Finite Group Databasebeta

← #21456066

Subgroups — #21456066

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#16840236C211yesmaximal, characteristic
2#16840100C212yesmaximal, complemented
3#16840059C212yesmaximal, complemented
4#16839964C212yesmaximal, complemented
5#16839912C212yesmaximal
6#16839860C212yesmaximal, complemented
7C4×#11758201C212yesmaximal, complemented
8#16839823C211yesmaximal, characteristic, complemented
9C61×#541C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C2×#11758201C2212yes—
12C2×#11758201C2212yes—
13C4×D244C2212yes—
14C4×D244C2212yes—
15#14519739—22no—
16#14519736C2211yescharacteristic
17C22⋊C4×D61—22no—
18#14519710C2212yescomplemented
19#14519708C2212yescomplemented
20C4⋊#92418C2212yescomplemented
21#14519701C2212yescomplemented
22#14519701C2212yescomplemented
23#14519697C2212yes—
24#14519697C2212yes—
25C22⋊#92418C2212yes—
26#14519688C2211yescharacteristic, complemented
27C4×#92418C2211yescharacteristic, complemented
28C4⋊Q8×C61C2211yescharacteristic, complemented
29#126×C61—22no—
30#125×C61—22no—
31#125×C61C2211yescharacteristic, complemented
32C22⋊Q8×C61C2212yes—
33C4×Q8×C61C2212yescomplemented
34#117×C61C2211yescharacteristic
35C23×D61—21no—
36C2×Q8×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C2×D244—21no—
39C2×D244—24no—
40C2×D244C2312yes—
41C2×C4×D61—22no—
42C2×C4×D61—22no—
43C4⋊C4×C61—22no—
44C4⋊C4×C61—22no—
45C4⋊C4×C61—22no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61D412yes—
48C4⋊C4×C61C2312yes—
49C22⋊C4×C61—22no—
50C22⋊C4×C61D412yes—
51C42×C61—22no—
52C42×C61C2311yescharacteristic
53C42×C61C2311yescharacteristic
54C22⋊Dic61—21no—
55#11758201—24no—
56#11758201—24no—
57#11758198—22no—
58#11758198—22no—
59C4⋊Dic61C2312yes—
60C4×Dic61—21no—
61C2×#92418C2312yes—
62C2×#92418C2312yes—
63C23×C61C2×D411yescharacteristic
64C22×D61—22no—
65C22×D61—24no—
66C22×D61—82no—
67Q8×C61—22no—
68Q8×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2411yescharacteristic
76C2×Dic61—22no—
77D244—24no—
78D244—22no—
79D244#4114yes—
80C4×D61—82no—
81C4×D61—82no—
82#92418—22no—
83#92418—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×C61—42no—
95C4×C61—42no—
96C4×C61C2×#4112yes—
97Dic61—42no—
98#3123—611nomaximal, Sylow
99C2×C61—41no—
100C2×C61#52511yescharacteristic
101C2×C61#57712yes—
102D61—44no—
103#541D6111yescharacteristic, complemented
104#518—611no—
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×D4—611no—
114C2×SD16—612no—
115C2×SD16—612no—
116C4⋊Q8C2×D6111yescharacteristic, complemented
117#126—22no—
118#125—22no—
119#125C2×D6111yescharacteristic, complemented
120C22⋊Q8C2×D6112yes—
121C4×Q8C2×D6112yescomplemented
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⋊C8—612no—
131#103—612no—
132#103—612no—
133#102—612no—
134#102—612no—
135C22⋊C8—612no—
136#97—611no—
137C4×C8—611no—
138C24—1221no—
139C2×Q8C22×D6112yes—
140C2×D4—612no—
141C2×D4—1224no—
142C2×D4—1221no—
143C22×C4—1222no—
144C22×C4—1222no—
145C22×C4C22×D6111yescharacteristic
146SD16—1224no—
147SD16—1224no—
148C2×C8—612no—
149C2×C8—612no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—612no—
155C4⋊C4C22⋊D6112yes—
156C4⋊C4C22×D6112yes—
157C22⋊C4—22no—
158C22⋊C4—1221no—
159C22⋊C4—1222no—
160C22⋊C4—1222no—
161C22⋊C4C22⋊D6112yes—
162C42—22no—
163C42—1221no—
164C42C22×D6111yescharacteristic
165C42C22×D6111yescharacteristic
166C23—1224no—
167C23—1222no—
168C23—4882no—
169C23C2×C22⋊D6111yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—614no—
173D4—1224no—
174D4—1222no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—1222no—
179C2×C4—4882no—
180C2×C4—4882no—
181C2×C4C2×C22⋊D6112yes—
182C2×C4C2×C22⋊D6111yescharacteristic
183C2×C4C2×C22⋊D6112yes—
184C2×C4C23×D6111yescharacteristic
185C8—1222no—
186C8—1222no—
187C22—21no—
188C22—22no—
189C22—1224no—
190C22—4884no—
191C22—2442no—
192C22—2442no—
193C22C22×C22⋊D6111yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—2442no—
200C4#41×D6112yes—
201C2—41no—
202C2—2444no—
203C2#1684026911yescharacteristic
204C2#1684057012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#541C2
socleC22×C61C22×D4
hypercenter#541D61
hypocenterC61#3123
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #16840100C2semidirect
3. #16840059C2semidirect
4. #16839964C2semidirect
6. #16839860C2semidirect
7. C4×#11758201C2semidirect
8. #16839823C2semidirect
9. C61×#541C2semidirect
18. #14519710C22semidirect
19. #14519708C22semidirect
20. C4⋊#92418C22semidirect
21. #14519701C22semidirect
22. #14519701C22semidirect
26. #14519688C22semidirect
27. C4×#92418C22semidirect
28. C4⋊Q8×C61C22semidirect
31. #125×C61C22semidirect
33. C4×Q8×C61C22semidirect
103. #541D61semidirect
112. C61#3123semidirect
116. C4⋊Q8C2×D61semidirect
119. #125C2×D61semidirect
121. C4×Q8C2×D61semidirect