Finite Group Databasebeta

← #21452041

Subgroups — #21452041

Order 7808.

796 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519764C211yesmaximal, characteristic, complemented
2C2×#14519763C211yesmaximal, characteristic, complemented
3C2×#14519746C211yesmaximal, characteristic, complemented
4#16839678C211yesmaximal, characteristic, complemented
5#16839676C211yesmaximal, characteristic, complemented
6#16839674C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839670C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839665C211yesmaximal, characteristic, complemented
11#16839662C211yesmaximal, characteristic, complemented
12#16839655C211yesmaximal, characteristic, complemented
13#16839650C211yesmaximal, characteristic, complemented
14#16839618C211yesmaximal, characteristic, complemented
15C2×#120×C61C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic, complemented
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic, complemented
21#14519764—24no—
22#14519763—24no—
23#14519746—24no—
24C2×C4⋊Dic61C2211yescharacteristic, 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×C22⋊Dic61C2211yescharacteristic, complemented
36C2×C22⋊Dic61C2211yescharacteristic, complemented
37C2×C22⋊Dic61C2211yescharacteristic, complemented
38C2×#11758198C2211yescharacteristic, complemented
39C2×#11758198C2211yescharacteristic, complemented
40C2×#11758198C2211yescharacteristic, complemented
41C2×C4×Dic61C2211yescharacteristic, complemented
42C2×C4×Dic61C2211yescharacteristic, 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—41no—
59C24×C61—41no—
60C24×C61—41no—
61C24×C61—41no—
62C24×C61C2311yescharacteristic
63C24×C61C2311yescharacteristic
64C24×C61C2311yescharacteristic
65C24×C61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C2×D4×C61—22no—
68C2×D4×C61—22no—
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×C61—22no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C22×C4×C61C2311yescharacteristic
77C22×C4×C61C2311yescharacteristic
78C22×C4×C61C2311yescharacteristic
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—22no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—22no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C22×Dic61C2311yescharacteristic
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C22×Dic61C2311yescharacteristic
95C22×Dic61C2311yescharacteristic
96C22×Dic61C2311yescharacteristic
97C22×Dic61C2311yescharacteristic
98C2×Dic122—22no—
99C2×Dic122—22no—
100C2×Dic122—41no—
101C22⋊C4×C61—22no—
102C22⋊C4×C61—22no—
103C22⋊C4×C61D414yescomplemented
104C22⋊Dic61—22no—
105C22⋊Dic61—22no—
106C22⋊Dic61—22no—
107C22⋊Dic61—22no—
108C22⋊Dic61—22no—
109C22⋊Dic61—22no—
110C22⋊Dic61—41no—
111C22⋊Dic61—41no—
112C22⋊Dic61—41no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115C22⋊Dic61D414yescomplemented
116#11758198—22no—
117#11758198—22no—
118#11758198—41no—
119C4⋊Dic61—41no—
120#11758196—41no—
121C4×Dic61—22no—
122C4×Dic61—22no—
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—21no—
142C23×C61—21no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—44no—
149C23×C61—44no—
150C23×C61—44no—
151C23×C61—44no—
152C23×C61—44no—
153C23×C61—44no—
154C23×C61—44no—
155C23×C61C2×D412yes—
156C23×C61C2×D412yes—
157C23×C61#4112yes—
158C23×C61C2411yescharacteristic
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—21no—
166D4×C61—44no—
167D4×C61—44no—
168D4×C61—44no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61C2×D412yes—
177C2×C4×C61C2×D412yes—
178C22⋊D61—44no—
179C22⋊D61—44no—
180C22⋊D61—44no—
181C22⋊D61—44no—
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—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61C2×D412yes—
202C2×Dic61C2×D412yes—
203Dic122—44no—
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—416no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—41no—
222C22×C61—41no—
223C22×C61—41no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61—41no—
227C22×C61—41no—
228C22×C61—41no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61C22×D411yescharacteristic
234C22×C61C22×D411yescharacteristic
235C22×C61C2×#4111yescharacteristic
236C22×C61H(5,𝔽2)11yescharacteristic
237C22×C61H(5,𝔽2)11yescharacteristic
238C22×C61H(5,𝔽2)11yescharacteristic
239C22×C61H(5,𝔽2)11yescharacteristic
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C4×C61—22no—
248C4×C61—22no—
249C4×C61—41no—
250Dic61—22no—
251Dic61—22no—
252Dic61—41no—
253Dic61—41no—
254Dic61—41no—
255Dic61—41no—
256Dic61—41no—
257#2670—611nomaximal, Sylow
258C2×C61—42no—
259C2×C61—42no—
260C2×C61—42no—
261C2×C61—81no—
262C2×C61#53511yescharacteristic
263C2×C61#53511yescharacteristic
264C2×C61#53811yescharacteristic
265C2×C61D4211yescharacteristic
266C2×C61#54611yescharacteristic
267C2×C61#54611yescharacteristic
268C2×C61H(3,𝔽4)11yescharacteristic
269D61—81no—
270C2×#124—611no—
271C2×#124—611no—
272C2×#120—611no—
273C2×#120D6111yescharacteristic, complemented
274#394—611no—
275#394—611no—
276#393—611no—
277#392—611no—
278#392—611no—
279#392—611no—
280#390—611no—
281#390—611no—
282#388—611no—
283#388—611no—
284#379—611no—
285C61#267011yescharacteristic, complemented, Sylow
286C25C2×D6111yescharacteristic
287C22×Q8—611no—
288C22×D4—611no—
289C22×D4—611no—
290C22×D4—611no—
291C22×D4—611no—
292C22×D4C2×D6111yescharacteristic
293C22×D4C2×D6111yescharacteristic
294C22×D4C2×D6111yescharacteristic
295#124—1224no—
296#124—1224no—
297#120—24no—
298#120—1224no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4—611no—
303C2×C22⋊C4—611no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—611no—
307C2×C22⋊C4—611no—
308C2×C22⋊C4—611no—
309C2×C22⋊C4—611no—
310C2×C22⋊C4—611no—
311C2×C22⋊C4—611no—
312C2×C22⋊C4—611no—
313C2×C22⋊C4—611no—
314C2×C22⋊C4—611no—
315C2×C22⋊C4—611no—
316C2×C22⋊C4C2×D6111yescharacteristic
317C2×C22⋊C4C2×D6111yescharacteristic
318C2×C22⋊C4C2×D6111yescharacteristic
319C2×C42—611no—
320C2×C42—611no—
321#95—611no—
322#95—611no—
323#95—611no—
324#95—611no—
325C24—22no—
326C24—22no—
327C24—22no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—41no—
332C24—611no—
333C24C22×D6111yescharacteristic
334C24C22×D6111yescharacteristic
335C24C22×D6111yescharacteristic
336C24C22×D6111yescharacteristic
337C2×Q8—1222no—
338C2×Q8—1222no—
339C2×Q8—2441no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—1222no—
350C2×D4—1222no—
351C2×D4—1222no—
352C2×D4—1222no—
353C2×D4—1222no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4—2441no—
359C2×D4—2441no—
360C2×D4—2441no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4C22×D6111yescharacteristic
369C22×C4C22×D6111yescharacteristic
370C22×C4C22×D6111yescharacteristic
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—614no—
376C22⋊C4—1222no—
377C22⋊C4—1222no—
378C22⋊C4—1222no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C22⋊C4—1222no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4C22⋊D6114yescomplemented
391C42—1222no—
392C42—1222no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—44no—
419C23—44no—
420C23—44no—
421C23—44no—
422C23—44no—
423C23—44no—
424C23—44no—
425C23—1221no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23—1221no—
430C23—1221no—
431C23—1221no—
432C23D4×D6112yes—
433C23#1175822412yes—
434C23C2×C22⋊D6112yes—
435C23C23×D6111yescharacteristic
436Q8—2444no—
437D4—44no—
438D4—44no—
439D4—44no—
440D4—2444no—
441D4—2444no—
442D4—2444no—
443D4—2444no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—612no—
452C2×C4—612no—
453C2×C4—1221no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—1221no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—1221no—
461C2×C4—1221no—
462C2×C4—1221no—
463C2×C4—1221no—
464C2×C4—1221no—
465C2×C4—1221no—
466C2×C4—1221no—
467C2×C4—1221no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4C2×C22⋊D6112yes—
473C2×C4C2×C22⋊D6112yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—416no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—2441no—
504C22—2441no—
505C22—2441no—
506C22—2441no—
507C22—2441no—
508C22—2441no—
509C22—2441no—
510C22C2×D4×D6111yescharacteristic
511C22C22×C22⋊D6111yescharacteristic
512C22C2×#1175822411yescharacteristic
513C22#1451982211yescharacteristic
514C22#1451982211yescharacteristic
515C22#1451982211yescharacteristic
516C22#1451982211yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—1222no—
521C4—1222no—
522C4—2441no—
523C4—2441no—
524C4—2441no—
525C4—2441no—
526C4—2441no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—4881no—
532C2#1684032711yescharacteristic
533C2#1684032911yescharacteristic
534C2#1684034711yescharacteristic
535C2D4×C22⋊D6111yescharacteristic
536C2#1684039911yescharacteristic
537C2#1684040611yescharacteristic
538C2#1684050511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#120×C61C2
hypercenterC2×#120D61
hypocenterC61#2670
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×#14519763C2semidirect
3. C2×#14519746C2semidirect
4. #16839678C2semidirect
5. #16839676C2semidirect
6. #16839674C2semidirect
7. #16839670C2semidirect
8. #16839670C2semidirect
9. #16839670C2semidirect
10. #16839665C2semidirect
11. #16839662C2semidirect
12. #16839655C2semidirect
13. #16839650C2semidirect
14. #16839618C2semidirect
15. C2×#120×C61C2semidirect
16. C22×Dic122C22semidirect
20. C22×C22⋊D61C22semidirect
24. C2×C4⋊Dic61C22semidirect
25. C2×#11758196C22semidirect
35. C2×C22⋊Dic61C22semidirect
36. C2×C22⋊Dic61C22semidirect
37. C2×C22⋊Dic61C22semidirect
38. C2×#11758198C22semidirect
39. C2×#11758198C22semidirect
40. C2×#11758198C22semidirect
41. C2×C4×Dic61C22semidirect
42. C2×C4×Dic61C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
103. C22⋊C4×C61D4semidirect
115. C22⋊Dic61D4semidirect
273. C2×#120D61semidirect
285. C61#2670semidirect
390. C22⋊C4C22⋊D61semidirect