Finite Group Databasebeta

← C2×#21447028 #29707597

Subgroups — C2×#21447028 #29707597

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×#16840326C211yesmaximal, characteristic
2C2×#16839804C211yesmaximal, characteristic, complemented
3C2×#16839763C211yesmaximal, characteristic, complemented
4C22×#14519693C211yesmaximal, characteristic, complemented
5C2×#16839664C211yesmaximal, characteristic, complemented
6#21447028C218yesmaximal, direct product factor
7C2×#16839522C211yesmaximal, characteristic, complemented
8C22×#104×C61C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11#16840326—22no—
12#16840326—22no—
13#16840326—22no—
14#16840326C2214yes—
15C2×#14519773—21no—
16C2×#14519766—21no—
17C2×#14519751—21no—
18C2×#14519751—21no—
19C2×#14519745—22no—
20C2×#14519736C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758198—22no—
23#16839804—22no—
24#16839804C2214yescomplemented
25C2×#14519711—21no—
26C2×#14519709—21no—
27#16839763—22no—
28#16839763C2214yescomplemented
29C2×#14519701—21no—
30C2×#14519698—21no—
31C2×#14519693—24no—
32C2×#14519693C2214yescomplemented
33#16839664—22no—
34#16839664C2214yescomplemented
35#16839522C2214yescomplemented
36C22×#41×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C2×#104×C61—24no—
40C2×#104×C61C2214yescomplemented
41C24×D61D412yes—
42C22×D244—22no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—22no—
48C22×D244—22no—
49C22×D244—22no—
50C22×D244D412yes—
51C22×D244C2312yes—
52C22×C22⋊D61—22no—
53C22×C22⋊D61—22no—
54C23×Dic61—21no—
55C2×#11758194—21no—
56C2×#11758194—22no—
57C2×#11758194—22no—
58C2×#11758194C2312yes—
59C22×#92418—21no—
60#14519773—24no—
61#14519773—24no—
62#14519766—24no—
63#14519766—24no—
64#14519751—24no—
65#14519751—24no—
66#14519751—24no—
67#14519751—24no—
68#14519745—28no—
69#14519745—28no—
70#14519736—21no—
71#14519736—21no—
72#14519736D412yes—
73#14519736C2312yes—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61D411yescharacteristic
80C2×C4⋊Dic61D411yescharacteristic
81C2×C4⋊Dic61C2312yes—
82C2×C22⋊Dic61—21no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×#11758198—28no—
86C2×#11758198—48no—
87C2×C4×Dic61—21no—
88#14519711—24no—
89#14519709—24no—
90#14519701—24no—
91#14519698—24no—
92#14519693—28no—
93C2×#41×C61—21no—
94C2×#41×C61—21no—
95C2×#41×C61—22no—
96C2×#41×C61—22no—
97C2×#41×C61—22no—
98C2×#41×C61—22no—
99C2×#41×C61D412yes—
100C2×#41×C61C2312yes—
101C22×Q8×C61D411yescharacteristic
102C22×D4×C61—21no—
103C22×D4×C61D411yescharacteristic
104C23×C4×C61—21no—
105C23×C4×C61—21no—
106C23×C4×C61C2311yescharacteristic
107C2×M16×C61—21no—
108C2×M16×C61—22no—
109C2×M16×C61D414yescomplemented
110C2×M16×C61C2312yes—
111C22×C8×C61—21no—
112C2×C42×C61—22no—
113C2×C42×C61—22no—
114C2×C42×C61—21no—
115C2×C42×C61C2312yes—
116#104×C61—28no—
117C24×C61—21no—
118C24×C61C2×D411yescharacteristic
119C23×D61—22no—
120C23×D61—24no—
121C23×D61—22no—
122C23×D61—24no—
123C23×D61—44no—
124C23×D61—44no—
125C23×D61C2×D414yes—
126#41×C61—24no—
127#41×C61—24no—
128#41×C61—22no—
129#41×C61—22no—
130#41×C61—22no—
131#41×C61—22no—
132#41×C61—42no—
133#41×C61—42no—
134#41×C61—42no—
135#41×C61—42no—
136C2×Q8×C61—21no—
137C2×Q8×C61—22no—
138C2×Q8×C61—22no—
139C2×Q8×C61C2×D412yes—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—21no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—42no—
146C2×D4×C61—42no—
147C2×D4×C61C2×D412yes—
148C22×C4×C61—24no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D412yes—
163C22×C4×C61#4112yes—
164C22×C4×C61#4112yes—
165C22×C4×C61#4112yes—
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—28no—
168C2×C22⋊D61—28no—
169C2×C22⋊D61—84no—
170C2×C22⋊D61—84no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—44no—
175C22×Dic61—41no—
176C22×Dic61—41no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—24no—
180C2×D244—24no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—42no—
188C2×D244—42no—
189C2×D244—42no—
190C2×D244—42no—
191C2×D244—42no—
192C2×D244—42no—
193C2×D244—42no—
194C2×D244—42no—
195M16×C61—24no—
196M16×C61—22no—
197M16×C61C2×D414yescomplemented
198C2×C8×C61—24no—
199C2×C8×C61—22no—
200C42×C61—22no—
201C42×C61—22no—
202C42×C61—42no—
203C22⋊Dic61—22no—
204C22⋊Dic61—22no—
205#11758198—28no—
206#11758198—28no—
207#11758198—416no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—22no—
211C4⋊Dic61—22no—
212C4⋊Dic61—41no—
213C4⋊Dic61—41no—
214C4⋊Dic61C2×D412yes—
215C4⋊Dic61C2×D412yes—
216C4×Dic61—22no—
217C4×Dic61—22no—
218#11758194—22no—
219#11758194—22no—
220#11758194—42no—
221C2×#92418—22no—
222C2×#92418—42no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61#12011yescharacteristic
230C23×C61#12011yescharacteristic
231C23×C61#12112yes—
232C23×C61#12312yes—
233C23×C61C22×D411yescharacteristic
234C22×D61—24no—
235C22×D61—24no—
236C22×D61—24no—
237C22×D61—44no—
238C22×D61—44no—
239C22×D61—416no—
240C22×D61—44no—
241C22×D61—44no—
242C22×D61—44no—
243C22×D61—44no—
244C22×D61—82no—
245C22×D61—82no—
246C22×D61—88no—
247Q8×C61—22no—
248Q8×C61—22no—
249Q8×C61—42no—
250D4×C61—22no—
251D4×C61—22no—
252D4×C61—42no—
253D4×C61—42no—
254D4×C61—44no—
255D4×C61—42no—
256C2×C4×C61—24no—
257C2×C4×C61—22no—
258C2×C4×C61—42no—
259C2×C4×C61—48no—
260C2×C4×C61—42no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—44no—
265C2×C4×C61#12011yescharacteristic
266C2×C4×C61#12011yescharacteristic
267C2×C4×C61#12112yes—
268C2×C4×C61#12112yes—
269C2×C4×C61#12112yes—
270C2×C4×C61#12112yes—
271C2×C4×C61#12112yes—
272C2×C4×C61#12312yes—
273C2×C4×C61#12312yes—
274C2×C4×C61#12312yes—
275C2×C4×C61#12412yes—
276C2×C4×C61#12412yes—
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C22×D411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C2×#4111yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C22⋊D61—88no—
284C22⋊D61—88no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—42no—
288C2×Dic61—42no—
289C2×Dic61—44no—
290C2×Dic61—42no—
291C2×Dic61—82no—
292C2×Dic61—82no—
293D244—42no—
294D244—42no—
295D244—42no—
296D244—42no—
297D244—44no—
298D244—44no—
299C8×C61—24no—
300#92418—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—42no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61—84no—
312C22×C61#39412yes—
313C22×C61#39412yes—
314C22×C61#45312yes—
315C22×C61#45512yes—
316C22×C61C2×#12011yescharacteristic
317C22×C61C2×#12111yescharacteristic
318C22×C61C2×#12311yescharacteristic
319C2×D61—48no—
320C2×D61—44no—
321C2×D61—44no—
322C2×D61—44no—
323C2×D61—88no—
324C2×D61—88no—
325C2×D61—84no—
326C4×C61—44no—
327C4×C61—42no—
328C4×C61#39412yes—
329C4×C61#39412yes—
330C4×C61C2×#12111yescharacteristic
331C4×C61C2×#12111yescharacteristic
332C4×C61C2×#12311yescharacteristic
333C4×C61C2×#12411yescharacteristic
334Dic61—42no—
335Dic61—42no—
336Dic61—82no—
337C2×#535—611no—
338C2×#428—611no—
339C22×#104D6111yescharacteristic, complemented
340C2×#417—611no—
341C22×#100—611no—
342C2×#390—611no—
343#2037—618no—
344C2×#339—611no—
345C2×C61—21no—
346C2×C61—21no—
347C2×C61—22no—
348C2×C61—82no—
349C2×C61#203714yescomplemented
350C2×C61C2×#39411yescharacteristic
351C2×C61C2×#45311yescharacteristic
352C2×C61C2×#45511yescharacteristic
353D61—84no—
354C22×#41C2×D6111yescharacteristic
355C23×D4—611no—
356C22×M16—611no—
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×C42C2×D6111yescharacteristic
371#428—614no—
372#428—1222no—
373C2×#107—1221no—
374C2×#106—1221no—
375C2×#104—24no—
376C2×#104C2×D6114yescomplemented
377#417—614no—
378#417—1222no—
379C2×#103—1221no—
380C2×#102—1221no—
381C2×#100—614no—
382C2×#100—1224no—
383#390—614no—
384#390—1222no—
385#339—614no—
386C61C2×#203711yescharacteristic, complemented, Sylow
387C25—612no—
388C2×#41—21no—
389C2×#41—21no—
390C2×#41—22no—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41—22no—
394C2×#41D24412yes—
395C2×#41C22×D6112yes—
396C22×Q8D24411yescharacteristic
397C22×D4—21no—
398C22×D4—612no—
399C22×D4—612no—
400C22×D4—1222no—
401C22×D4—1222no—
402C22×D4—1221no—
403C22×D4—1221no—
404C22×D4—1222no—
405C22×D4—1221no—
406C22×D4—1221no—
407C22×D4—1222no—
408C22×D4—1222no—
409C22×D4—1222no—
410C22×D4D24411yescharacteristic
411C23×C4—21no—
412C23×C4—21no—
413C23×C4—1221no—
414C23×C4C22×D6111yescharacteristic
415C2×M16—21no—
416C2×M16—22no—
417C2×M16—612no—
418C2×M16—1221no—
419C2×M16—1222no—
420C2×M16—1222no—
421C2×M16C22⋊D6114yescomplemented
422C2×M16C22×D6112yes—
423C22×C8—21no—
424C22×C8—1221no—
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—22no—
453C2×C42—22no—
454C2×C42—21no—
455C2×C42—1221no—
456C2×C42C22×D6112yes—
457#107—1224no—
458#106—1224no—
459#104—28no—
460#103—1224no—
461#102—1224no—
462#100—1228no—
463C24—21no—
464C24—614no—
465C24—1222no—
466C24—1224no—
467C24—1222no—
468C24—1224no—
469C24—2444no—
470C24—2444no—
471C24D4×D6111yescharacteristic
472#41—22no—
473#41—22no—
474#41—22no—
475#41—22no—
476#41—24no—
477#41—24no—
478#41—42no—
479#41—42no—
480#41—42no—
481#41—42no—
482C2×Q8—21no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8C2×D24412yes—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—1228no—
494C2×D4—1228no—
495C2×D4—1222no—
496C2×D4—1222no—
497C2×D4—1222no—
498C2×D4—1222no—
499C2×D4—1222no—
500C2×D4—1222no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1224no—
504C2×D4—1224no—
505C2×D4—4884no—
506C2×D4—4884no—
507C2×D4—2442no—
508C2×D4—2442no—
509C2×D4—2442no—
510C2×D4—2442no—
511C2×D4—2442no—
512C2×D4—2442no—
513C2×D4—2442no—
514C2×D4—2442no—
515C2×D4C2×D24412yes—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1222no—
528C22×C4—2444no—
529C22×C4—2441no—
530C22×C4—2441no—
531C22×C4C2×D24411yescharacteristic
532C22×C4C2×D24411yescharacteristic
533C22×C4#1175822212yes—
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—1222no—
544M16—1222no—
545M16—2442no—
546M16C2×C22⋊D6114yescomplemented
547C2×C8—22no—
548C2×C8—24no—
549C2×C8—1222no—
550C2×C8—2442no—
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—22no—
565C42—22no—
566C42—42no—
567C42—1222no—
568C42—1222no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—1224no—
576C23—1224no—
577C23—1224no—
578C23—4888no—
579C23—4882no—
580C23—4882no—
581C23—24416no—
582C23—2444no—
583C23—2444no—
584C23—2444no—
585C23—2444no—
586C23—2444no—
587C23—2444no—
588C23#1451974711yescharacteristic
589C23#1451974711yescharacteristic
590C23#1451974812yes—
591C23#1451975912yes—
592C23C2×D4×D6111yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—42no—
596D4—22no—
597D4—22no—
598D4—42no—
599D4—42no—
600D4—44no—
601D4—42no—
602D4—4888no—
603D4—4888no—
604D4—2442no—
605D4—2442no—
606D4—2442no—
607D4—2442no—
608D4—2444no—
609D4—2444no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—42no—
613C2×C4—48no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—44no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—4882no—
622C2×C4—4882no—
623C2×C4—2444no—
624C2×C4—2442no—
625C2×C4—2442no—
626C2×C4—2442no—
627C2×C4#1451974711yescharacteristic
628C2×C4#1451974711yescharacteristic
629C2×C4#1451974812yes—
630C2×C4#1451974912yes—
631C2×C4#1451974912yes—
632C2×C4#1451975112yes—
633C2×C4#1451975112yes—
634C2×C4#1451975912yes—
635C2×C4#1451976112yes—
636C2×C4#1451976112yes—
637C2×C4#1451976312yes—
638C2×C4#1451976312yes—
639C2×C4C2×D4×D6111yescharacteristic
640C2×C4C22×C22⋊D6111yescharacteristic
641C2×C4C22×D24411yescharacteristic
642C2×C4C2×#1175822411yescharacteristic
643C2×C4C2×#1175822411yescharacteristic
644C2×C4C2×#1175822211yescharacteristic
645C8—24no—
646C8—2442no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—24no—
652C22—24no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—84no—
657C22—4884no—
658C22—4888no—
659C22—4888no—
660C22—2448no—
661C22—2444no—
662C22—2444no—
663C22—2444no—
664C22#1683967812yes—
665C22#1683967812yes—
666C22#1683993112yes—
667C22#1683994112yes—
668C22C2×#1451974711yescharacteristic
669C22C2×#1451974811yescharacteristic
670C22C2×#1451975911yescharacteristic
671C4—44no—
672C4—42no—
673C4—4882no—
674C4—2442no—
675C4—2442no—
676C4#1683967812yes—
677C4#1683967812yes—
678C4C2×#1451974911yescharacteristic
679C4C2×#1451975111yescharacteristic
680C4C2×#1451976111yescharacteristic
681C4C2×#1451976311yescharacteristic
682C2—21no—
683C2—22no—
684C2—21no—
685C2—82no—
686C2—4884no—
687C2#2144702814yesdirect product factor
688C2C2×#1683967811yescharacteristic
689C2C2×#1683993111yescharacteristic
690C2C2×#1683994111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#104×C61C2
socleC23×C61#120
prime radicalC2×#16840326C2
hypercenterC22×#104D61
hypocenterC61C2×#2037
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#16839804C2semidirect
3. C2×#16839763C2semidirect
4. C22×#14519693C2semidirect
5. C2×#16839664C2semidirect
6. #21447028C2direct (N × H)
7. C2×#16839522C2semidirect
8. C22×#104×C61C2semidirect
24. #16839804C22semidirect
28. #16839763C22semidirect
32. C2×#14519693C22semidirect
34. #16839664C22semidirect
35. #16839522C22semidirect
40. C2×#104×C61C22semidirect
109. C2×M16×C61D4semidirect
197. M16×C61C2×D4semidirect
339. C22×#104D61semidirect
349. C2×C61#2037semidirect
376. C2×#104C2×D61semidirect
386. C61C2×#2037semidirect
421. C2×M16C22⋊D61semidirect
546. M16C2×C22⋊D61semidirect
687. C2#21447028direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403262
C2×#168398042
C2×#168397632
C22×#145196932
C2×#168396642
#214470282
C2×#168395222
C22×#104×C612
C2×#203761