Finite Group Databasebeta

← #21449186

Subgroups — #21449186

Order 7808.

1246 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D61C211yesmaximal, characteristic, complemented
2C2×#14519750C211yesmaximal, characteristic, complemented
3C2×#14519748C211yesmaximal, characteristic, complemented
4C2×#14519745C211yesmaximal, characteristic, complemented
5C2×#14519745C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
7#16839678C211yesmaximal, characteristic, complemented
8#16839676C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839640C211yesmaximal, characteristic, complemented
11#16839638C211yesmaximal, characteristic, complemented
12#16839638C211yesmaximal, characteristic, complemented
13#16839636C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic, complemented
15C61×#392C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C24×D61C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic, complemented
23C22×C22⋊D61C2211yescharacteristic, complemented
24C2×D4×D61—24no—
25C2×D4×D61—24no—
26C2×D4×D61—24no—
27C22×C4×D61C2211yescharacteristic
28C22×C4×D61C2211yescharacteristic, complemented
29C22×C4×D61C2211yescharacteristic, complemented
30#14519750—24no—
31#14519748—24no—
32#14519745—24no—
33#14519745—24no—
34C2×C4⋊Dic61C2211yescharacteristic, complemented
35C2×#11758196C2211yescharacteristic, complemented
36C2×C22⋊Dic61C2211yescharacteristic, complemented
37C2×C22⋊Dic61C2211yescharacteristic, complemented
38C2×C22⋊Dic61C2211yescharacteristic, complemented
39C2×C22⋊Dic61C2211yescharacteristic, complemented
40C2×C22⋊Dic61C2211yescharacteristic, complemented
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic
44C2×#11758198C2211yescharacteristic, complemented
45C2×#11758198C2211yescharacteristic, complemented
46C2×#11758198C2211yescharacteristic, complemented
47C2×#11758198C2211yescharacteristic, complemented
48C22⋊C4×D61—24no—
49#14519684C2211yescharacteristic, complemented
50#14519684C2211yescharacteristic, complemented
51#14519684C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C22×D4×C61C2211yescharacteristic, complemented
54C22×D4×C61C2211yescharacteristic, complemented
55C2×C22⋊C4×C61C2211yescharacteristic, complemented
56C2×C22⋊C4×C61C2211yescharacteristic, complemented
57C2×C22⋊C4×C61C2211yescharacteristic, complemented
58#95×C61C2211yescharacteristic, complemented
59C24×C61C2311yescharacteristic
60C24×C61C2311yescharacteristic
61C24×C61C2311yescharacteristic
62C23×D61—22no—
63C23×D61—22no—
64C23×D61—22no—
65C23×D61—22no—
66C23×D61—22no—
67C23×D61—22no—
68C23×D61—22no—
69C23×D61—22no—
70C23×D61—22no—
71C23×D61—41no—
72C23×D61—41no—
73C23×D61—41no—
74C23×D61—41no—
75C23×D61D414yescomplemented
76C23×D61C2311yescharacteristic
77C23×D61C2311yescharacteristic
78C23×D61C2311yescharacteristic
79C2×D4×C61—22no—
80C2×D4×C61—22no—
81C2×D4×C61—22no—
82C2×D4×C61—22no—
83C2×D4×C61—22no—
84C2×D4×C61—22no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C22×C4×C61C2311yescharacteristic
89C22×C4×C61C2311yescharacteristic
90C22×C4×C61C2311yescharacteristic
91C22×C4×C61C2311yescharacteristic
92C2×C22⋊D61—22no—
93C2×C22⋊D61—22no—
94C2×C22⋊D61—22no—
95C2×C22⋊D61—22no—
96C2×C22⋊D61—22no—
97C2×C22⋊D61—22no—
98C2×C22⋊D61—22no—
99C2×C22⋊D61—22no—
100C2×C22⋊D61—22no—
101C2×C22⋊D61—22no—
102C2×C22⋊D61—22no—
103C2×C22⋊D61—22no—
104C2×C22⋊D61—22no—
105C2×C22⋊D61—41no—
106C2×C22⋊D61D414yescomplemented
107C22×Dic61C2311yescharacteristic
108C22×Dic61C2311yescharacteristic
109C22×Dic61C2311yescharacteristic
110C22×Dic61C2311yescharacteristic
111C22×Dic61C2311yescharacteristic
112D4×D61—232no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244D414yescomplemented
116C2×C4×D61—22no—
117C2×C4×D61—22no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C22⋊C4×C61—22no—
126C22⋊C4×C61—22no—
127C22⋊C4×C61—41no—
128C22⋊Dic61—22no—
129C22⋊Dic61—22no—
130C22⋊Dic61—22no—
131C22⋊Dic61—22no—
132C22⋊Dic61—22no—
133#11758198—22no—
134#11758198—22no—
135#11758198—22no—
136#11758198—22no—
137#11758198—22no—
138#11758198—41no—
139#11758198D414yescomplemented
140C4⋊Dic61—22no—
141#11758196—22no—
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—21no—
161C23×C61C2×D412yes—
162C23×C61C2×D412yes—
163C23×C61C2411yescharacteristic
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—28no—
173C22×D61—21no—
174C22×D61—21no—
175C22×D61—21no—
176C22×D61—21no—
177C22×D61—21no—
178C22×D61—21no—
179C22×D61—28no—
180C22×D61—28no—
181C22×D61—44no—
182C22×D61—44no—
183C22×D61—44no—
184C22×D61—44no—
185C22×D61—44no—
186C22×D61—44no—
187C22×D61—44no—
188C22×D61—44no—
189C22×D61—44no—
190C22×D61—44no—
191C22×D61—44no—
192C22×D61C2×D412yes—
193C22×D61C2×D412yes—
194C22×D61C2×D412yes—
195C22×D61C2×D412yes—
196C22×D61C2×D412yes—
197C22×D61C2×D412yes—
198C22×D61#4112yes—
199D4×C61—28no—
200D4×C61—44no—
201D4×C61—44no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61C2×D412yes—
213C2×C4×C61C2×D412yescomplemented
214C22⋊D61—28no—
215C22⋊D61—28no—
216C22⋊D61—44no—
217C22⋊D61—44no—
218C22⋊D61—44no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61C2×D412yes—
233C2×Dic61C2×D412yescomplemented
234D244—28no—
235C4×D61—28no—
236C4×D61—44no—
237C4×D61—44no—
238C22×C61—22no—
239C22×C61—22no—
240C22×C61—22no—
241C22×C61—22no—
242C22×C61—22no—
243C22×C61—22no—
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×C61—41no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61C22×D411yescharacteristic
260C22×C61C22×D411yescharacteristic
261C22×C61C22×D411yescharacteristic
262C22×C61C22×D411yescharacteristic
263C22×C61C2×#4111yescharacteristic
264C22×C61H(5,𝔽2)11yescharacteristic
265C22×C61H(5,𝔽2)11yescharacteristic
266C2×D61—22no—
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—22no—
270C2×D61—22no—
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—22no—
274C2×D61—22no—
275C2×D61—22no—
276C2×D61—22no—
277C2×D61—22no—
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—22no—
281C2×D61—416no—
282C2×D61—416no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61#12014yescomplemented
288C2×D61#12114yescomplemented
289C4×C61—22no—
290C4×C61—22no—
291C4×C61—41no—
292C4×C61—41no—
293Dic61—22no—
294Dic61—22no—
295Dic61—41no—
296Dic61—41no—
297Dic61—41no—
298#2410—611nomaximal, Sylow
299C2×C61—42no—
300C2×C61—42no—
301C2×C61—81no—
302C2×C61C2×#12011yescharacteristic
303C2×C61C2×#12111yescharacteristic
304C2×C61#53411yescharacteristic
305C2×C61D4211yescharacteristic
306C2×C61D4211yescharacteristic
307C2×C61#54611yescharacteristic
308C2×C61#54611yescharacteristic
309D61—24no—
310D61—24no—
311D61—42no—
312C23×D4—611no—
313C2×#121—611no—
314C2×#121—611no—
315C2×#120—611no—
316C2×#120—611no—
317C22×C22⋊C4—611no—
318#394—611no—
319#394—611no—
320#392—611no—
321#392D6111yescharacteristic, complemented
322#386—611no—
323#386—611no—
324#386—611no—
325#385—611no—
326#379—611no—
327C61#241011yescharacteristic, complemented, Sylow
328C25—611no—
329C25—611no—
330C22×D4—611no—
331C22×D4—611no—
332C22×D4—611no—
333C22×D4—611no—
334C22×D4—611no—
335C22×D4—611no—
336C22×D4—1224no—
337C22×D4—1224no—
338C22×D4—1224no—
339C22×D4C2×D6111yescharacteristic
340C22×D4C2×D6111yescharacteristic, complemented
341C22×D4C2×D6111yescharacteristic, complemented
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—611no—
345#121—1224no—
346#121—1224no—
347#120—1224no—
348#120—1224no—
349C2×C4⋊C4—611no—
350C2×C4⋊C4—611no—
351C2×C22⋊C4—611no—
352C2×C22⋊C4—611no—
353C2×C22⋊C4—611no—
354C2×C22⋊C4—611no—
355C2×C22⋊C4—611no—
356C2×C22⋊C4—611no—
357C2×C22⋊C4—611no—
358C2×C22⋊C4—611no—
359C2×C22⋊C4—611no—
360C2×C22⋊C4—611no—
361C2×C22⋊C4—611no—
362C2×C22⋊C4—611no—
363C2×C22⋊C4—1224no—
364C2×C22⋊C4C2×D6111yescharacteristic, complemented
365C2×C22⋊C4C2×D6111yescharacteristic, complemented
366C2×C22⋊C4C2×D6111yescharacteristic, complemented
367#95—611no—
368#95—611no—
369#95—611no—
370#95C2×D6111yescharacteristic, complemented
371C24—611no—
372C24—611no—
373C24—611no—
374C24—614no—
375C24—1222no—
376C24—1222no—
377C24—1222no—
378C24—1222no—
379C24—1222no—
380C24—1222no—
381C24—1222no—
382C24—1222no—
383C24—1222no—
384C24—2441no—
385C24—2441no—
386C24—2441no—
387C24—2441no—
388C24C22×D6111yescharacteristic
389C24C22×D6111yescharacteristic
390C24C22×D6111yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—614no—
401C2×D4—614no—
402C2×D4—1222no—
403C2×D4—1222no—
404C2×D4—1222no—
405C2×D4—1222no—
406C2×D4—12232no—
407C2×D4—1222no—
408C2×D4—1222no—
409C2×D4—1222no—
410C2×D4—1222no—
411C2×D4—1222no—
412C2×D4—1222no—
413C2×D4—1222no—
414C2×D4—1222no—
415C2×D4—1222no—
416C2×D4—1222no—
417C2×D4—1222no—
418C2×D4—2441no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—1222no—
425C22×C4—1222no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—2441no—
432C22×C4—2441no—
433C22×C4C22×D6111yescharacteristic
434C22×C4C22×D6111yescharacteristic
435C22×C4C22×D6111yescharacteristic
436C22×C4C22×D6111yescharacteristic
437C4⋊C4—1222no—
438C4⋊C4—1222no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C22⋊C4—614no—
443C22⋊C4—1222no—
444C22⋊C4—1222no—
445C22⋊C4—1222no—
446C22⋊C4—1222no—
447C22⋊C4—1222no—
448C22⋊C4—1222no—
449C22⋊C4—1222no—
450C22⋊C4—1222no—
451C22⋊C4—1222no—
452C22⋊C4—1222no—
453C22⋊C4—2441no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—612no—
474C23—612no—
475C23—612no—
476C23—612no—
477C23—612no—
478C23—612no—
479C23—612no—
480C23—1228no—
481C23—1228no—
482C23—1228no—
483C23—1221no—
484C23—1221no—
485C23—1221no—
486C23—1221no—
487C23—1221no—
488C23—1221no—
489C23—1221no—
490C23—1221no—
491C23—1221no—
492C23—1221no—
493C23—1221no—
494C23—1221no—
495C23—1221no—
496C23—1221no—
497C23—2444no—
498C23—2444no—
499C23—2444no—
500C23—2444no—
501C23—2444no—
502C23—2444no—
503C23—2444no—
504C23—2444no—
505C23—2444no—
506C23—2444no—
507C23—2444no—
508C23D4×D6112yes—
509C23D4×D6112yes—
510C23C23×D6111yescharacteristic
511D4—28no—
512D4—44no—
513D4—44no—
514D4—1228no—
515D4—1228no—
516D4—1228no—
517D4—2444no—
518D4—2444no—
519D4—2444no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—1228no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—2444no—
547C2×C4—2444no—
548C2×C4D4×D6112yes—
549C2×C4D4×D6112yescomplemented
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—614no—
572C22—614no—
573C22—1222no—
574C22—1222no—
575C22—1222no—
576C22—1222no—
577C22—1222no—
578C22—1222no—
579C22—1222no—
580C22—1222no—
581C22—1222no—
582C22—1222no—
583C22—1222no—
584C22—1222no—
585C22—1222no—
586C22—1222no—
587C22—1222no—
588C22—24416no—
589C22—24416no—
590C22—2441no—
591C22—2441no—
592C22—2441no—
593C22—2441no—
594C22C2×D4×D6111yescharacteristic
595C22C2×D4×D6111yescharacteristic
596C22C2×D4×D6111yescharacteristic
597C22C2×D4×D6111yescharacteristic
598C22#41×D6111yescharacteristic
599C22#1451982211yescharacteristic
600C22#1451982211yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—1222no—
606C4—1222no—
607C4—2441no—
608C4—2441no—
609C4—2441no—
610C2—42no—
611C2—42no—
612C2—81no—
613C2—1224no—
614C2—1224no—
615C2—2442no—
616C2#120×D6111yescharacteristic
617C2#121×D6111yescharacteristic
618C2#1684032211yescharacteristic
619C2#1684039411yescharacteristic
620C2#1684039711yescharacteristic
621C2#1684040111yescharacteristic
622C2#1684040911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2410
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D61C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519748C2semidirect
4. C2×#14519745C2semidirect
5. C2×#14519745C2semidirect
6. C2×C22⋊C4×D61C2semidirect
7. #16839678C2semidirect
8. #16839676C2semidirect
9. #16839670C2semidirect
10. #16839640C2semidirect
11. #16839638C2semidirect
12. #16839638C2semidirect
13. #16839636C2semidirect
14. #16839617C2semidirect
15. C61×#392C2semidirect
22. C22×C22⋊D61C22semidirect
23. C22×C22⋊D61C22semidirect
28. C22×C4×D61C22semidirect
29. C22×C4×D61C22semidirect
34. C2×C4⋊Dic61C22semidirect
35. C2×#11758196C22semidirect
36. C2×C22⋊Dic61C22semidirect
37. C2×C22⋊Dic61C22semidirect
38. C2×C22⋊Dic61C22semidirect
39. C2×C22⋊Dic61C22semidirect
40. C2×C22⋊Dic61C22semidirect
44. C2×#11758198C22semidirect
45. C2×#11758198C22semidirect
46. C2×#11758198C22semidirect
47. C2×#11758198C22semidirect
49. #14519684C22semidirect
50. #14519684C22semidirect
51. #14519684C22semidirect
53. C22×D4×C61C22semidirect
54. C22×D4×C61C22semidirect
55. C2×C22⋊C4×C61C22semidirect
56. C2×C22⋊C4×C61C22semidirect
57. C2×C22⋊C4×C61C22semidirect
58. #95×C61C22semidirect
75. C23×D61D4semidirect
106. C2×C22⋊D61D4semidirect
115. C2×D244D4semidirect
139. #11758198D4semidirect
213. C2×C4×C61C2×D4semidirect
233. C2×Dic61C2×D4semidirect
287. C2×D61#120semidirect
288. C2×D61#121semidirect
321. #392D61semidirect
327. C61#2410semidirect
340. C22×D4C2×D61semidirect
341. C22×D4C2×D61semidirect
364. C2×C22⋊C4C2×D61semidirect
365. C2×C22⋊C4C2×D61semidirect
366. C2×C22⋊C4C2×D61semidirect
370. #95C2×D61semidirect
549. C2×C4D4×D61semidirect