Finite Group Databasebeta

← #21456110

Subgroups — #21456110

Order 7808.

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

normal subgroups only

This group has 382 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#16840367C211yesmaximal, characteristic
2#16840086C212yesmaximal, complemented
3#16840069C212yesmaximal, complemented
4#16839962C212yesmaximal, complemented
5#16839901C212yesmaximal, complemented
6#16839860C212yesmaximal, complemented
7C4×#11758201C212yesmaximal, complemented
8#16839823C211yesmaximal, characteristic, complemented
9C61×#519C211yesmaximal, characteristic, complemented
10C2×#11758201C2212yes—
11C2×#11758201C2212yes—
12#14519774C2211yescharacteristic
13#14519769C2211yescharacteristic
14#14519762—22no—
15#14519751C2212yes—
16#14519750—22no—
17C4×D244C2212yes—
18#14519710C2212yes—
19#14519708C2212yes—
20C4⋊#92418C2212yes—
21#14519701C2212yes—
22#14519701C2212yes—
23#14519697C2212yes—
24#14519697C2212yes—
25C22⋊#92418C2212yes—
26#14519688C2211yescharacteristic
27C4×#92418C2211yescharacteristic
28C22×Q8×C61C2211yescharacteristic
29C4×Q8×C61—22no—
30C4×Q8×C61C2212yes—
31C4×Q8×C61C2212yes—
32#117×C61—22no—
33#117×C61C2211yescharacteristic
34#117×C61C2211yescharacteristic
35C2×Q8×C61—24no—
36C2×Q8×C61—21no—
37C2×Q8×C61C2312yes—
38C22×C4×C61—21no—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—22no—
41C2×D244—22no—
42C2×D244C2312yes—
43C2×C4×D61—22no—
44C4⋊C4×C61—22no—
45C4⋊C4×C61—22no—
46C4⋊C4×C61D412yes—
47C4⋊C4×C61C2312yes—
48C22⋊C4×C61—21no—
49C22⋊C4×C61D412yes—
50C42×C61—22no—
51C42×C61—22no—
52C42×C61—21no—
53C42×C61C2311yescharacteristic
54C42×C61C2311yescharacteristic
55#11758201—24no—
56#11758201—24no—
57#11758198—22no—
58#11758198—22no—
59C4⋊Dic61C2312yes—
60#11758196—22no—
61C2×#92418C2312yes—
62C2×#92418C2312yes—
63C23×C61C2×D411yescharacteristic
64C22×D61—22no—
65Q8×C61—24no—
66Q8×C61—22no—
67Q8×C61#4114yes—
68C2×C4×C61—24no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D412yes—
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2411yescharacteristic
76C22⋊D61—82no—
77C2×Dic61—22no—
78D244—22no—
79D244—22no—
80D244—82no—
81C4×D61—82no—
82#92418—22no—
83#92418—22no—
84C22×C61—21no—
85C22×C61—22no—
86C22×C61C22×D411yescharacteristic
87C2×D61—42no—
88C2×D61—42no—
89C2×D61—42no—
90C4×C61—24no—
91C4×C61—21no—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61—42no—
95C4×C61C2×#4112yes—
96Dic61—42no—
97#3126—611nomaximal, Sylow
98C2×C61—41no—
99C2×C61#52511yescharacteristic
100C2×C61#57712yes—
101D61—82no—
102#540—611no—
103#519D6111yescharacteristic, complemented
104#482—612no—
105#479—612no—
106#460—612no—
107#448—612no—
108#440—612no—
109C4×SD16—612no—
110#433—611no—
111C61#312611yescharacteristic, complemented, Sylow
112C22×Q8C2×D6111yescharacteristic
113C2×SD16—612no—
114C2×SD16—612no—
115#127—611no—
116#125—611no—
117#123—1222no—
118#121—612no—
119#121—1222no—
120C4×Q8—22no—
121C4×Q8C2×D6112yes—
122C4×Q8C2×D6112yes—
123C4×D4—612no—
124#117—22no—
125#117C2×D6111yescharacteristic
126#117C2×D6111yescharacteristic
127#107—612no—
128#106—612no—
129C4⋊C8—612no—
130#103—612no—
131#103—612no—
132#102—612no—
133#102—612no—
134C22⋊C8—612no—
135#97—611no—
136C4×C8—611no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8C22×D6112yes—
140C2×D4—612no—
141C2×D4—1222no—
142C2×D4—1222no—
143C22×C4—21no—
144C22×C4—1222no—
145C22×C4C22×D6111yescharacteristic
146SD16—1224no—
147SD16—1224no—
148C2×C8—612no—
149C2×C8—612no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—612no—
153C4⋊C4—1222no—
154C4⋊C4C22⋊D6112yes—
155C4⋊C4C22×D6112yes—
156C22⋊C4—21no—
157C22⋊C4—1222no—
158C22⋊C4—1222no—
159C22⋊C4C22⋊D6112yes—
160C42—22no—
161C42—22no—
162C42—21no—
163C42C22×D6111yescharacteristic
164C42C22×D6111yescharacteristic
165C23—1222no—
166C23C2×C22⋊D6111yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#1175822214yes—
170D4—1222no—
171D4—1222no—
172D4—4882no—
173D4—4882no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—1222no—
179C2×C4—4882no—
180C2×C4C2×C22⋊D6112yes—
181C2×C4C2×C22⋊D6112yes—
182C2×C4C2×C22⋊D6111yescharacteristic
183C2×C4C23×D6111yescharacteristic
184C8—1222no—
185C8—1222no—
186C22—21no—
187C22—22no—
188C22—2442no—
189C22—2442no—
190C22—2442no—
191C22C22×C22⋊D6111yescharacteristic
192C4—24no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—2442no—
198C4C2×#1175822212yes—
199C2—41no—
200C2—4882no—
201C2#1684027311yescharacteristic
202C2#1684057012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#519C2
socleC22×C61C22×D4
hypercenter#519D61
hypocenterC61#3126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #16840086C2semidirect
3. #16840069C2semidirect
4. #16839962C2semidirect
5. #16839901C2semidirect
6. #16839860C2semidirect
7. C4×#11758201C2semidirect
8. #16839823C2semidirect
9. C61×#519C2semidirect
103. #519D61semidirect
111. C61#3126semidirect