Finite Group Databasebeta

← C2×#17989506 #22626256

Subgroups — C2×#17989506 #22626256

Order 9344.

216 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 66 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×#14556666C211yesmaximal, characteristic
2C2×#14556661C211yesmaximal, characteristic
3#17989506C214yesmaximal, direct product factor
4C2×Q16×D73C211yesmaximal, characteristic
5C2×#11924038—21no—
6#14556666—21no—
7#14556666C2212yes—
8C2×#11924031—21no—
9#14556661—21no—
10#14556661C2212yes—
11C2×Q8×D73—21no—
12C2×Dic292C411yescharacteristic
13C2×#11924018—21no—
14Q16×D73—21no—
15Q16×D73—21no—
16Q16×D73C412yes—
17Q16×D73C2212yes—
18C2×C8×D73C2211yescharacteristic
19C2×Q16×C73C411yescharacteristic
20#11924038—22no—
21#11924038—41no—
22C2×#10596833—41no—
23#11924031—22no—
24C2×Dic146—21no—
25C2×Dic146—41no—
26Q8×D73—22no—
27Q8×D73—22no—
28Q8×D73—41no—
29Q8×D73—41no—
30C2×C4×D73—41no—
31C2×C4×D73D411yescharacteristic
32Dic292—21no—
33Dic292C2×C412yes—
34#11924018—22no—
35#11924018—22no—
36C2×#10596831D411yescharacteristic
37C8×D73C2×C411yescharacteristic
38C8×D73D411yescharacteristic
39C8×D73D411yescharacteristic
40C8×D73C2311yescharacteristic
41C2×Q8×C73—21no—
42Q16×C73—21no—
43Q16×C73C2×C412yes—
44C2×C8×C73C2×C411yescharacteristic
45C22×D73SD1611yescharacteristic
46Q8×C73—22no—
47Q8×C73—41no—
48C2×C4×C73—41no—
49C2×C4×C73C22⋊C411yescharacteristic
50C2×Dic73—41no—
51C2×Dic73D811yescharacteristic
52C4×D73—42no—
53C4×D73—42no—
54C4×D73C22⋊C411yescharacteristic
55C4×D73D811yescharacteristic
56C4×D73SD1611yescharacteristic
57C4×D73C2×D411yescharacteristic
58Dic146—22no—
59Dic146—41no—
60Dic146—42no—
61Dic146—42no—
62#10596833—42no—
63C8×C73C22⋊C411yescharacteristic
64C8×C73C22×C411yescharacteristic
65#10596831C22⋊C411yescharacteristic
66#10596831C2×D411yescharacteristic
67C22×C73#10211yescharacteristic
68C2×D73—22no—
69C2×D73#10211yescharacteristic
70C2×D73C2×SD1611yescharacteristic
71C4×C73—42no—
72C4×C73#10211yescharacteristic
73C4×C73C2×C22⋊C411yescharacteristic
74Dic73—42no—
75Dic73#10211yescharacteristic
76Dic73C2×D811yescharacteristic
77C2×C73#36212yescomplemented
78C2×C73C2×#10211yescharacteristic
79D73—21no—
80D73—21no—
81C2×#362—731nomaximal, Sylow
82C73C2×#36211yescharacteristic, complemented, Sylow
83C22×Q16—731no—
84C2×M32—731no—
85C2×#108—731no—
86#362—734no—
87C22×Q8—1461no—
88C2×Q16—732no—
89C2×Q16—732no—
90C2×Q16—731no—
91C2×Q16—1461no—
92C2×Q16—1461no—
93C2×Q16—1461no—
94C2×Q16#6440811yescharacteristic
95C2×M16—1461no—
96C22×C8—731no—
97M32—732no—
98M32—1461no—
99C2×C16—1461no—
100#108—732no—
101#108—1461no—
102C2×Q8—21no—
103C2×Q8—2921no—
104C2×Q8—2921no—
105C2×Q8—2921no—
106C2×Q8—1462no—
107C2×Q8—1462no—
108C2×Q8—1461no—
109C22×C4—2921no—
110C22×C4—731no—
111Q16—21no—
112Q16—732no—
113Q16—1462no—
114Q16—1462no—
115Q16—1461no—
116Q16C2×#6440812yes—
117M16—2921no—
118M16—1462no—
119C2×C8—2921no—
120C2×C8—731no—
121C2×C8—731no—
122C2×C8—731no—
123C2×C8—731no—
124C2×C8—731no—
125C2×C8C2×#6440811yescharacteristic
126C16—1462no—
127C23—731no—
128Q8—22no—
129Q8—41no—
130Q8—2922no—
131Q8—2922no—
132Q8—2921no—
133Q8—1462no—
134C2×C4—41no—
135C2×C4—2922no—
136C2×C4—2922no—
137C2×C4—2921no—
138C2×C4—731no—
139C2×C4—731no—
140C2×C4—731no—
141C2×C4—731no—
142C2×C4—731no—
143C2×C4C22⋊#6440811yescharacteristic
144C8—2922no—
145C8—731no—
146C8—731no—
147C8C22⋊#6440811yescharacteristic
148C8C22×#6440811yescharacteristic
149C22—731no—
150C22—731no—
151C22—1462no—
152C22#1455665311yescharacteristic
153C4—42no—
154C4—2922no—
155C4—731no—
156C4—731no—
157C4#1455665311yescharacteristic
158C4C2×C22⋊#6440811yescharacteristic
159C2—1461no—
160C2—1461no—
161C2#1798950612yesdirect product factor
162C2C2×#1455665311yescharacteristic
subgroupG/H
centerC22#14556653
commutatorC8×C73C22×C4
FrattiniC8C22×#64408
FittingC2×Q16×C73C4
socleC22×C73#102
hypercenterC2×Q16#64408
hypocenterC73C2×#362
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #17989506C2direct (N × H)
77. C2×C73#362semidirect
82. C73C2×#362semidirect
161. C2#17989506direct (N × H)