Finite Group Databasebeta

← C22×#347×C107 #41059291

Subgroups — C22×#347×C107 #41059291

Order 27392.

782 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M32×C107C212yesmaximal
2C22×#97×C107C211yesmaximal, characteristic
3C2×#347×C107C2112yesmaximal, direct product factor
4C23×C8×C107C411yescharacteristic
5C23×C8×C107C2211yescharacteristic
6C22×C42×C107C411yescharacteristic
7C2×M32×C107C4112yescomplemented
8C2×M32×C107C22112yes—
9C22×C16×C107C414yescomplemented
10C2×#97×C107C416yes—
11C2×#97×C107C2216yes—
12#347×C107C22116yesdirect product factor
13C23×C4×C107—21no—
14C23×C4×C107C2×C411yescharacteristic
15C22×C8×C107—21no—
16C22×C8×C107—23no—
17C22×C8×C107C2×C416yes—
18C22×C8×C107C2×C413yes—
19C22×C8×C107C2×C416yes—
20C22×C8×C107C2×C412yes—
21C22×C8×C107C2313yes—
22C2×C42×C107—23no—
23C2×C42×C107C2×C416yes—
24M32×C107C2×C4124yescomplemented
25M32×C107C2318yes—
26C2×C16×C107C2×C4124yescomplemented
27#97×C107C2×C4112yes—
28#97×C107C2314yes—
29C24×C107M1611yescharacteristic
30C22×C4×C107—26no—
31C22×C4×C107—44no—
32C22×C4×C107C4213yes—
33C22×C4×C107C4211yescharacteristic
34C22×C4×C107M1613yes—
35C22×C4×C107M1611yescharacteristic
36C22×C4×C107M1613yes—
37C22×C4×C107C22×C413yes—
38C2×C8×C107—26no—
39C2×C8×C107—26no—
40C2×C8×C107C4216yes—
41C2×C8×C107C4216yes—
42C2×C8×C107C22×C414yes—
43C2×C8×C107C22×C413yes—
44C2×C8×C107C22×C416yes—
45C2×C8×C107C22×C416yes—
46C2×C8×C107C2411yescharacteristic
47C42×C107—26no—
48C42×C107C22×C414yes—
49C16×C107C22×C4116yescomplemented
50C23×C107—24no—
51C23×C107#9713yes—
52C23×C107#9711yescharacteristic
53C23×C107C2×M1613yes—
54C2×C4×C107—24no—
55C2×C4×C107—412no—
56C2×C4×C107#9716yes—
57C2×C4×C107#9713yes—
58C2×C4×C107#9713yes—
59C2×C4×C107C2×C4213yes—
60C2×C4×C107C2×C4213yes—
61C2×C4×C107C2×M1613yes—
62C2×C4×C107C2×M1613yes—
63C2×C4×C107C2×M1613yes—
64C2×C4×C107C23×C411yescharacteristic
65C8×C107—24no—
66C8×C107C2×C4216yes—
67C8×C107C23×C412yes—
68C22×C107—26no—
69C22×C107—26no—
70C22×C107#34714yesdirect product factor
71C22×C107C2×#9713yes—
72C22×C107C2×#9713yes—
73C22×C107C22×M1611yescharacteristic
74C4×C107—44no—
75C4×C107C2×#9713yes—
76C4×C107C2×#9713yes—
77C4×C107C22×C4211yescharacteristic
78C4×C107C22×M1611yescharacteristic
79C22×#347C10711yesmaximal, characteristic, direct product factor, Sylow
80C2×C107—21no—
81C2×C107—23no—
82C2×C107C2×#34716yesdirect product factor
83C2×C107C22×#9711yescharacteristic
84C22×M32C2×C10712yes—
85C22×#97C2×C10711yescharacteristic
86C2×#347C2×C107112yesdirect product factor
87C107C22×#34711yescharacteristic, direct product factor, Sylow
88C23×C8C4×C10711yescharacteristic
89C23×C8C22×C10711yescharacteristic
90C22×C42C4×C10711yescharacteristic
91C2×M32C4×C107112yescomplemented
92C2×M32C22×C107112yes—
93C22×C16C4×C10714yescomplemented
94C2×#97C4×C10716yes—
95C2×#97C22×C10716yes—
96#347C22×C107116yesdirect product factor
97C23×C4—21no—
98C23×C4C2×C4×C10711yescharacteristic
99C22×C8—23no—
100C22×C8—21no—
101C22×C8C2×C4×C10716yes—
102C22×C8C2×C4×C10713yes—
103C22×C8C2×C4×C10712yes—
104C22×C8C2×C4×C10716yes—
105C22×C8C23×C10713yes—
106C2×C42—23no—
107C2×C42C2×C4×C10716yes—
108M32C2×C4×C107124yescomplemented
109M32C23×C10718yes—
110C2×C16C2×C4×C107124yescomplemented
111#97C2×C4×C107112yes—
112#97C23×C10714yes—
113C24M16×C10711yescharacteristic
114C22×C4—26no—
115C22×C4—44no—
116C22×C4C42×C10713yes—
117C22×C4C42×C10711yescharacteristic
118C22×C4M16×C10713yes—
119C22×C4M16×C10713yes—
120C22×C4M16×C10711yescharacteristic
121C22×C4C22×C4×C10713yes—
122C2×C8—26no—
123C2×C8—26no—
124C2×C8C42×C10716yes—
125C2×C8C42×C10716yes—
126C2×C8C22×C4×C10714yes—
127C2×C8C22×C4×C10713yes—
128C2×C8C22×C4×C10716yes—
129C2×C8C22×C4×C10716yes—
130C2×C8C24×C10711yescharacteristic
131C42—26no—
132C42C22×C4×C10714yes—
133C16C22×C4×C107116yescomplemented
134C23—24no—
135C23#97×C10713yes—
136C23#97×C10711yescharacteristic
137C23C2×M16×C10713yes—
138C2×C4—24no—
139C2×C4—412no—
140C2×C4#97×C10716yes—
141C2×C4#97×C10713yes—
142C2×C4#97×C10713yes—
143C2×C4C2×C42×C10713yes—
144C2×C4C2×C42×C10713yes—
145C2×C4C2×M16×C10713yes—
146C2×C4C2×M16×C10713yes—
147C2×C4C2×M16×C10713yes—
148C2×C4C23×C4×C10711yescharacteristic
149C8—24no—
150C8C2×C42×C10716yes—
151C8C23×C4×C10712yes—
152C22—26no—
153C22—26no—
154C22#347×C10714yesdirect product factor
155C22C2×#97×C10713yes—
156C22C2×#97×C10713yes—
157C22C22×M16×C10711yescharacteristic
158C4—44no—
159C4C2×#97×C10713yes—
160C4C2×#97×C10713yes—
161C4C22×C42×C10711yescharacteristic
162C4C22×M16×C10711yescharacteristic
163C2—21no—
164C2—23no—
165C2C2×#347×C10716yesdirect product factor
166C2C22×#97×C10711yescharacteristic
subgroupG/H
centerC22×C4×C107C42
commutatorC4C22×C42×C107
Frattini, cosocleC2×C8C24×C107
socleC23×C107#97
prime radicalC24×C107M16
LCSG ▷ C4 ▷ C1
UCSC1 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#347×C107C2direct (N × H)
7. C2×M32×C107C4semidirect
9. C22×C16×C107C4semidirect
12. #347×C107C22direct (N × H)
24. M32×C107C2×C4semidirect
26. C2×C16×C107C2×C4semidirect
49. C16×C107C22×C4semidirect
70. C22×C107#347direct (N × H)
79. C22×#347C107direct (N × H)
82. C2×C107C2×#347direct (N × H)
86. C2×#347C2×C107direct (N × H)
87. C107C22×#347direct (N × H)
91. C2×M32C4×C107semidirect
93. C22×C16C4×C107semidirect
96. #347C22×C107direct (N × H)
108. M32C2×C4×C107semidirect
110. C2×C16C2×C4×C107semidirect
133. C16C22×C4×C107semidirect
154. C22#347×C107direct (N × H)
165. C2C2×#347×C107direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×M32×C1072
C22×#97×C1072
C2×#347×C1072
C22×#347107