Finite Group Databasebeta

← #29575413

Subgroups — #29575413

Order 15616.

928 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839724C211yesmaximal, characteristic
2C2×#16839636C211yesmaximal, characteristic
3#21445728C211yesmaximal, characteristic
4C2×#16839487C211yesmaximal, characteristic, complemented
5C2×#16839487C211yesmaximal, characteristic, complemented
6#21443662C211yesmaximal, characteristic, complemented
7C61×#1280C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758189—21no—
10C22×C4⋊Dic61C411yescharacteristic
11C22×#11758196C2211yescharacteristic
12C22×#11758198C411yescharacteristic
13C22×#11758198C411yescharacteristic
14#16839724—22no—
15#16839724—22no—
16C2×C22⋊#92418C2211yescharacteristic
17C2×C22⋊#92418C2211yescharacteristic
18C2×#14519689—21no—
19C2×#14519689—21no—
20C2×#14519689—21no—
21#16839636—21no—
22#16839636—21no—
23#16839636—21no—
24#16839636—21no—
25C2×#14519684C411yescharacteristic
26#16839487—22no—
27#16839487—22no—
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C24×D61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2×C411yescharacteristic
34C23×Dic61C2×C411yescharacteristic
35C22×C4×D61—21no—
36C22×C4×D61—21no—
37C22×C4×D61—21no—
38C22×C4×D61—21no—
39C22×C4×D61—42no—
40C22×C4×D61—42no—
41C22×C4×D61D411yescharacteristic
42C22×C4×D61D411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C2×#11758189—24no—
46C2×#11758189—42no—
47C2×#11758189—42no—
48C22×#92418—21no—
49C22×#92418—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—42no—
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×#11758196—21no—
56C2×#11758196—21no—
57C2×#11758196—21no—
58C2×#11758196—21no—
59C2×#11758198—21no—
60C2×#11758198—21no—
61C2×#11758198—22no—
62C2×#11758198—22no—
63C2×#11758198—21no—
64C2×#11758198—21no—
65C2×#11758198—42no—
66C22⋊#92418—21no—
67C22⋊#92418—21no—
68C22⋊#92418—21no—
69C22⋊#92418D412yes—
70#14519689—24no—
71#14519689—42no—
72#14519689—42no—
73#14519684—21no—
74#14519684—21no—
75C23×C4×C61C2×C411yescharacteristic
76C23×C4×C61C2×C411yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C22×C8×C61—21no—
79C22×C8×C61—21no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61—21no—
82C22⋊C8×C61—21no—
83C22⋊C8×C61D412yes—
84#95×C61—21no—
85#95×C61—21no—
86C24×C61C22×C411yescharacteristic
87C23×D61—21no—
88C23×D61—21no—
89C23×D61—22no—
90C23×D61—22no—
91C23×D61—21no—
92C23×D61—21no—
93C23×D61—21no—
94C23×D61—21no—
95C23×D61—41no—
96C23×D61—41no—
97C23×D61C22⋊C411yescharacteristic
98C23×D61C22⋊C411yescharacteristic
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61—41no—
107C22×C4×C61—41no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61M1612yescomplemented
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×Dic61—21no—
118C22×Dic61—21no—
119C22×Dic61—21no—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—22no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—41no—
130C22×Dic61—41no—
131C22×Dic61—41no—
132C22×Dic61C22⋊C411yescharacteristic
133C22×Dic61C22⋊C411yescharacteristic
134C22×Dic61M1612yescomplemented
135C2×C4×D61—22no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—22no—
147C2×C4×D61—44no—
148C2×C4×D61—44no—
149C2×C4×D61—44no—
150C2×C4×D61—44no—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×C8×C61—22no—
156C2×C8×C61—41no—
157C2×C8×C61—41no—
158C2×C8×C61—41no—
159C2×C8×C61—41no—
160C2×C8×C61—41no—
161#11758198—24no—
162#11758198—24no—
163#11758198—42no—
164#11758198—42no—
165C4⋊Dic61—42no—
166C4⋊Dic61—42no—
167#11758196—41no—
168#11758196—41no—
169#11758196—41no—
170#11758196—41no—
171C2×#92418—22no—
172C2×#92418—41no—
173C2×#92418—41no—
174C2×#92418—41no—
175C2×#92418—41no—
176C2×#92418—41no—
177#11758189—48no—
178C23×C61—21no—
179C23×C61—21no—
180C23×C61—21no—
181C23×C61—21no—
182C23×C61C2×C22⋊C411yescharacteristic
183C23×C61C4×D411yescharacteristic
184C23×C61C4×D411yescharacteristic
185C23×C61C2×M1611yescharacteristic
186C23×C61C2×M1611yescharacteristic
187C23×C61#13111yescharacteristic
188C23×C61#13111yescharacteristic
189C22×D61—24no—
190C22×D61—24no—
191C22×D61—21no—
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—21no—
201C22×D61—21no—
202C22×D61—21no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61#9912yes—
218C22×D61#10112yes—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—22no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—42no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—42no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—81no—
236C2×C4×C61—81no—
237C2×C4×C61#12011yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12311yescharacteristic
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—22no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—81no—
259C2×Dic61—81no—
260C2×Dic61#9912yes—
261C4×D61—24no—
262C4×D61—24no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—42no—
266C4×D61—42no—
267C4×D61—42no—
268C4×D61—42no—
269C8×C61—42no—
270C8×C61—81no—
271#92418—42no—
272#92418—81no—
273#9085—611nomaximal, Sylow
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61#38611yescharacteristic
287C22×C61#40711yescharacteristic
288C22×C61#40811yescharacteristic
289C22×C61C2×#9911yescharacteristic
290C22×C61C2×#9911yescharacteristic
291C22×C61C2×#10111yescharacteristic
292C22×C61#41311yescharacteristic
293C22×C61#43511yescharacteristic
294C22×C61#43511yescharacteristic
295C22×C61#43611yescharacteristic
296C22×C61#43611yescharacteristic
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—44no—
304C2×D61—44no—
305C2×D61—44no—
306C2×D61—44no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—41no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61—42no—
320C4×C61—81no—
321Dic61—22no—
322Dic61—42no—
323Dic61—41no—
324Dic61—81no—
325C2×#407—611no—
326C2×#385—611no—
327#1779—611no—
328C2×#324—611no—
329C2×#324—611no—
330#1280—611no—
331#1280D6111yescharacteristic, complemented
332C2×C61—21no—
333C2×C61—21no—
334C2×C61—21no—
335C2×C61—21no—
336C2×C61#146311yescharacteristic
337C2×C61#146511yescharacteristic
338C2×C61#146811yescharacteristic
339C2×C61#147211yescharacteristic
340C2×C61#187011yescharacteristic
341C2×C61#189811yescharacteristic
342C2×C61#190111yescharacteristic
343D61—42no—
344D61—42no—
345C24×C4—611no—
346C22×M16—1221no—
347C22×C4⋊C4—611no—
348C22×C4⋊C4—611no—
349C22×C22⋊C4—611no—
350C22×C22⋊C4—611no—
351#407—1222no—
352#407—1222no—
353C2×C22⋊C8—611no—
354C2×C22⋊C8—611no—
355C2×C22⋊C8—1221no—
356C2×C22⋊C8—1221no—
357C2×C22⋊C8—1221no—
358C2×C22⋊C8C2×D6111yescharacteristic
359C2×C22⋊C8C2×D6111yescharacteristic
360#385—1221no—
361#385—1221no—
362#385—1221no—
363#385—1221no—
364C2×#95—611no—
365C2×#95C2×D6111yescharacteristic
366#324—1222no—
367#324—1222no—
368C61#908511yescharacteristic, complemented, Sylow
369C25—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—1221no—
378C23×C4—1221no—
379C23×C4—1221no—
380C23×C4—1221no—
381C23×C4—2442no—
382C23×C4—2442no—
383C23×C4C4×D6111yescharacteristic
384C23×C4C4×D6111yescharacteristic
385C23×C4C22×D6111yescharacteristic
386C2×M16—1224no—
387C2×M16—2442no—
388C2×M16—2442no—
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—1221no—
392C22×C8—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—2442no—
402C2×C22⋊C4—1222no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1222no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—2442no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—612no—
413C22⋊C8—1224no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—2442no—
418C22⋊C8—2442no—
419C22⋊C8D24412yes—
420#95—21no—
421#95—21no—
422#95—1221no—
423#95—1221no—
424C24—611no—
425C24—611no—
426C24—1222no—
427C24—1222no—
428C24—1221no—
429C24—1221no—
430C24—1221no—
431C24—1221no—
432C24—1221no—
433C24—1221no—
434C24—2441no—
435C24—2441no—
436C24C2×C4×D6111yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—612no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—2441no—
476C22×C4—2441no—
477C22×C4—2441no—
478C22×C4—2441no—
479C22×C4—2444no—
480C22×C4—2444no—
481C22×C4—2444no—
482C22×C4—2444no—
483C22×C4—2441no—
484C22×C4—2441no—
485C22×C4—2441no—
486C22×C4#1175818912yescomplemented
487C22×C4C2×D24411yescharacteristic
488C22×C4#1175822211yescharacteristic
489C22×C4D4×D6111yescharacteristic
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4#1175822611yescharacteristic
493M16—2448no—
494C2×C8—22no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—1222no—
501C2×C8—2441no—
502C2×C8—2441no—
503C2×C8—2441no—
504C2×C8—2441no—
505C2×C8—2441no—
506C4⋊C4—2442no—
507C4⋊C4—2442no—
508C4⋊C4—2441no—
509C4⋊C4—2441no—
510C4⋊C4—2441no—
511C4⋊C4—2441no—
512C22⋊C4—1224no—
513C22⋊C4—1224no—
514C22⋊C4—2442no—
515C22⋊C4—2442no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—612no—
521C23—612no—
522C23—1224no—
523C23—1224no—
524C23—1221no—
525C23—1221no—
526C23—1221no—
527C23—1221no—
528C23—1221no—
529C23—1221no—
530C23—1221no—
531C23—1221no—
532C23—1221no—
533C23—1221no—
534C23—1221no—
535C23—1221no—
536C23—2442no—
537C23—2442no—
538C23—2442no—
539C23—2442no—
540C23—2442no—
541C23—2442no—
542C23—2442no—
543C23—2442no—
544C23—2442no—
545C23—2442no—
546C23—2441no—
547C23—2441no—
548C23—2441no—
549C23—2441no—
550C23C22⋊C4×D6111yescharacteristic
551C23#1451973911yescharacteristic
552C23C4×D24411yescharacteristic
553C23M16×D6111yescharacteristic
554C23C2×#1175818911yescharacteristic
555C23#1451978311yescharacteristic
556C23#1451978511yescharacteristic
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—81no—
574C2×C4—81no—
575C2×C4—612no—
576C2×C4—1224no—
577C2×C4—1224no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1222no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1221no—
586C2×C4—4881no—
587C2×C4—4881no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4#1451974711yescharacteristic
604C2×C4#1451975011yescharacteristic
605C2×C4#1451975211yescharacteristic
606C2×C4#1451976211yescharacteristic
607C8—42no—
608C8—81no—
609C8—4881no—
610C8—2442no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—1222no—
624C22—1222no—
625C22—1222no—
626C22—1222no—
627C22—1222no—
628C22—1222no—
629C22—2444no—
630C22—2444no—
631C22—2444no—
632C22—2444no—
633C22—2441no—
634C22—2441no—
635C22—2441no—
636C22—2441no—
637C22—2441no—
638C22—2441no—
639C22—2441no—
640C22—2441no—
641C22#1683964011yescharacteristic
642C22#1683972411yescharacteristic
643C22#1683972711yescharacteristic
644C22#99×D6111yescharacteristic
645C22#99×D6111yescharacteristic
646C22#101×D6111yescharacteristic
647C22#1683974311yescharacteristic
648C22#1683983211yescharacteristic
649C22#1683983511yescharacteristic
650C22#1683983911yescharacteristic
651C22#1683984111yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—81no—
658C4—1222no—
659C4—4881no—
660C4—2441no—
661C4—2442no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—2442no—
667C2—2442no—
668C2#2144414711yescharacteristic
669C2#2144415411yescharacteristic
670C2#2144416411yescharacteristic
671C2#2144418111yescharacteristic
672C2#2144611511yescharacteristic
673C2#2144627111yescharacteristic
674C2#2144628611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1280D61
hypocenterC61#9085
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
4. C2×#16839487C2semidirect
5. C2×#16839487C2semidirect
6. #21443662C2semidirect
7. C61×#1280C2semidirect
110. C22×C4×C61M16semidirect
134. C22×Dic61M16semidirect
331. #1280D61semidirect
368. C61#9085semidirect
486. C22×C4#11758189semidirect

Maximal subgroups

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

subgroupindex
C2×#168397242
C2×#168396362
#214457282
C2×#168394872
#214436622
C61×#12802
#908561