Finite Group Databasebeta

← C2×#17988393 #22611654

Subgroups — C2×#17988393 #22611654

Order 9344.

224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14556613C211yesmaximal, characteristic
2C22×#11924003C211yesmaximal, characteristic, complemented
3#17988393C214yesmaximal, direct product factor
4C2×#108×C73C211yesmaximal, characteristic, complemented
5C2×#11924028—21no—
6#14556613—21no—
7#14556613—21no—
8#14556613C412yes—
9#14556613C2212yes—
10C2×Dic292C411yescharacteristic
11C2×#11924017—21no—
12C2×D584C411yescharacteristic
13C2×#11924003—21no—
14C2×#11924003—21no—
15C2×#11924003C2212yescomplemented
16C2×M16×C73—21no—
17C22×C8×C73C2211yescharacteristic
18#108×C73—21no—
19#108×C73C2212yescomplemented
20#11924028—22no—
21#11924028—22no—
22#11924028—41no—
23#11924028—41no—
24C2×Dic146—21no—
25C2×D292—21no—
26C2×C22⋊D73—41no—
27C2×C4×D73—41no—
28Dic292—21no—
29Dic292C2×C412yes—
30#11924017—22no—
31#11924017—22no—
32D584—21no—
33D584C2×C412yes—
34#11924003—22no—
35C22×C4×C73D411yescharacteristic
36M16×C73—22no—
37M16×C73—41no—
38C2×C8×C73—41no—
39C2×C8×C73C2×C411yescharacteristic
40C2×C8×C73C2×C411yescharacteristic
41C2×C8×C73D411yescharacteristic
42C2×C8×C73D411yescharacteristic
43C2×C8×C73D411yescharacteristic
44C2×C8×C73C2311yescharacteristic
45C23×C73SD1611yescharacteristic
46C22×D73—41no—
47C2×C4×C73C22⋊C411yescharacteristic
48C2×C4×C73C22⋊C411yescharacteristic
49C2×C4×C73D811yescharacteristic
50C2×C4×C73D811yescharacteristic
51C2×C4×C73SD1611yescharacteristic
52C2×C4×C73C2×D411yescharacteristic
53C22⋊D73—42no—
54C22⋊D73—42no—
55C2×Dic73—41no—
56D292—22no—
57D292—41no—
58C4×D73—42no—
59C4×D73—42no—
60Dic146—22no—
61Dic146—41no—
62C8×C73—42no—
63C8×C73C22⋊C411yescharacteristic
64C8×C73C22⋊C411yescharacteristic
65C8×C73C22×C411yescharacteristic
66C8×C73C2×D411yescharacteristic
67C22×C73—22no—
68C22×C73#10211yescharacteristic
69C22×C73#10211yescharacteristic
70C22×C73C2×SD1611yescharacteristic
71C2×D73—42no—
72C2×D73—82no—
73C4×C73#10211yescharacteristic
74C4×C73#10211yescharacteristic
75C4×C73C2×C22⋊C411yescharacteristic
76C4×C73C2×D811yescharacteristic
77Dic73—42no—
78C2×C73—21no—
79C2×C73—21no—
80C2×C73#35912yescomplemented
81C2×C73C2×#10211yescharacteristic
82D73—82no—
83C2×#359—731nomaximal, Sylow
84C73C2×#35911yescharacteristic, complemented, Sylow
85C2×#135—731no—
86C22×C16—731no—
87C2×#108D7311yescharacteristic, complemented
88#359—734no—
89C2×#41—1461no—
90#135—732no—
91#135—732no—
92#135—1461no—
93#135—1461no—
94C2×Q16—731no—
95C2×SD16—1461no—
96C2×D8—731no—
97C2×M16—21no—
98C22×C8C2×D7311yescharacteristic
99C2×C16—732no—
100C2×C16—1461no—
101C2×C16—1461no—
102#108—21no—
103#108C2×D7312yescomplemented
104#41—2921no—
105#41—2921no—
106#41—1462no—
107#41—1462no—
108C2×Q8—1461no—
109C2×D4—2921no—
110C2×D4—1461no—
111C22×C4—2921no—
112C22×C4C22⋊D7311yescharacteristic
113Q16—732no—
114Q16—1461no—
115SD16—1462no—
116SD16—1462no—
117D8—732no—
118D8—1461no—
119M16—22no—
120M16—41no—
121C2×C8—41no—
122C2×C8C4×D7311yescharacteristic
123C2×C8C4×D7311yescharacteristic
124C2×C8D29211yescharacteristic
125C2×C8D29211yescharacteristic
126C2×C8C22⋊D7311yescharacteristic
127C2×C8C22×D7311yescharacteristic
128C16—1462no—
129C23—2921no—
130C23#1192401511yescharacteristic
131Q8—2921no—
132Q8—1462no—
133D4—2922no—
134D4—2922no—
135D4—2921no—
136D4—1462no—
137C2×C4—2921no—
138C2×C4—2922no—
139C2×C4—2922no—
140C2×C4#1192400511yescharacteristic
141C2×C4#1192400511yescharacteristic
142C2×C4#1192401311yescharacteristic
143C2×C4#1192401311yescharacteristic
144C2×C4#1192401511yescharacteristic
145C2×C4C2×C22⋊D7311yescharacteristic
146C8—42no—
147C8#1192400511yescharacteristic
148C8#1192400511yescharacteristic
149C8C2×C4×D7311yescharacteristic
150C8C2×D29211yescharacteristic
151C22—22no—
152C22—2922no—
153C22—5842no—
154C22#1455651111yescharacteristic
155C22#1455651111yescharacteristic
156C22C2×#1192401511yescharacteristic
157C4—2922no—
158C4#1455651111yescharacteristic
159C4#1455651111yescharacteristic
160C4C2×#1192400511yescharacteristic
161C4C2×#1192401311yescharacteristic
162C2—21no—
163C2—21no—
164C2—5842no—
165C2#1798839312yesdirect product factor
166C2C2×#1455651111yescharacteristic
subgroupG/H
centerC2×C4#11924013
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
FittingC2×#108×C73C2
socleC22×C73#102
hypercenterC2×#108D73
hypocenterC73C2×#359
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. C22×#11924003C2semidirect
3. #17988393C2direct (N × H)
4. C2×#108×C73C2semidirect
15. C2×#11924003C22semidirect
19. #108×C73C22semidirect
80. C2×C73#359semidirect
84. C73C2×#359semidirect
87. C2×#108D73semidirect
103. #108C2×D73semidirect
165. C2#17988393direct (N × H)