Finite Group Databasebeta

← #21452031

Subgroups — #21452031

Order 7808.

932 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519773C211yesmaximal, characteristic, complemented
2C2×#14519751C211yesmaximal, characteristic, complemented
3C2×#14519747C211yesmaximal, characteristic, complemented
4C2×#14519745C211yesmaximal, characteristic, complemented
5C2×#14519745C211yesmaximal, characteristic, complemented
6#16839679C211yesmaximal, characteristic, complemented
7#16839678C211yesmaximal, characteristic, complemented
8#16839671C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839670C211yesmaximal, characteristic, complemented
11#16839670C211yesmaximal, characteristic, complemented
12#16839655C211yesmaximal, characteristic, complemented
13#16839652C211yesmaximal, characteristic, complemented
14#16839641C211yesmaximal, characteristic, complemented
15C2×#121×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C22×C22⋊D61C2211yescharacteristic
24C22×C22⋊D61C2211yescharacteristic, complemented
25C22×C22⋊D61C2211yescharacteristic, complemented
26#14519773—24no—
27#14519751—24no—
28#14519747—24no—
29#14519745—24no—
30#14519745—24no—
31C2×C4⋊Dic61C2211yescharacteristic, complemented
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic, complemented
35C2×C22⋊Dic61C2211yescharacteristic, complemented
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic, complemented
43C2×#11758198C2211yescharacteristic, complemented
44C2×C4×Dic61C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48#14519684C2211yescharacteristic, complemented
49C22×D4×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic, complemented
52C23×C4×C61C2211yescharacteristic, complemented
53#121×C61—24no—
54C2×C4⋊C4×C61C2211yescharacteristic, complemented
55C2×C22⋊C4×C61C2211yescharacteristic
56C2×C22⋊C4×C61C2211yescharacteristic, complemented
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C24×C61C2311yescharacteristic
60C23×D61—22no—
61C23×D61—22no—
62C23×D61—22no—
63C23×D61—41no—
64C23×D61—41no—
65C23×D61—41no—
66C23×D61—41no—
67C23×D61C2311yescharacteristic
68C23×D61C2311yescharacteristic
69C23×D61C2311yescharacteristic
70C2×D4×C61—22no—
71C2×D4×C61—22no—
72C2×D4×C61—22no—
73C2×D4×C61—22no—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—41no—
82C22×C4×C61C2311yescharacteristic
83C22×C4×C61C2311yescharacteristic
84C22×C4×C61C2311yescharacteristic
85C22×C4×C61C2311yescharacteristic
86C2×C22⋊D61—22no—
87C2×C22⋊D61—22no—
88C2×C22⋊D61—22no—
89C2×C22⋊D61—22no—
90C2×C22⋊D61—22no—
91C2×C22⋊D61—22no—
92C2×C22⋊D61—22no—
93C2×C22⋊D61—22no—
94C2×C22⋊D61—22no—
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—41no—
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C2×C22⋊D61—41no—
105C2×C22⋊D61—41no—
106C2×C22⋊D61D414yescomplemented
107C22×Dic61C2311yescharacteristic
108C22×Dic61C2311yescharacteristic
109C22×Dic61C2311yescharacteristic
110C22×Dic61C2311yescharacteristic
111C22×Dic61C2311yescharacteristic
112C2×D244—22no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—22no—
116C2×D244—41no—
117C2×D244—41no—
118C4⋊C4×C61—22no—
119C22⋊C4×C61—22no—
120C22⋊C4×C61D414yescomplemented
121C22⋊Dic61—22no—
122C22⋊Dic61—22no—
123C22⋊Dic61—41no—
124C22⋊Dic61—41no—
125#11758198—22no—
126#11758198—22no—
127#11758198—22no—
128#11758198—22no—
129#11758198—22no—
130#11758198—22no—
131#11758198—41no—
132#11758198D414yescomplemented
133C4⋊Dic61—22no—
134C4×Dic61—22no—
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—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61—21no—
154C23×C61C2×D412yes—
155C23×C61C2×D412yes—
156C23×C61C2411yescharacteristic
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61—21no—
172C22×D61—21no—
173C22×D61—21no—
174C22×D61—21no—
175C22×D61—21no—
176C22×D61—44no—
177C22×D61—44no—
178C22×D61—44no—
179C22×D61—44no—
180C22×D61—44no—
181C22×D61—44no—
182C22×D61—44no—
183C22×D61C2×D412yes—
184C22×D61C2×D412yes—
185D4×C61—44no—
186D4×C61—44no—
187D4×C61—44no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—44no—
198C2×C4×C61C2×D412yes—
199C2×C4×C61C2×D412yes—
200C2×C4×C61C2×D412yes—
201C22⋊D61—44no—
202C22⋊D61—44no—
203C22⋊D61—44no—
204C22⋊D61—44no—
205C22⋊D61—44no—
206C22⋊D61—44no—
207C22⋊D61—44no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61—21no—
215C2×Dic61—21no—
216C2×Dic61—21no—
217C2×Dic61—21no—
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61C2×D412yes—
222C2×Dic61C2×D412yes—
223D244—44no—
224D244—44no—
225C22×C61—22no—
226C22×C61—22no—
227C22×C61—22no—
228C22×C61—22no—
229C22×C61—22no—
230C22×C61—22no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61—41no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61—41no—
240C22×C61—41no—
241C22×C61—41no—
242C22×C61—41no—
243C22×C61—41no—
244C22×C61—41no—
245C22×C61—41no—
246C22×C61C22×D411yescharacteristic
247C22×C61C22×D411yescharacteristic
248C22×C61C22×D411yescharacteristic
249C22×C61H(5,𝔽2)11yescharacteristic
250C22×C61H(5,𝔽2)11yescharacteristic
251C22×C61H(5,𝔽2)11yescharacteristic
252C22×C61H(5,𝔽2)11yescharacteristic
253C2×D61—22no—
254C2×D61—22no—
255C2×D61—22no—
256C2×D61—22no—
257C2×D61—22no—
258C2×D61—22no—
259C2×D61—416no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—41no—
263C2×D61—41no—
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C4×C61—22no—
276C4×C61—22no—
277C4×C61—22no—
278C4×C61—41no—
279Dic61—22no—
280Dic61—22no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284#2669—611nomaximal, Sylow
285C2×C61—42no—
286C2×C61—42no—
287C2×C61—81no—
288C2×C61#53411yescharacteristic
289C2×C61#53511yescharacteristic
290C2×C61#53511yescharacteristic
291C2×C61D4211yescharacteristic
292C2×C61D4211yescharacteristic
293C2×C61D4211yescharacteristic
294C2×C61#56011yescharacteristic
295D61—42no—
296D61—42no—
297D61—81no—
298C2×#127—611no—
299C2×#121—611no—
300C2×#121D6111yescharacteristic, complemented
301C2×#120—611no—
302C2×#120—611no—
303C2×#120—611no—
304#394—611no—
305#394—611no—
306#392—611no—
307#392—611no—
308#392—611no—
309#392—611no—
310#388—611no—
311#388—611no—
312#386—611no—
313C61#266911yescharacteristic, complemented, Sylow
314C25—611no—
315C22×D4—611no—
316C22×D4—611no—
317C22×D4—611no—
318C22×D4—611no—
319C22×D4—611no—
320C22×D4—611no—
321C22×D4—611no—
322C22×D4—611no—
323C22×D4—611no—
324C22×D4C2×D6111yescharacteristic
325C22×D4C2×D6111yescharacteristic
326C22×D4C2×D6111yescharacteristic, complemented
327C23×C4C2×D6111yescharacteristic, complemented
328#127—1224no—
329#121—24no—
330#121—1224no—
331#120—1224no—
332#120—1224no—
333#120—1224no—
334C2×C4⋊C4—611no—
335C2×C4⋊C4C2×D6111yescharacteristic, complemented
336C2×C22⋊C4—611no—
337C2×C22⋊C4—611no—
338C2×C22⋊C4—611no—
339C2×C22⋊C4—611no—
340C2×C22⋊C4—611no—
341C2×C22⋊C4—611no—
342C2×C22⋊C4—611no—
343C2×C22⋊C4—611no—
344C2×C22⋊C4—611no—
345C2×C22⋊C4—611no—
346C2×C22⋊C4—611no—
347C2×C22⋊C4—611no—
348C2×C22⋊C4C2×D6111yescharacteristic
349C2×C22⋊C4C2×D6111yescharacteristic, complemented
350C2×C42—611no—
351#95—611no—
352#95—611no—
353#95—611no—
354#95—611no—
355C24—611no—
356C24—611no—
357C24—611no—
358C24—1222no—
359C24—1222no—
360C24—1222no—
361C24—2441no—
362C24—2441no—
363C24—2441no—
364C24—2441no—
365C24C22×D6111yescharacteristic
366C24C22×D6111yescharacteristic
367C24C22×D6111yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—614no—
378C2×D4—1222no—
379C2×D4—1222no—
380C2×D4—1222no—
381C2×D4—1222no—
382C2×D4—1222no—
383C2×D4—1222no—
384C2×D4—1222no—
385C2×D4—1222no—
386C2×D4—1222no—
387C2×D4—1222no—
388C2×D4—1222no—
389C2×D4—1222no—
390C2×D4—1222no—
391C2×D4—2441no—
392C2×D4—2441no—
393C2×D4—2441no—
394C2×D4—2441no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2441no—
398C2×D4—2441no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4—2441no—
402C2×D4—2441no—
403C2×D4—2441no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—41no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4C22×D6111yescharacteristic
413C22×C4C22×D6111yescharacteristic
414C22×C4C22×D6111yescharacteristic
415C22×C4C22×D6111yescharacteristic
416C4⋊C4—22no—
417C4⋊C4—1222no—
418C22⋊C4—22no—
419C22⋊C4—614no—
420C22⋊C4—1222no—
421C22⋊C4—1222no—
422C22⋊C4—1222no—
423C22⋊C4—1222no—
424C22⋊C4—1222no—
425C22⋊C4—1222no—
426C22⋊C4—1222no—
427C22⋊C4—1222no—
428C22⋊C4—2441no—
429C22⋊C4—2441no—
430C22⋊C4—2441no—
431C22⋊C4C22⋊D6114yescomplemented
432C42—1222no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—612no—
453C23—612no—
454C23—1221no—
455C23—1221no—
456C23—1221no—
457C23—1221no—
458C23—1221no—
459C23—1221no—
460C23—1221no—
461C23—1221no—
462C23—1221no—
463C23—1221no—
464C23—1221no—
465C23—1221no—
466C23—1221no—
467C23—1221no—
468C23—1221no—
469C23—1221no—
470C23—1221no—
471C23—1221no—
472C23—1221no—
473C23—2444no—
474C23—2444no—
475C23—2444no—
476C23—2444no—
477C23—2444no—
478C23—2444no—
479C23—2444no—
480C23D4×D6112yes—
481C23C2×C22⋊D6112yes—
482C23C23×D6111yescharacteristic
483D4—44no—
484D4—44no—
485D4—44no—
486D4—2444no—
487D4—2444no—
488D4—2444no—
489D4—2444no—
490D4—2444no—
491D4—2444no—
492D4—2444no—
493D4—2444no—
494D4—2444no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—44no—
505C2×C4—612no—
506C2×C4—612no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4D4×D6112yes—
521C2×C4C2×C22⋊D6112yes—
522C2×C4C2×C22⋊D6112yes—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—1222no—
545C22—1222no—
546C22—1222no—
547C22—1222no—
548C22—1222no—
549C22—1222no—
550C22—24416no—
551C22—2441no—
552C22—2441no—
553C22—2441no—
554C22—2441no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22—2441no—
561C22—2441no—
562C22—2441no—
563C22—2441no—
564C22—2441no—
565C22—2441no—
566C22C2×D4×D6111yescharacteristic
567C22C2×D4×D6111yescharacteristic
568C22C22×C22⋊D6111yescharacteristic
569C22#1451982211yescharacteristic
570C22#1451982211yescharacteristic
571C22#1451982311yescharacteristic
572C22#1451982311yescharacteristic
573C4—22no—
574C4—22no—
575C4—22no—
576C4—41no—
577C4—1222no—
578C4—1222no—
579C4—2441no—
580C4—2441no—
581C4—2441no—
582C2—42no—
583C2—42no—
584C2—81no—
585C2—4881no—
586C2—2442no—
587C2—2442no—
588C2#1684032011yescharacteristic
589C2#1684032611yescharacteristic
590C2#1684032811yescharacteristic
591C2D4×C22⋊D6111yescharacteristic
592C2D4×C22⋊D6111yescharacteristic
593C2#1684039611yescharacteristic
594C2#1684050011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2669
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519773C2semidirect
2. C2×#14519751C2semidirect
3. C2×#14519747C2semidirect
4. C2×#14519745C2semidirect
5. C2×#14519745C2semidirect
6. #16839679C2semidirect
7. #16839678C2semidirect
8. #16839671C2semidirect
9. #16839670C2semidirect
10. #16839670C2semidirect
11. #16839670C2semidirect
12. #16839655C2semidirect
13. #16839652C2semidirect
14. #16839641C2semidirect
15. C2×#121×C61C2semidirect
24. C22×C22⋊D61C22semidirect
25. C22×C22⋊D61C22semidirect
31. C2×C4⋊Dic61C22semidirect
34. C2×C22⋊Dic61C22semidirect
35. C2×C22⋊Dic61C22semidirect
42. C2×#11758198C22semidirect
43. C2×#11758198C22semidirect
44. C2×C4×Dic61C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. #14519684C22semidirect
51. C22×D4×C61C22semidirect
52. C23×C4×C61C22semidirect
54. C2×C4⋊C4×C61C22semidirect
56. C2×C22⋊C4×C61C22semidirect
106. C2×C22⋊D61D4semidirect
120. C22⋊C4×C61D4semidirect
132. #11758198D4semidirect
300. C2×#121D61semidirect
313. C61#2669semidirect
326. C22×D4C2×D61semidirect
327. C23×C4C2×D61semidirect
335. C2×C4⋊C4C2×D61semidirect
349. C2×C22⋊C4C2×D61semidirect
431. C22⋊C4C22⋊D61semidirect