Finite Group Databasebeta

← #21456554

Subgroups — #21456554

Order 7808.

446 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 119 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#16840309C212yesmaximal, complemented
2#16840159C211yesmaximal, characteristic, complemented
3#16840137C211yesmaximal, characteristic, complemented
4#16840107C212yesmaximal, complemented
5#16840016C211yesmaximal, characteristic, complemented
6#16840014C212yesmaximal, complemented
7#16840012C211yesmaximal, characteristic, complemented
8#16839875C211yesmaximal, characteristic, complemented
9#16839872C212yesmaximal, complemented
10#16839714C211yesmaximal, characteristic, complemented
11C61×#442C211yesmaximal, characteristic, complemented
12C2×#11758222—22no—
13C2×D488C2211yescharacteristic
14C2×#11758199C2212yes—
15C2×#11758189C2211yescharacteristic
16C2×#11758189C2211yescharacteristic
17#14519776C2212yes—
18#14519773C2212yes—
19#14519763—22no—
20#14519752C2212yes—
21#14519750—22no—
22#14519748C2212yes—
23C4×D244C2212yes—
24C4×C22⋊D61—22no—
25C42×D61C2211yescharacteristic
26#14519709C2211yescharacteristic
27#14519708C2212yes—
28#14519699C2212yes—
29#14519698C2212yes—
30#14519697C2212yes—
31#14519688C2211yescharacteristic
32C8×Dic61C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34C2×D8×C61C2211yescharacteristic
35C4×D4×C61C2212yes—
36#106×C61C2211yescharacteristic
37#102×C61C2212yes—
38#97×C61C2211yescharacteristic
39C2×D4×C61C2312yes—
40C22×C4×C61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61—22no—
43C2×C22⋊D61—22no—
44#11758222—48no—
45C2×D244—22no—
46C2×D244C2312yes—
47C2×C4×D61—22no—
48C2×C4×D61D412yes—
49C2×C4×D61C2311yescharacteristic
50C2×Dic122—22no—
51D8×C61—22no—
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2311yescharacteristic
54C4⋊C4×C61C2312yes—
55C22⋊C4×C61—22no—
56C42×C61C2311yescharacteristic
57C22⋊Dic61—22no—
58#11758199—24no—
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61C2312yes—
62#11758196—22no—
63C4×Dic61D412yes—
64C4×Dic61C2311yescharacteristic
65C2×#92418C2311yescharacteristic
66C2×#92418C2311yescharacteristic
67D488—22no—
68#11758189—22no—
69#11758189—22no—
70C23×C61—22no—
71C22×D61—22no—
72C22×D61C2×D411yescharacteristic
73D4×C61—22no—
74D4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—44no—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2411yescharacteristic
79C22⋊D61—44no—
80C22⋊D61—44no—
81C22⋊D61—44no—
82C2×Dic61—22no—
83C2×Dic61C2×D411yescharacteristic
84C2×Dic61C2×D412yes—
85D244—22no—
86D244—22no—
87D244—44no—
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—24no—
91C4×D61—44no—
92Dic122—44no—
93C8×C61—21no—
94C8×C61#4112yescomplemented
95#92418—21no—
96#92418#4112yescomplemented
97C22×C61—42no—
98C22×C61—42no—
99C22×C61—42no—
100C22×C61C22×D411yescharacteristic
101C2×D61—21no—
102C2×D61—22no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C4×C61—22no—
107C4×C61—42no—
108C4×C61C2×#4111yescharacteristic
109C4×C61C2×#4111yescharacteristic
110Dic61—21no—
111Dic61—42no—
112Dic61AGL(1,ℤ/8)14yes—
113#3184—611nomaximal, Sylow
114C2×C61—82no—
115C2×C61#53211yescharacteristic
116C2×C61C2×AGL(1,ℤ/8)12yes—
117D61—41no—
118D61—82no—
119#532—612no—
120#498—611no—
121#493—611no—
122#486—612no—
123#469—611no—
124#469—611no—
125#469—612no—
126#442—612no—
127#442—611no—
128#442D6111yescharacteristic, complemented
129C4×M16—611no—
130C61#318411yescharacteristic, complemented, Sylow
131C2×#41—1222no—
132C2×D8—612no—
133C2×D8—611no—
134C2×D8C2×D6111yescharacteristic
135C2×M16—611no—
136C2×M16—611no—
137C4⋊Q8—612no—
138#127—612no—
139#124—1222no—
140#121—612no—
141#121—612no—
142#121—1222no—
143C4×D4—612no—
144C4×D4—1222no—
145C4×D4C2×D6112yes—
146C2×C42—611no—
147#106—611no—
148#106—612no—
149#106C2×D6111yescharacteristic
150#102—612no—
151#102—612no—
152#102—612no—
153#102C2×D6112yes—
154#97—611no—
155#97C2×D6111yescharacteristic
156C4×C8—611no—
157C4×C8—611no—
158#41—2448no—
159C2×Q8—1222no—
160C2×D4—612no—
161C2×D4—1222no—
162C2×D4—1222no—
163C2×D4—1222no—
164C2×D4—1222no—
165C2×D4C22×D6112yes—
166C22×C4—22no—
167C22×C4—612no—
168C22×C4—611no—
169C22×C4—1222no—
170D8—22no—
171D8—1224no—
172D8—1222no—
173M16—1222no—
174M16—1222no—
175C2×C8—611no—
176C2×C8—611no—
177C2×C8C22×D6111yescharacteristic
178C2×C8C22×D6111yescharacteristic
179C4⋊C4—612no—
180C4⋊C4—1222no—
181C4⋊C4C22×D6112yes—
182C22⋊C4—22no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C42—612no—
187C42—611no—
188C42C22×D6111yescharacteristic
189C23—22no—
190C23—611no—
191C23—1222no—
192Q8—2444no—
193D4—22no—
194D4—22no—
195D4—1222no—
196D4—1222no—
197D4—2444no—
198D4—2444no—
199D4—2444no—
200D4—2444no—
201C2×C4—22no—
202C2×C4—44no—
203C2×C4—612no—
204C2×C4—611no—
205C2×C4—1224no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—2444no—
210C2×C4D4×D6112yes—
211C2×C4C23×D6111yescharacteristic
212C8—21no—
213C8—612no—
214C8—1221no—
215C8#1175822212yescomplemented
216C22—42no—
217C22—42no—
218C22—42no—
219C22—1222no—
220C22—1221no—
221C22—2442no—
222C22—2442no—
223C22—2442no—
224C22C2×D4×D6111yescharacteristic
225C4—22no—
226C4—42no—
227C4—614no—
228C4—1221no—
229C4—2442no—
230C4#41×D6111yescharacteristic
231C4C2×#1175822211yescharacteristic
232C2—82no—
233C2—4882no—
234C2—2441no—
235C2#1684030911yescharacteristic
236C2AGL(1,ℤ/8)×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#3184
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16840309C2semidirect
2. #16840159C2semidirect
3. #16840137C2semidirect
4. #16840107C2semidirect
5. #16840016C2semidirect
6. #16840014C2semidirect
7. #16840012C2semidirect
8. #16839875C2semidirect
9. #16839872C2semidirect
10. #16839714C2semidirect
11. C61×#442C2semidirect
94. C8×C61#41semidirect
96. #92418#41semidirect
128. #442D61semidirect
130. C61#3184semidirect
215. C8#11758222semidirect