Finite Group Databasebeta

← #21455342

Subgroups — #21455342

Order 7808.

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

normal subgroups only

This group has 490 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
1C22×#11758201C211yesmaximal, characteristic, complemented
2#16840326C211yesmaximal, characteristic
3#16840240C211yesmaximal, characteristic, complemented
4#16839986C214yesmaximal, complemented
5#16839960C214yesmaximal, complemented
6#16839790C211yesmaximal, characteristic, complemented
7#16839768C211yesmaximal, characteristic, complemented
8#16839758C211yesmaximal, characteristic, complemented
9C2×#137×C61C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C2×#11758201—24no—
12C2×#11758201C2214yes—
13C22×#92418C2211yescharacteristic
14#14519773C2212yes—
15#14519766C2212yes—
16#14519751—22no—
17#14519745—22no—
18Q8×Dic61—22no—
19Q8×Dic61C2214yescomplemented
20#14519736—22no—
21#14519736C2211yescharacteristic
22#14519736C2211yescharacteristic
23#14519706C2214yescomplemented
24#14519701C2212yescomplemented
25#14519699C2214yes—
26#14519698C2212yescomplemented
27C2×#41×C61C2211yescharacteristic
28C22×Q8×C61C2211yescharacteristic
29#137×C61—24no—
30C2×Q16×C61C2212yescomplemented
31C2×SD16×C61C2212yescomplemented
32C2×M16×C61C2211yescharacteristic
33C23×D61—21no—
34#41×C61—22no—
35#41×C61—22no—
36C2×Q8×C61—21no—
37C2×Q8×C61—22no—
38C2×Q8×C61D414yescomplemented
39C2×Q8×C61C2311yescharacteristic
40C2×Q8×C61C2312yes—
41C2×D4×C61—21no—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—24no—
47C2×D244—22no—
48C2×D244—22no—
49C2×D244—21no—
50C2×D244C2312yes—
51Q16×C61—24no—
52SD16×C61—24no—
53M16×C61—22no—
54C2×C8×C61C2312yes—
55C22⋊Dic61—21no—
56C22⋊Dic61D412yes—
57#11758201—28no—
58#11758198—24no—
59C4⋊Dic61—24no—
60C4⋊Dic61D412yes—
61C4⋊Dic61C2312yes—
62C4×Dic61—21no—
63C4×Dic61—24no—
64C4×Dic61C2312yes—
65C2×#92418—22no—
66C2×#92418C2312yes—
67C23×C61—21no—
68C23×C61C2×D411yescharacteristic
69C22×D61—22no—
70C22×D61—42no—
71C22×D61—82no—
72Q8×C61—24no—
73Q8×C61—22no—
74Q8×C61—21no—
75Q8×C61—21no—
76Q8×C61C2×D414yes—
77D4×C61—21no—
78D4×C61—21no—
79D4×C61—42no—
80C2×C4×C61—24no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—42no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D412yes—
86C2×C4×C61#4112yes—
87C2×C4×C61C2411yescharacteristic
88C22⋊D61—84no—
89C2×Dic61—22no—
90C2×Dic61C2×D414yes—
91D244—22no—
92D244—22no—
93D244—42no—
94C8×C61—22no—
95#92418—22no—
96C22×C61—22no—
97C22×C61—41no—
98C22×C61—42no—
99C22×C61#12112yes—
100C22×C61C22×D411yescharacteristic
101C2×D61—42no—
102C2×D61—44no—
103C2×D61—84no—
104C4×C61—24no—
105C4×C61—41no—
106C4×C61#12112yes—
107C4×C61C22×D411yescharacteristic
108C4×C61C2×#4111yescharacteristic
109Dic61—24no—
110Dic61—42no—
111#3043—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61—81no—
114C2×C61C2×#12111yescharacteristic
115C2×C61#57712yes—
116D61—82no—
117C2×#137D6111yescharacteristic, complemented
118C22×SD16—611no—
119#535—611no—
120#519—611no—
121#464—614no—
122#460—614no—
123#424—611no—
124#418—611no—
125#416—611no—
126C61#304311yescharacteristic, complemented, Sylow
127C2×#41C2×D6111yescharacteristic
128C22×Q8C2×D6111yescharacteristic
129C22×D4—611no—
130#137—24no—
131C2×Q16C2×D6112yescomplemented
132C2×SD16—614no—
133C2×SD16—1224no—
134C2×SD16C2×D6112yescomplemented
135C2×M16C2×D6111yescharacteristic
136C22×C8—611no—
137#127—612no—
138#124—612no—
139#121—1222no—
140#120—1222no—
141C4×Q8—614no—
142C4×Q8—1222no—
143#117—611no—
144#117—611no—
145#117—1222no—
146C4⋊C8—614no—
147#103—612no—
148#102—612no—
149#102—614no—
150C24—1221no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8C22⋊D6114yescomplemented
156C2×Q8C22×D6111yescharacteristic
157C2×Q8C22×D6112yes—
158C2×D4—21no—
159C2×D4—612no—
160C2×D4—1224no—
161C2×D4—1221no—
162C2×D4—1222no—
163C2×D4—1222no—
164C2×D4C22×D6111yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C22×D6111yescharacteristic
168Q16—24no—
169SD16—24no—
170SD16—1228no—
171M16—22no—
172C2×C8—612no—
173C2×C8—1222no—
174C2×C8C22×D6112yes—
175C4⋊C4—612no—
176C4⋊C4—612no—
177C4⋊C4—1224no—
178C22⋊C4—612no—
179C22⋊C4—1224no—
180C22⋊C4—1221no—
181C42—612no—
182C42—1224no—
183C42—1221no—
184C23—21no—
185C23—1222no—
186C23—4882no—
187C23—2442no—
188C23D4×D6111yescharacteristic
189Q8—22no—
190Q8—24no—
191Q8—21no—
192Q8—21no—
193Q8C2×C22⋊D6114yes—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—1222no—
198D4—1222no—
199D4—4884no—
200D4—2442no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—614no—
206C2×C4—1222no—
207C2×C4D4×D6111yescharacteristic
208C2×C4#1175822412yes—
209C2×C4C2×C22⋊D6112yes—
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—1222no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—4884no—
217C22—2442no—
218C22—2444no—
219C22#1451974912yes—
220C22C2×D4×D6111yescharacteristic
221C4—24no—
222C4—41no—
223C4—1224no—
224C4—2442no—
225C4#1451974912yes—
226C4C22×C22⋊D6111yescharacteristic
227C4C2×#1175822411yescharacteristic
228C2—22no—
229C2—81no—
230C2—4882no—
231C2C2×#1451974911yescharacteristic
232C2#1684057112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3043
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#11758201C2semidirect
3. #16840240C2semidirect
4. #16839986C2semidirect
5. #16839960C2semidirect
6. #16839790C2semidirect
7. #16839768C2semidirect
8. #16839758C2semidirect
9. C2×#137×C61C2semidirect
19. Q8×Dic61C22semidirect
23. #14519706C22semidirect
24. #14519701C22semidirect
26. #14519698C22semidirect
30. C2×Q16×C61C22semidirect
31. C2×SD16×C61C22semidirect
38. C2×Q8×C61D4semidirect
117. C2×#137D61semidirect
126. C61#3043semidirect
131. C2×Q16C2×D61semidirect
134. C2×SD16C2×D61semidirect
155. C2×Q8C22⋊D61semidirect