Finite Group Databasebeta

← #21449278

Subgroups — #21449278

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×#14519745C211yesmaximal, characteristic
2C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#16839697C211yesmaximal, characteristic, complemented
5#16839690C211yesmaximal, characteristic, complemented
6#16839678C211yesmaximal, characteristic, complemented
7#16839676C211yesmaximal, characteristic, complemented
8#16839655C211yesmaximal, characteristic, complemented
9#16839652C211yesmaximal, characteristic, complemented
10#16839641C211yesmaximal, characteristic, complemented
11#16839638C211yesmaximal, characteristic, complemented
12#16839633C211yesmaximal, characteristic, complemented
13#16839619C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic, complemented
15C2×#123×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519745—24no—
22C4×C22⋊D61—24no—
23C2×C4⋊Dic61C2211yescharacteristic, complemented
24C2×#11758196C2211yescharacteristic, complemented
25C2×#11758196C2211yescharacteristic, complemented
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic, complemented
30C2×C22⋊Dic61C2211yescharacteristic, complemented
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C22⋊C4×D61—24no—
40C2×C4×Dic61C2211yescharacteristic, complemented
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47C22×D4×C61C2211yescharacteristic
48C23×C4×C61C2211yescharacteristic, complemented
49#123×C61—24no—
50C2×C4⋊C4×C61C2211yescharacteristic, complemented
51C2×C4⋊C4×C61C2211yescharacteristic, complemented
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic, complemented
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—22no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61C2311yescharacteristic
65C23×D61C2311yescharacteristic
66C2×D4×C61—22no—
67C2×D4×C61—22no—
68C2×D4×C61—41no—
69C22×C4×C61—22no—
70C22×C4×C61—22no—
71C22×C4×C61—41no—
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61D414yes—
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—22no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—22no—
97C22⋊C4×C61—22no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61D414yescomplemented
100C22⋊Dic61—22no—
101C22⋊Dic61—22no—
102C22⋊Dic61—22no—
103C22⋊Dic61—41no—
104C22⋊Dic61—41no—
105#11758198—22no—
106#11758198—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111#11758198—22no—
112#11758198—41no—
113C4⋊Dic61—41no—
114#11758196—22no—
115#11758196—41no—
116C4×Dic61—22no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61C2×D412yes—
130C23×C61C2×D412yes—
131C23×C61C2411yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—28no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—44no—
144C22×D61—44no—
145C22×D61—44no—
146C22×D61—44no—
147C22×D61—44no—
148C22×D61—44no—
149C22×D61C2×D412yes—
150C22×D61#4112yes—
151C22×D61#4112yes—
152C22×D61#4112yes—
153D4×C61—44no—
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—44no—
168C2×C4×C61C2×D412yes—
169C2×C4×C61C2×D412yes—
170C22⋊D61—28no—
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—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61C2×D412yes—
190C4×D61—44no—
191C4×D61—44no—
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—22no—
195C22×C61—22no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61C22×D411yescharacteristic
207C22×C61C22×D411yescharacteristic
208C22×C61C2×#4111yescharacteristic
209C22×C61C2×#4111yescharacteristic
210C22×C61C2×#4111yescharacteristic
211C22×C61H(5,𝔽2)11yescharacteristic
212C22×C61H(5,𝔽2)11yescharacteristic
213C2×D61—22no—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—416no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61#12314yescomplemented
228C4×C61—22no—
229C4×C61—22no—
230C4×C61—41no—
231C4×C61—41no—
232C4×C61—41no—
233Dic61—22no—
234Dic61—41no—
235Dic61—41no—
236Dic61—41no—
237Dic61—41no—
238Dic61—41no—
239#2418—611nomaximal, Sylow
240C2×C61—42no—
241C2×C61—42no—
242C2×C61C2×#12311yescharacteristic
243C2×C61#52511yescharacteristic
244C2×C61#53811yescharacteristic
245C2×C61D4211yescharacteristic
246C2×C61#54611yescharacteristic
247C2×C61#54611yescharacteristic
248C2×C61#55111yescharacteristic
249D61—24no—
250D61—42no—
251C2×#123D6111yescharacteristic, complemented
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#388—611no—
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×D4C2×D6111yescharacteristic
271C23×C4—611no—
272C23×C4—611no—
273C23×C4C2×D6111yescharacteristic, complemented
274#123—24no—
275#120—1224no—
276C4×D4—1224no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4C2×D6111yescharacteristic, complemented
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, complemented
299C2×C42—611no—
300#95—611no—
301#95—611no—
302#95—611no—
303#95—611no—
304#95—611no—
305#95—611no—
306C24—611no—
307C24—611no—
308C24—1222no—
309C24—1222no—
310C24—1222no—
311C24—1222no—
312C24—1222no—
313C24—2441no—
314C24—2441no—
315C24C22×D6111yescharacteristic
316C24C22×D6111yescharacteristic
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—614no—
321C2×D4—1222no—
322C2×D4—1222no—
323C2×D4—1222no—
324C2×D4—1222no—
325C2×D4—2441no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—1222no—
336C22×C4—1222no—
337C22×C4—1222no—
338C22×C4—1222no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4C22×D6111yescharacteristic
342C22×C4C22×D6111yescharacteristic
343C22×C4C22×D6111yescharacteristic
344C22×C4C22×D6111yescharacteristic
345C22×C4C22×D6111yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—1222no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C22⋊C4—22no—
352C22⋊C4—22no—
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—2441no—
364C22⋊C4—2441no—
365C22⋊C4—2441no—
366C22⋊C4C22⋊D6114yescomplemented
367C42—1222no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—612no—
381C23—612no—
382C23—612no—
383C23—612no—
384C23—1228no—
385C23—1221no—
386C23—1221no—
387C23—1221no—
388C23—1221no—
389C23—1221no—
390C23—1221no—
391C23—1221no—
392C23—1221no—
393C23—1221no—
394C23—1221no—
395C23—2444no—
396C23—2444no—
397C23—2444no—
398C23—2444no—
399C23—2444no—
400C23—2444no—
401C23D4×D6112yes—
402C23C2×C22⋊D6112yes—
403C23C23×D6111yescharacteristic
404D4—44no—
405D4—1228no—
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—44no—
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—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—2444no—
440C2×C4—2444no—
441C2×C4C2×C22⋊D6112yes—
442C2×C4C2×C22⋊D6112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—614no—
458C22—1222no—
459C22—1222no—
460C22—1222no—
461C22—1222no—
462C22—1222no—
463C22—1222no—
464C22—1222no—
465C22—1222no—
466C22—1222no—
467C22—24416no—
468C22—2441no—
469C22—2441no—
470C22—2441no—
471C22—2441no—
472C22C2×D4×D6111yescharacteristic
473C22C22×C22⋊D6111yescharacteristic
474C22#41×D6111yescharacteristic
475C22#41×D6111yescharacteristic
476C22#41×D6111yescharacteristic
477C22#1451982211yescharacteristic
478C22#1451982311yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—1222no—
485C4—2441no—
486C4—2441no—
487C4—2441no—
488C4—2441no—
489C4—2441no—
490C2—42no—
491C2—42no—
492C2—1224no—
493C2—2442no—
494C2#123×D6111yescharacteristic
495C2#1684026911yescharacteristic
496C2#1684034811yescharacteristic
497C2D4×C22⋊D6111yescharacteristic
498C2#1684040011yescharacteristic
499C2#1684040411yescharacteristic
500C2#1684044011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#123×C61C2
hypercenterC2×#123D61
hypocenterC61#2418
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D61C2semidirect
3. C2×C22⋊C4×D61C2semidirect
4. #16839697C2semidirect
5. #16839690C2semidirect
6. #16839678C2semidirect
7. #16839676C2semidirect
8. #16839655C2semidirect
9. #16839652C2semidirect
10. #16839641C2semidirect
11. #16839638C2semidirect
12. #16839633C2semidirect
13. #16839619C2semidirect
14. #16839617C2semidirect
15. C2×#123×C61C2semidirect
23. C2×C4⋊Dic61C22semidirect
24. C2×#11758196C22semidirect
25. C2×#11758196C22semidirect
29. C2×C22⋊Dic61C22semidirect
30. C2×C22⋊Dic61C22semidirect
40. C2×C4×Dic61C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
48. C23×C4×C61C22semidirect
50. C2×C4⋊C4×C61C22semidirect
51. C2×C4⋊C4×C61C22semidirect
54. C2×C22⋊C4×C61C22semidirect
99. C22⋊C4×C61D4semidirect
227. C2×D61#123semidirect
251. C2×#123D61semidirect
266. C61#2418semidirect
273. C23×C4C2×D61semidirect
280. C2×C4⋊C4C2×D61semidirect
281. C2×C4⋊C4C2×D61semidirect
298. C2×C22⋊C4C2×D61semidirect
366. C22⋊C4C22⋊D61semidirect