Finite Group Databasebeta

← #22626043

Subgroups — #22626043

Order 9344.

256 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 88 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×#14556659C212yesmaximal
2#17989533C211yesmaximal, characteristic
3C4×C4⋊#64408C211yesmaximal, characteristic
4#17989461C212yesmaximal
5C4⋊C8×D73C211yesmaximal, characteristic
6C2×C4⋊#64408—21no—
7C2×C4⋊#64408—21no—
8C2×C4⋊#64408C2212yes—
9C2×C4⋊#64408C2211yescharacteristic
10C2×C4⋊#64408C2211yescharacteristic
11C2×C4×#64408—21no—
12#14556659—24no—
13(C2×#64408)⋊C4—21no—
14C2×C8×D73C2212yes—
15C42×D73C2211yescharacteristic
16C4⋊#10596831C411yescharacteristic, complemented
17#14556520C412yescomplemented
18C4⋊C8×C73C411yescharacteristic, complemented
19C22×#64408—21no—
20C22×#64408—21no—
21C22×#64408—22no—
22C4⋊#64408—22no—
23C4⋊#64408—21no—
24C4⋊#64408—21no—
25C4⋊#64408—22no—
26C4⋊#64408—42no—
27C4⋊#64408—42no—
28C4⋊#64408D412yes—
29C4⋊#64408Q812yes—
30C4×#64408—42no—
31C2×C4×D73D411yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×C4×D73C2311yescharacteristic
34C2×#10596831C2×C412yes—
35C8×D73—22no—
36C8×D73—22no—
37C4×Dic73C2×C411yescharacteristic
38C4×Dic73Q811yescharacteristic
39C4×Dic73Q811yescharacteristic
40C2×C8×C73C2×C412yes—
41C42×C73C2×C411yescharacteristic
42C22×D73C2×D411yescharacteristic
43C2×#64408—22no—
44C2×#64408—22no—
45C2×#64408—41no—
46C2×#64408—41no—
47C2×#64408—41no—
48C2×#64408—41no—
49C2×#64408—42no—
50C2×#64408—42no—
51C2×#64408—42no—
52C2×C4×C73C4⋊C411yescharacteristic
53C2×C4×C73C4⋊C411yescharacteristic
54C2×C4×C73C22×C411yescharacteristic
55C2×Dic73C4⋊C411yescharacteristic
56C2×Dic73C4⋊C411yescharacteristic
57C2×Dic73C2×Q811yescharacteristic
58C4×D73—21no—
59C4×D73—21no—
60C4×D73SD1612yes—
61C4×D73SD1612yes—
62C4×D73C2×D411yescharacteristic
63C4×D73C2×Q811yescharacteristic
64C4×D73#4111yescharacteristic
65C4×D73#4111yescharacteristic
66C8×C73—22no—
67#10596831—22no—
68C22×C73C2×C4⋊C411yescharacteristic
69C2×D73#12111yescharacteristic
70C2×D73C22⋊Q811yescharacteristic
71C2×D73C2×SD1611yescharacteristic
72C2×D73C2×SD1611yescharacteristic
73C2×D73AGL(1,ℤ/8)11yescharacteristic
74C2×D73#13711yescharacteristic
75#64408—42no—
76#64408—42no—
77#64408—82no—
78C4×C73—21no—
79C4×C73#10612yescomplemented
80C4×C73C4×D411yescharacteristic
81C4×C73C4×Q811yescharacteristic
82Dic73—21no—
83Dic73#10612yescomplemented
84Dic73#12511yescharacteristic
85Dic73C4⋊Q811yescharacteristic
86C2×C73#38911yescharacteristic
87C2×C73C2×#10611yescharacteristic
88C2×C73#42811yescharacteristic
89D73#46011yescharacteristic
90D73#46111yescharacteristic
91D73#47511yescharacteristic
92D73#47611yescharacteristic
93#1948—731nomaximal, Sylow
94C73#194811yescharacteristic, complemented, Sylow
95C2×#106—732no—
96C2×C4⋊C8—731no—
97#384—731no—
98C4×C4⋊C4—731no—
99#340—732no—
100C22×C8—732no—
101C2×C4⋊C4—731no—
102C2×C4⋊C4—731no—
103C2×C4⋊C4—732no—
104C2×C4⋊C4—1461no—
105C2×C4⋊C4—1461no—
106C2×C42—731no—
107C2×C42—1461no—
108#106—1464no—
109C4⋊C8—732no—
110C4⋊C8—731no—
111C4⋊C8#6440811yescharacteristic, complemented
112#95—1461no—
113C22×C4—731no—
114C22×C4—731no—
115C22×C4—731no—
116C22×C4—1462no—
117C22×C4—1461no—
118C22×C4—1461no—
119C2×C8—732no—
120C2×C8—1462no—
121C2×C8—1462no—
122C2×C8C2×#6440812yes—
123C4⋊C4—2922no—
124C4⋊C4—2922no—
125C4⋊C4—732no—
126C4⋊C4—732no—
127C4⋊C4—1462no—
128C4⋊C4—1462no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C42—2922no—
132C42—731no—
133C42—731no—
134C42—731no—
135C42C2×#6440811yescharacteristic
136C23—731no—
137C2×C4—2921no—
138C2×C4—2921no—
139C2×C4—2921no—
140C2×C4—2921no—
141C2×C4—2922no—
142C2×C4—2922no—
143C2×C4—2922no—
144C2×C4—731no—
145C2×C4—731no—
146C2×C4—731no—
147C2×C4—731no—
148C2×C4—732no—
149C2×C4—732no—
150C2×C4—731no—
151C2×C4—731no—
152C2×C4—731no—
153C2×C4—1461no—
154C2×C4—1461no—
155C2×C4—1462no—
156C2×C4—1462no—
157C2×C4C4⋊#6440811yescharacteristic
158C2×C4C4⋊#6440811yescharacteristic
159C2×C4C22×#6440811yescharacteristic
160C8—22no—
161C8—1462no—
162C22—731no—
163C22—731no—
164C22—731no—
165C22—731no—
166C22—731no—
167C22—731no—
168C22C2×C4⋊#6440811yescharacteristic
169C4—21no—
170C4—2922no—
171C4—2922no—
172C4—5842no—
173C4—731no—
174C4—731no—
175C4—732no—
176C4—1461no—
177C4#1455665912yescomplemented
178C4D4×#6440811yescharacteristic
179C4Q8×#6440811yescharacteristic
180C2—731no—
181C2—731no—
182C2—731no—
183C2—731no—
184C2#1798953811yescharacteristic
185C2C2×#1455665911yescharacteristic
186C2#1798959811yescharacteristic
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4⋊C8×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC4⋊C8#64408
hypocenterC73#1948
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
16. C4⋊#10596831C4semidirect
17. #14556520C4semidirect
18. C4⋊C8×C73C4semidirect
79. C4×C73#106semidirect
83. Dic73#106semidirect
94. C73#1948semidirect
111. C4⋊C8#64408semidirect
177. C4#14556659semidirect