Finite Group Databasebeta

← #22620327

Subgroups — #22620327

Order 9344.

424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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#17989137C211yesmaximal, characteristic
2#17988949C214yesmaximal, complemented
3#17988939C212yesmaximal, complemented
4#17988935C212yesmaximal, complemented
5#17988586C214yesmaximal, complemented
6C4×#11924012C211yesmaximal, characteristic, complemented
7C2×C4⋊Q8×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2212yes—
9C2×#11924012C2212yes—
10#14556591C2211yescharacteristic
11#14556588C2211yescharacteristic
12#14556579C2212yes—
13#14556565—21no—
14#14556565—21no—
15C4×D292—21no—
16C4×D292—21no—
17#14556514C2218yes—
18#14556511C2218yes—
19#14556502C2212yes—
20C4×#10596831C2212yes—
21C22×Q8×C73—21no—
22C4⋊Q8×C73—21no—
23C4⋊Q8×C73—21no—
24C4⋊Q8×C73C2212yes—
25C4⋊Q8×C73C2212yes—
26C2×C4⋊C4×C73—21no—
27C2×C4⋊C4×C73C2212yes—
28C2×C42×C73C2211yescharacteristic
29#11924028—28no—
30C2×Dic146C2312yes—
31C2×D292—21no—
32C2×D292—21no—
33C2×D292C2312yes—
34C2×C22⋊D73—22no—
35C2×C4×D73—22no—
36#11924012—24no—
37C2×#10596831C2314yes—
38C4⋊Dic73—21no—
39C4⋊Dic73—21no—
40#11924005—22no—
41#11924005—22no—
42C2×Q8×C73—22no—
43C2×Q8×C73—22no—
44C2×Q8×C73—44no—
45C22×C4×C73—22no—
46C22×C4×C73D411yescharacteristic
47C22×C4×C73D411yescharacteristic
48C22×C4×C73C2311yescharacteristic
49C4⋊C4×C73—22no—
50C4⋊C4×C73—22no—
51C4⋊C4×C73—22no—
52C4⋊C4×C73C2314yes—
53C42×C73D411yescharacteristic
54C42×C73D411yescharacteristic
55C42×C73C2311yescharacteristic
56C42×C73C2311yescharacteristic
57C23×C73C2×D411yescharacteristic
58C22×D73—22no—
59Q8×C73—44no—
60Q8×C73—44no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—24no—
64C2×C4×C73—44no—
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73#4114yes—
71C2×C4×C73C2411yescharacteristic
72C22⋊D73—44no—
73C2×Dic73—22no—
74D292—24no—
75D292—42no—
76D292—42no—
77C4×D73—44no—
78Dic146—24no—
79#10596831—24no—
80C22×C73—21no—
81C22×C73—21no—
82C22×C73#12412yes—
83C22×C73C22×D411yescharacteristic
84C2×D73—42no—
85C2×D73—42no—
86C2×D73—42no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C73—44no—
90C4×C73#12412yes—
91C4×C73AGL(1,ℤ/8)12yes—
92C4×C73#13712yes—
93C4×C73C2×#4112yes—
94Dic73—42no—
95C2×C73—22no—
96C2×C73C2×#12411yescharacteristic
97C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
98C2×C73C2×#13711yescharacteristic
99D73—82no—
100#3141—731nomaximal, Sylow
101C73#314111yescharacteristic, complemented, Sylow
102#532—731no—
103C2×C4⋊Q8D7311yescharacteristic, complemented
104#489—734no—
105#487—732no—
106#486—732no—
107#417—734no—
108C4×M16—731no—
109C2×#41—732no—
110C22×Q8—21no—
111C2×M16—732no—
112C4⋊Q8—21no—
113C4⋊Q8—21no—
114C4⋊Q8—731no—
115C4⋊Q8C2×D7312yes—
116C4⋊Q8C2×D7312yes—
117#127—731no—
118#124—732no—
119#121—1461no—
120#121—1461no—
121C4×D4—1461no—
122C4×D4—1461no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4C2×D7312yes—
125C2×C42C2×D7311yescharacteristic
126#103—738no—
127#102—738no—
128#97—732no—
129C4×C8—732no—
130#41—1468no—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—44no—
134C2×Q8—732no—
135C2×D4—732no—
136C2×D4—1462no—
137C2×D4—1461no—
138C2×D4—1461no—
139C22×C4—22no—
140C22×C4—1462no—
141C22×C4C22⋊D7311yescharacteristic
142C22×C4C22⋊D7311yescharacteristic
143C22×C4C22×D7311yescharacteristic
144M16—1464no—
145C2×C8—734no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—22no—
149C4⋊C4—1461no—
150C4⋊C4—1461no—
151C4⋊C4C22×D7314yes—
152C22⋊C4—1462no—
153C22⋊C4—1462no—
154C42C22⋊D7311yescharacteristic
155C42C22⋊D7311yescharacteristic
156C42C22×D7311yescharacteristic
157C42C22×D7311yescharacteristic
158C23—1462no—
159C23C2×C22⋊D7311yescharacteristic
160Q8—44no—
161Q8—44no—
162Q8—1464no—
163D4—2924no—
164D4—2922no—
165D4—2922no—
166D4—1464no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—44no—
171C2×C4—2924no—
172C2×C4—1462no—
173C2×C4C2×C22⋊D7311yescharacteristic
174C2×C4C2×C22⋊D7311yescharacteristic
175C2×C4C2×C22⋊D7311yescharacteristic
176C2×C4C2×C22⋊D7311yescharacteristic
177C2×C4C2×C22⋊D7311yescharacteristic
178C2×C4#1192402914yes—
179C2×C4C23×D7311yescharacteristic
180C8—1464no—
181C22—21no—
182C22—21no—
183C22—2922no—
184C22—2922no—
185C22—2922no—
186C22#1455658012yes—
187C22C22×C22⋊D7311yescharacteristic
188C4—21no—
189C4—21no—
190C4—44no—
191C4—2922no—
192C4#1455658012yes—
193C4#1455661712yes—
194C4#1455662212yes—
195C4C2×#1192402912yes—
196C2—22no—
197C2—5842no—
198C2C2×#1455658011yescharacteristic
199C2C2×#1455661711yescharacteristic
200C2C2×#1455662211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×C4⋊Q8×C73C2
socleC22×C73C22×D4
hypercenterC2×C4⋊Q8D73
hypocenterC73#3141
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17988949C2semidirect
3. #17988939C2semidirect
4. #17988935C2semidirect
5. #17988586C2semidirect
6. C4×#11924012C2semidirect
7. C2×C4⋊Q8×C73C2semidirect
101. C73#3141semidirect
103. C2×C4⋊Q8D73semidirect