Finite Group Databasebeta

← #22611846

Subgroups — #22611846

Order 9344.

226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q16×D73C211yesmaximal, characteristic, complemented
2C2×#14556535C211yesmaximal, characteristic, complemented
3#17988820C211yesmaximal, characteristic
4#17988392C211yesmaximal, characteristic, complemented
5#17988391C211yesmaximal, characteristic, complemented
6#17988366C211yesmaximal, characteristic, complemented
7C2×SD32×C73C211yesmaximal, characteristic, complemented
8C2×Q8×D73—21no—
9C2×Dic292C2211yescharacteristic
10C2×#11924018—21no—
11Q16×D73—22no—
12Q16×D73—22no—
13C2×C8×D73C2211yescharacteristic
14#14556562—21no—
15#14556535—22no—
16C2×#11924003C2211yescharacteristic
17#14556525C2211yescharacteristic
18#14556512—21no—
19C2×Q16×C73C2211yescharacteristic
20C2×D8×C73C2211yescharacteristic
21SD32×C73—22no—
22C2×C16×C73C2211yescharacteristic
23C2×Dic146—21no—
24C2×Dic146—41no—
25Q8×D73—24no—
26Q8×D73—42no—
27C2×C22⋊D73—41no—
28C2×C4×D73—41no—
29C2×C4×D73D411yescharacteristic
30Dic292—21no—
31Dic292D412yescomplemented
32#11924018—24no—
33C2×#10596831D411yescharacteristic
34C8×D73—21no—
35C8×D73—21no—
36C4⋊Dic73—21no—
37C22⋊Dic73—41no—
38#11924003—21no—
39C2×Q8×C73—21no—
40C2×D4×C73—21no—
41Q16×C73—21no—
42Q16×C73D412yescomplemented
43D8×C73—21no—
44D8×C73—21no—
45C2×C8×C73C2311yescharacteristic
46C16×C73—21no—
47C23×C73—41no—
48C22×D73D811yescharacteristic
49Q8×C73—22no—
50Q8×C73—41no—
51D4×C73—41no—
52D4×C73—41no—
53C2×C4×C73—41no—
54C2×C4×C73C2×D411yescharacteristic
55C22⋊D73—82no—
56C2×Dic73—41no—
57C2×Dic73—41no—
58C2×Dic73D811yescharacteristic
59C4×D73—21no—
60C4×D73—21no—
61C4×D73—44no—
62Dic146—22no—
63Dic146—44no—
64Dic146—41no—
65C8×C73C2×D411yescharacteristic
66C8×C73C2×D411yescharacteristic
67#10596831—21no—
68C22×C73—81no—
69C22×C73—81no—
70C22×C73—81no—
71C22×C73C2×D811yescharacteristic
72C2×D73—21no—
73C2×D73—21no—
74C2×D73SD3212yescomplemented
75C4×C73—42no—
76C4×C73#12011yescharacteristic
77C4×C73AGL(1,ℤ/8)11yescharacteristic
78Dic73—21no—
79Dic73—42no—
80Dic73—81no—
81C2×C73—161no—
82C2×C73#44711yescharacteristic
83C2×C73C2×SD3211yescharacteristic
84C2×C73#51011yescharacteristic
85D73—22no—
86#2185—731nomaximal, Sylow
87C73#218511yescharacteristic, complemented, Sylow
88C22×Q16—731no—
89C2×SD32—731no—
90C2×SD32D7311yescharacteristic, complemented
91#466—731no—
92#358—731no—
93#358—731no—
94C22⋊C16—731no—
95C22×Q8—1461no—
96C2×Q16—731no—
97C2×Q16—1461no—
98C2×Q16—1462no—
99C2×Q16—1462no—
100C2×Q16C2×D7311yescharacteristic
101C2×D8C2×D7311yescharacteristic
102C22×C8—731no—
103#121—1461no—
104SD32—22no—
105SD32—1462no—
106C2×C16—731no—
107C2×C16C2×D7311yescharacteristic
108#107—731no—
109#102—1461no—
110C2×Q8—21no—
111C2×Q8—2921no—
112C2×Q8—2922no—
113C2×Q8—1464no—
114C2×Q8—1461no—
115C2×D4—21no—
116C2×D4—2921no—
117C22×C4—2921no—
118C22×C4—731no—
119Q16—21no—
120Q16—732no—
121Q16—1464no—
122Q16—1461no—
123Q16C22⋊D7312yescomplemented
124D8—21no—
125D8—21no—
126C2×C8—731no—
127C2×C8—1461no—
128C2×C8—1461no—
129C2×C8C22×D7311yescharacteristic
130C4⋊C4—1461no—
131C22⋊C4—2921no—
132C16—21no—
133C16—1461no—
134C23—41no—
135C23—731no—
136Q8—22no—
137Q8—41no—
138Q8—2924no—
139Q8—2921no—
140Q8—1462no—
141D4—41no—
142D4—41no—
143D4—5842no—
144C2×C4—41no—
145C2×C4—2924no—
146C2×C4—2921no—
147C2×C4—2921no—
148C2×C4—731no—
149C2×C4—1461no—
150C2×C4—1461no—
151C2×C4D4×D7311yescharacteristic
152C8—1461no—
153C8D4×D7311yescharacteristic
154C8C2×C22⋊D7311yescharacteristic
155C22—81no—
156C22—81no—
157C22—81no—
158C22—732no—
159C22—1461no—
160C22—1461no—
161C22D8×D7311yescharacteristic
162C4—42no—
163C4—2922no—
164C4—5841no—
165C4—1461no—
166C4#1455655911yescharacteristic
167C4#1455661511yescharacteristic
168C2—161no—
169C2—1462no—
170C2#1798871911yescharacteristic
171C2SD32×D7311yescharacteristic
172C2#1798902611yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC2×SD32×C73C2
socleC22×C73C2×D8
hypercenterC2×SD32D73
hypocenterC73#2185
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D73C2semidirect
2. C2×#14556535C2semidirect
4. #17988392C2semidirect
5. #17988391C2semidirect
6. #17988366C2semidirect
7. C2×SD32×C73C2semidirect
31. Dic292D4semidirect
42. Q16×C73D4semidirect
74. C2×D73SD32semidirect
87. C73#2185semidirect
90. C2×SD32D73semidirect
123. Q16C22⋊D73semidirect