Finite Group Databasebeta

← #21444155

Subgroups — #21444155

Order 7808.

316 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×C22⋊D61C211yesmaximal, characteristic
2#16839726C211yesmaximal, characteristic, complemented
3#16839487C212yesmaximal, complemented
4#16839485C212yesmaximal, complemented
5C61×#407C211yesmaximal, characteristic, complemented
6C22×C22⋊D61C411yescharacteristic
7C22×C4×D61C411yescharacteristic
8C2×#11758194—21no—
9C4×C22⋊D61—21no—
10C4×C22⋊D61—21no—
11C4×C22⋊D61—21no—
12C4×C22⋊D61—21no—
13C2×#11758196C2211yescharacteristic
14C2×C22⋊Dic61C411yescharacteristic
15C2×#11758198C2211yescharacteristic
16C2×C4×Dic61C411yescharacteristic
17C22⋊#92418—21no—
18C22⋊#92418C2212yes—
19C23×C4×C61C2211yescharacteristic
20C2×M16×C61—21no—
21C22⋊C8×C61—21no—
22C22⋊C8×C61C2212yes—
23C24×C61C2×C411yescharacteristic
24C23×D61C2×C411yescharacteristic
25C22×C4×C61—42no—
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—22no—
35C2×C22⋊D61—22no—
36C22×Dic61C2×C411yescharacteristic
37C22×Dic61C2×C411yescharacteristic
38C22×Dic61C2×C411yescharacteristic
39C2×C4×D61—21no—
40C2×C4×D61—21no—
41C2×C4×D61—42no—
42M16×C61—42no—
43C2×C8×C61—22no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46#11758198—21no—
47#11758198—21no—
48#11758196—21no—
49#11758196—21no—
50C4×Dic61—21no—
51C4×Dic61—21no—
52#11758194—42no—
53C2×#92418—22no—
54C23×C61—21no—
55C23×C61—21no—
56C23×C61—41no—
57C23×C61—41no—
58C23×C61C22⋊C411yescharacteristic
59C23×C61C22⋊C411yescharacteristic
60C23×C61C22×C411yescharacteristic
61C22×D61—21no—
62C22×D61—21no—
63C22×D61—41no—
64C22×D61—41no—
65C22×D61M1612yescomplemented
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61C22⋊C411yescharacteristic
73C2×C4×C61C22⋊C411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C22⋊D61—24no—
77C22⋊D61—24no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61M1612yescomplemented
85C4×D61—42no—
86C4×D61—42no—
87C8×C61—42no—
88#92418—42no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—42no—
98C22×C61—42no—
99C22×C61C2×C22⋊C411yescharacteristic
100C22×C61C2×M1611yescharacteristic
101C22×C61C2×M1611yescharacteristic
102C2×D61—22no—
103C2×D61—42no—
104C2×D61—41no—
105C2×D61—41no—
106C2×D61—42no—
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61#9912yes—
111Dic61—22no—
112Dic61—41no—
113Dic61—41no—
114#1465—611nomaximal, Sylow
115C2×C61—21no—
116C2×C61—21no—
117C2×C61—41no—
118C2×C61—41no—
119C2×C61#40711yescharacteristic
120C2×C61C2×#9911yescharacteristic
121C2×C61#41311yescharacteristic
122D61—42no—
123C2×C4×D4—611no—
124#407—611no—
125#407D6111yescharacteristic, complemented
126#324—612no—
127#323—612no—
128C61#146511yescharacteristic, complemented, Sylow
129C22×D4—611no—
130C23×C4—611no—
131C23×C4C2×D6111yescharacteristic
132C2×M16—21no—
133C2×M16—1221no—
134C4×D4—1221no—
135C4×D4—1221no—
136C4×D4—1221no—
137C4×D4—1221no—
138C2×C4⋊C4—611no—
139C2×C22⋊C4—611no—
140C2×C22⋊C4—611no—
141C2×C42—611no—
142C22⋊C8—21no—
143C22⋊C8—612no—
144C22⋊C8—1221no—
145C22⋊C8C2×D6112yes—
146C24—611no—
147C24C4×D6111yescharacteristic
148C2×D4—1222no—
149C2×D4—1222no—
150C2×D4—1221no—
151C2×D4—1221no—
152C22×C4—42no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—1221no—
157C22×C4—1221no—
158C22×C4—2442no—
159C22×C4C4×D6111yescharacteristic
160C22×C4D24411yescharacteristic
161C22×C4D24411yescharacteristic
162C22×C4C22⋊D6111yescharacteristic
163C22×C4C22⋊D6111yescharacteristic
164C22×C4C22×D6111yescharacteristic
165M16—42no—
166M16—2442no—
167C2×C8—22no—
168C2×C8—1222no—
169C4⋊C4—1221no—
170C4⋊C4—1221no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1221no—
174C22⋊C4—1221no—
175C42—1221no—
176C42—1221no—
177C23—21no—
178C23—21no—
179C23—41no—
180C23—41no—
181C23—612no—
182C23—1221no—
183C23—1221no—
184C23—2441no—
185C23—2441no—
186C23#1175819811yescharacteristic
187C23#1175819811yescharacteristic
188C23C2×C4×D6111yescharacteristic
189D4—1224no—
190D4—1224no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—612no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4#1175819811yescharacteristic
207C2×C4#1175819811yescharacteristic
208C2×C4C2×D24411yescharacteristic
209C2×C4C2×C22⋊D6111yescharacteristic
210C8—42no—
211C8—2442no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—42no—
221C22—42no—
222C22—1222no—
223C22—2442no—
224C22—2442no—
225C22—2441no—
226C22—2441no—
227C22C2×#1175819811yescharacteristic
228C22M16×D6111yescharacteristic
229C22M16×D6111yescharacteristic
230C4—21no—
231C4—21no—
232C4—21no—
233C4—1222no—
234C4—2441no—
235C4—2441no—
236C4#1451969112yes—
237C2—21no—
238C2—21no—
239C2—41no—
240C2—41no—
241C2—2442no—
242C2#1683972511yescharacteristic
243C2C2×#1451969111yescharacteristic
244C2#1683974411yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#407C2
socleC22×C61C2×C22⋊C4
hypercenter#407D61
hypocenterC61#1465
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #16839726C2semidirect
3. #16839487C2semidirect
4. #16839485C2semidirect
5. C61×#407C2semidirect
65. C22×D61M16semidirect
84. C2×Dic61M16semidirect
125. #407D61semidirect
128. C61#1465semidirect