Finite Group Databasebeta

← #21455331

Subgroups — #21455331

Order 7808.

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

normal subgroups only

This group has 494 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×#14519803C211yesmaximal, characteristic
2C22×#11758200C211yesmaximal, characteristic, complemented
3#16840338C211yesmaximal, characteristic, complemented
4#16839977C214yesmaximal, complemented
5#16839967C214yesmaximal, complemented
6#16839789C211yesmaximal, characteristic, complemented
7#16839770C211yesmaximal, characteristic, complemented
8#16839756C211yesmaximal, characteristic, complemented
9C61×#518C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C22×Dic122C2211yescharacteristic
12#14519803—24no—
13C2×#11758200—24no—
14C2×#11758200C2212yes—
15C2×#11758200C2214yes—
16C2×#11758199C2212yes—
17C2×#11758194C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19#14519777C2212yescomplemented
20#14519765C2212yescomplemented
21#14519761—22no—
22#14519757—22no—
23C4⋊#92418C2214yescomplemented
24#14519700C2212yescomplemented
25#14519700C2214yescomplemented
26#14519697C2212yescomplemented
27C22×D4×C61C2211yescharacteristic
28C4×D4×C61—22no—
29C4×D4×C61C2214yes—
30#117×C61C2211yescharacteristic
31#117×C61C2211yescharacteristic
32C2×C22⋊C4×C61—22no—
33C24×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61—22no—
36C2×D4×C61D414yes—
37C2×D4×C61C2312yes—
38C22×C4×C61—24no—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—21no—
41C22×Dic61—21no—
42#11758222—22no—
43#11758222—22no—
44C2×D244C2311yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122—22no—
47C2×Dic122—22no—
48C2×Dic122—21no—
49C2×Dic122C2312yes—
50C2×Dic122C2311yescharacteristic
51C4⋊C4×C61D412yes—
52C4⋊C4×C61C2312yes—
53C22⋊C4×C61—21no—
54C22⋊C4×C61—24no—
55C22⋊C4×C61D412yes—
56C42×C61—21no—
57C42×C61C2312yes—
58#11758200—28no—
59#11758200—24no—
60#11758199—24no—
61#11758198—24no—
62C4⋊Dic61—24no—
63#11758194—22no—
64C2×#92418—22no—
65C2×#92418C2312yes—
66C2×#92418C2312yes—
67C23×C61—22no—
68C23×C61—24no—
69C23×C61—82no—
70C23×C61C2×D411yescharacteristic
71C22×D61—21no—
72D4×C61—24no—
73D4×C61—22no—
74D4×C61C2×D414yes—
75C2×C4×C61—22no—
76C2×C4×C61—84no—
77C2×C4×C61C2×D414yes—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D412yes—
80C2×C4×C61#4112yes—
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—42no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—42no—
86D244—21no—
87D244—21no—
88C4×D61—42no—
89Dic122—22no—
90Dic122—21no—
91Dic122—22no—
92Dic122—21no—
93Dic122—42no—
94#92418—22no—
95#92418—22no—
96C22×C61—22no—
97C22×C61—24no—
98C22×C61—44no—
99C22×C61—84no—
100C22×C61#12112yes—
101C22×C61C22×D411yescharacteristic
102C2×D61—41no—
103C2×D61—42no—
104C4×C61—24no—
105C4×C61—42no—
106C4×C61#12112yes—
107C4×C61C22×D411yescharacteristic
108C4×C61C2×#4111yescharacteristic
109Dic61—42no—
110Dic61—41no—
111#3042—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61—44no—
114C2×C61C2×#12111yescharacteristic
115C2×C61#57712yes—
116D61—81no—
117C2×AGL(1,ℤ/8)—611no—
118C22×SD16—611no—
119#536—611no—
120#518D6111yescharacteristic, complemented
121#463—614no—
122#461—614no—
123#424—611no—
124#419—611no—
125#416—611no—
126C61#304211yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C22×Q8—611no—
129C22×D4C2×D6111yescharacteristic
130AGL(1,ℤ/8)—1224no—
131C2×SD16—614no—
132C2×SD16—612no—
133C2×SD16—1224no—
134C2×D8—612no—
135C2×M16—611no—
136C22×C8—611no—
137C4⋊Q8—612no—
138#124—612no—
139#123—1222no—
140C22⋊Q8—1222no—
141C4×D4—22no—
142C4×D4C2×D6114yes—
143#117C2×D6111yescharacteristic
144#117C2×D6111yescharacteristic
145C2×C22⋊C4—22no—
146C4⋊C8—614no—
147#103—612no—
148#103—614no—
149#102—612no—
150C24—21no—
151#41—1222no—
152#41—1222no—
153C2×Q8—612no—
154C2×Q8—611no—
155C2×Q8—1221no—
156C2×Q8—1222no—
157C2×Q8—1222no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—611no—
161C2×D4—1221no—
162C2×D4D24414yes—
163C2×D4C22×D6112yes—
164C22×C4—24no—
165C22×C4—1221no—
166C22×C4—1221no—
167C22×C4C22×D6111yescharacteristic
168SD16—1228no—
169SD16—1224no—
170D8—1224no—
171M16—1222no—
172C2×C8—612no—
173C2×C8—612no—
174C2×C8—1222no—
175C4⋊C4—1224no—
176C4⋊C4C22⋊D6112yes—
177C4⋊C4C22×D6112yes—
178C22⋊C4—21no—
179C22⋊C4—24no—
180C22⋊C4—1224no—
181C22⋊C4C22⋊D6112yes—
182C42—21no—
183C42C22×D6112yes—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—1221no—
188C23C2×C22⋊D6111yescharacteristic
189Q8—1222no—
190Q8—1221no—
191Q8—1222no—
192Q8—1221no—
193Q8—2442no—
194D4—22no—
195D4—24no—
196D4—1221no—
197D4—1221no—
198D4—2442no—
199D4C2×D24414yes—
200C2×C4—22no—
201C2×C4—84no—
202C2×C4—1222no—
203C2×C4—1221no—
204C2×C4—2442no—
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—24no—
215C22—44no—
216C22—84no—
217C22—2441no—
218C22—2442no—
219C22#1451975112yes—
220C22C22×C22⋊D6111yescharacteristic
221C4—24no—
222C4—42no—
223C4—2441no—
224C4—2442no—
225C4#1451975112yes—
226C4C22×D24411yescharacteristic
227C4C2×#1175822211yescharacteristic
228C2—22no—
229C2—44no—
230C2—4881no—
231C2C2×#1451975111yescharacteristic
232C2#1684057312yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#518C2
socleC22×C61C22×D4
hypercenter#518D61
hypocenterC61#3042
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C22×#11758200C2semidirect
3. #16840338C2semidirect
4. #16839977C2semidirect
5. #16839967C2semidirect
6. #16839789C2semidirect
7. #16839770C2semidirect
8. #16839756C2semidirect
9. C61×#518C2semidirect
19. #14519777C22semidirect
20. #14519765C22semidirect
23. C4⋊#92418C22semidirect
24. #14519700C22semidirect
25. #14519700C22semidirect
26. #14519697C22semidirect
120. #518D61semidirect
126. C61#3042semidirect