Finite Group Databasebeta

← #21449192

Subgroups — #21449192

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×#14519751C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic, complemented
4C2×#14519747C211yesmaximal, characteristic, complemented
5C2×#14519747C211yesmaximal, characteristic, complemented
6C22×#11758198C211yesmaximal, characteristic, complemented
7#16839680C211yesmaximal, characteristic, complemented
8#16839678C211yesmaximal, characteristic, complemented
9#16839672C211yesmaximal, characteristic, complemented
10#16839671C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic, complemented
12#16839639C211yesmaximal, characteristic, complemented
13#16839636C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C24×D61C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×D244C2211yescharacteristic
20C22×D244C2211yescharacteristic, complemented
21C22×D244C2211yescharacteristic, complemented
22C22×C22⋊D61C2211yescharacteristic
23C22×C22⋊D61C2211yescharacteristic
24C22×C22⋊D61C2211yescharacteristic, complemented
25C22×C22⋊D61C2211yescharacteristic, complemented
26C2×D4×D61—24no—
27C2×D4×D61—24no—
28C2×D4×D61—24no—
29C23×Dic61C2211yescharacteristic, complemented
30C22×C4×D61C2211yescharacteristic
31#14519751—24no—
32#14519749—24no—
33#14519747—24no—
34#14519747—24no—
35C2×C4⋊Dic61C2211yescharacteristic, complemented
36C2×#11758196C2211yescharacteristic, complemented
37C2×C22⋊Dic61C2211yescharacteristic, complemented
38C2×#11758198—24no—
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic, complemented
43C2×#11758198C2211yescharacteristic, complemented
44C2×#11758198C2211yescharacteristic, complemented
45C2×#11758198C2211yescharacteristic, complemented
46C2×#11758198C2211yescharacteristic, complemented
47C2×#11758198C2211yescharacteristic, complemented
48C2×#11758198C2211yescharacteristic, complemented
49C2×#11758198C2211yescharacteristic, complemented
50#14519684C2211yescharacteristic, complemented
51#14519684C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C23×C4×C61C2211yescharacteristic, complemented
54C2×C22⋊C4×C61C2211yescharacteristic, complemented
55C2×C22⋊C4×C61C2211yescharacteristic, complemented
56C2×C22⋊C4×C61C2211yescharacteristic, complemented
57#95×C61C2211yescharacteristic, complemented
58#95×C61C2211yescharacteristic, complemented
59C24×C61C2311yescharacteristic
60C24×C61C2311yescharacteristic
61C23×D61—22no—
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—41no—
71C23×D61—41no—
72C23×D61—41no—
73C23×D61—41no—
74C23×D61D414yescomplemented
75C23×D61C2311yescharacteristic
76C23×D61C2311yescharacteristic
77C23×D61C2311yescharacteristic
78C23×D61C2311yescharacteristic
79C2×D4×C61—22no—
80C2×D4×C61—22no—
81C2×D4×C61D414yescomplemented
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—41no—
85C22×C4×C61C2311yescharacteristic
86C22×C4×C61C2311yescharacteristic
87C22×C4×C61C2311yescharacteristic
88C22×C4×C61C2311yescharacteristic
89C22×C4×C61C2311yescharacteristic
90C2×C22⋊D61—22no—
91C2×C22⋊D61—22no—
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—41no—
101C2×C22⋊D61D414yescomplemented
102C22×Dic61—22no—
103C22×Dic61—22no—
104C22×Dic61—41no—
105C22×Dic61C2311yescharacteristic
106C22×Dic61C2311yescharacteristic
107C22×Dic61C2311yescharacteristic
108C22×Dic61C2311yescharacteristic
109D4×D61—232no—
110C2×D244—22no—
111C2×D244—22no—
112C2×D244—22no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—22no—
116C2×D244—22no—
117C2×D244—22no—
118C2×D244—22no—
119C2×D244—41no—
120C2×D244—41no—
121C2×D244—41no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C22⋊C4×C61—22no—
126C22⋊C4×C61—22no—
127C22⋊C4×C61—41no—
128C22⋊Dic61—22no—
129#11758198—22no—
130#11758198—22no—
131#11758198—22no—
132#11758198—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×C61C2×D412yes—
153C23×C61C2×D412yes—
154C23×C61C2×D412yes—
155C23×C61C2×D412yes—
156C23×C61C2411yescharacteristic
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—28no—
162C22×D61—28no—
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—28no—
176C22×D61—21no—
177C22×D61—21no—
178C22×D61—21no—
179C22×D61—21no—
180C22×D61—21no—
181C22×D61—21no—
182C22×D61—21no—
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×D61—44no—
193C22×D61—44no—
194C22×D61C2×D412yes—
195C22×D61C2×D412yes—
196C22×D61C2×D412yes—
197C22×D61C2×D412yes—
198C22×D61#4112yes—
199D4×C61—28no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
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×C61—21no—
213C2×C4×C61—44no—
214C2×C4×C61C2×D412yes—
215C2×C4×C61C2×D412yescomplemented
216C22⋊D61—28no—
217C22⋊D61—28no—
218C22⋊D61—44no—
219C22⋊D61—44no—
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—44no—
231C2×Dic61C2×D412yes—
232C2×Dic61C2×D412yescomplemented
233D244—28no—
234D244—44no—
235D244—44no—
236D244—44no—
237C4×D61—28no—
238C22×C61—22no—
239C22×C61—22no—
240C22×C61—22no—
241C22×C61—22no—
242C22×C61—22no—
243C22×C61—22no—
244C22×C61—22no—
245C22×C61—22no—
246C22×C61—22no—
247C22×C61—41no—
248C22×C61—41no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61#12014yescomplemented
252C22×C61C22×D411yescharacteristic
253C22×C61C22×D411yescharacteristic
254C22×C61C22×D411yescharacteristic
255C22×C61C22×D411yescharacteristic
256C22×C61C2×#4111yescharacteristic
257C22×C61H(5,𝔽2)11yescharacteristic
258C22×C61H(5,𝔽2)11yescharacteristic
259C2×D61—22no—
260C2×D61—22no—
261C2×D61—22no—
262C2×D61—22no—
263C2×D61—22no—
264C2×D61—22no—
265C2×D61—22no—
266C2×D61—22no—
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—22no—
270C2×D61—22no—
271C2×D61—416no—
272C2×D61—416no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—41no—
288C2×D61#12114yescomplemented
289C4×C61—22no—
290C4×C61—22no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294Dic61—22no—
295Dic61—22no—
296Dic61—41no—
297Dic61—41no—
298#2410—611nomaximal, Sylow
299C2×C61—24no—
300C2×C61—42no—
301C2×C61C2×#12011yescharacteristic
302C2×C61C2×#12111yescharacteristic
303C2×C61#53411yescharacteristic
304C2×C61D4211yescharacteristic
305C2×C61D4211yescharacteristic
306C2×C61#54611yescharacteristic
307C2×C61#54611yescharacteristic
308D61—24no—
309D61—42no—
310D61—42no—
311D61—81no—
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#392—611no—
322#386—611no—
323#386—611no—
324#386D6111yescharacteristic, complemented
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—611no—
337C22×D4—611no—
338C22×D4—1224no—
339C22×D4—1224no—
340C22×D4—1224no—
341C22×D4C2×D6111yescharacteristic
342C23×C4—611no—
343C23×C4—611no—
344C23×C4C2×D6111yescharacteristic, complemented
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#95C2×D6111yescharacteristic, complemented
370#95C2×D6111yescharacteristic, complemented
371C24—611no—
372C24—611no—
373C24—611no—
374C24—614no—
375C24—611no—
376C24—1222no—
377C24—1222no—
378C24—1222no—
379C24—1222no—
380C24—1222no—
381C24—1222no—
382C24—1222no—
383C24—1222no—
384C24—1222no—
385C24—2441no—
386C24—2441no—
387C24—2441no—
388C24—2441no—
389C24C22×D6111yescharacteristic
390C24C22×D6111yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—614no—
394C2×D4—1222no—
395C2×D4—1222no—
396C2×D4—1222no—
397C2×D4—1222no—
398C2×D4—1222no—
399C2×D4—1222no—
400C2×D4—1222no—
401C2×D4—1222no—
402C2×D4—1222no—
403C2×D4—12232no—
404C2×D4—1222no—
405C2×D4—1222no—
406C2×D4—1222no—
407C2×D4—1222no—
408C2×D4—1222no—
409C2×D4—1222no—
410C2×D4—1222no—
411C2×D4—1222no—
412C2×D4—1222no—
413C2×D4—1222no—
414C2×D4—2441no—
415C2×D4—2441no—
416C2×D4—2441no—
417C2×D4—2441no—
418C2×D4D24414yescomplemented
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—2441no—
432C22×C4C22×D6111yescharacteristic
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—612no—
465C23—612no—
466C23—612no—
467C23—612no—
468C23—612no—
469C23—1228no—
470C23—1228no—
471C23—1221no—
472C23—1221no—
473C23—1221no—
474C23—1221no—
475C23—1221no—
476C23—1221no—
477C23—1221no—
478C23—1221no—
479C23—1221no—
480C23—1221no—
481C23—1221no—
482C23—1221no—
483C23—1221no—
484C23—1221no—
485C23—1221no—
486C23—1221no—
487C23—1228no—
488C23—1221no—
489C23—1221no—
490C23—1221no—
491C23—1221no—
492C23—1221no—
493C23—1221no—
494C23—1221no—
495C23—2444no—
496C23—2444no—
497C23—2444no—
498C23—2444no—
499C23—2444no—
500C23—2444no—
501C23—2444no—
502C23—2444no—
503C23—2444no—
504C23—2444no—
505C23—2444no—
506C23C2×D24412yes—
507C23C2×D24412yes—
508C23D4×D6112yes—
509C23D4×D6112yes—
510C23C23×D6111yescharacteristic
511D4—28no—
512D4—1228no—
513D4—1228no—
514D4—1228no—
515D4—2444no—
516D4—2444no—
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—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—44no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—1228no—
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—1221no—
547C2×C4—2444no—
548C2×C4C2×D24412yes—
549C2×C4D4×D6112yescomplemented
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—614no—
564C22—1222no—
565C22—1222no—
566C22—1222no—
567C22—1222no—
568C22—1222no—
569C22—1222no—
570C22—1222no—
571C22—1222no—
572C22—1222no—
573C22—1222no—
574C22—1222no—
575C22—1222no—
576C22—24416no—
577C22—24416no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22—2441no—
587C22—2441no—
588C22—2441no—
589C22—2441no—
590C22—2441no—
591C22—2441no—
592C22—2441no—
593C22#1451974714yescomplemented
594C22C2×D4×D6111yescharacteristic
595C22C2×D4×D6111yescharacteristic
596C22C2×D4×D6111yescharacteristic
597C22C22×D24411yescharacteristic
598C22#41×D6111yescharacteristic
599C22#1451982211yescharacteristic
600C22#1451982311yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—1222no—
607C4—1222no—
608C4—2441no—
609C4—2441no—
610C2—24no—
611C2—42no—
612C2—1224no—
613C2—4881no—
614C2—2442no—
615C2—2442no—
616C2C2×#1451974711yescharacteristic
617C2#121×D6111yescharacteristic
618C2#1684032011yescharacteristic
619C2#1684039411yescharacteristic
620C2D4×D24411yescharacteristic
621C2#1684040411yescharacteristic
622C2#1684040711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2410
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×D4×D61C2semidirect
2. C2×#14519751C2semidirect
3. C2×#14519749C2semidirect
4. C2×#14519747C2semidirect
5. C2×#14519747C2semidirect
6. C22×#11758198C2semidirect
7. #16839680C2semidirect
8. #16839678C2semidirect
9. #16839672C2semidirect
10. #16839671C2semidirect
11. #16839640C2semidirect
12. #16839639C2semidirect
13. #16839636C2semidirect
14. #16839617C2semidirect
15. C61×#386C2semidirect
20. C22×D244C22semidirect
21. C22×D244C22semidirect
24. C22×C22⋊D61C22semidirect
25. C22×C22⋊D61C22semidirect
29. C23×Dic61C22semidirect
35. C2×C4⋊Dic61C22semidirect
36. C2×#11758196C22semidirect
37. C2×C22⋊Dic61C22semidirect
42. C2×#11758198C22semidirect
43. C2×#11758198C22semidirect
44. C2×#11758198C22semidirect
45. C2×#11758198C22semidirect
46. C2×#11758198C22semidirect
47. C2×#11758198C22semidirect
48. C2×#11758198C22semidirect
49. C2×#11758198C22semidirect
50. #14519684C22semidirect
51. #14519684C22semidirect
53. C23×C4×C61C22semidirect
54. C2×C22⋊C4×C61C22semidirect
55. C2×C22⋊C4×C61C22semidirect
56. C2×C22⋊C4×C61C22semidirect
57. #95×C61C22semidirect
58. #95×C61C22semidirect
74. C23×D61D4semidirect
81. C2×D4×C61D4semidirect
101. C2×C22⋊D61D4semidirect
139. #11758198D4semidirect
215. C2×C4×C61C2×D4semidirect
232. C2×Dic61C2×D4semidirect
251. C22×C61#120semidirect
288. C2×D61#121semidirect
324. #386D61semidirect
327. C61#2410semidirect
344. C23×C4C2×D61semidirect
364. C2×C22⋊C4C2×D61semidirect
365. C2×C22⋊C4C2×D61semidirect
366. C2×C22⋊C4C2×D61semidirect
369. #95C2×D61semidirect
370. #95C2×D61semidirect
418. C2×D4D244semidirect
549. C2×C4D4×D61semidirect
593. C22#14519747semidirect