⋊C4—26no—
127C4⋊C4—12212no—
128C4⋊C4—1226no—
129C22⋊C4—26no—
130C22⋊C4—1226no—
131C22⋊C4—1226no—
132C22⋊C4—1226no—
133C23—23no—
134C23—23no—
135C23—616no—
136C23—612no—
137C23—616no—
138C23—612no—
139C23—12224no—
140C23—1223no—
141C23—1223no—
142C23—24412no—
143C23—2444no—
144C23Q8×D6112yes—
145C23C23×D6111yescharacteristic
146C2×C4—26no—
147C2×C4—23no—
148C2×C4—26no—
149C2×C4—616no—
150C2×C4—12224no—
151C2×C4—1226no—
152C2×C4—1223no—
153C2×C4—1226no—
154C2×C4—24412no—
155C2×C4D4×D6116yes—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—6112no—
160C22—6112no—
161C22—614no—
162C22—1226no—
163C22—24416no—
164C22—2443no—
165C22—2441no—
166C22C2×D4×D6113yes—
167C22C2×Q8×D6111yescharacteristic
168C22#41×D6113yes—
169C4—26no—
170C4—43no—
171C4—1226no—
172C4—2443no—
173C2—42no—
174C2—618no—
175C2—2442no—
176C2C22⋊Q8×D6113yes—
177C2#123×D6113yes—
178C2#127×D6111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61C2×#399
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D61C2semidirect
3. #16839699C2semidirect
4. #16839698C2semidirect
5. #16839697C2semidirect
6. #95×D61C2semidirect
7. C61×#399C2semidirect
11. C2×C4⋊Dic61C22semidirect
12. C2×#11758196C22semidirect
18. #14519684C22semidirect
19. C2×C4⋊C4×C61C22semidirect
21. #95×C61C22semidirect
89. D61#399direct (N × H)
95. #399D61direct (N × H)
97. C61C2×#399semidirect
104. C2×C4⋊C4C2×D61semidirect
111. #95C2×D61semidirect