Finite Group Databasebeta

← #21450281

Subgroups — #21450281

Order 7808.

568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 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
2C2×#14519736C211yesmaximal, characteristic, complemented
3#16839678C214yesmaximal, complemented
4#16839664C211yesmaximal, characteristic, complemented
5#16839664C211yesmaximal, characteristic, complemented
6#16839654C214yesmaximal, complemented
7#16839632C211yesmaximal, characteristic, complemented
8#16839628C211yesmaximal, characteristic, complemented
9C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12#14519751—24no—
13#14519736—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2214yes—
18C2×C22⋊Dic61C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2214yes—
21C2×#11758198C2214yes—
22C2×C4×Dic61C2212yes—
23#14519684C2214yes—
24C23×C4×C61C2211yescharacteristic
25C2×C22⋊C4×C61C2212yes—
26C2×C42×C61C2211yescharacteristic
27C2×C42×C61C2211yescharacteristic
28#95×C61C2212yes—
29C24×C61C2311yescharacteristic
30C23×D61C2312yes—
31C22×C4×C61—22no—
32C22×C4×C61—22no—
33C22×C4×C61D414yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—24no—
39C2×C22⋊D61—44no—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C2×D244—22no—
44C2×D244—22no—
45C2×D244—22no—
46C22⋊C4×C61—24no—
47C42×C61—22no—
48C42×C61—22no—
49C22⋊Dic61—24no—
50#11758198—24no—
51#11758198—28no—
52#11758198—44no—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61—44no—
57C4×Dic61—24no—
58C23×C61—22no—
59C23×C61—21no—
60C23×C61—21no—
61C23×C61—22no—
62C23×C61C2×D412yes—
63C23×C61C2411yescharacteristic
64C22×D61—22no—
65C22×D61—24no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—24no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—28no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D412yes—
79C2×C4×C61#4114yes—
80C2×C4×C61#4112yes—
81C2×C4×C61#4112yes—
82C22⋊D61—48no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—24no—
87C2×Dic61—24no—
88C2×Dic61—24no—
89D244—44no—
90C22×C61—22no—
91C22×C61—22no—
92C22×C61—22no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61C22×D411yescharacteristic
96C22×C61C2×#4111yescharacteristic
97C22×C61C2×#4111yescharacteristic
98C22×C61C2×#4112yes—
99C22×C61H(5,𝔽2)12yes—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—44no—
104C2×D61—44no—
105C4×C61—22no—
106C4×C61—24no—
107C4×C61—42no—
108C4×C61#12314yes—
109Dic61—42no—
110Dic61—42no—
111Dic61—42no—
112#2500—611nomaximal, Sylow
113C2×C61—42no—
114C2×C61C2×#12311yescharacteristic
115C2×C61#53211yescharacteristic
116C2×C61#53511yescharacteristic
117C2×C61#55312yes—
118C2×C61#55512yes—
119D61—82no—
120C2×#121—611no—
121C2×#117—611no—
122#394—614no—
123#390—611no—
124#390—611no—
125#388—614no—
126#384—611no—
127#382—611no—
128C4×C22⋊C4D6111yescharacteristic, complemented
129C61#250011yescharacteristic, complemented, Sylow
130C22×D4—612no—
131C22×D4—611no—
132C23×C4C2×D6111yescharacteristic
133#121—1224no—
134#117—1224no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4—611no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—614no—
139C2×C22⋊C4—612no—
140C2×C22⋊C4—612no—
141C2×C22⋊C4—614no—
142C2×C22⋊C4—614no—
143C2×C22⋊C4C2×D6112yes—
144C2×C42—612no—
145C2×C42C2×D6111yescharacteristic
146C2×C42C2×D6111yescharacteristic
147#95—614no—
148#95C2×D6112yes—
149C24—612no—
150C24C22×D6111yescharacteristic
151C2×D4—1224no—
152C2×D4—1222no—
153C2×D4—1222no—
154C2×D4—1222no—
155C2×D4—2444no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—612no—
159C22×C4—612no—
160C22×C4—612no—
161C22×C4D24414yes—
162C22×C4C22×D6112yes—
163C22×C4C22×D6111yescharacteristic
164C22×C4C22×D6112yes—
165C22×C4C22×D6111yescharacteristic
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C4⋊C4—2444no—
170C22⋊C4—24no—
171C22⋊C4—1224no—
172C22⋊C4—1224no—
173C22⋊C4—1228no—
174C22⋊C4—2444no—
175C42—22no—
176C42—22no—
177C42—1224no—
178C23—21no—
179C23—21no—
180C23—22no—
181C23—22no—
182C23—1222no—
183C23—1222no—
184C23—1222no—
185C23—1224no—
186C23—1224no—
187C23C2×D24412yes—
188C23C23×D6111yescharacteristic
189D4—2448no—
190D4—2444no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—28no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1224no—
203C2×C4—1224no—
204C2×C4—1224no—
205C2×C4C2×D24412yes—
206C2×C4C2×D24412yes—
207C2×C4#1175822214yes—
208C2×C4#1175822412yes—
209C2×C4#1175822412yes—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—42no—
214C22—42no—
215C22—2444no—
216C22—2444no—
217C22—2442no—
218C22—2442no—
219C22—2442no—
220C22C22×D24411yescharacteristic
221C22C2×#1175822411yescharacteristic
222C22C2×#1175822411yescharacteristic
223C22C2×#1175822212yes—
224C22#1451982312yes—
225C4—24no—
226C4—22no—
227C4—42no—
228C4—2442no—
229C4—2442no—
230C4—2442no—
231C4#1451976114yes—
232C2—42no—
233C2—4882no—
234C2C2×#1451976111yescharacteristic
235C2#1684031211yescharacteristic
236C2#1684033111yescharacteristic
237C2#1684045812yes—
238C2#1684047712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC4×C22⋊C4×C61C2
hypercenterC4×C22⋊C4D61
hypocenterC61#2500
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14519736C2semidirect
3. #16839678C2semidirect
4. #16839664C2semidirect
5. #16839664C2semidirect
6. #16839654C2semidirect
7. #16839632C2semidirect
8. #16839628C2semidirect
9. C4×C22⋊C4×C61C2semidirect
128. C4×C22⋊C4D61semidirect
129. C61#2500semidirect