Finite Group Databasebeta

← #21457455

Subgroups — #21457455

Order 7808.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519810C211yesmaximal, characteristic, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3#16840421C211yesmaximal, characteristic, complemented
4#16840408C211yesmaximal, characteristic, complemented
5#16840146C211yesmaximal, characteristic, complemented
6#16840020C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16839985C211yesmaximal, characteristic, complemented
9#16839978C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839915C211yesmaximal, characteristic, complemented
12#16839909C211yesmaximal, characteristic, complemented
13#16839903C211yesmaximal, characteristic, complemented
14C4×#11758190C211yesmaximal, characteristic, complemented
15C61×#436C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C22×Dic122C2211yescharacteristic, complemented
19C22×D244C2211yescharacteristic
20#14519810—24no—
21#14519805—24no—
22C2×Dic244C2211yescharacteristic, complemented
23C2×Dic244C2211yescharacteristic, complemented
24C2×#11758190C2211yescharacteristic
25C2×#11758190C2211yescharacteristic
26C2×#11758190C2211yescharacteristic
27C2×#11758190C2211yescharacteristic
28C2×#11758190C2211yescharacteristic, complemented
29C2×D488C2211yescharacteristic
30C2×D488C2211yescharacteristic
31#14519765C2211yescharacteristic
32#14519765C2211yescharacteristic, complemented
33#14519763—21no—
34#14519762—21no—
35#14519756C2211yescharacteristic
36#14519756C2211yescharacteristic
37#14519755—21no—
38#14519751C2211yescharacteristic
39#14519751C2211yescharacteristic, complemented
40#14519750—21no—
41#14519749—21no—
42#14519745—21no—
43C4×Dic122C2211yescharacteristic, complemented
44C4×D244C2211yescharacteristic
45#14519737—21no—
46C22⋊C4×D61—21no—
47#14519709C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519702C2211yescharacteristic, complemented
50#14519702C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic
52#14519699C2211yescharacteristic
53#14519699C2211yescharacteristic, complemented
54C2×M16×C61C2211yescharacteristic
55C2×M16×C61C2211yescharacteristic, complemented
56C4×D4×C61C2211yescharacteristic
57C4⋊C8×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C22⋊C8×C61C2211yescharacteristic, complemented
60C4×C8×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×D4×C61D411yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70#11758222—22no—
71#11758222—22no—
72#11758222—41no—
73#11758222—41no—
74C2×D244—22no—
75C2×D244—21no—
76C2×D244—41no—
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×Dic122—22no—
84C2×Dic122—21no—
85C2×Dic122—41no—
86C2×Dic122C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88C2×Dic122C2311yescharacteristic
89M16×C61—22no—
90M16×C61—22no—
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C2×C8×C61C2311yescharacteristic
95C4⋊C4×C61D411yescharacteristic
96C22⋊C4×C61D411yescharacteristic
97C22⋊C4×C61D411yescharacteristic
98C42×C61C2311yescharacteristic
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108C4⋊Dic61C2311yescharacteristic
109C4⋊Dic61C2311yescharacteristic
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113C4×Dic61—21no—
114Dic244—22no—
115Dic244—22no—
116D488—22no—
117D488—22no—
118#11758190—22no—
119#11758190—22no—
120#11758190—41no—
121#11758190—41no—
122#11758190D414yescomplemented
123C23×C61C2×D411yescharacteristic
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—81no—
131D4×C61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2411yescharacteristic
141C22⋊D61—42no—
142C22⋊D61—42no—
143C22⋊D61—42no—
144C22⋊D61—81no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—42no—
151D244—21no—
152D244—21no—
153D244—21no—
154D244—21no—
155D244—21no—
156D244—42no—
157D244C2×D412yes—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—81no—
161Dic122—21no—
162Dic122—21no—
163Dic122—21no—
164Dic122—21no—
165Dic122—21no—
166Dic122—42no—
167Dic122C2×D412yes—
168C8×C61—21no—
169C8×C61—21no—
170C8×C61—21no—
171C8×C61C2×D412yes—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61C22×D411yescharacteristic
179C2×D61—22no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—84no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61C22×D411yescharacteristic
194C4×C61H(5,𝔽2)11yescharacteristic
195Dic61—22no—
196Dic61—41no—
197Dic61—41no—
198Dic61—41no—
199Dic61—41no—
200#3275—611nomaximal, Sylow
201C2×C61—41no—
202C2×C61—41no—
203C2×C61D4211yescharacteristic
204C2×C61#57511yescharacteristic
205C2×C61#57711yescharacteristic
206D61—42no—
207D61—81no—
208D61—81no—
209C2×#137—611no—
210C2×AGL(1,ℤ/8)—611no—
211#548—611no—
212#546—611no—
213#495—611no—
214#470—611no—
215#469—611no—
216#464—611no—
217#463—611no—
218#452—611no—
219#450—611no—
220#449—611no—
221#448—611no—
222C4×SD16—611no—
223#436D6111yescharacteristic, complemented
224C61#327511yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C2×#41—611no—
227C22×Q8—611no—
228C22×D4—611no—
229#137—1224no—
230AGL(1,ℤ/8)—1224no—
231C2×Q16—611no—
232C2×Q16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—611no—
236C2×SD16—611no—
237C2×SD16—611no—
238C2×D8—611no—
239C2×D8—611no—
240C2×M16C2×D6111yescharacteristic
241C2×M16C2×D6111yescharacteristic, complemented
242#124—611no—
243#124—611no—
244#124—1221no—
245#123—1221no—
246C22⋊Q8—611no—
247C22⋊Q8—611no—
248C22⋊Q8—1221no—
249#121—611no—
250#121—611no—
251#121—1221no—
252#121—1221no—
253#120—1221no—
254C4×Q8—611no—
255C4×D4—611no—
256C4×D4—1221no—
257C4×D4C2×D6111yescharacteristic
258C2×C22⋊C4—1221no—
259#106—611no—
260C4⋊C8C2×D6111yescharacteristic, complemented
261#103—611no—
262#103—611no—
263#103—611no—
264#102—611no—
265#102—611no—
266#102—611no—
267C22⋊C8C2×D6111yescharacteristic
268C22⋊C8C2×D6111yescharacteristic, complemented
269C4×C8C2×D6111yescharacteristic, complemented
270C24—1221no—
271#41—1222no—
272#41—1222no—
273#41—2441no—
274#41—2441no—
275C2×Q8—611no—
276C2×Q8—611no—
277C2×Q8—611no—
278C2×Q8—1222no—
279C2×Q8—1221no—
280C2×Q8—2441no—
281C2×D4—611no—
282C2×D4—611no—
283C2×D4—611no—
284C2×D4—1222no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—2441no—
291C2×D4D24411yescharacteristic
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4C22×D6111yescharacteristic
297C22×C4C22×D6111yescharacteristic
298Q16—1222no—
299Q16—1222no—
300SD16—614no—
301SD16—1222no—
302SD16—1222no—
303SD16—2441no—
304SD16—2441no—
305D8—1222no—
306D8—1222no—
307M16—22no—
308M16—22no—
309C2×C8C22×D6111yescharacteristic
310C2×C8C22×D6111yescharacteristic
311C2×C8C22×D6111yescharacteristic
312C2×C8C22×D6111yescharacteristic
313C4⋊C4—611no—
314C4⋊C4—611no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4D24411yescharacteristic
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4D24411yescharacteristic
329C22⋊C4D24411yescharacteristic
330C42—1221no—
331C42C22×D6111yescharacteristic
332C23—1221no—
333C23—1221no—
334C23—1221no—
335C23—4881no—
336C23—2442no—
337C23—2442no—
338C23C2×D24411yescharacteristic
339C23C2×D24411yescharacteristic
340Q8—612no—
341Q8—1221no—
342Q8—1221no—
343Q8—1221no—
344Q8—1221no—
345Q8—1221no—
346Q8—2442no—
347D4—41no—
348D4—612no—
349D4—1221no—
350D4—1221no—
351D4—1221no—
352D4—1221no—
353D4—1221no—
354D4—4881no—
355D4—2442no—
356D4—2442no—
357D4—2442no—
358D4—2442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—4881no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4C2×D24411yescharacteristic
373C2×C4C2×D24411yescharacteristic
374C2×C4C2×D24411yescharacteristic
375C2×C4C2×D24411yescharacteristic
376C2×C4C23×D6111yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D6112yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—1222no—
388C22—4884no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22C22×D24411yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—1222no—
403C4—2441no—
404C4—2441no—
405C4—2441no—
406C4—2441no—
407C4C2×D4×D6111yescharacteristic
408C4#1451982311yescharacteristic
409C2—41no—
410C2—41no—
411C2—4881no—
412C2—4881no—
413C2—2442no—
414C2D4×D24411yescharacteristic
415C2#1684056211yescharacteristic
416C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#436C2
socleC22×C61C22×D4
hypercenter#436D61
hypocenterC61#3275
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
2. C2×#14519805C2semidirect
3. #16840421C2semidirect
4. #16840408C2semidirect
5. #16840146C2semidirect
6. #16840020C2semidirect
7. #16840015C2semidirect
8. #16839985C2semidirect
9. #16839978C2semidirect
10. #16839926C2semidirect
11. #16839915C2semidirect
12. #16839909C2semidirect
13. #16839903C2semidirect
14. C4×#11758190C2semidirect
15. C61×#436C2semidirect
18. C22×Dic122C22semidirect
22. C2×Dic244C22semidirect
23. C2×Dic244C22semidirect
28. C2×#11758190C22semidirect
32. #14519765C22semidirect
39. #14519751C22semidirect
43. C4×Dic122C22semidirect
47. #14519709C22semidirect
48. #14519702C22semidirect
49. #14519702C22semidirect
50. #14519702C22semidirect
53. #14519699C22semidirect
55. C2×M16×C61C22semidirect
57. C4⋊C8×C61C22semidirect
59. C22⋊C8×C61C22semidirect
60. C4×C8×C61C22semidirect
122. #11758190D4semidirect
223. #436D61semidirect
224. C61#3275semidirect
241. C2×M16C2×D61semidirect
260. C4⋊C8C2×D61semidirect
268. C22⋊C8C2×D61semidirect
269. C4×C8C2×D61semidirect