Finite Group Databasebeta

← C67×#1911 #22556342

Subgroups — C67×#1911 #22556342

Order 8576.

362 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#535×C67C211yesmaximal, characteristic
2#518×C67C211yesmaximal, characteristic, complemented
3#421×C67C212yesmaximal, complemented
4C2×#100×C67C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C67C212yesmaximal, complemented
6C2×#41×C67C2211yescharacteristic
7C22×D4×C67C2211yescharacteristic
8C2×M16×C67C2212yes—
9#127×C67C412yescomplemented
10#124×C67C412yescomplemented
11#121×C67—22no—
12#120×C67—22no—
13C4×D4×C67—24no—
14#117×C67C2211yescharacteristic
15#117×C67C2212yes—
16C2×C22⋊C4×C67—22no—
17#104×C67—24no—
18#100×C67—22no—
19C24×C67D412yes—
20#41×C67—22no—
21#41×C67—22no—
22C2×Q8×C67C2×C411yescharacteristic, complemented
23C2×D4×C67—21no—
24C2×D4×C67—24no—
25C2×D4×C67—22no—
26C2×D4×C67—22no—
27C2×D4×C67C2×C412yes—
28C2×D4×C67C2×C411yescharacteristic, complemented
29C2×D4×C67D412yes—
30C22×C4×C67—24no—
31C22×C4×C67—21no—
32C22×C4×C67C2311yescharacteristic
33M16×C67—22no—
34M16×C67—22no—
35C2×C8×C67—22no—
36C4⋊C4×C67—22no—
37C4⋊C4×C67—21no—
38C22⋊C4×C67—24no—
39C22⋊C4×C67—24no—
40C22⋊C4×C67—22no—
41C22⋊C4×C67—21no—
42C42×C67C2×C412yescomplemented
43C42×C67D414yescomplemented
44C23×C67—22no—
45C23×C67—22no—
46C23×C67—21no—
47C23×C67—82no—
48C23×C67C22⋊C414yes—
49C23×C67C2×D411yescharacteristic
50Q8×C67—22no—
51D4×C67—24no—
52D4×C67—22no—
53D4×C67—24no—
54D4×C67—41no—
55D4×C67—41no—
56D4×C67—84no—
57C2×C4×C67—22no—
58C2×C4×C67—21no—
59C2×C4×C67—24no—
60C2×C4×C67—42no—
61C2×C4×C67—84no—
62C2×C4×C67C22×C411yescharacteristic
63C2×C4×C67C2×D412yes—
64C2×C4×C67C2×D411yescharacteristic
65C2×C4×C67#4112yes—
66C8×C67—42no—
67C22×C67—24no—
68C22×C67—41no—
69C22×C67—44no—
70C22×C67—44no—
71C22×C67—42no—
72C22×C67—41no—
73C22×C67—82no—
74C22×C67C2×C22⋊C411yescharacteristic
75C22×C67#12011yescharacteristic
76C22×C67#12311yescharacteristic
77C4×C67—44no—
78C4×C67—42no—
79C4×C67—41no—
80C4×C67C4×D412yes—
81C4×C67#12112yes—
82C2×C67—21no—
83C2×C67—21no—
84C2×C67—21no—
85C2×C67—44no—
86C2×C67—81no—
87C2×C67#38611yescharacteristic
88#1911C6711yesmaximal, characteristic, direct product factor, Sylow
89C67#191111yescharacteristic, direct product factor, Sylow
90#535C2×C6711yescharacteristic
91#518C2×C6711yescharacteristic, complemented
92#421C2×C6712yescomplemented
93C2×#100C2×C6711yescharacteristic, complemented
94H(3,ℤ/4)C2×C6712yescomplemented
95C2×#41C22×C6711yescharacteristic
96C22×D4C22×C6711yescharacteristic
97C2×M16C22×C6712yes—
98#127C4×C6712yescomplemented
99#124C4×C6712yescomplemented
100#121—22no—
101#120—22no—
102C4×D4—24no—
103#117C22×C6711yescharacteristic
104#117C22×C6712yes—
105C2×C22⋊C4—22no—
106#104—24no—
107#100—22no—
108C24D4×C6712yes—
109#41—22no—
110#41—22no—
111C2×Q8C2×C4×C6711yescharacteristic, complemented
112C2×D4—21no—
113C2×D4—24no—
114C2×D4—22no—
115C2×D4—22no—
116C2×D4C2×C4×C6712yes—
117C2×D4C2×C4×C6711yescharacteristic, complemented
118C2×D4D4×C6712yes—
119C22×C4—24no—
120C22×C4—21no—
121C22×C4C23×C6711yescharacteristic
122M16—22no—
123M16—22no—
124C2×C8—22no—
125C4⋊C4—22no—
126C4⋊C4—21no—
127C22⋊C4—24no—
128C22⋊C4—24no—
129C22⋊C4—22no—
130C22⋊C4—21no—
131C42C2×C4×C6712yescomplemented
132C42D4×C6714yescomplemented
133C23—22no—
134C23—22no—
135C23—21no—
136C23—82no—
137C23C22⋊C4×C6714yes—
138C23C2×D4×C6711yescharacteristic
139Q8—22no—
140D4—24no—
141D4—22no—
142D4—24no—
143D4—41no—
144D4—41no—
145D4—84no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—24no—
149C2×C4—42no—
150C2×C4—84no—
151C2×C4C22×C4×C6711yescharacteristic
152C2×C4C2×D4×C6712yes—
153C2×C4C2×D4×C6711yescharacteristic
154C2×C4#41×C6712yes—
155C8—42no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—42no—
161C22—41no—
162C22—82no—
163C22C2×C22⋊C4×C6711yescharacteristic
164C22#120×C6711yescharacteristic
165C22#123×C6711yescharacteristic
166C4—44no—
167C4—42no—
168C4—41no—
169C4C4×D4×C6712yes—
170C4#121×C6712yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—81no—
176C2#386×C6711yescharacteristic
subgroupG/H
center, socleC2×C67#386
commutatorC2×C4C22×C4×C67
Frattini, cosocleC22×C4C23×C67
prime radical#535×C67C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. #518×C67C2semidirect
3. #421×C67C2semidirect
4. C2×#100×C67C2semidirect
5. H(3,ℤ/4)×C67C2semidirect
9. #127×C67C4semidirect
10. #124×C67C4semidirect
22. C2×Q8×C67C2×C4semidirect
28. C2×D4×C67C2×C4semidirect
42. C42×C67C2×C4semidirect
43. C42×C67D4semidirect
88. #1911C67direct (N × H)
89. C67#1911direct (N × H)
91. #518C2×C67semidirect
92. #421C2×C67semidirect
93. C2×#100C2×C67semidirect
94. H(3,ℤ/4)C2×C67semidirect
98. #127C4×C67semidirect
99. #124C4×C67semidirect
111. C2×Q8C2×C4×C67semidirect
117. C2×D4C2×C4×C67semidirect
131. C42C2×C4×C67semidirect
132. C42D4×C67semidirect

Maximal subgroups

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

subgroupindex
#535×C672
#518×C672
#421×C672
C2×#100×C672
H(3,ℤ/4)×C672
#191167