Finite Group Databasebeta

← #21461234

Subgroups — #21461234

Order 7808.

286 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 60 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#16840733C211yesmaximal, characteristic, complemented
2#16840704C211yesmaximal, characteristic, complemented
3#16840616C212yesmaximal, complemented
4#16840613C212yesmaximal, complemented
5#16840269C211yesmaximal, characteristic
6C2×#11758213—21no—
7C2×C4⋊#6923—21no—
8C2×C22⋊#6923—21no—
9#14519834C2212yes—
10C22⋊#92420—21no—
11(C2×#6923)⋊C4C2212yes—
12C22×C4×D61C2211yescharacteristic
13#14519758—21no—
14#14519753C411yescharacteristic, complemented
15#14519753C2211yescharacteristic
16#14519748C411yescharacteristic, complemented
17#14519748C2211yescharacteristic
18#14519745—21no—
19C4×C22⋊D61—21no—
20C4×C22⋊D61—21no—
21#14519736C411yescharacteristic, complemented
22C2×#41×C61C411yescharacteristic, complemented
23C23×D61D411yescharacteristic
24C22×#6923—22no—
25#41×C61—42no—
26C2×Q8×C61C2×C411yescharacteristic
27C2×D4×C61—21no—
28C2×D4×C61C2×C411yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C2×C411yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C22×Dic61D411yescharacteristic
34C2×C4×D61—42no—
35C2×C4×D61C2×C411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×C4×D61D411yescharacteristic
38C2×C4×D61C2311yescharacteristic
39C22⋊#6923—42no—
40C2×#92420—22no—
41C4⋊#6923—42no—
42#11758213—42no—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46#11758198—21no—
47#11758198—21no—
48C4⋊Dic61C2×C411yescharacteristic
49C4⋊Dic61C2×C411yescharacteristic
50#11758196—21no—
51#11758196—21no—
52C4×Dic61—21no—
53C23×C61—21no—
54C23×C61C22⋊C411yescharacteristic
55C22×D61—21no—
56C22×D61—21no—
57C22×D61—41no—
58C22×D61—41no—
59C22×D61C22⋊C411yescharacteristic
60C22×D61C2×D411yescharacteristic
61C2×#6923—42no—
62C2×#6923—42no—
63C2×#6923—42no—
64Q8×C61—41no—
65D4×C61—41no—
66D4×C61—42no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—42no—
70C2×C4×C61C22⋊C411yescharacteristic
71C2×C4×C61C22×C411yescharacteristic
72C22⋊D61—42no—
73C22⋊D61—41no—
74C22⋊D61—41no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—41no—
78C2×Dic61C22⋊C411yescharacteristic
79C2×Dic61C2×D411yescharacteristic
80C4×D61—22no—
81C4×D61—22no—
82C4×D61—41no—
83C4×D61—41no—
84#92420—42no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61C2×C22⋊C411yescharacteristic
92C2×D61—21no—
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—21no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61AGL(1,ℤ/8)11yescharacteristic
100C2×D61#13711yescharacteristic
101#6923—82no—
102C4×C61—21no—
103C4×C61—41no—
104C4×C61#9912yes—
105Dic61—21no—
106Dic61—21no—
107Dic61—41no—
108Dic61—41no—
109#1513—611nomaximal, Sylow
110C2×C61—41no—
111C2×C61—81no—
112C2×C61C2×#9911yescharacteristic
113C2×C61#41711yescharacteristic
114C2×C61#42111yescharacteristic
115D61—21no—
116D61—21no—
117D61—41no—
118#525—611no—
119#407—611no—
120#380—611no—
121#328—612no—
122#327—612no—
123C61#151311yescharacteristic, complemented, Sylow
124C2×#41#692311yescharacteristic, complemented
125C23×C4—611no—
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—1221no—
137C2×C22⋊C4—1221no—
138C22⋊C8—612no—
139C22⋊C8—1221no—
140#95—612no—
141C24—611no—
142#41—42no—
143C2×Q8C2×#692311yescharacteristic
144C2×D4—21no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4C2×#692311yescharacteristic
148C22×C4—21no—
149C22×C4—611no—
150C22×C4—611no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—1222no—
155C22×C4—2442no—
156C22×C4C2×#692311yescharacteristic
157M16—2442no—
158C2×C8—1222no—
159C4⋊C4—611no—
160C4⋊C4—611no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C4⋊C4—2442no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—2442no—
170C42—1221no—
171C23—21no—
172C23—611no—
173C23—611no—
174C23—1221no—
175C23—1221no—
176C23—2441no—
177C23—2441no—
178C23C22⋊#692311yescharacteristic
179Q8—41no—
180D4—41no—
181D4—42no—
182D4—2441no—
183D4—2441no—
184D4—2442no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—42no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4C22⋊#692311yescharacteristic
201C2×C4C22×#692311yescharacteristic
202C8—2442no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—611no—
210C22—611no—
211C22—1221no—
212C22—1221no—
213C22—1221no—
214C22—1221no—
215C22—1221no—
216C22—2442no—
217C22—2442no—
218C22C2×C22⋊#692311yescharacteristic
219C4—21no—
220C4—41no—
221C4—1221no—
222C4—1221no—
223C4—4882no—
224C4—2441no—
225C4—2441no—
226C4#1451983512yes—
227C2—41no—
228C2—81no—
229C2—1221no—
230C2—1221no—
231C2—2441no—
232C2C2×#1451983511yescharacteristic
233C2#1684075311yescharacteristic
234C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×#41×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×#41#6923
hypocenterC61#1513
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #16840733C2semidirect
2. #16840704C2semidirect
3. #16840616C2semidirect
4. #16840613C2semidirect
14. #14519753C4semidirect
16. #14519748C4semidirect
21. #14519736C4semidirect
22. C2×#41×C61C4semidirect
123. C61#1513semidirect
124. C2×#41#6923semidirect