Finite Group Databasebeta

← #21455333

Subgroups — #21455333

Order 7808.

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
1C22×#11758200C211yesmaximal, characteristic, complemented
2#16840333C211yesmaximal, characteristic, complemented
3#16840237C211yesmaximal, characteristic, complemented
4#16839975C214yesmaximal, complemented
5#16839965C214yesmaximal, complemented
6#16839790C211yesmaximal, characteristic, complemented
7#16839772C211yesmaximal, characteristic, complemented
8#16839758C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×#11758200—24no—
12C2×#11758200C2214yes—
13C22×#92418C2211yescharacteristic
14#14519775C2212yescomplemented
15#14519764C2212yescomplemented
16#14519758—22no—
17#14519756—22no—
18D4×Dic61—22no—
19D4×Dic61C2214yes—
20#14519736C2211yescharacteristic
21#14519736C2211yescharacteristic
22C2×C22⋊Dic61—22no—
23#14519706C2214yescomplemented
24#14519702C2214yescomplemented
25#14519701C2212yescomplemented
26#14519698C2212yescomplemented
27C2×#41×C61C2211yescharacteristic
28C22×D4×C61C2211yescharacteristic
29AGL(1,ℤ/8)×C61—24no—
30C2×SD16×C61C2212yes—
31C2×D8×C61C2212yes—
32C2×M16×C61C2211yescharacteristic
33C24×C61—21no—
34#41×C61—22no—
35#41×C61—22no—
36C2×Q8×C61C2311yescharacteristic
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61—22no—
40C2×D4×C61D414yes—
41C2×D4×C61C2311yescharacteristic
42C2×D4×C61C2312yes—
43C22×C4×C61—21no—
44C22×C4×C61C2311yescharacteristic
45C22×Dic61—21no—
46C22×Dic61—24no—
47C2×Dic122—22no—
48C2×Dic122—22no—
49C2×Dic122—21no—
50C2×Dic122C2312yes—
51SD16×C61—24no—
52D8×C61—24no—
53M16×C61—22no—
54C2×C8×C61C2312yes—
55C22⋊Dic61—21no—
56C22⋊Dic61—24no—
57C22⋊Dic61—24no—
58C22⋊Dic61D412yes—
59#11758200—28no—
60C4⋊Dic61D412yes—
61C4⋊Dic61C2312yes—
62#11758196—24no—
63C4×Dic61—21no—
64C4×Dic61C2312yes—
65C2×#92418—22no—
66C2×#92418C2312yes—
67C23×C61—22no—
68C23×C61—24no—
69C23×C61—21no—
70C23×C61—82no—
71C23×C61C2×D411yescharacteristic
72Q8×C61—21no—
73Q8×C61—21no—
74D4×C61—24no—
75D4×C61—21no—
76D4×C61—22no—
77D4×C61—21no—
78D4×C61—42no—
79D4×C61C2×D414yes—
80C2×C4×C61—21no—
81C2×C4×C61—42no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D412yes—
84C2×C4×C61#4112yes—
85C2×C4×C61C2411yescharacteristic
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—42no—
89C2×Dic61—84no—
90C2×Dic61C2×D414yes—
91Dic122—22no—
92Dic122—22no—
93Dic122—42no—
94C8×C61—22no—
95#92418—22no—
96C22×C61—22no—
97C22×C61—24no—
98C22×C61—44no—
99C22×C61—41no—
100C22×C61—42no—
101C22×C61—84no—
102C22×C61#12112yes—
103C22×C61C22×D411yescharacteristic
104C4×C61—41no—
105C4×C61#12112yes—
106C4×C61C22×D411yescharacteristic
107C4×C61C2×#4111yescharacteristic
108Dic61—24no—
109Dic61—42no—
110Dic61—42no—
111#3042—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61—44no—
114C2×C61—81no—
115C2×C61C2×#12111yescharacteristic
116C2×C61#57712yes—
117C2×AGL(1,ℤ/8)D6111yescharacteristic
118C22×SD16—611no—
119#536—611no—
120#518—611no—
121#463—614no—
122#461—614no—
123#424—611no—
124#419—611no—
125#416—611no—
126C61#304211yescharacteristic, complemented, Sylow
127C2×#41C2×D6111yescharacteristic
128C22×Q8—611no—
129C22×D4C2×D6111yescharacteristic
130AGL(1,ℤ/8)—24no—
131C2×SD16—614no—
132C2×SD16—1224no—
133C2×SD16C2×D6112yes—
134C2×D8C2×D6112yes—
135C2×M16C2×D6111yescharacteristic
136C22×C8—611no—
137C4⋊Q8—612no—
138#124—612no—
139#123—1222no—
140C22⋊Q8—1222no—
141C4×D4—614no—
142C4×D4—1222no—
143#117—611no—
144#117—611no—
145C2×C22⋊C4—1222no—
146C4⋊C8—614no—
147#103—612no—
148#103—614no—
149#102—612no—
150C24—21no—
151#41—22no—
152#41—22no—
153C2×Q8—612no—
154C2×Q8—1221no—
155C2×Q8—1222no—
156C2×Q8—1222no—
157C2×Q8C22×D6111yescharacteristic
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4C22⋊D6114yes—
162C2×D4C22×D6111yescharacteristic
163C2×D4C22×D6112yes—
164C22×C4—21no—
165C22×C4—1224no—
166C22×C4—1221no—
167C22×C4C22×D6111yescharacteristic
168SD16—24no—
169SD16—1228no—
170D8—24no—
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—1224no—
181C22⋊C4—1221no—
182C42—612no—
183C42—1221no—
184C23—22no—
185C23—24no—
186C23—21no—
187C23—82no—
188C23D4×D6111yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—1222no—
192Q8—1222no—
193Q8—2442no—
194D4—21no—
195D4—22no—
196D4—21no—
197D4—24no—
198D4—42no—
199D4C2×C22⋊D6114yes—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—614no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—4884no—
206C2×C4—2442no—
207C2×C4D4×D6111yescharacteristic
208C2×C4#1175822412yes—
209C2×C4C2×C22⋊D6112yes—
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—1222no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—41no—
217C22—42no—
218C22—84no—
219C22#1451974912yes—
220C22C2×D4×D6111yescharacteristic
221C4—41no—
222C4—1224no—
223C4—2442no—
224C4—2442no—
225C4#1451974912yes—
226C4C22×C22⋊D6111yescharacteristic
227C4C2×#1175822411yescharacteristic
228C2—22no—
229C2—44no—
230C2—81no—
231C2C2×#1451974911yescharacteristic
232C2#1684057212yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×AGL(1,ℤ/8)×C61C2
socleC22×C61C22×D4
hypercenterC2×AGL(1,ℤ/8)D61
hypocenterC61#3042
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#11758200C2semidirect
2. #16840333C2semidirect
3. #16840237C2semidirect
4. #16839975C2semidirect
5. #16839965C2semidirect
6. #16839790C2semidirect
7. #16839772C2semidirect
8. #16839758C2semidirect
14. #14519775C22semidirect
15. #14519764C22semidirect
23. #14519706C22semidirect
24. #14519702C22semidirect
25. #14519701C22semidirect
26. #14519698C22semidirect
126. C61#3042semidirect