Finite Group Databasebeta

← #22611383

Subgroups — #22611383

Order 9344.

190 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 59 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#17988614C211yesmaximal, characteristic, complemented
2#17988605C211yesmaximal, characteristic
3#17988581C211yesmaximal, characteristic
4#17988569C211yesmaximal, characteristic
5#17988357C211yesmaximal, characteristic, complemented
6#17988351C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10C2×#11924012C2211yescharacteristic
11C22×#10596831C2211yescharacteristic
12C4⋊#10596831—22no—
13#14556519—22no—
14#14556514—21no—
15#14556511—21no—
16#14556509—21no—
17#14556507—21no—
18C2×M16×C73C2211yescharacteristic
19#117×C73C2211yescharacteristic
20#117×C73C2211yescharacteristic
21#11924028—21no—
22#11924028—21no—
23#11924028—21no—
24#11924028—21no—
25C2×Dic146D411yescharacteristic
26C2×D292D411yescharacteristic
27C2×C22⋊D73—21no—
28C2×C4×D73—21no—
29#11924012—21no—
30#11924012—21no—
31#11924012—21no—
32#11924012—21no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C2×#10596831—21no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38C22×C4×C73C2311yescharacteristic
39M16×C73—21no—
40M16×C73—21no—
41C2×C8×C73—21no—
42C4⋊C4×C73—21no—
43C4⋊C4×C73—21no—
44C22⋊C4×C73—21no—
45C22⋊C4×C73—21no—
46C42×C73—21no—
47C42×C73D412yes—
48C23×C73#4111yescharacteristic
49C22×D73—21no—
50C2×C4×C73—22no—
51C2×C4×C73—41no—
52C2×C4×C73C2×D411yescharacteristic
53C2×C4×C73C2×D411yescharacteristic
54C2×C4×C73#4111yescharacteristic
55C2×C4×C73#4111yescharacteristic
56C2×C4×C73#4111yescharacteristic
57C2×C4×C73#4111yescharacteristic
58C22⋊D73—41no—
59C22⋊D73—41no—
60C2×Dic73—21no—
61D292—21no—
62D292—21no—
63C4×D73—41no—
64C4×D73—41no—
65Dic146—21no—
66Dic146—21no—
67C8×C73—41no—
68#10596831—41no—
69#10596831—41no—
70#10596831—41no—
71C22×C73—41no—
72C22×C73#12311yescharacteristic
73C22×C73#12311yescharacteristic
74C22×C73#12611yescharacteristic
75C2×D73—41no—
76C2×D73—81no—
77C4×C73—42no—
78C4×C73—81no—
79C4×C73#12111yescharacteristic
80C4×C73#12311yescharacteristic
81C4×C73#12411yescharacteristic
82C4×C73#12611yescharacteristic
83Dic73—41no—
84C2×C73—21no—
85C2×C73—21no—
86C2×C73—21no—
87C2×C73#39711yescharacteristic
88D73—81no—
89#2080—731nomaximal, Sylow
90C73#208011yescharacteristic, complemented, Sylow
91#424—731no—
92#421—731no—
93#416—731no—
94#413—731no—
95#344—731no—
96#341—731no—
97H(3,ℤ/4)D7311yescharacteristic, complemented
98C2×#41—731no—
99C2×M16—731no—
100C2×M16—731no—
101C2×M16C2×D7311yescharacteristic
102C22×C8—731no—
103#117C2×D7311yescharacteristic
104#117C2×D7311yescharacteristic
105C4⋊C8—1462no—
106#104—1462no—
107#103—1461no—
108#102—1461no—
109#101—1461no—
110#100—1461no—
111#41—1461no—
112#41—1461no—
113#41—1461no—
114#41—1461no—
115C2×Q8—731no—
116C2×D4—731no—
117C2×D4—1461no—
118C22×C4—1461no—
119C22×C4C22×D7311yescharacteristic
120M16—21no—
121M16—21no—
122M16—1461no—
123M16—1461no—
124M16—1461no—
125M16—1461no—
126C2×C8—21no—
127C2×C8—1461no—
128C2×C8—1461no—
129C2×C8—1461no—
130C2×C8—1461no—
131C2×C8—1461no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C42—21no—
137C42D29212yes—
138C23—1461no—
139C23#1192402711yescharacteristic
140Q8—1461no—
141Q8—1461no—
142D4—2921no—
143D4—2921no—
144D4—1461no—
145D4—1461no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—2921no—
149C2×C4—2921no—
150C2×C4—1461no—
151C2×C4D4×D7311yescharacteristic
152C2×C4C2×D29211yescharacteristic
153C2×C4#1192402711yescharacteristic
154C2×C4#1192402811yescharacteristic
155C2×C4#1192402811yescharacteristic
156C2×C4#1192402911yescharacteristic
157C8—41no—
158C8—2921no—
159C8—2921no—
160C8—2921no—
161C22—41no—
162C22—2921no—
163C22—5841no—
164C22#1455657311yescharacteristic
165C22#1455657511yescharacteristic
166C22#1455658611yescharacteristic
167C4—42no—
168C4—81no—
169C4—2921no—
170C4#1455656611yescharacteristic
171C4#1455657311yescharacteristic
172C4#1455657911yescharacteristic
173C4#1455658611yescharacteristic
174C2—21no—
175C2—21no—
176C2—21no—
177C2—5841no—
178C2#1798851411yescharacteristic
subgroupG/H
centerC4#14556579
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingH(3,ℤ/4)×C73C2
socleC2×C73#397
hypercenterH(3,ℤ/4)D73
hypocenterC73#2080
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #17988614C2semidirect
5. #17988357C2semidirect
6. #17988351C2semidirect
7. H(3,ℤ/4)×C73C2semidirect
90. C73#2080semidirect
97. H(3,ℤ/4)D73semidirect