Finite Group Databasebeta

← #22621052

Subgroups — #22621052

Order 9344.

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

normal subgroups only

This group has 404 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#17988990C212yesmaximal, complemented
3#17988935C212yesmaximal, complemented
4#17988900C214yesmaximal, complemented
5#17988864C214yesmaximal, complemented
6#17988640C211yesmaximal, characteristic, complemented
7C2×C4⋊Q8×C73C211yesmaximal, characteristic, complemented
8C2×#11924028—21no—
9#14556591C2211yescharacteristic
10#14556588C2211yescharacteristic
11#14556579—21no—
12#14556565—21no—
13#14556565C2212yes—
14C4×D292—21no—
15C4×D292C2212yes—
16#14556524C2218yes—
17C4⋊#10596831C2212yes—
18#14556511C2218yes—
19C22⋊#10596831C2212yes—
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—44no—
30C2×Dic146—21no—
31C2×D292—21no—
32C2×D292—21no—
33C2×D292C2312yes—
34C2×C22⋊D73—22no—
35C2×C4×D73—22no—
36C2×#10596831C2314yes—
37C4⋊Dic73—21no—
38C4⋊Dic73C2312yes—
39#11924005—22no—
40#11924005—22no—
41C2×Q8×C73—22no—
42C2×Q8×C73—22no—
43C2×Q8×C73—44no—
44C22×C4×C73—22no—
45C22×C4×C73D411yescharacteristic
46C22×C4×C73D411yescharacteristic
47C22×C4×C73C2311yescharacteristic
48C4⋊C4×C73—22no—
49C4⋊C4×C73—22no—
50C4⋊C4×C73—22no—
51C4⋊C4×C73C2314yes—
52C42×C73D411yescharacteristic
53C42×C73D411yescharacteristic
54C42×C73C2311yescharacteristic
55C42×C73C2311yescharacteristic
56C23×C73C2×D411yescharacteristic
57C22×D73—22no—
58Q8×C73—44no—
59Q8×C73—44no—
60C2×C4×C73—22no—
61C2×C4×C73—22no—
62C2×C4×C73—24no—
63C2×C4×C73—44no—
64C2×C4×C73D814yes—
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2411yescharacteristic
71C22⋊D73—44no—
72C2×Dic73—22no—
73D292—24no—
74D292—42no—
75D292—42no—
76C4×D73—44no—
77Dic146—42no—
78#10596831—24no—
79C22×C73—21no—
80C22×C73—21no—
81C22×C73C2×D812yes—
82C22×C73C22×D411yescharacteristic
83C2×D73—42no—
84C2×D73—42no—
85C2×D73—42no—
86C4×C73—21no—
87C4×C73—21no—
88C4×C73—44no—
89C4×C73C2×D812yes—
90C4×C73C2×D812yes—
91C4×C73#13712yes—
92C4×C732−1+412yes—
93Dic73—42no—
94C2×C73—22no—
95C2×C73#53611yescharacteristic
96C2×C73C22×D811yescharacteristic
97C2×C73C2×#13711yescharacteristic
98D73—82no—
99#3226—731nomaximal, Sylow
100C73#322611yescharacteristic, complemented, Sylow
101#532—731no—
102C2×C4⋊Q8D7311yescharacteristic, complemented
103#500—732no—
104#486—732no—
105#480—734no—
106#474—734no—
107#431—731no—
108C2×#41—1461no—
109C22×Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8—731no—
113C4⋊Q8C2×D7312yes—
114C4⋊Q8C2×D7312yes—
115#127—731no—
116#124—1461no—
117#121—732no—
118#121—1461no—
119C4×D4—732no—
120C4×D4—1461no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D7312yes—
123C2×C42C2×D7311yescharacteristic
124#107—738no—
125C4⋊C8—732no—
126#102—738no—
127C22⋊C8—732no—
128C4×C8—732no—
129#41—2924no—
130C2×Q8—22no—
131C2×Q8—22no—
132C2×Q8—44no—
133C2×Q8—1461no—
134C2×D4—732no—
135C2×D4—1462no—
136C2×D4—1461no—
137C2×D4—1461no—
138C22×C4—22no—
139C22×C4—1462no—
140C22×C4C22⋊D7311yescharacteristic
141C22×C4C22⋊D7311yescharacteristic
142C22×C4C22×D7311yescharacteristic
143C2×C8—734no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C4⋊C4—732no—
148C4⋊C4—1461no—
149C4⋊C4C22×D7314yes—
150C22⋊C4—1462no—
151C22⋊C4—1462no—
152C42C22⋊D7311yescharacteristic
153C42C22⋊D7311yescharacteristic
154C42C22×D7311yescharacteristic
155C42C22×D7311yescharacteristic
156C23—1462no—
157C23C2×C22⋊D7311yescharacteristic
158Q8—44no—
159Q8—44no—
160Q8—2922no—
161D4—2924no—
162D4—2922no—
163D4—2922no—
164D4—1464no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—44no—
169C2×C4—2924no—
170C2×C4—1462no—
171C2×C4#1192401314yes—
172C2×C4C2×C22⋊D7311yescharacteristic
173C2×C4C2×C22⋊D7311yescharacteristic
174C2×C4C2×C22⋊D7311yescharacteristic
175C2×C4C2×C22⋊D7311yescharacteristic
176C2×C4C2×C22⋊D7311yescharacteristic
177C2×C4C23×D7311yescharacteristic
178C8—1464no—
179C22—21no—
180C22—21no—
181C22—2922no—
182C22—2922no—
183C22—2922no—
184C22C2×#1192401312yes—
185C22C22×C22⋊D7311yescharacteristic
186C4—21no—
187C4—21no—
188C4—44no—
189C4—2922no—
190C4C2×#1192401312yes—
191C4C2×#1192401312yes—
192C4#1455662212yes—
193C4#1455663912yes—
194C2—22no—
195C2—5842no—
196C2#1798916111yescharacteristic
197C2C22×#1192401311yescharacteristic
198C2C2×#1455662211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×C4⋊Q8×C73C2
socleC22×C73C22×D4
hypercenterC2×C4⋊Q8D73
hypocenterC73#3226
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. #17988990C2semidirect
3. #17988935C2semidirect
4. #17988900C2semidirect
5. #17988864C2semidirect
6. #17988640C2semidirect
7. C2×C4⋊Q8×C73C2semidirect
100. C73#3226semidirect
102. C2×C4⋊Q8D73semidirect