Finite Group Databasebeta

← #21451300

Subgroups — #21451300

Order 7808.

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

normal subgroups only

This group has 596 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
1C22×#11758196C211yesmaximal, characteristic, complemented
2#16839700C212yesmaximal, complemented
3#16839676C212yesmaximal, complemented
4#16839656C214yesmaximal, complemented
5#16839642C212yesmaximal, complemented
6#16839642C212yesmaximal, complemented
7C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
8C2×#121×C61C211yesmaximal, characteristic
9C23×Dic61C2211yescharacteristic
10C23×Dic61C2211yescharacteristic
11C2×#11758196—24no—
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2214yes—
16C2×C22⋊Dic61C2214yes—
17C2×C4×Dic61C2212yes—
18#14519684C2212yes—
19#14519684C2214yes—
20#14519684C2214yes—
21C22×D4×C61C2212yes—
22C22×D4×C61C2211yescharacteristic
23C23×C4×C61C2211yescharacteristic
24#121×C61—24no—
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61C2212yes—
27C24×C61C2312yes—
28C24×C61C2311yescharacteristic
29C2×D4×C61—24no—
30C2×D4×C61—28no—
31C2×D4×C61—22no—
32C2×D4×C61—42no—
33C22×C4×C61—42no—
34C22×C4×C61D414yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61—22no—
39C22×Dic61—24no—
40C22×Dic61—22no—
41C22×Dic61—42no—
42C22×Dic61C2312yes—
43C22×Dic61C2314yes—
44C22×Dic61C2312yes—
45C4⋊C4×C61—22no—
46C22⋊C4×C61—24no—
47C22⋊Dic61—24no—
48C22⋊Dic61—28no—
49C22⋊Dic61—44no—
50#11758196—24no—
51#11758196—24no—
52C4×Dic61—42no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61—22no—
56C23×C61—24no—
57C23×C61—24no—
58C23×C61—24no—
59C23×C61C2×D412yes—
60C23×C61#4114yes—
61C23×C61C2411yescharacteristic
62D4×C61—44no—
63D4×C61—48no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—24no—
68C2×C4×C61—44no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D412yes—
71C2×Dic61—28no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—24no—
76C2×Dic61—24no—
77C2×Dic61—24no—
78C2×Dic61—24no—
79C2×Dic61—44no—
80C2×Dic61#4114yes—
81C22×C61—22no—
82C22×C61—22no—
83C22×C61—28no—
84C22×C61—42no—
85C22×C61—42no—
86C22×C61—42no—
87C22×C61—48no—
88C22×C61#12414yes—
89C22×C61C22×D411yescharacteristic
90C22×C61C2×#4112yes—
91C22×C61C2×#4112yes—
92C22×C61H(5,𝔽2)12yes—
93C4×C61—22no—
94C4×C61—22no—
95C4×C61—42no—
96Dic61—24no—
97Dic61—42no—
98Dic61—44no—
99#2591—611nomaximal, Sylow
100C2×C61—24no—
101C2×C61—82no—
102C2×C61#52511yescharacteristic
103C2×C61C2×#12411yescharacteristic
104C2×C61#53411yescharacteristic
105C2×C61#55314yes—
106C2×#121D6111yescharacteristic
107C22×C4⋊C4—611no—
108#400—612no—
109#394—612no—
110#388—614no—
111#386—612no—
112#386—612no—
113C4×C22⋊C4—611no—
114C61#259111yescharacteristic, complemented, Sylow
115C22×D4C2×D6112yes—
116C22×D4C2×D6111yescharacteristic
117C23×C4—611no—
118C23×C4—611no—
119C23×C4C2×D6111yescharacteristic
120#121—24no—
121C2×C4⋊C4—612no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—1224no—
124C2×C4⋊C4C2×D6111yescharacteristic
125C2×C22⋊C4—612no—
126C2×C22⋊C4—614no—
127C2×C22⋊C4—614no—
128C2×C22⋊C4C2×D6112yes—
129C2×C42—612no—
130#95—612no—
131#95—614no—
132#95—614no—
133C24C22×D6112yes—
134C24C22×D6111yescharacteristic
135C2×D4—28no—
136C2×D4—24no—
137C2×D4—22no—
138C2×D4—42no—
139C22×C4—42no—
140C22×C4—612no—
141C22×C4—614no—
142C22×C4—612no—
143C22×C4—1224no—
144C22×C4—1222no—
145C22×C4—1222no—
146C22×C4—2442no—
147C22×C4C22⋊D6114yes—
148C22×C4C22×D6112yes—
149C22×C4C22×D6111yescharacteristic
150C22×C4C22×D6111yescharacteristic
151C4⋊C4—22no—
152C4⋊C4—1224no—
153C4⋊C4—1224no—
154C22⋊C4—24no—
155C22⋊C4—1228no—
156C22⋊C4—1224no—
157C22⋊C4—2444no—
158C42—2442no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23—24no—
163C23—24no—
164C23—24no—
165C23#1175822414yes—
166C23C2×C22⋊D6112yes—
167C23C23×D6111yescharacteristic
168D4—44no—
169D4—48no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—44no—
175C2×C4—614no—
176C2×C4—1228no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1224no—
181C2×C4—1224no—
182C2×C4—1224no—
183C2×C4—1224no—
184C2×C4—2444no—
185C2×C4C2×C22⋊D6112yes—
186C2×C4C2×C22⋊D6112yes—
187C22—28no—
188C22—22no—
189C22—22no—
190C22—48no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22#1451976414yes—
195C22C22×C22⋊D6111yescharacteristic
196C22#41×D6112yes—
197C22C2×#1175822412yes—
198C22#1451982212yes—
199C4—22no—
200C4—22no—
201C4—42no—
202C4—1224no—
203C4—2444no—
204C4—2442no—
205C2—24no—
206C2—82no—
207C2#1684026911yescharacteristic
208C2C2×#1451976411yescharacteristic
209C2#1684032111yescharacteristic
210C2#1684045514yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2591
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#11758196C2semidirect
2. #16839700C2semidirect
3. #16839676C2semidirect
4. #16839656C2semidirect
5. #16839642C2semidirect
6. #16839642C2semidirect
7. C4×C22⋊Dic61C2semidirect
114. C61#2591semidirect