Finite Group Databasebeta

← #21458531

Subgroups — #21458531

Order 7808.

396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#16840473C211yesmaximal, characteristic, complemented
2#16840432C211yesmaximal, characteristic, complemented
3#16840125C212yesmaximal, complemented
4#16840060C212yesmaximal, complemented
5#16840049C211yesmaximal, characteristic, complemented
6#16839956C212yesmaximal, complemented
7#16839954C211yesmaximal, characteristic, complemented
8#16839892C211yesmaximal, characteristic, complemented
9#16839871C212yesmaximal, complemented
10C4×D488C211yesmaximal, characteristic, complemented
11C61×#486C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C2×D488C2211yescharacteristic
14C2×#11758199C2212yes—
15#14519773C2212yes—
16#14519768C2212yes—
17#14519757—21no—
18#14519753—22no—
19#14519749—22no—
20#14519748—21no—
21C4×Dic122C2211yescharacteristic
22C4×D244C2211yescharacteristic
23C4×D244C2211yescharacteristic
24D4×Dic61C2212yes—
25#14519739C2212yes—
26C4⋊C4×D61—21no—
27#14519711C2211yescharacteristic
28#14519708C2212yes—
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519699C2211yescharacteristic
32#14519699C2211yescharacteristic
33#14519698C2212yes—
34#14519697C2212yes—
35#14519687C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37#127×C61C2211yescharacteristic
38#102×C61C2212yes—
39#102×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61C2312yes—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C22×Dic61—22no—
48#11758224—44no—
49C2×D244C2311yescharacteristic
50C2×D244C2311yescharacteristic
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—22no—
54C2×Dic122D411yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C2×C8×C61C2311yescharacteristic
57C4⋊C4×C61—21no—
58C4⋊C4×C61C2312yes—
59C42×C61C2311yescharacteristic
60C22⋊Dic61—22no—
61#11758199—24no—
62#11758198—21no—
63#11758198—21no—
64#11758198—22no—
65C4⋊Dic61—22no—
66C4⋊Dic61D411yescharacteristic
67C4⋊Dic61C2311yescharacteristic
68C4⋊Dic61C2311yescharacteristic
69#11758196—22no—
70#11758196D412yes—
71C4×Dic61C2312yes—
72C2×#92418C2312yes—
73D488—22no—
74C23×C61—22no—
75C22×D61—21no—
76C22×D61—21no—
77Q8×C61—81no—
78D4×C61—22no—
79D4×C61—22no—
80D4×C61—42no—
81D4×C61—81no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C22⋊D61—44no—
87C22⋊D61—82no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—44no—
91C2×Dic61C2×D412yes—
92C2×Dic61C2×D412yes—
93D244—21no—
94D244—21no—
95D244—21no—
96D244#4112yescomplemented
97C4×D61—42no—
98C4×D61—42no—
99C4×D61—82no—
100Dic122—22no—
101C8×C61—21no—
102C8×C61—21no—
103#92418—22no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61C22×D411yescharacteristic
108C2×D61—22no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C4×C61—21no—
115C4×C61—42no—
116C4×C61AGL(1,ℤ/8)12yes—
117C4×C61C2×#4111yescharacteristic
118C4×C612−1+411yescharacteristic
119Dic61—22no—
120Dic61—22no—
121Dic61—41no—
122Dic61—41no—
123#3366—611nomaximal, Sylow
124C2×C61—82no—
125C2×C61#54811yescharacteristic
126C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C61#57611yescharacteristic
128D61—42no—
129D61—81no—
130#554—611no—
131#550—611no—
132#490—612no—
133#486D6111yescharacteristic, complemented
134#478—612no—
135#476—611no—
136#459—611no—
137#459—612no—
138#446—611no—
139#442—612no—
140C4×D8—611no—
141C61#336611yescharacteristic, complemented, Sylow
142C2×#41—1221no—
143C2×D8—612no—
144C2×D8—611no—
145C4⋊Q8C2×D6111yescharacteristic
146#127—612no—
147#127C2×D6111yescharacteristic
148#125—612no—
149C22⋊Q8—1221no—
150C22⋊Q8—1222no—
151#121—1221no—
152#121—1222no—
153C4×Q8—611no—
154C4×D4—612no—
155C4×D4—612no—
156C4×D4—611no—
157C4×D4—611no—
158C2×C4⋊C4—1221no—
159#107—611no—
160#106—612no—
161C4⋊C8—612no—
162C4⋊C8—611no—
163#102—612no—
164#102—611no—
165#102—611no—
166#102—612no—
167#102C2×D6112yes—
168#102C2×D6112yes—
169#97—612no—
170C4×C8C2×D6111yescharacteristic
171#41—2444no—
172C2×Q8—21no—
173C2×Q8—611no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—611no—
177C2×D4—611no—
178C2×D4—1222no—
179C2×D4—1222no—
180C2×D4C22×D6112yes—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—1221no—
184C22×C4—1221no—
185D8—1222no—
186D8—1224no—
187C2×C8—612no—
188C2×C8C22×D6111yescharacteristic
189C2×C8C22×D6111yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—611no—
192C4⋊C4—612no—
193C4⋊C4—611no—
194C4⋊C4—611no—
195C4⋊C4—1222no—
196C4⋊C4—1222no—
197C4⋊C4C22×D6112yes—
198C22⋊C4—1222no—
199C22⋊C4—1222no—
200C22⋊C4—1221no—
201C22⋊C4—1221no—
202C42—612no—
203C42C22×D6111yescharacteristic
204C23—22no—
205C23—1221no—
206C23—1221no—
207Q8—81no—
208Q8—1222no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—81no—
213D4—612no—
214D4—1221no—
215D4—1221no—
216D4—1221no—
217D4—4882no—
218D4—2444no—
219C2×C4—22no—
220C2×C4—612no—
221C2×C4—612no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—4882no—
225C2×C4—2444no—
226C2×C4—2442no—
227C2×C4—2442no—
228C2×C4D4×D6111yescharacteristic
229C2×C4D4×D6111yescharacteristic
230C2×C4C23×D6111yescharacteristic
231C8—21no—
232C8—21no—
233C8—1222no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—1222no—
238C22—2441no—
239C22—2441no—
240C22—2441no—
241C22—2441no—
242C22—2441no—
243C22C2×D4×D6111yescharacteristic
244C4—21no—
245C4—42no—
246C4—1222no—
247C4—1222no—
248C4—2441no—
249C4—2441no—
250C4#1451980412yes—
251C4#41×D6111yescharacteristic
252C4#1451982411yescharacteristic
253C2—82no—
254C2—4881no—
255C2—2442no—
256C2#1684042011yescharacteristic
257C2C2×#1451980411yescharacteristic
258C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3366
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16840473C2semidirect
2. #16840432C2semidirect
3. #16840125C2semidirect
4. #16840060C2semidirect
5. #16840049C2semidirect
6. #16839956C2semidirect
7. #16839954C2semidirect
8. #16839892C2semidirect
9. #16839871C2semidirect
10. C4×D488C2semidirect
11. C61×#486C2semidirect
96. D244#41semidirect
133. #486D61semidirect
141. C61#3366semidirect