Finite Group Databasebeta

← #21457591

Subgroups — #21457591

Order 7808.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840579C211yesmaximal, characteristic, complemented
2#16840578C211yesmaximal, characteristic, complemented
3#16840572C211yesmaximal, characteristic, complemented
4#16840568C211yesmaximal, characteristic, complemented
5#16840153C211yesmaximal, characteristic, complemented
6#16840038C211yesmaximal, characteristic, complemented
7#16840036C211yesmaximal, characteristic, complemented
8#16840024C211yesmaximal, characteristic, complemented
9#16839947C211yesmaximal, characteristic, complemented
10#16839943C211yesmaximal, characteristic, complemented
11#16839942C211yesmaximal, characteristic, complemented
12#16839933C211yesmaximal, characteristic, complemented
13#16839883C211yesmaximal, characteristic, complemented
14#16839882C211yesmaximal, characteristic, complemented
15C61×#471C211yesmaximal, characteristic, complemented
16#14519825C2211yescharacteristic
17#14519824C2211yescharacteristic
18#14519824C2211yescharacteristic, complemented
19#14519822C2211yescharacteristic
20#14519810—21no—
21#14519810—21no—
22#14519810C2211yescharacteristic
23#14519810C2211yescharacteristic
24#14519810C2211yescharacteristic
25#14519810C2211yescharacteristic, complemented
26#14519809—21no—
27#14519808C2211yescharacteristic
28#14519806—21no—
29#14519806—21no—
30#14519806—21no—
31#14519804—21no—
32#14519803C2211yescharacteristic
33#14519801—21no—
34#14519799—21no—
35#14519799C2211yescharacteristic
36#14519798—21no—
37#14519798—21no—
38#14519797C2211yescharacteristic
39#14519796—21no—
40C2×Dic244—21no—
41C2×Dic244C2211yescharacteristic, complemented
42C2×#11758202C2211yescharacteristic, complemented
43Q16×D61—21no—
44C2×#11758200C2211yescharacteristic
45SD16×D61—21no—
46SD16×D61—21no—
47#14519785C2211yescharacteristic
48#14519785C2211yescharacteristic, complemented
49#14519783C2211yescharacteristic
50#14519775C2211yescharacteristic, complemented
51#14519764C2211yescharacteristic
52#14519712C2211yescharacteristic, complemented
53#14519704C2211yescharacteristic, complemented
54#14519703C2211yescharacteristic
55#14519703C2211yescharacteristic
56#14519703C2211yescharacteristic, complemented
57#14519695C2211yescharacteristic, complemented
58#14519695C2211yescharacteristic, complemented
59#14519687C2211yescharacteristic, complemented
60#137×C61C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C61C2211yescharacteristic
62C2×SD16×C61C2211yescharacteristic
63#131×C61C2211yescharacteristic, complemented
64#108×C61C2211yescharacteristic, complemented
65#101×C61C2211yescharacteristic, complemented
66#100×C61C2211yescharacteristic
67#41×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C2×C22⋊D61—41no—
71#11758226—21no—
72#11758226—21no—
73Q8×D61—21no—
74Q8×D61—21no—
75Q8×D61—21no—
76Q8×D61—21no—
77#11758224—21no—
78#11758224—21no—
79#11758224—21no—
80#11758224—21no—
81#11758224—41no—
82#11758224—41no—
83D4×D61—21no—
84D4×D61—21no—
85#11758222—21no—
86#11758222—21no—
87#11758222—41no—
88#11758222C2311yescharacteristic
89#11758222C2311yescharacteristic
90#11758222C2311yescharacteristic
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122C2311yescharacteristic
94C2×Dic122C2311yescharacteristic
95Q16×C61—21no—
96SD16×C61—21no—
97SD16×C61—21no—
98SD16×C61—21no—
99SD16×C61—21no—
100D8×C61—21no—
101M16×C61—21no—
102M16×C61C2311yescharacteristic
103M16×C61C2311yescharacteristic
104M16×C61C2311yescharacteristic
105C2×C8×C61—21no—
106C2×C8×C61C2311yescharacteristic
107C22⋊Dic61—41no—
108#11758202—21no—
109#11758202—21no—
110#11758202—21no—
111#11758202D411yescharacteristic
112#11758201—21no—
113#11758201D411yescharacteristic
114#11758200—21no—
115#11758200—21no—
116#11758200—21no—
117#11758200D411yescharacteristic
118#11758199—21no—
119#11758199D411yescharacteristic
120#11758196—41no—
121C4×Dic61C2311yescharacteristic
122#11758194C2311yescharacteristic
123C2×#92418C2311yescharacteristic
124Dic244—21no—
125Dic244—21no—
126Dic244—21no—
127Dic244—21no—
128Dic244—21no—
129Dic244—21no—
130Dic244D411yescharacteristic
131D488D411yescharacteristic
132#11758190—21no—
133#11758190—21no—
134#11758190—21no—
135#11758190—21no—
136#11758190D411yescharacteristic
137#11758190D411yescharacteristic
138#11758189—21no—
139#11758189—21no—
140#11758189—21no—
141C8×D61—21no—
142C8×D61—21no—
143C8×D61—21no—
144C23×C61—21no—
145C22×D61—41no—
146Q8×C61—21no—
147Q8×C61—21no—
148Q8×C61C2×D411yescharacteristic
149D4×C61—21no—
150D4×C61—21no—
151D4×C61—21no—
152D4×C61C2×D411yescharacteristic
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61C2411yescharacteristic
156C22⋊D61—21no—
157C22⋊D61—21no—
158C22⋊D61—21no—
159C22⋊D61—41no—
160C22⋊D61—41no—
161C22⋊D61—41no—
162C22⋊D61—41no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169D244—41no—
170D244C2×D411yescharacteristic
171D244C2×D411yescharacteristic
172D244C2×D411yescharacteristic
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—21no—
176C4×D61—41no—
177C4×D61—41no—
178C4×D61—41no—
179C4×D61—41no—
180Dic122—21no—
181Dic122—21no—
182Dic122—21no—
183Dic122—21no—
184Dic122—41no—
185Dic122—41no—
186Dic122—41no—
187Dic122C2×D411yescharacteristic
188Dic122C2×D411yescharacteristic
189Dic122C2×D411yescharacteristic
190C8×C61—21no—
191C8×C61—21no—
192C8×C61—21no—
193C8×C61C2×D411yescharacteristic
194C8×C61C2×D411yescharacteristic
195#92418—21no—
196#92418C2×D411yescharacteristic
197#92418C2×D411yescharacteristic
198C22×C61—21no—
199C22×C61—41no—
200C22×C61—81no—
201C22×C61H(5,𝔽2)11yescharacteristic
202C2×D61—21no—
203C2×D61—21no—
204C2×D61—21no—
205C2×D61—161no—
206C4×C61—21no—
207C4×C61—41no—
208C4×C61C22×D411yescharacteristic
209C4×C61C22×D411yescharacteristic
210Dic61—21no—
211Dic61—21no—
212Dic61—21no—
213Dic61—41no—
214Dic61—41no—
215Dic61—41no—
216#3289—611nomaximal, Sylow
217C2×C61—21no—
218C2×C61—41no—
219C2×C61—81no—
220C2×C61D4211yescharacteristic
221D61—41no—
222D61—41no—
223D61—41no—
224#578—611no—
225#578—611no—
226#577—611no—
227#577—611no—
228#497—611no—
229#473—611no—
230#473—611no—
231#471—611no—
232#471D6111yescharacteristic, complemented
233#456—611no—
234#456—611no—
235#455—611no—
236#454—611no—
237#444—611no—
238#444—611no—
239C61#328911yescharacteristic, complemented, Sylow
2402−1+4—611no—
2412−1+4—611no—
2422−1+4—611no—
243H(5,𝔽2)—611no—
244#137—611no—
245#137—611no—
246#137—611no—
247#137—611no—
248#137—611no—
249#137—1221no—
250#137—1221no—
251#137—1221no—
252#137—1221no—
253#137—1221no—
254#137—1221no—
255#137C2×D6111yescharacteristic, complemented
256AGL(1,ℤ/8)—611no—
257AGL(1,ℤ/8)—1221no—
258AGL(1,ℤ/8)—1221no—
259AGL(1,ℤ/8)C2×D6111yescharacteristic
260#135—611no—
261#135—611no—
262#135—1221no—
263#135—1221no—
264#135—1221no—
265#135—1221no—
266C2×Q16—611no—
267C2×Q16—611no—
268C2×Q16—1221no—
269C2×Q16—1221no—
270C2×SD16—611no—
271C2×SD16—1221no—
272C2×SD16—1221no—
273C2×SD16C2×D6111yescharacteristic
274#131—611no—
275#131—611no—
276#131—611no—
277#131C2×D6111yescharacteristic, complemented
278C4⋊Q8—611no—
279#124—611no—
280#108—611no—
281#108C2×D6111yescharacteristic, complemented
282#104—611no—
283#104—611no—
284#104—611no—
285#104—611no—
286#101—611no—
287#101—611no—
288#101C2×D6111yescharacteristic, complemented
289#100C2×D6111yescharacteristic
290#97—611no—
291#41—611no—
292#41—611no—
293#41—611no—
294#41—1221no—
295#41—1221no—
296#41—1221no—
297#41—1221no—
298#41—1221no—
299#41—1221no—
300#41—1221no—
301#41—1221no—
302#41—2441no—
303#41—2441no—
304#41—2441no—
305#41C22×D6111yescharacteristic
306C2×Q8—611no—
307C2×Q8—611no—
308C2×Q8—1221no—
309C2×Q8—1221no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×Q8C22×D6111yescharacteristic
315C2×D4—1221no—
316C2×D4—1221no—
317C2×D4—2441no—
318C2×D4C22×D6111yescharacteristic
319Q16—21no—
320Q16—611no—
321Q16—611no—
322Q16—1221no—
323Q16—1221no—
324Q16—1221no—
325Q16—1221no—
326Q16—1221no—
327Q16—1221no—
328Q16—1221no—
329Q16—1221no—
330Q16—1221no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—611no—
336SD16—611no—
337SD16—611no—
338SD16—611no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16—1221no—
346SD16—1221no—
347D8—21no—
348D8—611no—
349D8—611no—
350D8—1221no—
351M16—21no—
352M16—611no—
353M16—1221no—
354M16—1221no—
355M16—1221no—
356M16C22×D6111yescharacteristic
357M16C22×D6111yescharacteristic
358M16C22×D6111yescharacteristic
359C2×C8—21no—
360C2×C8—611no—
361C2×C8—1221no—
362C2×C8—1221no—
363C2×C8—1221no—
364C2×C8C22×D6111yescharacteristic
365C4⋊C4—2441no—
366C22⋊C4—2441no—
367C42—611no—
368C23—21no—
369C23—2441no—
370Q8—21no—
371Q8—21no—
372Q8—611no—
373Q8—611no—
374Q8—611no—
375Q8—1221no—
376Q8—1221no—
377Q8—1221no—
378Q8—1221no—
379Q8—2441no—
380Q8—2441no—
381Q8—2441no—
382Q8D4×D6111yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—611no—
387D4—611no—
388D4—611no—
389D4—1221no—
390D4—1221no—
391D4—1221no—
392D4—2441no—
393D4—2441no—
394D4—2441no—
395D4—2441no—
396D4—2441no—
397D4D4×D6111yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4C23×D6111yescharacteristic
414C8—21no—
415C8—21no—
416C8—21no—
417C8—611no—
418C8—611no—
419C8—1221no—
420C8D4×D6111yescharacteristic
421C8D4×D6111yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—1221no—
426C22—1221no—
427C22—1221no—
428C22—9761no—
429C22#1451982311yescharacteristic
430C4—21no—
431C4—41no—
432C4—1221no—
433C4—1221no—
434C4—1221no—
435C4—2441no—
436C4—2441no—
437C4—2441no—
438C4C2×D4×D6111yescharacteristic
439C4C2×D4×D6111yescharacteristic
440C2—21no—
441C2—41no—
442C2—81no—
443C2—2441no—
444C2—2441no—
445C2—2441no—
446C2#1684039611yescharacteristic
subgroupG/H
centerC2#16840396
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#471C2
socleC2×C61D42
hypercenter#471D61
hypocenterC61#3289
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #16840579C2semidirect
2. #16840578C2semidirect
3. #16840572C2semidirect
4. #16840568C2semidirect
5. #16840153C2semidirect
6. #16840038C2semidirect
7. #16840036C2semidirect
8. #16840024C2semidirect
9. #16839947C2semidirect
10. #16839943C2semidirect
11. #16839942C2semidirect
12. #16839933C2semidirect
13. #16839883C2semidirect
14. #16839882C2semidirect
15. C61×#471C2semidirect
18. #14519824C22semidirect
25. #14519810C22semidirect
41. C2×Dic244C22semidirect
42. C2×#11758202C22semidirect
48. #14519785C22semidirect
50. #14519775C22semidirect
52. #14519712C22semidirect
53. #14519704C22semidirect
56. #14519703C22semidirect
57. #14519695C22semidirect
58. #14519695C22semidirect
59. #14519687C22semidirect
60. #137×C61C22semidirect
63. #131×C61C22semidirect
64. #108×C61C22semidirect
65. #101×C61C22semidirect
232. #471D61semidirect
239. C61#3289semidirect
255. #137C2×D61semidirect
277. #131C2×D61semidirect
281. #108C2×D61semidirect
288. #101C2×D61semidirect