Finite Group Databasebeta

← C2×#21446254 #29681698

Subgroups — C2×#21446254 #29681698

Order 15616.

2310 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758189C211yesmaximal, characteristic, complemented
2C22×#14519748C211yesmaximal, characteristic
3C22×#14519698C211yesmaximal, characteristic, complemented
4C2×#16839619C211yesmaximal, characteristic, complemented
5#21446254C218yesmaximal, direct product factor
6C2×#16839525C211yesmaximal, characteristic, complemented
7C2×#16839524C211yesmaximal, characteristic, complemented
8C22×#102×C61C211yesmaximal, characteristic, complemented
9C23×C22⋊D61—21no—
10C23×C4×D61C2211yescharacteristic
11C22×#11758189—24no—
12C22×#11758189—24no—
13C22×#11758189—24no—
14C22×#11758189C2214yescomplemented
15C23×#92418C2211yescharacteristic
16C2×#14519748—22no—
17C2×#14519748—24no—
18C2×#14519748C418yescomplemented
19C2×#14519748C2214yes—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61—21no—
23C22×#11758198—21no—
24C2×#14519698—24no—
25C2×#14519698C2214yescomplemented
26#16839619—22no—
27#16839619C2214yescomplemented
28C2×#14519684—21no—
29#16839525C2214yescomplemented
30#16839524C2214yescomplemented
31C23×D4×C61C2211yescharacteristic
32C23×C8×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C2×#102×C61—24no—
35C2×#102×C61C2214yescomplemented
36C24×D61D411yescharacteristic
37C22×C22⋊D61—28no—
38C22×C22⋊D61—24no—
39C22×C22⋊D61—44no—
40C22×C22⋊D61—44no—
41C23×Dic61—21no—
42C23×Dic61—21no—
43C23×Dic61D411yescharacteristic
44C22×C4×D61—22no—
45C22×C4×D61—22no—
46C22×C4×D61—22no—
47C22×C4×D61—22no—
48C22×C4×D61C2×C414yes—
49C22×C4×D61D412yes—
50C22×C4×D61D414yes—
51C22×C4×D61C2312yes—
52C2×#11758189—232no—
53C2×#11758189—28no—
54C2×#11758189—28no—
55C2×#11758189—28no—
56C22×#92418—22no—
57C22×#92418—22no—
58C22×#92418D414yescomplemented
59C22×#92418C2312yes—
60#14519748—216no—
61#14519748—28no—
62#14519748C2×C4116yescomplemented
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61C2×C414yes—
69C2×C4⋊Dic61C2312yes—
70C2×C4⋊Dic61C2312yes—
71C2×C22⋊Dic61—28no—
72C2×C22⋊Dic61—24no—
73C2×#11758198—24no—
74C2×#11758198—44no—
75#14519698—28no—
76#14519684—24no—
77C25×C61—21no—
78C22×D4×C61—22no—
79C22×D4×C61—22no—
80C22×D4×C61—21no—
81C22×D4×C61—22no—
82C22×D4×C61—22no—
83C22×D4×C61—22no—
84C22×D4×C61C2×C414yes—
85C22×D4×C61C2312yes—
86C23×C4×C61—21no—
87C23×C4×C61C2311yescharacteristic
88C22×C8×C61—22no—
89C22×C8×C61—22no—
90C22×C8×C61D414yescomplemented
91C22×C8×C61C2312yes—
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61C2312yes—
96#102×C61—28no—
97C24×C61—24no—
98C24×C61—22no—
99C24×C61—42no—
100C24×C61—42no—
101C24×C61—42no—
102C24×C61—42no—
103C24×C61—42no—
104C24×C61—42no—
105C24×C61C2×D411yescharacteristic
106C23×D61—22no—
107C23×D61—22no—
108C23×D61—22no—
109C23×D61—22no—
110C23×D61—22no—
111C23×D61—22no—
112C23×D61C22⋊C414yes—
113C23×D61C2×D412yes—
114C2×D4×C61—24no—
115C2×D4×C61—28no—
116C2×D4×C61—28no—
117C2×D4×C61—22no—
118C2×D4×C61—22no—
119C2×D4×C61—22no—
120C2×D4×C61—22no—
121C2×D4×C61—22no—
122C2×D4×C61—44no—
123C2×D4×C61—42no—
124C2×D4×C61—42no—
125C2×D4×C61—44no—
126C2×D4×C61C22×C414yes—
127C22×C4×C61—22no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61C22×C412yes—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D412yes—
136C22×C4×C61#4112yes—
137C22×C4×C61#4112yes—
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—216no—
140C2×C22⋊D61—48no—
141C2×C22⋊D61—48no—
142C2×C22⋊D61—432no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—24no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—42no—
149C22×Dic61—42no—
150C22×Dic61—42no—
151C22×Dic61—42no—
152C22×Dic61—42no—
153C22×Dic61C22⋊C414yes—
154C22×Dic61C2×D412yes—
155C2×C4×D61—28no—
156C2×C4×D61—28no—
157C2×C4×D61—28no—
158C2×C4×D61—24no—
159C2×C4×D61—24no—
160C2×C4×D61—28no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61C22⋊C418yes—
166C2×C4×D61C22×C414yes—
167C2×C4×D61C2×D414yes—
168C2×C8×C61—28no—
169C2×C8×C61—22no—
170C2×C8×C61—22no—
171C2×C8×C61C2×D414yescomplemented
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—42no—
175C22⋊Dic61—216no—
176#11758198—48no—
177C4⋊Dic61—24no—
178C4⋊Dic61—22no—
179C4⋊Dic61—22no—
180C4⋊Dic61—22no—
181C4⋊Dic61—42no—
182C4⋊Dic61C22×C414yes—
183C2×#92418—28no—
184C2×#92418—22no—
185C2×#92418—22no—
186C2×#92418C2×D414yescomplemented
187#11758189—232no—
188C23×C61—24no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—48no—
196C23×C61—48no—
197C23×C61—48no—
198C23×C61—84no—
199C23×C61—84no—
200C23×C61—84no—
201C23×C61—84no—
202C23×C61C2×C22⋊C412yes—
203C23×C61#12112yes—
204C23×C61#12112yes—
205C23×C61AGL(1,ℤ/8)12yes—
206C23×C61AGL(1,ℤ/8)12yes—
207C23×C61AGL(1,ℤ/8)12yes—
208C23×C61#13712yes—
209C23×C61C22×D411yescharacteristic
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—28no—
217C22×D61—28no—
218C22×D61—28no—
219C22×D61—44no—
220C22×D61—44no—
221C22×D61—44no—
222C22×D61—44no—
223C22×D61C2×C22⋊C414yes—
224D4×C61—24no—
225D4×C61—24no—
226D4×C61—42no—
227D4×C61—42no—
228D4×C61—48no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—84no—
233C2×C4×C61C2×C22⋊C412yes—
234C2×C4×C61C4×D414yes—
235C2×C4×C61C4×D414yes—
236C2×C4×C61#12014yes—
237C2×C4×C61#12112yes—
238C2×C4×C61#12112yes—
239C2×C4×C61#12314yes—
240C2×C4×C61C23×C411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C22⋊D61—432no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—28no—
250C2×Dic61—24no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—48no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—84no—
258C2×Dic61C2×C22⋊C414yes—
259C4×D61—24no—
260C4×D61—24no—
261C4×D61—24no—
262C4×D61—24no—
263C4×D61—216no—
264C8×C61—24no—
265#92418—24no—
266C2×#1895—611nomaximal, Sylow
267C22×C61—44no—
268C22×C61—44no—
269C22×C61—44no—
270C22×C61—816no—
271C22×C61—82no—
272C22×C61—82no—
273C22×C61—82no—
274C22×C61—82no—
275C22×C61#38614yes—
276C22×C61#41714yes—
277C22×C61#41814yes—
278C22×C61#46814yes—
279C22×C61#46814yes—
280C22×C61#46914yes—
281C22×C61#46914yes—
282C22×C61C22×C22⋊C411yescharacteristic
283C22×C61C2×#12111yescharacteristic
284C22×C61C2×#12111yescharacteristic
285C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C61C2×#13711yescharacteristic
289C2×D61—24no—
290C2×D61—24no—
291C2×D61—24no—
292C2×D61—416no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C4×C61—82no—
298C4×C61#38614yes—
299C4×C61C2×C4×D411yescharacteristic
300C4×C61C2×C4×D411yescharacteristic
301C4×C61C2×#12011yescharacteristic
302C4×C61C2×#12311yescharacteristic
303Dic61—24no—
304Dic61—44no—
305Dic61—82no—
306C23×M16—611no—
307C22×#121—611no—
308C22×#102—611no—
309C22×#102D6111yescharacteristic, complemented
310C2×#380—611no—
311#1895—618no—
312C2×#340—611no—
313C2×#340—611no—
314C2×C61—84no—
315C2×C61#189518yescomplemented
316C2×C61C2×#38611yescharacteristic
317C2×C61C2×#41811yescharacteristic
318C2×C61C2×#41711yescharacteristic
319C2×C61C2×#46811yescharacteristic
320C2×C61C2×#46811yescharacteristic
321C2×C61C2×#46911yescharacteristic
322C2×C61C2×#46911yescharacteristic
323D61—44no—
324C23×D4—1221no—
325C23×D4C2×D6111yescharacteristic
326C24×C4—611no—
327C22×M16—614no—
328C22×M16—1224no—
329C22×M16—1224no—
330C22×M16—1224no—
331C23×C8—611no—
332C23×C8C2×D6111yescharacteristic
333C2×#121—618no—
334C2×#121—614no—
335C2×#121—1224no—
336C2×#121—1222no—
337C22×C4⋊C4—611no—
338C22×C4⋊C4—611no—
339C22×C4⋊C4C2×D6111yescharacteristic
340C22×C22⋊C4—1221no—
341C22×C22⋊C4—1221no—
342C2×#102—24no—
343C2×#102—614no—
344C2×#102—1224no—
345C2×#102C2×D6114yescomplemented
346#380—614no—
347#380—1222no—
348C2×#95—1221no—
349#340—614no—
350#340—614no—
351C61C2×#189511yescharacteristic, complemented, Sylow
352C25—21no—
353C25—611no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—1224no—
361C22×D4—1228no—
362C22×D4—2444no—
363C22×D4—2444no—
364C22×D4C4×D6114yes—
365C22×D4C22×D6112yes—
366C23×C4—21no—
367C23×C4—611no—
368C23×C4—614no—
369C23×C4—614no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—1222no—
373C23×C4—1222no—
374C23×C4—1222no—
375C23×C4—1222no—
376C23×C4—1221no—
377C23×C4—1221no—
378C23×C4C22×D6111yescharacteristic
379C2×M16—1228no—
380C2×M16—1228no—
381C2×M16—12232no—
382C2×M16—1228no—
383C22×C8—22no—
384C22×C8—22no—
385C22×C8—614no—
386C22×C8—612no—
387C22×C8—1222no—
388C22×C8—1222no—
389C22×C8C22⋊D6114yescomplemented
390C22×C8C22×D6112yes—
391#121—6116no—
392#121—1228no—
393#121—12216no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—614no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4C22×D6112yes—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1228no—
408C2×C22⋊C4—1224no—
409C2×C22⋊C4—2444no—
410#102—28no—
411#102—1228no—
412#95—1224no—
413C24—22no—
414C24—24no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—612no—
422C24—614no—
423C24—1222no—
424C24—1222no—
425C24—1222no—
426C24—1222no—
427C24—1222no—
428C24—1222no—
429C24D4×D6111yescharacteristic
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—24no—
436C2×D4—28no—
437C2×D4—28no—
438C2×D4—44no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—12216no—
443C2×D4—24432no—
444C2×D4—2448no—
445C2×D4—2448no—
446C2×D4C2×C4×D6114yes—
447C22×C4—22no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—612no—
452C22×C4—614no—
453C22×C4—614no—
454C22×C4—614no—
455C22×C4—618no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1228no—
463C22×C4—1228no—
464C22×C4—1228no—
465C22×C4—1224no—
466C22×C4—1224no—
467C22×C4—1228no—
468C22×C4—1222no—
469C22×C4—1224no—
470C22×C4—1222no—
471C22×C4—2442no—
472C22×C4—2442no—
473C22×C4—2442no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4C2×C4×D6112yes—
477C22×C4#1175822212yes—
478C22×C4D4×D6112yes—
479C22×C4D4×D6112yes—
480C22×C4D4×D6111yescharacteristic
481C22×C4#1175822412yes—
482C22×C4C2×C22⋊D6112yes—
483C22×C4C23×D6111yescharacteristic
484M16—12232no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—28no—
488C2×C8—614no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8—1228no—
492C2×C8C2×C22⋊D6114yescomplemented
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—42no—
496C4⋊C4—614no—
497C4⋊C4—1222no—
498C4⋊C4—1224no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—2442no—
502C22⋊C4—12216no—
503C22⋊C4—2448no—
504C23—24no—
505C23—42no—
506C23—42no—
507C23—48no—
508C23—48no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—48no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23—84no—
518C23—614no—
519C23—1222no—
520C23—1222no—
521C23—1228no—
522C23—1228no—
523C23—1222no—
524C23—1222no—
525C23—1222no—
526C23—1222no—
527C23—1228no—
528C23—2444no—
529C23—2444no—
530C23—2444no—
531C23—2444no—
532C23C22⋊C4×D6112yes—
533C23#1451974812yes—
534C23#1451975012yes—
535C23#1451980112yes—
536C23#1451980112yes—
537C23#1451980412yes—
538C23#1451980612yes—
539C23C2×D4×D6111yescharacteristic
540D4—24no—
541D4—24no—
542D4—42no—
543D4—42no—
544D4—48no—
545D4—24432no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—84no—
550C2×C4—614no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1228no—
554C2×C4—1224no—
555C2×C4—1224no—
556C2×C4—1224no—
557C2×C4—1224no—
558C2×C4—12216no—
559C2×C4—1224no—
560C2×C4—4884no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2448no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4C22⋊C4×D6112yes—
568C2×C4#1451973714yes—
569C2×C4C4×C22⋊D6114yes—
570C2×C4#1451974514yes—
571C2×C4#1451974812yes—
572C2×C4#1451975012yes—
573C2×C4#1451975914yes—
574C2×C4C22×C4×D6111yescharacteristic
575C2×C4C2×D4×D6111yescharacteristic
576C2×C4C2×D4×D6111yescharacteristic
577C2×C4C22×C22⋊D6111yescharacteristic
578C2×C4C2×#1175822411yescharacteristic
579C2×C4C2×#1175822211yescharacteristic
580C8—24no—
581C8—1224no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—816no—
590C22—1224no—
591C22—1224no—
592C22—1224no—
593C22—2442no—
594C22—2442no—
595C22—2442no—
596C22—2442no—
597C22—24416no—
598C22#1683963814yes—
599C22#1683976014yes—
600C22#1683976514yes—
601C22#1684000514yes—
602C22#1684000714yes—
603C22#1684001214yes—
604C22#1684001414yes—
605C22C2×C22⋊C4×D6111yescharacteristic
606C22C2×#1451974811yescharacteristic
607C22C2×#1451975011yescharacteristic
608C22C2×#1451980111yescharacteristic
609C22C2×#1451980111yescharacteristic
610C22C2×#1451980411yescharacteristic
611C22C2×#1451980611yescharacteristic
612C4—82no—
613C4—1224no—
614C4—4882no—
615C4—2444no—
616C4#1683963814yes—
617C4C2×#1451973711yescharacteristic
618C4C2×C4×C22⋊D6111yescharacteristic
619C4C2×#1451974511yescharacteristic
620C4C2×#1451975911yescharacteristic
621C2—84no—
622C2—2444no—
623C2#2144625418yesdirect product factor
624C2C2×#1683963811yescharacteristic
625C2C2×#1683976511yescharacteristic
626C2C2×#1683976011yescharacteristic
627C2C2×#1684000511yescharacteristic
628C2C2×#1684000711yescharacteristic
629C2C2×#1684001211yescharacteristic
630C2C2×#1684001411yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC24×C61C2×D4
prime radicalC22×#14519748C2
cosocleC22×C4×C61C24
hypercenterC22×#102D61
hypocenterC61C2×#1895
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C23×#11758189C2semidirect
3. C22×#14519698C2semidirect
4. C2×#16839619C2semidirect
5. #21446254C2direct (N × H)
6. C2×#16839525C2semidirect
7. C2×#16839524C2semidirect
8. C22×#102×C61C2semidirect
14. C22×#11758189C22semidirect
18. C2×#14519748C4semidirect
25. C2×#14519698C22semidirect
27. #16839619C22semidirect
29. #16839525C22semidirect
30. #16839524C22semidirect
35. C2×#102×C61C22semidirect
58. C22×#92418D4semidirect
62. #14519748C2×C4semidirect
90. C22×C8×C61D4semidirect
171. C2×C8×C61C2×D4semidirect
186. C2×#92418C2×D4semidirect
309. C22×#102D61semidirect
315. C2×C61#1895semidirect
345. C2×#102C2×D61semidirect
351. C61C2×#1895semidirect
389. C22×C8C22⋊D61semidirect
492. C2×C8C2×C22⋊D61semidirect
623. C2#21446254direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117581892
C22×#145197482
C22×#145196982
C2×#168396192
#214462542
C2×#168395252
C2×#168395242
C22×#102×C612
C2×#189561