Finite Group Databasebeta

← C2×#21447030 #29707599

Subgroups — C2×#21447030 #29707599

Order 15616.

1714 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840329C211yesmaximal, characteristic
2C2×#16839804C211yesmaximal, characteristic, complemented
3C22×#14519703C211yesmaximal, characteristic, complemented
4C2×#16839764C211yesmaximal, characteristic, complemented
5C2×#16839665C211yesmaximal, characteristic, complemented
6#21447030C218yesmaximal, direct product factor
7C2×#16839523C211yesmaximal, characteristic, complemented
8C22×#100×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840329—22no—
11#16840329—22no—
12#16840329—22no—
13#16840329C2214yes—
14C2×#14519773—21no—
15C2×#14519764—21no—
16C2×#14519748—21no—
17C2×#14519748—21no—
18C2×#14519746—22no—
19C2×#14519736C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61—22no—
22C22×C4×Dic61C2211yescharacteristic
23#16839804—22no—
24#16839804C2214yescomplemented
25C2×#14519711—21no—
26C2×#14519709—21no—
27C2×#14519703—24no—
28C2×#14519703C2214yescomplemented
29#16839764—22no—
30#16839764C2214yescomplemented
31C2×#14519702—21no—
32C2×#14519699—21no—
33#16839665—22no—
34#16839665C2214yescomplemented
35#16839523C2214yescomplemented
36C23×D4×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C22×M16×C61C2211yescharacteristic
39C2×#100×C61—24no—
40C2×#100×C61C2214yescomplemented
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—22no—
44C2×#11758222—22no—
45C2×#11758222—22no—
46C2×#11758222—22no—
47C2×#11758222D412yes—
48C2×#11758222C2312yes—
49C22×Dic122D411yescharacteristic
50C22×D244D411yescharacteristic
51C22×C22⋊D61—21no—
52C22×C22⋊D61—22no—
53C22×C22⋊D61—22no—
54C23×Dic61—21no—
55C23×Dic61—21no—
56C22×C4×D61—21no—
57#14519773—24no—
58#14519773—24no—
59#14519764—24no—
60#14519764—24no—
61#14519748—24no—
62#14519748—24no—
63#14519748—24no—
64#14519748—24no—
65#14519746—28no—
66#14519746—28no—
67#14519736—21no—
68#14519736—21no—
69#14519736D412yes—
70#14519736C2312yes—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61D411yescharacteristic
77C2×C4⋊Dic61D411yescharacteristic
78C2×C4⋊Dic61C2312yes—
79C2×C22⋊Dic61—22no—
80C2×C22⋊Dic61—22no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—28no—
83C2×C22⋊Dic61—48no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—22no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2312yes—
89#14519711—24no—
90#14519709—24no—
91#14519703—28no—
92#14519702—24no—
93#14519699—24no—
94C25×C61D412yes—
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61—22no—
98C22×D4×C61—21no—
99C22×D4×C61—21no—
100C22×D4×C61—22no—
101C22×D4×C61—22no—
102C22×D4×C61—22no—
103C22×D4×C61D412yes—
104C22×D4×C61C2312yes—
105C23×C4×C61C2311yescharacteristic
106C2×M16×C61—21no—
107C2×M16×C61—22no—
108C2×M16×C61—21no—
109C2×M16×C61—22no—
110C2×M16×C61—22no—
111C2×M16×C61D414yescomplemented
112C2×M16×C61C2312yes—
113C2×M16×C61C2312yes—
114C22×C8×C61—21no—
115C22×C8×C61—21no—
116#100×C61—28no—
117C24×C61—22no—
118C24×C61—24no—
119C24×C61—22no—
120C24×C61—24no—
121C24×C61—44no—
122C24×C61—44no—
123C24×C61C2×D411yescharacteristic
124C24×C61C2×D414yes—
125C23×D61—21no—
126C2×D4×C61—22no—
127C2×D4×C61—22no—
128C2×D4×C61—24no—
129C2×D4×C61—24no—
130C2×D4×C61—22no—
131C2×D4×C61—22no—
132C2×D4×C61—22no—
133C2×D4×C61—22no—
134C2×D4×C61—22no—
135C2×D4×C61—22no—
136C2×D4×C61—42no—
137C2×D4×C61—42no—
138C2×D4×C61—42no—
139C2×D4×C61—42no—
140C2×D4×C61—42no—
141C2×D4×C61—42no—
142C2×D4×C61—42no—
143C2×D4×C61—42no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D412yes—
150C22×C4×C61#4112yes—
151C22×C4×C61#4112yes—
152C22×C4×C61#4112yes—
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—28no—
157C2×C22⋊D61—28no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—42no—
160C2×C22⋊D61—84no—
161C2×C22⋊D61—84no—
162C22×Dic61—24no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61—44no—
171C22×Dic61—41no—
172C22×Dic61—41no—
173#11758222—24no—
174#11758222—24no—
175#11758222—22no—
176#11758222—22no—
177#11758222—22no—
178#11758222—22no—
179#11758222—42no—
180#11758222—42no—
181#11758222—42no—
182#11758222—42no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244—21no—
186C2×D244C2×D412yes—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×Dic122—22no—
192C2×Dic122—22no—
193C2×Dic122—21no—
194C2×Dic122C2×D412yes—
195M16×C61—24no—
196M16×C61—22no—
197M16×C61—22no—
198M16×C61—22no—
199M16×C61—42no—
200M16×C61C2×D414yescomplemented
201C2×C8×C61—24no—
202C2×C8×C61—22no—
203C2×C8×C61—22no—
204C2×C8×C61—42no—
205C22⋊Dic61—28no—
206C22⋊Dic61—28no—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—416no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—22no—
213C4⋊Dic61—22no—
214C4⋊Dic61—41no—
215C4⋊Dic61—41no—
216C4⋊Dic61C2×D412yes—
217C4⋊Dic61C2×D412yes—
218C4×Dic61—22no—
219C4×Dic61—22no—
220C4×Dic61—22no—
221C4×Dic61—22no—
222C4×Dic61—42no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—44no—
229C23×C61—44no—
230C23×C61—416no—
231C23×C61—44no—
232C23×C61—44no—
233C23×C61—44no—
234C23×C61—44no—
235C23×C61—82no—
236C23×C61—82no—
237C23×C61—88no—
238C23×C61#12011yescharacteristic
239C23×C61#12011yescharacteristic
240C23×C61#12112yes—
241C23×C61#12312yes—
242C23×C61C22×D411yescharacteristic
243C22×D61—22no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—42no—
247D4×C61—42no—
248D4×C61—42no—
249D4×C61—42no—
250D4×C61—42no—
251D4×C61—44no—
252D4×C61—44no—
253C2×C4×C61#12011yescharacteristic
254C2×C4×C61#12011yescharacteristic
255C2×C4×C61#12112yes—
256C2×C4×C61#12112yes—
257C2×C4×C61#12112yes—
258C2×C4×C61#12112yes—
259C2×C4×C61#12112yes—
260C2×C4×C61#12312yes—
261C2×C4×C61#12312yes—
262C2×C4×C61#12312yes—
263C2×C4×C61#12412yes—
264C2×C4×C61#12412yes—
265C2×C4×C61C22×D411yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C2×#4111yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C22⋊D61—42no—
272C22⋊D61—42no—
273C22⋊D61—44no—
274C22⋊D61—88no—
275C22⋊D61—88no—
276C2×Dic61—24no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—42no—
281C2×Dic61—48no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61—44no—
287C2×Dic61—42no—
288C2×Dic61—82no—
289C2×Dic61—82no—
290D244—22no—
291D244—22no—
292D244—42no—
293C4×D61—42no—
294C4×D61—42no—
295C4×D61—44no—
296Dic122—22no—
297Dic122—22no—
298Dic122—42no—
299C8×C61—24no—
300C8×C61—42no—
301C2×#2037—611nomaximal, Sylow
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—24no—
307C22×C61—24no—
308C22×C61—48no—
309C22×C61—44no—
310C22×C61—44no—
311C22×C61—44no—
312C22×C61—84no—
313C22×C61—88no—
314C22×C61—88no—
315C22×C61#39412yes—
316C22×C61#39412yes—
317C22×C61#45312yes—
318C22×C61#45512yes—
319C22×C61C2×#12011yescharacteristic
320C22×C61C2×#12111yescharacteristic
321C22×C61C2×#12311yescharacteristic
322C2×D61—42no—
323C2×D61—42no—
324C2×D61—42no—
325C2×D61—84no—
326C4×C61#39412yes—
327C4×C61#39412yes—
328C4×C61C2×#12111yescharacteristic
329C4×C61C2×#12111yescharacteristic
330C4×C61C2×#12311yescharacteristic
331C4×C61C2×#12411yescharacteristic
332Dic61—44no—
333Dic61—42no—
334Dic61—42no—
335Dic61—42no—
336Dic61—82no—
337C2×#535—611no—
338C2×#428—611no—
339C22×#104—611no—
340C2×#417—611no—
341C22×#100D6111yescharacteristic, complemented
342C2×#390—611no—
343#2037—618no—
344C2×#339—611no—
345C2×C61—21no—
346C2×C61—21no—
347C2×C61—22no—
348C2×C61—84no—
349C2×C61#203714yescomplemented
350C2×C61C2×#39411yescharacteristic
351C2×C61C2×#45311yescharacteristic
352C2×C61C2×#45511yescharacteristic
353D61—82no—
354C22×#41—611no—
355C23×D4C2×D6111yescharacteristic
356C22×M16C2×D6111yescharacteristic
357C22×M16C2×D6111yescharacteristic
358#535—614no—
359#535—1222no—
360#535—1222no—
361#535—1222no—
362C2×#127—1221no—
363C2×#124—1221no—
364C2×#121—1221no—
365C2×#121—1221no—
366C2×#120—1222no—
367C2×#117—611no—
368C22×C4⋊C4—611no—
369C22×C22⋊C4—1222no—
370C22×C42—611no—
371#428—614no—
372#428—1222no—
373C2×#107—1221no—
374C2×#106—1221no—
375C2×#104—614no—
376C2×#104—1224no—
377#417—614no—
378#417—1222no—
379C2×#103—1221no—
380C2×#102—1221no—
381C2×#100—24no—
382C2×#100C2×D6114yescomplemented
383#390—614no—
384#390—1222no—
385#339—614no—
386C61C2×#203711yescharacteristic, complemented, Sylow
387C25D24412yes—
388C2×#41—612no—
389C2×#41—612no—
390C2×#41—1221no—
391C2×#41—1221no—
392C2×#41—1222no—
393C2×#41—1222no—
394C2×#41—1222no—
395C2×#41—1222no—
396C22×Q8—611no—
397C22×D4—22no—
398C22×D4—21no—
399C22×D4—21no—
400C22×D4—21no—
401C22×D4—21no—
402C22×D4—22no—
403C22×D4—22no—
404C22×D4—22no—
405C22×D4—611no—
406C22×D4—1222no—
407C22×D4—1222no—
408C22×D4—1221no—
409C22×D4D24412yes—
410C22×D4C22×D6112yes—
411C23×C4—1221no—
412C23×C4—1221no—
413C23×C4—1221no—
414C23×C4C22×D6111yescharacteristic
415C2×M16—21no—
416C2×M16—22no—
417C2×M16—21no—
418C2×M16—22no—
419C2×M16—22no—
420C2×M16C22⋊D6114yescomplemented
421C2×M16C22×D6112yes—
422C2×M16C22×D6112yes—
423C22×C8—21no—
424C22×C8—21no—
425#127—1224no—
426#127—1224no—
427#124—1224no—
428#124—1224no—
429#121—1224no—
430#121—1224no—
431#121—1224no—
432#121—1224no—
433#120—1228no—
434#120—1228no—
435#117—612no—
436#117—612no—
437#117—1221no—
438#117—1221no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—612no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C22⋊C4—1222no—
448C2×C22⋊C4—1222no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1228no—
451C2×C22⋊C4—2448no—
452C2×C42—612no—
453C2×C42—1221no—
454C2×C42—1222no—
455C2×C42—1222no—
456C2×C42—1221no—
457#107—1224no—
458#106—1224no—
459#104—1228no—
460#103—1224no—
461#102—1224no—
462#100—28no—
463C24—22no—
464C24—24no—
465C24—22no—
466C24—24no—
467C24—44no—
468C24—44no—
469C24—1221no—
470C24C2×D24411yescharacteristic
471C24C2×D24414yes—
472#41—1222no—
473#41—1222no—
474#41—1222no—
475#41—1222no—
476#41—1224no—
477#41—1224no—
478#41—2442no—
479#41—2442no—
480#41—2442no—
481#41—2442no—
482C2×Q8—612no—
483C2×Q8—1221no—
484C2×Q8—1222no—
485C2×Q8—1222no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—612no—
505C2×D4—1228no—
506C2×D4—1228no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1221no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—4884no—
513C2×D4—4884no—
514C2×D4—2442no—
515C2×D4—2442no—
516C22×C4—1224no—
517C22×C4—1222no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1222no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—2444no—
525C22×C4—2441no—
526C22×C4—2441no—
527C22×C4—2442no—
528C22×C4—2442no—
529C22×C4—2442no—
530C22×C4—2442no—
531C22×C4C2×D24411yescharacteristic
532C22×C4#1175822212yes—
533C22×C4D4×D6111yescharacteristic
534C22×C4D4×D6111yescharacteristic
535C22×C4D4×D6111yescharacteristic
536C22×C4D4×D6111yescharacteristic
537C22×C4#1175822412yes—
538C22×C4#1175822412yes—
539C22×C4C2×C22⋊D6112yes—
540C22×C4C23×D6111yescharacteristic
541M16—22no—
542M16—24no—
543M16—22no—
544M16—22no—
545M16—42no—
546M16C2×C22⋊D6114yescomplemented
547C2×C8—22no—
548C2×C8—24no—
549C2×C8—22no—
550C2×C8—42no—
551C4⋊C4—612no—
552C4⋊C4—612no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1222no—
556C4⋊C4—1222no—
557C4⋊C4—2441no—
558C4⋊C4—2441no—
559C22⋊C4—1228no—
560C22⋊C4—1228no—
561C22⋊C4—1222no—
562C22⋊C4—1222no—
563C22⋊C4—24416no—
564C42—1222no—
565C42—1222no—
566C42—1222no—
567C42—1222no—
568C42—2442no—
569C23—22no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—44no—
575C23—44no—
576C23—416no—
577C23—44no—
578C23—44no—
579C23—44no—
580C23—44no—
581C23—82no—
582C23—82no—
583C23—88no—
584C23—1222no—
585C23—2442no—
586C23—2442no—
587C23—2442no—
588C23#1451974711yescharacteristic
589C23#1451974711yescharacteristic
590C23#1451975112yes—
591C23#1451976112yes—
592C23C22×D24411yescharacteristic
593Q8—1222no—
594Q8—1222no—
595Q8—2442no—
596D4—42no—
597D4—42no—
598D4—42no—
599D4—42no—
600D4—44no—
601D4—44no—
602D4—1222no—
603D4—1222no—
604D4—4888no—
605D4—4888no—
606D4—2442no—
607D4—2442no—
608D4—2444no—
609D4—2442no—
610C2×C4—1224no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—4882no—
615C2×C4—4882no—
616C2×C4—2444no—
617C2×C4—2442no—
618C2×C4—2442no—
619C2×C4—2448no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4—2442no—
623C2×C4—2442no—
624C2×C4—2442no—
625C2×C4—2442no—
626C2×C4—2444no—
627C2×C4#1451974711yescharacteristic
628C2×C4#1451974711yescharacteristic
629C2×C4#1451974812yes—
630C2×C4#1451974812yes—
631C2×C4#1451974912yes—
632C2×C4#1451974912yes—
633C2×C4#1451975112yes—
634C2×C4#1451975912yes—
635C2×C4#1451975912yes—
636C2×C4#1451976112yes—
637C2×C4#1451976312yes—
638C2×C4#1451976312yes—
639C2×C4C2×D4×D6111yescharacteristic
640C2×C4C2×D4×D6111yescharacteristic
641C2×C4C22×C22⋊D6111yescharacteristic
642C2×C4C2×#1175822411yescharacteristic
643C2×C4C2×#1175822411yescharacteristic
644C2×C4C2×#1175822211yescharacteristic
645C8—24no—
646C8—42no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—24no—
652C22—24no—
653C22—48no—
654C22—44no—
655C22—44no—
656C22—44no—
657C22—84no—
658C22—88no—
659C22—88no—
660C22—4884no—
661C22—2442no—
662C22—2442no—
663C22—2442no—
664C22#1683967812yes—
665C22#1683967812yes—
666C22#1683993212yes—
667C22#1683994212yes—
668C22C2×#1451974711yescharacteristic
669C22C2×#1451975111yescharacteristic
670C22C2×#1451976111yescharacteristic
671C4—4882no—
672C4—2444no—
673C4—2442no—
674C4—2442no—
675C4—2442no—
676C4#1683967812yes—
677C4#1683967812yes—
678C4C2×#1451974811yescharacteristic
679C4C2×#1451974911yescharacteristic
680C4C2×#1451975911yescharacteristic
681C4C2×#1451976311yescharacteristic
682C2—21no—
683C2—21no—
684C2—22no—
685C2—84no—
686C2—4882no—
687C2#2144703014yesdirect product factor
688C2C2×#1683967811yescharacteristic
689C2C2×#1683993211yescharacteristic
690C2C2×#1683994211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#100×C61C2
socleC23×C61#120
prime radicalC2×#16840329C2
hypercenterC22×#100D61
hypocenterC61C2×#2037
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#100

Complements

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

NH ≅ G/Ntype
2. C2×#16839804C2semidirect
3. C22×#14519703C2semidirect
4. C2×#16839764C2semidirect
5. C2×#16839665C2semidirect
6. #21447030C2direct (N × H)
7. C2×#16839523C2semidirect
8. C22×#100×C61C2semidirect
24. #16839804C22semidirect
28. C2×#14519703C22semidirect
30. #16839764C22semidirect
34. #16839665C22semidirect
35. #16839523C22semidirect
40. C2×#100×C61C22semidirect
111. C2×M16×C61D4semidirect
200. M16×C61C2×D4semidirect
341. C22×#100D61semidirect
349. C2×C61#2037semidirect
382. C2×#100C2×D61semidirect
386. C61C2×#2037semidirect
420. C2×M16C22⋊D61semidirect
546. M16C2×C22⋊D61semidirect
687. C2#21447030direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403292
C2×#168398042
C22×#145197032
C2×#168397642
C2×#168396652
#214470302
C2×#168395232
C22×#100×C612
C2×#203761