Finite Group Databasebeta

← #21457319

Subgroups — #21457319

Order 7808.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519805C211yesmaximal, characteristic, complemented
2C22×#11758190C211yesmaximal, characteristic, complemented
3#16840421C211yesmaximal, characteristic, complemented
4D4×D244C211yesmaximal, characteristic, complemented
5#16840151C211yesmaximal, characteristic, complemented
6#16840008C211yesmaximal, characteristic, complemented
7#16839998C211yesmaximal, characteristic, complemented
8#16839978C211yesmaximal, characteristic, complemented
9#16839963C211yesmaximal, characteristic, complemented
10#16839915C211yesmaximal, characteristic, complemented
11#16839909C211yesmaximal, characteristic, complemented
12#16839903C211yesmaximal, characteristic, complemented
13#16839898C211yesmaximal, characteristic, complemented
14#16839864C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic, complemented
17C22×Dic122C2211yescharacteristic, complemented
18C22×D244C2211yescharacteristic
19C22×D244C2211yescharacteristic
20C2×D4×D61—21no—
21#14519805—24no—
22C2×#11758190—24no—
23C2×#11758190C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×#11758190C2211yescharacteristic, complemented
26C2×#11758190C2211yescharacteristic, complemented
27C2×#11758190C2211yescharacteristic, complemented
28C2×#11758190C2211yescharacteristic, complemented
29C2×D488C2211yescharacteristic
30C2×D488C2211yescharacteristic, complemented
31C2×D488C2211yescharacteristic, complemented
32#14519774C2211yescharacteristic
33#14519765C2211yescharacteristic, complemented
34#14519763—21no—
35#14519756C2211yescharacteristic, complemented
36#14519755—21no—
37#14519752—21no—
38#14519751C2211yescharacteristic
39#14519751C2211yescharacteristic
40#14519751C2211yescharacteristic, complemented
41#14519749—21no—
42#14519747—21no—
43#14519747—21no—
44C4×Dic122C2211yescharacteristic, complemented
45C4×D244C2211yescharacteristic
46#14519737—21no—
47#14519711C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519702C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic, complemented
52#14519699C2211yescharacteristic, complemented
53#14519699C2211yescharacteristic, complemented
54C2×M16×C61C2211yescharacteristic, complemented
55C22×C8×C61C2211yescharacteristic, complemented
56C4×D4×C61C2211yescharacteristic
57C4⋊C8×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C22⋊C8×C61C2211yescharacteristic, complemented
60#97×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C2×D4×C61D411yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C22×Dic61—21no—
71D4×D61—44no—
72#11758222—22no—
73#11758222—41no—
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244C2311yescharacteristic
83C2×D244C2311yescharacteristic
84C2×D244C2311yescharacteristic
85C2×D244C2311yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×Dic122—22no—
89C2×Dic122—21no—
90C2×Dic122—41no—
91C2×Dic122C2311yescharacteristic
92C2×Dic122C2311yescharacteristic
93M16×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61C2311yescharacteristic
96C2×C8×C61C2311yescharacteristic
97C2×C8×C61C2311yescharacteristic
98C2×C8×C61C2311yescharacteristic
99C4⋊C4×C61D411yescharacteristic
100C22⋊C4×C61D411yescharacteristic
101C22⋊C4×C61D411yescharacteristic
102C42×C61C2311yescharacteristic
103C22⋊Dic61—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110C4⋊Dic61C2311yescharacteristic
111C4⋊Dic61C2311yescharacteristic
112#11758196—21no—
113#11758196—21no—
114C4×Dic61—21no—
115D488—22no—
116D488—22no—
117D488—41no—
118#11758190—22no—
119#11758190—22no—
120#11758190—22no—
121#11758190—22no—
122#11758190—41no—
123#11758190D414yescomplemented
124C23×C61C2×D411yescharacteristic
125C23×C61C2×D411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C22×D61—81no—
135C22×D61—81no—
136D4×C61—22no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61C2×D411yescharacteristic
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2×D411yescharacteristic
145C2×C4×C61C2411yescharacteristic
146C22⋊D61—42no—
147C22⋊D61—42no—
148C22⋊D61—42no—
149C22⋊D61—42no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—42no—
155D244—21no—
156D244—21no—
157D244—21no—
158D244—21no—
159D244—21no—
160D244—21no—
161D244—21no—
162D244—42no—
163D244—42no—
164D244—42no—
165D244—81no—
166D244C2×D412yes—
167C4×D61—42no—
168C4×D61—42no—
169Dic122—21no—
170Dic122—21no—
171Dic122—21no—
172Dic122—42no—
173Dic122C2×D412yescomplemented
174C8×C61—21no—
175C8×C61—21no—
176C8×C61—21no—
177C8×C61C2×D412yescomplemented
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61AGL(1,ℤ/8)12yescomplemented
184C22×C61C22×D411yescharacteristic
185C2×D61—22no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—84no—
198C2×D61—84no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61C22×D411yescharacteristic
204C4×C61H(5,𝔽2)11yescharacteristic
205Dic61—22no—
206Dic61—41no—
207Dic61—41no—
208Dic61—41no—
209#3265—611nomaximal, Sylow
210C2×C61—22no—
211C2×C61—41no—
212C2×C61D4211yescharacteristic
213C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C61#57711yescharacteristic
215D61—42no—
216D61—81no—
217D61—81no—
218D61—81no—
219C2×AGL(1,ℤ/8)—611no—
220C22×SD16—611no—
221#548—611no—
222D42—611no—
223#496—611no—
224#468—611no—
225#466—611no—
226#463—611no—
227#460—611no—
228#450—611no—
229#449—611no—
230#448—611no—
231#447—611no—
232#440—611no—
233#435D6111yescharacteristic, complemented
234C61#326511yescharacteristic, complemented, Sylow
235C2×#41—611no—
236C22×Q8—611no—
237C22×D4—611no—
238C22×D4—611no—
239C22×D4—1221no—
240AGL(1,ℤ/8)—1224no—
241C2×SD16—611no—
242C2×SD16—611no—
243C2×SD16—611no—
244C2×SD16—611no—
245C2×SD16—611no—
246C2×SD16—611no—
247C2×SD16—1224no—
248C2×D8—611no—
249C2×D8—611no—
250C2×D8—611no—
251C2×M16C2×D6111yescharacteristic, complemented
252C22×C8C2×D6111yescharacteristic, complemented
253#127—611no—
254#124—611no—
255#124—1221no—
256C22⋊Q8—611no—
257C22⋊Q8—1221no—
258#121—611no—
259#121—611no—
260#121—611no—
261#121—1221no—
262#121—1221no—
263#120—1221no—
264#120—1221no—
265C4×Q8—611no—
266C4×D4—611no—
267C4×D4—1221no—
268C4×D4C2×D6111yescharacteristic
269#107—611no—
270C4⋊C8C2×D6111yescharacteristic, complemented
271#103—611no—
272#103—611no—
273#102—611no—
274#102—611no—
275#102—611no—
276#102—611no—
277C22⋊C8C2×D6111yescharacteristic, complemented
278C22⋊C8C2×D6111yescharacteristic, complemented
279#97C2×D6111yescharacteristic, complemented
280C24—1221no—
281C24—1221no—
282#41—1222no—
283#41—2441no—
284C2×Q8—611no—
285C2×Q8—611no—
286C2×Q8—1222no—
287C2×Q8—1221no—
288C2×Q8—2441no—
289C2×D4—611no—
290C2×D4—611no—
291C2×D4—611no—
292C2×D4—611no—
293C2×D4—1222no—
294C2×D4—1222no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—2441no—
304C2×D4—2441no—
305C2×D4—2444no—
306C2×D4D24411yescharacteristic
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4C22×D6111yescharacteristic
311C22×C4C22×D6111yescharacteristic
312SD16—614no—
313SD16—1222no—
314SD16—1222no—
315SD16—1222no—
316SD16—1222no—
317SD16—2441no—
318D8—1222no—
319D8—1222no—
320D8—2441no—
321M16—22no—
322C2×C8—22no—
323C2×C8C22×D6111yescharacteristic
324C2×C8C22×D6111yescharacteristic
325C2×C8C22×D6111yescharacteristic
326C2×C8C22×D6111yescharacteristic
327C4⋊C4—611no—
328C4⋊C4—611no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4D24411yescharacteristic
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4D24411yescharacteristic
340C22⋊C4D24411yescharacteristic
341C42—1221no—
342C42C22×D6111yescharacteristic
343C23—1221no—
344C23—1221no—
345C23—1221no—
346C23—1221no—
347C23—4881no—
348C23—4881no—
349C23—2442no—
350C23—2442no—
351C23—2442no—
352C23—2442no—
353C23C2×D24411yescharacteristic
354C23C2×D24411yescharacteristic
355Q8—612no—
356Q8—1221no—
357Q8—1221no—
358Q8—1221no—
359Q8—2442no—
360D4—22no—
361D4—612no—
362D4—1221no—
363D4—1221no—
364D4—1221no—
365D4—1221no—
366D4—1221no—
367D4—1221no—
368D4—1221no—
369D4—4881no—
370D4—2442no—
371D4—2442no—
372D4—2442no—
373D4—2442no—
374D4—2442no—
375D4—2442no—
376D4—2442no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4C2×D24411yescharacteristic
389C2×C4C2×D24411yescharacteristic
390C2×C4C2×D24411yescharacteristic
391C2×C4C2×D24411yescharacteristic
392C2×C4C23×D6111yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8D4×D6112yescomplemented
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—1222no—
403C22—4884no—
404C22—4884no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22—2441no—
410C22—2441no—
411C22—2441no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22#1451980512yescomplemented
417C22C22×D24411yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—1222no—
423C4—2441no—
424C4—2441no—
425C4—2441no—
426C4C2×D4×D6111yescharacteristic
427C4#1451982311yescharacteristic
428C2—22no—
429C2—41no—
430C2—4881no—
431C2—4881no—
432C2—4881no—
433C2—2442no—
434C2D4×D24411yescharacteristic
435C2C2×#1451980511yescharacteristic
436C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3265
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. C22×#11758190C2semidirect
3. #16840421C2semidirect
4. D4×D244C2semidirect
5. #16840151C2semidirect
6. #16840008C2semidirect
7. #16839998C2semidirect
8. #16839978C2semidirect
9. #16839963C2semidirect
10. #16839915C2semidirect
11. #16839909C2semidirect
12. #16839903C2semidirect
13. #16839898C2semidirect
14. #16839864C2semidirect
15. C61×#435C2semidirect
16. C2×#11758222C22semidirect
17. C22×Dic122C22semidirect
25. C2×#11758190C22semidirect
26. C2×#11758190C22semidirect
27. C2×#11758190C22semidirect
28. C2×#11758190C22semidirect
30. C2×D488C22semidirect
31. C2×D488C22semidirect
33. #14519765C22semidirect
35. #14519756C22semidirect
40. #14519751C22semidirect
44. C4×Dic122C22semidirect
47. #14519711C22semidirect
48. #14519702C22semidirect
49. #14519702C22semidirect
51. #14519699C22semidirect
52. #14519699C22semidirect
53. #14519699C22semidirect
54. C2×M16×C61C22semidirect
55. C22×C8×C61C22semidirect
57. C4⋊C8×C61C22semidirect
58. C22⋊C8×C61C22semidirect
59. C22⋊C8×C61C22semidirect
60. #97×C61C22semidirect
123. #11758190D4semidirect
173. Dic122C2×D4semidirect
177. C8×C61C2×D4semidirect
183. C22×C61AGL(1,ℤ/8)semidirect
233. #435D61semidirect
234. C61#3265semidirect
251. C2×M16C2×D61semidirect
252. C22×C8C2×D61semidirect
270. C4⋊C8C2×D61semidirect
277. C22⋊C8C2×D61semidirect
278. C22⋊C8C2×D61semidirect
279. #97C2×D61semidirect
396. C8D4×D61semidirect
416. C22#14519805semidirect