Finite Group Databasebeta

← #21455439

Subgroups — #21455439

Order 7808.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14519805C211yesmaximal, characteristic, complemented
2C2×M16×D61C211yesmaximal, characteristic, complemented
3#16840274C211yesmaximal, characteristic, complemented
4C2×#14519752C211yesmaximal, characteristic, complemented
5#16840016C212yesmaximal, complemented
6#16840009C212yesmaximal, complemented
7#16839999C212yesmaximal, complemented
8#16839992C212yesmaximal, complemented
9#16839766C211yesmaximal, characteristic, complemented
10#16839761C211yesmaximal, characteristic, complemented
11C61×#428C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244—21no—
14C22×D244C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519805—24no—
17C2×#11758190C2212yescomplemented
18C2×D488C2212yescomplemented
19C2×#11758194C2211yescharacteristic
20C2×#11758189C2212yescomplemented
21M16×D61—24no—
22C2×C8×D61C2212yescomplemented
23#14519761—21no—
24#14519757C2211yescharacteristic, complemented
25#14519757C2211yescharacteristic, complemented
26#14519752—21no—
27#14519752—21no—
28#14519752C2212yes—
29#14519752C2212yes—
30#14519752C2211yescharacteristic, complemented
31#14519752C2211yescharacteristic, complemented
32#14519747—21no—
33C4×D244—21no—
34C4×D244—21no—
35C2×#11758198—21no—
36#14519700C2212yescomplemented
37#14519697C2212yescomplemented
38#14519697C2212yescomplemented
39#14519697C2212yescomplemented
40C2×M16×C61C2211yescharacteristic
41#117×C61C2211yescharacteristic
42C2×C4⋊C4×C61C2211yescharacteristic
43#107×C61C2212yescomplemented
44#106×C61C2212yescomplemented
45C23×D61—21no—
46C23×D61D411yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—21no—
50C22×Dic61D411yescharacteristic
51#11758222—22no—
52#11758222—22no—
53C2×D244—22no—
54C2×D244—22no—
55C2×D244—22no—
56C2×D244—22no—
57C2×D244—21no—
58C2×D244—21no—
59C2×D244—21no—
60C2×D244—44no—
61C2×D244C2312yes—
62C2×D244C2311yescharacteristic
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—21no—
66C2×C4×D61D411yescharacteristic
67C2×C4×D61D411yescharacteristic
68C2×C4×D61C2311yescharacteristic
69C2×C4×D61C2311yescharacteristic
70C2×Dic122C2311yescharacteristic
71M16×C61D414yescomplemented
72C2×C8×C61C2312yes—
73C4⋊C4×C61—21no—
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2312yes—
76C4⋊C4×C61C2311yescharacteristic
77C22⋊C4×C61—21no—
78C42×C61—21no—
79#11758198—21no—
80#11758198—21no—
81#11758198—22no—
82#11758198—22no—
83#11758198—21no—
84#11758198—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87#11758194—22no—
88C2×#92418C2312yes—
89D488—24no—
90#11758190—24no—
91#11758189—24no—
92C8×D61—24no—
93C23×C61C2×D411yescharacteristic
94C22×D61—22no—
95C22×D61—22no—
96C22×D61—21no—
97C22×D61—22no—
98C22×D61—41no—
99C22×D61—42no—
100C22×D61—42no—
101C22×D61—42no—
102C22×D61C2×D411yescharacteristic
103C22×D61C2×D411yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61—42no—
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2×D412yes—
110C2×C4×C61#4112yes—
111C2×C4×C61C2411yescharacteristic
112C22⋊D61—42no—
113C2×Dic61—22no—
114C2×Dic61—21no—
115C2×Dic61C2×D411yescharacteristic
116C2×Dic61C2×D411yescharacteristic
117D244—22no—
118D244—21no—
119D244—22no—
120D244—21no—
121D244—42no—
122D244—44no—
123D244—42no—
124D244—44no—
125D244—42no—
126C4×D61—22no—
127C4×D61—22no—
128C4×D61—21no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—21no—
132C4×D61—42no—
133Dic122—21no—
134Dic122—21no—
135C8×C61C2×D414yescomplemented
136#92418—22no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61#12112yes—
140C22×C61C22×D411yescharacteristic
141C2×D61—21no—
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—44no—
147C2×D61—41no—
148C2×D61—42no—
149C2×D61—42no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—42no—
153C2×D61—84no—
154C2×D61AGL(1,ℤ/8)12yescomplemented
155C4×C61—42no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61#12112yes—
159C4×C61C22×D411yescharacteristic
160C4×C61C2×#4111yescharacteristic
161Dic61—21no—
162Dic61—21no—
163Dic61—41no—
164#3055—611nomaximal, Sylow
165C2×C61—22no—
166C2×C61C2×#12111yescharacteristic
167C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C61#57511yescharacteristic
169D61—22no—
170D61—41no—
171D61—81no—
172D61—82no—
173C2×AGL(1,ℤ/8)—611no—
174C22×M16—611no—
175#525—611no—
176C2×#121—611no—
177#469—612no—
178#468—612no—
179#466—612no—
180#465—612no—
181#428D6111yescharacteristic, complemented
182#418—611no—
183#417—611no—
184C61#305511yescharacteristic, complemented, Sylow
185C2×#41—611no—
186C22×D4—611no—
187C22×D4—1221no—
188C23×C4—611no—
189AGL(1,ℤ/8)—1224no—
190C2×SD16—612no—
191C2×D8—612no—
192C2×M16—611no—
193C2×M16—612no—
194C2×M16—1224no—
195C2×M16C2×D6111yescharacteristic
196C22×C8—612no—
197#123—1221no—
198C22⋊Q8—611no—
199C22⋊Q8—611no—
200#121—612no—
201#121—612no—
202#121—611no—
203#121—611no—
204#121—1221no—
205#121—1221no—
206#120—1221no—
207C4×D4—1221no—
208C4×D4—1221no—
209#117C2×D6111yescharacteristic
210C2×C4⋊C4C2×D6111yescharacteristic
211C2×C22⋊C4—1221no—
212#107C2×D6112yescomplemented
213#106C2×D6112yescomplemented
214#103—612no—
215#102—612no—
216#102—612no—
217#102—612no—
218C24—611no—
219C24—1221no—
220#41—1222no—
221#41—1222no—
222C2×Q8—611no—
223C2×D4—611no—
224C2×D4—612no—
225C2×D4—1221no—
226C2×D4—1221no—
227C2×D4—1222no—
228C2×D4—1222no—
229C2×D4—1221no—
230C2×D4—1222no—
231C2×D4—1221no—
232C2×D4—1222no—
233C2×D4—2444no—
234C22×C4—21no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1222no—
241C22×C4—1222no—
242C22×C4—1221no—
243C22×C4C22×D6111yescharacteristic
244SD16—1224no—
245D8—1224no—
246M16—1222no—
247M16—1224no—
248M16D24414yescomplemented
249C2×C8—612no—
250C2×C8—1224no—
251C2×C8C22×D6112yes—
252C4⋊C4—21no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C4⋊C4C22×D6112yes—
258C22⋊C4—21no—
259C22⋊C4—1222no—
260C22⋊C4—1222no—
261C22⋊C4—1221no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C42—21no—
266C23—611no—
267C23—611no—
268C23—1222no—
269C23—1222no—
270C23—1221no—
271C23—1222no—
272C23—2441no—
273C23—2442no—
274C23—2442no—
275C23—2442no—
276C23D4×D6111yescharacteristic
277Q8—1221no—
278Q8—1221no—
279D4—1221no—
280D4—1222no—
281D4—1222no—
282D4—1221no—
283D4—2442no—
284D4—2444no—
285D4—2442no—
286D4—2444no—
287D4—2442no—
288D4—2442no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—1222no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1222no—
301C2×C4—1222no—
302C2×C4—1221no—
303C2×C4—2442no—
304C2×C4C2×D24412yes—
305C2×C4D4×D6111yescharacteristic
306C2×C4#1175822612yes—
307C2×C4C23×D6111yescharacteristic
308C8—1222no—
309C8C2×D24414yescomplemented
310C22—21no—
311C22—21no—
312C22—612no—
313C22—1221no—
314C22—1221no—
315C22—1221no—
316C22—1221no—
317C22—1221no—
318C22—4884no—
319C22—2444no—
320C22—2441no—
321C22—2442no—
322C22—2442no—
323C22—2441no—
324C22—2441no—
325C22—2442no—
326C22#1451975212yes—
327C22C2×D4×D6111yescharacteristic
328C4—42no—
329C4—41no—
330C4—41no—
331C4—1221no—
332C4—1221no—
333C4—2441no—
334C4#1451975212yes—
335C4C22×D24411yescharacteristic
336C4C2×#1175822611yescharacteristic
337C2—22no—
338C2—1222no—
339C2—4882no—
340C2—4881no—
341C2—2441no—
342C2C2×#1451975211yescharacteristic
343C2AGL(1,ℤ/8)×D6111yescharacteristic
344C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#428C2
socleC22×C61C22×D4
hypercenter#428D61
hypocenterC61#3055
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. C2×M16×D61C2semidirect
3. #16840274C2semidirect
4. C2×#14519752C2semidirect
5. #16840016C2semidirect
6. #16840009C2semidirect
7. #16839999C2semidirect
8. #16839992C2semidirect
9. #16839766C2semidirect
10. #16839761C2semidirect
11. C61×#428C2semidirect
17. C2×#11758190C22semidirect
18. C2×D488C22semidirect
20. C2×#11758189C22semidirect
22. C2×C8×D61C22semidirect
24. #14519757C22semidirect
25. #14519757C22semidirect
30. #14519752C22semidirect
31. #14519752C22semidirect
36. #14519700C22semidirect
37. #14519697C22semidirect
38. #14519697C22semidirect
39. #14519697C22semidirect
43. #107×C61C22semidirect
44. #106×C61C22semidirect
71. M16×C61D4semidirect
135. C8×C61C2×D4semidirect
154. C2×D61AGL(1,ℤ/8)semidirect
181. #428D61semidirect
184. C61#3055semidirect
212. #107C2×D61semidirect
213. #106C2×D61semidirect
248. M16D244semidirect
309. C8C2×D244semidirect