Finite Group Databasebeta

← #21455183

Subgroups — #21455183

Order 7808.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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#16840560C212yesmaximal, complemented
2#16840336C211yesmaximal, characteristic, complemented
3#16839945C214yesmaximal, complemented
4#16839935C214yesmaximal, complemented
5#16839779C212yesmaximal, complemented
6C2×#14519696C211yesmaximal, characteristic, complemented
7C2×2−1+4×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—22no—
10#14519807C2214yescomplemented
11#14519803—22no—
12#14519802C2214yescomplemented
13#14519797—24no—
14C2×#11758194C2212yes—
15#14519775C2212yescomplemented
16#14519766C2212yescomplemented
17#14519760—22no—
18#14519753—22no—
19#14519736C2211yescharacteristic
20#14519704C2218yescomplemented
21#14519696C2214yescomplemented
222−1+4×C61—24no—
232−1+4×C61—22no—
242−1+4×C61C2214yes—
25C2×#41×C61—22no—
26C2×#41×C61—22no—
27C2×#41×C61C2212yes—
28C22×Q8×C61—22no—
29C22×Q8×C61C2211yescharacteristic
30#41×C61—28no—
31#41×C61—28no—
32#41×C61—28no—
33#41×C61—28no—
34#41×C61—22no—
35#41×C61—22no—
36#41×C61D414yes—
37#41×C61C2314yes—
38C2×Q8×C61—22no—
39C2×Q8×C61—28no—
40C2×Q8×C61—28no—
41C2×Q8×C61—22no—
42C2×Q8×C61—22no—
43C2×Q8×C61D412yes—
44C2×Q8×C61D412yes—
45C2×Q8×C61C2312yes—
46C2×D4×C61—22no—
47C2×D4×C61—22no—
48C2×D4×C61D412yes—
49C22×C4×C61—24no—
50C22×C4×C61—22no—
51C22×C4×C61D412yes—
52C22×C4×C61C2311yescharacteristic
53C2×C22⋊D61—21no—
54#11758222—22no—
55#11758222—22no—
56C2×D244C2311yescharacteristic
57C2×C4×D61—21no—
58C2×Dic122C2311yescharacteristic
59C22⋊Dic61—21no—
60#11758202—24no—
61#11758201—24no—
62#11758200—24no—
63#11758199—24no—
64#11758198—24no—
65C4⋊Dic61—21no—
66#11758196—24no—
67C4×Dic61C2312yes—
68#11758194—22no—
69#11758194C2314yes—
70C2×#92418—22no—
71C23×C61—22no—
72C23×C61C2×D411yescharacteristic
73C22×D61—21no—
74Q8×C61—28no—
75Q8×C61—22no—
76Q8×C61—24no—
77Q8×C61—24no—
78Q8×C61C2×D414yes—
79D4×C61—28no—
80D4×C61—24no—
81D4×C61—24no—
82D4×C61—22no—
83D4×C61C2×D414yes—
84C2×C4×C61—216no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—24no—
89C2×C4×C61—24no—
90C2×C4×C61C2×D414yes—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D412yes—
93C2×C4×C61C2×D412yes—
94C2×C4×C61C2411yescharacteristic
95C22⋊D61—41no—
96C22⋊D61—41no—
97C2×Dic61—22no—
98C2×Dic61—21no—
99D244—22no—
100C4×D61—42no—
101Dic122—22no—
102#92418—24no—
103C22×C61—24no—
104C22×C61—41no—
105C22×C61—44no—
106C22×C61#12011yescharacteristic
107C22×C61#12011yescharacteristic
108C22×C61C22×D411yescharacteristic
109C2×D61—42no—
110C2×D61—41no—
111C4×C61—24no—
112C4×C61—24no—
113C4×C61#12012yes—
114C4×C61C22×D412yes—
115Dic61—42no—
116Dic61—41no—
117#3020—611nomaximal, Sylow
118C2×C61—21no—
119C2×C61—21no—
120C2×C61—21no—
121C2×C61—44no—
122C2×C61C2×#12011yescharacteristic
123D61—81no—
124C2×2−1+4D6111yescharacteristic, complemented
125#575—612no—
126#536—611no—
127#456—614no—
128#454—614no—
129#421—612no—
130C2×#101—611no—
131C61#302011yescharacteristic, complemented, Sylow
1322−1+4—24no—
1332−1+4—22no—
1342−1+4C2×D6114yes—
135C2×#41—22no—
136C2×#41—22no—
137C2×#41—611no—
138C2×#41C2×D6112yes—
139C22×Q8—22no—
140C22×Q8C2×D6111yescharacteristic
141#137—614no—
142#137—1222no—
143AGL(1,ℤ/8)—614no—
144AGL(1,ℤ/8)—1222no—
145#135—1224no—
146C2×M16—612no—
147C4⋊Q8—612no—
148#124—612no—
149#123—1222no—
150C22⋊Q8—1222no—
151#117—611no—
152#104—618no—
153#101—614no—
154#41—28no—
155#41—28no—
156#41—28no—
157#41—28no—
158#41—22no—
159#41—22no—
160#41—1222no—
161#41—1222no—
162#41C22⋊D6114yes—
163#41C22×D6114yes—
164C2×Q8—22no—
165C2×Q8—28no—
166C2×Q8—28no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—611no—
170C2×Q8C22⋊D6112yes—
171C2×Q8C22⋊D6112yes—
172C2×Q8C22×D6112yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—611no—
176C2×D4—1221no—
177C2×D4C22⋊D6112yes—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—1221no—
181C22×C4C22⋊D6112yes—
182C22×C4C22×D6111yescharacteristic
183Q16—1224no—
184SD16—1224no—
185SD16—1224no—
186D8—1224no—
187M16—614no—
188M16—1222no—
189C2×C8—1222no—
190C4⋊C4—1224no—
191C4⋊C4—1221no—
192C22⋊C4—1221no—
193C22⋊C4—1224no—
194C42—612no—
195C23—22no—
196C23—1221no—
197C23C2×C22⋊D6111yescharacteristic
198Q8—28no—
199Q8—24no—
200Q8—22no—
201Q8—24no—
202Q8—1222no—
203Q8C2×C22⋊D6114yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—1222no—
209D4—2441no—
210D4—2441no—
211D4C2×C22⋊D6114yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—1222no—
219C2×C4—1221no—
220C2×C4—2442no—
221C2×C4C2×C22⋊D6114yes—
222C2×C4C2×C22⋊D6112yes—
223C2×C4C2×C22⋊D6112yes—
224C2×C4C2×C22⋊D6111yescharacteristic
225C2×C4C23×D6111yescharacteristic
226C8—1224no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—2442no—
231C22—2441no—
232C22#1451974611yescharacteristic
233C22#1451974611yescharacteristic
234C22C22×C22⋊D6111yescharacteristic
235C4—24no—
236C4—24no—
237C4—2442no—
238C4—2441no—
239C4#1451974612yes—
240C4C22×C22⋊D6112yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—4881no—
246C2C2×#1451974611yescharacteristic
subgroupG/H
centerC2C2×#14519746
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×2−1+4×C61C2
socleC2×C61C2×#120
hypercenterC2×2−1+4D61
hypocenterC61#3020
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #16840560C2semidirect
2. #16840336C2semidirect
3. #16839945C2semidirect
4. #16839935C2semidirect
5. #16839779C2semidirect
6. C2×#14519696C2semidirect
7. C2×2−1+4×C61C2semidirect
10. #14519807C22semidirect
12. #14519802C22semidirect
15. #14519775C22semidirect
16. #14519766C22semidirect
20. #14519704C22semidirect
21. #14519696C22semidirect
124. C2×2−1+4D61semidirect
131. C61#3020semidirect