Finite Group Databasebeta

← #21457589

Subgroups — #21457589

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#16840578C211yesmaximal, characteristic, complemented
2#16840577C211yesmaximal, characteristic, complemented
3#16840571C211yesmaximal, characteristic, complemented
4#16840570C211yesmaximal, characteristic, complemented
5#16840154C211yesmaximal, characteristic, complemented
6#16840036C211yesmaximal, characteristic, complemented
7#16840035C211yesmaximal, characteristic, complemented
8#16840028C211yesmaximal, characteristic, complemented
9#16840027C211yesmaximal, characteristic, complemented
10#16839944C211yesmaximal, characteristic, complemented
11#16839941C211yesmaximal, characteristic, complemented
12#16839936C211yesmaximal, characteristic, complemented
13#16839881C211yesmaximal, characteristic, complemented
14#16839881C211yesmaximal, characteristic, complemented
15C61×#456C211yesmaximal, characteristic, complemented
16#14519825C2211yescharacteristic
17#14519824C2211yescharacteristic, complemented
18#14519823C2211yescharacteristic
19#14519810C2211yescharacteristic
20#14519809—21no—
21#14519809—21no—
22#14519808—21no—
23#14519808—21no—
24#14519808C2211yescharacteristic
25#14519808C2211yescharacteristic, complemented
26#14519807—21no—
27#14519807C2211yescharacteristic
28#14519806—21no—
29#14519805C2211yescharacteristic
30#14519804—21no—
31#14519802—21no—
32#14519802C2211yescharacteristic
33#14519800—21no—
34#14519798—21no—
35#14519797—21no—
36#14519797—21no—
37#14519797C2211yescharacteristic
38#14519797C2211yescharacteristic
39C2×#11758202—21no—
40C2×#11758202C2211yescharacteristic, complemented
41C2×#11758202C2211yescharacteristic, complemented
42Q16×D61—21no—
43C2×#11758201—21no—
44C2×#11758201C2211yescharacteristic
45C2×#11758201C2211yescharacteristic
46SD16×D61—21no—
47#14519785C2211yescharacteristic
48#14519785C2211yescharacteristic, complemented
49#14519784C2211yescharacteristic
50#14519784C2211yescharacteristic, complemented
51#14519765C2211yescharacteristic
52#14519712C2211yescharacteristic, complemented
53#14519712C2211yescharacteristic, complemented
54#14519705C2211yescharacteristic
55#14519705C2211yescharacteristic, complemented
56#14519696C2211yescharacteristic, complemented
57#14519695C2211yescharacteristic, complemented
58#14519693C2211yescharacteristic
59#14519688C2211yescharacteristic, complemented
602−1+4×C61C2211yescharacteristic
61#137×C61C2211yescharacteristic
62#137×C61C2211yescharacteristic, complemented
63C4⋊Q8×C61C2211yescharacteristic, complemented
64#104×C61C2211yescharacteristic
65#104×C61C2211yescharacteristic, complemented
66#101×C61C2211yescharacteristic, complemented
67#41×C61—21no—
68#41×C61—21no—
69#41×C61—41no—
70#41×C61C2311yescharacteristic
71#41×C61C2311yescharacteristic
72C2×Q8×C61—21no—
73C2×Q8×C61—21no—
74C2×Q8×C61C2311yescharacteristic
75C2×Q8×C61C2311yescharacteristic
76#11758226—21no—
77#11758226—21no—
78#11758226—21no—
79Q8×D61—21no—
80Q8×D61—21no—
81Q8×D61—21no—
82#11758224—21no—
83#11758224—41no—
84D4×D61—21no—
85D4×D61—41no—
86#11758222—21no—
87#11758222—21no—
88#11758222—41no—
89#11758222C2311yescharacteristic
90#11758222C2311yescharacteristic
91C2×D244—21no—
92C2×D244C2311yescharacteristic
93C2×Dic122—21no—
94C2×Dic122C2311yescharacteristic
95Q16×C61—21no—
96Q16×C61—21no—
97SD16×C61—21no—
98SD16×C61—21no—
99M16×C61C2311yescharacteristic
100M16×C61C2311yescharacteristic
101C4⋊C4×C61—41no—
102C42×C61C2311yescharacteristic
103#11758202—21no—
104#11758202—21no—
105#11758202—21no—
106#11758202—21no—
107#11758202—21no—
108#11758202—21no—
109#11758202—21no—
110#11758202D411yescharacteristic
111#11758202D411yescharacteristic
112#11758201—21no—
113#11758201—21no—
114#11758201—21no—
115#11758201—21no—
116#11758201—21no—
117#11758201—21no—
118#11758201—21no—
119#11758201D411yescharacteristic
120#11758201D411yescharacteristic
121#11758200—21no—
122#11758200D411yescharacteristic
123#11758200D411yescharacteristic
124#11758199—21no—
125#11758199D411yescharacteristic
126#11758199D411yescharacteristic
127#11758198—41no—
128#11758194—21no—
129#11758194—21no—
130#11758194C2311yescharacteristic
131#11758194C2311yescharacteristic
132C2×#92418—21no—
133C2×#92418—21no—
134C2×#92418C2311yescharacteristic
135C2×#92418C2311yescharacteristic
136Dic244—21no—
137D488—21no—
138#11758190—21no—
139#11758190—21no—
140#11758189—21no—
141#11758189—21no—
142C8×D61—21no—
143C8×D61—21no—
144C22×D61—21no—
145C22×D61—41no—
146Q8×C61—21no—
147Q8×C61—21no—
148Q8×C61—21no—
149Q8×C61—21no—
150Q8×C61—41no—
151Q8×C61C2×D411yescharacteristic
152Q8×C61C2×D411yescharacteristic
153D4×C61—21no—
154D4×C61—21no—
155D4×C61—41no—
156D4×C61C2×D411yescharacteristic
157D4×C61C2×D411yescharacteristic
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61C2411yescharacteristic
166C22⋊D61—21no—
167C22⋊D61—21no—
168C22⋊D61—41no—
169C22⋊D61—41no—
170C2×Dic61—21no—
171C2×Dic61—41no—
172D244—21no—
173D244—21no—
174D244—41no—
175D244—41no—
176D244C2×D411yescharacteristic
177D244C2×D411yescharacteristic
178C4×D61—21no—
179C4×D61—21no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184Dic122—21no—
185Dic122—21no—
186Dic122—41no—
187Dic122—41no—
188Dic122C2×D411yescharacteristic
189Dic122C2×D411yescharacteristic
190C8×C61—21no—
191C8×C61—21no—
192#92418—21no—
193#92418—21no—
194#92418C2×D411yescharacteristic
195#92418C2×D411yescharacteristic
196#92418C2×D411yescharacteristic
197#92418C2×D411yescharacteristic
198C22×C61—21no—
199C22×C61—21no—
200C22×C61H(5,𝔽2)11yescharacteristic
201C2×D61—21no—
202C2×D61—21no—
203C2×D61—41no—
204C2×D61—81no—
205C2×D61—161no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—41no—
209C4×C61—41no—
210C4×C61—41no—
211C4×C61C22×D411yescharacteristic
212C4×C61C22×D411yescharacteristic
213Dic61—21no—
214Dic61—21no—
215Dic61—41no—
216#3289—611nomaximal, Sylow
217C2×C61—21no—
218C2×C61—41no—
219C2×C61—41no—
220C2×C61D4211yescharacteristic
221D61—41no—
222D61—41no—
223D61—81no—
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#471—611no—
233#456—611no—
234#456D6111yescharacteristic, complemented
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+4C2×D6111yescharacteristic
243H(5,𝔽2)—611no—
244#137—611no—
245#137—611no—
246#137—611no—
247#137—611no—
248#137—1221no—
249#137—1221no—
250#137—1221no—
251#137—1221no—
252#137—1221no—
253#137—1221no—
254#137C2×D6111yescharacteristic
255#137C2×D6111yescharacteristic, complemented
256AGL(1,ℤ/8)—611no—
257AGL(1,ℤ/8)—611no—
258AGL(1,ℤ/8)—1221no—
259AGL(1,ℤ/8)—1221no—
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—611no—
272C2×SD16—1221no—
273C2×SD16—1221no—
274#131—611no—
275#131—611no—
276#131—611no—
277#131—611no—
278C4⋊Q8C2×D6111yescharacteristic, complemented
279#124—611no—
280#108—611no—
281#108—611no—
282#104—611no—
283#104—611no—
284#104C2×D6111yescharacteristic
285#104C2×D6111yescharacteristic, complemented
286#101—611no—
287#101—611no—
288#101C2×D6111yescharacteristic, complemented
289#100—611no—
290#97—611no—
291#41—21no—
292#41—21no—
293#41—41no—
294#41—611no—
295#41—611no—
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#41C22×D6111yescharacteristic
305#41C22×D6111yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—611no—
309C2×Q8—1221no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8C22×D6111yescharacteristic
314C2×Q8C22×D6111yescharacteristic
315C2×D4—611no—
316C2×D4—1221no—
317C2×D4—1221no—
318C2×D4—2441no—
319Q16—21no—
320Q16—21no—
321Q16—611no—
322Q16—611no—
323Q16—1221no—
324Q16—1221no—
325Q16—1221no—
326Q16—1221no—
327Q16—1221no—
328Q16—1221no—
329Q16—1221no—
330Q16—1221no—
331SD16—21no—
332SD16—21no—
333SD16—611no—
334SD16—611no—
335SD16—611no—
336SD16—611no—
337SD16—1221no—
338SD16—1221no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16—1221no—
346SD16—1221no—
347D8—611no—
348D8—611no—
349D8—1221no—
350D8—1221no—
351M16—611no—
352M16—611no—
353M16—1221no—
354M16—1221no—
355M16—1221no—
356M16—1221no—
357M16C22×D6111yescharacteristic
358M16C22×D6111yescharacteristic
359C2×C8—611no—
360C2×C8—611no—
361C2×C8—1221no—
362C2×C8—1221no—
363C2×C8—1221no—
364C2×C8—1221no—
365C4⋊C4—41no—
366C22⋊C4—2441no—
367C42C22×D6111yescharacteristic
368C23—1221no—
369C23—2441no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—41no—
375Q8—611no—
376Q8—611no—
377Q8—1221no—
378Q8—1221no—
379Q8—2441no—
380Q8—2441no—
381Q8D4×D6111yescharacteristic
382Q8D4×D6111yescharacteristic
383D4—21no—
384D4—21no—
385D4—41no—
386D4—611no—
387D4—611no—
388D4—1221no—
389D4—1221no—
390D4—1221no—
391D4—1221no—
392D4—2441no—
393D4—2441no—
394D4—2441no—
395D4—2441no—
396D4D4×D6111yescharacteristic
397D4D4×D6111yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4C23×D6111yescharacteristic
414C8—21no—
415C8—21no—
416C8—611no—
417C8—611no—
418C8—611no—
419C8—611no—
420C8—1221no—
421C8—1221no—
422C22—21no—
423C22—21no—
424C22—1221no—
425C22—1221no—
426C22—9761no—
427C22—4881no—
428C22—2441no—
429C22#1451982211yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—1221no—
436C4—1221no—
437C4—2441no—
438C4C2×D4×D6111yescharacteristic
439C4C2×D4×D6111yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—4881no—
444C2—2441no—
445C2—2441no—
446C2#1684039411yescharacteristic
subgroupG/H
centerC2#16840394
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#456C2
socleC2×C61D42
hypercenter#456D61
hypocenterC61#3289
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #16840578C2semidirect
2. #16840577C2semidirect
3. #16840571C2semidirect
4. #16840570C2semidirect
5. #16840154C2semidirect
6. #16840036C2semidirect
7. #16840035C2semidirect
8. #16840028C2semidirect
9. #16840027C2semidirect
10. #16839944C2semidirect
11. #16839941C2semidirect
12. #16839936C2semidirect
13. #16839881C2semidirect
14. #16839881C2semidirect
15. C61×#456C2semidirect
17. #14519824C22semidirect
25. #14519808C22semidirect
40. C2×#11758202C22semidirect
41. C2×#11758202C22semidirect
48. #14519785C22semidirect
50. #14519784C22semidirect
52. #14519712C22semidirect
53. #14519712C22semidirect
55. #14519705C22semidirect
56. #14519696C22semidirect
57. #14519695C22semidirect
59. #14519688C22semidirect
62. #137×C61C22semidirect
63. C4⋊Q8×C61C22semidirect
65. #104×C61C22semidirect
66. #101×C61C22semidirect
234. #456D61semidirect
239. C61#3289semidirect
255. #137C2×D61semidirect
278. C4⋊Q8C2×D61semidirect
285. #104C2×D61semidirect
288. #101C2×D61semidirect