Finite Group Databasebeta

← #21457590

Subgroups — #21457590

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#16840577C211yesmaximal, characteristic, complemented
2#16840570C211yesmaximal, characteristic, complemented
3#16840569C211yesmaximal, characteristic, complemented
4#16840155C211yesmaximal, characteristic, complemented
5#16840035C211yesmaximal, characteristic, complemented
6#16840034C211yesmaximal, characteristic, complemented
7#16840027C211yesmaximal, characteristic, complemented
8#16840025C211yesmaximal, characteristic, complemented
9#16839945C211yesmaximal, characteristic, complemented
10#16839943C211yesmaximal, characteristic, complemented
11#16839938C211yesmaximal, characteristic, complemented
12#16839935C211yesmaximal, characteristic, complemented
13#16839884C211yesmaximal, characteristic, complemented
14#16839882C211yesmaximal, characteristic, complemented
15C61×#578C211yesmaximal, characteristic, complemented
16#14519824C2211yescharacteristic
17#14519823C2211yescharacteristic
18#14519809—21no—
19#14519808—21no—
20#14519808—21no—
21#14519808C2211yescharacteristic
22#14519808C2211yescharacteristic
23#14519807—21no—
24#14519807C2211yescharacteristic
25#14519807C2211yescharacteristic, complemented
26#14519802—21no—
27#14519802C2211yescharacteristic
28#14519802C2211yescharacteristic
29#14519801—21no—
30#14519798—21no—
31#14519797—21no—
32#14519797—21no—
33#14519797C2211yescharacteristic
34C2×#11758202—21no—
35C2×#11758202C2211yescharacteristic, complemented
36C2×#11758190C2211yescharacteristic
37C2×#11758201—21no—
38C2×#11758201C2211yescharacteristic
39SD16×D61—21no—
40#14519784C2211yescharacteristic
41#14519784C2211yescharacteristic, complemented
42#14519783C2211yescharacteristic
43#14519775C2211yescharacteristic, complemented
44#14519766C2211yescharacteristic
45#14519713C2211yescharacteristic, complemented
46#14519712C2211yescharacteristic, complemented
47#14519704C2211yescharacteristic
48#14519704C2211yescharacteristic, complemented
49#14519704C2211yescharacteristic, complemented
50#14519703C2211yescharacteristic
51#14519696C2211yescharacteristic, complemented
52#14519696C2211yescharacteristic, complemented
53#14519695C2211yescharacteristic, complemented
54#14519693C2211yescharacteristic
55#14519687C2211yescharacteristic, complemented
562−1+4×C61C2211yescharacteristic
572−1+4×C61C2211yescharacteristic, complemented
58#137×C61—21no—
59#137×C61—21no—
60#137×C61C2211yescharacteristic
61#137×C61C2211yescharacteristic, complemented
62#135×C61—21no—
63#135×C61C2211yescharacteristic
64C2×Q16×C61—21no—
65C2×Q16×C61C2211yescharacteristic, complemented
66#131×C61C2211yescharacteristic, complemented
67#41×C61—21no—
68#41×C61—21no—
69#41×C61—21no—
70#41×C61—21no—
71#41×C61—41no—
72#41×C61—41no—
73#41×C61C2311yescharacteristic
74#41×C61C2311yescharacteristic
75#41×C61C2311yescharacteristic
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61C2311yescharacteristic
81C2×Q8×C61C2311yescharacteristic
82#11758226—21no—
83Q8×D61—21no—
84#11758224—21no—
85#11758224—41no—
86D4×D61—21no—
87D4×D61—41no—
88#11758222—21no—
89#11758222—21no—
90#11758222C2311yescharacteristic
91C2×D244—21no—
92C2×D244C2311yescharacteristic
93C2×Dic122—21no—
94C2×Dic122C2311yescharacteristic
95Q16×C61—21no—
96Q16×C61—21no—
97Q16×C61—21no—
98Q16×C61—21no—
99Q16×C61D411yescharacteristic
100SD16×C61—21no—
101SD16×C61—21no—
102SD16×C61D411yescharacteristic
103SD16×C61D411yescharacteristic
104D8×C61D411yescharacteristic
105M16×C61—21no—
106M16×C61C2311yescharacteristic
107C2×C8×C61—21no—
108C2×C8×C61C2311yescharacteristic
109#11758202—21no—
110#11758202—21no—
111#11758202—21no—
112#11758202—21no—
113#11758202—21no—
114#11758202—21no—
115#11758202D411yescharacteristic
116#11758201—21no—
117#11758201—21no—
118#11758201—21no—
119#11758201—21no—
120#11758201—21no—
121#11758201—21no—
122#11758201D411yescharacteristic
123#11758200—21no—
124#11758200—21no—
125#11758200D411yescharacteristic
126#11758199—21no—
127#11758199—21no—
128#11758199D411yescharacteristic
129#11758198—41no—
130#11758196—41no—
131C4×Dic61C2311yescharacteristic
132#11758194—21no—
133#11758194—21no—
134#11758194C2311yescharacteristic
135#11758194C2311yescharacteristic
136#11758194C2311yescharacteristic
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418C2311yescharacteristic
140#11758190—21no—
141#11758190—21no—
142#11758189—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×C61—41no—
152Q8×C61C2×D411yescharacteristic
153Q8×C61C2×D411yescharacteristic
154Q8×C61C2×D411yescharacteristic
155D4×C61—21no—
156D4×C61—21no—
157D4×C61—21no—
158D4×C61—41no—
159D4×C61—41no—
160D4×C61C2×D411yescharacteristic
161D4×C61C2×D411yescharacteristic
162D4×C61C2×D411yescharacteristic
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61C2411yescharacteristic
173C22⋊D61—21no—
174C22⋊D61—41no—
175C22⋊D61—41no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—41no—
179D244—21no—
180D244—21no—
181D244—41no—
182D244C2×D411yescharacteristic
183C4×D61—21no—
184C4×D61—41no—
185C4×D61—41no—
186Dic122—21no—
187Dic122—21no—
188Dic122—41no—
189Dic122C2×D411yescharacteristic
190C8×C61—21no—
191C8×C61C2×D411yescharacteristic
192C8×C61C2×D411yescharacteristic
193#92418—21no—
194#92418—21no—
195#92418—21no—
196#92418C2×D411yescharacteristic
197#92418C2×D411yescharacteristic
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61H(5,𝔽2)11yescharacteristic
202C2×D61—21no—
203C2×D61—41no—
204C2×D61—81no—
205C2×D61—161no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—41no—
210C4×C61—41no—
211C4×C61C22×D411yescharacteristic
212C4×C61C22×D411yescharacteristic
213Dic61—21no—
214Dic61—41no—
215Dic61—41no—
216#3289—611nomaximal, Sylow
217C2×C61—21no—
218C2×C61—41no—
219C2×C61—41no—
220C2×C61—41no—
221C2×C61D4211yescharacteristic
222D61—41no—
223D61—81no—
224#578—611no—
225#578D6111yescharacteristic, complemented
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#456—611no—
235#455—611no—
236#454—611no—
237#444—611no—
238#444—611no—
239C61#328911yescharacteristic, complemented, Sylow
2402−1+4—611no—
2412−1+4C2×D6111yescharacteristic
2422−1+4C2×D6111yescharacteristic, complemented
243H(5,𝔽2)—611no—
244#137—21no—
245#137—21no—
246#137—611no—
247#137—611no—
248#137—611no—
249#137—611no—
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—21no—
261#135—611no—
262#135—1221no—
263#135—1221no—
264#135—1221no—
265#135C2×D6111yescharacteristic
266C2×Q16—21no—
267C2×Q16—611no—
268C2×Q16—1221no—
269C2×Q16C2×D6111yescharacteristic, complemented
270C2×SD16—611no—
271C2×SD16—611no—
272C2×SD16—1221no—
273C2×SD16—1221no—
274#131—611no—
275#131—611no—
276#131—611no—
277#131C2×D6111yescharacteristic, complemented
278C4⋊Q8—611no—
279#124—611no—
280#108—611no—
281#108—611no—
282#104—611no—
283#104—611no—
284#104—611no—
285#104—611no—
286#101—611no—
287#101—611no—
288#101—611no—
289#100—611no—
290#97—611no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—41no—
296#41—41no—
297#41—611no—
298#41—1221no—
299#41—1221no—
300#41—1221no—
301#41—1221no—
302#41—2441no—
303#41C22×D6111yescharacteristic
304#41C22×D6111yescharacteristic
305#41C22×D6111yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—611no—
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—21no—
322Q16—21no—
323Q16—611no—
324Q16—1221no—
325Q16—1221no—
326Q16—1221no—
327Q16—1221no—
328Q16—1221no—
329Q16—1221no—
330Q16C22⋊D6111yescharacteristic
331SD16—21no—
332SD16—21no—
333SD16—611no—
334SD16—611no—
335SD16—1221no—
336SD16—1221no—
337SD16—1221no—
338SD16—1221no—
339SD16—1221no—
340SD16—1221no—
341SD16—1221no—
342SD16—1221no—
343SD16—1221no—
344SD16—1221no—
345SD16C22⋊D6111yescharacteristic
346SD16C22⋊D6111yescharacteristic
347D8—611no—
348D8—1221no—
349D8—1221no—
350D8C22⋊D6111yescharacteristic
351M16—21no—
352M16—611no—
353M16—611no—
354M16—611no—
355M16—1221no—
356M16—1221no—
357M16—1221no—
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—1221no—
369C23—2441no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—41no—
375Q8—41no—
376Q8—611no—
377Q8—1221no—
378Q8—1221no—
379Q8—2441no—
380Q8D4×D6111yescharacteristic
381Q8C2×C22⋊D6111yescharacteristic
382Q8C2×C22⋊D6111yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—41no—
387D4—41no—
388D4—611no—
389D4—1221no—
390D4—1221no—
391D4—1221no—
392D4—2441no—
393D4—2441no—
394D4—2441no—
395D4D4×D6111yescharacteristic
396D4C2×C22⋊D6111yescharacteristic
397D4C2×C22⋊D6111yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4C23×D6111yescharacteristic
414C8—21no—
415C8—611no—
416C8—611no—
417C8—1221no—
418C8—1221no—
419C8—1221no—
420C8C2×C22⋊D6111yescharacteristic
421C8C2×C22⋊D6111yescharacteristic
422C22—21no—
423C22—21no—
424C22—21no—
425C22—1221no—
426C22—9761no—
427C22—4881no—
428C22—2441no—
429C22#1451982211yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—41no—
434C4—41no—
435C4—1221no—
436C4—2441no—
437C4—2441no—
438C4C2×D4×D6111yescharacteristic
439C4C22×C22⋊D6111yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2—4881no—
445C2—2441no—
446C2D4×C22⋊D6111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#578C2
socleC2×C61D42
hypercenter#578D61
hypocenterC61#3289
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #16840577C2semidirect
2. #16840570C2semidirect
3. #16840569C2semidirect
4. #16840155C2semidirect
5. #16840035C2semidirect
6. #16840034C2semidirect
7. #16840027C2semidirect
8. #16840025C2semidirect
9. #16839945C2semidirect
10. #16839943C2semidirect
11. #16839938C2semidirect
12. #16839935C2semidirect
13. #16839884C2semidirect
14. #16839882C2semidirect
15. C61×#578C2semidirect
25. #14519807C22semidirect
35. C2×#11758202C22semidirect
41. #14519784C22semidirect
43. #14519775C22semidirect
45. #14519713C22semidirect
46. #14519712C22semidirect
48. #14519704C22semidirect
49. #14519704C22semidirect
51. #14519696C22semidirect
52. #14519696C22semidirect
53. #14519695C22semidirect
55. #14519687C22semidirect
57. 2−1+4×C61C22semidirect
61. #137×C61C22semidirect
65. C2×Q16×C61C22semidirect
66. #131×C61C22semidirect
225. #578D61semidirect
239. C61#3289semidirect
242. 2−1+4C2×D61semidirect
255. #137C2×D61semidirect
269. C2×Q16C2×D61semidirect
277. #131C2×D61semidirect