Finite Group Databasebeta

← #21451294

Subgroups — #21451294

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
1C2×#14519751C211yesmaximal, characteristic
2C22×#11758196C211yesmaximal, characteristic, complemented
3#16839702C212yesmaximal, complemented
4#16839680C212yesmaximal, complemented
5#16839653C214yesmaximal, complemented
6#16839639C212yesmaximal, complemented
7#16839639C212yesmaximal, complemented
8C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C22⋊D61C2212yes—
11C23×Dic61C2211yescharacteristic
12C23×Dic61C2211yescharacteristic
13#14519751—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196—24no—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758198C2214yes—
19C2×#11758198C2212yes—
20C2×#11758198C2214yes—
21#14519684C2214yes—
22#14519684C2214yes—
23C23×C4×C61C2211yescharacteristic
24C2×C22⋊C4×C61C2212yes—
25C2×C42×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—28no—
36C22×Dic61—22no—
37C22×Dic61—24no—
38C22×Dic61—22no—
39C22×Dic61—42no—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C2×D244—22no—
44C2×D244—42no—
45C22⋊C4×C61—24no—
46C42×C61—42no—
47#11758198—24no—
48#11758198—28no—
49#11758198—44no—
50C4⋊Dic61—22no—
51#11758196—24no—
52#11758196—24no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61C2×D412yes—
56C23×C61#4114yes—
57C23×C61C2411yescharacteristic
58C22×D61—22no—
59C22×D61—24no—
60C22×D61—24no—
61C22×D61—24no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—24no—
65C2×C4×C61—24no—
66C2×C4×C61—24no—
67C2×C4×C61—44no—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×D412yes—
70C22⋊D61—48no—
71C2×Dic61—28no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—24no—
77C2×Dic61—24no—
78C2×Dic61—44no—
79C2×Dic61#4114yes—
80D244—44no—
81C22×C61—22no—
82C22×C61—22no—
83C22×C61—28no—
84C22×C61#12414yes—
85C22×C61C22×D411yescharacteristic
86C22×C61C2×#4112yes—
87C22×C61C2×#4112yes—
88C22×C61H(5,𝔽2)12yes—
89C2×D61—42no—
90C2×D61—42no—
91C2×D61—42no—
92C2×D61—48no—
93C4×C61—22no—
94C4×C61—22no—
95C4×C61—44no—
96Dic61—24no—
97Dic61—42no—
98Dic61—42no—
99#2591—611nomaximal, Sylow
100C2×C61—24no—
101C2×C61#52511yescharacteristic
102C2×C61C2×#12411yescharacteristic
103C2×C61#53411yescharacteristic
104C2×C61#55314yes—
105D61—82no—
106C2×#121—611no—
107C22×C4⋊C4—611no—
108#400—612no—
109#394—612no—
110#388—614no—
111#386—612no—
112#386—612no—
113C4×C22⋊C4D6111yescharacteristic, complemented
114C61#259111yescharacteristic, complemented, Sylow
115C22×D4—612no—
116C22×D4—611no—
117C23×C4—611no—
118C23×C4—611no—
119C23×C4C2×D6111yescharacteristic
120#121—1224no—
121C2×C4⋊C4—612no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—611no—
124C2×C4⋊C4—1224no—
125C2×C22⋊C4—612no—
126C2×C22⋊C4—614no—
127C2×C22⋊C4—614no—
128C2×C22⋊C4C2×D6112yes—
129C2×C42C2×D6112yes—
130#95—614no—
131#95—614no—
132#95C2×D6112yes—
133C24—612no—
134C24C22×D6111yescharacteristic
135C2×D4—1224no—
136C2×D4—1228no—
137C2×D4—1222no—
138C2×D4—2442no—
139C22×C4—42no—
140C22×C4—612no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4—1224no—
144C22×C4—1222no—
145C22×C4—1222no—
146C22×C4—2442no—
147C22×C4D24414yes—
148C22×C4C22×D6114yes—
149C22×C4C22×D6111yescharacteristic
150C22×C4C22×D6111yescharacteristic
151C4⋊C4—1224no—
152C4⋊C4—1224no—
153C4⋊C4—1222no—
154C22⋊C4—24no—
155C22⋊C4—1228no—
156C22⋊C4—1224no—
157C22⋊C4—2444no—
158C42—42no—
159C23—22no—
160C23—22no—
161C23—1222no—
162C23—1224no—
163C23—1224no—
164C23—1224no—
165C23C2×D24412yes—
166C23#1175822214yes—
167C23C23×D6111yescharacteristic
168D4—2444no—
169D4—2448no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—24no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—614no—
177C2×C4—1228no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1224no—
183C2×C4—1224no—
184C2×C4—2444no—
185C2×C4C2×D24412yes—
186C2×C4C2×D24412yes—
187C22—28no—
188C22—22no—
189C22—22no—
190C22—2448no—
191C22—2442no—
192C22—2442no—
193C22—2442no—
194C22#1451976514yes—
195C22C22×D24411yescharacteristic
196C22#41×D6112yes—
197C22C2×#1175822212yes—
198C22#1451982212yes—
199C4—22no—
200C4—22no—
201C4—44no—
202C4—1224no—
203C4—2442no—
204C4—2442no—
205C2—24no—
206C2—4882no—
207C2#1684027411yescharacteristic
208C2C2×#1451976511yescharacteristic
209C2#1684032411yescharacteristic
210C2#1684046114yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC4×C22⋊C4×C61C2
hypercenterC4×C22⋊C4D61
hypocenterC61#2591
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#11758196C2semidirect
3. #16839702C2semidirect
4. #16839680C2semidirect
5. #16839653C2semidirect
6. #16839639C2semidirect
7. #16839639C2semidirect
8. C4×C22⋊C4×C61C2semidirect
113. C4×C22⋊C4D61semidirect
114. C61#2591semidirect