Finite Group Databasebeta

← #21452022

Subgroups — #21452022

Order 7808.

816 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519749C211yesmaximal, characteristic, complemented
2C2×#14519745C211yesmaximal, characteristic, complemented
3C2×#14519745C211yesmaximal, characteristic, complemented
4#16839697C211yesmaximal, characteristic, complemented
5#16839690C211yesmaximal, characteristic, complemented
6#16839688C211yesmaximal, characteristic, complemented
7#16839677C211yesmaximal, characteristic, complemented
8#16839676C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839642C211yesmaximal, characteristic, complemented
11#16839641C211yesmaximal, characteristic, complemented
12#16839641C211yesmaximal, characteristic, complemented
13#16839639C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic, complemented
15C2×#121×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C23×Dic61C2211yescharacteristic, complemented
22#14519749—24no—
23#14519745—24no—
24#14519745—24no—
25C2×#11758196C2211yescharacteristic, complemented
26C2×#11758196C2211yescharacteristic, complemented
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic, complemented
31C2×C22⋊Dic61C2211yescharacteristic, complemented
32C2×C22⋊Dic61C2211yescharacteristic, complemented
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47C22×D4×C61C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic, complemented
50C23×C4×C61C2211yescharacteristic, complemented
51#121×C61—24no—
52C2×C4⋊C4×C61C2211yescharacteristic, complemented
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic, complemented
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C24×C61C2311yescharacteristic
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—41no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61—41no—
65C23×D61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C2×D4×C61—22no—
68C2×D4×C61—22no—
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61D414yescomplemented
76C22×C4×C61—22no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61C2311yescharacteristic
80C22×C4×C61C2311yescharacteristic
81C22×C4×C61C2311yescharacteristic
82C22×C4×C61C2311yescharacteristic
83C2×C22⋊D61—22no—
84C2×C22⋊D61—22no—
85C2×C22⋊D61—22no—
86C2×C22⋊D61—22no—
87C2×C22⋊D61—22no—
88C2×C22⋊D61—22no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61D414yescomplemented
95C22×Dic61—22no—
96C22×Dic61—41no—
97C22×Dic61—41no—
98C22×Dic61C2311yescharacteristic
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102C22×Dic61C2311yescharacteristic
103C22×Dic61C2311yescharacteristic
104C4⋊C4×C61—22no—
105C22⋊C4×C61—22no—
106C22⋊C4×C61—22no—
107C22⋊Dic61—22no—
108C22⋊Dic61—22no—
109C22⋊Dic61—22no—
110C22⋊Dic61—41no—
111C22⋊Dic61—41no—
112C22⋊Dic61—41no—
113#11758198—22no—
114#11758198—22no—
115#11758198—22no—
116#11758198—22no—
117#11758198—22no—
118#11758198—41no—
119#11758198—41no—
120#11758198—41no—
121#11758196—22no—
122#11758196—41no—
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×C61C2×D412yes—
142C23×C61C2×D412yes—
143C23×C61C2×D412yes—
144C23×C61C2411yescharacteristic
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—44no—
158C22×D61—44no—
159C22×D61—44no—
160C22×D61—44no—
161C22×D61—44no—
162C22×D61—44no—
163C22×D61—44no—
164C22×D61C2×D412yes—
165C22×D61#4112yes—
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×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—44no—
181C2×C4×C61C2×D412yes—
182C22⋊D61—44no—
183C22⋊D61—44no—
184C22⋊D61—44no—
185C22⋊D61—44no—
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×Dic61—21no—
202C2×Dic61—21no—
203C2×Dic61—44no—
204C2×Dic61C2×D412yes—
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—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×C61C22×D411yescharacteristic
227C22×C61C22×D411yescharacteristic
228C22×C61C2×#4111yescharacteristic
229C22×C61H(5,𝔽2)11yescharacteristic
230C22×C61H(5,𝔽2)11yescharacteristic
231C22×C61H(5,𝔽2)11yescharacteristic
232C22×C61H(5,𝔽2)11yescharacteristic
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—22no—
239C2×D61—416no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—41no—
248C4×C61—22no—
249C4×C61—41no—
250C4×C61—41no—
251C4×C61—41no—
252Dic61—22no—
253Dic61—41no—
254Dic61—41no—
255Dic61—41no—
256Dic61—41no—
257Dic61—41no—
258#2668—611nomaximal, Sylow
259C2×C61—42no—
260C2×C61—42no—
261C2×C61—42no—
262C2×C61#53411yescharacteristic
263C2×C61#53411yescharacteristic
264C2×C61#53811yescharacteristic
265C2×C61D4211yescharacteristic
266C2×C61#54611yescharacteristic
267C2×C61#54611yescharacteristic
268C2×C61#56011yescharacteristic
269D61—42no—
270D61—42no—
271C2×#121—611no—
272C2×#121D6111yescharacteristic, complemented
273C2×#120—611no—
274C2×#120—611no—
275#399—611no—
276#397—611no—
277#397—611no—
278#394—611no—
279#394—611no—
280#392—611no—
281#386—611no—
282#386—611no—
283#386—611no—
284#386—611no—
285#379—611no—
286C61#266811yescharacteristic, complemented, Sylow
287C25—611no—
288C22×D4—611no—
289C22×D4—611no—
290C22×D4—611no—
291C22×D4—611no—
292C22×D4C2×D6111yescharacteristic
293C22×D4C2×D6111yescharacteristic
294C22×D4C2×D6111yescharacteristic, complemented
295C23×C4—611no—
296C23×C4C2×D6111yescharacteristic, complemented
297#121—24no—
298#121—1224no—
299#120—1224no—
300#120—1224no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4C2×D6111yescharacteristic, complemented
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⋊C4—611no—
317C2×C22⋊C4—611no—
318C2×C22⋊C4C2×D6111yescharacteristic
319C2×C22⋊C4C2×D6111yescharacteristic, complemented
320#95—611no—
321#95—611no—
322#95—611no—
323#95—611no—
324#95—611no—
325#95—611no—
326C24—611no—
327C24—611no—
328C24—1222no—
329C24—1222no—
330C24—1222no—
331C24—2441no—
332C24—2441no—
333C24—2441no—
334C24—2441no—
335C24C22×D6111yescharacteristic
336C24C22×D6111yescharacteristic
337C24C22×D6111yescharacteristic
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—614no—
347C2×D4—1222no—
348C2×D4—1222no—
349C2×D4—1222no—
350C2×D4—1222no—
351C2×D4—1222no—
352C2×D4—1222no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4C22⋊D6114yescomplemented
359C22×C4—22no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—1222no—
369C22×C4—2441no—
370C22×C4—2441no—
371C22×C4C22×D6111yescharacteristic
372C22×C4C22×D6111yescharacteristic
373C22×C4C22×D6111yescharacteristic
374C22×C4C22×D6111yescharacteristic
375C4⋊C4—22no—
376C4⋊C4—1222no—
377C4⋊C4—2441no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—1222no—
381C22⋊C4—1222no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—1222no—
385C22⋊C4—1222no—
386C22⋊C4—1222no—
387C22⋊C4—1222no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
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—612no—
413C23—612no—
414C23—1221no—
415C23—1221no—
416C23—1221no—
417C23—1221no—
418C23—1221no—
419C23—1221no—
420C23—1221no—
421C23—1221no—
422C23—1221no—
423C23—1221no—
424C23—1221no—
425C23—1221no—
426C23—2444no—
427C23—2444no—
428C23—2444no—
429C23—2444no—
430C23—2444no—
431C23—2444no—
432C23—2444no—
433C23D4×D6112yes—
434C23C2×C22⋊D6112yes—
435C23C2×C22⋊D6112yes—
436C23C23×D6111yescharacteristic
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—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—44no—
456C2×C4—612no—
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×C4—1221no—
473C2×C4—1221no—
474C2×C4—2444no—
475C2×C4C2×C22⋊D6112yes—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
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—1222no—
498C22—1222no—
499C22—1222no—
500C22—1222no—
501C22—1222no—
502C22—1222no—
503C22—24416no—
504C22—2441no—
505C22—2441no—
506C22—2441no—
507C22—2441no—
508C22—2441no—
509C22—2441no—
510C22—2441no—
511C22—2441no—
512C22C2×D4×D6111yescharacteristic
513C22C22×C22⋊D6111yescharacteristic
514C22#41×D6111yescharacteristic
515C22#1451982211yescharacteristic
516C22#1451982211yescharacteristic
517C22#1451982211yescharacteristic
518C22#1451982311yescharacteristic
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—1222no—
524C4—2441no—
525C4—2441no—
526C4—2441no—
527C4—2441no—
528C4—2441no—
529C2—42no—
530C2—42no—
531C2—42no—
532C2—2442no—
533C2—2442no—
534C2#1684032011yescharacteristic
535C2#1684032111yescharacteristic
536C2#1684034411yescharacteristic
537C2D4×C22⋊D6111yescharacteristic
538C2#1684040011yescharacteristic
539C2#1684040111yescharacteristic
540C2#1684050011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2668
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519749C2semidirect
2. C2×#14519745C2semidirect
3. C2×#14519745C2semidirect
4. #16839697C2semidirect
5. #16839690C2semidirect
6. #16839688C2semidirect
7. #16839677C2semidirect
8. #16839676C2semidirect
9. #16839670C2semidirect
10. #16839642C2semidirect
11. #16839641C2semidirect
12. #16839641C2semidirect
13. #16839639C2semidirect
14. #16839617C2semidirect
15. C2×#121×C61C2semidirect
21. C23×Dic61C22semidirect
25. C2×#11758196C22semidirect
26. C2×#11758196C22semidirect
30. C2×C22⋊Dic61C22semidirect
31. C2×C22⋊Dic61C22semidirect
32. C2×C22⋊Dic61C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
49. C22×D4×C61C22semidirect
50. C23×C4×C61C22semidirect
52. C2×C4⋊C4×C61C22semidirect
54. C2×C22⋊C4×C61C22semidirect
75. C2×D4×C61D4semidirect
94. C2×C22⋊D61D4semidirect
272. C2×#121D61semidirect
286. C61#2668semidirect
294. C22×D4C2×D61semidirect
296. C23×C4C2×D61semidirect
303. C2×C4⋊C4C2×D61semidirect
319. C2×C22⋊C4C2×D61semidirect
358. C2×D4C22⋊D61semidirect