Finite Group Databasebeta

← #21455340

Subgroups — #21455340

Order 7808.

490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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
2C22×#11758201C211yesmaximal, characteristic, complemented
3#16840331C211yesmaximal, characteristic
4#16839984C214yesmaximal, complemented
5#16839962C214yesmaximal, complemented
6#16839789C211yesmaximal, characteristic, complemented
7#16839766C211yesmaximal, characteristic, complemented
8#16839756C211yesmaximal, characteristic, complemented
9C61×#519C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C22×D244C2211yescharacteristic
12#14519808—24no—
13C2×#11758202C2212yescomplemented
14C2×#11758201—24no—
15C2×#11758201C2214yes—
16C2×#11758201C2212yescomplemented
17C2×#11758194C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19#14519774C2212yes—
20#14519765C2212yes—
21#14519752—22no—
22#14519747—22no—
23C4⋊#92418C2214yescomplemented
24#14519700C2212yescomplemented
25#14519697C2214yes—
26#14519697C2212yescomplemented
27C22×Q8×C61C2211yescharacteristic
28C4×Q8×C61—22no—
29C4×Q8×C61C2214yescomplemented
30#117×C61—22no—
31#117×C61C2211yescharacteristic
32#117×C61C2211yescharacteristic
33C23×D61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61—22no—
36C2×Q8×C61D414yescomplemented
37C2×Q8×C61C2312yes—
38C22×C4×C61—21no—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—21no—
41#11758222—22no—
42#11758222—22no—
43C2×D244—22no—
44C2×D244—22no—
45C2×D244—21no—
46C2×D244—24no—
47C2×D244C2312yes—
48C2×D244C2311yescharacteristic
49C2×C4×D61—21no—
50C2×Dic122C2311yescharacteristic
51C4⋊C4×C61—24no—
52C4⋊C4×C61D412yes—
53C4⋊C4×C61C2312yes—
54C22⋊C4×C61—21no—
55C22⋊C4×C61D412yes—
56C42×C61—24no—
57C42×C61—21no—
58C42×C61C2312yes—
59#11758202—24no—
60#11758201—24no—
61#11758201—28no—
62#11758198—24no—
63#11758194—22no—
64C2×#92418—22no—
65C2×#92418C2312yes—
66C2×#92418C2312yes—
67C23×C61C2×D411yescharacteristic
68C22×D61—22no—
69C22×D61—21no—
70C22×D61—42no—
71C22×D61—82no—
72Q8×C61—24no—
73Q8×C61—22no—
74Q8×C61C2×D414yes—
75C2×C4×C61—24no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D414yes—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D412yes—
81C2×C4×C61#4112yes—
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—42no—
84C2×Dic61—21no—
85D244—22no—
86D244—21no—
87D244—22no—
88D244—21no—
89D244—42no—
90D244—84no—
91C4×D61—42no—
92Dic122—21no—
93Dic122—21no—
94#92418—22no—
95#92418—22no—
96C22×C61—22no—
97C22×C61#12112yes—
98C22×C61C22×D411yescharacteristic
99C2×D61—41no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—44no—
103C2×D61—84no—
104C4×C61—24no—
105C4×C61—24no—
106C4×C61—42no—
107C4×C61#12112yes—
108C4×C61C22×D411yescharacteristic
109C4×C61C2×#4111yescharacteristic
110Dic61—41no—
111#3043—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61C2×#12111yescharacteristic
114C2×C61#57712yes—
115D61—81no—
116D61—82no—
117C2×#137—611no—
118C22×SD16—611no—
119#535—611no—
120#519D6111yescharacteristic, complemented
121#464—614no—
122#460—614no—
123#424—611no—
124#418—611no—
125#416—611no—
126C61#304311yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C22×Q8C2×D6111yescharacteristic
129C22×D4—611no—
130#137—1224no—
131C2×Q16—612no—
132C2×SD16—614no—
133C2×SD16—612no—
134C2×SD16—1224no—
135C2×M16—611no—
136C22×C8—611no—
137#127—612no—
138#124—612no—
139#121—1222no—
140#120—1222no—
141C4×Q8—22no—
142C4×Q8C2×D6114yescomplemented
143#117—22no—
144#117C2×D6111yescharacteristic
145#117C2×D6111yescharacteristic
146C4⋊C8—614no—
147#103—612no—
148#102—614no—
149#102—612no—
150C24—1221no—
151#41—1222no—
152#41—1222no—
153C2×Q8—22no—
154C2×Q8—21no—
155C2×Q8—611no—
156C2×Q8D24414yescomplemented
157C2×Q8C22×D6112yes—
158C2×D4—612no—
159C2×D4—611no—
160C2×D4—1221no—
161C2×D4—1222no—
162C2×D4—1222no—
163C2×D4—1224no—
164C2×D4—1221no—
165C22×C4—21no—
166C22×C4—1221no—
167C22×C4C22×D6111yescharacteristic
168Q16—1224no—
169SD16—1228no—
170SD16—1224no—
171M16—1222no—
172C2×C8—612no—
173C2×C8—612no—
174C2×C8—1222no—
175C4⋊C4—24no—
176C4⋊C4C22⋊D6112yes—
177C4⋊C4C22×D6112yes—
178C22⋊C4—21no—
179C22⋊C4—1224no—
180C22⋊C4C22⋊D6112yes—
181C42—24no—
182C42—21no—
183C42C22×D6112yes—
184C23—1222no—
185C23—1221no—
186C23—4882no—
187C23—2442no—
188C23C2×C22⋊D6111yescharacteristic
189Q8—22no—
190Q8—24no—
191Q8—1221no—
192Q8—1221no—
193Q8C2×D24414yes—
194D4—1222no—
195D4—1221no—
196D4—1222no—
197D4—1221no—
198D4—4884no—
199D4—2442no—
200D4—2442no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—1221no—
205C2×C4—2442no—
206C2×C4C2×D24412yes—
207C2×C4#1175822212yes—
208C2×C4C2×C22⋊D6114yes—
209C2×C4C2×C22⋊D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—1222no—
212C8—1222no—
213C22—22no—
214C22—4884no—
215C22—2441no—
216C22—2442no—
217C22—2442no—
218C22—2444no—
219C22#1451975112yes—
220C22C22×C22⋊D6111yescharacteristic
221C4—24no—
222C4—24no—
223C4—42no—
224C4—2441no—
225C4#1451975112yes—
226C4C22×D24411yescharacteristic
227C4C2×#1175822211yescharacteristic
228C2—22no—
229C2—4882no—
230C2—4881no—
231C2C2×#1451975111yescharacteristic
232C2#1684057012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#519C2
socleC22×C61C22×D4
hypercenter#519D61
hypocenterC61#3043
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
2. C22×#11758201C2semidirect
4. #16839984C2semidirect
5. #16839962C2semidirect
6. #16839789C2semidirect
7. #16839766C2semidirect
8. #16839756C2semidirect
9. C61×#519C2semidirect
13. C2×#11758202C22semidirect
16. C2×#11758201C22semidirect
23. C4⋊#92418C22semidirect
24. #14519700C22semidirect
26. #14519697C22semidirect
29. C4×Q8×C61C22semidirect
36. C2×Q8×C61D4semidirect
120. #519D61semidirect
126. C61#3043semidirect
142. C4×Q8C2×D61semidirect
156. C2×Q8D244semidirect