Finite Group Databasebeta

← #21456802

Subgroups — #21456802

Order 7808.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14519765C211yesmaximal, characteristic, complemented
2#16840149C212yesmaximal, complemented
3#16840124C212yesmaximal, complemented
4#16839977C214yesmaximal, complemented
5#16839900C212yesmaximal, complemented
6#16839895C212yesmaximal, complemented
7#16839819C211yesmaximal, characteristic, complemented
8C61×#532C211yesmaximal, characteristic, complemented
9C22×Dic122C2211yescharacteristic
10C22×D244C2211yescharacteristic
11C2×#11758200C2214yescomplemented
12C2×#11758199C2214yes—
13#14519765—21no—
14#14519765—21no—
15#14519765C2212yes—
16#14519765C2212yes—
17C2×#11758198—21no—
18C2×#11758198—21no—
19C4⋊#92418C2212yescomplemented
20#14519700C2214yescomplemented
21#14519697C2214yes—
22C22⋊#92418C2212yes—
23#14519688C2212yescomplemented
24C2×#41×C61—21no—
25C4⋊Q8×C61C2211yescharacteristic, complemented
26#127×C61C2211yescharacteristic, complemented
27#124×C61—21no—
28#121×C61—21no—
29#121×C61C2212yes—
30C4×D4×C61—21no—
31C4×D4×C61C2212yescomplemented
32C2×C42×C61C2211yescharacteristic
33C23×D61—21no—
34#41×C61—44no—
35C2×Q8×C61—21no—
36C2×D4×C61—22no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61C2312yes—
40C22×C4×C61—22no—
41C22×C4×C61D411yescharacteristic
42C22×C4×C61D411yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61—21no—
45C2×D244—21no—
46C2×D244—42no—
47C2×D244C2312yes—
48C2×Dic122—21no—
49C2×Dic122—42no—
50C2×Dic122C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2312yes—
53C22⋊C4×C61—22no—
54C22⋊C4×C61—22no—
55C42×C61D411yescharacteristic
56C42×C61D411yescharacteristic
57C42×C61C2311yescharacteristic
58C42×C61C2311yescharacteristic
59#11758200—44no—
60#11758199—44no—
61#11758198—22no—
62#11758198—22no—
63#11758198—22no—
64#11758198—22no—
65C2×#92418C2314yes—
66C23×C61—22no—
67C23×C61C2×D411yescharacteristic
68C22×D61—22no—
69C22×D61—42no—
70C22×D61—42no—
71C22×D61—42no—
72Q8×C61—42no—
73D4×C61—24no—
74D4×C61—42no—
75D4×C61—42no—
76D4×C61—44no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—41no—
81C2×C4×C61—44no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C2×Dic61—22no—
89C2×Dic61—42no—
90D244—24no—
91D244—42no—
92Dic122—24no—
93Dic122—42no—
94#92418—24no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—42no—
98C22×C61—42no—
99C22×C61—42no—
100C22×C61AGL(1,ℤ/8)12yes—
101C22×C61C22×D411yescharacteristic
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—84no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—42no—
112C4×C61H(5,𝔽2)12yes—
113Dic61—42no—
114#3213—611nomaximal, Sylow
115C2×C61—22no—
116C2×C61—82no—
117C2×C61#53511yescharacteristic
118C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
119C2×C61#57511yescharacteristic
120D61—82no—
121#532D6111yescharacteristic, complemented
122C2×#124—611no—
123#496—612no—
124#489—612no—
125#463—614no—
126#448—612no—
127#447—612no—
128#432—611no—
129C61#321311yescharacteristic, complemented, Sylow
130C2×#41—21no—
131C22×Q8—611no—
132C22×D4—611no—
133C2×SD16—614no—
134C2×D8—614no—
135C4⋊Q8C2×D6111yescharacteristic, complemented
136#127C2×D6111yescharacteristic, complemented
137#124—21no—
138#124—612no—
139#124—612no—
140#124—1221no—
141#124—1221no—
142#121—21no—
143#121C2×D6112yes—
144C4×D4—21no—
145C4×D4C2×D6112yescomplemented
146C2×C22⋊C4—1221no—
147C2×C22⋊C4—1221no—
148C2×C42C2×D6111yescharacteristic
149C4⋊C8—612no—
150#103—614no—
151#102—614no—
152C22⋊C8—612no—
153#97—612no—
154C24—1221no—
155#41—44no—
156C2×Q8—21no—
157C2×Q8—612no—
158C2×Q8—1221no—
159C2×Q8—2442no—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—612no—
164C2×D4—1221no—
165C2×D4—2442no—
166C2×D4C22×D6112yes—
167C22×C4—22no—
168C22×C4—1221no—
169C22×C4C22⋊D6111yescharacteristic
170C22×C4C22⋊D6111yescharacteristic
171C22×C4C22×D6111yescharacteristic
172SD16—2444no—
173D8—2444no—
174C2×C8—614no—
175C4⋊C4—21no—
176C4⋊C4C22×D6112yes—
177C22⋊C4—22no—
178C22⋊C4—22no—
179C22⋊C4—1222no—
180C22⋊C4—1222no—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C42C22⋊D6111yescharacteristic
184C42C22⋊D6111yescharacteristic
185C42C22×D6111yescharacteristic
186C42C22×D6111yescharacteristic
187C23—22no—
188C23—1222no—
189C23—2442no—
190C23—2442no—
191C23—2442no—
192C23C2×C22⋊D6111yescharacteristic
193Q8—42no—
194Q8—1224no—
195Q8—2442no—
196D4—24no—
197D4—42no—
198D4—42no—
199D4—44no—
200D4—1224no—
201D4—2442no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—41no—
206C2×C4—44no—
207C2×C4—1222no—
208C2×C4—2442no—
209C2×C4C2×C22⋊D6111yescharacteristic
210C2×C4C2×C22⋊D6111yescharacteristic
211C2×C4C2×C22⋊D6111yescharacteristic
212C2×C4C2×C22⋊D6111yescharacteristic
213C2×C4C2×C22⋊D6111yescharacteristic
214C2×C4C23×D6111yescharacteristic
215C8—1224no—
216C22—21no—
217C22—21no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—4884no—
222C22—2442no—
223C22—2442no—
224C22—2442no—
225C22#1451980312yes—
226C22C22×C22⋊D6111yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—2442no—
234C4#1451982312yes—
235C2—22no—
236C2—82no—
237C2—4882no—
238C2#1684032611yescharacteristic
239C2C2×#1451980311yescharacteristic
240C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#532C2
socleC22×C61C22×D4
hypercenter#532D61
hypocenterC61#3213
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#14519765C2semidirect
2. #16840149C2semidirect
3. #16840124C2semidirect
4. #16839977C2semidirect
5. #16839900C2semidirect
6. #16839895C2semidirect
7. #16839819C2semidirect
8. C61×#532C2semidirect
11. C2×#11758200C22semidirect
19. C4⋊#92418C22semidirect
20. #14519700C22semidirect
23. #14519688C22semidirect
25. C4⋊Q8×C61C22semidirect
26. #127×C61C22semidirect
31. C4×D4×C61C22semidirect
121. #532D61semidirect
129. C61#3213semidirect
135. C4⋊Q8C2×D61semidirect
136. #127C2×D61semidirect
145. C4×D4C2×D61semidirect