Finite Group Databasebeta

← #30603012

Subgroups — #30603012

Order 15616.

1354 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519839C212yesmaximal
2C2×C4×C4⋊#6923C211yesmaximal, characteristic, complemented
3C2×#16840635C212yesmaximal, complemented
4#21461480C211yesmaximal, characteristic, complemented
5#390×D61C211yesmaximal, characteristic
6C22×D61⋊C8C2212yes—
7C22×C4⋊#6923C2212yes—
8C22×C4×#6923—21no—
9C2×#14519839—24no—
10C2×#14519839—24no—
11C2×#14519839C418yescomplemented
12C4×C4⋊#6923—24no—
13C2×(C2×#6923)⋊C4—21no—
14#16840635—24no—
15#16840628—21no—
16#16840628—21no—
17C22×D4×D61C2211yescharacteristic
18C2×C4⋊C4×D61C2211yescharacteristic
19C2×C22⋊C4×D61—21no—
20C2×C22⋊C4×D61—21no—
21C2×C42×D61C2211yescharacteristic
22#16839665C411yescharacteristic, complemented
23#16839664C411yescharacteristic, complemented
24#16839663C411yescharacteristic, complemented
25#16839662—21no—
26#16839662—21no—
27C61×#390C411yescharacteristic, complemented
28C23×#6923—22no—
29C2×D61⋊C8—22no—
30C2×D61⋊C8—22no—
31C2×D61⋊C8—22no—
32C2×D61⋊C8—22no—
33C2×D61⋊C8—22no—
34C2×D61⋊C8C2×C414yes—
35C22×#92420—22no—
36C2×C4⋊#6923—22no—
37C2×C4⋊#6923—22no—
38C2×C4⋊#6923—22no—
39C2×C4⋊#6923C2×C414yes—
40C2×C4⋊#6923D414yes—
41C2×C4⋊#6923D414yes—
42C2×C4×#6923—24no—
43C2×C4×#6923—42no—
44C2×C4×#6923—42no—
45#14519839—216no—
46(C2×#6923)⋊C4—24no—
47C24×D61—21no—
48C22×D244C2×C411yescharacteristic
49C22×C22⋊D61—21no—
50C2×D4×D61—22no—
51C2×D4×D61—22no—
52C2×D4×D61—22no—
53C2×D4×D61—22no—
54C2×D4×D61—22no—
55C2×D4×D61C2×C414yes—
56C22×C4×D61—21no—
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×C4⋊Dic61C2×C411yescharacteristic
61C2×#11758196—21no—
62C4⋊C4×D61—22no—
63C4⋊C4×D61—22no—
64C2×C22⋊Dic61—21no—
65C2×C22⋊Dic61—21no—
66C2×#11758198—21no—
67C2×#11758198—21no—
68C2×#11758198—21no—
69C2×#11758198—21no—
70C22⋊C4×D61—44no—
71C22⋊C4×D61—42no—
72C22⋊C4×D61—42no—
73C2×C4×Dic61C2×C411yescharacteristic
74C2×C4×Dic61D411yescharacteristic
75C2×C4×Dic61D411yescharacteristic
76C42×D61—22no—
77C42×D61—22no—
78C22×D4×C61C2×C411yescharacteristic
79C2×C4⋊C4×C61C2×C411yescharacteristic
80C2×C22⋊C4×C61—21no—
81C2×C22⋊C4×C61—21no—
82C2×C42×C61C2×C411yescharacteristic
83C24×C61—21no—
84C23×D61—21no—
85C23×D61—24no—
86C23×D61—41no—
87C23×D61—42no—
88C23×D61—41no—
89C23×D61—41no—
90C23×D61—41no—
91C23×D61—42no—
92C23×D61—41no—
93C23×D61—42no—
94C23×D61—41no—
95C23×D61C2×D411yescharacteristic
96C22×#6923—24no—
97C22×#6923—24no—
98C22×#6923—24no—
99C22×#6923—42no—
100C22×#6923—42no—
101C22×#6923—42no—
102C22×#6923—42no—
103C2×D4×C61—21no—
104C2×D4×C61—22no—
105C2×D4×C61—22no—
106C2×D4×C61C4212yescomplemented
107C22×C4×C61—21no—
108C22×C4×C61C22⋊C411yescharacteristic
109C22×C4×C61C22⋊C411yescharacteristic
110C22×C4×C61C22×C411yescharacteristic
111C2×C22⋊D61—24no—
112C2×C22⋊D61—42no—
113C2×C22⋊D61—41no—
114C2×C22⋊D61—41no—
115C22×Dic61—21no—
116C22×Dic61C22⋊C411yescharacteristic
117C22×Dic61C22⋊C411yescharacteristic
118C22×Dic61C2×D411yescharacteristic
119D4×D61—24no—
120D4×D61—24no—
121D4×D61—24no—
122D4×D61—24no—
123D4×D61—42no—
124D4×D61—42no—
125D4×D61—42no—
126D4×D61—42no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—21no—
130C2×D244C4212yescomplemented
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—42no—
140C2×C4×D61—41no—
141C2×C4×D61—41no—
142C2×C4×D61—42no—
143C2×C4×D61D812yes—
144C2×C4×D61SD1612yes—
145C2×C4×D61C22×C412yes—
146C2×C4×D61C2×D412yes—
147C2×C4×D61C2×D412yes—
148C2×C4×D61#4112yes—
149C2×C4×D61#4112yes—
150C2×C4×D61#4112yes—
151C2×#92420—24no—
152C2×#92420—42no—
153C2×#92420—42no—
154C4⋊#6923—24no—
155C4⋊#6923—24no—
156C4⋊#6923—24no—
157C4⋊#6923C22⋊C418yescomplemented
158C4×#6923—48no—
159D61⋊C8—24no—
160D61⋊C8—24no—
161D61⋊C8—42no—
162D61⋊C8—42no—
163C4⋊C4×C61—22no—
164C22⋊C4×C61—42no—
165C22⋊C4×C61—42no—
166C42×C61—22no—
167C22⋊Dic61—42no—
168C22⋊Dic61—42no—
169#11758198—42no—
170#11758198—42no—
171#11758198—42no—
172#11758198—42no—
173C4⋊Dic61—22no—
174#11758196—41no—
175#11758196—41no—
176C4×Dic61—22no—
177C4×Dic61—22no—
178C4×Dic61—22no—
179C23×C61—22no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61—41no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61C2×C22⋊C411yescharacteristic
187C22×D61—22no—
188C22×D61—41no—
189C22×D61—41no—
190C22×D61—41no—
191C22×D61—41no—
192C22×D61—41no—
193C22×D61—41no—
194C22×D61—44no—
195C22×D61—44no—
196C22×D61—44no—
197C22×D61—44no—
198C22×D61—44no—
199C22×D61—44no—
200C22×D61—81no—
201C22×D61—81no—
202C22×D61—82no—
203C22×D61—82no—
204C22×D61—82no—
205C22×D61—82no—
206C22×D61—82no—
207C22×D61—81no—
208C22×D61—81no—
209C22×D61—82no—
210C22×D61C4×D412yes—
211C22×D61#12011yescharacteristic
212C22×D61#12112yes—
213C22×D61#12311yescharacteristic
214C22×D61C2×D811yescharacteristic
215C22×D61C2×SD1611yescharacteristic
216C22×D61#13512yes—
217C22×D61AGL(1,ℤ/8)12yes—
218C22×D61AGL(1,ℤ/8)11yescharacteristic
219C22×D61#13711yescharacteristic
220C2×#6923—28no—
221C2×#6923—44no—
222C2×#6923—44no—
223C2×#6923—44no—
224C2×#6923—44no—
225C2×#6923—44no—
226C2×#6923—44no—
227D4×C61—24no—
228D4×C61—42no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61#10212yescomplemented
238C2×C4×C61C2×C4211yescharacteristic
239C2×C4×C61#11711yescharacteristic
240C2×C4×C61C4×D412yes—
241C2×C4×C61C4×D412yes—
242C22⋊D61—44no—
243C22⋊D61—44no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61#10212yescomplemented
253C2×Dic61C4×D412yes—
254C2×Dic61#12112yes—
255C2×Dic61#12411yescharacteristic
256C2×Dic61#12711yescharacteristic
257D244—24no—
258D244—42no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—82no—
266C4×D61—82no—
267C4×D61C2×C22⋊C412yes—
268C4×D61#11712yes—
269C4×D61C4×D412yes—
270C4×D61C4×D412yes—
271C4×D61#12112yes—
272C4×D61#12312yes—
273C4×D61#12412yes—
274C4×D61#12612yes—
275#92420—44no—
276#10931—611nomaximal, Sylow
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61C4×C22⋊C411yescharacteristic
285C22×C61#38611yescharacteristic
286C22×C61#39011yescharacteristic
287C22×C61C2×#10211yescharacteristic
288C22×C61#41611yescharacteristic
289C22×C61#41711yescharacteristic
290C22×C61#41811yescharacteristic
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C2×D61—84no—
299C2×D61—84no—
300C2×D61—84no—
301C2×D61—84no—
302C2×D61#38612yes—
303C2×D61#38812yes—
304C2×D61C4×D812yes—
305C2×D61C4×SD1612yes—
306C2×D61#44012yes—
307C2×D61#44212yes—
308C2×D61#44711yescharacteristic
309C2×D61#44811yescharacteristic
310C2×D61#44912yes—
311C2×D61#45912yes—
312C2×D61#46012yes—
313C2×D61#46312yes—
314C2×D61#46412yes—
315C2×D61#48011yescharacteristic
316C2×D61#48111yescharacteristic
317C2×D61#48212yes—
318#6923—48no—
319C4×C61—22no—
320C4×C61—41no—
321C4×C61—81no—
322C4×C61C4×C22⋊C412yes—
323C4×C61#38812yes—
324Dic61—22no—
325Dic61—41no—
326Dic61—81no—
327Dic61#38812yes—
328Dic61#39012yes—
329C22×#102—612no—
330C2×#390—611no—
331C2×C4×C4⋊C4—611no—
332C2×#340—612no—
333C2×#336—611no—
334C2×C61—82no—
335C2×C61#143711yescharacteristic
336C2×C61C4×#10211yescharacteristic
337C2×C61#176211yescharacteristic
338C2×C61#187411yescharacteristic
339C2×C61#187511yescharacteristic
340C2×C61#198211yescharacteristic
341C2×C61#198311yescharacteristic
342D61—82no—
343D61#187912yes—
344D61#188012yes—
345D61#192512yes—
346D61#192612yes—
347C23×D4—611no—
348C23×C8—612no—
349C22×C4⋊C4—612no—
350C22×C4⋊C4—611no—
351C22×C22⋊C4—1221no—
352C22×C22⋊C4—1221no—
353C22×C42—611no—
354C22×C42—1221no—
355C2×#102—618no—
356C2×#102—1224no—
357C2×#102—1224no—
358#390—611no—
359#390—611no—
360#390—611no—
361#390—1221no—
362#390—1221no—
363#390#692311yescharacteristic, complemented
364C4×C4⋊C4—1224no—
365C2×#95—1221no—
366#340—1224no—
367#336—1221no—
368#336—1221no—
369C61#1093111yescharacteristic, complemented, Sylow
370C25—1221no—
371C22×D4—614no—
372C22×D4—611no—
373C22×D4—1222no—
374C22×D4—1222no—
375C22×D4—1222no—
376C22×D4—1222no—
377C22×D4—1222no—
378C22×D4—1221no—
379C22×D4C2×#692311yescharacteristic
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—1221no—
384C23×C4—1222no—
385C22×C8—614no—
386C22×C8—1222no—
387C22×C8—1222no—
388C22×C8—1222no—
389C22×C8—1222no—
390C22×C8—1222no—
391C22×C8—1222no—
392C2×C4⋊C4—614no—
393C2×C4⋊C4—614no—
394C2×C4⋊C4—614no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—1222no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1222no—
399C2×C4⋊C4—1222no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4C2×#692311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—2442no—
412C2×C22⋊C4—2442no—
413C2×C22⋊C4—2444no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—1222no—
418C2×C42—1222no—
419C2×C42—1224no—
420C2×C42—2442no—
421C2×C42—2442no—
422C2×C42C2×#692311yescharacteristic
423#102—12216no—
424#95—1224no—
425C24—21no—
426C24—611no—
427C24—1224no—
428C24—1221no—
429C24—2441no—
430C24—2441no—
431C24—2442no—
432C24—2441no—
433C24—2441no—
434C24—2442no—
435C24—2442no—
436C24—2441no—
437C24—2441no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—612no—
442C2×D4—1224no—
443C2×D4—1224no—
444C2×D4—1224no—
445C2×D4—1224no—
446C2×D4—1224no—
447C2×D4—1221no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—2442no—
451C2×D4—2442no—
452C2×D4—2442no—
453C2×D4—2442no—
454C2×D4—2442no—
455C2×D4—2441no—
456C2×D4—2441no—
457C2×D4C4×#692312yescomplemented
458C22×C4—21no—
459C22×C4—611no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—612no—
463C22×C4—612no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—611no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—611no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1224no—
479C22×C4—1224no—
480C22×C4—1224no—
481C22×C4—1221no—
482C22×C4—2441no—
483C22×C4—2441no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4—2442no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4C22⋊#692311yescharacteristic
491C22×C4C22⋊#692311yescharacteristic
492C22×C4C22×#692311yescharacteristic
493C2×C8—1224no—
494C2×C8—1224no—
495C2×C8—1224no—
496C2×C8—2442no—
497C2×C8—2442no—
498C2×C8—2442no—
499C2×C8—2442no—
500C4⋊C4—22no—
501C4⋊C4—618no—
502C4⋊C4—1224no—
503C4⋊C4—1224no—
504C4⋊C4—1224no—
505C4⋊C4—1222no—
506C4⋊C4—2441no—
507C4⋊C4—2441no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—2442no—
511C22⋊C4—2442no—
512C22⋊C4—2442no—
513C22⋊C4—2442no—
514C22⋊C4—2442no—
515C22⋊C4—2442no—
516C42—22no—
517C42—1222no—
518C42—1222no—
519C42—1222no—
520C42—2448no—
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—611no—
529C23—611no—
530C23—612no—
531C23—611no—
532C23—611no—
533C23—612no—
534C23—611no—
535C23—611no—
536C23—612no—
537C23—612no—
538C23—1222no—
539C23—4881no—
540C23—4881no—
541C23—4881no—
542C23—4881no—
543C23—4882no—
544C23—4882no—
545C23—4882no—
546C23—4882no—
547C23—4882no—
548C23—4882no—
549C23—2444no—
550C23—2444no—
551C23—2444no—
552C23—2444no—
553C23—2444no—
554C23—2444no—
555C23—2441no—
556C23—2441no—
557C23—2441no—
558C23—2441no—
559C23—2441no—
560C23—2441no—
561C23C2×C22⋊#692311yescharacteristic
562D4—24no—
563D4—42no—
564D4—1224no—
565D4—2444no—
566D4—2444no—
567D4—2442no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—612no—
577C2×C4—611no—
578C2×C4—611no—
579C2×C4—612no—
580C2×C4—612no—
581C2×C4—612no—
582C2×C4—612no—
583C2×C4—612no—
584C2×C4—612no—
585C2×C4—612no—
586C2×C4—612no—
587C2×C4—612no—
588C2×C4—612no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1228no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—4882no—
600C2×C4—4882no—
601C2×C4—2442no—
602C2×C4—2442no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2444no—
607C2×C4—2444no—
608C2×C4—2444no—
609C2×C4—2444no—
610C2×C4—2444no—
611C2×C4—2444no—
612C2×C4#1451983912yescomplemented
613C2×C4C2×C4×#692311yescharacteristic
614C2×C4#1451985611yescharacteristic
615C2×C4D4×#692312yes—
616C2×C4D4×#692312yes—
617C8—2444no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—612no—
626C22—612no—
627C22—611no—
628C22—611no—
629C22—611no—
630C22—611no—
631C22—612no—
632C22—612no—
633C22—612no—
634C22—612no—
635C22—612no—
636C22—612no—
637C22—612no—
638C22—612no—
639C22—612no—
640C22—612no—
641C22—4884no—
642C22—4884no—
643C22—4884no—
644C22—4884no—
645C22—4881no—
646C22—4881no—
647C22—4881no—
648C22—4881no—
649C22—2442no—
650C22—2442no—
651C22—2442no—
652C22C4×C22⋊#692311yescharacteristic
653C22#1684071011yescharacteristic
654C22#1684071411yescharacteristic
655C22C2×#1451983911yescharacteristic
656C22#1684075211yescharacteristic
657C22#1684075311yescharacteristic
658C22#1684075411yescharacteristic
659C4—22no—
660C4—41no—
661C4—81no—
662C4—612no—
663C4—612no—
664C4—1222no—
665C4—4881no—
666C4—2448no—
667C4—2441no—
668C4C22⋊C4×#692312yes—
669C4#1684071212yes—
670C2—82no—
671C2—612no—
672C2—612no—
673C2—612no—
674C2—612no—
675C2—4882no—
676C2#2146100011yescharacteristic
677C2C4×#1451983911yescharacteristic
678C2#2146158911yescharacteristic
679C2#2146180611yescharacteristic
680C2#2146180711yescharacteristic
681C2#2146198611yescharacteristic
682C2#2146198711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC22×C4×D61C23
hypercenter#390#6923
hypocenterC61#10931
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊#6923C2semidirect
3. C2×#16840635C2semidirect
4. #21461480C2semidirect
11. C2×#14519839C4semidirect
22. #16839665C4semidirect
23. #16839664C4semidirect
24. #16839663C4semidirect
27. C61×#390C4semidirect
106. C2×D4×C61C42semidirect
130. C2×D244C42semidirect
157. C4⋊#6923C22⋊C4semidirect
237. C2×C4×C61#102semidirect
252. C2×Dic61#102semidirect
363. #390#6923semidirect
369. C61#10931semidirect
457. C2×D4C4×#6923semidirect
612. C2×C4#14519839semidirect

Maximal subgroups

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

subgroupindex
C22×#145198392
C2×C4×C4⋊#69232
C2×#168406352
#214614802
#390×D612
#1093161