Finite Group Databasebeta

← #21451177

Subgroups — #21451177

Order 7808.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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#16839697C212yesmaximal, complemented
3#16839673C212yesmaximal, complemented
4#16839664C212yesmaximal
5#16839660C212yesmaximal, complemented
6#16839633C214yesmaximal, complemented
7#16839628C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C4×D61C2212yes—
11C4×D244—24no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2212yes—
14C2×#11758196C2214yes—
15C2×#11758198C2212yes—
16C2×#11758198C2214yes—
17C2×#11758198C2214yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2214yes—
21C22×Q8×C61C2211yescharacteristic
22C4×Q8×C61—24no—
23C2×C4⋊C4×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2212yes—
25C2×C42×C61C2212yes—
26C2×C42×C61C2211yescharacteristic
27C23×D61C2312yes—
28C2×Q8×C61—22no—
29C2×Q8×C61—24no—
30C22×C4×C61C2312yes—
31C22×C4×C61C2311yescharacteristic
32C22×C4×C61C2311yescharacteristic
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61C2312yes—
36C22×Dic61C2314yes—
37C2×D244—22no—
38C2×D244—22no—
39C2×D244Q814yescomplemented
40C2×C4×D61—24no—
41C2×C4×D61—44no—
42C4⋊C4×C61—24no—
43C4⋊C4×C61—22no—
44C42×C61—24no—
45C42×C61D414yes—
46#11758198—24no—
47#11758198—28no—
48#11758198—44no—
49C4⋊Dic61—22no—
50C4⋊Dic61—24no—
51#11758196—44no—
52C23×C61C2411yescharacteristic
53C22×D61—22no—
54C22×D61—24no—
55C22×D61—22no—
56C22×D61—24no—
57C22×D61C2×Q814yes—
58Q8×C61—28no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61C2×D412yes—
67C2×C4×C61C2×D412yes—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×Q812yes—
70C2×C4×C61#4114yes—
71C2×C4×C61#4112yes—
72C2×Dic61—22no—
73C2×Dic61—24no—
74C2×Dic61—24no—
75C2×Dic61—24no—
76C2×Dic61—24no—
77D244—28no—
78C4×D61—48no—
79C22×C61C22×D411yescharacteristic
80C22×C61C22×Q811yescharacteristic
81C22×C61C2×#4112yes—
82C22×C61C2×#4111yescharacteristic
83C22×C61H(5,𝔽2)12yes—
84C2×D61—24no—
85C2×D61—28no—
86C2×D61—42no—
87C2×D61—42no—
88C2×D61—44no—
89C4×C61—22no—
90C4×C61—24no—
91C4×C61—22no—
92C4×C61—42no—
93C4×C61C22⋊Q814yes—
94Dic61—42no—
95Dic61—44no—
96#2580—611nomaximal, Sylow
97C2×C61C2×C22⋊Q811yescharacteristic
98C2×C61#52511yescharacteristic
99C2×C61#53511yescharacteristic
100C2×C61#55412yes—
101C2×C61#55912yes—
102D61—44no—
103C2×C4×Q8D6111yescharacteristic, complemented
104C2×C4×D4—611no—
105#399—612no—
106#393—612no—
107#390—612no—
108#389—612no—
109#385—614no—
110#382—611no—
111C61#258011yescharacteristic, complemented, Sylow
112C22×Q8C2×D6111yescharacteristic
113C22×D4—611no—
114C23×C4—612no—
115C4×Q8—24no—
116C4×D4—1224no—
117C2×C4⋊C4—611no—
118C2×C4⋊C4—612no—
119C2×C4⋊C4—614no—
120C2×C4⋊C4C2×D6112yes—
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C22⋊C4—612no—
123C2×C22⋊C4—614no—
124C2×C22⋊C4—614no—
125C2×C42C2×D6112yes—
126C2×C42C2×D6111yescharacteristic
127#95—612no—
128#95—612no—
129#95—614no—
130C24—612no—
131C2×Q8—24no—
132C2×Q8—22no—
133C2×D4—614no—
134C2×D4—1222no—
135C2×D4—1222no—
136C22×C4—614no—
137C22×C4—612no—
138C22×C4—1224no—
139C22×C4—2444no—
140C22×C4C22×D6112yes—
141C22×C4C22×D6112yes—
142C22×C4C22×D6111yescharacteristic
143C22×C4C22×D6111yescharacteristic
144C22×C4C22×D6111yescharacteristic
145C4⋊C4—24no—
146C4⋊C4—22no—
147C4⋊C4—1224no—
148C4⋊C4—1222no—
149C4⋊C4—2444no—
150C22⋊C4—1228no—
151C22⋊C4—1224no—
152C22⋊C4—2444no—
153C42—24no—
154C42C22⋊D6114yes—
155C23—614no—
156C23—1222no—
157C23—1224no—
158C23—1222no—
159C23—1224no—
160C23C23×D6111yescharacteristic
161Q8—28no—
162D4—1228no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—1222no—
171C2×C4—1224no—
172C2×C4—1224no—
173C2×C4—1224no—
174C2×C4—1224no—
175C2×C4—2448no—
176C2×C4#1175822214yes—
177C2×C4Q8×D6112yes—
178C2×C4#1175822612yes—
179C2×C4C2×C22⋊D6112yes—
180C2×C4C2×C22⋊D6112yes—
181C2×C4C2×C22⋊D6112yes—
182C22—1228no—
183C22—1224no—
184C22—2444no—
185C22—2442no—
186C22—2442no—
187C22C22×C22⋊D6111yescharacteristic
188C22C2×Q8×D6111yescharacteristic
189C22C2×#1175822212yes—
190C22C2×#1175822611yescharacteristic
191C22#1451982312yes—
192C4—24no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—2444no—
197C4—2442no—
198C4#1451975314yes—
199C2—2444no—
200C2C2×#1451975311yescharacteristic
201C2#1684027311yescharacteristic
202C2#1684032611yescharacteristic
203C2#1684047212yes—
204C2#1684049712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×Q8×C61C2
hypercenterC2×C4×Q8D61
hypocenterC61#2580
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #16839697C2semidirect
3. #16839673C2semidirect
5. #16839660C2semidirect
6. #16839633C2semidirect
7. #16839628C2semidirect
8. C2×C4×Q8×C61C2semidirect
39. C2×D244Q8semidirect
103. C2×C4×Q8D61semidirect
111. C61#2580semidirect