Finite Group Databasebeta

← #21456072

Subgroups — #21456072

Order 7808.

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

normal subgroups only

This group has 394 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#16840374C211yesmaximal, characteristic, complemented
2#16840236C211yesmaximal, characteristic
3#16840104C212yesmaximal, complemented
4#16840063C212yesmaximal, complemented
5#16839968C212yesmaximal, complemented
6#16839915C212yesmaximal
7#16839864C212yesmaximal, complemented
8C4×#11758190C212yesmaximal, complemented
9C61×#433C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C2×#11758190C2212yes—
12C2×#11758190C2212yes—
13#14519777C2211yescharacteristic, complemented
14#14519770—22no—
15#14519769C2211yescharacteristic, complemented
16#14519767—22no—
17#14519756C2212yes—
18C4×Dic122C2212yescomplemented
19C4×D244C2212yes—
20C4×D244C2212yes—
21#14519739—22no—
22#14519736C2211yescharacteristic
23C22⋊C4×D61—22no—
24#14519711C2212yescomplemented
25#14519709C2212yescomplemented
26#14519702C2212yescomplemented
27#14519702C2212yescomplemented
28#14519699C2212yes—
29#14519699C2212yes—
30#117×C61C2211yescharacteristic
31C4⋊C8×C61C2212yescomplemented
32C22⋊C8×C61C2212yes—
33#97×C61C2211yescharacteristic, complemented
34C4×C8×C61C2211yescharacteristic, complemented
35C23×D61—21no—
36C22×C4×C61C2311yescharacteristic
37C2×D244—21no—
38C2×D244—24no—
39C2×D244C2312yes—
40C2×C4×D61—22no—
41C2×C4×D61—22no—
42C2×Dic122C2312yes—
43C2×C8×C61C2312yes—
44C2×C8×C61C2312yes—
45C4⋊C4×C61D412yes—
46C22⋊C4×C61D412yes—
47C42×C61C2311yescharacteristic
48C42×C61C2311yescharacteristic
49C22⋊Dic61—21no—
50C22⋊Dic61—22no—
51#11758198—22no—
52#11758198—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61C2312yes—
55C4⋊Dic61C2312yes—
56#11758196—22no—
57#11758196—22no—
58#11758196—22no—
59C4×Dic61—21no—
60C4×Dic61—22no—
61#11758190—24no—
62#11758190—24no—
63C23×C61C2×D411yescharacteristic
64C22×D61—22no—
65C22×D61—24no—
66C22×D61—82no—
67C2×C4×C61—22no—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2411yescharacteristic
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75D244—24no—
76D244—22no—
77D244#4114yes—
78C4×D61—82no—
79C4×D61—82no—
80Dic122—22no—
81Dic122—22no—
82C8×C61—22no—
83C8×C61—22no—
84C22×C61—21no—
85C22×C61—22no—
86C22×C61C22×D411yescharacteristic
87C2×D61—24no—
88C2×D61—42no—
89C2×D61—42no—
90C2×D61—84no—
91C4×C61—21no—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61C2×#4112yes—
95Dic61—42no—
96Dic61—42no—
97Dic61—42no—
98#3123—611nomaximal, Sylow
99C2×C61—41no—
100C2×C61#52511yescharacteristic
101C2×C61#57712yes—
102D61—44no—
103#541—611no—
104#518—611no—
105#485—612no—
106#478—612no—
107#461—612no—
108#450—612no—
109#440—612no—
110C4×SD16—612no—
111#433D6111yescharacteristic, complemented
112C61#312311yescharacteristic, complemented, Sylow
113C22×D4—611no—
114C2×SD16—612no—
115C2×SD16—612no—
116C4⋊Q8—611no—
117#126—1222no—
118#125—611no—
119#125—1222no—
120C22⋊Q8—612no—
121C4×Q8—612no—
122C4×D4—612no—
123C4×D4—612no—
124C4×D4—1222no—
125#117—611no—
126#117C2×D6111yescharacteristic
127C2×C22⋊C4—1222no—
128#107—612no—
129#106—612no—
130C4⋊C8C2×D6112yescomplemented
131#103—612no—
132#103—612no—
133#102—612no—
134#102—612no—
135C22⋊C8C2×D6112yes—
136#97C2×D6111yescharacteristic, complemented
137C4×C8C2×D6111yescharacteristic, complemented
138C24—1221no—
139C2×Q8—612no—
140C2×D4—612no—
141C2×D4—1224no—
142C2×D4—1221no—
143C22×C4—1222no—
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⋊C4—1222no—
156C4⋊C4D24412yes—
157C22⋊C4—1221no—
158C22⋊C4—1222no—
159C22⋊C4—1222no—
160C22⋊C4—1222no—
161C22⋊C4D24412yes—
162C42—1221no—
163C42—1222no—
164C42C22×D6111yescharacteristic
165C42C22×D6111yescharacteristic
166C23—1224no—
167C23—1222no—
168C23—4882no—
169C23C2×D24411yescharacteristic
170Q8—1222no—
171Q8—1222no—
172D4—614no—
173D4—1224no—
174D4—1222no—
175C2×C4—22no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—4882no—
180C2×C4—4882no—
181C2×C4C2×D24412yes—
182C2×C4C2×D24411yescharacteristic
183C2×C4C2×D24412yes—
184C2×C4C23×D6111yescharacteristic
185C8—22no—
186C8—22no—
187C22—21no—
188C22—22no—
189C22—1224no—
190C22—4884no—
191C22—2442no—
192C22—2442no—
193C22C22×D24411yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—2442no—
198C4—2442no—
199C4—2442no—
200C4#41×D6112yes—
201C2—41no—
202C2—2444no—
203C2#1684027411yescharacteristic
204C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3123
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
1. #16840374C2semidirect
3. #16840104C2semidirect
4. #16840063C2semidirect
5. #16839968C2semidirect
7. #16839864C2semidirect
8. C4×#11758190C2semidirect
9. C61×#433C2semidirect
13. #14519777C22semidirect
15. #14519769C22semidirect
18. C4×Dic122C22semidirect
24. #14519711C22semidirect
25. #14519709C22semidirect
26. #14519702C22semidirect
27. #14519702C22semidirect
31. C4⋊C8×C61C22semidirect
33. #97×C61C22semidirect
34. C4×C8×C61C22semidirect
111. #433D61semidirect
112. C61#3123semidirect
130. C4⋊C8C2×D61semidirect
136. #97C2×D61semidirect
137. C4×C8C2×D61semidirect