Finite Group Databasebeta

← C41×#1616 #19105396

Subgroups — C41×#1616 #19105396

Order 5248.

246 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C41×#537C211yesmaximal, characteristic
2C41×#481C212yesmaximal, complemented
3C41×#400C211yesmaximal, characteristic, complemented
4C41×#327C212yesmaximal, complemented
5C41×#324C211yesmaximal, characteristic, complemented
6C2×#41×C41—21no—
7C22⋊Q8×C41—22no—
8#121×C41—22no—
9#121×C41—21no—
10#121×C41C2212yes—
11C2×C4⋊C4×C41C2211yescharacteristic
12C2×C4⋊C4×C41C2211yescharacteristic
13#106×C41—22no—
14#102×C41—22no—
15C22⋊C8×C41C2212yes—
16#95×C41—21no—
17#95×C41—21no—
18#95×C41C2211yescharacteristic
19#41×C41—42no—
20#41×C41—42no—
21C2×Q8×C41—21no—
22C2×D4×C41—21no—
23C2×D4×C41—22no—
24C2×D4×C41—21no—
25C2×D4×C41D412yes—
26C22×C4×C41—22no—
27C22×C4×C41—21no—
28C22×C4×C41—21no—
29C22×C4×C41D411yescharacteristic
30C22×C4×C41D411yescharacteristic
31C22×C4×C41C2311yescharacteristic
32C2×C8×C41—22no—
33C4⋊C4×C41—21no—
34C4⋊C4×C41—22no—
35C4⋊C4×C41—22no—
36C4⋊C4×C41D412yes—
37C22⋊C4×C41—22no—
38C22⋊C4×C41—22no—
39C23×C41—22no—
40C23×C41C2×D411yescharacteristic
41Q8×C41—42no—
42D4×C41—42no—
43D4×C41—42no—
44D4×C41—42no—
45D4×C41—42no—
46D4×C41—81no—
47C2×C4×C41—21no—
48C2×C4×C41—21no—
49C2×C4×C41—21no—
50C2×C4×C41—22no—
51C2×C4×C41—41no—
52C2×C4×C41—44no—
53C2×C4×C41—41no—
54C2×C4×C41—41no—
55C2×C4×C41—41no—
56C2×C4×C41—42no—
57C2×C4×C41—41no—
58C2×C4×C41—41no—
59C2×C4×C41SD1612yes—
60C2×C4×C41C2×D412yes—
61C8×C41—42no—
62C22×C41—21no—
63C22×C41—21no—
64C22×C41—42no—
65C22×C41—42no—
66C22×C41—42no—
67C22×C41#12011yescharacteristic
68C22×C41C2×SD1611yescharacteristic
69C22×C41AGL(1,ℤ/8)11yescharacteristic
70C4×C41—22no—
71C4×C41—22no—
72C4×C41—42no—
73C4×C41—41no—
74C4×C41—81no—
75C4×C41—81no—
76#1616C4111yesmaximal, characteristic, direct product factor, Sylow
77C2×C41—21no—
78C2×C41—21no—
79C2×C41—82no—
80C2×C41#45011yescharacteristic
81C2×C41#45411yescharacteristic
82C2×C41#45811yescharacteristic
83#537C2×C4111yescharacteristic
84#481C2×C4112yescomplemented
85#400C2×C4111yescharacteristic, complemented
86#327C2×C4112yescomplemented
87#324C2×C4111yescharacteristic, complemented
88C41#161611yescharacteristic, direct product factor, Sylow
89C2×#41—21no—
90C22⋊Q8—22no—
91#121—22no—
92#121—21no—
93#121C22×C4112yes—
94C2×C4⋊C4C22×C4111yescharacteristic
95C2×C4⋊C4C22×C4111yescharacteristic
96#106—22no—
97#102—22no—
98C22⋊C8C22×C4112yes—
99#95—21no—
100#95—21no—
101#95C22×C4111yescharacteristic
102#41—42no—
103#41—42no—
104C2×Q8—21no—
105C2×D4—21no—
106C2×D4—22no—
107C2×D4—21no—
108C2×D4D4×C4112yes—
109C22×C4—22no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4D4×C4111yescharacteristic
113C22×C4D4×C4111yescharacteristic
114C22×C4C23×C4111yescharacteristic
115C2×C8—22no—
116C4⋊C4—21no—
117C4⋊C4—22no—
118C4⋊C4—22no—
119C4⋊C4D4×C4112yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C23—22no—
123C23C2×D4×C4111yescharacteristic
124Q8—42no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—44no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4SD16×C4112yes—
143C2×C4C2×D4×C4112yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22#120×C4111yescharacteristic
151C22C2×SD16×C4111yescharacteristic
152C22AGL(1,ℤ/8)×C4111yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—41no—
157C4—81no—
158C4—81no—
159C2—21no—
160C2—21no—
161C2—82no—
162C2C41×#45011yescharacteristic
163C2C41×#45411yescharacteristic
164C2C41×#45811yescharacteristic
subgroupG/H
center, socleC22×C41#120
commutator, Frattini, cosocleC22×C4C23×C41
prime radicalC41×#537C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#481C2semidirect
3. C41×#400C2semidirect
4. C41×#327C2semidirect
5. C41×#324C2semidirect
76. #1616C41direct (N × H)
84. #481C2×C41semidirect
85. #400C2×C41semidirect
86. #327C2×C41semidirect
87. #324C2×C41semidirect
88. C41#1616direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#5372
C41×#4812
C41×#4002
C41×#3272
C41×#3242
#161641