Finite Group Databasebeta

← #21458487

Subgroups — #21458487

Order 7808.

392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840492C211yesmaximal, characteristic, complemented
2#16840432C211yesmaximal, characteristic
3#16840107C212yesmaximal, complemented
4#16840050C212yesmaximal, complemented
5#16840049C211yesmaximal, characteristic, complemented
6#16839961C212yesmaximal, complemented
7#16839959C211yesmaximal, characteristic, complemented
8C8×Dic122C211yesmaximal, characteristic, complemented
9#16839853C212yesmaximal, complemented
10C4×#11758190C211yesmaximal, characteristic, complemented
11C61×#486C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C2×#11758190C2211yescharacteristic
14C2×#11758200C2212yes—
15#14519776—21no—
16#14519776C2212yes—
17#14519775—22no—
18#14519773C2212yes—
19#14519749—22no—
20#14519748—21no—
21C4×Dic122C2211yescharacteristic
22C4×Dic122C2211yescharacteristic
23#14519742—21no—
24#14519742C2212yes—
25C4×D244C2211yescharacteristic
26D4×Dic61C2212yes—
27#14519709C2211yescharacteristic
28#14519708C2212yes—
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519699C2211yescharacteristic
33#14519698C2212yes—
34#14519697C2212yes—
35C8×Dic61C2212yes—
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×C4×D61—21no—
51C2×Dic122—22no—
52C2×Dic122D411yescharacteristic
53C2×Dic122C2311yescharacteristic
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2312yes—
58C42×C61C2311yescharacteristic
59C22⋊Dic61—22no—
60#11758200—24no—
61#11758198—21no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2311yescharacteristic
65#11758196—21no—
66#11758196—22no—
67#11758196—22no—
68#11758196D412yes—
69C4×Dic61—21no—
70C4×Dic61—22no—
71C4×Dic61C2312yes—
72C2×#92418C2312yes—
73#11758190—22no—
74C23×C61—22no—
75C22×D61—21no—
76Q8×C61—81no—
77D4×C61—22no—
78D4×C61—22no—
79D4×C61—42no—
80D4×C61—81no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C22⋊D61—44no—
86C22⋊D61—82no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—44no—
91C2×Dic61C2×D412yes—
92C2×Dic61C2×D412yes—
93D244—21no—
94D244—21no—
95C4×D61—42no—
96Dic122—21no—
97Dic122—82no—
98Dic122SD1614yescomplemented
99Dic122#4112yescomplemented
100C8×C61—21no—
101C8×C61—21no—
102#92418—22no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61C22×D411yescharacteristic
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—41no—
110C4×C61—21no—
111C4×C61—42no—
112C4×C61C2×SD1612yes—
113C4×C61C2×#4111yescharacteristic
114C4×C612−1+411yescharacteristic
115Dic61—22no—
116Dic61—22no—
117Dic61—41no—
118Dic61—41no—
119Dic61C2×SD1614yes—
120#3362—611nomaximal, Sylow
121C2×C61—82no—
122C2×C61#54811yescharacteristic
123C2×C61C22×SD1611yescharacteristic
124C2×C61#57611yescharacteristic
125D61—81no—
126Q82—611no—
127#550—611no—
128#486—612no—
129#486D6111yescharacteristic, complemented
130#476—611no—
131#476—612no—
132#460—611no—
133#460—612no—
134C8×Q8—611no—
135C4×SD16—612no—
136C4×SD16—611no—
137C61#336211yescharacteristic, complemented, Sylow
138C2×#41—1221no—
139C2×SD16—612no—
140C2×SD16—611no—
141C4⋊Q8—612no—
142C4⋊Q8—1221no—
143C4⋊Q8—1222no—
144C4⋊Q8C2×D6111yescharacteristic
145#127—612no—
146#127C2×D6111yescharacteristic
147#121—1221no—
148#121—1222no—
149C4×Q8—611no—
150C4×Q8—612no—
151C4×Q8—611no—
152C4×Q8—1221no—
153C4×D4—612no—
154C4×D4—611no—
155#106—611no—
156#106—612no—
157C4⋊C8—612no—
158C4⋊C8—611no—
159#103—611no—
160#102—612no—
161#102—611no—
162#102—612no—
163#102C2×D6112yes—
164#102C2×D6112yes—
165C4×C8—612no—
166C4×C8C2×D6111yescharacteristic
167#41—2444no—
168C2×Q8—21no—
169C2×Q8—611no—
170C2×Q8—611no—
171C2×Q8—1222no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—611no—
175C2×D4—1222no—
176C2×D4—1222no—
177C2×D4C22×D6112yes—
178C22×C4—1222no—
179C22×C4—1221no—
180SD16—1222no—
181SD16—1224no—
182C2×C8—612no—
183C2×C8C22×D6111yescharacteristic
184C2×C8C22×D6111yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—612no—
187C4⋊C4—611no—
188C4⋊C4—611no—
189C4⋊C4—611no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1221no—
193C4⋊C4C22×D6112yes—
194C22⋊C4—1222no—
195C22⋊C4—1221no—
196C42—612no—
197C42—1222no—
198C42—1221no—
199C42C22×D6111yescharacteristic
200C23—22no—
201C23—1221no—
202Q8—81no—
203Q8—614no—
204Q8—612no—
205Q8—1221no—
206Q8—4882no—
207D4—22no—
208D4—22no—
209D4—42no—
210D4—81no—
211D4—1221no—
212D4—1221no—
213D4—4882no—
214D4—2444no—
215C2×C4—22no—
216C2×C4—612no—
217C2×C4—612no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—2444no—
222C2×C4—2442no—
223C2×C4D4×D6111yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4C23×D6111yescharacteristic
226C8—21no—
227C8—21no—
228C8—1222no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—2441no—
233C22—2441no—
234C22—2441no—
235C22C2×D4×D6111yescharacteristic
236C4—21no—
237C4—42no—
238C4—614no—
239C4—1222no—
240C4—1222no—
241C4—2441no—
242C4—2441no—
243C4SD16×D6112yes—
244C4#41×D6111yescharacteristic
245C4#1451982411yescharacteristic
246C2—82no—
247C2—4881no—
248C2#1684042011yescharacteristic
249C2C2×SD16×D6111yescharacteristic
250C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3362
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. #16840492C2semidirect
3. #16840107C2semidirect
4. #16840050C2semidirect
5. #16840049C2semidirect
6. #16839961C2semidirect
7. #16839959C2semidirect
8. C8×Dic122C2semidirect
9. #16839853C2semidirect
10. C4×#11758190C2semidirect
11. C61×#486C2semidirect
98. Dic122SD16semidirect
99. Dic122#41semidirect
129. #486D61semidirect
137. C61#3362semidirect