Finite Group Databasebeta

← #21449944

Subgroups — #21449944

Order 7808.

786 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×#14519764C211yesmaximal, characteristic, complemented
2C2×#14519754C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic61C211yesmaximal, characteristic, complemented
4#16839687C211yesmaximal, characteristic, complemented
5#16839676C211yesmaximal, characteristic, complemented
6#16839676C211yesmaximal, characteristic, complemented
7#16839674C211yesmaximal, characteristic, complemented
8#16839665C211yesmaximal, characteristic, complemented
9#16839656C211yesmaximal, characteristic, complemented
10#16839656C211yesmaximal, characteristic, complemented
11#16839642C211yesmaximal, characteristic, complemented
12#16839642C211yesmaximal, characteristic, complemented
13#16839618C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C2×#120×C61C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic, complemented
17C23×Dic61C2211yescharacteristic
18C23×Dic61C2211yescharacteristic
19#14519764—24no—
20#14519754—24no—
21C2×C4⋊Dic61C2211yescharacteristic, complemented
22C2×#11758196C2211yescharacteristic, complemented
23C2×#11758196C2211yescharacteristic, complemented
24C2×C22⋊Dic61—24no—
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic, complemented
36C2×C22⋊Dic61C2211yescharacteristic, complemented
37C2×C22⋊Dic61C2211yescharacteristic, complemented
38C2×C22⋊Dic61C2211yescharacteristic, complemented
39C2×C4×Dic61C2211yescharacteristic, complemented
40C2×C4×Dic61C2211yescharacteristic, complemented
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47C25×C61C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51#120×C61—24no—
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic
55C24×C61—22no—
56C24×C61—22no—
57C24×C61—22no—
58C24×C61—22no—
59C24×C61—22no—
60C24×C61—41no—
61C24×C61—41no—
62C24×C61C2311yescharacteristic
63C24×C61C2311yescharacteristic
64C24×C61C2311yescharacteristic
65C24×C61C2311yescharacteristic
66C2×D4×C61—22no—
67C2×D4×C61—22no—
68C2×D4×C61—22no—
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×C61—22no—
72C2×D4×C61—22no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C22×C4×C61C2311yescharacteristic
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22×Dic61—22no—
81C22×Dic61—22no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61C2311yescharacteristic
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C22×Dic61C2311yescharacteristic
90C22×Dic61C2311yescharacteristic
91C22×Dic61C2311yescharacteristic
92C2×Dic122—22no—
93C2×Dic122—22no—
94C2×Dic122—41no—
95C22⋊C4×C61—22no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61D414yes—
98C22⋊Dic61—22no—
99C22⋊Dic61—22no—
100C22⋊Dic61—22no—
101C22⋊Dic61—22no—
102C22⋊Dic61—22no—
103C22⋊Dic61—22no—
104C22⋊Dic61—22no—
105C22⋊Dic61—22no—
106C22⋊Dic61—22no—
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111C22⋊Dic61D414yescomplemented
112C4⋊Dic61—22no—
113#11758196—22no—
114#11758196—22no—
115C4×Dic61—22no—
116C4×Dic61—41no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—28no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—44no—
142C23×C61—44no—
143C23×C61—44no—
144C23×C61—44no—
145C23×C61—44no—
146C23×C61—44no—
147C23×C61C2×D412yes—
148C23×C61C2×D412yes—
149C23×C61#4112yes—
150C23×C61#4112yes—
151C23×C61#4112yes—
152C23×C61C2411yescharacteristic
153D4×C61—44no—
154D4×C61—44no—
155D4×C61—44no—
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×C61C2×D412yes—
164C2×C4×C61C2×D412yes—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
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×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—44no—
188C2×Dic61—44no—
189C2×Dic61C2×D412yes—
190C2×Dic61C2×D412yes—
191Dic122—44no—
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—22no—
195C22×C61—22no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—22no—
199C22×C61—22no—
200C22×C61—22no—
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—416no—
205C22×C61—41no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61#12414yescomplemented
221C22×C61C22×D411yescharacteristic
222C22×C61C22×D411yescharacteristic
223C22×C61C2×#4111yescharacteristic
224C22×C61C2×#4111yescharacteristic
225C22×C61C2×#4111yescharacteristic
226C22×C61H(5,𝔽2)11yescharacteristic
227C22×C61H(5,𝔽2)11yescharacteristic
228C4×C61—22no—
229C4×C61—22no—
230C4×C61—41no—
231Dic61—22no—
232Dic61—22no—
233Dic61—41no—
234Dic61—41no—
235Dic61—41no—
236Dic61—41no—
237Dic61—41no—
238Dic61—41no—
239#2472—611nomaximal, Sylow
240C2×C61—24no—
241C2×C61—42no—
242C2×C61—42no—
243C2×C61—81no—
244C2×C61#52511yescharacteristic
245C2×C61C2×#12411yescharacteristic
246C2×C61#53811yescharacteristic
247C2×C61D4211yescharacteristic
248C2×C61#54611yescharacteristic
249C2×C61#54611yescharacteristic
250C2×C61#55111yescharacteristic
251C2×#124—611no—
252C2×C22⋊Q8—611no—
253C2×#120D6111yescharacteristic
254C22×C22⋊C4—611no—
255#397—611no—
256#394—611no—
257#394—611no—
258#393—611no—
259#390—611no—
260#388—611no—
261#388—611no—
262#386—611no—
263#386—611no—
264#379—611no—
265C4×C22⋊C4—611no—
266C61#247211yescharacteristic, complemented, Sylow
267C25C2×D6111yescharacteristic
268C22×Q8—611no—
269C22×D4C2×D6111yescharacteristic
270C22×D4C2×D6111yescharacteristic
271C22×D4C2×D6111yescharacteristic
272C23×C4—611no—
273C23×C4—611no—
274#124—1224no—
275C22⋊Q8—1224no—
276#120—24no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊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—611no—
292C2×C22⋊C4—611no—
293C2×C22⋊C4—611no—
294C2×C22⋊C4—1224no—
295C2×C22⋊C4C2×D6111yescharacteristic
296C2×C22⋊C4C2×D6111yescharacteristic
297C2×C22⋊C4C2×D6111yescharacteristic
298C2×C42—611no—
299C2×C42—611no—
300#95—611no—
301#95—611no—
302#95—611no—
303#95—611no—
304#95—611no—
305#95—611no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24C22×D6111yescharacteristic
314C24C22×D6111yescharacteristic
315C24C22×D6111yescharacteristic
316C24C22×D6111yescharacteristic
317C2×Q8—1222no—
318C2×Q8—1222no—
319C2×Q8—2441no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—41no—
328C2×D4—41no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—611no—
336C22×C4—611no—
337C22×C4—1222no—
338C22×C4—1222no—
339C22×C4—1222no—
340C22×C4—1222no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4C22×D6111yescharacteristic
344C22×C4C22×D6111yescharacteristic
345C22×C4C22×D6111yescharacteristic
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—614no—
352C22⋊C4—1222no—
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—2441no—
362C22⋊C4—2441no—
363C22⋊C4—2441no—
364C22⋊C4—2441no—
365C22⋊C4C22⋊D6114yes—
366C42—1222no—
367C42—2441no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—44no—
396C23—44no—
397C23—44no—
398C23D4×D6112yes—
399C23#1175822412yes—
400C23#1175822412yes—
401C23#1175822412yes—
402C23C2×C22⋊D6112yes—
403C23C23×D6111yescharacteristic
404Q8—2444no—
405D4—44no—
406D4—44no—
407D4—44no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—612no—
416C2×C4—612no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1221no—
420C2×C4—1221no—
421C2×C4—1221no—
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—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22#1451976414yescomplemented
472C22C2×D4×D6111yescharacteristic
473C22C22×C22⋊D6111yescharacteristic
474C22C2×#1175822411yescharacteristic
475C22C2×#1175822411yescharacteristic
476C22C2×#1175822411yescharacteristic
477C22#1451982211yescharacteristic
478C22#1451982211yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—1222no—
483C4—1222no—
484C4—2441no—
485C4—2441no—
486C4—2441no—
487C4—2441no—
488C4—2441no—
489C4—2441no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—81no—
494C2#1684026811yescharacteristic
495C2C2×#1451976411yescharacteristic
496C2#1684034711yescharacteristic
497C2D4×C22⋊D6111yescharacteristic
498C2#1684039911yescharacteristic
499C2#1684040611yescharacteristic
500C2#1684044311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#120×C61C2
hypercenterC2×#120D61
hypocenterC61#2472
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14519764C2semidirect
2. C2×#14519754C2semidirect
3. C22×C22⋊Dic61C2semidirect
4. #16839687C2semidirect
5. #16839676C2semidirect
6. #16839676C2semidirect
7. #16839674C2semidirect
8. #16839665C2semidirect
9. #16839656C2semidirect
10. #16839656C2semidirect
11. #16839642C2semidirect
12. #16839642C2semidirect
13. #16839618C2semidirect
14. C22⋊C4×Dic61C2semidirect
16. C22×Dic122C22semidirect
21. C2×C4⋊Dic61C22semidirect
22. C2×#11758196C22semidirect
23. C2×#11758196C22semidirect
35. C2×C22⋊Dic61C22semidirect
36. C2×C22⋊Dic61C22semidirect
37. C2×C22⋊Dic61C22semidirect
38. C2×C22⋊Dic61C22semidirect
39. C2×C4×Dic61C22semidirect
40. C2×C4×Dic61C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
111. C22⋊Dic61D4semidirect
220. C22×C61#124semidirect
266. C61#2472semidirect
471. C22#14519764semidirect