Finite Group Databasebeta

← #21444360

Subgroups — #21444360

Order 7808.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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#16840273C211yesmaximal, characteristic
2#16839726C211yesmaximal, characteristic, complemented
3#16839498C212yesmaximal, complemented
4#16839495C212yesmaximal, complemented
5C61×#380C211yesmaximal, characteristic, complemented
6C2×#11758222C411yescharacteristic, complemented
7C2×#11758194—21no—
8#14519760—21no—
9#14519756C411yescharacteristic, complemented
10#14519756C2211yescharacteristic
11#14519751C411yescharacteristic, complemented
12#14519751C2211yescharacteristic
13#14519746—21no—
14C4×C22⋊D61—21no—
15C4×C22⋊D61—21no—
16#14519736C411yescharacteristic, complemented
17C22⋊#92418—21no—
18C22⋊#92418C2212yes—
19C23×C4×C61C2211yescharacteristic
20C2×C4⋊C4×C61—21no—
21C2×C22⋊C4×C61—21no—
22#95×C61C2212yes—
23C24×C61D411yescharacteristic
24C22×C4×C61—22no—
25C22×C4×C61—42no—
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61C2×C411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35#11758222—42no—
36C2×D244C2×C411yescharacteristic
37C2×C4×D61—21no—
38C2×Dic122C2×C411yescharacteristic
39C4⋊C4×C61—42no—
40C22⋊C4×C61—42no—
41C22⋊Dic61—21no—
42C22⋊Dic61—21no—
43C22⋊Dic61—21no—
44#11758198—21no—
45#11758198—21no—
46C4⋊Dic61C2×C411yescharacteristic
47C4⋊Dic61C2×C411yescharacteristic
48#11758196—21no—
49#11758196—21no—
50C4×Dic61—21no—
51#11758194—42no—
52C2×#92418—22no—
53C23×C61—21no—
54C23×C61—21no—
55C23×C61—41no—
56C23×C61—41no—
57C23×C61C22⋊C411yescharacteristic
58C23×C61C22⋊C411yescharacteristic
59C23×C61C2×D411yescharacteristic
60C22×D61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61—42no—
70C2×C4×C61C22⋊C411yescharacteristic
71C2×C4×C61C22⋊C411yescharacteristic
72C2×C4×C61C22×C411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C22⋊D61—42no—
75C22⋊D61—42no—
76C22⋊D61—41no—
77C22⋊D61—41no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81D244—41no—
82C4×D61—42no—
83Dic122—41no—
84#92418—42no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61C2×C22⋊C411yescharacteristic
96C22×C61AGL(1,ℤ/8)11yescharacteristic
97C22×C61#13711yescharacteristic
98C2×D61—41no—
99C2×D61—41no—
100C2×D61—41no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—82no—
105C4×C61#9912yes—
106Dic61—41no—
107Dic61—41no—
108Dic61—41no—
109#1513—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—21no—
112C2×C61—41no—
113C2×C61—41no—
114C2×C61C2×#9911yescharacteristic
115C2×C61#41711yescharacteristic
116C2×C61#42111yescharacteristic
117D61—81no—
118#525—611no—
119#407—611no—
120#380D6111yescharacteristic, complemented
121#328—612no—
122#327—612no—
123C61#151311yescharacteristic, complemented, Sylow
124C2×#41—611no—
125C23×C4C2×D6111yescharacteristic
126C2×M16—1221no—
127#123—1221no—
128C22⋊Q8—611no—
129C22⋊Q8—611no—
130#121—611no—
131#121—611no—
132#120—1221no—
133C4×D4—1221no—
134C4×D4—1221no—
135#117—611no—
136C2×C4⋊C4—21no—
137C2×C22⋊C4—21no—
138C22⋊C8—612no—
139C22⋊C8—1221no—
140#95C2×D6112yes—
141C24C22⋊D6111yescharacteristic
142#41—2442no—
143C2×Q8—611no—
144C2×D4—611no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—1221no—
151C22×C4C4×D6111yescharacteristic
152C22×C4C4×D6111yescharacteristic
153C22×C4D24411yescharacteristic
154C22×C4D24411yescharacteristic
155C22×C4C22⋊D6111yescharacteristic
156C22×C4C22×D6111yescharacteristic
157M16—2442no—
158C2×C8—1222no—
159C4⋊C4—42no—
160C4⋊C4—611no—
161C4⋊C4—611no—
162C4⋊C4—1221no—
163C4⋊C4—1221no—
164C22⋊C4—42no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C42—1221no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—1221no—
176C23#1175819811yescharacteristic
177C23#1175819811yescharacteristic
178C23C2×C22⋊D6111yescharacteristic
179Q8—2441no—
180D4—2441no—
181D4—2442no—
182D4—2442no—
183D4—2441no—
184D4—2441no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—2442no—
198C2×C4#1175819811yescharacteristic
199C2×C4#1175819811yescharacteristic
200C2×C4C2×C4×D6111yescharacteristic
201C2×C4C2×D24411yescharacteristic
202C8—2442no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—2441no—
214C22—2441no—
215C22—2441no—
216C22C2×#1175819811yescharacteristic
217C22#1451980311yescharacteristic
218C22#1451980811yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—82no—
223C4—2441no—
224C4—2441no—
225C4—2441no—
226C4#1451969112yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—4881no—
232C2C2×#1451969111yescharacteristic
233C2#1683976111yescharacteristic
234C2#1683978011yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#380C2
socleC22×C61C2×C22⋊C4
hypercenter#380D61
hypocenterC61#1513
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #16839726C2semidirect
3. #16839498C2semidirect
4. #16839495C2semidirect
5. C61×#380C2semidirect
6. C2×#11758222C4semidirect
9. #14519756C4semidirect
11. #14519751C4semidirect
16. #14519736C4semidirect
120. #380D61semidirect
123. C61#1513semidirect