Finite Group Databasebeta

← #21452033

Subgroups — #21452033

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×#14519750C211yesmaximal, characteristic, complemented
3C2×#14519748C211yesmaximal, characteristic, complemented
4C2×#14519746C211yesmaximal, characteristic, complemented
5C2×#14519746C211yesmaximal, characteristic, complemented
6#16839678C211yesmaximal, characteristic, complemented
7#16839676C211yesmaximal, characteristic, complemented
8#16839671C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839670C211yesmaximal, characteristic, complemented
11#16839670C211yesmaximal, characteristic, complemented
12#16839656C211yesmaximal, characteristic, complemented
13#16839655C211yesmaximal, characteristic, complemented
14#16839638C211yesmaximal, characteristic, complemented
15C2×#120×C61C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic, complemented
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C22×C22⋊D61C2211yescharacteristic, complemented
24C22×C22⋊D61C2211yescharacteristic, complemented
25C22×C4×D61C2211yescharacteristic, complemented
26#14519773—24no—
27#14519750—24no—
28#14519748—24no—
29#14519746—24no—
30#14519746—24no—
31C2×C4⋊Dic61C2211yescharacteristic, complemented
32C2×#11758196C2211yescharacteristic, complemented
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic
38C2×C22⋊Dic61C2211yescharacteristic
39C2×C22⋊Dic61C2211yescharacteristic, complemented
40C2×C22⋊Dic61C2211yescharacteristic, complemented
41C2×#11758198C2211yescharacteristic, complemented
42C2×#11758198C2211yescharacteristic, complemented
43C2×#11758198C2211yescharacteristic, complemented
44C2×C4×Dic61C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48#14519684C2211yescharacteristic, complemented
49C25×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52C22×D4×C61C2211yescharacteristic
53#120×C61—24no—
54C2×C22⋊C4×C61C2211yescharacteristic
55C2×C22⋊C4×C61C2211yescharacteristic
56C2×C22⋊C4×C61C2211yescharacteristic
57C24×C61—22no—
58C24×C61—22no—
59C24×C61—22no—
60C24×C61—41no—
61C24×C61—41no—
62C24×C61—41no—
63C24×C61—41no—
64C24×C61C2311yescharacteristic
65C24×C61C2311yescharacteristic
66C24×C61C2311yescharacteristic
67C24×C61C2311yescharacteristic
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—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C22×C4×C61C2311yescharacteristic
80C22×C4×C61C2311yescharacteristic
81C22×C4×C61C2311yescharacteristic
82C2×C22⋊D61—22no—
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—22no—
90C2×C22⋊D61—22no—
91C2×C22⋊D61—22no—
92C2×C22⋊D61—22no—
93C2×C22⋊D61—22no—
94C2×C22⋊D61—41no—
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⋊D61D414yescomplemented
106C22×Dic61C2311yescharacteristic
107C22×Dic61C2311yescharacteristic
108C22×Dic61C2311yescharacteristic
109C22×Dic61C2311yescharacteristic
110C22×Dic61C2311yescharacteristic
111C22×Dic61C2311yescharacteristic
112C2×D244—22no—
113C2×D244—22no—
114C2×D244—41no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—41no—
118C22⋊C4×C61—22no—
119C22⋊C4×C61—22no—
120C22⋊C4×C61D414yescomplemented
121C22⋊Dic61—22no—
122C22⋊Dic61—22no—
123C22⋊Dic61—22no—
124C22⋊Dic61—22no—
125C22⋊Dic61—22no—
126C22⋊Dic61—22no—
127C22⋊Dic61—41no—
128C22⋊Dic61D414yescomplemented
129#11758198—22no—
130#11758198—41no—
131#11758198—41no—
132C4⋊Dic61—22no—
133#11758196—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×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—44no—
161C23×C61—44no—
162C23×C61—44no—
163C23×C61—44no—
164C23×C61—44no—
165C23×C61—44no—
166C23×C61—44no—
167C23×C61C2×D412yes—
168C23×C61C2×D412yes—
169C23×C61C2×D412yes—
170C23×C61C2411yescharacteristic
171C22×D61—21no—
172C22×D61—21no—
173C22×D61—21no—
174C22×D61—21no—
175C22×D61—21no—
176C22×D61—21no—
177C22×D61—21no—
178C22×D61—21no—
179C22×D61—21no—
180C22×D61—21no—
181C22×D61—21no—
182C22×D61—21no—
183C22×D61—21no—
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×C61C2×D412yes—
196C2×C4×C61C2×D412yes—
197C22⋊D61—44no—
198C22⋊D61—44no—
199C22⋊D61—44no—
200C22⋊D61—44no—
201C22⋊D61—44no—
202C22⋊D61—44no—
203C22⋊D61—44no—
204C22⋊D61—44no—
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—21no—
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×Dic61C2×D412yes—
221C2×Dic61C2×D412yes—
222C2×Dic61C2×D412yes—
223D244—44no—
224C4×D61—44no—
225C22×C61—22no—
226C22×C61—22no—
227C22×C61—22no—
228C22×C61—22no—
229C22×C61—22no—
230C22×C61—22no—
231C22×C61—22no—
232C22×C61—22no—
233C22×C61—22no—
234C22×C61—416no—
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×C61—41no—
247C22×C61—41no—
248C22×C61—41no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61—41no—
254C22×C61C22×D411yescharacteristic
255C22×C61C22×D411yescharacteristic
256C22×C61C22×D411yescharacteristic
257C22×C61H(5,𝔽2)11yescharacteristic
258C22×C61H(5,𝔽2)11yescharacteristic
259C22×C61H(5,𝔽2)11yescharacteristic
260C22×C61H(5,𝔽2)11yescharacteristic
261C2×D61—22no—
262C2×D61—22no—
263C2×D61—22no—
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—41no—
278Dic61—22no—
279Dic61—22no—
280Dic61—22no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284#2669—611nomaximal, Sylow
285C2×C61—42no—
286C2×C61—42no—
287C2×C61—42no—
288C2×C61—81no—
289C2×C61#53411yescharacteristic
290C2×C61#53511yescharacteristic
291C2×C61#53511yescharacteristic
292C2×C61D4211yescharacteristic
293C2×C61D4211yescharacteristic
294C2×C61D4211yescharacteristic
295C2×C61#56011yescharacteristic
296D61—42no—
297D61—81no—
298C2×#127—611no—
299C2×#121—611no—
300C2×#121—611no—
301C2×#120—611no—
302C2×#120—611no—
303C2×#120D6111yescharacteristic, complemented
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
314C25C2×D6111yescharacteristic
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
327C23×C4—611no—
328#127—1224no—
329#121—1224no—
330#121—1224no—
331#120—24no—
332#120—1224no—
333#120—1224no—
334C2×C4⋊C4—611no—
335C2×C4⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
348C2×C22⋊C4C2×D6111yescharacteristic
349C2×C22⋊C4C2×D6111yescharacteristic
350C2×C42—611no—
351#95—611no—
352#95—611no—
353#95—611no—
354#95—611no—
355C24—22no—
356C24—22no—
357C24—22no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—611no—
363C24—611no—
364C24C22×D6111yescharacteristic
365C24C22×D6111yescharacteristic
366C24C22×D6111yescharacteristic
367C24C22×D6111yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—41no—
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—1222no—
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—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—2441no—
413C22×C4C22×D6111yescharacteristic
414C22×C4C22×D6111yescharacteristic
415C22×C4C22×D6111yescharacteristic
416C4⋊C4—1222no—
417C4⋊C4—1222no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—614no—
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—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—44no—
459C23—44no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—44no—
465C23—612no—
466C23—1221no—
467C23—1221no—
468C23—1221no—
469C23—1221no—
470C23—1221no—
471C23—1221no—
472C23—1221no—
473C23—1221no—
474C23—1221no—
475C23—1221no—
476C23—1221no—
477C23—1221no—
478C23—1221no—
479C23D4×D6112yes—
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—612no—
503C2×C4—612no—
504C2×C4—612no—
505C2×C4—1221no—
506C2×C4—1221no—
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×C4—2444no—
521C2×C4C2×C22⋊D6112yes—
522C2×C4C2×C22⋊D6112yes—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—416no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—1222no—
553C22—1222no—
554C22—1222no—
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#1451982211yescharacteristic
572C22#1451982211yescharacteristic
573C4—22no—
574C4—22no—
575C4—41no—
576C4—1222no—
577C4—1222no—
578C4—1222no—
579C4—2441no—
580C4—2441no—
581C4—2441no—
582C2—42no—
583C2—42no—
584C2—42no—
585C2—81no—
586C2—4881no—
587C2—2442no—
588C2#1684032211yescharacteristic
589C2#1684032711yescharacteristic
590C2#1684032911yescharacteristic
591C2#1684039411yescharacteristic
592C2D4×C22⋊D6111yescharacteristic
593C2D4×C22⋊D6111yescharacteristic
594C2#1684050111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#120×C61C2
hypercenterC2×#120D61
hypocenterC61#2669
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14519773C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519748C2semidirect
4. C2×#14519746C2semidirect
5. C2×#14519746C2semidirect
6. #16839678C2semidirect
7. #16839676C2semidirect
8. #16839671C2semidirect
9. #16839670C2semidirect
10. #16839670C2semidirect
11. #16839670C2semidirect
12. #16839656C2semidirect
13. #16839655C2semidirect
14. #16839638C2semidirect
15. C2×#120×C61C2semidirect
16. C22×D244C22semidirect
23. C22×C22⋊D61C22semidirect
24. C22×C22⋊D61C22semidirect
25. C22×C4×D61C22semidirect
31. C2×C4⋊Dic61C22semidirect
32. C2×#11758196C22semidirect
39. C2×C22⋊Dic61C22semidirect
40. C2×C22⋊Dic61C22semidirect
41. C2×#11758198C22semidirect
42. C2×#11758198C22semidirect
43. C2×#11758198C22semidirect
44. C2×C4×Dic61C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. #14519684C22semidirect
105. C2×C22⋊D61D4semidirect
120. C22⋊C4×C61D4semidirect
128. C22⋊Dic61D4semidirect
303. C2×#120D61semidirect
313. C61#2669semidirect
431. C22⋊C4C22⋊D61semidirect