Finite Group Databasebeta

← #21457310

Subgroups — #21457310

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×#14519803C211yesmaximal, characteristic, complemented
2C22×#11758200C211yesmaximal, characteristic, complemented
3#16840421C211yesmaximal, characteristic, complemented
4#16840149C211yesmaximal, characteristic, complemented
5#16840006C211yesmaximal, characteristic, complemented
6#16839996C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839959C211yesmaximal, characteristic, complemented
9#16839913C211yesmaximal, characteristic, complemented
10#16839905C211yesmaximal, characteristic, complemented
11#16839900C211yesmaximal, characteristic, complemented
12#16839896C211yesmaximal, characteristic, complemented
13#16839862C211yesmaximal, characteristic, complemented
14#16839834C211yesmaximal, characteristic, complemented
15D42×C61C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic, complemented
17C22×Dic122C2211yescharacteristic, complemented
18#14519803—24no—
19C2×#11758200—24no—
20C2×#11758200C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758200C2211yescharacteristic, complemented
23C2×#11758200C2211yescharacteristic, complemented
24C2×#11758200C2211yescharacteristic, complemented
25C2×#11758200C2211yescharacteristic, complemented
26C2×#11758199C2211yescharacteristic
27C2×#11758199C2211yescharacteristic, complemented
28C2×#11758199C2211yescharacteristic, complemented
29C2×#11758194C2211yescharacteristic, complemented
30C22×#92418C2211yescharacteristic, complemented
31#14519765C2211yescharacteristic, complemented
32#14519763—21no—
33#14519756C2211yescharacteristic, complemented
34#14519755—21no—
35#14519751C2211yescharacteristic, complemented
36#14519749—21no—
37C4×Dic122C2211yescharacteristic, complemented
38#14519737—21no—
39#14519710C2211yescharacteristic, complemented
40C4⋊#92418C2211yescharacteristic, complemented
41#14519700C2211yescharacteristic, complemented
42#14519700C2211yescharacteristic, complemented
43#14519698C2211yescharacteristic
44#14519698C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic, complemented
46#14519697C2211yescharacteristic, complemented
47C22⋊#92418C2211yescharacteristic, complemented
48C22⋊#92418C2211yescharacteristic, complemented
49#14519688C2211yescharacteristic, complemented
50C22×D4×C61—21no—
51C22×D4×C61C2211yescharacteristic
52C22×D4×C61C2211yescharacteristic
53#127×C61C2211yescharacteristic
54#121×C61—21no—
55#121×C61C2211yescharacteristic
56#121×C61C2211yescharacteristic
57#120×C61—21no—
58#120×C61—21no—
59C4×D4×C61C2211yescharacteristic
60C4×D4×C61C2211yescharacteristic
61C24×C61—21no—
62C24×C61—21no—
63C2×D4×C61—22no—
64C2×D4×C61—22no—
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—44no—
74C2×D4×C61D411yescharacteristic
75C2×D4×C61C2311yescharacteristic
76C2×D4×C61C2311yescharacteristic
77C2×D4×C61C2311yescharacteristic
78C22×C4×C61—21no—
79C22×C4×C61C2311yescharacteristic
80C22×C4×C61C2311yescharacteristic
81C2×C22⋊D61—21no—
82C2×C22⋊D61—21no—
83C22×Dic61—21no—
84#11758222—22no—
85#11758222—41no—
86C2×D244C2311yescharacteristic
87C2×C4×D61—21no—
88C2×Dic122—22no—
89C2×Dic122—21no—
90C2×Dic122—41no—
91C2×Dic122C2311yescharacteristic
92C2×Dic122C2311yescharacteristic
93C4⋊C4×C61D411yescharacteristic
94C4⋊C4×C61C2311yescharacteristic
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊C4×C61—21no—
98C22⋊C4×C61D411yescharacteristic
99C22⋊C4×C61D411yescharacteristic
100C42×C61C2311yescharacteristic
101C22⋊Dic61—21no—
102#11758200—22no—
103#11758200—22no—
104#11758200—22no—
105#11758200—22no—
106#11758200—41no—
107#11758200D414yescomplemented
108#11758199—22no—
109#11758199—22no—
110#11758199—41no—
111#11758198—21no—
112#11758198—21no—
113#11758198—21no—
114C4⋊Dic61C2311yescharacteristic
115#11758196—21no—
116#11758196—21no—
117C4×Dic61—21no—
118#11758194—22no—
119C2×#92418—22no—
120C2×#92418C2311yescharacteristic
121C2×#92418C2311yescharacteristic
122C2×#92418C2311yescharacteristic
123C2×#92418C2311yescharacteristic
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—42no—
128C23×C61—42no—
129C23×C61—42no—
130C23×C61—42no—
131C23×C61—81no—
132C23×C61—81no—
133C23×C61C2×D411yescharacteristic
134C23×C61C2×D411yescharacteristic
135C22×D61—21no—
136D4×C61—22no—
137D4×C61—21no—
138D4×C61—21no—
139D4×C61—21no—
140D4×C61—21no—
141D4×C61—21no—
142D4×C61—42no—
143D4×C61—42no—
144D4×C61—42no—
145D4×C61—42no—
146D4×C61—42no—
147D4×C61—81no—
148D4×C61C2×D412yes—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—42no—
155C2×C4×C61C2×D411yescharacteristic
156C2×C4×C61C2×D411yescharacteristic
157C2×C4×C61C2×D411yescharacteristic
158C2×C4×C61C2×D411yescharacteristic
159C2×C4×C61C2411yescharacteristic
160C22⋊D61—42no—
161C22⋊D61—42no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—42no—
166D244—21no—
167D244—21no—
168C4×D61—42no—
169Dic122—21no—
170Dic122—21no—
171Dic122—21no—
172Dic122—42no—
173Dic122C2×D412yescomplemented
174#92418—21no—
175#92418—21no—
176#92418—21no—
177#92418C2×D412yescomplemented
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—22no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—84no—
193C22×C61—84no—
194C22×C61AGL(1,ℤ/8)12yescomplemented
195C22×C61C22×D411yescharacteristic
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—41no—
204C4×C61C22×D411yescharacteristic
205C4×C61H(5,𝔽2)11yescharacteristic
206Dic61—22no—
207Dic61—41no—
208Dic61—41no—
209#3265—611nomaximal, Sylow
210C2×C61—22no—
211C2×C61—41no—
212C2×C61—42no—
213C2×C61—81no—
214C2×C61—81no—
215C2×C61D4211yescharacteristic
216C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
217C2×C61#57711yescharacteristic
218D61—81no—
219C2×AGL(1,ℤ/8)—611no—
220C22×SD16—611no—
221#548—611no—
222D42D6111yescharacteristic, complemented
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#435—611no—
234C61#326511yescharacteristic, complemented, Sylow
235C2×#41—611no—
236C22×Q8—611no—
237C22×D4—21no—
238C22×D4C2×D6111yescharacteristic
239C22×D4C2×D6111yescharacteristic
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×M16—611no—
252C22×C8—611no—
253#127C2×D6111yescharacteristic
254#124—611no—
255#124—1221no—
256C22⋊Q8—611no—
257C22⋊Q8—1221no—
258#121—21no—
259#121—611no—
260#121—1221no—
261#121C2×D6111yescharacteristic
262#121C2×D6111yescharacteristic
263#120—21no—
264#120—21no—
265C4×Q8—611no—
266C4×D4—1221no—
267C4×D4C2×D6111yescharacteristic
268C4×D4C2×D6111yescharacteristic
269#107—611no—
270C4⋊C8—611no—
271#103—611no—
272#103—611no—
273#102—611no—
274#102—611no—
275#102—611no—
276#102—611no—
277C22⋊C8—611no—
278C22⋊C8—611no—
279#97—611no—
280C24—21no—
281C24—21no—
282#41—1222no—
283#41—2441no—
284C2×Q8—611no—
285C2×Q8—611no—
286C2×Q8—1222no—
287C2×Q8—1221no—
288C2×Q8—2441no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—611no—
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4C22⋊D6111yescharacteristic
304C2×D4C22×D6111yescharacteristic
305C2×D4C22×D6111yescharacteristic
306C2×D4C22×D6111yescharacteristic
307C22×C4—21no—
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—1222no—
322C2×C8—611no—
323C2×C8—611no—
324C2×C8—611no—
325C2×C8—611no—
326C2×C8—1222no—
327C4⋊C4—611no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4C22⋊D6111yescharacteristic
331C4⋊C4C22×D6111yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4C22⋊D6111yescharacteristic
340C22⋊C4C22⋊D6111yescharacteristic
341C42—1221no—
342C42C22×D6111yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—1221no—
353C23C2×C22⋊D6111yescharacteristic
354C23C2×C22⋊D6111yescharacteristic
355Q8—612no—
356Q8—1221no—
357Q8—1221no—
358Q8—1221no—
359Q8—2442no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—1221no—
373D4—1221no—
374D4—2442no—
375D4—2442no—
376D4D4×D6112yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4C2×C22⋊D6111yescharacteristic
389C2×C4C2×C22⋊D6111yescharacteristic
390C2×C4C2×C22⋊D6111yescharacteristic
391C2×C4C2×C22⋊D6111yescharacteristic
392C2×C4C23×D6111yescharacteristic
393C8—612no—
394C8—1221no—
395C8—1221no—
396C8—1221no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22#1451980312yescomplemented
417C22C22×C22⋊D6111yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—1222no—
424C4—2441no—
425C4—2441no—
426C4C2×D4×D6111yescharacteristic
427C4#1451982211yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—4881no—
434C2D4×C22⋊D6111yescharacteristic
435C2C2×#1451980311yescharacteristic
436C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingD42×C61C2
socleC22×C61C22×D4
hypercenterD42D61
hypocenterC61#3265
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#14519803C2semidirect
2. C22×#11758200C2semidirect
3. #16840421C2semidirect
4. #16840149C2semidirect
5. #16840006C2semidirect
6. #16839996C2semidirect
7. #16839977C2semidirect
8. #16839959C2semidirect
9. #16839913C2semidirect
10. #16839905C2semidirect
11. #16839900C2semidirect
12. #16839896C2semidirect
13. #16839862C2semidirect
14. #16839834C2semidirect
15. D42×C61C2semidirect
16. C2×#11758222C22semidirect
17. C22×Dic122C22semidirect
22. C2×#11758200C22semidirect
23. C2×#11758200C22semidirect
24. C2×#11758200C22semidirect
25. C2×#11758200C22semidirect
27. C2×#11758199C22semidirect
28. C2×#11758199C22semidirect
29. C2×#11758194C22semidirect
30. C22×#92418C22semidirect
31. #14519765C22semidirect
33. #14519756C22semidirect
35. #14519751C22semidirect
37. C4×Dic122C22semidirect
39. #14519710C22semidirect
40. C4⋊#92418C22semidirect
41. #14519700C22semidirect
42. #14519700C22semidirect
44. #14519698C22semidirect
45. #14519698C22semidirect
46. #14519697C22semidirect
47. C22⋊#92418C22semidirect
48. C22⋊#92418C22semidirect
49. #14519688C22semidirect
107. #11758200D4semidirect
173. Dic122C2×D4semidirect
177. #92418C2×D4semidirect
194. C22×C61AGL(1,ℤ/8)semidirect
222. D42D61semidirect
234. C61#3265semidirect
416. C22#14519803semidirect