Finite Group Databasebeta

← #22625837

Subgroups — #22625837

Order 9344.

306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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#17989558C211yesmaximal, characteristic
2C4×C22⋊#64408C211yesmaximal, characteristic
3#17989457C214yesmaximal, complemented
4C2×#14556549C211yesmaximal, characteristic
5C2×#11924038C2212yes—
6C2×C22⋊#64408—21no—
7C2×C4×#64408C2212yes—
8#14556648—21no—
9C22⋊#10596833—21no—
10(C2×#64408)⋊C4—21no—
11C22×C4×D73C2211yescharacteristic
12#14556549—21no—
13#14556549—21no—
14#14556549C412yescomplemented
15#14556549C2212yes—
16C2×C4⋊Dic73C411yescharacteristic, complemented
17C2×#11924005—21no—
18C2×C4×Dic73—21no—
19C2×C4⋊C4×C73C411yescharacteristic, complemented
20C22×#64408—22no—
21#11924038—24no—
22C2×#10596833—22no—
23C22⋊#64408—24no—
24C4×#64408—24no—
25C23×D73D411yescharacteristic
26C22×Dic73—21no—
27C22×Dic73D411yescharacteristic
28C2×C4×D73—24no—
29C2×C4×D73C2×C411yescharacteristic
30C2×C4×D73D411yescharacteristic
31C2×C4×D73D411yescharacteristic
32C2×C4×D73C2311yescharacteristic
33C4⋊Dic73—21no—
34C4⋊Dic73C2×C412yes—
35#11924005—22no—
36#11924005—22no—
37C4×Dic73—22no—
38C4×Dic73—22no—
39C22×C4×C73—21no—
40C22×C4×C73C2×C411yescharacteristic
41C4⋊C4×C73—21no—
42C4⋊C4×C73C2×C412yes—
43C23×C73C22⋊C411yescharacteristic
44C22×D73—22no—
45C22×D73—22no—
46C22×D73—41no—
47C22×D73C22⋊C411yescharacteristic
48C22×D73C2×D411yescharacteristic
49C2×#64408—24no—
50C2×#64408—42no—
51C2×#64408—42no—
52C2×C4×C73—22no—
53C2×C4×C73—22no—
54C2×C4×C73—42no—
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22×C411yescharacteristic
57C2×Dic73—22no—
58C2×Dic73—22no—
59C2×Dic73—42no—
60C2×Dic73C22⋊C411yescharacteristic
61C2×Dic73C2×D411yescharacteristic
62C4×D73—22no—
63C4×D73—22no—
64C4×D73—22no—
65C4×D73#4114yes—
66#10596833—42no—
67C22×C73—21no—
68C22×C73—21no—
69C22×C73#10412yes—
70C22×C73C2×C22⋊C411yescharacteristic
71C2×D73—21no—
72C2×D73—21no—
73C2×D73—21no—
74C2×D73—21no—
75C2×D73—21no—
76C2×D73—44no—
77C2×D73#12312yes—
78#64408—44no—
79C4×C73—21no—
80C4×C73—42no—
81C4×C73#11712yes—
82Dic73—21no—
83Dic73—42no—
84Dic73#12312yes—
85C2×C73—22no—
86C2×C73#38111yescharacteristic
87C2×C73C2×#10411yescharacteristic
88C2×C73#42111yescharacteristic
89D73—22no—
90D73—41no—
91#1826—731nomaximal, Sylow
92C73#182611yescharacteristic, complemented, Sylow
93C2×#117—731no—
94#407—731no—
95C4×C22⋊C4—731no—
96#339—734no—
97C23×C4—731no—
98C2×M16—732no—
99#117—732no—
100#117—732no—
101#117—1461no—
102#117—1461no—
103C2×C4⋊C4—731no—
104C2×C4⋊C4#6440811yescharacteristic, complemented
105C2×C22⋊C4—1461no—
106C2×C22⋊C4—1461no—
107C2×C42—732no—
108C2×C42—1461no—
109C22⋊C8—1461no—
110C22⋊C8—1461no—
111#95—1461no—
112C24—731no—
113C22×C4—21no—
114C22×C4—731no—
115C22×C4—731no—
116C22×C4—731no—
117C22×C4—731no—
118C22×C4—731no—
119C22×C4—1464no—
120C22×C4—1462no—
121C22×C4—1461no—
122C22×C4C2×#6440811yescharacteristic
123M16—1464no—
124C2×C8—1462no—
125C4⋊C4—21no—
126C4⋊C4—732no—
127C4⋊C4—1461no—
128C4⋊C4C2×#6440812yes—
129C22⋊C4—1462no—
130C22⋊C4—1462no—
131C22⋊C4—1464no—
132C42—1462no—
133C42—1462no—
134C42—1464no—
135C23—2921no—
136C23—731no—
137C23—731no—
138C23—1462no—
139C23—1462no—
140C23C22⋊#6440811yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—2922no—
145C2×C4—2922no—
146C2×C4—2922no—
147C2×C4—731no—
148C2×C4—734no—
149C2×C4—731no—
150C2×C4—1462no—
151C2×C4—1462no—
152C2×C4—1464no—
153C2×C4—1462no—
154C2×C4—1462no—
155C2×C4—1462no—
156C2×C4C22⋊#6440811yescharacteristic
157C2×C4C22×#6440811yescharacteristic
158C8—2922no—
159C22—21no—
160C22—21no—
161C22—2924no—
162C22—732no—
163C22—1461no—
164C22—1461no—
165C22—1461no—
166C22—1461no—
167C22—1461no—
168C22#1455665512yes—
169C22C2×C22⋊#6440811yescharacteristic
170C4—21no—
171C4—42no—
172C4—2924no—
173C4—2922no—
174C4—732no—
175C4—1461no—
176C4#1455667012yes—
177C2—22no—
178C2—2921no—
179C2—1462no—
180C2#1798953011yescharacteristic
181C2C2×#1455665511yescharacteristic
182C2#1798958611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1826
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #17989457C2semidirect
14. #14556549C4semidirect
16. C2×C4⋊Dic73C4semidirect
19. C2×C4⋊C4×C73C4semidirect
92. C73#1826semidirect
104. C2×C4⋊C4#64408semidirect