Finite Group Databasebeta

← #21456221

Subgroups — #21456221

Order 7808.

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

normal subgroups only

This group has 392 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#16840313C211yesmaximal, characteristic
2#125×D61C211yesmaximal, characteristic, complemented
3#16840130C211yesmaximal, characteristic, complemented
4#16840128C211yesmaximal, characteristic, complemented
5#16840127C211yesmaximal, characteristic, complemented
6#16840118C214yesmaximal, complemented
7#16839762C214yesmaximal, complemented
8#16839714C211yesmaximal, characteristic, complemented
9C61×#491C211yesmaximal, characteristic, complemented
10C2×#11758226C2212yes—
11C2×#11758189C2212yes—
12#14519774C2211yescharacteristic
13#14519769C2211yescharacteristic
14#14519768C2212yes—
15#14519767—22no—
16#14519766C2212yes—
17#14519752—22no—
18#14519739—22no—
19C4⋊C4×D61—22no—
20C4⋊C4×D61C2212yes—
21C42×D61C2211yescharacteristic
22#14519701C2214yes—
23#14519699C2214yes—
24#14519697C2214yes—
25#14519688C2211yescharacteristic
26C8×Dic61C2212yes—
27C4⋊Q8×C61C2211yescharacteristic
28#125×C61C2211yescharacteristic
29#103×C61C2214yes—
30#97×C61C2211yescharacteristic
31C2×Q8×C61C2312yes—
32#11758226—28no—
33C2×D244—22no—
34C2×D244—22no—
35C2×D244C2312yes—
36C2×C4×D61—22no—
37C2×C4×D61—22no—
38C2×C4×D61D412yes—
39C2×C4×D61C2311yescharacteristic
40C2×C8×C61C2312yes—
41C4⋊C4×C61—22no—
42C4⋊C4×C61—22no—
43C4⋊C4×C61C2312yes—
44C42×C61C2311yescharacteristic
45#11758198—24no—
46C4⋊Dic61—22no—
47C4⋊Dic61C2312yes—
48#11758196—22no—
49#11758196—22no—
50#11758196—22no—
51C4×Dic61D412yes—
52C4×Dic61C2311yescharacteristic
53C2×#92418C2312yes—
54#11758189—24no—
55C22×D61—22no—
56C22×D61C2×D411yescharacteristic
57Q8×C61—24no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61C2×D412yes—
61C2×C4×C61C2411yescharacteristic
62C2×Dic61—22no—
63C2×Dic61C2×D412yes—
64C2×Dic61C2×D411yescharacteristic
65D244—24no—
66D244—44no—
67D244—44no—
68C4×D61—42no—
69C4×D61—44no—
70C4×D61—44no—
71C4×D61#4114yes—
72C8×C61—22no—
73#92418—22no—
74C22×C61C22×D411yescharacteristic
75C2×D61—22no—
76C2×D61—42no—
77C2×D61—44no—
78C2×D61#12412yes—
79C4×C61—22no—
80C4×C61—42no—
81C4×C61—42no—
82C4×C61C2×#4112yes—
83Dic61—22no—
84Dic61—42no—
85Dic61#12412yes—
86#3142—611nomaximal, Sylow
87C2×C61C2×#12411yescharacteristic
88C2×C61#57512yes—
89D61—22no—
90D61—82no—
91#532—611no—
92C2×#125—611no—
93#491—611no—
94#491D6111yescharacteristic, complemented
95#490—611no—
96#490—611no—
97#488—614no—
98#417—614no—
99C4×M16—611no—
100C61#314211yescharacteristic, complemented, Sylow
101C2×#41—612no—
102C2×M16—612no—
103C4⋊Q8C2×D6111yescharacteristic
104#127—611no—
105#125—612no—
106#125—611no—
107#125—1222no—
108#125C2×D6111yescharacteristic
109#124—612no—
110#121—1222no—
111C4×D4—1222no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—1222no—
114C2×C42—611no—
115#103—614no—
116#103C2×D6114yes—
117#102—614no—
118#102—614no—
119#97—611no—
120#97C2×D6111yescharacteristic
121C4×C8—612no—
122#41—1228no—
123C2×Q8C22×D6112yes—
124C2×D4—612no—
125C2×D4—1222no—
126C2×D4—1222no—
127C22×C4—611no—
128C22×C4—612no—
129C22×C4—1222no—
130C22×C4—1222no—
131M16—1224no—
132C2×C8—612no—
133C2×C8C22×D6112yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—612no—
137C4⋊C4—1222no—
138C4⋊C4—1222no—
139C4⋊C4—1222no—
140C4⋊C4—1222no—
141C4⋊C4C22×D6112yes—
142C22⋊C4—1224no—
143C42—612no—
144C42—611no—
145C42C22×D6111yescharacteristic
146C23—611no—
147C23—1222no—
148Q8—24no—
149D4—1224no—
150D4—2444no—
151D4—2444no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—611no—
155C2×C4—614no—
156C2×C4—612no—
157C2×C4—1222no—
158C2×C4—2442no—
159C2×C4—2444no—
160C2×C4—2444no—
161C2×C4D4×D6112yes—
162C2×C4C23×D6111yescharacteristic
163C8—22no—
164C8—1222no—
165C22—612no—
166C22—1222no—
167C22—2442no—
168C22—2444no—
169C22C2×D4×D6111yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—612no—
174C4—1222no—
175C4—2442no—
176C4#41×D6112yes—
177C2—1222no—
178C2—4882no—
179C2#124×D6111yescharacteristic
180C2#1684056112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#491C2
socleC22×C61C22×D4
hypercenter#491D61
hypocenterC61#3142
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #125×D61C2semidirect
3. #16840130C2semidirect
4. #16840128C2semidirect
5. #16840127C2semidirect
6. #16840118C2semidirect
7. #16839762C2semidirect
8. #16839714C2semidirect
9. C61×#491C2semidirect
94. #491D61semidirect
100. C61#3142semidirect