Finite Group Databasebeta

← #22619440

Subgroups — #22619440

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×#14556617C211yesmaximal, characteristic
2#17989161C211yesmaximal, characteristic, complemented
3#17989062C211yesmaximal, characteristic, complemented
4#17988804C214yesmaximal, complemented
5#17988790C214yesmaximal, complemented
6#17988613C211yesmaximal, characteristic, complemented
7#17988596C211yesmaximal, characteristic, complemented
8#17988584C211yesmaximal, characteristic, complemented
9C22×SD16×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11#14556617—24no—
12C2×#11924016C2212yes—
13C2×#11924013C2212yes—
14C2×#11924012C2211yescharacteristic
15#14556589C2212yescomplemented
16#14556580C2212yescomplemented
17#14556574—22no—
18#14556567—22no—
19D4×Dic73—22no—
20D4×Dic73C2214yes—
21#14556550C2211yescharacteristic
22#14556550C2211yescharacteristic
23C2×C22⋊Dic73—22no—
24#14556520C2214yescomplemented
25#14556516C2212yescomplemented
26#14556515C2214yescomplemented
27#14556513C2212yescomplemented
28C22×Q8×C73C2211yescharacteristic
29C22×D4×C73C2211yescharacteristic
30C2×SD16×C73—24no—
31C2×SD16×C73C2214yes—
32C22×C8×C73C2211yescharacteristic
33#11924028—22no—
34#11924028—22no—
35C2×Dic146C2311yescharacteristic
36C2×D292C2311yescharacteristic
37C2×C22⋊D73—21no—
38C22×Dic73—24no—
39C2×C4×D73—21no—
40#11924016—24no—
41#11924013—24no—
42#11924012—22no—
43C2×#10596831C2312yes—
44C4⋊Dic73D412yes—
45C4⋊Dic73C2312yes—
46#11924007—24no—
47C22⋊Dic73—21no—
48C22⋊Dic73—24no—
49C22⋊Dic73D412yes—
50#11924005—24no—
51C4×Dic73—21no—
52C4×Dic73C2312yes—
53C24×C73—21no—
54C2×Q8×C73—21no—
55C2×Q8×C73—22no—
56C2×Q8×C73—22no—
57C2×Q8×C73C2312yes—
58C2×D4×C73—21no—
59C2×D4×C73—22no—
60C2×D4×C73D414yes—
61C2×D4×C73C2312yes—
62C22×C4×C73—21no—
63C22×C4×C73C2311yescharacteristic
64SD16×C73—28no—
65C2×C8×C73—22no—
66C2×C8×C73C2312yes—
67C23×C73—22no—
68C23×C73—24no—
69C23×C73—82no—
70C23×C73C2×D411yescharacteristic
71C22×D73—21no—
72Q8×C73—22no—
73Q8×C73—22no—
74Q8×C73—42no—
75D4×C73—24no—
76D4×C73—22no—
77D4×C73C2×D414yes—
78C2×C4×C73—22no—
79C2×C4×C73—42no—
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D412yes—
82C2×C4×C73#4112yes—
83C2×C4×C73C2411yescharacteristic
84C22⋊D73—42no—
85C2×Dic73—22no—
86C2×Dic73—21no—
87C2×Dic73—84no—
88C2×Dic73C2×D414yes—
89D292—21no—
90D292—21no—
91C4×D73—42no—
92Dic146—21no—
93Dic146—21no—
94C8×C73—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—42no—
105C4×C73#12112yes—
106C4×C73C22×D411yescharacteristic
107C4×C73C2×#4111yescharacteristic
108Dic73—24no—
109Dic73—41no—
110Dic73—42no—
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×SD16D7311yescharacteristic, complemented
120#536—731no—
121#518—731no—
122#463—734no—
123#461—734no—
124#424—731no—
125#419—731no—
126#416—731no—
127C2×#41—731no—
128C22×Q8C2×D7311yescharacteristic
129C22×D4C2×D7311yescharacteristic
130AGL(1,ℤ/8)—1464no—
131C2×SD16—24no—
132C2×SD16—732no—
133C2×SD16C2×D7314yes—
134C2×D8—732no—
135C2×M16—731no—
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#117—731no—
145C2×C22⋊C4—1462no—
146C4⋊C8—734no—
147#103—734no—
148#103—732no—
149#102—732no—
150C24—21no—
151#41—1462no—
152#41—1462no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—731no—
157C2×Q8C22×D7312yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—731no—
161C2×D4—1461no—
162C2×D4C22⋊D7314yes—
163C2×D4C22×D7312yes—
164C22×C4—21no—
165C22×C4—1461no—
166C22×C4—1464no—
167C22×C4C22×D7311yescharacteristic
168SD16—28no—
169SD16—1464no—
170D8—1464no—
171M16—1462no—
172C2×C8—22no—
173C2×C8—732no—
174C2×C8C22×D7312yes—
175C4⋊C4—732no—
176C4⋊C4—732no—
177C4⋊C4—1464no—
178C22⋊C4—732no—
179C22⋊C4—1464no—
180C22⋊C4—1464no—
181C22⋊C4—1461no—
182C42—732no—
183C42—1461no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—1461no—
188C23D4×D7311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—1461no—
193Q8—1461no—
194D4—24no—
195D4—22no—
196D4—2922no—
197D4—1461no—
198D4—1461no—
199D4C2×C22⋊D7314yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—2922no—
203C2×C4—5844no—
204C2×C4—734no—
205C2×C4—1462no—
206C2×C4—1461no—
207C2×C4D4×D7311yescharacteristic
208C2×C4C2×C22⋊D7312yes—
209C2×C4#1192402712yes—
210C2×C4C23×D7311yescharacteristic
211C8—22no—
212C8—1462no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—2922no—
218C22—2921no—
219C22#1455656312yes—
220C22C2×D4×D7311yescharacteristic
221C4—42no—
222C4—2922no—
223C4—2921no—
224C4—1464no—
225C4#1455656312yes—
226C4C22×C22⋊D7311yescharacteristic
227C4C2×#1192402711yescharacteristic
228C2—22no—
229C2—44no—
230C2—5841no—
231C2C2×#1455656311yescharacteristic
232C2#1798939312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC22×SD16×C73C2
socleC22×C73C22×D4
hypercenterC22×SD16D73
hypocenterC73#3042
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #17989161C2semidirect
3. #17989062C2semidirect
4. #17988804C2semidirect
5. #17988790C2semidirect
6. #17988613C2semidirect
7. #17988596C2semidirect
8. #17988584C2semidirect
9. C22×SD16×C73C2semidirect
15. #14556589C22semidirect
16. #14556580C22semidirect
24. #14556520C22semidirect
25. #14556516C22semidirect
26. #14556515C22semidirect
27. #14556513C22semidirect
117. C73#3042semidirect
119. C22×SD16D73semidirect