Finite Group Databasebeta

← C103×#33999 #39939274

Subgroups — C103×#33999 #39939274

Order 26368.

3598 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C103C213yesmaximal
2C103×#2276C214yesmaximal, complemented
3C103×#2275C2112yesmaximal, complemented
4C4×#117×C103C219yesmaximal, complemented
5C2×#376×C103C213yesmaximal, complemented
6C22×#41×C103C2211yescharacteristic
7C4×#41×C103C4148yescomplemented
8C2×C4×Q8×C103C2216yes—
9C2×C4×D4×C103C22118yes—
10C2×#117×C103C2219yes—
11C22×C42×C103C2219yes—
12C4×C4⋊C4×C103C22136yes—
13C4×C22⋊C4×C103C22136yes—
14#376×C103C2211yescharacteristic
15#376×C103C2219yes—
16#376×C103C22112yes—
17C2×#95×C103C22112yes—
18C43×C103C2216yes—
19C2×#41×C103C2×C4124yes—
20C22×Q8×C103C2311yescharacteristic
21C22×D4×C103C2313yes—
22C23×C4×C103C23118yes—
23C23×C4×C103C2313yes—
24C4×Q8×C103C2×C4148yescomplemented
25C4×D4×C103C2×C41144yescomplemented
26#117×C103C2×C4172yescomplemented
27C2×C4⋊C4×C103C23118yes—
28C2×C22⋊C4×C103C23118yes—
29C2×C42×C103C2×C4172yescomplemented
30C2×C42×C103C23124yes—
31C2×C42×C103C23118yes—
32C2×C42×C103C2319yes—
33C2×C42×C103C2313yes—
34#95×C103C2314yes—
35#95×C103C23136yes—
36C24×C103C2413yes—
37#41×C103C42164yescomplemented
38C2×Q8×C103C22×C4112yes—
39C2×D4×C103C22×C4136yes—
40C22×C4×C103—436no—
41C22×C4×C103C22×C4172yes—
42C22×C4×C103C22×C4136yes—
43C22×C4×C103C2416yes—
44C22×C4×C103C24118yes—
45C22×C4×C103C2413yes—
46C22×C4×C103C2411yescharacteristic
47C4⋊C4×C103C22×C4172yes—
48C22⋊C4×C103C22×C4172yes—
49C42×C103—424no—
50C42×C103C22×C4112yes—
51C42×C103C22×C4136yes—
52C42×C103C22×C4172yes—
53C23×C103—212no—
54C23×C103C23×C4118yes—
55C23×C103C2511yescharacteristic
56Q8×C103C2×C42116yes—
57D4×C103C2×C42148yes—
58C2×C4×C103—236no—
59C2×C4×C103—212no—
60C2×C4×C103—472no—
61C2×C4×C103C2×C42148yes—
62C2×C4×C103C23×C4112yes—
63C2×C4×C103C23×C4136yes—
64C2×C4×C103C23×C416yes—
65C2×C4×C103C23×C4118yes—
66C22×C103—236no—
67C22×C103C22×C42112yes—
68C22×C103C24×C413yes—
69C22×C103#58514yes—
70C4×C103—212no—
71C4×C103—236no—
72C4×C103C22×C4214yes—
73C4×C103C22×C42112yes—
74#33999C10311yesmaximal, characteristic, direct product factor, Sylow
75C2×C103—212no—
76C2×C103C23×C4211yescharacteristic
77C2×C103#342816yes—
78C2×C4×#41C2×C10313yes—
79#2276C2×C10314yescomplemented
80#2275C2×C103112yescomplemented
81C4×#117C2×C10319yescomplemented
82C2×#376C2×C10313yescomplemented
83C103#3399911yescharacteristic, direct product factor, Sylow
84C22×#41C22×C10311yescharacteristic
85C4×#41C4×C103148yescomplemented
86C2×C4×Q8C22×C10316yes—
87C2×C4×D4C22×C103118yes—
88C2×#117C22×C10319yes—
89C22×C42C22×C10319yes—
90C4×C4⋊C4C22×C103136yes—
91C4×C22⋊C4C22×C103136yes—
92#376C22×C10311yescharacteristic
93#376C22×C10319yes—
94#376C22×C103112yes—
95C2×#95C22×C103112yes—
96C43C22×C10316yes—
97C2×#41C2×C4×C103124yes—
98C22×Q8C23×C10311yescharacteristic
99C22×D4C23×C10313yes—
100C23×C4C23×C103118yes—
101C23×C4C23×C10313yes—
102C4×Q8C2×C4×C103148yescomplemented
103C4×D4C2×C4×C1031144yescomplemented
104#117C2×C4×C103172yescomplemented
105C2×C4⋊C4C23×C103118yes—
106C2×C22⋊C4C23×C103118yes—
107C2×C42C2×C4×C103172yescomplemented
108C2×C42C23×C103124yes—
109C2×C42C23×C10319yes—
110C2×C42C23×C103118yes—
111C2×C42C23×C10313yes—
112#95C23×C10314yes—
113#95C23×C103136yes—
114C24C24×C10313yes—
115#41C42×C103164yescomplemented
116C2×Q8C22×C4×C103112yes—
117C2×D4C22×C4×C103136yes—
118C22×C4—436no—
119C22×C4C22×C4×C103172yes—
120C22×C4C22×C4×C103136yes—
121C22×C4C24×C10316yes—
122C22×C4C24×C103118yes—
123C22×C4C24×C10313yes—
124C22×C4C24×C10311yescharacteristic
125C4⋊C4C22×C4×C103172yes—
126C22⋊C4C22×C4×C103172yes—
127C42—424no—
128C42C22×C4×C103112yes—
129C42C22×C4×C103136yes—
130C42C22×C4×C103172yes—
131C23—212no—
132C23C23×C4×C103118yes—
133C23C25×C10311yescharacteristic
134Q8C2×C42×C103116yes—
135D4C2×C42×C103148yes—
136C2×C4—236no—
137C2×C4—212no—
138C2×C4—472no—
139C2×C4C2×C42×C103148yes—
140C2×C4C23×C4×C103112yes—
141C2×C4C23×C4×C103136yes—
142C2×C4C23×C4×C10316yes—
143C2×C4C23×C4×C103118yes—
144C22—236no—
145C22C22×C42×C103112yes—
146C22C24×C4×C10313yes—
147C22#585×C10314yes—
148C4—212no—
149C4—236no—
150C4C22×C42×C10314yes—
151C4C22×C42×C103112yes—
152C2—212no—
153C2C23×C42×C10311yescharacteristic
154C2C103×#342816yes—
subgroupG/H
centerC22×C4×C103C24
commutatorC2C23×C42×C103
Frattini, cosocleC23C25×C103
socleC23×C103C25
prime radicalC22×#41×C103C22
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2276C2semidirect
3. C103×#2275C2semidirect
4. C4×#117×C103C2semidirect
5. C2×#376×C103C2semidirect
7. C4×#41×C103C4semidirect
24. C4×Q8×C103C2×C4semidirect
25. C4×D4×C103C2×C4semidirect
26. #117×C103C2×C4semidirect
29. C2×C42×C103C2×C4semidirect
37. #41×C103C42semidirect
74. #33999C103direct (N × H)
79. #2276C2×C103semidirect
80. #2275C2×C103semidirect
81. C4×#117C2×C103semidirect
82. C2×#376C2×C103semidirect
83. C103#33999direct (N × H)
85. C4×#41C4×C103semidirect
102. C4×Q8C2×C4×C103semidirect
103. C4×D4C2×C4×C103semidirect
104. #117C2×C4×C103semidirect
107. C2×C42C2×C4×C103semidirect
115. #41C42×C103semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C1032
C103×#22762
C103×#22752
C4×#117×C1032
C2×#376×C1032
#33999103