Finite Group Databasebeta

← #21449286

Subgroups — #21449286

Order 7808.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519759C211yesmaximal, characteristic, complemented
2C2×#14519747C211yesmaximal, characteristic
3C2×C4×D244C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
5#16839699C211yesmaximal, characteristic, complemented
6#16839687C211yesmaximal, characteristic, complemented
7#16839679C211yesmaximal, characteristic, complemented
8#16839678C211yesmaximal, characteristic, complemented
9#16839653C211yesmaximal, characteristic, complemented
10#16839640C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic, complemented
12#16839636C211yesmaximal, characteristic, complemented
13#16839619C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, 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#14519759—24no—
24#14519747—24no—
25C4×D244—24no—
26C2×C4⋊Dic61C2211yescharacteristic, complemented
27C2×C4⋊Dic61C2211yescharacteristic, complemented
28C2×C4⋊Dic61C2211yescharacteristic, complemented
29C2×#11758196C2211yescharacteristic, complemented
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic, complemented
41C2×#11758198C2211yescharacteristic, complemented
42C2×#11758198C2211yescharacteristic, complemented
43C22⋊C4×D61—24no—
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48C2×C4⋊C4×C61C2211yescharacteristic, complemented
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C42×C61C2211yescharacteristic, complemented
53#95×C61C2211yescharacteristic, complemented
54#95×C61C2211yescharacteristic, complemented
55C24×C61C2311yescharacteristic
56C23×D61—22no—
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—41no—
62C23×D61—41no—
63C23×D61C2311yescharacteristic
64C23×D61C2311yescharacteristic
65C23×D61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C2×C22⋊D61—22no—
73C2×C22⋊D61—22no—
74C2×C22⋊D61—41no—
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C2×D244—22no—
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—41no—
85C2×D244D414yes—
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61D414yescomplemented
99C42×C61—22no—
100C22⋊Dic61—22no—
101C22⋊Dic61—22no—
102#11758198—22no—
103#11758198—22no—
104#11758198—22no—
105#11758198—22no—
106#11758198—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111#11758198—41no—
112#11758198—41no—
113C4⋊Dic61—22no—
114C4⋊Dic61—22no—
115C4⋊Dic61—41no—
116#11758196—22no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61C2×D412yes—
124C23×C61C2411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—28no—
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—21no—
141C22×D61—21no—
142C22×D61—44no—
143C22×D61—44no—
144C22×D61—44no—
145C22×D61—44no—
146C22×D61—44no—
147C22×D61—44no—
148C22×D61C2×D412yes—
149C22×D61C2×D412yes—
150C22×D61#4112yes—
151C22×D61#4112yes—
152C22×D61#4112yes—
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×C61—21no—
168C2×C4×C61C2×D412yes—
169C2×C4×C61C2×D412yes—
170C2×C4×C61C2×D412yes—
171C22⋊D61—44no—
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×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187D244—28no—
188D244—44no—
189C4×D61—44no—
190C4×D61—44no—
191C4×D61—44no—
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—22no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61C22×D411yescharacteristic
200C22×C61C22×D411yescharacteristic
201C22×C61C2×#4111yescharacteristic
202C22×C61C2×#4111yescharacteristic
203C22×C61C2×#4111yescharacteristic
204C22×C61H(5,𝔽2)11yescharacteristic
205C22×C61H(5,𝔽2)11yescharacteristic
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—22no—
218C2×D61—416no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61#12314yescomplemented
228C4×C61—22no—
229C4×C61—22no—
230C4×C61—22no—
231C4×C61—41no—
232C4×C61—41no—
233C4×C61—41no—
234Dic61—41no—
235Dic61—41no—
236Dic61—41no—
237Dic61—41no—
238Dic61—41no—
239#2418—611nomaximal, Sylow
240C2×C61—42no—
241C2×C61C2×#12311yescharacteristic
242C2×C61#52511yescharacteristic
243C2×C61#53811yescharacteristic
244C2×C61D4211yescharacteristic
245C2×C61#54611yescharacteristic
246C2×C61#54611yescharacteristic
247C2×C61#55111yescharacteristic
248D61—24no—
249D61—42no—
250D61—42no—
251C2×#123—611no—
252C2×#120—611no—
253C2×C4×D4—611no—
254C22×C22⋊C4—611no—
255#399—611no—
256#397—611no—
257#394—611no—
258#394—611no—
259#388—611no—
260#388D6111yescharacteristic, complemented
261#386—611no—
262#386—611no—
263#385—611no—
264#380—611no—
265#379—611no—
266C61#241811yescharacteristic, complemented, Sylow
267C25—611no—
268C22×D4—611no—
269C22×D4—611no—
270C22×D4—611no—
271C23×C4—611no—
272C23×C4—611no—
273C23×C4—611no—
274#123—1224no—
275#120—1224no—
276C4×D4—1224no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4C2×D6111yescharacteristic, complemented
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—611no—
292C2×C22⋊C4—611no—
293C2×C22⋊C4—611no—
294C2×C22⋊C4—611no—
295C2×C22⋊C4—1224no—
296C2×C22⋊C4C2×D6111yescharacteristic
297C2×C22⋊C4C2×D6111yescharacteristic
298C2×C22⋊C4C2×D6111yescharacteristic
299C2×C42C2×D6111yescharacteristic, complemented
300#95—611no—
301#95—611no—
302#95—611no—
303#95—611no—
304#95C2×D6111yescharacteristic, complemented
305#95C2×D6111yescharacteristic, complemented
306C24—611no—
307C24—611no—
308C24—611no—
309C24—1222no—
310C24—1222no—
311C24—1222no—
312C24—1222no—
313C24—1222no—
314C24—2441no—
315C24—2441no—
316C24C22×D6111yescharacteristic
317C2×D4—614no—
318C2×D4—1222no—
319C2×D4—1222no—
320C2×D4—1222no—
321C2×D4—1222no—
322C2×D4—1222no—
323C2×D4—1222no—
324C2×D4—2441no—
325C2×D4—2441no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—1222no—
332C22×C4—1222no—
333C22×C4—1222no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—1222no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4C22×D6111yescharacteristic
341C22×C4C22×D6111yescharacteristic
342C22×C4C22×D6111yescharacteristic
343C22×C4C22×D6111yescharacteristic
344C22×C4C22×D6111yescharacteristic
345C22×C4C22×D6111yescharacteristic
346C4⋊C4—41no—
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C4⋊C4—1222no—
350C4⋊C4—2441no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—1222no—
354C22⋊C4—1222no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C22⋊C4—1222no—
359C22⋊C4—1222no—
360C22⋊C4—1222no—
361C22⋊C4—1222no—
362C22⋊C4—1222no—
363C22⋊C4—1222no—
364C22⋊C4—2441no—
365C22⋊C4—2441no—
366C22⋊C4D24414yescomplemented
367C42—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—612no—
375C23—612no—
376C23—612no—
377C23—612no—
378C23—612no—
379C23—1228no—
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—1221no—
395C23—1221no—
396C23—2444no—
397C23—2444no—
398C23—2444no—
399C23—2444no—
400C23—2444no—
401C23—2444no—
402C23C2×D24412yes—
403C23C23×D6111yescharacteristic
404D4—1228no—
405D4—2444no—
406D4—2444no—
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—21no—
421C2×C4—21no—
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—1221no—
436C2×C4—1221no—
437C2×C4—2444no—
438C2×C4—2444no—
439C2×C4—2444no—
440C2×C4C2×D24412yes—
441C2×C4C2×D24412yes—
442C2×C4D4×D6112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—614no—
451C22—1222no—
452C22—1222no—
453C22—1222no—
454C22—1222no—
455C22—1222no—
456C22—1222no—
457C22—1222no—
458C22—1222no—
459C22—1222no—
460C22—1222no—
461C22—1222no—
462C22—1222no—
463C22—24416no—
464C22—2441no—
465C22—2441no—
466C22—2441no—
467C22—2441no—
468C22—2441no—
469C22—2441no—
470C22—2441no—
471C22—2441no—
472C22C2×D4×D6111yescharacteristic
473C22C22×D24411yescharacteristic
474C22#41×D6111yescharacteristic
475C22#41×D6111yescharacteristic
476C22#41×D6111yescharacteristic
477C22#1451982211yescharacteristic
478C22#1451982311yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—2441no—
486C4—2441no—
487C4—2441no—
488C4—2441no—
489C4—2441no—
490C2—42no—
491C2—1224no—
492C2—2442no—
493C2—2442no—
494C2#123×D6111yescharacteristic
495C2#1684027411yescharacteristic
496C2#1684034611yescharacteristic
497C2D4×D24411yescharacteristic
498C2#1684040711yescharacteristic
499C2#1684040911yescharacteristic
500C2#1684043711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#388C2
hypercenter#388D61
hypocenterC61#2418
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14519759C2semidirect
3. C2×C4×D244C2semidirect
4. C2×C22⋊C4×D61C2semidirect
5. #16839699C2semidirect
6. #16839687C2semidirect
7. #16839679C2semidirect
8. #16839678C2semidirect
9. #16839653C2semidirect
10. #16839640C2semidirect
11. #16839640C2semidirect
12. #16839636C2semidirect
13. #16839619C2semidirect
14. #16839617C2semidirect
15. C61×#388C2semidirect
22. C22×C4×D61C22semidirect
26. C2×C4⋊Dic61C22semidirect
27. C2×C4⋊Dic61C22semidirect
28. C2×C4⋊Dic61C22semidirect
29. C2×#11758196C22semidirect
40. C2×#11758198C22semidirect
41. C2×#11758198C22semidirect
42. C2×#11758198C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. C2×C4⋊C4×C61C22semidirect
52. C2×C42×C61C22semidirect
53. #95×C61C22semidirect
54. #95×C61C22semidirect
98. C22⋊C4×C61D4semidirect
227. C2×D61#123semidirect
260. #388D61semidirect
266. C61#2418semidirect
281. C2×C4⋊C4C2×D61semidirect
299. C2×C42C2×D61semidirect
304. #95C2×D61semidirect
305. #95C2×D61semidirect
366. C22⋊C4D244semidirect