Finite Group Databasebeta

← #21453849

Subgroups — #21453849

Order 7808.

528 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14519756C211yesmaximal, characteristic, complemented
2C2×#14519751C211yesmaximal, characteristic
3#16839699C212yesmaximal, complemented
4#16839694C212yesmaximal, complemented
5#16839680C212yesmaximal, complemented
6#16839678C214yesmaximal, complemented
7#16839675C212yesmaximal, complemented
8C61×#381C211yesmaximal, characteristic, complemented
9C22×Dic122C2211yescharacteristic
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12#14519756—24no—
13#14519751—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2214yes—
17C2×#11758196C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2214yes—
21C2×#11758198C2214yes—
22#14519684C2214yes—
23C23×C4×C61C2211yescharacteristic
24C2×C22⋊C4×C61C2212yes—
25#95×C61C2212yes—
26#95×C61C2212yes—
27C24×C61C2311yescharacteristic
28C23×D61C2312yes—
29C22×C4×C61—42no—
30C22×C4×C61D414yes—
31C22×C4×C61C2314yes—
32C22×C4×C61C2311yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C2×C22⋊D61—24no—
35C2×C22⋊D61—44no—
36C22×Dic61C2312yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C2×D244—22no—
40C2×D244—42no—
41C2×Dic122—22no—
42C2×Dic122—42no—
43C22⋊C4×C61—42no—
44C22⋊Dic61—24no—
45#11758198—24no—
46#11758198—44no—
47#11758198—44no—
48C4⋊Dic61—22no—
49C4⋊Dic61—22no—
50C4⋊Dic61—44no—
51#11758196—24no—
52C23×C61—22no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61C2×D412yes—
56C23×C61C2411yescharacteristic
57C22×D61—22no—
58C22×D61—24no—
59C22×D61—24no—
60C22×D61—24no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—24no—
64C2×C4×C61—24no—
65C2×C4×C61—24no—
66C2×C4×C61—44no—
67C2×C4×C61C2×D412yes—
68C2×C4×C61C2×D412yes—
69C22⋊D61—48no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—24no—
75C2×Dic61—22no—
76C2×Dic61—24no—
77D244—44no—
78Dic122—44no—
79C22×C61—22no—
80C22×C61—22no—
81C22×C61—22no—
82C22×C61—44no—
83C22×C61C22×D411yescharacteristic
84C22×C61H(5,𝔽2)12yes—
85C22×C61H(5,𝔽2)12yes—
86C22×C612−1+412yes—
87C2×D61—42no—
88C2×D61—42no—
89C2×D61—42no—
90C2×D61—48no—
91C4×C61—22no—
92C4×C61—22no—
93C4×C61—44no—
94Dic61—42no—
95Dic61—42no—
96Dic61—42no—
97#2816—611nomaximal, Sylow
98C2×C61—42no—
99C2×C61#53411yescharacteristic
100C2×C61#53511yescharacteristic
101C2×C61#53611yescharacteristic
102C2×C61#56214yes—
103D61—82no—
104C2×C22⋊Q8—611no—
105C2×#121—611no—
106#399—612no—
107#398—612no—
108#394—614no—
109#394—612no—
110#393—612no—
111#381D6111yescharacteristic, complemented
112C61#281611yescharacteristic, complemented, Sylow
113C22×Q8—611no—
114C22×D4—612no—
115C22×D4—611no—
116C23×C4C2×D6111yescharacteristic
117C22⋊Q8—1224no—
118#121—1224no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4—612no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—614no—
123C2×C22⋊C4—612no—
124C2×C22⋊C4—612no—
125C2×C22⋊C4—614no—
126C2×C22⋊C4—614no—
127C2×C22⋊C4C2×D6112yes—
128#95—614no—
129#95C2×D6112yes—
130#95C2×D6112yes—
131C24—612no—
132C24C22×D6111yescharacteristic
133C2×Q8—1222no—
134C2×Q8—2442no—
135C2×D4—1224no—
136C2×D4—1222no—
137C2×D4—2442no—
138C2×D4—2444no—
139C22×C4—42no—
140C22×C4—612no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4D24414yes—
144C22×C4C22×D6114yes—
145C22×C4C22×D6111yescharacteristic
146C22×C4C22×D6111yescharacteristic
147C4⋊C4—1224no—
148C4⋊C4—1222no—
149C4⋊C4—1222no—
150C4⋊C4—2444no—
151C22⋊C4—42no—
152C22⋊C4—1224no—
153C22⋊C4—1224no—
154C22⋊C4—2444no—
155C22⋊C4—2444no—
156C23—22no—
157C23—22no—
158C23—22no—
159C23—1222no—
160C23—1224no—
161C23—1224no—
162C23—1224no—
163C23C2×D24412yes—
164C23C23×D6111yescharacteristic
165Q8—2444no—
166D4—2444no—
167D4—2448no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—44no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—1224no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1224no—
181C2×C4C2×D24412yes—
182C2×C4C2×D24412yes—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—44no—
187C22—2448no—
188C22—2442no—
189C22—2442no—
190C22—2442no—
191C22C22×D24411yescharacteristic
192C22#1451982212yes—
193C22#1451982312yes—
194C22#1451982412yes—
195C4—22no—
196C4—22no—
197C4—44no—
198C4—2442no—
199C4—2442no—
200C4—2442no—
201C2—42no—
202C2—4882no—
203C2#1684032411yescharacteristic
204C2#1684033111yescharacteristic
205C2#1684033811yescharacteristic
206C2#1684050914yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#381C2
hypercenter#381D61
hypocenterC61#2816
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#14519756C2semidirect
3. #16839699C2semidirect
4. #16839694C2semidirect
5. #16839680C2semidirect
6. #16839678C2semidirect
7. #16839675C2semidirect
8. C61×#381C2semidirect
111. #381D61semidirect
112. C61#2816semidirect