Finite Group Databasebeta

← #21457320

Subgroups — #21457320

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×#14519801C211yesmaximal, characteristic, complemented
2C2×SD16×D61C211yesmaximal, characteristic, complemented
3#16840420C211yesmaximal, characteristic, complemented
4D4×D244C211yesmaximal, characteristic, complemented
5#16840152C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16839997C211yesmaximal, characteristic, complemented
8#16839963C211yesmaximal, characteristic, complemented
9#16839911C211yesmaximal, characteristic, complemented
10#16839908C211yesmaximal, characteristic, complemented
11#16839902C211yesmaximal, characteristic, complemented
12#16839894C211yesmaximal, characteristic, complemented
13#16839862C211yesmaximal, characteristic, complemented
14#16839832C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic, complemented
17C2×Q8×D61C2211yescharacteristic, complemented
18C22×D244—21no—
19C2×D4×D61C2211yescharacteristic
20C2×D4×D61C2211yescharacteristic
21#14519801—24no—
22C2×#11758190C2211yescharacteristic, complemented
23C2×#11758190C2211yescharacteristic, complemented
24C2×#11758200C2211yescharacteristic
25C2×#11758201C2211yescharacteristic, complemented
26C2×#11758201C2211yescharacteristic, complemented
27SD16×D61—24no—
28C2×#11758199C2211yescharacteristic, complemented
29C2×#11758199C2211yescharacteristic, complemented
30C2×#11758189C2211yescharacteristic, complemented
31C2×C8×D61C2211yescharacteristic, complemented
32#14519774C2211yescharacteristic
33#14519763—21no—
34#14519754—21no—
35#14519753C2211yescharacteristic, complemented
36#14519752C2211yescharacteristic
37#14519752C2211yescharacteristic
38#14519751—21no—
39#14519750—21no—
40#14519748C2211yescharacteristic, complemented
41#14519747—21no—
42#14519747—21no—
43C4×Dic122C2211yescharacteristic, complemented
44C4×D244C2211yescharacteristic
45#14519737—21no—
46#14519710C2211yescharacteristic, complemented
47#14519700C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic, complemented
50#14519698C2211yescharacteristic
51#14519689C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519688C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic, complemented
57C4×D4×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61—21no—
72Q8×D61—22no—
73Q8×D61—41no—
74#11758224—22no—
75#11758224—41no—
76D4×D61—22no—
77D4×D61—22no—
78D4×D61—41no—
79D4×D61—41no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—44no—
85C2×D244D411yescharacteristic
86C2×D244C2311yescharacteristic
87C2×D244C2311yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61C2311yescharacteristic
90C2×C4×D61C2311yescharacteristic
91C2×Dic122—21no—
92C2×Dic122C2311yescharacteristic
93SD16×C61—22no—
94D8×C61—22no—
95C2×C8×C61C2311yescharacteristic
96C2×C8×C61C2311yescharacteristic
97C4⋊C4×C61C2311yescharacteristic
98C22⋊C4×C61—21no—
99C22⋊C4×C61—21no—
100C22⋊C4×C61—21no—
101C42×C61C2311yescharacteristic
102C22⋊Dic61—21no—
103#11758201—22no—
104#11758201—41no—
105#11758200D414yescomplemented
106#11758199—22no—
107#11758199—41no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198D411yescharacteristic
112#11758198D411yescharacteristic
113C4⋊Dic61D411yescharacteristic
114C4⋊Dic61C2311yescharacteristic
115#11758196—21no—
116#11758196—21no—
117C4×Dic61—21no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120#11758190—22no—
121#11758190—22no—
122#11758189—22no—
123C8×D61—22no—
124C23×C61—21no—
125C23×C61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—81no—
133C22×D61—81no—
134C22×D61C2×D411yescharacteristic
135C22×D61C2×D411yescharacteristic
136Q8×C61—21no—
137Q8×C61—21no—
138D4×C61—21no—
139D4×C61—21no—
140D4×C61—21no—
141D4×C61C2×D412yes—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—42no—
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2×D411yescharacteristic
147C2×C4×C61C2411yescharacteristic
148C22⋊D61—42no—
149C22⋊D61—42no—
150C22⋊D61—42no—
151C22⋊D61—42no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—42no—
155C2×Dic61C2×D411yescharacteristic
156C2×Dic61C2×D411yescharacteristic
157D244—22no—
158D244—21no—
159D244—21no—
160D244—21no—
161D244—21no—
162D244—42no—
163D244—42no—
164D244—42no—
165D244—81no—
166C4×D61—21no—
167C4×D61—21no—
168C4×D61—21no—
169C4×D61—21no—
170C4×D61—42no—
171Dic122—21no—
172Dic122—42no—
173Dic122C2×D412yescomplemented
174C8×C61—21no—
175C8×C61—21no—
176#92418—21no—
177#92418C2×D412yescomplemented
178C22×C61—22no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61C22×D411yescharacteristic
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—84no—
197C2×D61—84no—
198C2×D61AGL(1,ℤ/8)12yescomplemented
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—41no—
202C4×C61—41no—
203C4×C61C22×D411yescharacteristic
204C4×C61H(5,𝔽2)11yescharacteristic
205Dic61—22no—
206Dic61—21no—
207Dic61—21no—
208Dic61—41no—
209#3265—611nomaximal, Sylow
210C2×C61—42no—
211C2×C61—81no—
212C2×C61D4211yescharacteristic
213C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C61#57711yescharacteristic
215D61—22no—
216D61—41no—
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#463D6111yescharacteristic, complemented
227#460—611no—
228#450—611no—
229#449—611no—
230#448—611no—
231#447—611no—
232#440—611no—
233#435—611no—
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—1224no—
247C2×SD16C2×D6111yescharacteristic
248C2×D8—611no—
249C2×D8—611no—
250C2×D8C2×D6111yescharacteristic
251C2×M16—611no—
252C22×C8—611no—
253#127—611no—
254#124—1221no—
255#124C2×D6111yescharacteristic, complemented
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#103C2×D6111yescharacteristic, complemented
273#102—611no—
274#102—611no—
275#102—611no—
276#102C2×D6111yescharacteristic, complemented
277C22⋊C8—611no—
278C22⋊C8—611no—
279#97—611no—
280C24—1221no—
281C24—1221no—
282#41—1222no—
283#41—2441no—
284C2×Q8—611no—
285C2×Q8—1221no—
286C2×Q8—1222no—
287C2×Q8—2441no—
288C2×Q8C22×D6111yescharacteristic
289C2×D4—611no—
290C2×D4—611no—
291C2×D4—611no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1222no—
297C2×D4—1222no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—2444no—
303C2×D4—2441no—
304C2×D4—2441no—
305C2×D4C22×D6111yescharacteristic
306C2×D4C22×D6111yescharacteristic
307C22×C4—21no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—1221no—
311C22×C4—1221no—
312SD16—22no—
313SD16—614no—
314SD16—1222no—
315SD16—1222no—
316SD16—1222no—
317SD16—2441no—
318D8—22no—
319D8—1222no—
320D8—2441no—
321M16—1222no—
322C2×C8—611no—
323C2×C8—611no—
324C2×C8—1222no—
325C2×C8C22×D6111yescharacteristic
326C2×C8C22×D6111yescharacteristic
327C4⋊C4—611no—
328C4⋊C4—611no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4C22×D6111yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—611no—
336C22⋊C4—611no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C42—1221no—
342C42C22×D6111yescharacteristic
343C23—21no—
344C23—21no—
345C23—611no—
346C23—611no—
347C23—1221no—
348C23—1221no—
349C23—4881no—
350C23—4881no—
351C23—2442no—
352C23—2442no—
353C23—2442no—
354C23—2442no—
355Q8—21no—
356Q8—21no—
357Q8—612no—
358Q8—1221no—
359Q8—2442no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—1222no—
364D4—1221no—
365D4—1221no—
366D4—1221no—
367D4—1221no—
368D4—4881no—
369D4—2442no—
370D4—2442no—
371D4—2442no—
372D4—2442no—
373D4—2442no—
374D4—2442no—
375D4—2442no—
376D4D4×D6112yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—611no—
381C2×C4—611no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4D4×D6111yescharacteristic
391C2×C4D4×D6111yescharacteristic
392C2×C4C23×D6111yescharacteristic
393C8—21no—
394C8—21no—
395C8—612no—
396C8—1221no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—612no—
404C22—1221no—
405C22—1221no—
406C22—1221no—
407C22—1221no—
408C22—1221no—
409C22—4884no—
410C22—4884no—
411C22—2441no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22—2441no—
417C22C2×D4×D6111yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—1221no—
423C4—1221no—
424C4—1222no—
425C4—2441no—
426C4C2×D4×D6111yescharacteristic
427C4#1451982311yescharacteristic
428C2—42no—
429C2—81no—
430C2—1222no—
431C2—4881no—
432C2—4881no—
433C2—2441no—
434C2#1684039611yescharacteristic
435C2AGL(1,ℤ/8)×D6111yescharacteristic
436C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3265
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. C2×SD16×D61C2semidirect
3. #16840420C2semidirect
4. D4×D244C2semidirect
5. #16840152C2semidirect
6. #16840011C2semidirect
7. #16839997C2semidirect
8. #16839963C2semidirect
9. #16839911C2semidirect
10. #16839908C2semidirect
11. #16839902C2semidirect
12. #16839894C2semidirect
13. #16839862C2semidirect
14. #16839832C2semidirect
15. C61×#463C2semidirect
16. C2×#11758224C22semidirect
17. C2×Q8×D61C22semidirect
22. C2×#11758190C22semidirect
23. C2×#11758190C22semidirect
25. C2×#11758201C22semidirect
26. C2×#11758201C22semidirect
28. C2×#11758199C22semidirect
29. C2×#11758199C22semidirect
30. C2×#11758189C22semidirect
31. C2×C8×D61C22semidirect
35. #14519753C22semidirect
40. #14519748C22semidirect
43. C4×Dic122C22semidirect
46. #14519710C22semidirect
47. #14519700C22semidirect
48. #14519699C22semidirect
49. #14519699C22semidirect
51. #14519689C22semidirect
52. #14519689C22semidirect
53. #14519688C22semidirect
56. #124×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
105. #11758200D4semidirect
173. Dic122C2×D4semidirect
177. #92418C2×D4semidirect
198. C2×D61AGL(1,ℤ/8)semidirect
226. #463D61semidirect
234. C61#3265semidirect
255. #124C2×D61semidirect
270. C4⋊C8C2×D61semidirect
272. #103C2×D61semidirect
276. #102C2×D61semidirect