Finite Group Databasebeta

← #22619451

Subgroups — #22619451

Order 9344.

490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556624C211yesmaximal, characteristic, complemented
2C22×#11924016C211yesmaximal, characteristic, complemented
3#17989154C211yesmaximal, characteristic
4#17989064C211yesmaximal, characteristic, complemented
5#17988808C214yesmaximal, complemented
6#17988786C214yesmaximal, complemented
7#17988615C211yesmaximal, characteristic, complemented
8#17988581C211yesmaximal, characteristic, complemented
9#418×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C22×Dic146C2211yescharacteristic
12#14556624—24no—
13C2×Dic292C2212yescomplemented
14C2×#11924017C2212yescomplemented
15C2×#11924016—24no—
16C2×#11924016C2214yes—
17C22×#10596831C2211yescharacteristic
18#14556587C2212yes—
19#14556578C2212yes—
20#14556562—22no—
21#14556560—22no—
22C4×Dic146—22no—
23#14556556C2214yescomplemented
24#14556550C2211yescharacteristic
25#14556547—22no—
26#14556520C2214yescomplemented
27#14556514C2212yescomplemented
28#14556511C2212yescomplemented
29C22×D4×C73C2211yescharacteristic
30C2×M16×C73C2211yescharacteristic
31#117×C73C2211yescharacteristic
32#102×C73C2214yes—
33#11924028—22no—
34#11924028—22no—
35C2×Dic146—21no—
36C2×Dic146—22no—
37C2×Dic146D414yescomplemented
38C2×Dic146C2311yescharacteristic
39C2×Dic146C2312yes—
40C2×D292C2311yescharacteristic
41C2×C22⋊D73—21no—
42C2×C22⋊D73—24no—
43C22×Dic73—21no—
44C2×C4×D73—21no—
45Dic292—24no—
46#11924017—24no—
47#11924016—28no—
48C2×#10596831—22no—
49C2×#10596831C2312yes—
50C4⋊Dic73D412yes—
51#11924007—24no—
52C22⋊Dic73—24no—
53C22⋊Dic73D412yes—
54C4×Dic73—24no—
55C4×Dic73C2312yes—
56C24×C73—21no—
57C2×D4×C73—22no—
58C2×D4×C73—21no—
59C2×D4×C73—22no—
60C2×D4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62M16×C73—22no—
63C2×C8×C73C2312yes—
64C4⋊C4×C73C2312yes—
65C22⋊C4×C73—21no—
66C42×C73—21no—
67C23×C73—22no—
68C23×C73—42no—
69C23×C73—82no—
70C23×C73C2×D411yescharacteristic
71C22×D73—21no—
72D4×C73—22no—
73D4×C73—22no—
74D4×C73—42no—
75C2×C4×C73—22no—
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D412yes—
78C2×C4×C73#4112yes—
79C2×C4×C73C2411yescharacteristic
80C22⋊D73—42no—
81C22⋊D73—84no—
82C2×Dic73—24no—
83C2×Dic73—22no—
84C2×Dic73—21no—
85C2×Dic73C2×D414yes—
86D292—21no—
87D292—21no—
88C4×D73—42no—
89Dic146—24no—
90Dic146—22no—
91Dic146—21no—
92Dic146—21no—
93Dic146C2×D414yes—
94C8×C73—22no—
95#10596831—22no—
96C22×C73—22no—
97C22×C73—42no—
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—24no—
110Dic73—41no—
111C2×C73—22no—
112C2×C73—82no—
113C2×C73C2×#12111yescharacteristic
114C2×C73#57712yes—
115D73—81no—
116#3043—731nomaximal, Sylow
117C73#304311yescharacteristic, complemented, Sylow
118C2×#137—731no—
119C22×SD16—731no—
120#535—731no—
121#519—731no—
122#464—734no—
123#460—734no—
124#424—731no—
125#418D7311yescharacteristic, complemented
126#416—731no—
127C2×#41—731no—
128C22×Q8—731no—
129C22×D4C2×D7311yescharacteristic
130#137—1464no—
131C2×Q16—732no—
132C2×SD16—734no—
133C2×SD16—732no—
134C2×SD16—1464no—
135C2×M16C2×D7311yescharacteristic
136C22×C8—731no—
137#127—732no—
138#124—732no—
139#121—1462no—
140#120—1462no—
141C4×Q8—734no—
142C4×Q8—1462no—
143#117—731no—
144#117—1462no—
145#117C2×D7311yescharacteristic
146C4⋊C8—734no—
147#103—732no—
148#102—732no—
149#102C2×D7314yes—
150C24—21no—
151#41—1462no—
152#41—1462no—
153C2×Q8—734no—
154C2×Q8—732no—
155C2×Q8—731no—
156C2×Q8—1461no—
157C2×Q8—1462no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4—731no—
162C2×D4—1464no—
163C2×D4—1461no—
164C2×D4C22×D7312yes—
165C22×C4—1461no—
166C22×C4—1461no—
167C22×C4C22×D7311yescharacteristic
168Q16—1464no—
169SD16—1464no—
170SD16—1468no—
171M16—22no—
172C2×C8—732no—
173C2×C8—1462no—
174C2×C8C22×D7312yes—
175C4⋊C4—732no—
176C4⋊C4—1464no—
177C4⋊C4C22×D7312yes—
178C22⋊C4—21no—
179C22⋊C4—732no—
180C22⋊C4—1464no—
181C42—21no—
182C42—732no—
183C42—1464no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—1461no—
188C23D4×D7311yescharacteristic
189Q8—734no—
190Q8—1461no—
191Q8—1461no—
192Q8—1464no—
193Q8—1462no—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—2922no—
198D4—5844no—
199D4—1461no—
200D4—1461no—
201C2×C4—22no—
202C2×C4—2922no—
203C2×C4—734no—
204C2×C4—1461no—
205C2×C4—1464no—
206C2×C4—1462no—
207C2×C4D4×D7311yescharacteristic
208C2×C4D4×D7312yes—
209C2×C4#1192402812yes—
210C2×C4C23×D7311yescharacteristic
211C8—22no—
212C8—1462no—
213C22—22no—
214C22—44no—
215C22—42no—
216C22—84no—
217C22—2922no—
218C22—2921no—
219C22#1455656412yes—
220C22C2×D4×D7311yescharacteristic
221C4—42no—
222C4—2921no—
223C4—1464no—
224C4—1464no—
225C4#1455656412yes—
226C4C2×D4×D7311yescharacteristic
227C4C2×#1192402811yescharacteristic
228C2—22no—
229C2—82no—
230C2—5841no—
231C2C2×#1455656411yescharacteristic
232C2#1798939712yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#418×C73C2
socleC22×C73C22×D4
hypercenter#418D73
hypocenterC73#3043
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#14556624C2semidirect
2. C22×#11924016C2semidirect
4. #17989064C2semidirect
5. #17988808C2semidirect
6. #17988786C2semidirect
7. #17988615C2semidirect
8. #17988581C2semidirect
9. #418×C73C2semidirect
13. C2×Dic292C22semidirect
14. C2×#11924017C22semidirect
23. #14556556C22semidirect
26. #14556520C22semidirect
27. #14556514C22semidirect
28. #14556511C22semidirect
37. C2×Dic146D4semidirect
117. C73#3043semidirect
125. #418D73semidirect