Finite Group Databasebeta

← #21456191

Subgroups — #21456191

Order 7808.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#16840315C211yesmaximal, characteristic, complemented
2C2×#14519773C211yesmaximal, characteristic
3#16840125C214yesmaximal, complemented
4#16840107C214yesmaximal, complemented
5#16839768C211yesmaximal, characteristic, complemented
6#16839767C211yesmaximal, characteristic, complemented
7#16839766C211yesmaximal, characteristic, complemented
8M16×Dic61C211yesmaximal, characteristic, complemented
9C61×#418C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61—22no—
12C2×#11758194C2211yescharacteristic
13#14519776C2212yescomplemented
14#14519773—22no—
15#14519773C2212yes—
16#14519773C2212yes—
17#14519768C2212yescomplemented
18#14519754—22no—
19C4×Dic122—22no—
20#14519736C2211yescharacteristic
21C2×C4×Dic61C2211yescharacteristic
22#14519699C2214yescomplemented
23#14519698C2214yescomplemented
24#14519697C2214yescomplemented
25#14519687C2212yescomplemented
26C8×Dic61C2212yescomplemented
27C22×D4×C61C2211yescharacteristic
28C2×M16×C61C2211yescharacteristic
29#117×C61C2211yescharacteristic
30#102×C61C2214yescomplemented
31C24×C61—21no—
32C23×D61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—22no—
35C2×D4×C61—22no—
36C2×D4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—24no—
39C2×C22⋊D61—24no—
40C2×C22⋊D61—48no—
41C22×Dic61D412yes—
42C2×D244—22no—
43C2×D244—22no—
44C2×D244—21no—
45C2×D244C2312yes—
46C2×Dic122—22no—
47M16×C61—22no—
48C2×C8×C61C2312yes—
49C4⋊C4×C61C2312yes—
50C22⋊C4×C61—21no—
51C42×C61—21no—
52C22⋊Dic61—21no—
53C4⋊Dic61—22no—
54C4⋊Dic61C2312yes—
55#11758196—22no—
56#11758196—22no—
57C4×Dic61—21no—
58C4×Dic61D412yes—
59C4×Dic61C2311yescharacteristic
60C4×Dic61C2311yescharacteristic
61#11758194—22no—
62C2×#92418C2312yes—
63C23×C61—22no—
64C23×C61—44no—
65C23×C61—42no—
66C23×C61C2×D411yescharacteristic
67C22×D61—22no—
68C22×D61—44no—
69C22×D61—42no—
70D4×C61—22no—
71D4×C61—22no—
72D4×C61—42no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4112yes—
76C2×C4×C61#4112yes—
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—48no—
79C22⋊D61—48no—
80C2×Dic61—24no—
81C2×Dic61—22no—
82C2×Dic61C2×D412yes—
83C2×Dic61C2×D412yes—
84D244—22no—
85D244—22no—
86D244—42no—
87Dic122—44no—
88C8×C61—22no—
89#92418—22no—
90C22×C61—22no—
91C22×C61—42no—
92C22×C61—44no—
93C22×C61—84no—
94C22×C61#12412yes—
95C22×C61C22×D411yescharacteristic
96C2×D61—42no—
97C2×D61—44no—
98C2×D61—84no—
99C4×C61—42no—
100C4×C61#12412yes—
101C4×C61C2×#4111yescharacteristic
102C4×C61C2×#4111yescharacteristic
103Dic61—22no—
104Dic61—42no—
105Dic61AGL(1,ℤ/8)14yes—
106#3138—611nomaximal, Sylow
107C2×C61—22no—
108C2×C61—82no—
109C2×C61C2×#12411yescharacteristic
110C2×C61C2×AGL(1,ℤ/8)12yes—
111D61—82no—
112#533—611no—
113C2×#127—611no—
114#490—614no—
115#486—614no—
116#418—611no—
117#418—611no—
118#418—611no—
119#418D6111yescharacteristic, complemented
120C4×M16—611no—
121C61#313811yescharacteristic, complemented, Sylow
122C22×D4—611no—
123C22×D4—1222no—
124C22×D4C2×D6111yescharacteristic
125C2×M16—611no—
126C2×M16C2×D6111yescharacteristic
127C4⋊Q8—612no—
128#127—612no—
129#127—612no—
130#127—1222no—
131#125—612no—
132C22⋊Q8—1222no—
133C4×Q8—1222no—
134#117—611no—
135#117C2×D6111yescharacteristic
136C2×C42—611no—
137#102—614no—
138#102—614no—
139#102—614no—
140#102C2×D6114yescomplemented
141#97—612no—
142C4×C8—612no—
143C24—21no—
144C24—1221no—
145C2×Q8—1222no—
146C2×D4—22no—
147C2×D4—21no—
148C2×D4—22no—
149C2×D4—612no—
150C2×D4—1224no—
151C2×D4—1224no—
152C2×D4—1222no—
153C2×D4—1221no—
154C2×D4—1222no—
155C2×D4—2448no—
156C2×D4C22×D6112yes—
157C22×C4—612no—
158C22×C4C22×D6111yescharacteristic
159M16—22no—
160M16—1222no—
161C2×C8—612no—
162C2×C8C22×D6112yes—
163C4⋊C4—612no—
164C4⋊C4—1222no—
165C4⋊C4—1222no—
166C4⋊C4—1222no—
167C4⋊C4C22×D6112yes—
168C22⋊C4—21no—
169C22⋊C4—1221no—
170C42—21no—
171C42—612no—
172C42—611no—
173C42—611no—
174C42—1221no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—1222no—
179C23—2444no—
180C23—2442no—
181C23D4×D6111yescharacteristic
182Q8—2444no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—1222no—
187D4—1222no—
188D4—2448no—
189D4—2448no—
190D4—2442no—
191C2×C4—22no—
192C2×C4—612no—
193C2×C4—612no—
194C2×C4—1224no—
195C2×C4—1222no—
196C2×C4#1175822212yes—
197C2×C4D4×D6111yescharacteristic
198C2×C4#1175822412yes—
199C2×C4C23×D6111yescharacteristic
200C8—22no—
201C8—1222no—
202C22—22no—
203C22—42no—
204C22—44no—
205C22—84no—
206C22—4884no—
207C22—2442no—
208C22—2444no—
209C22#1451976312yes—
210C22C2×D4×D6111yescharacteristic
211C4—42no—
212C4—614no—
213C4—1222no—
214C4—2442no—
215C4#1451976312yes—
216C4C2×#1175822411yescharacteristic
217C4C2×#1175822211yescharacteristic
218C2—22no—
219C2—82no—
220C2—4882no—
221C2C2×#1451976311yescharacteristic
222C2AGL(1,ℤ/8)×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#418C2
socleC22×C61C22×D4
hypercenter#418D61
hypocenterC61#3138
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #16840315C2semidirect
3. #16840125C2semidirect
4. #16840107C2semidirect
5. #16839768C2semidirect
6. #16839767C2semidirect
7. #16839766C2semidirect
8. M16×Dic61C2semidirect
9. C61×#418C2semidirect
13. #14519776C22semidirect
17. #14519768C22semidirect
22. #14519699C22semidirect
23. #14519698C22semidirect
24. #14519697C22semidirect
25. #14519687C22semidirect
26. C8×Dic61C22semidirect
30. #102×C61C22semidirect
119. #418D61semidirect
121. C61#3138semidirect
140. #102C2×D61semidirect