Finite Group Databasebeta

← #21444166

Subgroups — #21444166

Order 7808.

280 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14519762C211yesmaximal, characteristic
2#16839724C211yesmaximal, characteristic, complemented
3C22⋊C8×D61C211yesmaximal, characteristic, complemented
4#16839488C211yesmaximal, characteristic, complemented
5#16839485C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic, complemented
7C61×#324C211yesmaximal, characteristic, complemented
8C22×D244C411yescharacteristic
9C22×C4×D61C2211yescharacteristic
10C2×#11758189—21no—
11C2×C8×D61—21no—
12#14519762—21no—
13#14519762—21no—
14#14519762—21no—
15#14519762—21no—
16C2×#11758196C411yescharacteristic
17C2×#11758198C411yescharacteristic
18C2×#11758198C411yescharacteristic
19C2×#11758198C2211yescharacteristic
20C22⋊#92418C2211yescharacteristic
21C22⋊#92418C2211yescharacteristic
22#14519689—21no—
23#14519689—21no—
24C2×C4⋊C4×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26C22⋊C8×C61C2211yescharacteristic
27C23×D61C2×C411yescharacteristic
28C23×D61C2×C411yescharacteristic
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61C2×C411yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C22×Dic61C2×C411yescharacteristic
33C22×Dic61C2×C411yescharacteristic
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—42no—
37C2×C4×D61—42no—
38C2×C4×D61D411yescharacteristic
39C2×C4×D61D411yescharacteristic
40C2×C4×D61D411yescharacteristic
41C2×C4×D61D411yescharacteristic
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46#11758198—21no—
47#11758198—21no—
48#11758198—21no—
49#11758198—21no—
50#11758198—21no—
51#11758198—21no—
52#11758196—21no—
53#11758196—21no—
54C2×#92418—21no—
55C2×#92418—21no—
56#11758189—42no—
57C8×D61—42no—
58C23×C61C22×C411yescharacteristic
59C22×D61—21no—
60C22×D61—21no—
61C22×D61—22no—
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—41no—
66C22×D61—41no—
67C22×D61—41no—
68C22×D61C22⋊C411yescharacteristic
69C22×D61C22⋊C411yescharacteristic
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×Dic61—21no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61C22⋊C411yescharacteristic
82C2×Dic61C22⋊C411yescharacteristic
83D244—42no—
84D244—42no—
85C4×D61—22no—
86C4×D61—22no—
87C4×D61—41no—
88C4×D61—41no—
89C8×C61—41no—
90C8×C61—41no—
91#92418—41no—
92#92418—41no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61C2×C22⋊C411yescharacteristic
96C22×C61#13111yescharacteristic
97C22×C61#13111yescharacteristic
98C2×D61—21no—
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—41no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—81no—
109C2×D61—81no—
110C2×D61#9912yes—
111C4×C61—21no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61—41no—
115Dic61—21no—
116Dic61—21no—
117Dic61—41no—
118#1468—611nomaximal, Sylow
119C2×C61—21no—
120C2×C61—21no—
121C2×C61#40811yescharacteristic
122C2×C61C2×#9911yescharacteristic
123C2×C61#41311yescharacteristic
124D61—22no—
125D61—41no—
126D61—81no—
127C2×#123—611no—
128#407—611no—
129C2×C22⋊C8—611no—
130#324—611no—
131#324D6111yescharacteristic, complemented
132#323—611no—
133#323—611no—
134C61#146811yescharacteristic, complemented, Sylow
135C22×D4—611no—
136C23×C4—611no—
137C2×M16—1221no—
138C22×C8—1221no—
139#123—1221no—
140#123—1221no—
141#123—1221no—
142#123—1221no—
143C2×C4⋊C4—611no—
144C2×C4⋊C4C2×D6111yescharacteristic
145C2×C22⋊C4—611no—
146C2×C22⋊C4—611no—
147C2×C22⋊C4—611no—
148C22⋊C8—611no—
149C22⋊C8—611no—
150C22⋊C8—1221no—
151C22⋊C8—1221no—
152C22⋊C8C2×D6111yescharacteristic
153C22⋊C8C2×D6111yescharacteristic
154C24—611no—
155C24—611no—
156C2×D4—1221no—
157C2×D4—1221no—
158C2×D4—2442no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4—611no—
165C22×C4—2442no—
166C22×C4C4×D6111yescharacteristic
167C22×C4C4×D6111yescharacteristic
168C22×C4C22×D6111yescharacteristic
169M16—2442no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—1221no—
173C2×C8—1221no—
174C2×C8—2442no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—1221no—
178C4⋊C4—1221no—
179C22⋊C4—1221no—
180C22⋊C4—1221no—
181C22⋊C4—1221no—
182C22⋊C4—1221no—
183C22⋊C4—1221no—
184C22⋊C4—1221no—
185C23—611no—
186C23—611no—
187C23—1222no—
188C23—1221no—
189C23—1221no—
190C23—1221no—
191C23—1221no—
192C23—1221no—
193C23—2441no—
194C23—2441no—
195C23—2441no—
196C23C2×C4×D6111yescharacteristic
197D4—2442no—
198D4—2442no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—611no—
206C2×C4—611no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1221no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4D4×D6111yescharacteristic
215C2×C4D4×D6111yescharacteristic
216C8—41no—
217C8—41no—
218C8—2441no—
219C8—2441no—
220C22—21no—
221C22—21no—
222C22—612no—
223C22—1221no—
224C22—1221no—
225C22—1221no—
226C22—1221no—
227C22—1221no—
228C22—4881no—
229C22—4881no—
230C22—2442no—
231C22—2442no—
232C22—2441no—
233C22—2441no—
234C22—2441no—
235C22C22⋊C4×D6111yescharacteristic
236C22#1451978311yescharacteristic
237C22#1451978511yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—1221no—
243C4—1221no—
244C4—2441no—
245C2—21no—
246C2—21no—
247C2—1222no—
248C2—4881no—
249C2—2441no—
250C2#1683972711yescharacteristic
251C2#99×D6111yescharacteristic
252C2#1683974511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#324C2
socleC22×C61C2×C22⋊C4
hypercenter#324D61
hypocenterC61#1468
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #16839724C2semidirect
3. C22⋊C8×D61C2semidirect
4. #16839488C2semidirect
5. #16839485C2semidirect
6. #16839485C2semidirect
7. C61×#324C2semidirect
131. #324D61semidirect
134. C61#1468semidirect