Finite Group Databasebeta

← #21455179

Subgroups — #21455179

Order 7808.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14519822C211yesmaximal, characteristic, complemented
2#16840562C212yesmaximal, complemented
3#16840329C211yesmaximal, characteristic, complemented
4#16839942C214yesmaximal, complemented
5#16839932C214yesmaximal, complemented
6#16839778C212yesmaximal, complemented
7C2×#100×C61C211yesmaximal, characteristic, complemented
8#14519822—22no—
9#14519822—24no—
10#14519822C2214yes—
11C2×#11758222C2212yes—
12C2×#11758222C2211yescharacteristic, complemented
13C2×#11758224—22no—
14C22×C22⋊D61—22no—
15C2×D4×D61—22no—
16#14519810—22no—
17#14519810C2214yescomplemented
18#14519805—22no—
19#14519805C2214yescomplemented
20#14519799—24no—
21#14519773C2212yescomplemented
22#14519764C2212yescomplemented
23#14519748—22no—
24#14519746—22no—
25#14519736C2211yescharacteristic, complemented
26#14519703C2218yescomplemented
27C22×D4×C61C2211yescharacteristic
28C2×M16×C61C2212yescomplemented
29#100×C61C2214yescomplemented
30C24×C61D412yes—
31C23×D61—22no—
32C2×D4×C61—22no—
33C2×D4×C61—22no—
34C2×D4×C61D412yes—
35C2×D4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—24no—
38C2×C22⋊D61—28no—
39C2×C22⋊D61—22no—
40C2×C22⋊D61—28no—
41C2×C22⋊D61—21no—
42C2×C22⋊D61—24no—
43C22×Dic61—22no—
44#11758224—28no—
45#11758224—28no—
46D4×D61—28no—
47D4×D61—28no—
48#11758222—22no—
49#11758222—22no—
50#11758222—22no—
51#11758222—22no—
52#11758222D414yescomplemented
53#11758222C2314yes—
54C2×D244D412yescomplemented
55C2×D244C2311yescharacteristic, complemented
56C2×C4×D61—22no—
57C2×C4×D61—21no—
58C2×Dic122D412yescomplemented
59C2×Dic122C2311yescharacteristic, complemented
60M16×C61—22no—
61M16×C61C2314yescomplemented
62C2×C8×C61—22no—
63C22⋊Dic61—21no—
64C22⋊Dic61—24no—
65C4⋊Dic61—21no—
66C4×Dic61C2312yescomplemented
67Dic244—24no—
68D488—24no—
69#11758190—24no—
70#11758190—24no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—82no—
74C23×C61C2×D414yes—
75C23×C61C2×D411yescharacteristic
76C22×D61—22no—
77C22×D61—28no—
78C22×D61—21no—
79C22×D61—84no—
80D4×C61—24no—
81D4×C61—24no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2411yescharacteristic
86C22⋊D61—216no—
87C22⋊D61—24no—
88C22⋊D61—24no—
89C22⋊D61—41no—
90C22⋊D61—41no—
91C22⋊D61—84no—
92C2×Dic61—28no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—21no—
96D244—22no—
97D244—22no—
98D244C2×D414yes—
99C4×D61—24no—
100C4×D61—24no—
101C4×D61—42no—
102Dic122—22no—
103Dic122—22no—
104Dic122C2×D414yes—
105C8×C61—24no—
106C22×C61—24no—
107C22×C61—41no—
108C22×C61—44no—
109C22×C61—44no—
110C22×C61—82no—
111C22×C61#12011yescharacteristic
112C22×C61#12011yescharacteristic
113C22×C61C22×D411yescharacteristic
114C2×D61—24no—
115C2×D61—44no—
116C2×D61—42no—
117C2×D61—41no—
118C2×D61—88no—
119C4×C61#12012yes—
120C4×C61C22×D412yes—
121Dic61—24no—
122Dic61—42no—
123Dic61—41no—
124#3019—611nomaximal, Sylow
125C2×C61—21no—
126C2×C61—21no—
127C2×C61—21no—
128C2×C61—44no—
129C2×C61C2×#12011yescharacteristic
130D61—44no—
131D61—81no—
132C2×H(5,𝔽2)—611no—
133#575—612no—
134#535—611no—
135#455—614no—
136#453—614no—
137#421—612no—
138C2×#100D6111yescharacteristic, complemented
139C61#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—614no—
141H(5,𝔽2)—1224no—
142H(5,𝔽2)—1222no—
143C2×#41—612no—
144C2×#41—611no—
145C2×#41—1222no—
146C22×D4—1222no—
147C22×D4—1222no—
148C22×D4C2×D6111yescharacteristic
149#137—614no—
150#137—1222no—
151AGL(1,ℤ/8)—614no—
152AGL(1,ℤ/8)—1222no—
153#135—1224no—
154C2×M16C2×D6112yescomplemented
155#127—612no—
156#124—612no—
157#121—1222no—
158#120—1222no—
159#117—611no—
160#104—618no—
161#100C2×D6114yescomplemented
162C24—1222no—
163C24D24412yes—
164#41—614no—
165#41—614no—
166#41—1228no—
167#41—1228no—
168#41—1222no—
169#41—1222no—
170#41—1222no—
171#41—1222no—
172C2×Q8—612no—
173C2×Q8—611no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—612no—
177C2×D4—611no—
178C2×D4—1228no—
179C2×D4—1228no—
180C2×D4—1224no—
181C2×D4—1228no—
182C2×D4—1222no—
183C2×D4—1228no—
184C2×D4—1224no—
185C2×D4—1221no—
186C2×D4D24412yes—
187C2×D4C22×D6112yes—
188C22×C4—1222no—
189C22×C4—1222no—
190C22×C4—1221no—
191C22×C4C22×D6111yescharacteristic
192Q16—1224no—
193SD16—1224no—
194SD16—1224no—
195D8—1224no—
196M16—22no—
197M16C22×D6114yescomplemented
198C2×C8—22no—
199C4⋊C4—1221no—
200C22⋊C4—1221no—
201C22⋊C4—1224no—
202C42—612no—
203C23—22no—
204C23—22no—
205C23—82no—
206C23—1228no—
207C23—1222no—
208C23—1221no—
209C23—4884no—
210C23C2×D24414yes—
211C23C2×D24411yescharacteristic
212Q8—614no—
213Q8—1222no—
214Q8—1222no—
215D4—24no—
216D4—24no—
217D4—614no—
218D4—12216no—
219D4—1224no—
220D4—1224no—
221D4—1222no—
222D4—1222no—
223D4—4884no—
224D4—2441no—
225D4—2441no—
226C2×C4—1228no—
227C2×C4—1222no—
228C2×C4—1224no—
229C2×C4—1224no—
230C2×C4—1222no—
231C2×C4—1221no—
232C2×C4—2442no—
233C2×C4C2×D24411yescharacteristic
234C2×C4D4×D6112yes—
235C2×C4D4×D6112yes—
236C2×C4C23×D6111yescharacteristic
237C8—24no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—82no—
243C22—1224no—
244C22—4888no—
245C22—2442no—
246C22—2444no—
247C22—2441no—
248C22#1451974711yescharacteristic
249C22#1451974711yescharacteristic
250C22C22×D24411yescharacteristic
251C4—1224no—
252C4—2442no—
253C4—2441no—
254C4#1451974712yes—
255C4C2×D4×D6112yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—4881no—
261C2—2444no—
262C2C2×#1451974711yescharacteristic
subgroupG/H
centerC2C2×#14519747
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#100×C61C2
socleC2×C61C2×#120
hypercenterC2×#100D61
hypocenterC61#3019
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#14519822C2semidirect
2. #16840562C2semidirect
3. #16840329C2semidirect
4. #16839942C2semidirect
5. #16839932C2semidirect
6. #16839778C2semidirect
7. C2×#100×C61C2semidirect
12. C2×#11758222C22semidirect
17. #14519810C22semidirect
19. #14519805C22semidirect
21. #14519773C22semidirect
22. #14519764C22semidirect
25. #14519736C22semidirect
26. #14519703C22semidirect
28. C2×M16×C61C22semidirect
29. #100×C61C22semidirect
52. #11758222D4semidirect
54. C2×D244D4semidirect
55. C2×D244C23semidirect
58. C2×Dic122D4semidirect
59. C2×Dic122C23semidirect
61. M16×C61C23semidirect
66. C4×Dic61C23semidirect
138. C2×#100D61semidirect
139. C61#3019semidirect
154. C2×M16C2×D61semidirect
161. #100C2×D61semidirect
197. M16C22×D61semidirect