Finite Group Databasebeta

← #29690415

Subgroups — #29690415

Order 15616.

786 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839784C211yesmaximal, characteristic
2#21448215C211yesmaximal, characteristic
3#21448212C211yesmaximal, characteristic
4#21446590C211yesmaximal, characteristic, complemented
5#21446589C211yesmaximal, characteristic, complemented
6#21446588C211yesmaximal, characteristic, complemented
7#21446587C211yesmaximal, characteristic, complemented
8#21446586C211yesmaximal, characteristic, complemented
9#21446585C211yesmaximal, characteristic, complemented
10#21446584C211yesmaximal, characteristic, complemented
11#21445853C211yesmaximal, characteristic
12#21445851C211yesmaximal, characteristic
13#21445851C211yesmaximal, characteristic
14#21445849C211yesmaximal, characteristic
15C61×#1949C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×C42×D61C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25#16839784C418yescomplemented
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29#16839629—21no—
30#16839629—21no—
31#16839628C2211yescharacteristic
32#16839627C2211yescharacteristic
33#16839627C2211yescharacteristic
34#16839624—21no—
35#16839624—21no—
36#16839619C2211yescharacteristic
37#16839619C2211yescharacteristic
38#16839619C2211yescharacteristic
39#16839619C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C4×#11758198—21no—
44#16839609—21no—
45#16839608—21no—
46#16839607—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C2×#11758189—41no—
64C2×#11758189—41no—
65C2×#11758189—41no—
66C2×#11758189—41no—
67C2×#11758189C2×C414yes—
68C2×#11758189C2×C414yes—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85C42×D61C2×C414yes—
86C42×D61Q814yes—
87#14519711—41no—
88#14519710—41no—
89#14519710—41no—
90#14519709—41no—
91#14519708—41no—
92#14519708—41no—
93C4⋊#92418C2×C414yes—
94#14519706C2×C414yes—
95#14519706C2×C414yes—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117#107×C61—41no—
118#106×C61—41no—
119C4⋊C8×C61C2×C414yes—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123C23×D61C2×D411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2411yescharacteristic
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61C2×D411yescharacteristic
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—41no—
143C2×C4×D61—41no—
144C2×C4×D61—41no—
145C2×C4×D61—41no—
146C2×C4×D61C4⋊C414yes—
147C2×C4×D61C4⋊C414yes—
148C2×C4×D61C22×C412yes—
149C2×C4×D61C2×Q812yes—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61C22×C412yes—
155C2×C8×C61C22×C412yes—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C42×C61—42no—
165C42×C61C22×C412yes—
166C42×C61C2×Q812yes—
167#11758198—42no—
168#11758198—42no—
169#11758198—42no—
170#11758198—42no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4×Dic61—42no—
180C4×Dic61—42no—
181C4×Dic61—42no—
182C4×Dic61C4⋊C414yes—
183C4×Dic61C4⋊C414yes—
184C4×Dic61C22×C412yes—
185C4×Dic61C2×Q812yes—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418C22×C412yes—
191C2×#92418C22×C412yes—
192#11758189—44no—
193#11758189—44no—
194C23×C61C22×D411yescharacteristic
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—21no—
201C22×D61C2×C4⋊C412yes—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61C2×C4⋊C412yes—
219C2×C4×C61C2×C4⋊C412yes—
220C2×C4×C61C23×C411yescharacteristic
221C2×C4×C61C22×Q811yescharacteristic
222C2×C4×C61H(5,𝔽2)11yescharacteristic
223C2×C4×C61H(5,𝔽2)11yescharacteristic
224C2×C4×C612−1+411yescharacteristic
225C2×C4×C612−1+411yescharacteristic
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61C2×C4⋊C412yes—
245C2×Dic61C2×C4⋊C412yes—
246C2×Dic61C2×C4⋊C412yes—
247C4×D61—22no—
248C4×D61—22no—
249C4×D61—22no—
250C4×D61—22no—
251C4×D61—44no—
252C4×D61—44no—
253C8×C61—22no—
254C8×C61—22no—
255#92418—22no—
256#92418—22no—
257#21965—611nomaximal, Sylow
258C22×C61C22×C4⋊C411yescharacteristic
259C22×C61#53711yescharacteristic
260C22×C61#53711yescharacteristic
261C22×C61#57511yescharacteristic
262C22×C61#57511yescharacteristic
263C22×C61#57511yescharacteristic
264C22×C61#57511yescharacteristic
265C2×D61—22no—
266C2×D61—22no—
267C2×D61—22no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C4×C61—22no—
273C4×C61—22no—
274C4×C61—81no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61#51811yescharacteristic
279C4×C61#51911yescharacteristic
280C4×C61#54411yescharacteristic
281C4×C61#54411yescharacteristic
282Dic61—22no—
283Dic61—22no—
284Dic61—22no—
285Dic61—81no—
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289C2×#423—611no—
290#2283—611no—
291#2283—611no—
292#1949—611no—
293#1949—611no—
294#1949—611no—
295#1949—611no—
296#1949—611no—
297#1949—611no—
298#1949—611no—
299#1949D6111yescharacteristic, complemented
300#1809—611no—
301#1809—611no—
302#1809—611no—
303#1809—611no—
304C2×C61#231611yescharacteristic
305C2×C61#291111yescharacteristic
306C2×C61#291111yescharacteristic
307C2×C61#325611yescharacteristic
308C2×C61#325611yescharacteristic
309C2×C61#325611yescharacteristic
310C2×C61#325611yescharacteristic
311D61—42no—
312C22×M16—611no—
313C22×M16—611no—
314C22×C42—611no—
315C2×#107—611no—
316C2×#107—611no—
317C2×#107—611no—
318C2×#107C2×D6111yescharacteristic
319C2×#106—611no—
320C2×#106—611no—
321C2×#106—611no—
322C2×#106C2×D6111yescharacteristic
323#423—618no—
324C2×C4⋊C8—611no—
325C2×C4⋊C8—611no—
326C2×C4⋊C8—611no—
327C2×C4⋊C8C2×D6111yescharacteristic
328#383—1221no—
329#383—1221no—
330#382—611no—
331#382—611no—
332#382—611no—
333#382C2×D6111yescharacteristic
334#381—1221no—
335#381—1221no—
336#380—611no—
337#380—611no—
338#380—611no—
339#380—611no—
340C4×C4⋊C4—611no—
341C4×C4⋊C4—611no—
342C4×C4⋊C4—611no—
343C4×C4⋊C4C2×D6111yescharacteristic
344C4×C22⋊C4—1221no—
345C4×C22⋊C4—1221no—
346#376—1221no—
347#376—1221no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340C2×D6111yescharacteristic
355#340C2×D6111yescharacteristic
356C61#2196511yescharacteristic, complemented, Sylow
357C23×C4—611no—
358C23×C4—611no—
359C23×C4—611no—
360C2×M16—614no—
361C2×M16—614no—
362C2×M16—2441no—
363C2×M16—2441no—
364C2×M16—2441no—
365C2×M16—2441no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8C22×D6111yescharacteristic
369C22×C8C22×D6111yescharacteristic
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4C22×D6111yescharacteristic
375C2×C4⋊C4C22×D6111yescharacteristic
376C2×C4⋊C4C22×D6111yescharacteristic
377C2×C4⋊C4C22×D6111yescharacteristic
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1221no—
382C2×C42—21no—
383C2×C42—611no—
384C2×C42—611no—
385C2×C42—611no—
386C2×C42—614no—
387C2×C42—614no—
388C2×C42—1221no—
389C2×C42—1221no—
390C2×C42—1221no—
391C2×C42C22×D6111yescharacteristic
392#107—41no—
393#107—2441no—
394#107—2441no—
395#107—2441no—
396#106—41no—
397#106—2441no—
398#106—2441no—
399#106—2441no—
400C4⋊C8—614no—
401C4⋊C8—614no—
402C4⋊C8—614no—
403C4⋊C8C4×D6114yes—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420C24—611no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—612no—
429C22×C4—612no—
430C22×C4—614no—
431C22×C4—614no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—2441no—
441C22×C4—2441no—
442C22×C4—2441no—
443C22×C4—2441no—
444C22×C4D4×D6111yescharacteristic
445C22×C4D4×D6111yescharacteristic
446C22×C4C23×D6111yescharacteristic
447M16—2444no—
448M16—2444no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—612no—
454C2×C8—612no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8C2×C4×D6112yes—
460C2×C8C2×C4×D6112yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C22⋊C4—2442no—
478C22⋊C4—2442no—
479C22⋊C4—2442no—
480C22⋊C4—2442no—
481C42—42no—
482C42—612no—
483C42—612no—
484C42—614no—
485C42—614no—
486C42—2442no—
487C42—2442no—
488C42—2442no—
489C42C2×C4×D6112yes—
490C42Q8×D6112yes—
491C23—612no—
492C23—1221no—
493C23—1221no—
494C23—1221no—
495C23—1221no—
496C23—1221no—
497C23—1221no—
498C23C2×D4×D6111yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—2444no—
529C2×C4—2444no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4C4⋊C4×D6112yes—
543C2×C4C4⋊C4×D6112yes—
544C2×C4C22×C4×D6111yescharacteristic
545C2×C4C2×Q8×D6111yescharacteristic
546C2×C4#1451982211yescharacteristic
547C2×C4#1451982311yescharacteristic
548C2×C4#1451982411yescharacteristic
549C2×C4#1451982511yescharacteristic
550C8—22no—
551C8—22no—
552C8—1222no—
553C8—1222no—
554C22—1222no—
555C22—1222no—
556C22—1222no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22—2441no—
561C22C2×C4⋊C4×D6111yescharacteristic
562C22#1684034111yescharacteristic
563C22#1684034211yescharacteristic
564C22#1684055811yescharacteristic
565C22#1684055911yescharacteristic
566C22#1684055911yescharacteristic
567C22#1684056111yescharacteristic
568C4—22no—
569C4—22no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—1222no—
575C4—1222no—
576C4—1222no—
577C4—4881no—
578C4—4881no—
579C4—4881no—
580C4—4881no—
581C4#1684023411yescharacteristic
582C4#1684023811yescharacteristic
583C4#1684038911yescharacteristic
584C4#1684039211yescharacteristic
585C2—2442no—
586C2#2144843411yescharacteristic
587C2#2145440611yescharacteristic
588C2#2145440711yescharacteristic
589C2#2145721711yescharacteristic
590C2#2145721811yescharacteristic
591C2#2145721911yescharacteristic
592C2#2145722211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1949C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1949D61
hypocenterC61#21965
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #21446590C2semidirect
5. #21446589C2semidirect
6. #21446588C2semidirect
7. #21446587C2semidirect
8. #21446586C2semidirect
9. #21446585C2semidirect
10. #21446584C2semidirect
15. C61×#1949C2semidirect
25. #16839784C4semidirect
299. #1949D61semidirect
356. C61#21965semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168397842
#214482152
#214482122
#214465902
#214465892
#214465882
#214465872
#214465862
#214465852
#214465842
#214458532
#214458512
#214458492
C61×#19492
#2196561