Finite Group Databasebeta

← #21455089

Subgroups — #21455089

Order 7808.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519823C211yesmaximal, characteristic, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3C22×D488C211yesmaximal, characteristic, complemented
4#16840326C211yesmaximal, characteristic, complemented
5#16839909C214yesmaximal, complemented
6#16839898C214yesmaximal, complemented
7#16839768C211yesmaximal, characteristic, complemented
8#16839759C211yesmaximal, characteristic, complemented
9C61×#408C211yesmaximal, characteristic, complemented
10#14519823—24no—
11#14519823—24no—
12C2×#11758226—21no—
13C2×#11758222C2211yescharacteristic
14C2×#11758222C2212yescomplemented
15C22×D244C2211yescharacteristic
16C22×D244C2211yescharacteristic, complemented
17C22×D244C2212yescomplemented
18C2×D4×D61—21no—
19C2×D4×D61—22no—
20#14519805—24no—
21C2×#11758190C2212yescomplemented
22C2×D488—24no—
23C2×D488C2214yescomplemented
24C2×D488C2212yescomplemented
25#14519773—21no—
26#14519766—21no—
27#14519751C2214yescomplemented
28#14519745—22no—
29#14519736C2211yescharacteristic, complemented
30#14519702C2212yescomplemented
31#14519699C2212yescomplemented
32#14519699C2214yescomplemented
33C2×#41×C61C2211yescharacteristic
34C2×M16×C61C2211yescharacteristic, complemented
35C22×C8×C61C2211yescharacteristic, complemented
36C22⋊C8×C61C2214yescomplemented
37C23×D61—21no—
38C23×D61—22no—
39C23×D61—21no—
40#41×C61—22no—
41#41×C61—22no—
42C2×Q8×C61D411yescharacteristic
43C2×D4×C61D412yes—
44C2×D4×C61D411yescharacteristic
45C22×C4×C61C2312yes—
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—21no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—24no—
50#11758226—28no—
51D4×D61—216no—
52D4×D61—28no—
53#11758222—22no—
54#11758222—24no—
55#11758222—24no—
56#11758222D414yescomplemented
57C2×D244—21no—
58C2×D244—22no—
59C2×D244—22no—
60C2×D244—24no—
61C2×D244—24no—
62C2×D244—22no—
63C2×D244—22no—
64C2×D244—21no—
65C2×D244D414yescomplemented
66C2×D244C2312yes—
67C2×D244C2312yes—
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—22no—
71C2×Dic122C2311yescharacteristic
72M16×C61—22no—
73C2×C8×C61—22no—
74C2×C8×C61C2312yes—
75C2×C8×C61C2312yes—
76C22⋊Dic61—21no—
77#11758198—24no—
78C4⋊Dic61C2312yes—
79C4×Dic61—21no—
80D488—28no—
81D488—24no—
82#11758190—24no—
83C23×C61C2×D412yes—
84C23×C61C2×D411yescharacteristic
85C22×D61—21no—
86C22×D61—22no—
87C22×D61—28no—
88C22×D61—24no—
89C22×D61—22no—
90C22×D61—42no—
91C22×D61—82no—
92C22×D61—84no—
93C22×D61—82no—
94Q8×C61—22no—
95D4×C61—24no—
96D4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61C2×D412yes—
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D412yes—
102C2×C4×C61C2×D412yes—
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—28no—
105C22⋊D61—24no—
106C22⋊D61—84no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109D244—28no—
110D244—24no—
111D244—21no—
112D244—22no—
113D244—22no—
114D244—22no—
115D244—42no—
116D244C2×D412yes—
117D244C2×D414yes—
118C4×D61—28no—
119C4×D61—24no—
120Dic122—21no—
121Dic122C2×D412yes—
122C8×C61—22no—
123C8×C61—22no—
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—24no—
127C22×C61#12012yes—
128C22×C61C22×D411yescharacteristic
129C2×D61—24no—
130C2×D61—22no—
131C2×D61—44no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—44no—
135C2×D61—84no—
136C2×D61—88no—
137C2×D61—84no—
138C4×C61—22no—
139C4×C61#12012yes—
140C4×C61C22×D411yescharacteristic
141C4×C61C22×D411yescharacteristic
142Dic61—22no—
143Dic61—42no—
144#3008—611nomaximal, Sylow
145C2×C61—22no—
146C2×C61—42no—
147C2×C61C2×#12011yescharacteristic
148C2×C61#57612yes—
149D61—44no—
150D61—42no—
151D61—82no—
152C2×H(5,𝔽2)—611no—
153C2×AGL(1,ℤ/8)—611no—
154C22×D8—611no—
155#535—611no—
156#449—614no—
157#447—614no—
158#418—611no—
159#416—611no—
160#408D6111yescharacteristic, complemented
161C61#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—1224no—
163H(5,𝔽2)—1224no—
164C2×#41—611no—
165C2×#41—612no—
166C2×#41—1221no—
167C2×#41C2×D6111yescharacteristic
168C22×D4—611no—
169C22×D4—611no—
170C22×D4—612no—
171C22×D4—1222no—
172C22×D4—1221no—
173AGL(1,ℤ/8)—1224no—
174C2×SD16—612no—
175C2×D8—614no—
176C2×D8—612no—
177C2×D8—1224no—
178C2×M16C2×D6111yescharacteristic, complemented
179C22×C8C2×D6111yescharacteristic, complemented
180#127—1221no—
181#124—1221no—
182#121—614no—
183#120—1222no—
184#117—611no—
185#103—612no—
186#102—612no—
187#102—614no—
188C22⋊C8C2×D6114yescomplemented
189C24—1222no—
190C24—1221no—
191C24—1221no—
192#41—22no—
193#41—22no—
194#41—614no—
195#41—1224no—
196#41—1224no—
197#41—1228no—
198#41—1222no—
199C2×Q8—611no—
200C2×Q8D24411yescharacteristic
201C2×D4—614no—
202C2×D4—612no—
203C2×D4—611no—
204C2×D4—612no—
205C2×D4—1224no—
206C2×D4—1224no—
207C2×D4—12216no—
208C2×D4—1228no—
209C2×D4—1222no—
210C2×D4—1221no—
211C2×D4—1224no—
212C2×D4—1222no—
213C2×D4—1221no—
214C2×D4—1221no—
215C2×D4—1222no—
216C2×D4—1222no—
217C2×D4—1222no—
218C2×D4D24412yes—
219C2×D4D24411yescharacteristic
220C22×C4—1222no—
221C22×C4—1221no—
222C22×C4C22×D6112yes—
223C22×C4C22×D6111yescharacteristic
224SD16—1224no—
225D8—1228no—
226D8—1224no—
227M16—22no—
228C2×C8—22no—
229C2×C8C22×D6112yes—
230C2×C8C22×D6112yes—
231C4⋊C4—612no—
232C22⋊C4—1221no—
233C22⋊C4—1224no—
234C42—1221no—
235C23—1228no—
236C23—1224no—
237C23—1222no—
238C23—1221no—
239C23—1222no—
240C23—4882no—
241C23—4882no—
242C23—4884no—
243C23—2442no—
244C23C2×D24412yes—
245C23C2×D24411yescharacteristic
246Q8—22no—
247Q8—612no—
248Q8—1221no—
249D4—24no—
250D4—22no—
251D4—614no—
252D4—612no—
253D4—1228no—
254D4—1228no—
255D4—1224no—
256D4—1221no—
257D4—1222no—
258D4—1222no—
259D4—1222no—
260D4—1224no—
261D4—4884no—
262D4—2442no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—1228no—
266C2×C4—1221no—
267C2×C4—1224no—
268C2×C4—1222no—
269C2×C4C2×D24412yes—
270C2×C4C2×D24411yescharacteristic
271C2×C4D4×D6112yes—
272C2×C4D4×D6112yes—
273C2×C4C23×D6111yescharacteristic
274C8—22no—
275C8—22no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—1224no—
280C22—1222no—
281C22—4884no—
282C22—4884no—
283C22—4888no—
284C22—2442no—
285C22—2444no—
286C22—2444no—
287C22—2442no—
288C22#1451974712yes—
289C22C22×D24411yescharacteristic
290C4—22no—
291C4—1222no—
292C4—2442no—
293C4#1451974712yes—
294C4C2×D4×D6111yescharacteristic
295C4C2×D4×D6111yescharacteristic
296C2—22no—
297C2—42no—
298C2—4882no—
299C2—2444no—
300C2—2442no—
301C2C2×#1451974711yescharacteristic
302C2#1684056712yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3008
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#14519823C2semidirect
2. C2×#14519805C2semidirect
3. C22×D488C2semidirect
4. #16840326C2semidirect
5. #16839909C2semidirect
6. #16839898C2semidirect
7. #16839768C2semidirect
8. #16839759C2semidirect
9. C61×#408C2semidirect
14. C2×#11758222C22semidirect
16. C22×D244C22semidirect
17. C22×D244C22semidirect
21. C2×#11758190C22semidirect
23. C2×D488C22semidirect
24. C2×D488C22semidirect
27. #14519751C22semidirect
29. #14519736C22semidirect
30. #14519702C22semidirect
31. #14519699C22semidirect
32. #14519699C22semidirect
34. C2×M16×C61C22semidirect
35. C22×C8×C61C22semidirect
36. C22⋊C8×C61C22semidirect
56. #11758222D4semidirect
65. C2×D244D4semidirect
160. #408D61semidirect
161. C61#3008semidirect
178. C2×M16C2×D61semidirect
179. C22×C8C2×D61semidirect
188. C22⋊C8C2×D61semidirect