Finite Group Databasebeta

← C2×#21446932 #29707204

Subgroups — C2×#21446932 #29707204

Order 15616.

2030 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519808C211yesmaximal, characteristic, complemented
2C22×#14519805C211yesmaximal, characteristic
3C23×#11758201C211yesmaximal, characteristic, complemented
4C22×#14519693C211yesmaximal, characteristic, complemented
5C2×#16839730C211yesmaximal, characteristic, complemented
6#21446932C218yesmaximal, direct product factor
7C2×#16839526C211yesmaximal, characteristic, complemented
8C22×#101×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×D244C2211yescharacteristic
11C2×#14519808—24no—
12C2×#14519808—24no—
13C2×#14519808—22no—
14C2×#14519808C2214yescomplemented
15C2×#14519805—24no—
16C2×#14519805—22no—
17C2×#14519805—24no—
18C2×#14519805C2214yes—
19C22×#11758202—21no—
20C22×#11758190—21no—
21C22×#11758201—22no—
22C22×#11758201—22no—
23C22×#11758201—24no—
24C22×#11758201—24no—
25C22×#11758201—21no—
26C22×#11758201C2214yescomplemented
27C22×D488—21no—
28C22×#11758194C2211yescharacteristic
29C23×#92418C2211yescharacteristic
30C2×#14519693—24no—
31C2×#14519693C2214yescomplemented
32#16839730—22no—
33#16839730C2214yescomplemented
34C2×#14519689—22no—
35#16839526C2214yescomplemented
36C23×Q8×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C22×M16×C61C2211yescharacteristic
39C2×#101×C61—24no—
40C2×#101×C61C2214yescomplemented
41C24×D61—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—22no—
45C2×#11758222—22no—
46C2×#11758222—22no—
47C2×#11758222—22no—
48C2×#11758222D412yes—
49C2×#11758222C2312yes—
50C22×Dic122D411yescharacteristic
51C22×D244—21no—
52C22×D244—22no—
53C22×D244—21no—
54C22×D244—21no—
55C22×D244—21no—
56C22×D244—22no—
57C22×D244—22no—
58C22×D244—21no—
59C22×D244D411yescharacteristic
60C22×D244D414yes—
61C22×D244C2312yes—
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64#14519808—216no—
65#14519808—28no—
66#14519808—28no—
67#14519805—216no—
68#14519805—28no—
69#14519805—28no—
70C2×#11758202—28no—
71C2×#11758202—24no—
72C2×#11758190—28no—
73C2×#11758190—24no—
74C2×#11758201—216no—
75C2×#11758201—216no—
76C2×#11758201—28no—
77C2×#11758201—28no—
78C2×#11758201—28no—
79C2×#11758201—24no—
80C2×#11758201—28no—
81C2×D488—28no—
82C2×D488—24no—
83C2×#11758194—22no—
84C2×#11758194—21no—
85C2×#11758194D414yes—
86C2×#11758194C2312yes—
87C22×#92418—22no—
88C22×#92418—22no—
89C22×#92418—21no—
90C22×#92418D412yes—
91C22×#92418D412yes—
92C22×#92418C2312yes—
93#14519693—28no—
94#14519689—28no—
95C22×Q8×C61—22no—
96C22×Q8×C61—21no—
97C22×Q8×C61—22no—
98C22×Q8×C61—21no—
99C22×Q8×C61—21no—
100C22×Q8×C61—21no—
101C22×Q8×C61—21no—
102C22×Q8×C61—22no—
103C22×Q8×C61D414yes—
104C22×Q8×C61C2312yes—
105C23×C4×C61—21no—
106C23×C4×C61C2311yescharacteristic
107C2×M16×C61—22no—
108C2×M16×C61—21no—
109C2×M16×C61—21no—
110C2×M16×C61—22no—
111C2×M16×C61—22no—
112C2×M16×C61D414yes—
113C2×M16×C61C2312yes—
114C2×M16×C61C2312yes—
115C22×C8×C61—21no—
116C22×C8×C61—21no—
117#101×C61—28no—
118C24×C61#4111yescharacteristic
119C23×D61—21no—
120C23×D61—24no—
121C23×D61—22no—
122C23×D61—41no—
123C23×D61—42no—
124C23×D61—41no—
125C23×D61—84no—
126C2×Q8×C61—24no—
127C2×Q8×C61—22no—
128C2×Q8×C61—24no—
129C2×Q8×C61—24no—
130C2×Q8×C61—24no—
131C2×Q8×C61—24no—
132C2×Q8×C61—22no—
133C2×Q8×C61—22no—
134C2×Q8×C61—22no—
135C2×Q8×C61—22no—
136C2×Q8×C61—42no—
137C2×Q8×C61—42no—
138C2×Q8×C61—41no—
139C2×Q8×C61—41no—
140C2×Q8×C61—42no—
141C2×Q8×C61—42no—
142C2×Q8×C61—42no—
143C2×Q8×C61C2×D414yes—
144C22×C4×C61—24no—
145C22×C4×C61—22no—
146C22×C4×C61—41no—
147C22×C4×C61—42no—
148C22×C4×C61—41no—
149C22×C4×C61C2×D412yes—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61#4111yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C22×Dic61—21no—
164#11758222—24no—
165#11758222—24no—
166#11758222—22no—
167#11758222—22no—
168#11758222—22no—
169#11758222—22no—
170#11758222—42no—
171#11758222—42no—
172#11758222—42no—
173#11758222—42no—
174C2×D244—24no—
175C2×D244—24no—
176C2×D244—24no—
177C2×D244—24no—
178C2×D244—22no—
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—24no—
185C2×D244—21no—
186C2×D244—22no—
187C2×D244—42no—
188C2×D244—42no—
189C2×D244—41no—
190C2×D244—41no—
191C2×D244—42no—
192C2×D244—42no—
193C2×D244—42no—
194C2×D244C2×D414yes—
195C2×D244C2×D412yes—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—21no—
203C2×Dic122C2×D412yes—
204M16×C61—24no—
205M16×C61—22no—
206M16×C61—22no—
207M16×C61—22no—
208M16×C61—42no—
209M16×C61C2×D414yes—
210C2×C8×C61—24no—
211C2×C8×C61—22no—
212C2×C8×C61—22no—
213C2×C8×C61—42no—
214#11758202—216no—
215#11758201—216no—
216#11758201—232no—
217#11758194—24no—
218#11758194—22no—
219#11758194C2×D414yes—
220C2×#92418—24no—
221C2×#92418—24no—
222C2×#92418—24no—
223C2×#92418—22no—
224C2×#92418—22no—
225C2×#92418—22no—
226C2×#92418C2×D414yes—
227D488—216no—
228#11758190—216no—
229C23×C61—24no—
230C23×C61#12111yescharacteristic
231C23×C61#12112yes—
232C23×C61#12112yes—
233C23×C61#12111yescharacteristic
234C23×C61C2×#4111yescharacteristic
235C22×D61—22no—
236C22×D61—24no—
237C22×D61—42no—
238C22×D61—42no—
239C22×D61—42no—
240C22×D61—44no—
241C22×D61—44no—
242C22×D61—44no—
243C22×D61—88no—
244C22×D61—84no—
245C22×D61—84no—
246C22×D61—88no—
247C22×D61—84no—
248Q8×C61—24no—
249Q8×C61—24no—
250Q8×C61—42no—
251Q8×C61—42no—
252Q8×C61—44no—
253Q8×C61—44no—
254C2×C4×C61—24no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—44no—
258C2×C4×C61—44no—
259C2×C4×C61#12012yes—
260C2×C4×C61#12012yes—
261C2×C4×C61#12012yes—
262C2×C4×C61#12012yes—
263C2×C4×C61#12012yes—
264C2×C4×C61#12012yes—
265C2×C4×C61#12111yescharacteristic
266C2×C4×C61#12111yescharacteristic
267C2×C4×C61#12112yes—
268C2×C4×C61#12112yes—
269C2×C4×C61#12712yes—
270C2×C4×C61#12712yes—
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61C22×D411yescharacteristic
273C2×C4×C61C22×D411yescharacteristic
274C2×C4×C61C22×D411yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C22×D411yescharacteristic
277C22⋊D61—42no—
278C22⋊D61—42no—
279C22⋊D61—44no—
280C2×Dic61—22no—
281C2×Dic61—42no—
282D244—24no—
283D244—22no—
284D244—24no—
285D244—22no—
286D244—42no—
287D244—42no—
288D244—44no—
289D244—44no—
290D244—42no—
291C4×D61—42no—
292C4×D61—42no—
293C4×D61—44no—
294Dic122—22no—
295Dic122—22no—
296Dic122—42no—
297C8×C61—24no—
298C8×C61—42no—
299#92418—24no—
300#92418—24no—
301C2×#2019—611nomaximal, Sylow
302C22×C61—24no—
303C22×C61—24no—
304C22×C61—22no—
305C22×C61—22no—
306C22×C61#39212yes—
307C22×C61#39212yes—
308C22×C61#47114yes—
309C22×C61C2×#12111yescharacteristic
310C22×C61C2×#12111yescharacteristic
311C22×C61C2×#12111yescharacteristic
312C2×D61—42no—
313C2×D61—44no—
314C2×D61—44no—
315C2×D61—84no—
316C2×D61—88no—
317C2×D61—84no—
318C2×D61—88no—
319C2×D61—84no—
320C2×D61—84no—
321C4×C61—44no—
322C4×C61#39212yes—
323C4×C61#39212yes—
324C4×C61C2×#12011yescharacteristic
325C4×C61C2×#12011yescharacteristic
326C4×C61C2×#12011yescharacteristic
327C4×C61C2×#12711yescharacteristic
328Dic61—42no—
329C22×#137—611no—
330C22×AGL(1,ℤ/8)—611no—
331C23×SD16—611no—
332C22×#101D6111yescharacteristic, complemented
333C22×#100—611no—
334C2×#408—611no—
335#2019—618no—
336C2×#341—611no—
337C2×C61—21no—
338C2×C61—21no—
339C2×C61—22no—
340C2×C61#201914yescomplemented
341C2×C61C2×#39211yescharacteristic
342C2×C61C2×#47112yes—
343D61—82no—
344D61—84no—
345C22×#41—611no—
346C23×Q8C2×D6111yescharacteristic
347C23×D4—611no—
348C2×#137—614no—
349C2×#137—1224no—
350C2×#137—1222no—
351C2×#137—1224no—
352C2×AGL(1,ℤ/8)—614no—
353C2×AGL(1,ℤ/8)—1224no—
354C2×AGL(1,ℤ/8)—1222no—
355C2×AGL(1,ℤ/8)—1224no—
356C22×Q16—1221no—
357C22×SD16—614no—
358C22×SD16—1221no—
359C22×SD16—1222no—
360C22×SD16—1222no—
361C22×SD16—1224no—
362C22×SD16—1221no—
363C22×SD16—1224no—
364C22×D8—1221no—
365C22×M16—611no—
366C22×M16C2×D6111yescharacteristic
367C22×M16C2×D6111yescharacteristic
368C23×C8—611no—
369C2×#101—24no—
370C2×#101C2×D6114yescomplemented
371C2×#100—614no—
372C2×#100—1224no—
373#408—614no—
374#408—1222no—
375C2×C22⋊C8—1222no—
376#341—614no—
377C61C2×#201911yescharacteristic, complemented, Sylow
378C25—1221no—
379C2×#41—612no—
380C2×#41—612no—
381C2×#41—1221no—
382C2×#41—1221no—
383C2×#41—1222no—
384C2×#41—1222no—
385C2×#41—1222no—
386C2×#41—1222no—
387C22×Q8—21no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—21no—
391C22×Q8—21no—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8—22no—
395C22×Q8—611no—
396C22×Q8D24414yes—
397C22×Q8C22×D6112yes—
398C22×D4—611no—
399C22×D4—614no—
400C22×D4—612no—
401C22×D4—1221no—
402C22×D4—1222no—
403C22×D4—1221no—
404C22×D4—1221no—
405C22×D4—1221no—
406C22×D4—1221no—
407C22×D4—1221no—
408C22×D4—1222no—
409C22×D4—1222no—
410C23×C4—21no—
411C23×C4—1221no—
412C23×C4C22×D6111yescharacteristic
413#137—1228no—
414#137—12216no—
415#137—1228no—
416AGL(1,ℤ/8)—1228no—
417AGL(1,ℤ/8)—12216no—
418AGL(1,ℤ/8)—1228no—
419C2×Q16—1224no—
420C2×Q16—1228no—
421C2×SD16—1224no—
422C2×SD16—1228no—
423C2×SD16—1228no—
424C2×SD16—1228no—
425C2×SD16—1224no—
426C2×SD16—12216no—
427C2×SD16—12216no—
428C2×SD16—1228no—
429C2×SD16—1228no—
430C2×D8—1224no—
431C2×D8—1228no—
432C2×M16—21no—
433C2×M16—22no—
434C2×M16—21no—
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—614no—
438C2×M16—612no—
439C2×M16—1222no—
440C2×M16—1221no—
441C2×M16C22⋊D6114yes—
442C2×M16C22×D6112yes—
443C2×M16C22×D6112yes—
444C22×C8—21no—
445C22×C8—21no—
446C22×C8—612no—
447C22×C8—612no—
448C22×C8—612no—
449C22×C8—1222no—
450C22×C8—1222no—
451C22×C8—1221no—
452#101—28no—
453#100—1228no—
454C22⋊C8—1228no—
455C24—1222no—
456C24—1224no—
457C24—1221no—
458C24—4884no—
459C24—2441no—
460C24—2441no—
461C24—2442no—
462C24#1175822211yescharacteristic
463#41—1222no—
464#41—1222no—
465#41—1222no—
466#41—1222no—
467#41—1224no—
468#41—1224no—
469#41—2442no—
470#41—2442no—
471#41—2442no—
472#41—2442no—
473C2×Q8—22no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—41no—
486C2×Q8—42no—
487C2×Q8—41no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—612no—
491C2×Q8—1221no—
492C2×Q8—1222no—
493C2×Q8—1222no—
494C2×Q8C2×D24414yes—
495C2×D4—612no—
496C2×D4—614no—
497C2×D4—1222no—
498C2×D4—1222no—
499C2×D4—1222no—
500C2×D4—1222no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—1222no—
505C2×D4—1224no—
506C2×D4—1224no—
507C2×D4—1224no—
508C2×D4—1224no—
509C2×D4—1222no—
510C2×D4—1224no—
511C2×D4—1221no—
512C2×D4—2442no—
513C2×D4—2442no—
514C2×D4—2442no—
515C2×D4—2442no—
516C2×D4—2441no—
517C2×D4—2441no—
518C2×D4—2442no—
519C2×D4—2442no—
520C2×D4—2442no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—41no—
524C22×C4—42no—
525C22×C4—41no—
526C22×C4—1221no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—2442no—
530C22×C4—2442no—
531C22×C4C2×D24412yes—
532C22×C4#1175822211yescharacteristic
533C22×C4D4×D6112yes—
534C22×C4D4×D6111yescharacteristic
535C22×C4D4×D6111yescharacteristic
536C22×C4D4×D6111yescharacteristic
537C22×C4D4×D6112yes—
538C22×C4D4×D6111yescharacteristic
539C22×C4C2×C22⋊D6112yes—
540C22×C4C23×D6111yescharacteristic
541Q16—12216no—
542SD16—12216no—
543SD16—12232no—
544SD16—12216no—
545D8—12216no—
546M16—22no—
547M16—24no—
548M16—22no—
549M16—22no—
550M16—42no—
551M16—614no—
552M16—1222no—
553M16—1224no—
554M16C2×C22⋊D6114yes—
555C2×C8—22no—
556C2×C8—24no—
557C2×C8—22no—
558C2×C8—42no—
559C2×C8—614no—
560C2×C8—1222no—
561C2×C8—1222no—
562C2×C8—1222no—
563C2×C8—1224no—
564C2×C8—1224no—
565C2×C8—1224no—
566C23—24no—
567C23—1224no—
568C23—1222no—
569C23—4888no—
570C23—4884no—
571C23—4888no—
572C23—4884no—
573C23—4884no—
574C23—2442no—
575C23—2442no—
576C23—2444no—
577C23—2442no—
578C23—2444no—
579C23—2444no—
580C23#1451975011yescharacteristic
581C23#1451975012yes—
582C23#1451975011yescharacteristic
583C23#1451975112yes—
584C23C2×#1175822211yescharacteristic
585Q8—24no—
586Q8—24no—
587Q8—42no—
588Q8—42no—
589Q8—44no—
590Q8—44no—
591Q8—1222no—
592Q8—1222no—
593Q8—2442no—
594D4—1222no—
595D4—1224no—
596D4—1224no—
597D4—1222no—
598D4—2442no—
599D4—2442no—
600D4—2444no—
601D4—2442no—
602D4—2442no—
603D4—2444no—
604D4—2444no—
605D4—2442no—
606C2×C4—24no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—1222no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4—2444no—
616C2×C4#1451974512yes—
617C2×C4#1451974512yes—
618C2×C4#1451974712yes—
619C2×C4#1451974712yes—
620C2×C4#1451974712yes—
621C2×C4#1451974712yes—
622C2×C4#1451975011yescharacteristic
623C2×C4#1451975012yes—
624C2×C4#1451975011yescharacteristic
625C2×C4#1451975112yes—
626C2×C4#1451977312yes—
627C2×C4#1451977312yes—
628C2×C4C2×D4×D6111yescharacteristic
629C2×C4C2×D4×D6111yescharacteristic
630C2×C4C2×D4×D6111yescharacteristic
631C2×C4C2×D4×D6111yescharacteristic
632C2×C4C22×C22⋊D6111yescharacteristic
633C2×C4C22×D24411yescharacteristic
634C8—24no—
635C8—42no—
636C8—1224no—
637C8—1224no—
638C22—24no—
639C22—24no—
640C22—22no—
641C22—22no—
642C22—4884no—
643C22—4884no—
644C22—4888no—
645C22—4888no—
646C22—4884no—
647C22—4884no—
648C22—2442no—
649C22—2444no—
650C22—2444no—
651C22#1683967112yes—
652C22#1683967112yes—
653C22#1684002814yes—
654C22C2×#1451975011yescharacteristic
655C22C2×#1451975011yescharacteristic
656C22C2×#1451975111yescharacteristic
657C4—44no—
658C4—2442no—
659C4#1683967112yes—
660C4#1683967112yes—
661C4C2×#1451974511yescharacteristic
662C4C2×#1451974711yescharacteristic
663C4C2×#1451974711yescharacteristic
664C4C2×#1451977311yescharacteristic
665C2—21no—
666C2—21no—
667C2—22no—
668C2—4884no—
669C2—4882no—
670C2#2144693214yesdirect product factor
671C2C2×#1683967111yescharacteristic
672C2C2×#1684002812yes—
subgroupG/H
centerC23#14519750
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#101×C61C2
socleC23×C61#121
prime radicalC22×#14519805C2
hypercenterC22×#101D61
hypocenterC61C2×#2019
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
1. C22×#14519808C2semidirect
3. C23×#11758201C2semidirect
4. C22×#14519693C2semidirect
5. C2×#16839730C2semidirect
6. #21446932C2direct (N × H)
7. C2×#16839526C2semidirect
8. C22×#101×C61C2semidirect
14. C2×#14519808C22semidirect
26. C22×#11758201C22semidirect
31. C2×#14519693C22semidirect
33. #16839730C22semidirect
35. #16839526C22semidirect
40. C2×#101×C61C22semidirect
332. C22×#101D61semidirect
340. C2×C61#2019semidirect
370. C2×#101C2×D61semidirect
377. C61C2×#2019semidirect
670. C2#21446932direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198082
C22×#145198052
C23×#117582012
C22×#145196932
C2×#168397302
#214469322
C2×#168395262
C22×#101×C612
C2×#201961