Finite Group Databasebeta

← #29586841

Subgroups — #29586841

Order 15616.

1370 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758201C211yesmaximal, characteristic
2C2×#16839771C211yesmaximal, characteristic, complemented
3C2×#16839768C211yesmaximal, characteristic
4C22×#14519693C211yesmaximal, characteristic
5C2×#16839526C211yesmaximal, characteristic, complemented
6#21445517C211yesmaximal, characteristic, complemented
7C22×#101×C61C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C22×#11758201—22no—
10C22×#11758201—22no—
11C22×#11758201—22no—
12C22×#11758201—22no—
13C22×#11758201—22no—
14C22×#11758201—22no—
15C22×#11758201C414yescomplemented
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19#16839771—22no—
20#16839771—22no—
21#16839768—22no—
22#16839768—22no—
23C2×#14519701—22no—
24C2×#14519699—22no—
25C2×#14519693—22no—
26C2×#14519693—22no—
27C2×#14519693—22no—
28#16839526—22no—
29#16839516—22no—
30C23×Q8×C61C2211yescharacteristic
31C22×M16×C61C2211yescharacteristic
32C22×M16×C61C2211yescharacteristic
33C2×#101×C61—22no—
34C2×#101×C61—22no—
35C2×#101×C61—22no—
36C24×D61—21no—
37C22×D244—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—21no—
48C22×D244C2×C412yes—
49C22×D244D412yes—
50C22×D244D412yes—
51C2×#11758201—28no—
52C2×#11758201—28no—
53C2×#11758201—28no—
54C2×#11758201—28no—
55C2×#11758201—28no—
56C2×#11758201—28no—
57C2×#11758201—28no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194—21no—
63C2×#11758194D412yes—
64C22×#92418—21no—
65C22×#92418—21no—
66C22×#92418—21no—
67C22×#92418—21no—
68C22×#92418—21no—
69C22×#92418C2×C412yes—
70C22×#92418D412yes—
71C22×#92418D412yes—
72#14519736—21no—
73#14519736—21no—
74#14519736—21no—
75#14519736—21no—
76C2×C4⋊Dic61D412yes—
77C2×C22⋊Dic61—21no—
78C2×C4×Dic61—21no—
79#14519701—28no—
80#14519699—28no—
81#14519693—28no—
82C22×Q8×C61—21no—
83C22×Q8×C61—21no—
84C22×Q8×C61—21no—
85C22×Q8×C61—21no—
86C22×Q8×C61—21no—
87C22×Q8×C61—21no—
88C22×Q8×C61—21no—
89C22×Q8×C61—21no—
90C22×Q8×C61—21no—
91C22×Q8×C61—21no—
92C22×Q8×C61—21no—
93C22×Q8×C61C2×C412yes—
94C22×Q8×C61D412yes—
95C22×Q8×C61D412yes—
96C23×C4×C61—21no—
97C23×C4×C61C2311yescharacteristic
98C2×M16×C61—21no—
99C2×M16×C61—21no—
100C2×M16×C61—21no—
101C2×M16×C61—21no—
102C2×M16×C61—21no—
103C2×M16×C61—21no—
104C2×M16×C61—21no—
105C2×M16×C61—21no—
106C2×M16×C61—21no—
107C2×M16×C61—21no—
108C2×M16×C61D412yes—
109C2×M16×C61D412yes—
110C22×C8×C61—21no—
111C22×C8×C61—21no—
112#101×C61—28no—
113C24×C61#4111yescharacteristic
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—41no—
118C23×D61—41no—
119C23×D61—41no—
120C23×D61—41no—
121C23×D61—84no—
122C2×Q8×C61—22no—
123C2×Q8×C61—22no—
124C2×Q8×C61—22no—
125C2×Q8×C61—22no—
126C2×Q8×C61—22no—
127C2×Q8×C61—22no—
128C2×Q8×C61—22no—
129C2×Q8×C61—22no—
130C2×Q8×C61—22no—
131C2×Q8×C61—22no—
132C2×Q8×C61—22no—
133C2×Q8×C61—22no—
134C2×Q8×C61—22no—
135C2×Q8×C61—22no—
136C2×Q8×C61—22no—
137C2×Q8×C61—41no—
138C2×Q8×C61—41no—
139C2×Q8×C61—41no—
140C2×Q8×C61—41no—
141C2×Q8×C61—41no—
142C2×Q8×C61—41no—
143C2×Q8×C61—41no—
144C2×Q8×C61—41no—
145C2×Q8×C61—41no—
146C2×Q8×C61—41no—
147C2×Q8×C61—41no—
148C2×Q8×C61—41no—
149C2×Q8×C61C22⋊C414yes—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—41no—
154C22×C4×C61—41no—
155C22×C4×C61—41no—
156C22×C4×C61—41no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61#4111yescharacteristic
169C22×C4×C61#4111yescharacteristic
170C22×C4×C61#4111yescharacteristic
171C22×Dic61—22no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—41no—
188C2×D244—41no—
189C2×D244—41no—
190C2×D244—41no—
191C2×D244—41no—
192C2×D244—41no—
193C2×D244—41no—
194C2×D244—41no—
195C2×D244—41no—
196C2×D244—41no—
197C2×D244—41no—
198C2×D244—41no—
199C2×D244C22⋊C414yes—
200M16×C61—22no—
201M16×C61—22no—
202M16×C61—22no—
203M16×C61—22no—
204M16×C61—41no—
205M16×C61—41no—
206M16×C61—41no—
207M16×C61—41no—
208C2×C8×C61—22no—
209C2×C8×C61—22no—
210C2×C8×C61—41no—
211C2×C8×C61—41no—
212C2×C8×C61—41no—
213C2×C8×C61—41no—
214C22⋊Dic61—41no—
215C22⋊Dic61—41no—
216#11758201—232no—
217C4⋊Dic61—22no—
218C4⋊Dic61—22no—
219C4×Dic61—41no—
220C4×Dic61—41no—
221#11758194—22no—
222#11758194—22no—
223#11758194—41no—
224#11758194—41no—
225C2×#92418—22no—
226C2×#92418—22no—
227C2×#92418—22no—
228C2×#92418—22no—
229C2×#92418—22no—
230C2×#92418—22no—
231C2×#92418—22no—
232C2×#92418—41no—
233C2×#92418—41no—
234C2×#92418C22⋊C414yes—
235C23×C61—24no—
236C23×C61C4×D411yescharacteristic
237C23×C61#12111yescharacteristic
238C23×C61#12111yescharacteristic
239C23×C61#12111yescharacteristic
240C23×C61#12311yescharacteristic
241C23×C61#12311yescharacteristic
242C23×C61#12411yescharacteristic
243C22×D61—24no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—42no—
250C22×D61—84no—
251C22×D61—84no—
252C22×D61—84no—
253C22×D61—84no—
254C22×D61—84no—
255C22×D61—84no—
256C22×D61—84no—
257Q8×C61—24no—
258Q8×C61—24no—
259Q8×C61—42no—
260Q8×C61—42no—
261Q8×C61—42no—
262Q8×C61—42no—
263Q8×C61—42no—
264Q8×C61—42no—
265C2×C4×C61—24no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—42no—
272C2×C4×C61C2×C22⋊C411yescharacteristic
273C2×C4×C61C2×C22⋊C411yescharacteristic
274C2×C4×C61C2×C22⋊C411yescharacteristic
275C2×C4×C61C4×D411yescharacteristic
276C2×C4×C61C4×D411yescharacteristic
277C2×C4×C61C4×D411yescharacteristic
278C2×C4×C61#12011yescharacteristic
279C2×C4×C61#12011yescharacteristic
280C2×C4×C61#12011yescharacteristic
281C2×C4×C61#12011yescharacteristic
282C2×C4×C61#12011yescharacteristic
283C2×C4×C61#12011yescharacteristic
284C2×C4×C61#12011yescharacteristic
285C2×C4×C61#12011yescharacteristic
286C2×C4×C61#12111yescharacteristic
287C2×C4×C61#12111yescharacteristic
288C2×C4×C61#12111yescharacteristic
289C2×C4×C61#12111yescharacteristic
290C2×C4×C61#12111yescharacteristic
291C2×C4×C61#12111yescharacteristic
292C2×C4×C61#12111yescharacteristic
293C2×C4×C61#12111yescharacteristic
294C2×C4×C61#12111yescharacteristic
295C2×C4×C61#12311yescharacteristic
296C2×C4×C61#12311yescharacteristic
297C2×C4×C61#12411yescharacteristic
298C2×C4×C61#12711yescharacteristic
299C2×C4×C61#12711yescharacteristic
300C2×Dic61—42no—
301C2×Dic61—44no—
302D244—24no—
303D244—24no—
304D244—42no—
305D244—42no—
306D244—42no—
307D244—42no—
308D244—42no—
309D244—42no—
310C8×C61—42no—
311C8×C61—42no—
312#92418—24no—
313#92418—42no—
314#11028—611nomaximal, Sylow
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—22no—
321C22×C61#38611yescharacteristic
322C22×C61#38611yescharacteristic
323C22×C61#39011yescharacteristic
324C22×C61#39211yescharacteristic
325C22×C61#39411yescharacteristic
326C22×C61#39411yescharacteristic
327C22×C61#39411yescharacteristic
328C22×C61#47114yes—
329C2×D61—44no—
330C2×D61—84no—
331C2×D61—84no—
332C2×D61—84no—
333C2×D61—84no—
334C2×D61—84no—
335C2×D61—84no—
336C2×D61—84no—
337C4×C61—44no—
338C4×C61#37911yescharacteristic
339C4×C61#38611yescharacteristic
340C4×C61#38611yescharacteristic
341C4×C61#39011yescharacteristic
342C4×C61#39211yescharacteristic
343C4×C61#39211yescharacteristic
344C4×C61#39211yescharacteristic
345C4×C61#39411yescharacteristic
346Dic61—82no—
347C23×SD16—611no—
348C2×#419—611no—
349C2×#418—611no—
350C22×#101D6111yescharacteristic, complemented
351C22×#100—611no—
352C2×#341—611no—
353#1729—611no—
354C2×C61—21no—
355C2×C61—21no—
356C2×C61—21no—
357C2×C61—21no—
358C2×C61#143811yescharacteristic
359C2×C61#197712yes—
360C2×C61#201912yes—
361C2×C61#204612yes—
362D61—84no—
363C23×Q8C2×D6111yescharacteristic
364C23×D4—611no—
365C22×SD16—614no—
366C22×SD16—1222no—
367C22×SD16—1222no—
368C22×SD16—1222no—
369C22×SD16—1222no—
370C22×SD16—1222no—
371C22×SD16—1222no—
372C22×M16—611no—
373C22×M16C2×D6111yescharacteristic
374C22×M16C2×D6111yescharacteristic
375C23×C8—611no—
376C2×#117—611no—
377#419—1222no—
378#419—1222no—
379#418—1222no—
380#418—1222no—
381C2×#103—1222no—
382C2×#102—1222no—
383C2×#101—22no—
384C2×#101—22no—
385C2×#101—22no—
386C2×#100—1222no—
387C2×#100—1222no—
388C2×#100—1222no—
389#341—1222no—
390#336—1222no—
391C61#1102811yescharacteristic, complemented, Sylow
392C25—1221no—
393C22×Q8—21no—
394C22×Q8—21no—
395C22×Q8—21no—
396C22×Q8—21no—
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8—21no—
400C22×Q8—21no—
401C22×Q8—21no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×Q8C4×D6112yes—
405C22×Q8D24412yes—
406C22×Q8C22⋊D6112yes—
407C22×D4—612no—
408C22×D4—612no—
409C22×D4—612no—
410C22×D4—1221no—
411C22×D4—1221no—
412C22×D4—1221no—
413C22×D4—1221no—
414C22×D4—1221no—
415C22×D4—1221no—
416C22×D4—1221no—
417C22×D4—1221no—
418C22×D4—1221no—
419C22×D4—1221no—
420C22×D4—1221no—
421C23×C4—21no—
422C23×C4C22×D6111yescharacteristic
423C2×SD16—1228no—
424C2×SD16—1228no—
425C2×SD16—1228no—
426C2×SD16—1228no—
427C2×SD16—1228no—
428C2×SD16—1228no—
429C2×SD16—1228no—
430C2×M16—21no—
431C2×M16—21no—
432C2×M16—21no—
433C2×M16—21no—
434C2×M16—21no—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—612no—
441C2×M16—1221no—
442C2×M16—1221no—
443C2×M16—1221no—
444C2×M16—1221no—
445C2×M16—1221no—
446C2×M16C22⋊D6112yes—
447C2×M16C22⋊D6112yes—
448C22×C8—21no—
449C22×C8—21no—
450C22×C8—612no—
451C22×C8—612no—
452C22×C8—612no—
453C22×C8—1221no—
454C22×C8—1221no—
455C22×C8—1221no—
456C22×C8—1221no—
457C22×C8—1221no—
458#117—1221no—
459#117—1221no—
460#117—1221no—
461#117—1221no—
462C2×C4⋊C4—612no—
463C2×C22⋊C4—1221no—
464C2×C42—1221no—
465#103—1228no—
466#102—1228no—
467#101—28no—
468#100—1228no—
469C24—1222no—
470C24—1222no—
471C24—1222no—
472C24—4884no—
473C24—2441no—
474C24—2441no—
475C24—2441no—
476C24—2441no—
477C24#1175822211yescharacteristic
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8#1175819814yes—
506C2×D4—614no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1222no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—1222no—
519C2×D4—1222no—
520C2×D4—1222no—
521C2×D4—1222no—
522C2×D4—2441no—
523C2×D4—2441no—
524C2×D4—2441no—
525C2×D4—2441no—
526C2×D4—2441no—
527C2×D4—2441no—
528C2×D4—2441no—
529C2×D4—2441no—
530C2×D4—2441no—
531C2×D4—2441no—
532C2×D4—2441no—
533C2×D4—2441no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—1222no—
542C22×C4C2×C4×D6111yescharacteristic
543C22×C4C2×D24411yescharacteristic
544C22×C4#1175822211yescharacteristic
545C22×C4D4×D6111yescharacteristic
546C22×C4D4×D6111yescharacteristic
547C22×C4D4×D6111yescharacteristic
548C22×C4D4×D6111yescharacteristic
549C22×C4D4×D6111yescharacteristic
550C22×C4D4×D6111yescharacteristic
551C22×C4#1175822411yescharacteristic
552C22×C4#1175822411yescharacteristic
553C22×C4C2×C22⋊D6111yescharacteristic
554C22×C4C2×C22⋊D6111yescharacteristic
555C22×C4C2×C22⋊D6111yescharacteristic
556SD16—12232no—
557M16—22no—
558M16—22no—
559M16—22no—
560M16—22no—
561M16—41no—
562M16—41no—
563M16—41no—
564M16—41no—
565M16—1222no—
566M16—1222no—
567M16—2441no—
568M16—2441no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—614no—
576C2×C8—1222no—
577C2×C8—1222no—
578C2×C8—1222no—
579C2×C8—1222no—
580C2×C8—1222no—
581C2×C8—1222no—
582C2×C8—1222no—
583C2×C8—2441no—
584C2×C8—2441no—
585C4⋊C4—1222no—
586C4⋊C4—1222no—
587C22⋊C4—2441no—
588C22⋊C4—2441no—
589C42—2441no—
590C42—2441no—
591C23—24no—
592C23—1224no—
593C23—4884no—
594C23—4884no—
595C23—4884no—
596C23—4884no—
597C23—4884no—
598C23—4884no—
599C23—4884no—
600C23—2442no—
601C23—2442no—
602C23—2442no—
603C23—2442no—
604C23—2442no—
605C23—2442no—
606C23C4×C22⋊D6111yescharacteristic
607C23#1451975011yescharacteristic
608C23#1451975011yescharacteristic
609C23#1451975111yescharacteristic
610C23#1451975911yescharacteristic
611C23#1451976011yescharacteristic
612C23#1451976311yescharacteristic
613Q8—24no—
614Q8—24no—
615Q8—42no—
616Q8—42no—
617Q8—42no—
618Q8—42no—
619Q8—42no—
620Q8—42no—
621D4—1224no—
622D4—1224no—
623D4—2442no—
624D4—2442no—
625D4—2442no—
626D4—2442no—
627D4—2442no—
628D4—2442no—
629C2×C4—24no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—2444no—
637C2×C4—2442no—
638C2×C4C22⋊C4×D6111yescharacteristic
639C2×C4C22⋊C4×D6111yescharacteristic
640C2×C4C2×#1175819811yescharacteristic
641C2×C4#1451973711yescharacteristic
642C2×C4#1451973711yescharacteristic
643C2×C4C4×C22⋊D6111yescharacteristic
644C2×C4#1451974511yescharacteristic
645C2×C4#1451974511yescharacteristic
646C2×C4#1451974511yescharacteristic
647C2×C4#1451974511yescharacteristic
648C2×C4#1451974611yescharacteristic
649C2×C4#1451974711yescharacteristic
650C2×C4#1451974711yescharacteristic
651C2×C4#1451974711yescharacteristic
652C2×C4#1451974811yescharacteristic
653C2×C4#1451974811yescharacteristic
654C2×C4#1451974911yescharacteristic
655C2×C4#1451974911yescharacteristic
656C2×C4#1451974911yescharacteristic
657C2×C4#1451974911yescharacteristic
658C2×C4#1451975011yescharacteristic
659C2×C4#1451975011yescharacteristic
660C2×C4#1451975111yescharacteristic
661C2×C4#1451975911yescharacteristic
662C2×C4#1451976111yescharacteristic
663C2×C4#1451976311yescharacteristic
664C2×C4#1451977311yescharacteristic
665C2×C4#1451977311yescharacteristic
666C8—42no—
667C8—42no—
668C8—1224no—
669C8—2442no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—4884no—
677C22—4884no—
678C22—4884no—
679C22—4884no—
680C22—4884no—
681C22—4884no—
682C22—4884no—
683C22—2444no—
684C22#1683963811yescharacteristic
685C22#1683964111yescharacteristic
686C22#1683966211yescharacteristic
687C22#1683967111yescharacteristic
688C22#1683967711yescharacteristic
689C22#1683967711yescharacteristic
690C22#1683967811yescharacteristic
691C22#1684002814yes—
692C4—44no—
693C4—4882no—
694C4#1683961711yescharacteristic
695C4#1683963811yescharacteristic
696C4#1683963911yescharacteristic
697C4#1683966211yescharacteristic
698C4#1683967011yescharacteristic
699C4#1683967011yescharacteristic
700C4#1683967111yescharacteristic
701C4#1683967811yescharacteristic
702C2—21no—
703C2—21no—
704C2—21no—
705C2—21no—
706C2—4884no—
707C2#2144405811yescharacteristic
708C2#2144672312yes—
709C2#2144693212yes—
710C2#2144707812yes—
subgroupG/H
centerC23#14519750
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC22×#101×C61C2
socleC23×C61#121
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenterC22×#101D61
hypocenterC61#11028
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
2. C2×#16839771C2semidirect
5. C2×#16839526C2semidirect
6. #21445517C2semidirect
7. C22×#101×C61C2semidirect
15. C22×#11758201C4semidirect
350. C22×#101D61semidirect
391. C61#11028semidirect

Maximal subgroups

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

subgroupindex
C23×#117582012
C2×#168397712
C2×#168397682
C22×#145196932
C2×#168395262
#214455172
C22×#101×C612
#1102861