Finite Group Databasebeta

← #22619513

Subgroups — #22619513

Order 9344.

520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14556613C211yesmaximal, characteristic, complemented
2C22×C8×D73C211yesmaximal, characteristic, complemented
3#17989099C212yesmaximal, complemented
4#17988829C212yesmaximal, complemented
5#17988824C212yesmaximal, complemented
6#17988817C214yesmaximal, complemented
7#17988581C212yesmaximal, complemented
8#427×C73C211yesmaximal, characteristic, complemented
9C2×#11924028C2212yes—
10C22×C4×D73C2211yescharacteristic
11#14556613—24no—
12C2×Dic292C2211yescharacteristic, complemented
13C2×#11924017C2212yescomplemented
14C2×D584C2211yescharacteristic, complemented
15C22×#10596831C2211yescharacteristic
16C2×C8×D73—24no—
17C2×C8×D73C2212yes—
18C2×C8×D73C2212yes—
19#14556575—22no—
20#14556571C2214yes—
21#14556566C2214yes—
22#14556561—22no—
23C4×D292—24no—
24#14556514C2214yescomplemented
25#14556511C2214yescomplemented
26C22×C8×C73C2211yescharacteristic
27#117×C73C2212yes—
28#107×C73C2212yescomplemented
29#106×C73C2212yescomplemented
30C23×D73D411yescharacteristic
31#11924028—24no—
32#11924028—24no—
33C2×Dic146C2312yes—
34C2×D292—24no—
35C2×D292C2312yes—
36C2×C22⋊D73—22no—
37C22×Dic73D411yescharacteristic
38C2×C4×D73—22no—
39C2×C4×D73—22no—
40C2×C4×D73—22no—
41C2×C4×D73D412yes—
42C2×C4×D73C2312yes—
43Dic292—22no—
44#11924017—24no—
45D584—22no—
46C2×#10596831—22no—
47C2×#10596831C2312yes—
48C8×D73—24no—
49C8×D73—24no—
50C4⋊Dic73—24no—
51#11924005—24no—
52#11924005—24no—
53C22×C4×C73C2311yescharacteristic
54C2×C8×C73D414yescomplemented
55C2×C8×C73C2311yescharacteristic
56C2×C8×C73C2311yescharacteristic
57C4⋊C4×C73C2314yes—
58C22⋊C4×C73—22no—
59C42×C73—22no—
60C23×C73C2×D411yescharacteristic
61C22×D73—22no—
62C22×D73—24no—
63C22×D73—22no—
64C22×D73C2×D412yes—
65C2×C4×C73—24no—
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D412yes—
68C2×C4×C73#4112yes—
69C2×C4×C73C2411yescharacteristic
70C22⋊D73—44no—
71C2×Dic73—22no—
72C2×Dic73—22no—
73C2×Dic73C2×D412yes—
74D292—22no—
75D292—22no—
76D292—48no—
77C4×D73—24no—
78C4×D73—22no—
79C4×D73—22no—
80C4×D73—44no—
81Dic146—22no—
82Dic146—22no—
83C8×C73C2×D412yes—
84C8×C73C2×D412yes—
85#10596831—22no—
86C22×C73—22no—
87C22×C73#12112yes—
88C22×C73C22×D411yescharacteristic
89C2×D73—28no—
90C2×D73—22no—
91C2×D73—22no—
92C2×D73—42no—
93C2×D73—44no—
94C2×D73#13514yescomplemented
95C4×C73—44no—
96C4×C73#12112yes—
97C4×C73C22×D411yescharacteristic
98C4×C73C2×#4111yescharacteristic
99Dic73—22no—
100Dic73—42no—
101C2×C73—22no—
102C2×C73C2×#12111yescharacteristic
103C2×C73C2×#13512yes—
104D73—24no—
105D73—82no—
106#3050—731nomaximal, Sylow
107C73#305011yescharacteristic, complemented, Sylow
108C2×#135—731no—
109C23×C8—731no—
110#525—732no—
111#467—732no—
112#466—732no—
113#465—734no—
114#427D7311yescharacteristic, complemented
115#416—732no—
116C2×#41—732no—
117C23×C4—731no—
118#135—1464no—
119C2×Q16—731no—
120C2×SD16—732no—
121C2×D8—731no—
122C22×C8—731no—
123C22×C8—732no—
124C22×C8—732no—
125C22×C8—1464no—
126C22×C8C2×D7311yescharacteristic
127#123—1462no—
128C22⋊Q8—734no—
129#121—734no—
130#120—1462no—
131C4×D4—1464no—
132#117C2×D7312yes—
133#107C2×D7312yescomplemented
134#106C2×D7312yescomplemented
135#103—734no—
136#102—734no—
137C24—731no—
138#41—1464no—
139#41—1464no—
140C2×Q8—732no—
141C2×D4—732no—
142C2×D4—1464no—
143C2×D4—1462no—
144C22×C4—731no—
145C22×C4—732no—
146C22×C4—732no—
147C22×C4—1462no—
148C22×C4—1462no—
149C22×C4—1462no—
150C22×C4C22×D7311yescharacteristic
151Q16—1462no—
152SD16—1464no—
153D8—1462no—
154C2×C8—732no—
155C2×C8—1462no—
156C2×C8—1464no—
157C2×C8—1464no—
158C2×C8D29214yescomplemented
159C2×C8C22×D7311yescharacteristic
160C2×C8C22×D7311yescharacteristic
161C4⋊C4—1464no—
162C4⋊C4C22×D7314yes—
163C22⋊C4—22no—
164C22⋊C4—1464no—
165C22⋊C4—1464no—
166C42—22no—
167C23—732no—
168C23—1464no—
169C23—1462no—
170C23—1462no—
171C23D4×D7311yescharacteristic
172Q8—1462no—
173Q8—1462no—
174D4—2928no—
175D4—2924no—
176D4—1462no—
177D4—1462no—
178C2×C4—24no—
179C2×C4—2924no—
180C2×C4—732no—
181C2×C4—1462no—
182C2×C4—1462no—
183C2×C4—1464no—
184C2×C4—1462no—
185C2×C4—1462no—
186C2×C4D4×D7311yescharacteristic
187C2×C4C2×D29212yes—
188C2×C4#1192402912yes—
189C2×C4C23×D7311yescharacteristic
190C8—1462no—
191C8C2×D29212yes—
192C8C2×D29212yes—
193C22—22no—
194C22—2922no—
195C22—2924no—
196C22—734no—
197C22—1468no—
198C22—1462no—
199C22—1462no—
200C22#1455656612yes—
201C22C2×D4×D7311yescharacteristic
202C4—44no—
203C4—2922no—
204C4—1462no—
205C4#1455656612yes—
206C4C22×D29211yescharacteristic
207C4C2×#1192402911yescharacteristic
208C2—22no—
209C2—5842no—
210C2—1464no—
211C2C2×#1455656611yescharacteristic
212C2#135×D7312yes—
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#427×C73C2
socleC22×C73C22×D4
hypercenter#427D73
hypocenterC73#3050
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. C2×#14556613C2semidirect
2. C22×C8×D73C2semidirect
3. #17989099C2semidirect
4. #17988829C2semidirect
5. #17988824C2semidirect
6. #17988817C2semidirect
7. #17988581C2semidirect
8. #427×C73C2semidirect
12. C2×Dic292C22semidirect
13. C2×#11924017C22semidirect
14. C2×D584C22semidirect
24. #14556514C22semidirect
25. #14556511C22semidirect
28. #107×C73C22semidirect
29. #106×C73C22semidirect
54. C2×C8×C73D4semidirect
94. C2×D73#135semidirect
107. C73#3050semidirect
114. #427D73semidirect
133. #107C2×D73semidirect
134. #106C2×D73semidirect
158. C2×C8D292semidirect