Finite Group Databasebeta

← #21456950

Subgroups — #21456950

Order 7808.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840167C211yesmaximal, characteristic, complemented
4#16840158C211yesmaximal, characteristic, complemented
5#16840108C211yesmaximal, characteristic, complemented
6#16840084C214yesmaximal, complemented
7#16840060C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#486C211yesmaximal, characteristic, complemented
10C2×#11758224—21no—
11#14519777C2211yescharacteristic
12#14519777C2211yescharacteristic
13#14519768C2212yes—
14#14519764—21no—
15#14519757—21no—
16#14519753—21no—
17#14519748—21no—
18#14519748C2212yes—
19Q8×Dic61—21no—
20#14519742—21no—
21D4×Dic61—21no—
22D4×Dic61C2212yes—
23#14519735C2212yes—
24C42×D61C2211yescharacteristic
25#14519711C2214yes—
26#14519708C2214yes—
27#14519706C2212yes—
28#14519698C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
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—44no—
42C2×C4×D61D411yescharacteristic
43C2×C4×D61D411yescharacteristic
44C2×C4×D61C2311yescharacteristic
45C2×Dic122—21no—
46C2×Dic122—21no—
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—22no—
57C4⋊Dic61C2312yes—
58C4⋊Dic61C2312yes—
59#11758196—22no—
60C4×Dic61—22no—
61C4×Dic61D411yescharacteristic
62C4×Dic61D411yescharacteristic
63C4×Dic61C2311yescharacteristic
64C2×#92418C2312yes—
65C23×C61—22no—
66C22×D61C2×D411yescharacteristic
67Q8×C61—42no—
68D4×C61—24no—
69D4×C61—42no—
70D4×C61—42no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2411yescharacteristic
75C22⋊D61—44no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—44no—
79C2×Dic61C2×D411yescharacteristic
80C2×Dic61C2×D411yescharacteristic
81C2×Dic61C2×D411yescharacteristic
82C4×D61—22no—
83C4×D61—22no—
84C4×D61—22no—
85Dic122—42no—
86Dic122—42no—
87C8×C61—22no—
88#92418—22no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61C22×D411yescharacteristic
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—21no—
96C4×C61—42no—
97C4×C61#13512yes—
98C4×C61AGL(1,ℤ/8)12yes—
99C4×C612−1+412yes—
100Dic61—21no—
101Dic61—21no—
102Dic61—21no—
103Dic61—42no—
104Dic61—42no—
105#3228—611nomaximal, Sylow
106C2×C61—82no—
107C2×C61#53611yescharacteristic
108C2×C61C2×#13511yescharacteristic
109C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
110D61—41no—
111#533—611no—
112#532—611no—
113#500—611no—
114#498—611no—
115#486—611no—
116#486D6111yescharacteristic, complemented
117#482—614no—
118#478—614no—
119#431—611no—
120C61#322811yescharacteristic, complemented, Sylow
121C2×#41—1221no—
122C4⋊Q8—611no—
123C4⋊Q8—611no—
124C4⋊Q8C2×D6111yescharacteristic
125#127C2×D6111yescharacteristic
126#125—612no—
127#124—1221no—
128C22⋊Q8—1221no—
129C22⋊Q8—1221no—
130#121—612no—
131#121—1221no—
132C4×Q8—1221no—
133C4×Q8—1221no—
134C4×D4—612no—
135C4×D4—1221no—
136#117—612no—
137C2×C42—611no—
138#107—614no—
139#106—614no—
140C4⋊C8—612no—
141#102—614no—
142#102C2×D6114yes—
143C22⋊C8—612no—
144C4×C8—611no—
145C4×C8C2×D6111yescharacteristic
146#41—2444no—
147C2×Q8—21no—
148C2×Q8—1221no—
149C2×Q8—1221no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—1222no—
153C2×D4C22×D6112yes—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—1222no—
158C2×C8—612no—
159C2×C8C22×D6112yes—
160C4⋊C4—21no—
161C4⋊C4—612no—
162C4⋊C4—612no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4C22×D6112yes—
168C22⋊C4—1222no—
169C22⋊C4—1222no—
170C22⋊C4—1222no—
171C42—611no—
172C42—611no—
173C42—611no—
174C42—1222no—
175C42C22×D6111yescharacteristic
176C23—22no—
177C23—611no—
178Q8—42no—
179Q8—2442no—
180Q8—2442no—
181D4—24no—
182D4—42no—
183D4—42no—
184D4—2444no—
185C2×C4—22no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—2444no—
195C2×C4D4×D6111yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C2×C4C23×D6111yescharacteristic
198C8—22no—
199C8—1222no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—1221no—
204C22—1221no—
205C22—1221no—
206C22C2×D4×D6111yescharacteristic
207C4—42no—
208C4—1221no—
209C4—1221no—
210C4—1221no—
211C4—2442no—
212C4—2442no—
213C4#1451979612yes—
214C4#1451980412yes—
215C4#1451982412yes—
216C2—82no—
217C2—2441no—
218C2#1684033211yescharacteristic
219C2C2×#1451979611yescharacteristic
220C2C2×#1451980411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3228
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. #16840167C2semidirect
4. #16840158C2semidirect
5. #16840108C2semidirect
6. #16840084C2semidirect
7. #16840060C2semidirect
8. #16839813C2semidirect
9. C61×#486C2semidirect
116. #486D61semidirect
120. C61#3228semidirect