Finite Group Databasebeta

← #21455315

Subgroups — #21455315

Order 7808.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519802C211yesmaximal, characteristic
2C2×#14519766C211yesmaximal, characteristic, complemented
3#41×Dic61C211yesmaximal, characteristic, complemented
4#16839986C214yesmaximal, complemented
5#16839979C214yesmaximal, complemented
6#16839785C211yesmaximal, characteristic, complemented
7#16839771C211yesmaximal, characteristic, complemented
8#16839768C211yesmaximal, characteristic, complemented
9C2×#137×C61C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11#14519802—24no—
12C2×#11758201C2212yes—
13C2×#11758199C2212yes—
14C2×#11758194C2211yescharacteristic
15#14519766—21no—
16#14519766—21no—
17#14519766C2214yes—
18Q8×Dic61C2212yescomplemented
19D4×Dic61—22no—
20D4×Dic61C2212yescomplemented
21#14519736—21no—
22#14519736C2211yescharacteristic
23C2×#11758198—22no—
24C2×C4×Dic61—21no—
25C2×C4×Dic61C2211yescharacteristic
26#14519706C2214yescomplemented
27#14519701C2214yescomplemented
28#14519699C2214yes—
29C2×#41×C61C2211yescharacteristic
30C22×Q8×C61C2211yescharacteristic
31#137×C61—24no—
32C2×Q16×C61C2212yescomplemented
33C2×SD16×C61C2212yescomplemented
34C2×M16×C61C2211yescharacteristic
35C23×D61—21no—
36#41×C61—22no—
37#41×C61D414yes—
38C2×Q8×C61—21no—
39C2×Q8×C61—22no—
40C2×Q8×C61—22no—
41C2×Q8×C61C2312yes—
42C2×Q8×C61C2311yescharacteristic
43C2×D4×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C2311yescharacteristic
48C22×Dic61—22no—
49C22×Dic61D412yes—
50C2×D244—22no—
51C2×D244—22no—
52C2×D244—21no—
53C2×D244C2312yes—
54Q16×C61—24no—
55SD16×C61—24no—
56M16×C61—22no—
57C2×C8×C61C2312yes—
58C22⋊Dic61—21no—
59C22⋊Dic61—22no—
60#11758201—24no—
61#11758199—24no—
62#11758198—24no—
63#11758198—24no—
64C4⋊Dic61—22no—
65C4⋊Dic61C2312yes—
66C4×Dic61—21no—
67C4×Dic61—22no—
68C4×Dic61D411yescharacteristic
69C4×Dic61D411yescharacteristic
70C4×Dic61C2312yes—
71#11758194—22no—
72C2×#92418C2312yes—
73C23×C61—21no—
74C23×C61C2×D411yescharacteristic
75C22×D61—22no—
76C22×D61—44no—
77C22×D61—42no—
78Q8×C61—21no—
79Q8×C61—22no—
80Q8×C61—22no—
81Q8×C61—42no—
82Q8×C61C2×D412yes—
83D4×C61—24no—
84D4×C61—21no—
85D4×C61C2×D412yes—
86C2×C4×C61—21no—
87C2×C4×C61—24no—
88C2×C4×C61—22no—
89C2×C4×C61—42no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D412yes—
92C2×C4×C61#4112yes—
93C2×C4×C61C2411yescharacteristic
94C2×Dic61—22no—
95C2×Dic61—42no—
96C2×Dic61—44no—
97C2×Dic61C2×D412yes—
98C2×Dic61C2×D412yes—
99D244—22no—
100D244—22no—
101D244—42no—
102C8×C61—22no—
103#92418—22no—
104C22×C61—22no—
105C22×C61—22no—
106C22×C61—42no—
107C22×C61#12112yes—
108C22×C61C22×D411yescharacteristic
109C2×D61—42no—
110C2×D61—44no—
111C2×D61—84no—
112C4×C61—22no—
113C4×C61—42no—
114C4×C61#12112yes—
115C4×C61C22×D411yescharacteristic
116C4×C61C2×#4111yescharacteristic
117Dic61—22no—
118Dic61—22no—
119Dic61—42no—
120#3040—611nomaximal, Sylow
121C2×C61—22no—
122C2×C61—42no—
123C2×C61C2×#12111yescharacteristic
124C2×C61#57512yes—
125D61—82no—
126C2×#137D6111yescharacteristic, complemented
127C2×AGL(1,ℤ/8)—611no—
128C2×#124—611no—
129C4×#41—611no—
130#464—614no—
131#463—614no—
132#423—611no—
133#419—611no—
134#418—611no—
135C61#304011yescharacteristic, complemented, Sylow
136C2×#41C2×D6111yescharacteristic
137C22×Q8C2×D6111yescharacteristic
138C22×D4—611no—
139#137—24no—
140AGL(1,ℤ/8)—1224no—
141C2×Q16C2×D6112yescomplemented
142C2×SD16—612no—
143C2×SD16C2×D6112yescomplemented
144C2×D8—612no—
145C2×M16—611no—
146C2×M16C2×D6111yescharacteristic
147#124—614no—
148#124—1221no—
149#124—1221no—
150C4×Q8—612no—
151C4×D4—612no—
152C4×D4—1222no—
153#117—611no—
154#117—1221no—
155C2×C22⋊C4—1222no—
156C2×C42—611no—
157C2×C42—1221no—
158C4⋊C8—614no—
159#103—614no—
160#102—614no—
161C24—1221no—
162#41—22no—
163#41C22⋊D6114yes—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8C22×D6112yes—
168C2×Q8C22×D6111yescharacteristic
169C2×D4—21no—
170C2×D4—612no—
171C2×D4—1221no—
172C2×D4—1222no—
173C2×D4—1222no—
174C2×D4C22×D6111yescharacteristic
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—612no—
178C22×C4—1222no—
179C22×C4C22×D6111yescharacteristic
180Q16—24no—
181SD16—24no—
182SD16—1224no—
183D8—1224no—
184M16—22no—
185M16—1222no—
186C2×C8—612no—
187C2×C8C22×D6112yes—
188C4⋊C4—612no—
189C4⋊C4—1222no—
190C22⋊C4—1224no—
191C22⋊C4—1224no—
192C22⋊C4—1222no—
193C22⋊C4—1221no—
194C42—611no—
195C42—611no—
196C42—612no—
197C42—1222no—
198C42—1221no—
199C23—21no—
200C23—1222no—
201C23—2444no—
202C23—2442no—
203C23D4×D6111yescharacteristic
204Q8—21no—
205Q8—22no—
206Q8—22no—
207Q8—42no—
208Q8C2×C22⋊D6112yes—
209D4—24no—
210D4—21no—
211D4—1222no—
212D4—1222no—
213D4—2442no—
214D4C2×C22⋊D6112yes—
215C2×C4—21no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—612no—
220C2×C4—612no—
221C2×C4—1222no—
222C2×C4—2442no—
223C2×C4—2444no—
224C2×C4D4×D6111yescharacteristic
225C2×C4#1175822412yes—
226C2×C4C2×C22⋊D6112yes—
227C2×C4C23×D6111yescharacteristic
228C8—22no—
229C8—1222no—
230C22—22no—
231C22—22no—
232C22—42no—
233C22—4884no—
234C22—2442no—
235C22—2444no—
236C22#1451974912yes—
237C22C2×D4×D6111yescharacteristic
238C4—22no—
239C4—42no—
240C4—1222no—
241C4—1222no—
242C4—2442no—
243C4#1451974912yes—
244C4C22×C22⋊D6111yescharacteristic
245C4C2×#1175822411yescharacteristic
246C2—22no—
247C2—42no—
248C2—4882no—
249C2C2×#1451974911yescharacteristic
250C2#1684056112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3040
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#14519766C2semidirect
3. #41×Dic61C2semidirect
4. #16839986C2semidirect
5. #16839979C2semidirect
6. #16839785C2semidirect
7. #16839771C2semidirect
8. #16839768C2semidirect
9. C2×#137×C61C2semidirect
18. Q8×Dic61C22semidirect
20. D4×Dic61C22semidirect
26. #14519706C22semidirect
27. #14519701C22semidirect
32. C2×Q16×C61C22semidirect
33. C2×SD16×C61C22semidirect
126. C2×#137D61semidirect
135. C61#3040semidirect
141. C2×Q16C2×D61semidirect
143. C2×SD16C2×D61semidirect