Finite Group Databasebeta

← #21456138

Subgroups — #21456138

Order 7808.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840317C211yesmaximal, characteristic, complemented
2#16840310C211yesmaximal, characteristic
3#16840115C214yesmaximal, complemented
4#16840114C211yesmaximal, characteristic, complemented
5#16840113C211yesmaximal, characteristic, complemented
6#16840108C211yesmaximal, characteristic, complemented
7#16839755C214yesmaximal, complemented
8C4×C8×D61C211yesmaximal, characteristic, complemented
9C61×#486C211yesmaximal, characteristic, complemented
10C2×#11758224C2212yes—
11C2×C8×D61C2212yes—
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519768C2212yes—
15#14519764C2212yes—
16#14519757—21no—
17#14519753—21no—
18#14519748—21no—
19#14519748—21no—
20Q8×Dic61—21no—
21#14519742—21no—
22D4×Dic61—21no—
23D4×Dic61—21no—
24#14519735C2212yes—
25C42×D61C2211yescharacteristic
26#14519702C2214yes—
27#14519700C2214yes—
28#14519698C2214yes—
29C4×#92418C2211yescharacteristic
30C8×Dic61C2212yes—
31C4⋊Q8×C61C2211yescharacteristic
32#127×C61C2211yescharacteristic
33#102×C61C2214yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61C2312yes—
39C2×C22⋊D61—22no—
40C22×Dic61—22no—
41#11758224—28no—
42C2×C4×D61D411yescharacteristic
43C2×C4×D61D411yescharacteristic
44C2×C4×D61C2311yescharacteristic
45C2×Dic122—21no—
46C2×Dic122C2312yes—
47C2×C8×C61C2312yes—
48C4⋊C4×C61—21no—
49C4⋊C4×C61C2312yes—
50C42×C61C2311yescharacteristic
51C22⋊Dic61—22no—
52C22⋊Dic61—22no—
53#11758198—22no—
54C4⋊Dic61—21no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61—22no—
58C4⋊Dic61C2312yes—
59#11758196—22no—
60C4×Dic61—22no—
61C4×Dic61D411yescharacteristic
62C4×Dic61D411yescharacteristic
63C4×Dic61C2311yescharacteristic
64C2×#92418C2312yes—
65C8×D61—24no—
66C23×C61—22no—
67C22×D61C2×D411yescharacteristic
68Q8×C61—42no—
69D4×C61—24no—
70D4×C61—42no—
71D4×C61—42no—
72C2×C4×C61—22no—
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2411yescharacteristic
76C22⋊D61—44no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—44no—
80C2×Dic61C2×D411yescharacteristic
81C2×Dic61C2×D411yescharacteristic
82C2×Dic61C2×D411yescharacteristic
83C4×D61—22no—
84C4×D61—22no—
85C4×D61#4114yes—
86Dic122—24no—
87Dic122—42no—
88C8×C61—22no—
89#92418—22no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61C22×D411yescharacteristic
94C2×D61—21no—
95C2×D61—21no—
96C2×D61#12412yes—
97C4×C61—42no—
98C4×C61#13512yes—
99C4×C61#13512yes—
100C4×C61C2×#4112yes—
101Dic61—21no—
102Dic61—21no—
103Dic61—42no—
104Dic61—42no—
105Dic61#12412yes—
106#3131—611nomaximal, Sylow
107C2×C61—82no—
108C2×C61C2×#12411yescharacteristic
109C2×C61C2×#13511yescharacteristic
110C2×C61C2×#13511yescharacteristic
111D61—22no—
112#533—611no—
113#532—611no—
114#488—614no—
115#487—611no—
116#487—611no—
117#486—611no—
118#486D6111yescharacteristic, complemented
119#416—614no—
120C2×C4×C8—611no—
121C61#313111yescharacteristic, complemented, Sylow
122C2×#41—612no—
123C22×C8—612no—
124C4⋊Q8—611no—
125C4⋊Q8—611no—
126C4⋊Q8C2×D6111yescharacteristic
127#127C2×D6111yescharacteristic
128#125—612no—
129#124—612no—
130C22⋊Q8—1221no—
131C22⋊Q8—1221no—
132#121—1221no—
133#121—1221no—
134C4×Q8—1221no—
135C4×Q8—1221no—
136C4×D4—1221no—
137C4×D4—1221no—
138#117—612no—
139C2×C42—611no—
140#103—614no—
141#103—614no—
142#102—614no—
143#102C2×D6114yes—
144C4×C8—612no—
145C4×C8—611no—
146C4×C8C2×D6111yescharacteristic
147#41—1228no—
148C2×Q8—21no—
149C2×Q8—612no—
150C2×Q8—1221no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—1222no—
154C2×D4C22×D6112yes—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—1222no—
159C2×C8—612no—
160C2×C8—1224no—
161C2×C8C22×D6112yes—
162C4⋊C4—21no—
163C4⋊C4—612no—
164C4⋊C4—1222no—
165C4⋊C4—1222no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C4⋊C4C22×D6112yes—
170C22⋊C4—1222no—
171C22⋊C4—1222no—
172C22⋊C4—1222no—
173C42—611no—
174C42—611no—
175C42—611no—
176C42—1222no—
177C42C22×D6111yescharacteristic
178C23—22no—
179C23—611no—
180Q8—42no—
181Q8—1224no—
182Q8—2442no—
183D4—24no—
184D4—42no—
185D4—42no—
186D4—2444no—
187C2×C4—22no—
188C2×C4—611no—
189C2×C4—614no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—2444no—
197C2×C4D4×D6111yescharacteristic
198C2×C4D4×D6111yescharacteristic
199C2×C4C23×D6111yescharacteristic
200C8—22no—
201C8—1222no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—612no—
206C22—1221no—
207C22—1221no—
208C22C2×D4×D6111yescharacteristic
209C4—42no—
210C4—612no—
211C4—1221no—
212C4—1221no—
213C4—2442no—
214C4—2442no—
215C4#1451979612yes—
216C4#1451979812yes—
217C4#41×D6112yes—
218C2—82no—
219C2—1222no—
220C2#124×D6111yescharacteristic
221C2C2×#1451979611yescharacteristic
222C2C2×#1451979811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3131
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840115C2semidirect
4. #16840114C2semidirect
5. #16840113C2semidirect
6. #16840108C2semidirect
7. #16839755C2semidirect
8. C4×C8×D61C2semidirect
9. C61×#486C2semidirect
118. #486D61semidirect
121. C61#3131semidirect