Finite Group Databasebeta

← #22626939

Subgroups — #22626939

Order 9344.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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×C4⋊#10596842C211yesmaximal, characteristic
2C2×C4×#10596842C211yesmaximal, characteristic
3C4⋊C4×#64408C211yesmaximal, characteristic
4C22×#10596842—21no—
5C22×#10596842—21no—
6C4⋊#10596842—21no—
7C4⋊#10596842C412yescomplemented
8C4×#10596842—21no—
9C4×#10596842C412yescomplemented
10C2×C4⋊#64408C411yescharacteristic
11C2×C4×#64408—21no—
12C2×C4×#64408C2211yescharacteristic
13(C2×#64408)⋊C4—21no—
14C4⋊C4×D73C411yescharacteristic
15C2×#10596842—22no—
16C2×#10596842—22no—
17C2×#10596842—22no—
18C2×#10596842—22no—
19C2×#10596842—41no—
20C2×#10596842—41no—
21C22×#64408—21no—
22C22×#64408D411yescharacteristic
23C22×#64408D411yescharacteristic
24C4⋊#64408—21no—
25C4⋊#64408C812yescomplemented
26C4×#64408—41no—
27C4×#64408—41no—
28C4×#64408C2×C411yescharacteristic
29C4×#64408C2×C411yescharacteristic
30C4×#64408D411yescharacteristic
31C4×#64408Q811yescharacteristic
32C2×C4×D73—21no—
33C2×C4×D73C2×C411yescharacteristic
34C4⋊Dic73C811yescharacteristic, complemented
35#11924007—21no—
36C4⋊C4×C73C811yescharacteristic, complemented
37C22×D73C22⋊C411yescharacteristic
38C2×#64408—21no—
39C2×#64408—21no—
40C2×#64408—22no—
41C2×#64408—41no—
42C2×#64408—41no—
43C2×#64408C22⋊C411yescharacteristic
44C2×#64408C22⋊C411yescharacteristic
45C2×#64408C4⋊C411yescharacteristic
46C2×#64408C4⋊C411yescharacteristic
47C2×#64408D811yescharacteristic
48C2×#64408SD1611yescharacteristic
49C2×#64408SD1611yescharacteristic
50C2×#64408Q1611yescharacteristic
51#10596842—24no—
52#10596842—42no—
53C2×C4×C73—21no—
54C2×C4×C73C2×C811yescharacteristic
55C2×Dic73—21no—
56C2×Dic73M1611yescharacteristic
57C4×D73—41no—
58C4×D73—41no—
59C4×D73C4211yescharacteristic
60C4×D73C4⋊C411yescharacteristic
61C4×D73C2×C811yescharacteristic
62C4×D73M1611yescharacteristic
63C22×C73C22⋊C811yescharacteristic
64C2×D73#9511yescharacteristic
65C2×D73C22⋊C811yescharacteristic
66C2×D73#10211yescharacteristic
67C2×D73#10311yescharacteristic
68C2×D73#10411yescharacteristic
69C2×D73#10411yescharacteristic
70#64408—21no—
71#64408—21no—
72#64408—42no—
73#64408#10211yescharacteristic
74#64408#10311yescharacteristic
75#64408#10611yescharacteristic
76#64408#10711yescharacteristic
77C4×C73—41no—
78C4×C73C4×C811yescharacteristic
79C4×C73C4⋊C811yescharacteristic
80Dic73—41no—
81Dic73#9711yescharacteristic
82Dic73C4⋊C811yescharacteristic
83C2×C73D4⋊C811yescharacteristic
84C2×C73Q8⋊C811yescharacteristic
85C2×C73#33611yescharacteristic
86D73D4⋊C811yescharacteristic
87D73Q8⋊C811yescharacteristic
88D73#33911yescharacteristic
89D73#34011yescharacteristic
90#1279—731nomaximal, Sylow
91C73#127911yescharacteristic, complemented, Sylow
92C2×C4⋊C8—731no—
93C2×C4×C8—731no—
94C4×C4⋊C4—731no—
95C22×C8—1461no—
96C22×C8—1461no—
97C2×C4⋊C4—731no—
98C2×C4⋊C4—731no—
99C2×C42—731no—
100C2×C42—1461no—
101C4⋊C8—732no—
102C4⋊C8—1461no—
103C4×C8—732no—
104C4×C8—1461no—
105#95—1461no—
106C22×C4—731no—
107C22×C4—731no—
108C22×C4—731no—
109C22×C4—1461no—
110C22×C4—1461no—
111C2×C8—2921no—
112C2×C8—2921no—
113C2×C8—1462no—
114C2×C8—1462no—
115C2×C8—1462no—
116C2×C8—1462no—
117C4⋊C4—732no—
118C4⋊C4—731no—
119C4⋊C4—1461no—
120C4⋊C4—1461no—
121C4⋊C4#1059684211yescharacteristic, complemented
122C42—2921no—
123C42—2921no—
124C42—731no—
125C42—731no—
126C42—731no—
127C42—731no—
128C23—731no—
129C2×C4—21no—
130C2×C4—2921no—
131C2×C4—2921no—
132C2×C4—2921no—
133C2×C4—2921no—
134C2×C4—731no—
135C2×C4—731no—
136C2×C4—731no—
137C2×C4—731no—
138C2×C4—731no—
139C2×C4—731no—
140C2×C4—731no—
141C2×C4—731no—
142C2×C4—731no—
143C2×C4—731no—
144C2×C4—731no—
145C2×C4—731no—
146C2×C4—731no—
147C2×C4—1462no—
148C2×C4—1461no—
149C2×C4—1461no—
150C2×C4—1461no—
151C2×C4C2×#1059684211yescharacteristic
152C8—2922no—
153C8—1464no—
154C22—731no—
155C22—731no—
156C22—731no—
157C22—731no—
158C22—731no—
159C22—731no—
160C22C22⋊#1059684211yescharacteristic
161C4—41no—
162C4—2922no—
163C4—2921no—
164C4—731no—
165C4—731no—
166C4—731no—
167C4—731no—
168C4—731no—
169C4—731no—
170C4—1461no—
171C4—1461no—
172C4C4×#1059684211yescharacteristic
173C4C4⋊#1059684211yescharacteristic
174C2—731no—
175C2—731no—
176C2—731no—
177C2—731no—
178C2D4⋊#1059684211yescharacteristic
179C2Q8⋊#1059684211yescharacteristic
180C2(C2×#10596842)⋊C411yescharacteristic
subgroupG/H
centerC22C22⋊#10596842
commutatorC4×C73C4×C8
FrattiniC2×C4C2×#10596842
FittingC4⋊C4×C73C8
socleC22×C73C22⋊C8
hypercenterC4⋊C4#10596842
hypocenterC73#1279
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
7. C4⋊#10596842C4semidirect
9. C4×#10596842C4semidirect
25. C4⋊#64408C8semidirect
34. C4⋊Dic73C8semidirect
36. C4⋊C4×C73C8semidirect
91. C73#1279semidirect
121. C4⋊C4#10596842semidirect