Finite Group Databasebeta

← #21450986

Subgroups — #21450986

Order 7808.

532 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 153 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×C4×D244C211yesmaximal, characteristic
2#16839701C212yesmaximal, complemented
3#16839679C212yesmaximal
4#16839652C214yesmaximal, complemented
5#16839619C212yesmaximal, complemented
6#16839619C212yesmaximal, complemented
7C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
8C2×#125×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C4×D61C2212yes—
11C4×D244—24no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2212yes—
14C2×#11758198C2212yes—
15C2×#11758198C2214yes—
16C2×#11758198C2214yes—
17C2×C4×Dic61C2212yes—
18#14519684C2212yes—
19#14519684C2214yes—
20#14519684C2214yes—
21#125×C61—24no—
22C2×C4⋊C4×C61C2212yes—
23C2×C4⋊C4×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2212yes—
26C2×C42×C61C2211yescharacteristic
27C23×D61C2312yes—
28C22×C4×C61C2312yes—
29C22×C4×C61C2312yes—
30C22×C4×C61C2311yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C22×C4×C61C2311yescharacteristic
33C22×Dic61C2312yes—
34C22×Dic61C2314yes—
35C2×D244—24no—
36C2×D244—22no—
37C2×C4×D61—24no—
38C2×C4×D61—24no—
39C2×C4×D61—24no—
40C4⋊C4×C61—24no—
41C4⋊C4×C61—24no—
42C4⋊C4×C61—22no—
43C4⋊C4×C61—22no—
44C42×C61D414yes—
45#11758198—28no—
46#11758198—24no—
47#11758198—44no—
48C4⋊Dic61—22no—
49C4⋊Dic61—24no—
50C4×Dic61—42no—
51C23×C61C2411yescharacteristic
52C22×D61—22no—
53C22×D61—22no—
54C22×D61—22no—
55C22×D61—22no—
56C22×D61—22no—
57C22×D61—22no—
58C22×D61#4114yes—
59C2×C4×C61—22no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—24no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61C2×D412yes—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×D412yes—
70C2×C4×C61#4114yes—
71C2×Dic61—22no—
72C2×Dic61—24no—
73C2×Dic61—24no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—24no—
77D244—28no—
78C4×D61—48no—
79C22×C61C22×D411yescharacteristic
80C22×C61C2×#4112yes—
81C22×C61C2×#4112yes—
82C22×C61H(5,𝔽2)11yescharacteristic
83C22×C612−1+411yescharacteristic
84C2×D61—24no—
85C2×D61—24no—
86C2×D61—24no—
87C2×D61—42no—
88C2×D61—42no—
89C2×D61—42no—
90C2×D61—42no—
91C4×C61—22no—
92C4×C61—22no—
93C4×C61—42no—
94C4×C61—42no—
95C4×C61#12414yes—
96Dic61—42no—
97Dic61—44no—
98#2562—611nomaximal, Sylow
99C2×C61#52511yescharacteristic
100C2×C61C2×#12411yescharacteristic
101C2×C61#53711yescharacteristic
102C2×C61#55212yes—
103C2×C61#55312yes—
104D61—44no—
105C2×#125D6111yescharacteristic, complemented
106C2×C4×D4—611no—
107#400—612no—
108#394—612no—
109#388—614no—
110#380—612no—
111#380—612no—
112C4×C4⋊C4—611no—
113C61#256211yescharacteristic, complemented, Sylow
114C22×D4—611no—
115C23×C4—612no—
116#125—24no—
117C4×D4—1224no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—612no—
120C2×C4⋊C4C2×D6111yescharacteristic
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C4⋊C4C2×D6112yes—
123C2×C4⋊C4C2×D6112yes—
124C2×C22⋊C4—612no—
125C2×C22⋊C4—614no—
126C2×C22⋊C4—614no—
127C2×C42—612no—
128C2×C42C2×D6111yescharacteristic
129#95—612no—
130#95—614no—
131#95—614no—
132C24—612no—
133C2×D4—1224no—
134C2×D4—1222no—
135C22×C4—612no—
136C22×C4—614no—
137C22×C4—1224no—
138C22×C4—1224no—
139C22×C4—1224no—
140C22×C4C22×D6112yes—
141C22×C4C22×D6112yes—
142C22×C4C22×D6111yescharacteristic
143C22×C4C22×D6111yescharacteristic
144C22×C4C22×D6111yescharacteristic
145C4⋊C4—24no—
146C4⋊C4—24no—
147C4⋊C4—22no—
148C4⋊C4—22no—
149C4⋊C4—1224no—
150C4⋊C4—1222no—
151C22⋊C4—1228no—
152C22⋊C4—1224no—
153C22⋊C4—2444no—
154C42—2442no—
155C42C22⋊D6114yes—
156C23—614no—
157C23—1222no—
158C23—1222no—
159C23—1222no—
160C23—1222no—
161C23—1222no—
162C23—1222no—
163C23C23×D6111yescharacteristic
164D4—1228no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—1222no—
174C2×C4—1224no—
175C2×C4—1224no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1224no—
179C2×C4—2448no—
180C2×C4#1175822614yes—
181C2×C4C2×C22⋊D6112yes—
182C2×C4C2×C22⋊D6112yes—
183C2×C4C2×C22⋊D6112yes—
184C22—1224no—
185C22—1224no—
186C22—1224no—
187C22—2442no—
188C22—2442no—
189C22—2442no—
190C22—2442no—
191C22C22×C22⋊D6111yescharacteristic
192C22#41×D6112yes—
193C22C2×#1175822612yes—
194C22#1451982311yescharacteristic
195C22#1451982411yescharacteristic
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—2444no—
201C4—2442no—
202C4#1451976614yes—
203C2—2444no—
204C2#1684026911yescharacteristic
205C2C2×#1451976611yescharacteristic
206C2#1684034011yescharacteristic
207C2#1684045012yes—
208C2#1684046512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#125×C61C2
hypercenterC2×#125D61
hypocenterC61#2562
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #16839701C2semidirect
4. #16839652C2semidirect
5. #16839619C2semidirect
6. #16839619C2semidirect
7. C4×C4⋊Dic61C2semidirect
8. C2×#125×C61C2semidirect
105. C2×#125D61semidirect
113. C61#2562semidirect