Finite Group Databasebeta

← #21455098

Subgroups — #21455098

Order 7808.

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

normal subgroups only

This group has 752 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
2C2×#14519810C211yesmaximal, characteristic, complemented
3C22×#11758190C211yesmaximal, characteristic, complemented
4#16840333C211yesmaximal, characteristic, complemented
5#16839926C214yesmaximal, complemented
6#16839915C214yesmaximal, complemented
7#16839768C211yesmaximal, characteristic, complemented
8#16839759C211yesmaximal, characteristic, complemented
9C61×#408C211yesmaximal, characteristic, complemented
10#14519823—24no—
11#14519823—24no—
12C2×#11758226—21no—
13C2×#11758222C2212yes—
14C2×#11758222C2211yescharacteristic
15C22×Dic122C2211yescharacteristic, complemented
16C22×D244C2212yes—
17C22×D244C2211yescharacteristic
18C2×D4×D61—22no—
19C2×D4×D61—21no—
20#14519810—24no—
21C2×Dic244C2212yescomplemented
22C2×#11758190—24no—
23C2×#11758190C2214yescomplemented
24C2×#11758190C2212yescomplemented
25#14519775—21no—
26#14519764—21no—
27#14519758—22no—
28#14519756C2214yescomplemented
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—22no—
38C23×D61—21no—
39#41×C61—22no—
40#41×C61—22no—
41C2×Q8×C61D411yescharacteristic
42C2×D4×C61D412yes—
43C2×D4×C61D411yescharacteristic
44C22×C4×C61C2312yes—
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—22no—
47C2×C22⋊D61—21no—
48C22×Dic61—21no—
49#11758226—28no—
50D4×D61—216no—
51D4×D61—28no—
52#11758222—22no—
53#11758222—24no—
54#11758222—24no—
55#11758222D414yes—
56C2×D244—22no—
57C2×D244—21no—
58C2×D244—22no—
59C2×D244—24no—
60C2×D244—24no—
61C2×D244D414yes—
62C2×D244C2311yescharacteristic
63C2×D244C2312yes—
64C2×C4×D61—22no—
65C2×C4×D61—21no—
66C2×Dic122—22no—
67C2×Dic122—22no—
68C2×Dic122—21no—
69C2×Dic122C2312yes—
70C2×Dic122C2311yescharacteristic
71M16×C61—22no—
72C2×C8×C61—22no—
73C2×C8×C61C2312yes—
74C2×C8×C61C2312yes—
75C22⋊Dic61—21no—
76C22⋊Dic61—24no—
77C4⋊Dic61C2312yes—
78#11758196—24no—
79C4×Dic61—21no—
80Dic244—24no—
81#11758190—24no—
82#11758190—28no—
83C23×C61C2×D412yes—
84C23×C61C2×D411yescharacteristic
85C22×D61—22no—
86C22×D61—21no—
87C22×D61—28no—
88C22×D61—24no—
89C22×D61—82no—
90C22×D61—84no—
91Q8×C61—22no—
92D4×C61—24no—
93D4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D412yes—
99C2×C4×C61C2×D412yes—
100C2×C4×C61C2411yescharacteristic
101C22⋊D61—28no—
102C22⋊D61—24no—
103C2×Dic61—21no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—42no—
107D244—28no—
108D244—24no—
109D244—21no—
110D244—22no—
111D244C2×D412yes—
112D244C2×D414yes—
113C4×D61—28no—
114C4×D61—24no—
115Dic122—21no—
116Dic122—22no—
117Dic122—22no—
118Dic122—42no—
119Dic122C2×D412yes—
120C8×C61—22no—
121C8×C61—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—24no—
125C22×C61#12012yes—
126C22×C61C22×D411yescharacteristic
127C2×D61—24no—
128C2×D61—22no—
129C2×D61—44no—
130C2×D61—42no—
131C2×D61—84no—
132C2×D61—88no—
133C4×C61—22no—
134C4×C61#12012yes—
135C4×C61C22×D411yescharacteristic
136C4×C61C22×D411yescharacteristic
137Dic61—22no—
138Dic61—42no—
139Dic61—42no—
140#3009—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61—42no—
143C2×C61C2×#12011yescharacteristic
144C2×C61#57712yes—
145D61—44no—
146D61—42no—
147C2×H(5,𝔽2)—611no—
148C2×#137—611no—
149C22×SD16—611no—
150#536—611no—
151#452—614no—
152#450—614no—
153#418—611no—
154#416—611no—
155#408D6111yescharacteristic, complemented
156C61#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—1224no—
158H(5,𝔽2)—1224no—
159C2×#41—611no—
160C2×#41—612no—
161C2×#41—1221no—
162C2×#41C2×D6111yescharacteristic
163C22×Q8—611no—
164C22×D4—611no—
165C22×D4—612no—
166C22×D4—1222no—
167C22×D4—1221no—
168#137—1224no—
169C2×Q16—612no—
170C2×SD16—614no—
171C2×SD16—612no—
172C2×SD16—1224no—
173C2×M16C2×D6111yescharacteristic, complemented
174C22×C8C2×D6111yescharacteristic, complemented
175C4⋊Q8—1221no—
176#124—1221no—
177#123—1222no—
178C22⋊Q8—614no—
179#117—611no—
180#103—612no—
181#102—612no—
182#102—614no—
183C22⋊C8C2×D6114yescomplemented
184C24—1222no—
185C24—1221no—
186#41—22no—
187#41—22no—
188#41—614no—
189#41—1224no—
190#41—1224no—
191#41—1228no—
192#41—1222no—
193C2×Q8—611no—
194C2×Q8—612no—
195C2×Q8—1221no—
196C2×Q8—1222no—
197C2×Q8—1222no—
198C2×Q8D24411yescharacteristic
199C2×D4—614no—
200C2×D4—612no—
201C2×D4—611no—
202C2×D4—1224no—
203C2×D4—1224no—
204C2×D4—12216no—
205C2×D4—1228no—
206C2×D4—1222no—
207C2×D4—1221no—
208C2×D4—1222no—
209C2×D4—1221no—
210C2×D4—1222no—
211C2×D4D24412yes—
212C2×D4D24411yescharacteristic
213C22×C4—1222no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4C22×D6112yes—
217C22×C4C22×D6111yescharacteristic
218Q16—1224no—
219SD16—1228no—
220SD16—1224no—
221M16—22no—
222C2×C8—22no—
223C2×C8C22×D6112yes—
224C2×C8C22×D6112yes—
225C4⋊C4—612no—
226C4⋊C4—1224no—
227C22⋊C4—1221no—
228C22⋊C4—1224no—
229C42—1221no—
230C23—1228no—
231C23—1224no—
232C23—1222no—
233C23—1221no—
234C23—4882no—
235C23—4884no—
236C23C2×D24412yes—
237C23C2×D24411yescharacteristic
238Q8—22no—
239Q8—612no—
240Q8—1221no—
241Q8—1222no—
242Q8—1222no—
243Q8—2442no—
244D4—24no—
245D4—22no—
246D4—614no—
247D4—612no—
248D4—1228no—
249D4—1228no—
250D4—1224no—
251D4—1221no—
252D4—1222no—
253D4—1224no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—1228no—
257C2×C4—1221no—
258C2×C4—1224no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—2442no—
262C2×C4C2×D24412yes—
263C2×C4C2×D24411yescharacteristic
264C2×C4D4×D6112yes—
265C2×C4D4×D6112yes—
266C2×C4C23×D6111yescharacteristic
267C8—22no—
268C8—22no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—1224no—
273C22—1222no—
274C22—4884no—
275C22—4888no—
276C22—2444no—
277C22—2442no—
278C22#1451974712yes—
279C22C22×D24411yescharacteristic
280C4—22no—
281C4—1222no—
282C4—2442no—
283C4—2442no—
284C4#1451974712yes—
285C4C2×D4×D6111yescharacteristic
286C4C2×D4×D6111yescharacteristic
287C2—22no—
288C2—42no—
289C2—2444no—
290C2—2442no—
291C2C2×#1451974711yescharacteristic
292C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3009
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
2. C2×#14519810C2semidirect
3. C22×#11758190C2semidirect
4. #16840333C2semidirect
5. #16839926C2semidirect
6. #16839915C2semidirect
7. #16839768C2semidirect
8. #16839759C2semidirect
9. C61×#408C2semidirect
15. C22×Dic122C22semidirect
21. C2×Dic244C22semidirect
23. C2×#11758190C22semidirect
24. C2×#11758190C22semidirect
28. #14519756C22semidirect
29. #14519736C22semidirect
30. #14519702C22semidirect
31. #14519699C22semidirect
32. #14519699C22semidirect
34. C2×M16×C61C22semidirect
35. C22×C8×C61C22semidirect
36. C22⋊C8×C61C22semidirect
155. #408D61semidirect
156. C61#3009semidirect
173. C2×M16C2×D61semidirect
174. C22×C8C2×D61semidirect
183. C22⋊C8C2×D61semidirect