Finite Group Databasebeta

← #21449941

Subgroups — #21449941

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×#14519753C211yesmaximal, characteristic, complemented
2C2×#14519745C211yesmaximal, characteristic
3C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#16839690C211yesmaximal, characteristic, complemented
5#16839678C211yesmaximal, characteristic, complemented
6#16839676C211yesmaximal, characteristic, complemented
7#16839673C211yesmaximal, characteristic, complemented
8#16839662C211yesmaximal, characteristic, complemented
9#16839655C211yesmaximal, characteristic, complemented
10#16839653C211yesmaximal, characteristic, complemented
11#16839638C211yesmaximal, characteristic, complemented
12#16839638C211yesmaximal, characteristic, complemented
13#16839617C211yesmaximal, characteristic, complemented
14C4×#11758198C211yesmaximal, characteristic, complemented
15C2×#124×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519753—24no—
22#14519745—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×Q8×C61C2211yescharacteristic, complemented
48C22×D4×C61C2211yescharacteristic
49#124×C61—24no—
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic, complemented
53C2×C22⋊C4×C61C2211yescharacteristic, complemented
54C2×C42×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×Q8×C61—22no—
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×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—22no—
82C2×C22⋊D61—41no—
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—
95C22⋊C4×C61—22no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61—22no—
98C22⋊C4×C61D414yescomplemented
99C42×C61—22no—
100C22⋊Dic61—22no—
101C22⋊Dic61—22no—
102C22⋊Dic61—41no—
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—41no—
112#11758198D414yes—
113C4⋊Dic61—22no—
114#11758196—22no—
115#11758196—22no—
116C4×Dic61—41no—
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×C61—21no—
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—
153Q8×C61—44no—
154D4×C61—44no—
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×C61C2×D412yes—
168C2×C4×C61C2×D412yes—
169C2×C4×C61C2×D412yes—
170C22⋊D61—44no—
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—41no—
196C22×C61—41no—
197C22×C61—41no—
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#12414yescomplemented
228C4×C61—22no—
229C4×C61—22no—
230C4×C61—22no—
231C4×C61—41no—
232C4×C61—41no—
233Dic61—22no—
234Dic61—41no—
235Dic61—41no—
236Dic61—41no—
237Dic61—41no—
238Dic61—41no—
239#2472—611nomaximal, Sylow
240C2×C61—42no—
241C2×C61—81no—
242C2×C61#52511yescharacteristic
243C2×C61C2×#12411yescharacteristic
244C2×C61#53811yescharacteristic
245C2×C61D4211yescharacteristic
246C2×C61#54611yescharacteristic
247C2×C61#54611yescharacteristic
248C2×C61#55111yescharacteristic
249D61—24no—
250D61—42no—
251C2×#124D6111yescharacteristic, complemented
252C2×C22⋊Q8—611no—
253C2×#120—611no—
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
267C25—611no—
268C22×Q8C2×D6111yescharacteristic, complemented
269C22×D4—611no—
270C22×D4—611no—
271C22×D4C2×D6111yescharacteristic
272C23×C4—611no—
273C23×C4—611no—
274#124—24no—
275C22⋊Q8—1224no—
276#120—1224no—
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—1224no—
294C2×C22⋊C4C2×D6111yescharacteristic
295C2×C22⋊C4C2×D6111yescharacteristic
296C2×C22⋊C4C2×D6111yescharacteristic, complemented
297C2×C22⋊C4C2×D6111yescharacteristic, complemented
298C2×C42—611no—
299C2×C42C2×D6111yescharacteristic, complemented
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×Q8—22no—
318C2×Q8—22no—
319C2×Q8—41no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—41no—
323C2×D4—1222no—
324C2×D4—1222no—
325C2×D4—1222no—
326C2×D4—1222no—
327C2×D4—1222no—
328C2×D4—2441no—
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—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—22no—
367C42—2441no—
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—21no—
381C23—612no—
382C23—612no—
383C23—612no—
384C23—612no—
385C23—1228no—
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×C22⋊D6112yes—
403C23C23×D6111yescharacteristic
404Q8—44no—
405D4—44no—
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—21no—
419C2×C4—21no—
420C2×C4—612no—
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—2444no—
439C2×C4—2444no—
440C2×C4D4×D6112yes—
441C2×C4C2×C22⋊D6112yes—
442C2×C4C2×C22⋊D6112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
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—22no—
482C4—41no—
483C4—41no—
484C4—1222no—
485C4—2441no—
486C4—2441no—
487C4—2441no—
488C4—2441no—
489C4—2441no—
490C2—42no—
491C2—81no—
492C2—1224no—
493C2—2442no—
494C2#1684026911yescharacteristic
495C2#124×D6111yescharacteristic
496C2#1684034611yescharacteristic
497C2D4×C22⋊D6111yescharacteristic
498C2#1684040011yescharacteristic
499C2#1684040511yescharacteristic
500C2#1684044211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#124×C61C2
hypercenterC2×#124D61
hypocenterC61#2472
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519753C2semidirect
3. C2×C22⋊C4×D61C2semidirect
4. #16839690C2semidirect
5. #16839678C2semidirect
6. #16839676C2semidirect
7. #16839673C2semidirect
8. #16839662C2semidirect
9. #16839655C2semidirect
10. #16839653C2semidirect
11. #16839638C2semidirect
12. #16839638C2semidirect
13. #16839617C2semidirect
14. C4×#11758198C2semidirect
15. C2×#124×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
47. C22×Q8×C61C22semidirect
52. C2×C22⋊C4×C61C22semidirect
53. C2×C22⋊C4×C61C22semidirect
54. C2×C42×C61C22semidirect
98. C22⋊C4×C61D4semidirect
227. C2×D61#124semidirect
251. C2×#124D61semidirect
266. C61#2472semidirect
268. C22×Q8C2×D61semidirect
296. C2×C22⋊C4C2×D61semidirect
297. C2×C22⋊C4C2×D61semidirect
299. C2×C42C2×D61semidirect
365. C22⋊C4C22⋊D61semidirect