Finite Group Databasebeta

← #22619443

Subgroups — #22619443

Order 9344.

494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14556617C211yesmaximal, characteristic
2C22×#11924016C211yesmaximal, characteristic, complemented
3#17989163C211yesmaximal, characteristic, complemented
4#17988802C214yesmaximal, complemented
5#17988792C214yesmaximal, complemented
6#17988614C211yesmaximal, characteristic, complemented
7#17988595C211yesmaximal, characteristic, complemented
8#17988581C211yesmaximal, characteristic, complemented
9#518×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C22×Dic146C2211yescharacteristic
12#14556617—24no—
13C2×#11924016—24no—
14C2×#11924016C2212yes—
15C2×#11924016C2214yes—
16C2×#11924013C2212yes—
17C2×#11924012C2211yescharacteristic
18C22×#10596831C2211yescharacteristic
19#14556591C2212yescomplemented
20#14556579C2212yescomplemented
21#14556575—22no—
22#14556571—22no—
23C4⋊#10596831C2214yescomplemented
24#14556514C2212yescomplemented
25#14556514C2214yescomplemented
26#14556511C2212yescomplemented
27C22×D4×C73C2211yescharacteristic
28C4×D4×C73—22no—
29C4×D4×C73C2214yes—
30#117×C73C2211yescharacteristic
31#117×C73C2211yescharacteristic
32C2×C22⋊C4×C73—22no—
33#11924028—22no—
34#11924028—22no—
35C2×Dic146—22no—
36C2×Dic146—22no—
37C2×Dic146—21no—
38C2×Dic146C2312yes—
39C2×Dic146C2311yescharacteristic
40C2×D292C2311yescharacteristic
41C2×C22⋊D73—21no—
42C22×Dic73—21no—
43C2×C4×D73—21no—
44#11924016—28no—
45#11924016—24no—
46#11924013—24no—
47#11924012—22no—
48C2×#10596831—22no—
49C2×#10596831C2312yes—
50C2×#10596831C2312yes—
51C4⋊Dic73—24no—
52#11924005—24no—
53C24×C73—21no—
54C2×D4×C73—21no—
55C2×D4×C73—22no—
56C2×D4×C73D414yes—
57C2×D4×C73C2312yes—
58C22×C4×C73—24no—
59C22×C4×C73C2311yescharacteristic
60C4⋊C4×C73D412yes—
61C4⋊C4×C73C2312yes—
62C22⋊C4×C73—21no—
63C22⋊C4×C73—24no—
64C22⋊C4×C73D412yes—
65C42×C73—21no—
66C42×C73C2312yes—
67C23×C73—22no—
68C23×C73—24no—
69C23×C73—82no—
70C23×C73C2×D411yescharacteristic
71C22×D73—21no—
72D4×C73—24no—
73D4×C73—22no—
74D4×C73C2×D414yes—
75C2×C4×C73—22no—
76C2×C4×C73—84no—
77C2×C4×C73C2×D414yes—
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D412yes—
80C2×C4×C73#4112yes—
81C2×C4×C73C2411yescharacteristic
82C22⋊D73—42no—
83C2×Dic73—22no—
84C2×Dic73—21no—
85C2×Dic73—42no—
86D292—21no—
87D292—21no—
88C4×D73—42no—
89Dic146—22no—
90Dic146—21no—
91Dic146—22no—
92Dic146—21no—
93Dic146—42no—
94#10596831—22no—
95#10596831—22no—
96C22×C73—22no—
97C22×C73—24no—
98C22×C73—44no—
99C22×C73—84no—
100C22×C73#12112yes—
101C22×C73C22×D411yescharacteristic
102C2×D73—41no—
103C2×D73—42no—
104C4×C73—24no—
105C4×C73—42no—
106C4×C73#12112yes—
107C4×C73C22×D411yescharacteristic
108C4×C73C2×#4111yescharacteristic
109Dic73—42no—
110Dic73—41no—
111C2×C73—22no—
112C2×C73—44no—
113C2×C73C2×#12111yescharacteristic
114C2×C73#57712yes—
115D73—81no—
116#3042—731nomaximal, Sylow
117C73#304211yescharacteristic, complemented, Sylow
118C2×AGL(1,ℤ/8)—731no—
119C22×SD16—731no—
120#536—731no—
121#518D7311yescharacteristic, complemented
122#463—734no—
123#461—734no—
124#424—731no—
125#419—731no—
126#416—731no—
127C2×#41—731no—
128C22×Q8—731no—
129C22×D4C2×D7311yescharacteristic
130AGL(1,ℤ/8)—1464no—
131C2×SD16—734no—
132C2×SD16—732no—
133C2×SD16—1464no—
134C2×D8—732no—
135C2×M16—731no—
136C22×C8—731no—
137C4⋊Q8—732no—
138#124—732no—
139#123—1462no—
140C22⋊Q8—1462no—
141C4×D4—22no—
142C4×D4C2×D7314yes—
143#117C2×D7311yescharacteristic
144#117C2×D7311yescharacteristic
145C2×C22⋊C4—22no—
146C4⋊C8—734no—
147#103—732no—
148#103—734no—
149#102—732no—
150C24—21no—
151#41—1462no—
152#41—1462no—
153C2×Q8—732no—
154C2×Q8—731no—
155C2×Q8—1462no—
156C2×Q8—1462no—
157C2×Q8—1461no—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—731no—
161C2×D4—1461no—
162C2×D4D29214yes—
163C2×D4C22×D7312yes—
164C22×C4—24no—
165C22×C4—1461no—
166C22×C4—1461no—
167C22×C4C22×D7311yescharacteristic
168SD16—1468no—
169SD16—1464no—
170D8—1464no—
171M16—1462no—
172C2×C8—732no—
173C2×C8—732no—
174C2×C8—1462no—
175C4⋊C4—1464no—
176C4⋊C4C22⋊D7312yes—
177C4⋊C4C22×D7312yes—
178C22⋊C4—21no—
179C22⋊C4—24no—
180C22⋊C4—1464no—
181C22⋊C4C22⋊D7312yes—
182C42—21no—
183C42C22×D7312yes—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—1461no—
188C23C2×C22⋊D7311yescharacteristic
189Q8—2922no—
190Q8—1462no—
191Q8—1461no—
192Q8—1462no—
193Q8—1461no—
194D4—24no—
195D4—22no—
196D4—2922no—
197D4—1461no—
198D4—1461no—
199D4C2×D29214yes—
200C2×C4—22no—
201C2×C4—84no—
202C2×C4—2922no—
203C2×C4—2922no—
204C2×C4—1462no—
205C2×C4—1461no—
206C2×C4C2×C22⋊D7314yes—
207C2×C4C2×C22⋊D7311yescharacteristic
208C2×C4C2×D29212yes—
209C2×C4#1192402812yes—
210C2×C4C23×D7311yescharacteristic
211C8—1462no—
212C8—1462no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—2922no—
218C22—2921no—
219C22#1455656512yes—
220C22C22×C22⋊D7311yescharacteristic
221C4—24no—
222C4—42no—
223C4—2921no—
224C4—2922no—
225C4#1455656512yes—
226C4C22×D29211yescharacteristic
227C4C2×#1192402811yescharacteristic
228C2—22no—
229C2—44no—
230C2—5841no—
231C2C2×#1455656511yescharacteristic
232C2#1798939812yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#518×C73C2
socleC22×C73C22×D4
hypercenter#518D73
hypocenterC73#3042
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C22×#11924016C2semidirect
3. #17989163C2semidirect
4. #17988802C2semidirect
5. #17988792C2semidirect
6. #17988614C2semidirect
7. #17988595C2semidirect
8. #17988581C2semidirect
9. #518×C73C2semidirect
19. #14556591C22semidirect
20. #14556579C22semidirect
23. C4⋊#10596831C22semidirect
24. #14556514C22semidirect
25. #14556514C22semidirect
26. #14556511C22semidirect
117. C73#3042semidirect
121. #518D73semidirect