Finite Group Databasebeta

← #22619444

Subgroups — #22619444

Order 9344.

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

normal subgroups only

This group has 494 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
1C2×#14556619C211yesmaximal, characteristic
2C22×#11924017C211yesmaximal, characteristic, complemented
3#17989163C211yesmaximal, characteristic, complemented
4#17989061C211yesmaximal, characteristic, complemented
5#17988803C214yesmaximal, complemented
6#17988793C214yesmaximal, complemented
7#17988597C211yesmaximal, characteristic, complemented
8#17988584C211yesmaximal, characteristic, complemented
9#424×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C22×Dic146C2211yescharacteristic
12C22×D292C2211yescharacteristic
13#14556619—24no—
14C2×#11924017—24no—
15C2×#11924017C2212yes—
16C2×#11924017C2214yes—
17C2×D584C2212yes—
18#14556591C2212yescomplemented
19#14556579C2212yescomplemented
20#14556575—22no—
21#14556571—22no—
22C4×D292C2214yes—
23#14556553—22no—
24#14556550C2211yescharacteristic
25C22⋊C4×D73—22no—
26#14556516C2212yescomplemented
27#14556516C2214yescomplemented
28#14556513C2212yescomplemented
29C2×M16×C73C2211yescharacteristic
30C22×C8×C73C2211yescharacteristic
31#117×C73C2211yescharacteristic
32C4⋊C8×C73C2214yescomplemented
33C23×D73—21no—
34#11924028—22no—
35#11924028—22no—
36C2×Dic146—22no—
37C2×Dic146—22no—
38C2×Dic146—21no—
39C2×Dic146C2312yes—
40C2×Dic146C2311yescharacteristic
41C2×D292—21no—
42C2×D292—22no—
43C2×D292D414yes—
44C2×D292C2311yescharacteristic
45C2×D292C2312yes—
46C2×C22⋊D73—21no—
47C22×Dic73—21no—
48C2×C4×D73—21no—
49C2×C4×D73—24no—
50#11924017—28no—
51#11924017—24no—
52D584—24no—
53C4⋊Dic73—24no—
54C4⋊Dic73C2312yes—
55C22⋊Dic73—21no—
56#11924005—24no—
57#11924005—24no—
58C4×Dic73—21no—
59C22×C4×C73C2311yescharacteristic
60M16×C73—22no—
61C2×C8×C73—22no—
62C2×C8×C73C2312yes—
63C2×C8×C73C2312yes—
64C4⋊C4×C73D412yes—
65C22⋊C4×C73D412yes—
66C42×C73C2312yes—
67C23×C73C2×D411yescharacteristic
68C22×D73—22no—
69C22×D73—24no—
70C22×D73—21no—
71C22×D73—82no—
72C2×C4×C73C2×D412yes—
73C2×C4×C73C2×D414yes—
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73#4112yes—
76C2×C4×C73C2411yescharacteristic
77C22⋊D73—42no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—21no—
81C2×Dic73—42no—
82D292—24no—
83D292—21no—
84D292—22no—
85D292—21no—
86D292C2×D414yes—
87C4×D73—42no—
88C4×D73—84no—
89Dic146—22no—
90Dic146—21no—
91Dic146—22no—
92Dic146—21no—
93Dic146—42no—
94C8×C73—22no—
95C8×C73—22no—
96C22×C73—22no—
97C22×C73#12112yes—
98C22×C73C22×D411yescharacteristic
99C2×D73—24no—
100C2×D73—44no—
101C2×D73—41no—
102C2×D73—42no—
103C2×D73—84no—
104C4×C73—24no—
105C4×C73#12112yes—
106C4×C73C22×D411yescharacteristic
107C4×C73C2×#4111yescharacteristic
108Dic73—42no—
109Dic73—41no—
110Dic73—42no—
111C2×C73—22no—
112C2×C73C2×#12111yescharacteristic
113C2×C73#57712yes—
114D73—44no—
115D73—81no—
116#3042—731nomaximal, Sylow
117C73#304211yescharacteristic, complemented, Sylow
118C2×AGL(1,ℤ/8)—731no—
119C22×SD16—731no—
120#536—731no—
121#518—731no—
122#463—734no—
123#461—734no—
124#424D7311yescharacteristic, complemented
125#419—731no—
126#416—731no—
127C2×#41—731no—
128C22×Q8—731no—
129C22×D4—731no—
130AGL(1,ℤ/8)—1464no—
131C2×SD16—734no—
132C2×SD16—732no—
133C2×SD16—1464no—
134C2×D8—732no—
135C2×M16C2×D7311yescharacteristic
136C22×C8C2×D7311yescharacteristic
137C4⋊Q8—732no—
138#124—732no—
139#123—1462no—
140C22⋊Q8—1462no—
141C4×D4—734no—
142C4×D4—1462no—
143#117—731no—
144#117C2×D7311yescharacteristic
145C2×C22⋊C4—1462no—
146C4⋊C8C2×D7314yescomplemented
147#103—732no—
148#103—734no—
149#102—732no—
150C24—1461no—
151#41—1462no—
152#41—1462no—
153C2×Q8—732no—
154C2×Q8—731no—
155C2×Q8—1462no—
156C2×Q8—1462no—
157C2×Q8—1461no—
158C2×D4—734no—
159C2×D4—732no—
160C2×D4—731no—
161C2×D4—1461no—
162C2×D4—1461no—
163C2×D4—1462no—
164C22×C4—1461no—
165C22×C4—1461no—
166C22×C4—1464no—
167C22×C4C22×D7311yescharacteristic
168SD16—1468no—
169SD16—1464no—
170D8—1464no—
171M16—22no—
172C2×C8—22no—
173C2×C8C22×D7312yes—
174C2×C8C22×D7312yes—
175C4⋊C4—732no—
176C4⋊C4—1464no—
177C4⋊C4D29212yes—
178C22⋊C4—1461no—
179C22⋊C4—1464no—
180C22⋊C4—1464no—
181C22⋊C4D29212yes—
182C42—1461no—
183C42C22×D7312yes—
184C23—5842no—
185C23—1461no—
186C23—1462no—
187C23—1464no—
188C23C2×D29211yescharacteristic
189Q8—2922no—
190Q8—1462no—
191Q8—1461no—
192Q8—1462no—
193Q8—1461no—
194D4—2922no—
195D4—734no—
196D4—1464no—
197D4—1461no—
198D4—1461no—
199D4—1462no—
200C2×C4—2922no—
201C2×C4—2922no—
202C2×C4—5844no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4—1461no—
206C2×C4D4×D7312yes—
207C2×C4C2×D29214yes—
208C2×C4C2×D29211yescharacteristic
209C2×C4#1192402912yes—
210C2×C4C23×D7311yescharacteristic
211C8—22no—
212C8—22no—
213C22—22no—
214C22—2924no—
215C22—2922no—
216C22—2921no—
217C22—5844no—
218C22—1464no—
219C22#1455656612yes—
220C22C22×D29211yescharacteristic
221C4—24no—
222C4—2922no—
223C4—2921no—
224C4—2922no—
225C4#1455656612yes—
226C4C2×D4×D7311yescharacteristic
227C4C2×#1192402911yescharacteristic
228C2—22no—
229C2—2924no—
230C2—5841no—
231C2C2×#1455656611yescharacteristic
232C2#1798939912yes—
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#424×C73C2
socleC22×C73C22×D4
hypercenter#424D73
hypocenterC73#3042
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×#11924017C2semidirect
3. #17989163C2semidirect
4. #17989061C2semidirect
5. #17988803C2semidirect
6. #17988793C2semidirect
7. #17988597C2semidirect
8. #17988584C2semidirect
9. #424×C73C2semidirect
18. #14556591C22semidirect
19. #14556579C22semidirect
26. #14556516C22semidirect
27. #14556516C22semidirect
28. #14556513C22semidirect
32. C4⋊C8×C73C22semidirect
117. C73#3042semidirect
124. #424D73semidirect
146. C4⋊C8C2×D73semidirect