Finite Group Databasebeta

← #21448798

Subgroups — #21448798

Order 7808.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519746C211yesmaximal, characteristic
2C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#14519737C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#16839662C211yesmaximal, characteristic, complemented
6#16839656C211yesmaximal, characteristic, complemented
7#16839650C211yesmaximal, characteristic, complemented
8#16839641C211yesmaximal, characteristic, complemented
9#16839639C211yesmaximal, characteristic, complemented
10#16839638C211yesmaximal, characteristic, complemented
11#16839635C211yesmaximal, characteristic, complemented
12#16839634C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic, complemented
22#14519746C418yescomplemented
23C4×C22⋊D61—24no—
24#14519737—24no—
25C2×#11758196C2211yescharacteristic, complemented
26C2×#11758196C2211yescharacteristic, complemented
27C2×#11758196C2211yescharacteristic, complemented
28C2×C22⋊Dic61—24no—
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×#11758198C2211yescharacteristic, complemented
37C2×#11758198C2211yescharacteristic, complemented
38C2×#11758198C2211yescharacteristic, complemented
39C2×C4×Dic61C2211yescharacteristic, complemented
40C2×C4×Dic61C2211yescharacteristic, complemented
41C2×C4×Dic61C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48C25×C61C2211yescharacteristic
49C23×C4×C61C2211yescharacteristic
50C23×C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61—24no—
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic
55C2×C22⋊C4×C61C2211yescharacteristic
56C24×C61—22no—
57C24×C61—22no—
58C24×C61—22no—
59C24×C61—22no—
60C24×C61—41no—
61C24×C61—41no—
62C24×C61C2×C414yescomplemented
63C24×C61C2311yescharacteristic
64C24×C61C2311yescharacteristic
65C24×C61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—22no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
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⋊D61—41no—
83C2×C22⋊D61C2×C414yescomplemented
84C2×C22⋊D61C2×C414yescomplemented
85C2×C22⋊D61C2×C414yescomplemented
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61—22no—
89C22×Dic61—22no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C22×Dic61C2311yescharacteristic
95C22×Dic61C2311yescharacteristic
96C22×Dic61C2311yescharacteristic
97C22×Dic61C2311yescharacteristic
98C22×Dic61C2311yescharacteristic
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—41no—
102C22⋊C4×C61—22no—
103C22⋊C4×C61—22no—
104C22⋊C4×C61—22no—
105C22⋊C4×C61D414yescomplemented
106C22⋊Dic61—22no—
107C22⋊Dic61—22no—
108C22⋊Dic61—22no—
109C22⋊Dic61C2×C414yescomplemented
110C22⋊Dic61C2×C414yescomplemented
111C22⋊Dic61C2×C414yescomplemented
112C22⋊Dic61D414yescomplemented
113#11758198—22no—
114#11758198—22no—
115#11758198—41no—
116#11758196—22no—
117#11758196—22no—
118#11758196—41no—
119C4×Dic61—22no—
120C4×Dic61—22no—
121C4×Dic61—41no—
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—28no—
131C23×C61—28no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—44no—
139C23×C61—44no—
140C23×C61—44no—
141C23×C61—44no—
142C23×C61—44no—
143C23×C61C22×C412yes—
144C23×C61C22×C412yes—
145C23×C61C22×C412yes—
146C23×C61C2×D412yes—
147C23×C61C2×D412yes—
148C23×C61#4112yes—
149C23×C61#4112yes—
150C23×C61C2411yescharacteristic
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61C22×C412yes—
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×C61—44no—
169C2×C4×C61—44no—
170C2×C4×C61C2×D412yes—
171C2×C4×C61C2×D412yes—
172C22⋊D61—28no—
173C22⋊D61—28no—
174C22⋊D61—44no—
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×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—44no—
192C2×Dic61—44no—
193C2×Dic61C22×C412yes—
194C2×Dic61C22×C412yes—
195C2×Dic61C22×C412yes—
196C2×Dic61C2×D412yes—
197C2×Dic61C2×D412yes—
198C4×D61—44no—
199C22×C61—22no—
200C22×C61—22no—
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—22no—
208C22×C61—22no—
209C22×C61—22no—
210C22×C61—22no—
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—22no—
214C22×C61—416no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61C4×D414yescomplemented
220C22×C61C4×D414yescomplemented
221C22×C61C23×C411yescharacteristic
222C22×C61C22×D411yescharacteristic
223C22×C61C22×D411yescharacteristic
224C22×C61C2×#4111yescharacteristic
225C22×C61C2×#4111yescharacteristic
226C22×C61H(5,𝔽2)11yescharacteristic
227C22×C61H(5,𝔽2)11yescharacteristic
228C2×D61—22no—
229C2×D61—22no—
230C2×D61—22no—
231C2×D61—41no—
232C2×D61—41no—
233C2×D61—41no—
234C2×D61—41no—
235C4×C61—22no—
236C4×C61—22no—
237C4×C61—41no—
238C4×C61—41no—
239Dic61—22no—
240Dic61—22no—
241Dic61—22no—
242Dic61—22no—
243Dic61—22no—
244Dic61—41no—
245Dic61—41no—
246#2358—611nomaximal, Sylow
247C2×C61—24no—
248C2×C61—24no—
249C2×C61—42no—
250C2×C61C2×C4×D411yescharacteristic
251C2×C61C2×C4×D411yescharacteristic
252C2×C61#51811yescharacteristic
253C2×C61D4211yescharacteristic
254C2×C61#54611yescharacteristic
255C2×C61#54611yescharacteristic
256C2×C61#55111yescharacteristic
257D61—42no—
258C2×#120—611no—
259C2×C4×D4—611no—
260C2×C4×D4—611no—
261C22×C22⋊C4—611no—
262C22×C22⋊C4D6111yescharacteristic, complemented
263#390—611no—
264#388—611no—
265#388—611no—
266#386—611no—
267#386—611no—
268#386—611no—
269#385—611no—
270#385—611no—
271C4×C22⋊C4—611no—
272C4×C22⋊C4—611no—
273C61#235811yescharacteristic, complemented, Sylow
274C25C2×D6111yescharacteristic
275C22×D4—611no—
276C22×D4—611no—
277C22×D4—611no—
278C23×C4—611no—
279C23×C4—611no—
280C23×C4—611no—
281C23×C4C2×D6111yescharacteristic
282C23×C4C2×D6111yescharacteristic
283#120—618no—
284C4×D4—1224no—
285C4×D4—1224no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—611no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—611no—
291C2×C22⋊C4—611no—
292C2×C22⋊C4—611no—
293C2×C22⋊C4—611no—
294C2×C22⋊C4—611no—
295C2×C22⋊C4—611no—
296C2×C22⋊C4—611no—
297C2×C22⋊C4—611no—
298C2×C22⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—1224no—
301C2×C22⋊C4C2×D6111yescharacteristic
302C2×C22⋊C4C2×D6111yescharacteristic
303C2×C22⋊C4C2×D6111yescharacteristic
304C2×C22⋊C4C2×D6111yescharacteristic
305C2×C42—611no—
306C2×C42—611no—
307C2×C42—611no—
308#95—611no—
309#95—611no—
310#95—611no—
311#95—611no—
312#95—611no—
313#95—611no—
314C24—22no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—611no—
321C24C4×D6114yescomplemented
322C24C22×D6111yescharacteristic
323C24C22×D6111yescharacteristic
324C24C22×D6111yescharacteristic
325C2×D4—614no—
326C2×D4—614no—
327C2×D4—614no—
328C2×D4—1222no—
329C2×D4—1222no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—2441no—
333C2×D4—2441no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4C22×D6111yescharacteristic
357C22×C4C22×D6111yescharacteristic
358C22×C4C22×D6111yescharacteristic
359C22×C4C22×D6111yescharacteristic
360C4⋊C4—1222no—
361C4⋊C4—1222no—
362C4⋊C4—2441no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—614no—
367C22⋊C4—614no—
368C22⋊C4—614no—
369C22⋊C4—614no—
370C22⋊C4—1222no—
371C22⋊C4—1222no—
372C22⋊C4—1222no—
373C22⋊C4—1222no—
374C22⋊C4—1222no—
375C22⋊C4—2441no—
376C22⋊C4C22⋊D6114yescomplemented
377C42—1222no—
378C42—1222no—
379C42—2441no—
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—21no—
393C23—21no—
394C23—28no—
395C23—28no—
396C23—44no—
397C23—44no—
398C23—44no—
399C23—44no—
400C23—44no—
401C23—612no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23C2×C4×D6112yes—
409C23C2×C4×D6112yes—
410C23C2×C4×D6112yes—
411C23#1175822212yes—
412C23D4×D6112yes—
413C23#1175822412yes—
414C23C2×C22⋊D6112yes—
415C23C23×D6111yescharacteristic
416D4—1228no—
417D4—1228no—
418D4—2444no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—612no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—612no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—1221no—
449C2×C4—1221no—
450C2×C4—1221no—
451C2×C4—1221no—
452C2×C4—2444no—
453C2×C4—2444no—
454C2×C4—2444no—
455C2×C4C2×C22⋊D6112yes—
456C2×C4C2×C22⋊D6112yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—416no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—1222no—
478C22—1222no—
479C22—1222no—
480C22—2441no—
481C22—2441no—
482C22—2441no—
483C22—2441no—
484C22#1451973714yescomplemented
485C22C4×C22⋊D6114yescomplemented
486C22C22×C4×D6111yescharacteristic
487C22C2×D4×D6111yescharacteristic
488C22C22×C22⋊D6111yescharacteristic
489C22C2×#1175822411yescharacteristic
490C22C2×#1175822211yescharacteristic
491C22#1451982211yescharacteristic
492C22#1451982211yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—1222no—
498C4—1222no—
499C4—1222no—
500C4—1222no—
501C4—1222no—
502C4—2441no—
503C4—2441no—
504C2—24no—
505C2—24no—
506C2—42no—
507C2—2442no—
508C2C2×#1451973711yescharacteristic
509C2C2×C4×C22⋊D6111yescharacteristic
510C2#1684023511yescharacteristic
511C2D4×C22⋊D6111yescharacteristic
512C2#1684040211yescharacteristic
513C2#1684040611yescharacteristic
514C2#1684043811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC22×C22⋊C4×C61C2
socleC23×C61C24
hypercenterC22×C22⋊C4D61
hypocenterC61#2358
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D61C2semidirect
3. C2×#14519737C2semidirect
4. C22×C22⋊Dic61C2semidirect
5. #16839662C2semidirect
6. #16839656C2semidirect
7. #16839650C2semidirect
8. #16839641C2semidirect
9. #16839639C2semidirect
10. #16839638C2semidirect
11. #16839635C2semidirect
12. #16839634C2semidirect
13. C22⋊C4×Dic61C2semidirect
14. C4×C22⋊Dic61C2semidirect
15. C22×C22⋊C4×C61C2semidirect
21. C22×C4×D61C22semidirect
22. #14519746C4semidirect
25. C2×#11758196C22semidirect
26. C2×#11758196C22semidirect
27. C2×#11758196C22semidirect
36. C2×#11758198C22semidirect
37. C2×#11758198C22semidirect
38. C2×#11758198C22semidirect
39. C2×C4×Dic61C22semidirect
40. C2×C4×Dic61C22semidirect
41. C2×C4×Dic61C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
62. C24×C61C2×C4semidirect
83. C2×C22⋊D61C2×C4semidirect
84. C2×C22⋊D61C2×C4semidirect
85. C2×C22⋊D61C2×C4semidirect
105. C22⋊C4×C61D4semidirect
109. C22⋊Dic61C2×C4semidirect
110. C22⋊Dic61C2×C4semidirect
111. C22⋊Dic61C2×C4semidirect
112. C22⋊Dic61D4semidirect
219. C22×C61C4×D4semidirect
220. C22×C61C4×D4semidirect
262. C22×C22⋊C4D61semidirect
273. C61#2358semidirect
321. C24C4×D61semidirect
376. C22⋊C4C22⋊D61semidirect
484. C22#14519737semidirect
485. C22C4×C22⋊D61semidirect