Finite Group Databasebeta

← #21455309

Subgroups — #21455309

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×#14519808C211yesmaximal, characteristic, complemented
2C2×#14519803C211yesmaximal, characteristic
3C4×#11758222C211yesmaximal, characteristic, complemented
4#16839981C214yesmaximal, complemented
5#16839974C214yesmaximal, complemented
6#16839786C211yesmaximal, characteristic, complemented
7#16839771C211yesmaximal, characteristic, complemented
8#16839767C211yesmaximal, characteristic, complemented
9C2×#124×C61C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11#14519808—24no—
12#14519803—24no—
13C2×#11758202C2212yescomplemented
14C2×#11758200C2212yes—
15C2×#11758201C2212yescomplemented
16C2×#11758199C2212yes—
17C2×#11758194C2211yescharacteristic
18C2×#11758194C2211yescharacteristic
19C4×Dic122C2212yescomplemented
20C4×D244C2212yescomplemented
21C4×C22⋊D61—22no—
22#14519736C2211yescharacteristic
23#14519734—21no—
24C42×D61—21no—
25C4⋊#92418C2214yescomplemented
26#14519701C2214yescomplemented
27#14519698C2214yes—
28C22×Q8×C61C2211yescharacteristic
29C22×D4×C61C2211yescharacteristic
30#124×C61—21no—
31#124×C61—21no—
32#124×C61C2214yes—
33C2×C22⋊C4×C61—22no—
34C2×C42×C61C2211yescharacteristic
35C24×C61—21no—
36C2×Q8×C61—21no—
37C2×Q8×C61—22no—
38C2×Q8×C61—22no—
39C2×Q8×C61C2312yes—
40C2×D4×C61—22no—
41C2×D4×C61—21no—
42C2×D4×C61—22no—
43C2×D4×C61C2312yes—
44C22×C4×C61—21no—
45C22×C4×C61D412yes—
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—21no—
48#11758222—22no—
49#11758222D414yes—
50C2×D244C2311yescharacteristic
51C2×C4×D61—21no—
52C2×C4×D61—22no—
53C2×Dic122C2311yescharacteristic
54C22⋊C4×C61—24no—
55C22⋊C4×C61—24no—
56C42×C61D411yescharacteristic
57C42×C61D411yescharacteristic
58C42×C61C2312yes—
59C22⋊Dic61—21no—
60#11758202—24no—
61#11758201—24no—
62#11758200—24no—
63#11758199—24no—
64#11758198—22no—
65C4⋊Dic61C2312yes—
66#11758196—22no—
67C4×Dic61—21no—
68C4×Dic61—22no—
69#11758194—22no—
70#11758194—22no—
71C2×#92418C2312yes—
72C2×#92418C2312yes—
73C23×C61—22no—
74C23×C61—44no—
75C23×C61—42no—
76C23×C61C2×D411yescharacteristic
77C22×D61—21no—
78Q8×C61—22no—
79Q8×C61—22no—
80Q8×C61—42no—
81D4×C61—22no—
82D4×C61—22no—
83D4×C61—42no—
84C2×C4×C61—22no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61C2×D412yes—
88C2×C4×C61C2×D412yes—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D412yes—
91C2×C4×C61#4112yes—
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—24no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96D244—21no—
97D244C2×D412yes—
98C4×D61—24no—
99C4×D61—44no—
100Dic122—21no—
101Dic122C2×D412yes—
102#92418—22no—
103#92418—22no—
104C22×C61—22no—
105C22×C61—42no—
106C22×C61—44no—
107C22×C61—84no—
108C22×C61#12112yes—
109C22×C61C22×D411yescharacteristic
110C2×D61—22no—
111C2×D61—42no—
112C4×C61—22no—
113C4×C61—22no—
114C4×C61—42no—
115C4×C61#12112yes—
116C4×C61C22×D411yescharacteristic
117C4×C61C2×#4111yescharacteristic
118Dic61—22no—
119Dic61—42no—
120#3040—611nomaximal, Sylow
121C2×C61—22no—
122C2×C61—82no—
123C2×C61C2×#12111yescharacteristic
124C2×C61#57512yes—
125D61—42no—
126C2×#137—611no—
127C2×AGL(1,ℤ/8)—611no—
128C2×#124D6111yescharacteristic, complemented
129C4×#41—611no—
130#464—614no—
131#463—614no—
132#423—611no—
133#419—611no—
134#418—611no—
135C61#304011yescharacteristic, complemented, Sylow
136C2×#41—611no—
137C22×Q8C2×D6111yescharacteristic
138C22×D4C2×D6111yescharacteristic
139#137—1224no—
140AGL(1,ℤ/8)—1224no—
141C2×Q16—612no—
142C2×SD16—612no—
143C2×SD16—612no—
144C2×D8—612no—
145C2×M16—611no—
146C2×M16—611no—
147#124—21no—
148#124—21no—
149#124C2×D6114yes—
150C4×Q8—612no—
151C4×D4—612no—
152C4×D4—1222no—
153#117—611no—
154#117—1221no—
155C2×C22⋊C4—22no—
156C2×C42—1221no—
157C2×C42C2×D6111yescharacteristic
158C4⋊C8—614no—
159#103—614no—
160#102—614no—
161C24—21no—
162#41—614no—
163#41—1222no—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—611no—
168C2×Q8C22×D6112yes—
169C2×D4—22no—
170C2×D4—22no—
171C2×D4—21no—
172C2×D4—611no—
173C2×D4—1221no—
174C2×D4C22×D6112yes—
175C22×C4—21no—
176C22×C4—1221no—
177C22×C4—1222no—
178C22×C4C22⋊D6112yes—
179C22×C4C22×D6111yescharacteristic
180Q16—1224no—
181SD16—1224no—
182SD16—1224no—
183D8—1224no—
184M16—1222no—
185M16—1222no—
186C2×C8—612no—
187C2×C8—612no—
188C4⋊C4—612no—
189C4⋊C4—1222no—
190C22⋊C4—24no—
191C22⋊C4—24no—
192C22⋊C4—1221no—
193C22⋊C4—1222no—
194C42—1221no—
195C42—1222no—
196C42C22⋊D6111yescharacteristic
197C42C22⋊D6111yescharacteristic
198C42C22×D6112yes—
199C23—22no—
200C23—44no—
201C23—42no—
202C23—1221no—
203C23C2×C22⋊D6111yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—42no—
207Q8—612no—
208Q8—1221no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—612no—
213D4—1224no—
214D4—1221no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—1221no—
219C2×C4—1224no—
220C2×C4—1222no—
221C2×C4—2444no—
222C2×C4D4×D6112yes—
223C2×C4#1175822412yes—
224C2×C4C2×C22⋊D6112yes—
225C2×C4C2×C22⋊D6112yes—
226C2×C4C2×C22⋊D6111yescharacteristic
227C2×C4C23×D6111yescharacteristic
228C8—1222no—
229C8—1222no—
230C22—22no—
231C22—42no—
232C22—44no—
233C22—84no—
234C22—1222no—
235C22—2442no—
236C22#1451974812yes—
237C22C22×C22⋊D6111yescharacteristic
238C4—22no—
239C4—22no—
240C4—42no—
241C4—1222no—
242C4—2442no—
243C4#1451974812yes—
244C4C2×D4×D6111yescharacteristic
245C4C2×#1175822411yescharacteristic
246C2—22no—
247C2—82no—
248C2—2442no—
249C2C2×#1451974811yescharacteristic
250C2#1684056012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#124×C61C2
socleC22×C61C22×D4
hypercenterC2×#124D61
hypocenterC61#3040
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
3. C4×#11758222C2semidirect
4. #16839981C2semidirect
5. #16839974C2semidirect
6. #16839786C2semidirect
7. #16839771C2semidirect
8. #16839767C2semidirect
9. C2×#124×C61C2semidirect
13. C2×#11758202C22semidirect
15. C2×#11758201C22semidirect
19. C4×Dic122C22semidirect
20. C4×D244C22semidirect
25. C4⋊#92418C22semidirect
26. #14519701C22semidirect
128. C2×#124D61semidirect
135. C61#3040semidirect