Finite Group Databasebeta

← #29649062

Subgroups — #29649062

Order 15616.

666 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454938C211yesmaximal, characteristic
2#21454933C211yesmaximal, characteristic
3C4×#14519785C211yesmaximal, characteristic
4#21444586C211yesmaximal, characteristic, complemented
5#21444585C211yesmaximal, characteristic, complemented
6#21444583C211yesmaximal, characteristic, complemented
7#21444580C211yesmaximal, characteristic, complemented
8#21444579C211yesmaximal, characteristic, complemented
9#21444577C211yesmaximal, characteristic, complemented
10#21444576C211yesmaximal, characteristic, complemented
11#21444570C211yesmaximal, characteristic, complemented
12#21444568C211yesmaximal, characteristic, complemented
13#21444564C211yesmaximal, characteristic, complemented
14#335×D61C211yesmaximal, characteristic, complemented
15C61×#1569C211yesmaximal, characteristic, complemented
16C2×#14519785C411yescharacteristic
17C2×#14519785C411yescharacteristic
18C4×#11758222C2211yescharacteristic
19#16839891—21no—
20#16839890—21no—
21#16839838—21no—
22#16839837—21no—
23#16839836—21no—
24#16839835—21no—
25#16839832—21no—
26#16839831—21no—
27#16839819C2211yescharacteristic
28#16839818C2211yescharacteristic
29#16839818C2211yescharacteristic
30#16839814C2211yescharacteristic
31#16839814C2211yescharacteristic
32#16839786C2211yescharacteristic
33#16839784C2211yescharacteristic
34#16839784C2211yescharacteristic
35C4⋊C8×D61C2211yescharacteristic
36C4⋊C8×D61C2211yescharacteristic
37#16839720C411yescharacteristic
38#16839720C411yescharacteristic
39#16839719C411yescharacteristic
40#16839719C411yescharacteristic
41#16839719C411yescharacteristic
42#16839719C411yescharacteristic
43C4×#11758189C2211yescharacteristic
44C4×#11758189C2211yescharacteristic
45C2×C4×#92418C2211yescharacteristic
46C4×C8×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839515C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839514C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839514C2211yescharacteristic
55#16839514C2211yescharacteristic
56#16839513C2211yescharacteristic
57#16839513C2211yescharacteristic
58#16839512C2211yescharacteristic
59#16839512C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C4×M16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68#14519785—24no—
69#14519785—24no—
70C2×#11758194—21no—
71C2×#11758189—21no—
72C2×#11758189—21no—
73C2×#11758189C2×C411yescharacteristic
74C2×#11758189C2×C411yescharacteristic
75C2×#11758189C2×C411yescharacteristic
76C2×#11758189C2×C411yescharacteristic
77C22×#92418C2×C411yescharacteristic
78C22×#92418C2×C411yescharacteristic
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61C2×C411yescharacteristic
82C2×C8×D61C2×C411yescharacteristic
83C2×C8×D61C2×C411yescharacteristic
84C2×C8×D61C2×C411yescharacteristic
85C4×Dic122D411yescharacteristic
86C4×Dic122Q811yescharacteristic
87C4×D244D411yescharacteristic
88C4×D244Q811yescharacteristic
89C4×C22⋊D61D411yescharacteristic
90C4×C22⋊D61D411yescharacteristic
91C4×C22⋊D61Q811yescharacteristic
92C4×C22⋊D61Q811yescharacteristic
93#14519736C2×C411yescharacteristic
94#14519734C2×C411yescharacteristic
95#14519734C2×C411yescharacteristic
96C42×D61C2311yescharacteristic
97C42×D61C2311yescharacteristic
98C4⋊#92418—21no—
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107C22⋊#92418—21no—
108#14519689—21no—
109#14519689—21no—
110#14519689—21no—
111#14519689—21no—
112#14519688—21no—
113#14519687—21no—
114#14519687—21no—
115#14519687C2×C411yescharacteristic
116#14519687C2×C411yescharacteristic
117#14519687C2×C411yescharacteristic
118#14519687C2×C411yescharacteristic
119C4×#92418C2×C411yescharacteristic
120C4×#92418C2×C411yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C8×Dic61—21no—
124C8×Dic61—21no—
125C8×Dic61C2×C411yescharacteristic
126C8×Dic61C2×C411yescharacteristic
127C8×Dic61C2×C411yescharacteristic
128C8×Dic61C2×C411yescharacteristic
129C2×M16×C61—21no—
130C2×M16×C61C2×C411yescharacteristic
131C2×M16×C61C2×C411yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139#97×C61—21no—
140#97×C61C2×C411yescharacteristic
141#97×C61C2×C411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×Q811yescharacteristic
147C2×C22⋊D61C4⋊C411yescharacteristic
148C2×C22⋊D61C4⋊C411yescharacteristic
149#11758222—22no—
150#11758222—22no—
151C2×D244C4⋊C411yescharacteristic
152C2×C4×D61C22×C411yescharacteristic
153C2×C4×D61C22×C411yescharacteristic
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2×Q811yescharacteristic
157C2×C4×D61C2×Q811yescharacteristic
158C2×Dic122C4⋊C411yescharacteristic
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—81no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61C22×C411yescharacteristic
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C42×C61C22×C411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C42×C61C2×Q811yescharacteristic
173C42×C61C2411yescharacteristic
174C22⋊Dic61C4⋊C411yescharacteristic
175C22⋊Dic61C4⋊C411yescharacteristic
176#11758198C4⋊C411yescharacteristic
177#11758198C4⋊C411yescharacteristic
178#11758198C4⋊C411yescharacteristic
179#11758198C4⋊C411yescharacteristic
180C4⋊Dic61C4⋊C411yescharacteristic
181C4⋊Dic61C4⋊C411yescharacteristic
182#11758196C4⋊C411yescharacteristic
183#11758196C4⋊C411yescharacteristic
184#11758196C4⋊C411yescharacteristic
185#11758196C4⋊C411yescharacteristic
186C4×Dic61C22×C411yescharacteristic
187C4×Dic61C22×C411yescharacteristic
188C4×Dic61C2×D411yescharacteristic
189C4×Dic61C2×D411yescharacteristic
190C4×Dic61C2×Q811yescharacteristic
191C4×Dic61C2×Q811yescharacteristic
192#11758194—81no—
193C2×#92418—22no—
194C2×#92418—22no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203#11758189—22no—
204#11758189—22no—
205#11758189—22no—
206#11758189—81no—
207#11758189—81no—
208#11758189M1614yescomplemented
209C8×D61—22no—
210C8×D61—22no—
211C8×D61—22no—
212C8×D61—81no—
213C8×D61—81no—
214C8×D61M1614yescomplemented
215C23×C61C2×C4⋊C411yescharacteristic
216C22×D61C2×C4⋊C411yescharacteristic
217C22×D61C2×C4⋊C411yescharacteristic
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—41no—
223C2×C4×C61C2×C4⋊C411yescharacteristic
224C2×C4×C61C2×C4⋊C411yescharacteristic
225C2×C4×C61C2×C4⋊C411yescharacteristic
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C22×Q811yescharacteristic
229C22⋊D61—22no—
230C22⋊D61—22no—
231C2×Dic61C2×C4⋊C411yescharacteristic
232C2×Dic61C2×C4⋊C411yescharacteristic
233C2×Dic61C2×C4⋊C411yescharacteristic
234C2×Dic61C2×C4⋊C411yescharacteristic
235C2×Dic61C2×C4⋊C411yescharacteristic
236C2×Dic61C2×C4⋊C411yescharacteristic
237D244—22no—
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61C2×M1612yes—
247C4×D61C2×M1612yes—
248Dic122—22no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61—41no—
255C8×C61C2×M1612yes—
256C8×C61C2×M1612yes—
257#92418—21no—
258#92418—21no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#92418C2×M1612yes—
264#92418C2×M1612yes—
265#17799—611nomaximal, Sylow
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—21no—
269C22×C61C22×C4⋊C411yescharacteristic
270C2×D61—21no—
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61#42312yes—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61C22×M1611yescharacteristic
281C4×C61C22×M1611yescharacteristic
282C4×C61#57611yescharacteristic
283C4×C61#57811yescharacteristic
284Dic61—21no—
285Dic61—21no—
286Dic61—21no—
287Dic61—21no—
288Dic61—21no—
289Dic61#42312yes—
290#2989—611no—
291#2989—611no—
292C4×#131—611no—
293#1569—611no—
294#1569—611no—
295#1569—611no—
296#1569D6111yescharacteristic, complemented
297#1568—611no—
298#1568—611no—
299#1567—611no—
300#1567—611no—
301#1565—611no—
302#1565—611no—
303#1564—611no—
304C2×#335—611no—
305C2×C61—41no—
306C2×C61C2×#42311yescharacteristic
307C2×C61#291311yescharacteristic
308C2×C61#291611yescharacteristic
309D61—22no—
310D61—41no—
311C2×#131—611no—
312C2×#131—611no—
313C4×#41—611no—
314#446—1221no—
315#446—1221no—
316#436—1221no—
317#436—1221no—
318#435—1221no—
319#435—1221no—
320#435—1221no—
321#435—1221no—
322#432—611no—
323#432—611no—
324#432—611no—
325#432C2×D6111yescharacteristic
326#431—611no—
327#431—611no—
328#423—611no—
329#423—611no—
330#423—611no—
331#423C2×D6111yescharacteristic
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334#405—611no—
335#405—611no—
336#405—611no—
337#405—611no—
338#405—611no—
339#405—611no—
340C4×M16—611no—
341C4×M16—611no—
342C4×M16C2×D6111yescharacteristic
343C2×C4×C8—611no—
344C2×C4×C8—611no—
345C2×C4×C8—611no—
346#335—611no—
347#335—611no—
348#335—611no—
349#335—611no—
350#335—611no—
351#335—611no—
352#335—611no—
353#335—611no—
354#335C2×D6111yescharacteristic
355#335C2×D6111yescharacteristic
356#334—611no—
357#334—611no—
358#334—611no—
359#334—611no—
360#334C2×D6111yescharacteristic
361#334C2×D6111yescharacteristic
362C61#1779911yescharacteristic, complemented, Sylow
363C2×#41—611no—
364#131—1224no—
365#131—1224no—
366C2×M16—21no—
367C2×M16—611no—
368C2×M16—611no—
369C2×M16—611no—
370C2×M16—611no—
371C2×M16—1221no—
372C2×M16—1221no—
373C2×M16—1221no—
374C2×M16C4×D6111yescharacteristic
375C2×M16C4×D6111yescharacteristic
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—611no—
380C22×C8—611no—
381C22×C8—611no—
382C22×C8—1221no—
383C22×C8—1221no—
384C4×Q8—611no—
385C4×Q8—611no—
386C4×D4—611no—
387C4×D4—611no—
388C4×D4—611no—
389C4×D4—611no—
390C4×D4—611no—
391C4×D4—611no—
392#117—611no—
393#117—611no—
394#117—611no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42C22×D6111yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408C4⋊C8C22×D6111yescharacteristic
409C4⋊C8C22×D6111yescharacteristic
410C4⋊C8C22×D6111yescharacteristic
411C4⋊C8C22×D6111yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418#97—21no—
419#97—611no—
420#97—611no—
421#97—611no—
422#97—611no—
423#97—1221no—
424#97—1221no—
425#97—1221no—
426#97C4×D6111yescharacteristic
427#97C4×D6111yescharacteristic
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—1221no—
437C4×C8—1221no—
438C4×C8C22×D6111yescharacteristic
439C4×C8C22×D6111yescharacteristic
440#41—1222no—
441#41—1222no—
442C2×Q8—611no—
443C2×D4—611no—
444C2×D4—611no—
445C2×D4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4C2×C4×D6111yescharacteristic
453C22×C4D4×D6111yescharacteristic
454C22×C4Q8×D6111yescharacteristic
455M16—22no—
456M16—22no—
457M16—81no—
458M16—614no—
459M16—1222no—
460M16—1222no—
461M16—1222no—
462M16—4881no—
463M16—4881no—
464M16—4881no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—614no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—1222no—
475C2×C8—1222no—
476C2×C8—1222no—
477C2×C8—1222no—
478C2×C8—1222no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—4881no—
484C2×C8—4881no—
485C2×C8C2×C4×D6111yescharacteristic
486C2×C8C2×C4×D6111yescharacteristic
487C2×C8C2×C4×D6111yescharacteristic
488C2×C8C2×C4×D6111yescharacteristic
489C4⋊C4—611no—
490C4⋊C4—611no—
491C4⋊C4—611no—
492C4⋊C4—611no—
493C4⋊C4—611no—
494C4⋊C4—611no—
495C22⋊C4—611no—
496C22⋊C4—611no—
497C22⋊C4—611no—
498C22⋊C4—611no—
499C22⋊C4—611no—
500C22⋊C4—611no—
501C42—611no—
502C42—611no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42C2×C4×D6111yescharacteristic
508C42D4×D6111yescharacteristic
509C42Q8×D6111yescharacteristic
510C42C23×D6111yescharacteristic
511C23—611no—
512C23—611no—
513C23C4⋊C4×D6111yescharacteristic
514Q8—1222no—
515D4—1222no—
516D4—1222no—
517D4—1222no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—611no—
524C2×C4—612no—
525C2×C4—612no—
526C2×C4—611no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—611no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4C4⋊C4×D6111yescharacteristic
540C2×C4C4⋊C4×D6111yescharacteristic
541C2×C4C4⋊C4×D6111yescharacteristic
542C2×C4C22×C4×D6111yescharacteristic
543C2×C4C2×D4×D6111yescharacteristic
544C2×C4C2×Q8×D6111yescharacteristic
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—612no—
552C8—612no—
553C8—1221no—
554C8—1221no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C8M16×D6112yes—
560C8M16×D6112yes—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—612no—
565C22—1221no—
566C22—1221no—
567C22—1221no—
568C22—1221no—
569C22—1221no—
570C22C2×C4⋊C4×D6111yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—612no—
576C4—1221no—
577C4—1221no—
578C4—1221no—
579C4—1221no—
580C4—1221no—
581C4C2×M16×D6111yescharacteristic
582C4C2×M16×D6111yescharacteristic
583C4#1684056611yescharacteristic
584C4#1684057811yescharacteristic
585C2—41no—
586C2—1222no—
587C2—2441no—
588C2#423×D6111yescharacteristic
589C2#2145441811yescharacteristic
590C2#2145442911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1569C2
socleC22×C61C22×C4⋊C4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenter#1569D61
hypocenterC61#17799
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
4. #21444586C2semidirect
5. #21444585C2semidirect
6. #21444583C2semidirect
7. #21444580C2semidirect
8. #21444579C2semidirect
9. #21444577C2semidirect
10. #21444576C2semidirect
11. #21444570C2semidirect
12. #21444568C2semidirect
13. #21444564C2semidirect
14. #335×D61C2semidirect
15. C61×#1569C2semidirect
208. #11758189M16semidirect
214. C8×D61M16semidirect
296. #1569D61semidirect
362. C61#17799semidirect

Maximal subgroups

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

subgroupindex
#214549382
#214549332
C4×#145197852
#214445862
#214445852
#214445832
#214445802
#214445792
#214445772
#214445762
#214445702
#214445682
#214445642
#335×D612
C61×#15692
#1779961