Finite Group Databasebeta

← #21452864

Subgroups — #21452864

Order 7808.

560 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839691C211yesmaximal, characteristic, complemented
2#16839690C211yesmaximal, characteristic, complemented
3#16839688C211yesmaximal, characteristic, complemented
4#16839675C211yesmaximal, characteristic, complemented
5#16839675C211yesmaximal, characteristic, complemented
6#16839674C211yesmaximal, characteristic, complemented
7#16839653C211yesmaximal, characteristic, complemented
8#16839653C211yesmaximal, characteristic, complemented
9#16839652C211yesmaximal, characteristic, complemented
10#16839651C211yesmaximal, characteristic, complemented
11#16839650C211yesmaximal, characteristic, complemented
12#16839617C211yesmaximal, characteristic
13#16839617C211yesmaximal, characteristic
14#16839617C211yesmaximal, characteristic
15C61×#388C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×Dic122C2211yescharacteristic, complemented
18C2×#11758196C2211yescharacteristic, complemented
19C2×#11758196C2211yescharacteristic, complemented
20C2×C22⋊Dic61C2211yescharacteristic
21C2×C22⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic, complemented
36#14519684C2211yescharacteristic, complemented
37#14519684C2211yescharacteristic, complemented
38#14519684C2211yescharacteristic, complemented
39#14519684C2211yescharacteristic, complemented
40#14519684C2211yescharacteristic, complemented
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44C2×C4⋊C4×C61C2211yescharacteristic, complemented
45C2×C22⋊C4×C61C2211yescharacteristic
46C2×C22⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C42×C61C2211yescharacteristic, complemented
49#95×C61C2211yescharacteristic, complemented
50#95×C61C2211yescharacteristic, complemented
51C24×C61C2311yescharacteristic
52C23×D61—22no—
53C23×D61—22no—
54C23×D61—22no—
55C23×D61—41no—
56C23×D61—41no—
57C23×D61—41no—
58C23×D61—41no—
59C23×D61C2311yescharacteristic
60C23×D61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C4⋊C4×C61—41no—
77C22⋊C4×C61—22no—
78C22⋊C4×C61—41no—
79C22⋊C4×C61—41no—
80C42×C61—41no—
81C22⋊Dic61—22no—
82C22⋊Dic61—41no—
83C22⋊Dic61—41no—
84#11758198—22no—
85#11758198—22no—
86#11758198—22no—
87#11758198—22no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—41no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61#4112yes—
106C23×C61C2411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—44no—
120C22×D61—44no—
121C22×D61—44no—
122C22×D61—44no—
123C22×D61—44no—
124C22×D61—44no—
125C22×D61—44no—
126C22×D61#4112yes—
127C22×D61#4112yes—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164Dic122—44no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61C2×#4111yescharacteristic
173C22×C61C2×#4111yescharacteristic
174C22×C61C2×#4111yescharacteristic
175C22×C61H(5,𝔽2)11yescharacteristic
176C22×C61H(5,𝔽2)11yescharacteristic
177C22×C61H(5,𝔽2)11yescharacteristic
178C22×C61H(5,𝔽2)11yescharacteristic
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—416no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C4×C61—41no—
195C4×C61—41no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—41no—
200Dic61—41no—
201Dic61—41no—
202Dic61—41no—
203Dic61—41no—
204Dic61—41no—
205Dic61—41no—
206#2736—611nomaximal, Sylow
207C2×C61—42no—
208C2×C61#53811yescharacteristic
209C2×C61#53811yescharacteristic
210C2×C61#53811yescharacteristic
211C2×C61#55111yescharacteristic
212C2×C61#55111yescharacteristic
213C2×C61#55111yescharacteristic
214C2×C61H(3,𝔽4)11yescharacteristic
215D61—42no—
216D61—42no—
217#397—611no—
218#397—611no—
219#397—611no—
220#393—611no—
221#393—611no—
222#393—611no—
223#388—611no—
224#388—611no—
225#388—611no—
226#388—611no—
227#388—611no—
228#388D6111yescharacteristic, complemented
229#379—611no—
230#379—611no—
231#379—611no—
232C61#273611yescharacteristic, complemented, Sylow
233C25—611no—
234C22×Q8—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4C2×D6111yescharacteristic, complemented
238C2×C22⋊C4—611no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—611no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4—611no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—611no—
245C2×C22⋊C4—611no—
246C2×C22⋊C4—611no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4—611no—
249C2×C22⋊C4—611no—
250C2×C22⋊C4—611no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4C2×D6111yescharacteristic
254C2×C22⋊C4C2×D6111yescharacteristic
255C2×C22⋊C4C2×D6111yescharacteristic
256C2×C42—611no—
257C2×C42C2×D6111yescharacteristic, complemented
258#95—611no—
259#95—611no—
260#95—611no—
261#95—611no—
262#95—611no—
263#95—611no—
264#95—611no—
265#95—611no—
266#95C2×D6111yescharacteristic, complemented
267#95C2×D6111yescharacteristic, complemented
268C24—611no—
269C24—611no—
270C24—1222no—
271C24—1222no—
272C24—1222no—
273C24—2441no—
274C24—2441no—
275C24—2441no—
276C24—2441no—
277C24C22×D6111yescharacteristic
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4C22×D6111yescharacteristic
288C22×C4C22×D6111yescharacteristic
289C22×C4C22×D6111yescharacteristic
290C22×C4C22×D6111yescharacteristic
291C22×C4C22×D6111yescharacteristic
292C22×C4C22×D6111yescharacteristic
293C4⋊C4—41no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—1222no—
300C22⋊C4—1222no—
301C22⋊C4—1222no—
302C22⋊C4—1222no—
303C22⋊C4—1222no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2441no—
313C22⋊C4—2441no—
314C42—41no—
315C42—2441no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—612no—
323C23—612no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336C23—2444no—
337C23—2444no—
338C23—2444no—
339C23—2444no—
340C23—2444no—
341C23—2444no—
342C23—2444no—
343C23#1175822212yes—
344C23C23×D6111yescharacteristic
345Q8—2444no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—1222no—
390C22—1222no—
391C22—1222no—
392C22—1222no—
393C22—1222no—
394C22—1222no—
395C22—24416no—
396C22—2441no—
397C22—2441no—
398C22—2441no—
399C22—2441no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22#41×D6111yescharacteristic
405C22#41×D6111yescharacteristic
406C22C2×#1175822211yescharacteristic
407C22#1451982211yescharacteristic
408C22#1451982211yescharacteristic
409C22#1451982311yescharacteristic
410C22#1451982311yescharacteristic
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—2441no—
418C4—2441no—
419C4—2441no—
420C4—2441no—
421C4—2441no—
422C4—2441no—
423C2—42no—
424C2—2442no—
425C2—2442no—
426C2#1684034411yescharacteristic
427C2#1684034511yescharacteristic
428C2#1684034811yescharacteristic
429C2#1684043611yescharacteristic
430C2#1684043711yescharacteristic
431C2#1684044111yescharacteristic
432C2#1684050411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#388C2
hypercenter#388D61
hypocenterC61#2736
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #16839691C2semidirect
2. #16839690C2semidirect
3. #16839688C2semidirect
4. #16839675C2semidirect
5. #16839675C2semidirect
6. #16839674C2semidirect
7. #16839653C2semidirect
8. #16839653C2semidirect
9. #16839652C2semidirect
10. #16839651C2semidirect
11. #16839650C2semidirect
15. C61×#388C2semidirect
17. C22×Dic122C22semidirect
18. C2×#11758196C22semidirect
19. C2×#11758196C22semidirect
35. C2×C4×Dic61C22semidirect
36. #14519684C22semidirect
37. #14519684C22semidirect
38. #14519684C22semidirect
39. #14519684C22semidirect
40. #14519684C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. C2×C4⋊C4×C61C22semidirect
48. C2×C42×C61C22semidirect
49. #95×C61C22semidirect
50. #95×C61C22semidirect
228. #388D61semidirect
232. C61#2736semidirect
237. C2×C4⋊C4C2×D61semidirect
257. C2×C42C2×D61semidirect
266. #95C2×D61semidirect
267. #95C2×D61semidirect