Finite Group Databasebeta

← #21456063

Subgroups — #21456063

Order 7808.

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

normal subgroups only

This group has 418 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, complemented
2#16840236C211yesmaximal, characteristic, complemented
3#16840087C212yesmaximal, complemented
4#16840063C212yesmaximal, complemented
5#16839958C212yesmaximal, complemented
6#16839898C212yesmaximal, complemented
7#16839875C212yesmaximal, complemented
8C4×D488C212yesmaximal, complemented
9C61×#433C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C2×D488C2212yes—
12C2×D488C2212yes—
13#14519774C2211yescharacteristic, complemented
14#14519769C2211yescharacteristic, complemented
15#14519762—22no—
16#14519751C2212yes—
17#14519750—22no—
18C4×D244C2212yes—
19C4×D244C2212yes—
20C4×D244C2212yescomplemented
21#14519739—22no—
22#14519736C2211yescharacteristic
23C22⋊C4×D61—22no—
24#14519711C2212yescomplemented
25#14519709C2212yescomplemented
26#14519699C2212yes—
27#14519699C2212yes—
28#14519699C2212yescomplemented
29#14519699C2212yescomplemented
30#117×C61C2211yescharacteristic
31C4⋊C8×C61C2212yescomplemented
32C22⋊C8×C61C2212yes—
33#97×C61C2211yescharacteristic, complemented
34C4×C8×C61C2211yescharacteristic, complemented
35C23×D61—21no—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—22no—
38C2×D244—21no—
39C2×D244—24no—
40C2×D244—22no—
41C2×D244C2312yes—
42C2×D244C2312yes—
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61—22no—
46C2×C8×C61C2312yes—
47C2×C8×C61C2312yes—
48C4⋊C4×C61D412yes—
49C22⋊C4×C61D412yes—
50C42×C61C2311yescharacteristic
51C42×C61C2311yescharacteristic
52C22⋊Dic61—21no—
53#11758198—22no—
54#11758198—22no—
55#11758198—22no—
56#11758198—22no—
57C4⋊Dic61C2312yes—
58C4⋊Dic61C2312yes—
59#11758196—22no—
60C4×Dic61—21no—
61D488—24no—
62D488—24no—
63C23×C61C2×D411yescharacteristic
64C22×D61—22no—
65C22×D61—24no—
66C22×D61—22no—
67C22×D61—82no—
68C2×C4×C61—22no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2411yescharacteristic
73C22⋊D61—82no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76D244—24no—
77D244—22no—
78D244—22no—
79D244—22no—
80D244—82no—
81D244#4114yes—
82C4×D61—82no—
83C4×D61—82no—
84C4×D61—82no—
85C8×C61—22no—
86C8×C61—22no—
87C22×C61—21no—
88C22×C61—22no—
89C22×C61C22×D411yescharacteristic
90C2×D61—24no—
91C2×D61—42no—
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—84no—
97C4×C61—21no—
98C4×C61—22no—
99C4×C61—22no—
100C4×C61C2×#4112yes—
101Dic61—42no—
102Dic61—42no—
103#3122—611nomaximal, Sylow
104C2×C61—41no—
105C2×C61#52511yescharacteristic
106C2×C61#57612yes—
107D61—44no—
108D61—82no—
109#540—611no—
110#518—611no—
111#482—612no—
112#478—612no—
113#459—612no—
114#447—612no—
115#442—612no—
116C4×D8—612no—
117#433D6111yescharacteristic, complemented
118C61#312211yescharacteristic, complemented, Sylow
119C22×D4—611no—
120C2×D8—612no—
121C2×D8—612no—
122#127—611no—
123#125—611no—
124#123—1222no—
125#121—612no—
126#121—1222no—
127C4×D4—612no—
128C4×D4—612no—
129C4×D4—612no—
130C4×D4—1222no—
131#117—611no—
132#117C2×D6111yescharacteristic
133C2×C22⋊C4—1222no—
134#107—612no—
135#106—612no—
136C4⋊C8C2×D6112yescomplemented
137#102—612no—
138#102—612no—
139#102—612no—
140#102—612no—
141C22⋊C8C2×D6112yes—
142#97C2×D6111yescharacteristic, complemented
143C4×C8C2×D6111yescharacteristic, complemented
144C24—1221no—
145C2×D4—612no—
146C2×D4—612no—
147C2×D4—1224no—
148C2×D4—1222no—
149C2×D4—1221no—
150C2×D4—1222no—
151C22×C4—1222no—
152C22×C4—1222no—
153C22×C4—1222no—
154C22×C4C22×D6111yescharacteristic
155D8—1224no—
156D8—1224no—
157C2×C8C22×D6112yes—
158C2×C8C22×D6112yes—
159C4⋊C4—612no—
160C4⋊C4—612no—
161C4⋊C4—1222no—
162C4⋊C4D24412yes—
163C22⋊C4—1221no—
164C22⋊C4—1222no—
165C22⋊C4—1222no—
166C22⋊C4—1222no—
167C22⋊C4—1222no—
168C22⋊C4D24412yes—
169C42—1221no—
170C42C22×D6111yescharacteristic
171C42C22×D6111yescharacteristic
172C23—1224no—
173C23—1222no—
174C23—1222no—
175C23—4882no—
176C23C2×D24411yescharacteristic
177D4—614no—
178D4—1224no—
179D4—1222no—
180D4—1222no—
181D4—1222no—
182D4—4882no—
183D4—4882no—
184C2×C4—22no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—4882no—
188C2×C4—4882no—
189C2×C4—4882no—
190C2×C4C2×D24411yescharacteristic
191C2×C4C2×D24412yes—
192C2×C4C2×D24412yes—
193C2×C4C23×D6111yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—1224no—
199C22—4884no—
200C22—2442no—
201C22—2442no—
202C22—2442no—
203C22—2442no—
204C22—2442no—
205C22C22×D24411yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—2442no—
210C4—2442no—
211C4#41×D6112yes—
212C2—41no—
213C2—4882no—
214C2—2444no—
215C2#1684027411yescharacteristic
216C2#1684056712yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3122
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. #16840367C2semidirect
2. #16840236C2semidirect
3. #16840087C2semidirect
4. #16840063C2semidirect
5. #16839958C2semidirect
6. #16839898C2semidirect
7. #16839875C2semidirect
8. C4×D488C2semidirect
9. C61×#433C2semidirect
13. #14519774C22semidirect
14. #14519769C22semidirect
20. C4×D244C22semidirect
24. #14519711C22semidirect
25. #14519709C22semidirect
28. #14519699C22semidirect
29. #14519699C22semidirect
31. C4⋊C8×C61C22semidirect
33. #97×C61C22semidirect
34. C4×C8×C61C22semidirect
117. #433D61semidirect
118. C61#3122semidirect
136. C4⋊C8C2×D61semidirect
142. #97C2×D61semidirect
143. C4×C8C2×D61semidirect