Finite Group Databasebeta

← #21444837

Subgroups — #21444837

Order 7808.

288 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#16840320C211yesmaximal, characteristic
2#16840080C211yesmaximal, characteristic, complemented
3#16839697C211yesmaximal, characteristic, complemented
4#16839497C211yesmaximal, characteristic, complemented
5#16839496C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic, complemented
7C61×#481C211yesmaximal, characteristic, complemented
8C2×D4×D61—21no—
9#14519762—21no—
10#14519759—21no—
11#14519751C2211yescharacteristic
12#14519749—21no—
13#14519747—21no—
14#14519745—21no—
15C2×#11758196—21no—
16C2×#11758198—21no—
17C2×#11758198C2211yescharacteristic
18#14519708—21no—
19#14519697—21no—
20C22⋊#92418C2211yescharacteristic, complemented
21#14519684C2211yescharacteristic, complemented
22#121×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic, complemented
24#106×C61—21no—
25#102×C61—21no—
26C22⋊C8×C61C2211yescharacteristic, complemented
27C23×D61—21no—
28C23×D61D411yescharacteristic
29C2×D4×C61—21no—
30C2×D4×C61D411yescharacteristic
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35C2×C22⋊D61—21no—
36C22×Dic61—21no—
37C22×Dic61D411yescharacteristic
38D4×D61—42no—
39D4×D61—42no—
40C2×D244—21no—
41C2×D244D411yescharacteristic
42C2×C4×D61—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61D411yescharacteristic
47C22⋊C4×C61—21no—
48C22⋊Dic61—21no—
49#11758198—21no—
50#11758198—21no—
51#11758198—21no—
52#11758198—21no—
53#11758198—42no—
54C4⋊Dic61D411yescharacteristic
55#11758196—21no—
56#11758196—42no—
57C2×#92418—21no—
58C23×C61—21no—
59C23×C61C2×D411yescharacteristic
60C22×D61—21no—
61C22×D61—21no—
62C22×D61—21no—
63C22×D61—42no—
64C22×D61—41no—
65C22×D61—41no—
66C22×D61—81no—
67C22×D61—81no—
68C22×D61SD1612yes—
69D4×C61—41no—
70D4×C61—41no—
71D4×C61—41no—
72C2×C4×C61—21no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C22⋊D61—42no—
80C22⋊D61—41no—
81C22⋊D61—41no—
82C22⋊D61—81no—
83C2×Dic61—22no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89D244—41no—
90D244—42no—
91C4×D61—42no—
92C8×C61—41no—
93#92418—41no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61#12011yescharacteristic
100C22×C61C2×SD1611yescharacteristic
101C22×C61AGL(1,ℤ/8)11yescharacteristic
102C2×D61—22no—
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—42no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—81no—
110C2×D61—84no—
111C4×C61—21no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61—81no—
115Dic61—42no—
116Dic61—41no—
117Dic61—41no—
118#1613—611nomaximal, Sylow
119C2×C61—21no—
120C2×C61—21no—
121C2×C61—81no—
122C2×C61#45011yescharacteristic
123C2×C61#45311yescharacteristic
124C2×C61#45811yescharacteristic
125D61—42no—
126D61—81no—
127#534—611no—
128#481—611no—
129#481D6111yescharacteristic, complemented
130#399—611no—
131#327—611no—
132#327—611no—
133#323—611no—
134C61#161311yescharacteristic, complemented, Sylow
135C22×D4—1221no—
136#123—1221no—
137#123—1221no—
138#121—611no—
139#121—1221no—
140#121C2×D6111yescharacteristic
141#120—1221no—
142#120—1221no—
143C2×C4⋊C4—1221no—
144C2×C4⋊C4C2×D6111yescharacteristic, complemented
145C2×C22⋊C4—611no—
146C2×C22⋊C4—1221no—
147#106—21no—
148#106—1221no—
149#102—21no—
150#102—1221no—
151C22⋊C8—611no—
152C22⋊C8C2×D6111yescharacteristic, complemented
153#95—611no—
154C24—611no—
155C24—1221no—
156C2×D4—21no—
157C2×D4—611no—
158C2×D4—1221no—
159C2×D4—1221no—
160C2×D4—1221no—
161C2×D4—1221no—
162C2×D4—2442no—
163C2×D4—2442no—
164C2×D4C22⋊D6111yescharacteristic
165C22×C4—21no—
166C22×C4—611no—
167C22×C4—1221no—
168C22×C4—1221no—
169C22×C4C22×D6111yescharacteristic
170C2×C8—21no—
171C2×C8—1221no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—611no—
175C4⋊C4—1221no—
176C4⋊C4—2442no—
177C4⋊C4C22⋊D6111yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—1221no—
180C22⋊C4—1221no—
181C22⋊C4—1221no—
182C22⋊C4—1221no—
183C22⋊C4—1221no—
184C22⋊C4—2442no—
185C23—21no—
186C23—612no—
187C23—1221no—
188C23—1221no—
189C23—1221no—
190C23—4881no—
191C23—4881no—
192C23—2441no—
193C23—2441no—
194C23—2442no—
195C23D4×D6111yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—4881no—
200D4—2441no—
201D4—2442no—
202D4—2442no—
203D4—2441no—
204D4—2441no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—1222no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—2442no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4D4×D6111yescharacteristic
218C2×C4C2×C22⋊D6111yescharacteristic
219C8—41no—
220C8—2441no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—1222no—
227C22—4881no—
228C22—4884no—
229C22—2442no—
230C22—2441no—
231C22—2441no—
232C22—2441no—
233C22—2441no—
234C22—2441no—
235C22#1451974511yescharacteristic
236C22SD16×D6111yescharacteristic
237C22#1451980411yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—2442no—
243C4—2441no—
244C4—2441no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—4881no—
249C2—2442no—
250C2#1683991111yescharacteristic
251C2#1683992811yescharacteristic
252C2#1683995111yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#481C2
socleC22×C61#120
hypercenter#481D61
hypocenterC61#1613
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #16840080C2semidirect
3. #16839697C2semidirect
4. #16839497C2semidirect
5. #16839496C2semidirect
6. #16839485C2semidirect
7. C61×#481C2semidirect
20. C22⋊#92418C22semidirect
21. #14519684C22semidirect
23. C2×C4⋊C4×C61C22semidirect
26. C22⋊C8×C61C22semidirect
129. #481D61semidirect
134. C61#1613semidirect
144. C2×C4⋊C4C2×D61semidirect
152. C22⋊C8C2×D61semidirect