Finite Group Databasebeta

← #21456071

Subgroups — #21456071

Order 7808.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840103C212yesmaximal, complemented
3#16840062C212yesmaximal, complemented
4#16839967C212yesmaximal, complemented
5#16839913C212yesmaximal
6#16839862C212yesmaximal, complemented
7C4×#11758200C212yesmaximal, complemented
8#16839823C211yesmaximal, characteristic, complemented
9C61×#518C211yesmaximal, characteristic
10C2×#11758200C2212yes—
11C2×#11758200C2212yes—
12#14519777C2211yescharacteristic, complemented
13#14519770—22no—
14#14519769C2211yescharacteristic, complemented
15#14519767—22no—
16#14519756C2212yes—
17C4×Dic122C2212yescomplemented
18#14519710C2212yescomplemented
19#14519708C2212yescomplemented
20C4⋊#92418C2212yescomplemented
21#14519700C2212yescomplemented
22#14519700C2212yescomplemented
23#14519698C2212yes—
24#14519698C2212yes—
25C22⋊#92418C2212yes—
26#14519688C2211yescharacteristic, complemented
27C4×#92418C2211yescharacteristic, complemented
28C22×D4×C61C2211yescharacteristic
29C4×D4×C61—22no—
30C4×D4×C61C2212yes—
31C4×D4×C61C2212yes—
32#117×C61C2211yescharacteristic
33#117×C61C2211yescharacteristic
34C2×C22⋊C4×C61—22no—
35C24×C61—21no—
36C2×D4×C61—24no—
37C2×D4×C61—21no—
38C2×D4×C61C2312yes—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61C2311yescharacteristic
42C2×Dic122C2312yes—
43C4⋊C4×C61D412yes—
44C4⋊C4×C61C2312yes—
45C22⋊C4×C61—21no—
46C22⋊C4×C61—22no—
47C22⋊C4×C61—22no—
48C22⋊C4×C61D412yes—
49C42×C61—21no—
50C42×C61C2311yescharacteristic
51C42×C61C2311yescharacteristic
52C22⋊Dic61—22no—
53#11758200—24no—
54#11758200—24no—
55C4⋊Dic61—22no—
56C4⋊Dic61C2312yes—
57#11758196—22no—
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—22no—
61C2×#92418C2312yes—
62C2×#92418C2312yes—
63C23×C61—24no—
64C23×C61—22no—
65C23×C61—82no—
66C23×C61C2×D411yescharacteristic
67D4×C61—24no—
68D4×C61—22no—
69D4×C61#4114yes—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—82no—
73C2×C4×C61—82no—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2411yescharacteristic
78C2×Dic61—22no—
79C2×Dic61—22no—
80Dic122—22no—
81Dic122—22no—
82#92418—22no—
83#92418—22no—
84C22×C61—21no—
85C22×C61—24no—
86C22×C61—22no—
87C22×C61—42no—
88C22×C61—42no—
89C22×C61—84no—
90C22×C61C22×D411yescharacteristic
91C4×C61—21no—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61—42no—
95C4×C61C2×#4112yes—
96Dic61—42no—
97Dic61—42no—
98#3123—611nomaximal, Sylow
99C2×C61—41no—
100C2×C61—44no—
101C2×C61#52511yescharacteristic
102C2×C61#57712yes—
103#541—611no—
104#518D6111yescharacteristic
105#485—612no—
106#478—612no—
107#461—612no—
108#450—612no—
109#440—612no—
110C4×SD16—612no—
111#433—611no—
112C61#312311yescharacteristic, complemented, Sylow
113C22×D4C2×D6111yescharacteristic
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—22no—
123C4×D4C2×D6112yes—
124C4×D4C2×D6112yes—
125#117C2×D6111yescharacteristic
126#117C2×D6111yescharacteristic
127C2×C22⋊C4—22no—
128#107—612no—
129#106—612no—
130C4⋊C8—612no—
131#103—612no—
132#103—612no—
133#102—612no—
134#102—612no—
135C22⋊C8—612no—
136#97—611no—
137C4×C8—611no—
138C24—21no—
139C2×Q8—612no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D6112yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D6111yescharacteristic
146SD16—1224no—
147SD16—1224no—
148C2×C8—612no—
149C2×C8—612no—
150C4⋊C4—612no—
151C4⋊C4—1222no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4C22⋊D6112yes—
156C4⋊C4C22×D6112yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—1222no—
161C22⋊C4C22⋊D6112yes—
162C42—21no—
163C42—1222no—
164C42C22×D6111yescharacteristic
165C42C22×D6111yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D6111yescharacteristic
170Q8—1222no—
171Q8—1222no—
172D4—24no—
173D4—22no—
174D4#1175822214yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4C2×C22⋊D6111yescharacteristic
182C2×C4C2×C22⋊D6112yes—
183C2×C4C2×C22⋊D6112yes—
184C2×C4C23×D6111yescharacteristic
185C8—1222no—
186C8—1222no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D6111yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—2442no—
199C4—2442no—
200C4C2×#1175822212yes—
201C2—41no—
202C2—44no—
203C2#1684027311yescharacteristic
204C2#1684057312yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#518C2
socleC22×C61C22×D4
hypercenter#518D61
hypocenterC61#3123
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #16840374C2semidirect
2. #16840103C2semidirect
3. #16840062C2semidirect
4. #16839967C2semidirect
6. #16839862C2semidirect
7. C4×#11758200C2semidirect
8. #16839823C2semidirect
12. #14519777C22semidirect
14. #14519769C22semidirect
17. C4×Dic122C22semidirect
18. #14519710C22semidirect
19. #14519708C22semidirect
20. C4⋊#92418C22semidirect
21. #14519700C22semidirect
22. #14519700C22semidirect
26. #14519688C22semidirect
27. C4×#92418C22semidirect
112. C61#3123semidirect