Finite Group Databasebeta

← #29586519

Subgroups — #29586519

Order 15616.

1922 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519751C211yesmaximal, characteristic
2C22×#14519697C212yesmaximal, complemented
3C22×C22⋊#92418C211yesmaximal, characteristic, complemented
4C2×#16839524C212yesmaximal, complemented
5C2×C61×#380C211yesmaximal, characteristic, complemented
6C23×D244C2211yescharacteristic
7C23×C22⋊D61—21no—
8C23×#92418C2212yes—
9C2×#14519751—24no—
10C2×#14519751—22no—
11C2×#14519751—24no—
12C2×#14519751C414yescomplemented
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758198—21no—
15C2×#14519697—24no—
16C2×#14519697—24no—
17C2×#14519697—24no—
18C2×C22⋊#92418—24no—
19C2×C22⋊#92418—22no—
20#16839524—24no—
21C24×C4×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2212yes—
23C22×C22⋊C4×C61—21no—
24C61×#380—24no—
25C2×#95×C61—21no—
26C24×D61—21no—
27C22×D244—22no—
28C22×D244—22no—
29C22×D244—22no—
30C22×D244—22no—
31C22×D244—21no—
32C22×D244—22no—
33C22×D244C2×C412yes—
34C22×D244D414yes—
35C22×C22⋊D61—28no—
36C22×C22⋊D61—24no—
37C22×C22⋊D61—44no—
38C22×C22⋊D61—42no—
39C22×C22⋊D61—42no—
40C23×Dic61—21no—
41C22×#92418—22no—
42C22×#92418—22no—
43C22×#92418—22no—
44C22×#92418—22no—
45C22×#92418—22no—
46C22×#92418—22no—
47C22×#92418D414yescomplemented
48#14519751—216no—
49#14519751—28no—
50#14519751—28no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61C2×C412yes—
54C2×C4⋊Dic61D414yes—
55C2×#11758198—28no—
56C2×#11758198—24no—
57#14519697—216no—
58C22⋊#92418—28no—
59C25×C61D411yescharacteristic
60C23×C4×C61—22no—
61C23×C4×C61—22no—
62C23×C4×C61—22no—
63C23×C4×C61—22no—
64C23×C4×C61—22no—
65C23×C4×C61—22no—
66C23×C4×C61—22no—
67C23×C4×C61C2×C412yes—
68C23×C4×C61D412yes—
69C23×C4×C61D411yescharacteristic
70C23×C4×C61C2311yescharacteristic
71C2×C4⋊C4×C61—22no—
72C2×C4⋊C4×C61—22no—
73C2×C4⋊C4×C61—22no—
74C2×C4⋊C4×C61—22no—
75C2×C4⋊C4×C61—22no—
76C2×C4⋊C4×C61D414yescomplemented
77C2×C22⋊C4×C61—24no—
78C2×C22⋊C4×C61—42no—
79C2×C22⋊C4×C61—42no—
80#95×C61—24no—
81C24×C61—22no—
82C24×C61—21no—
83C24×C61—22no—
84C24×C61—21no—
85C24×C61—22no—
86C24×C61—22no—
87C24×C61—21no—
88C24×C61—21no—
89C24×C61C22⋊C412yes—
90C24×C61D812yes—
91C24×C61SD1612yes—
92C24×C61C2×D411yescharacteristic
93C23×D61—22no—
94C23×D61—24no—
95C23×D61—41no—
96C23×D61—42no—
97C23×D61—41no—
98C23×D61—41no—
99C23×D61—41no—
100C23×D61—42no—
101C23×D61—42no—
102C23×D61—41no—
103C23×D61—41no—
104C22×C4×C61—21no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—21no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—24no—
111C22×C4×C61—24no—
112C22×C4×C61—22no—
113C22×C4×C61—24no—
114C22×C4×C61—24no—
115C22×C4×C61—22no—
116C22×C4×C61—24no—
117C22×C4×C61—42no—
118C22×C4×C61—42no—
119C22×C4×C61—42no—
120C22×C4×C61—42no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61—42no—
124C22×C4×C61—42no—
125C22×C4×C61—42no—
126C22×C4×C61—42no—
127C22×C4×C61—42no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61C22⋊C412yes—
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61#4112yes—
139C22×C4×C61#4112yes—
140C2×C22⋊D61—216no—
141C2×C22⋊D61—48no—
142C2×C22⋊D61—416no—
143C2×C22⋊D61—416no—
144C2×C22⋊D61—48no—
145C22×Dic61—22no—
146C22×Dic61—24no—
147C22×Dic61—41no—
148C22×Dic61—41no—
149C22×Dic61—42no—
150C2×D244—24no—
151C2×D244—24no—
152C2×D244—24no—
153C2×D244—24no—
154C2×D244—24no—
155C2×D244—24no—
156C2×D244—22no—
157C2×D244—24no—
158C2×D244—41no—
159C2×D244—42no—
160C2×D244—42no—
161C2×D244—42no—
162C2×D244—41no—
163C2×D244—42no—
164C2×D244—42no—
165C2×D244C22⋊C414yescomplemented
166C4⋊C4×C61—24no—
167C4⋊C4×C61—24no—
168C4⋊C4×C61—42no—
169C4⋊C4×C61—42no—
170C22⋊C4×C61—48no—
171#11758198—216no—
172C4⋊Dic61—22no—
173C4⋊Dic61—24no—
174C4⋊Dic61C22⋊C414yescomplemented
175C2×#92418—24no—
176C2×#92418—24no—
177C2×#92418—24no—
178C2×#92418—42no—
179C2×#92418—42no—
180C2×#92418—42no—
181C2×#92418—42no—
182C23×C61—22no—
183C23×C61—22no—
184C23×C61—22no—
185C23×C61—22no—
186C23×C61—22no—
187C23×C61—22no—
188C23×C61—22no—
189C23×C61—24no—
190C23×C61—22no—
191C23×C61—24no—
192C23×C61—24no—
193C23×C61—24no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61—42no—
197C23×C61—42no—
198C23×C61—42no—
199C23×C61—42no—
200C23×C61—42no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61#10214yescomplemented
205C23×C61C2×C22⋊C411yescharacteristic
206C23×C61#12012yes—
207C23×C61#12011yescharacteristic
208C23×C61#12112yes—
209C23×C61#12311yescharacteristic
210C23×C61C2×D811yescharacteristic
211C23×C61C2×SD1611yescharacteristic
212C23×C61#13512yes—
213C23×C61AGL(1,ℤ/8)11yescharacteristic
214C23×C61AGL(1,ℤ/8)12yes—
215C23×C61#13711yescharacteristic
216C22×D61—24no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—44no—
220C22×D61—44no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61—44no—
226C22×D61—44no—
227C22×D61—44no—
228C22×D61—44no—
229C22×D61—81no—
230C22×D61—81no—
231C22×D61—82no—
232C22×D61—82no—
233C22×D61—82no—
234C22×D61—82no—
235C22×D61—82no—
236C22×D61—81no—
237C22×D61—81no—
238C22×D61—82no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—44no—
245C2×C4×C61—44no—
246C2×C4×C61—44no—
247C2×C4×C61—44no—
248C2×C4×C61—44no—
249C2×C4×C61—44no—
250C2×C4×C61—44no—
251C2×C4×C61—82no—
252C2×C4×C61—82no—
253C2×C4×C61—82no—
254C2×C4×C61—82no—
255C2×C4×C61C2×C22⋊C411yescharacteristic
256C2×C4×C61C2×C22⋊C411yescharacteristic
257C2×C4×C61C4×D412yes—
258C2×C4×C61C4×D412yes—
259C2×C4×C61#12012yes—
260C2×C4×C61#12011yescharacteristic
261C2×C4×C61#12012yes—
262C2×C4×C61#12112yes—
263C2×C4×C61#12112yes—
264C2×C4×C61#12112yes—
265C2×C4×C61#12112yes—
266C2×C4×C61#12112yes—
267C2×C4×C61#12312yes—
268C2×C4×C61#12311yescharacteristic
269C2×C4×C61#12412yes—
270C2×C4×C61#12712yes—
271C22⋊D61—432no—
272C2×Dic61—24no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—44no—
276C2×Dic61—44no—
277D244—28no—
278D244—44no—
279D244—44no—
280D244—44no—
281#92418—44no—
282#10969—611nomaximal, Sylow
283C22×C61—24no—
284C22×C61—24no—
285C22×C61—24no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—42no—
289C22×C61—44no—
290C22×C61—44no—
291C22×C61—44no—
292C22×C61—44no—
293C22×C61—42no—
294C22×C61#37911yescharacteristic
295C22×C61#38611yescharacteristic
296C22×C61#38611yescharacteristic
297C22×C61#39212yes—
298C22×C61#39412yes—
299C22×C61C2×#10211yescharacteristic
300C22×C61#41611yescharacteristic
301C22×C61#41711yescharacteristic
302C22×C61#41811yescharacteristic
303C22×C61#44712yes—
304C22×C61#44711yescharacteristic
305C22×C61#44811yescharacteristic
306C22×C61#44912yes—
307C22×C61#44912yes—
308C22×C61#45012yes—
309C22×C61#45212yes—
310C22×C61#46512yes—
311C22×C61#46612yes—
312C22×C61#46812yes—
313C22×C61#46912yes—
314C22×C61#48011yescharacteristic
315C22×C61#48111yescharacteristic
316C22×C61#48212yes—
317C2×D61—44no—
318C2×D61—44no—
319C2×D61—44no—
320C2×D61—82no—
321C2×D61—82no—
322C2×D61—82no—
323C2×D61—82no—
324C2×D61—84no—
325C2×D61—84no—
326C2×D61—84no—
327C2×D61—84no—
328C4×C61—42no—
329C4×C61—84no—
330C4×C61#38612yes—
331C4×C61#39012yes—
332C4×C61#39212yes—
333C4×C61#39412yes—
334Dic61—44no—
335C22×#121—611no—
336C22×#102—612no—
337C22×C22⋊C8—611no—
338C2×#380D6111yescharacteristic, complemented
339C2×#340—612no—
340C2×C61—44no—
341C2×C61#143811yescharacteristic
342C2×C61#178611yescharacteristic
343C2×C61#178811yescharacteristic
344C2×C61#187411yescharacteristic
345C2×C61#187511yescharacteristic
346C2×C61#189311yescharacteristic
347C2×C61#189511yescharacteristic
348C2×C61#199912yes—
349C2×C61#200012yes—
350C2×C61#203312yes—
351C2×C61#203412yes—
352D61—84no—
353C23×D4—611no—
354C23×D4—1221no—
355C24×C4C2×D6111yescharacteristic
356C23×C8—612no—
357C2×#121—614no—
358C2×#121—1224no—
359C2×#121—1224no—
360C2×#121—1222no—
361C22×C4⋊C4—611no—
362C22×C4⋊C4C2×D6112yes—
363C22×C22⋊C4—21no—
364C22×C22⋊C4—1221no—
365C2×#102—1224no—
366C2×#102—1224no—
367C2×#102—1224no—
368C2×C22⋊C8—1224no—
369C2×C22⋊C8—1222no—
370#380—24no—
371C2×#95—21no—
372#340—1224no—
373C61#1096911yescharacteristic, complemented, Sylow
374C25—1221no—
375C25C22⋊D6111yescharacteristic
376C22×D4—612no—
377C22×D4—614no—
378C22×D4—1228no—
379C22×D4—1224no—
380C22×D4—1221no—
381C22×D4—1222no—
382C22×D4—1222no—
383C22×D4—1222no—
384C22×D4—1222no—
385C22×D4—1222no—
386C22×D4—2444no—
387C22×D4—2442no—
388C22×D4—2442no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—1221no—
397C23×C4C4×D6112yes—
398C23×C4D24412yes—
399C23×C4C22⋊D6111yescharacteristic
400C23×C4C22×D6111yescharacteristic
401C22×C8—614no—
402C22×C8—1222no—
403C22×C8—1222no—
404C22×C8—1222no—
405C22×C8—1222no—
406C22×C8—1222no—
407C22×C8—1222no—
408#121—1228no—
409#121—1228no—
410#121—12216no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—612no—
417C2×C4⋊C4—614no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1222no—
420C2×C4⋊C4C22⋊D6114yescomplemented
421C2×C22⋊C4—24no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—1228no—
425C2×C22⋊C4—1224no—
426#102—12216no—
427C22⋊C8—1228no—
428#95—24no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—22no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—1222no—
438C24—1224no—
439C24—2441no—
440C24—2441no—
441C24—2442no—
442C24—2441no—
443C24—2441no—
444C24—2441no—
445C24—2442no—
446C24—2442no—
447C24—2441no—
448C24#1175819812yes—
449C24#1175819912yes—
450C24#1175820112yes—
451C24C2×C22⋊D6111yescharacteristic
452C2×D4—614no—
453C2×D4—12216no—
454C2×D4—1222no—
455C2×D4—1224no—
456C2×D4—1224no—
457C2×D4—1224no—
458C2×D4—1224no—
459C2×D4—1224no—
460C2×D4—1224no—
461C2×D4—1224no—
462C2×D4—2448no—
463C2×D4—24416no—
464C2×D4—24416no—
465C2×D4—2448no—
466C2×D4—2441no—
467C2×D4—2442no—
468C2×D4—2442no—
469C2×D4—2442no—
470C2×D4—2441no—
471C2×D4—2442no—
472C2×D4—2442no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—1222no—
501C22×C4—1224no—
502C22×C4—2441no—
503C22×C4—2441no—
504C22×C4—2442no—
505C22×C4#1175819812yes—
506C22×C4C2×C4×D6111yescharacteristic
507C22×C4C2×D24411yescharacteristic
508C22×C4#1175822212yes—
509C22×C4D4×D6112yes—
510C22×C4D4×D6112yes—
511C22×C4D4×D6112yes—
512C22×C4#1175822412yes—
513C22×C4C2×C22⋊D6112yes—
514C2×C8—1224no—
515C2×C8—1224no—
516C2×C8—1224no—
517C2×C8—2442no—
518C2×C8—2442no—
519C2×C8—2442no—
520C2×C8—2442no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—614no—
526C4⋊C4—1222no—
527C4⋊C4—1224no—
528C22⋊C4—48no—
529C22⋊C4—12216no—
530C23—24no—
531C23—24no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—24no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—24no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—1224no—
553C23—4882no—
554C23—4882no—
555C23—4882no—
556C23—4882no—
557C23—4881no—
558C23—4881no—
559C23—4882no—
560C23—4881no—
561C23—4881no—
562C23—4882no—
563C23—2442no—
564C23—2442no—
565C23—2442no—
566C23—2442no—
567C23—2442no—
568C23—2444no—
569C23—2442no—
570C23—2444no—
571C23—2444no—
572C23—2444no—
573C23—2444no—
574C23—2444no—
575C23#1451969714yescomplemented
576C23C2×#1175819811yescharacteristic
577C23#1451974512yes—
578C23#1451974611yescharacteristic
579C23#1451974912yes—
580C23#1451976011yescharacteristic
581C23C2×#1175819911yescharacteristic
582C23C2×#1175820111yescharacteristic
583C23#1451979712yes—
584C23#1451980212yes—
585C23#1451980311yescharacteristic
586C23#1451980811yescharacteristic
587D4—1228no—
588D4—24432no—
589D4—2444no—
590D4—2444no—
591D4—2444no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4—1224no—
609C2×C4—2442no—
610C2×C4—2442no—
611C2×C4—2444no—
612C2×C4—2444no—
613C2×C4C22⋊C4×D6111yescharacteristic
614C2×C4C22⋊C4×D6111yescharacteristic
615C2×C4#1451973712yes—
616C2×C4C4×C22⋊D6112yes—
617C2×C4#1451974512yes—
618C2×C4#1451974711yescharacteristic
619C2×C4#1451974712yes—
620C2×C4#1451974812yes—
621C2×C4#1451974912yes—
622C2×C4#1451975012yes—
623C2×C4#1451975012yes—
624C2×C4#1451975112yes—
625C2×C4#1451975912yes—
626C2×C4#1451976111yescharacteristic
627C2×C4#1451976312yes—
628C2×C4#1451977312yes—
629C8—2444no—
630C22—24no—
631C22—24no—
632C22—24no—
633C22—44no—
634C22—44no—
635C22—42no—
636C22—42no—
637C22—44no—
638C22—44no—
639C22—42no—
640C22—42no—
641C22—4884no—
642C22—4884no—
643C22—4882no—
644C22—4882no—
645C22—4884no—
646C22—4884no—
647C22—4882no—
648C22—4882no—
649C22—2444no—
650C22—2444no—
651C22—2444no—
652C22#1683961711yescharacteristic
653C22#1683963911yescharacteristic
654C22#1683964111yescharacteristic
655C22#1683967012yes—
656C22#1683967712yes—
657C22C2×#1451969711yescharacteristic
658C22#1683975611yescharacteristic
659C22#1683976111yescharacteristic
660C22#1683976611yescharacteristic
661C22#1683989512yes—
662C22#1683989611yescharacteristic
663C22#1683990111yescharacteristic
664C22#1683990512yes—
665C22#1683990712yes—
666C22#1683991212yes—
667C22#1683992212yes—
668C22#1683999312yes—
669C22#1683999612yes—
670C22#1684001012yes—
671C22#1684001312yes—
672C22#1684007511yescharacteristic
673C22#1684008011yescharacteristic
674C22#1684008612yes—
675C4—42no—
676C4—84no—
677C4—2444no—
678C4#1683963812yes—
679C4#1683966212yes—
680C4#1683967112yes—
681C4#1683967812yes—
682C2—44no—
683C2—4884no—
684C2#2144405811yescharacteristic
685C2#2144574911yescharacteristic
686C2#2144575711yescharacteristic
687C2#2144613611yescharacteristic
688C2#2144614111yescharacteristic
689C2#2144624511yescharacteristic
690C2#2144625511yescharacteristic
691C2#2144681512yes—
692C2#2144682012yes—
693C2#2144700112yes—
694C2#2144700812yes—
subgroupG/H
centerC24C2×C22⋊D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#380C2
socleC24×C61C2×D4
prime radicalC22×#14519751C2
cosocleC23×C4×C61C23
hypercenterC2×#380D61
hypocenterC61#10969
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#14519697C2semidirect
3. C22×C22⋊#92418C2semidirect
4. C2×#16839524C2semidirect
5. C2×C61×#380C2semidirect
12. C2×#14519751C4semidirect
47. C22×#92418D4semidirect
76. C2×C4⋊C4×C61D4semidirect
165. C2×D244C22⋊C4semidirect
174. C4⋊Dic61C22⋊C4semidirect
204. C23×C61#102semidirect
338. C2×#380D61semidirect
373. C61#10969semidirect
420. C2×C4⋊C4C22⋊D61semidirect
575. C23#14519697semidirect

Maximal subgroups

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

subgroupindex
C22×#145197512
C22×#145196972
C22×C22⋊#924182
C2×#168395242
C2×C61×#3802
#1096961