Finite Group Databasebeta

← #21456111

Subgroups — #21456111

Order 7808.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840367C211yesmaximal, characteristic
2#16840239C211yesmaximal, characteristic, complemented
3#16840087C212yesmaximal, complemented
4#16840070C212yesmaximal, complemented
5#16839963C212yesmaximal, complemented
6#16839903C212yesmaximal, complemented
7#16839864C212yesmaximal, complemented
8C4×#11758190C212yesmaximal, complemented
9C61×#433C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C2×#11758190C2212yes—
12C2×#11758190C2212yes—
13#14519774C2211yescharacteristic
14#14519769C2211yescharacteristic
15#14519762—22no—
16#14519751C2212yes—
17#14519750—22no—
18C4×Dic122C2212yes—
19C4×Dic122C2212yes—
20#14519742—22no—
21C4×D244C2212yes—
22#14519736C2211yescharacteristic
23#14519733—22no—
24#14519711C2212yes—
25#14519709C2212yes—
26#14519702C2212yes—
27#14519702C2212yes—
28#14519699C2212yes—
29#14519699C2212yes—
30#117×C61C2211yescharacteristic
31C4⋊C8×C61C2212yes—
32C22⋊C8×C61C2212yes—
33#97×C61C2211yescharacteristic
34C4×C8×C61C2211yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37C22×Dic61—21no—
38C2×D244—22no—
39C2×D244C2312yes—
40C2×C4×D61—22no—
41C2×Dic122—21no—
42C2×Dic122—24no—
43C2×Dic122C2312yes—
44C2×C8×C61C2312yes—
45C2×C8×C61C2312yes—
46C4⋊C4×C61D412yes—
47C22⋊C4×C61D412yes—
48C42×C61C2311yescharacteristic
49C42×C61C2311yescharacteristic
50C22⋊Dic61—21no—
51#11758198—22no—
52#11758198—22no—
53C4⋊Dic61C2312yes—
54C4⋊Dic61C2312yes—
55#11758196—22no—
56#11758196—22no—
57#11758196—22no—
58C4×Dic61—22no—
59C4×Dic61—22no—
60C4×Dic61—21no—
61#11758190—24no—
62#11758190—24no—
63C23×C61C2×D411yescharacteristic
64C22×D61—22no—
65C2×C4×C61—22no—
66C2×C4×C61C2×D412yes—
67C2×C4×C61C2×D412yes—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2411yescharacteristic
70C22⋊D61—82no—
71C2×Dic61—24no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75D244—22no—
76D244—22no—
77D244—82no—
78C4×D61—82no—
79Dic122—24no—
80Dic122—22no—
81Dic122#4114yes—
82C8×C61—22no—
83C8×C61—22no—
84C22×C61—21no—
85C22×C61—22no—
86C22×C61C22×D411yescharacteristic
87C2×D61—42no—
88C2×D61—42no—
89C2×D61—42no—
90C4×C61—21no—
91C4×C61—22no—
92C4×C61—22no—
93C4×C61C2×#4112yes—
94Dic61—24no—
95Dic61—42no—
96Dic61—42no—
97#3126—611nomaximal, Sylow
98C2×C61—41no—
99C2×C61#52511yescharacteristic
100C2×C61#57712yes—
101D61—82no—
102#540—611no—
103#519—611no—
104#482—612no—
105#479—612no—
106#460—612no—
107#448—612no—
108#440—612no—
109C4×SD16—612no—
110#433D6111yescharacteristic, complemented
111C61#312611yescharacteristic, complemented, Sylow
112C22×Q8—611no—
113C2×SD16—612no—
114C2×SD16—612no—
115#127—611no—
116#125—611no—
117#123—1222no—
118#121—612no—
119#121—1222no—
120C4×Q8—612no—
121C4×Q8—612no—
122C4×Q8—1222no—
123C4×D4—612no—
124#117—611no—
125#117—1222no—
126#117C2×D6111yescharacteristic
127#107—612no—
128#106—612no—
129C4⋊C8C2×D6112yes—
130#103—612no—
131#103—612no—
132#102—612no—
133#102—612no—
134C22⋊C8C2×D6112yes—
135#97C2×D6111yescharacteristic
136C4×C8C2×D6111yescharacteristic
137C2×Q8—612no—
138C2×Q8—1224no—
139C2×Q8—1221no—
140C2×D4—612no—
141C2×D4—1222no—
142C2×D4—1222no—
143C22×C4—1221no—
144C22×C4—1222no—
145C22×C4C22×D6111yescharacteristic
146SD16—1224no—
147SD16—1224no—
148C2×C8C22×D6112yes—
149C2×C8C22×D6112yes—
150C4⋊C4—612no—
151C4⋊C4—612no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4D24412yes—
156C22⋊C4—1221no—
157C22⋊C4—1222no—
158C22⋊C4—1222no—
159C22⋊C4D24412yes—
160C42—1221no—
161C42—1222no—
162C42—1222no—
163C42C22×D6111yescharacteristic
164C42C22×D6111yescharacteristic
165C23—1222no—
166C23C2×D24411yescharacteristic
167Q8—614no—
168Q8—1224no—
169Q8—1222no—
170D4—1222no—
171D4—1222no—
172D4—4882no—
173D4—4882no—
174C2×C4—22no—
175C2×C4—1224no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—4882no—
180C2×C4C2×D24412yes—
181C2×C4C2×D24412yes—
182C2×C4C2×D24411yescharacteristic
183C2×C4C23×D6111yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—2442no—
189C22—2442no—
190C22—2442no—
191C22C22×D24411yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—1224no—
196C4—2442no—
197C4—2442no—
198C4#41×D6112yes—
199C2—41no—
200C2—4882no—
201C2#1684027411yescharacteristic
202C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #16840239C2semidirect
3. #16840087C2semidirect
4. #16840070C2semidirect
5. #16839963C2semidirect
6. #16839903C2semidirect
7. #16839864C2semidirect
8. C4×#11758190C2semidirect
9. C61×#433C2semidirect
110. #433D61semidirect
111. C61#3126semidirect