Finite Group Databasebeta

← #21449939

Subgroups — #21449939

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×#14519763C211yesmaximal, characteristic, complemented
2C2×#14519756C211yesmaximal, characteristic, complemented
3C2×#14519746C211yesmaximal, characteristic
4#16839690C211yesmaximal, characteristic, complemented
5#16839678C211yesmaximal, characteristic, complemented
6#16839677C211yesmaximal, characteristic, complemented
7#16839674C211yesmaximal, characteristic, complemented
8#16839662C211yesmaximal, characteristic, complemented
9#16839655C211yesmaximal, characteristic, complemented
10#16839650C211yesmaximal, characteristic, complemented
11#16839641C211yesmaximal, characteristic, complemented
12#16839641C211yesmaximal, characteristic, complemented
13#16839618C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic, complemented
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20#14519763—24no—
21#14519756—24no—
22#14519746—24no—
23C2×C4⋊Dic61C2211yescharacteristic, complemented
24C2×#11758196C2211yescharacteristic, complemented
25C2×#11758196C2211yescharacteristic, complemented
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×#11758198C2211yescharacteristic, complemented
36C2×#11758198C2211yescharacteristic, complemented
37C2×#11758198C2211yescharacteristic, complemented
38C2×#11758198C2211yescharacteristic, 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
48C23×C4×C61C2211yescharacteristic
49C23×C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61—24no—
51C2×C22⋊C4×C61C2211yescharacteristic
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
65C23×D61C2311yescharacteristic
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C2×C22⋊D61—22no—
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—22no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
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×C61—22no—
98C22⋊C4×C61D414yescomplemented
99C22⋊Dic61—22no—
100C22⋊Dic61—22no—
101C22⋊Dic61—22no—
102C22⋊Dic61—22no—
103C22⋊Dic61—22no—
104C22⋊Dic61—22no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107C22⋊Dic61D414yes—
108#11758198—22no—
109#11758198—22no—
110#11758198—41no—
111#11758198—41no—
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—44no—
135C23×C61—44no—
136C23×C61—44no—
137C23×C61—44no—
138C23×C61—44no—
139C23×C61—44no—
140C23×C61C2×D412yes—
141C23×C61C2×D412yes—
142C23×C61#4112yes—
143C23×C61#4112yes—
144C23×C61#4112yes—
145C23×C61C2411yescharacteristic
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—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—44no—
164C2×C4×C61—44no—
165C2×C4×C61C2×D412yes—
166C2×C4×C61C2×D412yes—
167C22⋊D61—44no—
168C22⋊D61—44no—
169C22⋊D61—44no—
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—21no—
188C2×Dic61—21no—
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#12414yescomplemented
214C22×C61C22×D411yescharacteristic
215C22×C61C22×D411yescharacteristic
216C22×C61C2×#4111yescharacteristic
217C22×C61C2×#4111yescharacteristic
218C22×C61C2×#4111yescharacteristic
219C22×C61H(5,𝔽2)11yescharacteristic
220C22×C61H(5,𝔽2)11yescharacteristic
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C4×C61—22no—
229C4×C61—22no—
230C4×C61—41no—
231C4×C61—41no—
232Dic61—22no—
233Dic61—22no—
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#52511yescharacteristic
244C2×C61C2×#12411yescharacteristic
245C2×C61#53811yescharacteristic
246C2×C61D4211yescharacteristic
247C2×C61#54611yescharacteristic
248C2×C61#54611yescharacteristic
249C2×C61#55111yescharacteristic
250D61—81no—
251C2×#124—611no—
252C2×C22⋊Q8—611no—
253C2×#120—611no—
254C22×C22⋊C4D6111yescharacteristic, complemented
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×D4—611no—
270C22×D4—611no—
271C22×D4—611no—
272C23×C4C2×D6111yescharacteristic
273C23×C4C2×D6111yescharacteristic
274#124—1224no—
275C22⋊Q8—1224no—
276#120—1224no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C22⋊C4—24no—
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⋊C4C2×D6111yescharacteristic
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—
313C24—611no—
314C24C22×D6111yescharacteristic
315C24C22×D6111yescharacteristic
316C24C22×D6111yescharacteristic
317C2×Q8—1222no—
318C2×Q8—1222no—
319C2×Q8—2441no—
320C2×D4—1222no—
321C2×D4—1222no—
322C2×D4—1222no—
323C2×D4—1222no—
324C2×D4—1222no—
325C2×D4—1222no—
326C2×D4—1222no—
327C2×D4—2441no—
328C2×D4—2441no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—611no—
336C22×C4—611no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4C22×D6111yescharacteristic
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—22no—
352C22⋊C4—614no—
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⋊D6114yescomplemented
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—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—1221no—
392C23—1221no—
393C23—1221no—
394C23—1221no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23#1175822212yes—
399C23#1175822212yes—
400C23D4×D6112yes—
401C23#1175822412yes—
402C23C2×C22⋊D6112yes—
403C23C23×D6111yescharacteristic
404Q8—2444no—
405D4—2444no—
406D4—2444no—
407D4—2444no—
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—44no—
419C2×C4—44no—
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—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
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—2441no—
465C22—2441no—
466C22—2441no—
467C22—2441no—
468C22—2441no—
469C22—2441no—
470C22—2441no—
471C22#1451976314yescomplemented
472C22C2×D4×D6111yescharacteristic
473C22C22×C22⋊D6111yescharacteristic
474C22C2×#1175822411yescharacteristic
475C22C2×#1175822211yescharacteristic
476C22C2×#1175822211yescharacteristic
477C22#1451982211yescharacteristic
478C22#1451982211yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—1222no—
484C4—1222no—
485C4—2441no—
486C4—2441no—
487C4—2441no—
488C4—2441no—
489C4—2441no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—4881no—
494C2#1684027311yescharacteristic
495C2C2×#1451976311yescharacteristic
496C2#1684035011yescharacteristic
497C2D4×C22⋊D6111yescharacteristic
498C2#1684040211yescharacteristic
499C2#1684040611yescharacteristic
500C2#1684043811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C22⋊C4×C61C2
hypercenterC22×C22⋊C4D61
hypocenterC61#2472
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519763C2semidirect
2. C2×#14519756C2semidirect
4. #16839690C2semidirect
5. #16839678C2semidirect
6. #16839677C2semidirect
7. #16839674C2semidirect
8. #16839662C2semidirect
9. #16839655C2semidirect
10. #16839650C2semidirect
11. #16839641C2semidirect
12. #16839641C2semidirect
13. #16839618C2semidirect
14. C4×C22⋊Dic61C2semidirect
15. C22×C22⋊C4×C61C2semidirect
16. C22×Dic122C22semidirect
23. C2×C4⋊Dic61C22semidirect
24. C2×#11758196C22semidirect
25. C2×#11758196C22semidirect
35. C2×#11758198C22semidirect
36. C2×#11758198C22semidirect
37. C2×#11758198C22semidirect
38. C2×#11758198C22semidirect
39. C2×C4×Dic61C22semidirect
40. C2×C4×Dic61C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
98. C22⋊C4×C61D4semidirect
213. C22×C61#124semidirect
254. C22×C22⋊C4D61semidirect
266. C61#2472semidirect
365. C22⋊C4C22⋊D61semidirect
471. C22#14519763semidirect