Finite Group Databasebeta

← #21449154

Subgroups — #21449154

Order 7808.

864 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11758222C211yesmaximal, characteristic
2C2×#14519760C212yesmaximal, complemented
3#16839682C212yesmaximal, complemented
4#16839679C212yesmaximal, complemented
5#16839641C212yesmaximal, complemented
6#16839633C214yesmaximal, complemented
7#16839625C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C61C211yesmaximal, characteristic, complemented
9C2×#11758222—24no—
10C2×#11758222—28no—
11C22×Dic122C2211yescharacteristic
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C22×C4×D61C2212yes—
15#14519760—28no—
16C2×#11758196C2214yes—
17C2×C22⋊Dic61C2212yes—
18C2×#11758198C2214yes—
19C2×#11758198C2214yes—
20#14519684C2212yes—
21#14519684C2214yes—
22#14519684C2212yes—
23C23×C4×C61C2211yescharacteristic
24C23×C4×C61C2211yescharacteristic
25C23×C4×C61C2211yescharacteristic
26C2×C4⋊C4×C61—24no—
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2212yes—
29C24×C61C2311yescharacteristic
30C23×D61C2312yes—
31C22×C4×C61—24no—
32C22×C4×C61—22no—
33C22×C4×C61—24no—
34C22×C4×C61—22no—
35C22×C4×C61—24no—
36C22×C4×C61D414yes—
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C2×C22⋊D61—24no—
42C2×C22⋊D61—24no—
43C2×C22⋊D61D418yes—
44C22×Dic61C2314yes—
45C22×Dic61C2312yes—
46#11758222—232no—
47C2×D244—24no—
48C2×D244—22no—
49C2×C4×D61—24no—
50C2×C4×D61—24no—
51C2×C4×D61—24no—
52C2×Dic122—22no—
53C2×Dic122—24no—
54C4⋊C4×C61—24no—
55C4⋊C4×C61—24no—
56C22⋊Dic61—24no—
57#11758198—28no—
58#11758198—28no—
59#11758196—28no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61C2×D414yes—
63C23×C61C2×D412yes—
64C23×C61C2411yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—24no—
68C22×D61—24no—
69C22×D61C2×D414yes—
70C2×C4×C61—28no—
71C2×C4×C61—28no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—24no—
77C2×C4×C61—22no—
78C2×C4×C61—44no—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D412yes—
81C2×C4×C61#4114yescomplemented
82C22⋊D61—216no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—24no—
86C2×Dic61—24no—
87C2×Dic61—24no—
88C2×Dic61C2×D414yes—
89D244—28no—
90C4×D61—216no—
91Dic122—28no—
92C22×C61—22no—
93C22×C61—22no—
94C22×C61—28no—
95C22×C61#12014yes—
96C22×C61C22×D412yes—
97C22×C61C22×D411yescharacteristic
98C22×C61C2×#4112yes—
99C22×C612−1+412yes—
100C2×D61—24no—
101C2×D61—28no—
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—44no—
105C4×C61—22no—
106C4×C61—22no—
107C4×C61—24no—
108C4×C61—42no—
109Dic61—24no—
110Dic61—44no—
111#2406—611nomaximal, Sylow
112C2×C61—24no—
113C2×C61C2×#12011yescharacteristic
114C2×C61#52511yescharacteristic
115C2×C61#53611yescharacteristic
116C2×C61#54714yes—
117D61—44no—
118C22×#41—611no—
119C2×#123—612no—
120C22×C4⋊C4D6111yescharacteristic, complemented
121#395—612no—
122#394—612no—
123#386—612no—
124#385—614no—
125#381—611no—
126C61#240611yescharacteristic, complemented, Sylow
127C2×#41—1228no—
128C2×#41—1224no—
129C22×Q8—611no—
130C22×D4—612no—
131C22×D4—611no—
132C23×C4—612no—
133C23×C4C2×D6111yescharacteristic
134C23×C4C2×D6111yescharacteristic
135C23×C4C2×D6111yescharacteristic
136#123—1228no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—614no—
139C2×C4⋊C4C2×D6112yes—
140C2×C4⋊C4C2×D6112yes—
141C2×C22⋊C4—612no—
142C2×C22⋊C4—614no—
143C2×C22⋊C4—614no—
144#95—612no—
145#95—612no—
146#95—614no—
147C24—612no—
148C24C22×D6111yescharacteristic
149#41—12232no—
150C2×Q8—1224no—
151C2×Q8—1222no—
152C2×D4—618no—
153C2×D4—1224no—
154C2×D4—1224no—
155C2×D4—1224no—
156C2×D4—1222no—
157C22×C4—24no—
158C22×C4—22no—
159C22×C4—24no—
160C22×C4—24no—
161C22×C4—22no—
162C22×C4—612no—
163C22×C4—614no—
164C22×C4—1224no—
165C22×C4—1224no—
166C22×C4—1224no—
167C22×C4C22⋊D6114yes—
168C22×C4C22×D6112yes—
169C22×C4C22×D6112yes—
170C22×C4C22×D6111yescharacteristic
171C22×C4C22×D6111yescharacteristic
172C4⋊C4—24no—
173C4⋊C4—24no—
174C4⋊C4—1228no—
175C22⋊C4—1228no—
176C22⋊C4—1224no—
177C22⋊C4—1228no—
178C23—22no—
179C23—22no—
180C23—614no—
181C23—1222no—
182C23—1222no—
183C23—1224no—
184C23—1224no—
185C23D4×D6114yes—
186C23C2×C22⋊D6112yes—
187C23C23×D6111yescharacteristic
188Q8—1228no—
189D4—1228no—
190D4—12216no—
191C2×C4—28no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—28no—
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—44no—
200C2×C4—614no—
201C2×C4—12216no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1224no—
205C2×C4—1224no—
206C2×C4—1224no—
207C2×C4#1175822214yescomplemented
208C2×C4C2×C22⋊D6112yes—
209C2×C4C2×C22⋊D6112yes—
210C22—22no—
211C22—22no—
212C22—28no—
213C22—1224no—
214C22—1228no—
215C22—2442no—
216C22—2442no—
217C22—2444no—
218C22#1451974514yes—
219C22C2×D4×D6112yes—
220C22C22×C22⋊D6111yescharacteristic
221C22C2×#1175822212yes—
222C22#1451982512yes—
223C4—22no—
224C4—22no—
225C4—24no—
226C4—42no—
227C4—1224no—
228C4—2444no—
229C2—24no—
230C2—2444no—
231C2C2×#1451974511yescharacteristic
232C2#1684027311yescharacteristic
233C2#1684033611yescharacteristic
234C2#1684041314yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C4⋊C4×C61C2
hypercenterC22×C4⋊C4D61
hypocenterC61#2406
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14519760C2semidirect
3. #16839682C2semidirect
4. #16839679C2semidirect
5. #16839641C2semidirect
6. #16839633C2semidirect
7. #16839625C2semidirect
8. C22×C4⋊C4×C61C2semidirect
81. C2×C4×C61#41semidirect
120. C22×C4⋊C4D61semidirect
126. C61#2406semidirect
207. C2×C4#11758222semidirect