Finite Group Databasebeta

← #21448481

Subgroups — #21448481

Order 7808.

808 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519747C211yesmaximal, characteristic
2C2×C4×D244C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#16839663C211yesmaximal, characteristic, complemented
5#16839662C211yesmaximal, characteristic, complemented
6#16839655C211yesmaximal, characteristic, complemented
7#16839654C211yesmaximal, characteristic, complemented
8#16839653C211yesmaximal, characteristic, complemented
9#16839640C211yesmaximal, characteristic, complemented
10#16839640C211yesmaximal, characteristic, complemented
11#16839638C211yesmaximal, characteristic, complemented
12#16839633C211yesmaximal, characteristic, complemented
13#16839617C211yesmaximal, characteristic, complemented
14#16839609C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic, complemented
23#14519747C418yescomplemented
24C4×D244—24no—
25C2×C4⋊Dic61C2211yescharacteristic, complemented
26C2×#11758196C2211yescharacteristic, complemented
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic, complemented
38C2×#11758198C2211yescharacteristic, complemented
39C2×#11758198C2211yescharacteristic, complemented
40C22⋊C4×D61—24no—
41C2×C4×Dic61C2211yescharacteristic, complemented
42C2×C4×Dic61C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47C2×C4⋊C4×C61C2211yescharacteristic, complemented
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C42×C61C2211yescharacteristic, complemented
52#95×C61C2211yescharacteristic, complemented
53#95×C61C2211yescharacteristic, complemented
54C24×C61C2311yescharacteristic
55C23×D61—22no—
56C23×D61—22no—
57C23×D61—41no—
58C23×D61—41no—
59C23×D61—41no—
60C23×D61—41no—
61C23×D61C2×C414yescomplemented
62C23×D61C2311yescharacteristic
63C23×D61C2311yescharacteristic
64C23×D61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C2×C22⋊D61—41no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61C2×C414yescomplemented
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C2×D244—22no—
80C2×D244—22no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244C2×C414yes—
84C2×D244C2×C414yescomplemented
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61D414yescomplemented
94C4⋊C4×C61—41no—
95C22⋊C4×C61—22no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61C2×C414yescomplemented
98C42×C61—22no—
99C22⋊Dic61—22no—
100C22⋊Dic61—41no—
101#11758198—22no—
102#11758198—22no—
103#11758198—22no—
104#11758198—22no—
105#11758198—22no—
106#11758198—41no—
107#11758198—41no—
108#11758198—41no—
109#11758198—41no—
110#11758198C2×C414yescomplemented
111#11758198C2×C414yescomplemented
112C4⋊Dic61—22no—
113#11758196—41no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61C22×C412yes—
123C23×C61C2411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—28no—
141C22×D61—44no—
142C22×D61—44no—
143C22×D61—44no—
144C22×D61—44no—
145C22×D61—44no—
146C22×D61—44no—
147C22×D61C22×C412yes—
148C22×D61C22×C412yes—
149C22×D61C22×C412yes—
150C22×D61C2×D412yes—
151C22×D61#4112yes—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61C22×C412yes—
168C2×C4×C61C22×C412yes—
169C2×C4×C61C2×D412yes—
170C22⋊D61—44no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61C22×C412yes—
185C2×Dic61C2×D412yes—
186D244—28no—
187D244—44no—
188C4×D61—44no—
189C4×D61—44no—
190C4×D61—44no—
191C22×C61—22no—
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61C23×C411yescharacteristic
199C22×C61C22×D411yescharacteristic
200C22×C61C2×#4111yescharacteristic
201C22×C61H(5,𝔽2)11yescharacteristic
202C22×C61H(5,𝔽2)11yescharacteristic
203C22×C61H(5,𝔽2)11yescharacteristic
204C22×C61H(5,𝔽2)11yescharacteristic
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—22no—
208C2×D61—22no—
209C2×D61—22no—
210C2×D61—22no—
211C2×D61—22no—
212C2×D61—22no—
213C2×D61—22no—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—416no—
218C2×D61—41no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61C4×D414yes—
227C4×C61—22no—
228C4×C61—22no—
229C4×C61—22no—
230C4×C61—41no—
231C4×C61—41no—
232C4×C61—41no—
233Dic61—22no—
234Dic61—22no—
235Dic61—41no—
236Dic61—41no—
237Dic61—41no—
238#2321—611nomaximal, Sylow
239C2×C61—42no—
240C2×C61C2×C4×D411yescharacteristic
241C2×C61#51811yescharacteristic
242C2×C61#51811yescharacteristic
243C2×C61#53411yescharacteristic
244C2×C61#53511yescharacteristic
245C2×C61#53811yescharacteristic
246C2×C61#53811yescharacteristic
247D61—24no—
248D61—42no—
249D61—42no—
250C2×#120—611no—
251C2×C4×D4—611no—
252C22×C22⋊C4—611no—
253#390—611no—
254#390—611no—
255#388—611no—
256#388—611no—
257#388—611no—
258#388D6111yescharacteristic, complemented
259#386—611no—
260#386—611no—
261#386—611no—
262#385—611no—
263#379—611no—
264C4×C22⋊C4—611no—
265C61#232111yescharacteristic, complemented, Sylow
266C25—611no—
267C22×D4—611no—
268C22×D4—611no—
269C22×D4—611no—
270C23×C4—611no—
271C23×C4—611no—
272C23×C4—611no—
273#120—618no—
274C4×D4—1224no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4C2×D6111yescharacteristic, complemented
278C2×C22⋊C4—611no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—611no—
289C2×C22⋊C4—611no—
290C2×C22⋊C4—611no—
291C2×C22⋊C4—1224no—
292C2×C22⋊C4C2×D6111yescharacteristic
293C2×C22⋊C4C2×D6111yescharacteristic
294C2×C22⋊C4C2×D6111yescharacteristic
295C2×C42—611no—
296C2×C42—611no—
297C2×C42C2×D6111yescharacteristic, complemented
298#95—611no—
299#95—611no—
300#95—611no—
301#95—611no—
302#95C2×D6111yescharacteristic, complemented
303#95C2×D6111yescharacteristic, complemented
304C24—611no—
305C24—611no—
306C24—611no—
307C24—614no—
308C24—1222no—
309C24—1222no—
310C24—2441no—
311C24—2441no—
312C24—2441no—
313C24—2441no—
314C24C22×D6111yescharacteristic
315C2×D4—614no—
316C2×D4—614no—
317C2×D4—614no—
318C2×D4—1222no—
319C2×D4—1222no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4—2441no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—614no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—1222no—
331C22×C4—1222no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4C22×D6111yescharacteristic
339C22×C4C22×D6111yescharacteristic
340C22×C4C22×D6111yescharacteristic
341C22×C4C22×D6111yescharacteristic
342C22×C4C22×D6111yescharacteristic
343C22×C4C22×D6111yescharacteristic
344C4⋊C4—41no—
345C4⋊C4—1222no—
346C4⋊C4—2441no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—614no—
350C22⋊C4—614no—
351C22⋊C4—1222no—
352C22⋊C4—1222no—
353C22⋊C4—1222no—
354C22⋊C4—1222no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C22⋊C4—2441no—
362C22⋊C4C4×D6114yescomplemented
363C42—22no—
364C42—2441no—
365C42—2441no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—612no—
373C23—612no—
374C23—612no—
375C23—612no—
376C23—612no—
377C23—1228no—
378C23—1221no—
379C23—1221no—
380C23—1221no—
381C23—1221no—
382C23—1221no—
383C23—1221no—
384C23—1221no—
385C23—1221no—
386C23—1221no—
387C23—1221no—
388C23—1221no—
389C23—1221no—
390C23—1221no—
391C23—1221no—
392C23—1221no—
393C23—1221no—
394C23—2444no—
395C23—2444no—
396C23—2444no—
397C23—2444no—
398C23—2444no—
399C23—2444no—
400C23C2×C4×D6112yes—
401C23C23×D6111yescharacteristic
402D4—1228no—
403D4—2444no—
404D4—2444no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—612no—
421C2×C4—612no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—2444no—
436C2×C4—2444no—
437C2×C4—2444no—
438C2×C4C2×C4×D6112yes—
439C2×C4C2×C4×D6112yes—
440C2×C4D4×D6112yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—614no—
449C22—1222no—
450C22—1222no—
451C22—1222no—
452C22—1222no—
453C22—1222no—
454C22—1222no—
455C22—1222no—
456C22—1222no—
457C22—1222no—
458C22—1222no—
459C22—1222no—
460C22—1222no—
461C22—24416no—
462C22—2441no—
463C22—2441no—
464C22—2441no—
465C22—2441no—
466C22—2441no—
467C22—2441no—
468C22—2441no—
469C22—2441no—
470C22C22×C4×D6111yescharacteristic
471C22C2×D4×D6111yescharacteristic
472C22#41×D6111yescharacteristic
473C22#1451982211yescharacteristic
474C22#1451982311yescharacteristic
475C22#1451982311yescharacteristic
476C22#1451982311yescharacteristic
477C4—22no—
478C4—22no—
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—1222no—
484C4—1222no—
485C4—2441no—
486C4—2441no—
487C4—2441no—
488C2—42no—
489C2—1224no—
490C2—2442no—
491C2—2442no—
492C2C4×D4×D6111yescharacteristic
493C2#1684023411yescharacteristic
494C2#1684023611yescharacteristic
495C2#1684032311yescharacteristic
496C2#1684032811yescharacteristic
497C2#1684034611yescharacteristic
498C2#1684035111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#388C2
socleC23×C61C24
hypercenter#388D61
hypocenterC61#2321
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D244C2semidirect
3. C2×C22⋊C4×D61C2semidirect
4. #16839663C2semidirect
5. #16839662C2semidirect
6. #16839655C2semidirect
7. #16839654C2semidirect
8. #16839653C2semidirect
9. #16839640C2semidirect
10. #16839640C2semidirect
11. #16839638C2semidirect
12. #16839633C2semidirect
13. #16839617C2semidirect
14. #16839609C2semidirect
15. C61×#388C2semidirect
22. C22×C4×D61C22semidirect
23. #14519747C4semidirect
25. C2×C4⋊Dic61C22semidirect
26. C2×#11758196C22semidirect
37. C2×#11758198C22semidirect
38. C2×#11758198C22semidirect
39. C2×#11758198C22semidirect
41. C2×C4×Dic61C22semidirect
42. C2×C4×Dic61C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. C2×C4⋊C4×C61C22semidirect
51. C2×C42×C61C22semidirect
52. #95×C61C22semidirect
53. #95×C61C22semidirect
61. C23×D61C2×C4semidirect
73. C2×C22⋊D61C2×C4semidirect
84. C2×D244C2×C4semidirect
93. C2×C4×D61D4semidirect
97. C22⋊C4×C61C2×C4semidirect
110. #11758198C2×C4semidirect
111. #11758198C2×C4semidirect
258. #388D61semidirect
265. C61#2321semidirect
277. C2×C4⋊C4C2×D61semidirect
297. C2×C42C2×D61semidirect
302. #95C2×D61semidirect
303. #95C2×D61semidirect
362. C22⋊C4C4×D61semidirect