Finite Group Databasebeta

← C2×#21446934 #29707206

Subgroups — C2×#21446934 #29707206

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×#14519807C211yesmaximal, characteristic, complemented
2C22×#14519802C211yesmaximal, characteristic
3C23×#11758190C211yesmaximal, characteristic, complemented
4C22×#14519695C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic, complemented
6#21446934C218yesmaximal, direct product factor
7C2×#16839527C211yesmaximal, characteristic, complemented
8C2×C61×#408C211yesmaximal, characteristic, complemented
9C23×Dic122C2211yescharacteristic
10C23×D244C2211yescharacteristic
11C2×#14519807—24no—
12C2×#14519807—22no—
13C2×#14519807—24no—
14C2×#14519807C2214yescomplemented
15C2×#14519802—24no—
16C2×#14519802—22no—
17C2×#14519802—24no—
18C2×#14519802C2214yes—
19C22×#11758202—21no—
20C22×#11758190—22no—
21C22×#11758190—22no—
22C22×#11758190—24no—
23C22×#11758190—24no—
24C22×#11758190C2214yescomplemented
25C22×#11758200—21no—
26C22×#11758201—21no—
27C22×#11758199—21no—
28C22×#11758194C2211yescharacteristic
29C22×#11758194C2211yescharacteristic
30C2×#14519695—24no—
31C2×#14519695C2214yescomplemented
32C2×#14519693—24no—
33C2×#14519693C2214yescomplemented
34#16839527C2214yescomplemented
35C22×#41×C61C2211yescharacteristic
36C22×M16×C61C2211yescharacteristic
37C23×C8×C61C2211yescharacteristic
38C61×#408—22no—
39C61×#408C2214yescomplemented
40C2×C22⋊C8×C61—22no—
41C24×D61—21no—
42C22×Dic122—21no—
43C22×Dic122—22no—
44C22×Dic122—21no—
45C22×Dic122—21no—
46C22×Dic122—22no—
47C22×Dic122—21no—
48C22×Dic122—22no—
49C22×Dic122—21no—
50C22×Dic122D414yes—
51C22×Dic122C2312yes—
52C22×D244—21no—
53C22×D244—22no—
54C22×D244—21no—
55C22×D244—21no—
56C22×D244—21no—
57C22×D244—22no—
58C22×D244—22no—
59C22×D244—21no—
60C22×D244D414yes—
61C22×D244C2312yes—
62C23×Dic61—21no—
63#14519807—216no—
64#14519807—28no—
65#14519807—28no—
66#14519802—216no—
67#14519802—28no—
68#14519802—28no—
69C2×#11758202—28no—
70C2×#11758202—24no—
71C2×#11758190—216no—
72C2×#11758190—216no—
73C2×#11758190—28no—
74C2×#11758190—28no—
75C2×#11758190—28no—
76C2×#11758200—28no—
77C2×#11758200—24no—
78C2×#11758201—28no—
79C2×#11758201—24no—
80C2×#11758199—28no—
81C2×#11758199—24no—
82C2×#11758194—22no—
83C2×#11758194—21no—
84C2×#11758194—22no—
85C2×#11758194—21no—
86C2×#11758194D414yes—
87C2×#11758194D414yes—
88C2×#11758194C2312yes—
89C2×#11758194C2312yes—
90C22×#92418—21no—
91C22×#92418—21no—
92#14519695—28no—
93#14519693—28no—
94C2×#41×C61—21no—
95C2×#41×C61—21no—
96C2×#41×C61—22no—
97C2×#41×C61—22no—
98C2×#41×C61—22no—
99C2×#41×C61—22no—
100C2×#41×C61D412yes—
101C2×#41×C61C2312yes—
102C22×Q8×C61D411yescharacteristic
103C22×D4×C61—21no—
104C22×D4×C61D411yescharacteristic
105C23×C4×C61—21no—
106C23×C4×C61C2311yescharacteristic
107C2×M16×C61—21no—
108C2×M16×C61—22no—
109C2×M16×C61—22no—
110C2×M16×C61C2312yes—
111C22×C8×C61—22no—
112C22×C8×C61—22no—
113C22×C8×C61—21no—
114C22×C8×C61D412yes—
115C22×C8×C61D412yes—
116C22×C8×C61C2312yes—
117C22⋊C8×C61—28no—
118C24×C61—21no—
119C24×C61#4111yescharacteristic
120C23×D61—24no—
121C23×D61—22no—
122C23×D61—42no—
123C23×D61—41no—
124C23×D61—41no—
125C23×D61—84no—
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—22no—
143C2×D4×C61—22no—
144C2×D4×C61—21no—
145C2×D4×C61—42no—
146C2×D4×C61—42no—
147C2×D4×C61C2×D412yes—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D412yes—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61#4111yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—24no—
164C22×Dic61—22no—
165C22×Dic61—42no—
166C22×Dic61—41no—
167C22×Dic61—41no—
168C2×D244—24no—
169C2×D244—24no—
170C2×D244—24no—
171C2×D244—24no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—24no—
177C2×D244—22no—
178C2×D244—42no—
179C2×D244—42no—
180C2×D244—42no—
181C2×D244—41no—
182C2×D244—41no—
183C2×D244—42no—
184C2×D244—42no—
185C2×D244C2×D414yes—
186C2×Dic122—24no—
187C2×Dic122—24no—
188C2×Dic122—24no—
189C2×Dic122—24no—
190C2×Dic122—22no—
191C2×Dic122—22no—
192C2×Dic122—22no—
193C2×Dic122—22no—
194C2×Dic122—24no—
195C2×Dic122—22no—
196C2×Dic122—42no—
197C2×Dic122—42no—
198C2×Dic122—42no—
199C2×Dic122—41no—
200C2×Dic122—41no—
201C2×Dic122—42no—
202C2×Dic122—42no—
203C2×Dic122C2×D414yes—
204M16×C61—22no—
205M16×C61—22no—
206M16×C61—42no—
207C2×C8×C61—24no—
208C2×C8×C61—24no—
209C2×C8×C61—22no—
210C2×C8×C61—22no—
211C2×C8×C61—22no—
212C2×C8×C61—42no—
213C2×C8×C61C2×D414yes—
214#11758202—216no—
215#11758201—216no—
216#11758200—216no—
217#11758199—216no—
218#11758194—24no—
219#11758194—24no—
220#11758194—22no—
221#11758194—22no—
222#11758194C2×D414yes—
223#11758194C2×D414yes—
224C2×#92418—24no—
225C2×#92418—24no—
226C2×#92418—22no—
227C2×#92418—22no—
228#11758190—232no—
229C23×C61—24no—
230C23×C61—22no—
231C23×C61—42no—
232C23×C61—44no—
233C23×C61#12112yes—
234C23×C61#12112yes—
235C23×C61#12111yescharacteristic
236C23×C61#12111yescharacteristic
237C23×C61C2×#4111yescharacteristic
238C22×D61—24no—
239C22×D61—42no—
240C22×D61—42no—
241C22×D61—44no—
242C22×D61—44no—
243C22×D61—88no—
244C22×D61—84no—
245C22×D61—84no—
246C22×D61—88no—
247C22×D61—84no—
248Q8×C61—22no—
249Q8×C61—22no—
250Q8×C61—42no—
251D4×C61—22no—
252D4×C61—22no—
253D4×C61—42no—
254D4×C61—42no—
255D4×C61—44no—
256D4×C61—42no—
257C2×C4×C61—22no—
258C2×C4×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61—42no—
261C2×C4×C61—44no—
262C2×C4×C61#12012yes—
263C2×C4×C61#12012yes—
264C2×C4×C61#12012yes—
265C2×C4×C61#12012yes—
266C2×C4×C61#12012yes—
267C2×C4×C61#12012yes—
268C2×C4×C61#12112yes—
269C2×C4×C61#12112yes—
270C2×C4×C61#12111yescharacteristic
271C2×C4×C61#12111yescharacteristic
272C2×C4×C61#12712yes—
273C2×C4×C61#12712yes—
274C2×C4×C61C22×D411yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C22×D411yescharacteristic
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C22×D411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×Dic61—24no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—44no—
284C2×Dic61—44no—
285D244—24no—
286D244—24no—
287D244—42no—
288D244—42no—
289D244—44no—
290D244—44no—
291Dic122—24no—
292Dic122—24no—
293Dic122—42no—
294Dic122—42no—
295Dic122—44no—
296Dic122—44no—
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—42no—
307C22×C61—44no—
308C22×C61—84no—
309C22×C61#39212yes—
310C22×C61#39212yes—
311C22×C61#47114yes—
312C22×C61C2×#12111yescharacteristic
313C22×C61C2×#12111yescharacteristic
314C22×C61C2×#12111yescharacteristic
315C2×D61—44no—
316C2×D61—84no—
317C2×D61—88no—
318C2×D61—88no—
319C2×D61—84no—
320C2×D61—84no—
321C4×C61—42no—
322C4×C61#39212yes—
323C4×C61#39212yes—
324C4×C61C2×#12011yescharacteristic
325C4×C61C2×#12011yescharacteristic
326C4×C61C2×#12011yescharacteristic
327C4×C61C2×#12711yescharacteristic
328Dic61—44no—
329C22×#137—611no—
330C22×AGL(1,ℤ/8)—611no—
331C23×SD16—611no—
332C22×#101—611no—
333C22×#100—611no—
334C2×#408D6111yescharacteristic, complemented
335#2019—618no—
336C2×#341—611no—
337C2×C61—21no—
338C2×C61—21no—
339C2×C61—22no—
340C2×C61—82no—
341C2×C61#201914yescomplemented
342C2×C61C2×#39211yescharacteristic
343C2×C61C2×#47112yes—
344D61—84no—
345C22×#41C2×D6111yescharacteristic
346C23×Q8—611no—
347C23×D4—611no—
348C2×#137—614no—
349C2×#137—1224no—
350C2×#137—1224no—
351C2×#137—1222no—
352C2×AGL(1,ℤ/8)—614no—
353C2×AGL(1,ℤ/8)—1224no—
354C2×AGL(1,ℤ/8)—1224no—
355C2×AGL(1,ℤ/8)—1222no—
356C22×Q16—1221no—
357C22×SD16—614no—
358C22×SD16—1224no—
359C22×SD16—1224no—
360C22×SD16—1221no—
361C22×SD16—1221no—
362C22×SD16—1222no—
363C22×SD16—1222no—
364C22×D8—1221no—
365C22×M16—611no—
366C22×M16—611no—
367C22×M16C2×D6111yescharacteristic
368C23×C8C2×D6111yescharacteristic
369C2×#101—614no—
370C2×#101—1224no—
371C2×#100—614no—
372C2×#100—1224no—
373#408—22no—
374#408C2×D6114yescomplemented
375C2×C22⋊C8—22no—
376#341—614no—
377C61C2×#201911yescharacteristic, complemented, Sylow
378C25—1221no—
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—22no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41—22no—
385C2×#41D24412yes—
386C2×#41C22×D6112yes—
387C22×Q8—614no—
388C22×Q8—612no—
389C22×Q8—1221no—
390C22×Q8—1222no—
391C22×Q8—1221no—
392C22×Q8—1221no—
393C22×Q8—1222no—
394C22×Q8—1222no—
395C22×Q8—1221no—
396C22×Q8—1221no—
397C22×Q8D24411yescharacteristic
398C22×D4—21no—
399C22×D4—614no—
400C22×D4—612no—
401C22×D4—1221no—
402C22×D4—1221no—
403C22×D4—1221no—
404C22×D4—1222no—
405C22×D4—1222no—
406C22×D4—1222no—
407C22×D4—1221no—
408C22×D4—1221no—
409C22×D4D24411yescharacteristic
410C23×C4—21no—
411C23×C4—1221no—
412C23×C4C22×D6111yescharacteristic
413#137—1228no—
414#137—1228no—
415#137—12216no—
416AGL(1,ℤ/8)—1228no—
417AGL(1,ℤ/8)—1228no—
418AGL(1,ℤ/8)—12216no—
419C2×Q16—1228no—
420C2×Q16—1224no—
421C2×SD16—1228no—
422C2×SD16—1228no—
423C2×SD16—12216no—
424C2×SD16—12216no—
425C2×SD16—1228no—
426C2×SD16—1228no—
427C2×SD16—1224no—
428C2×SD16—1224no—
429C2×SD16—1228no—
430C2×D8—1228no—
431C2×D8—1224no—
432C2×M16—21no—
433C2×M16—22no—
434C2×M16—22no—
435C2×M16—614no—
436C2×M16—614no—
437C2×M16—612no—
438C2×M16—612no—
439C2×M16—1221no—
440C2×M16—1221no—
441C2×M16—1222no—
442C2×M16—1222no—
443C2×M16C22×D6112yes—
444C22×C8—22no—
445C22×C8—22no—
446C22×C8—21no—
447C22×C8—1221no—
448C22×C8—1221no—
449C22×C8C22⋊D6112yes—
450C22×C8C22⋊D6112yes—
451C22×C8C22×D6112yes—
452#101—1228no—
453#100—1228no—
454C22⋊C8—28no—
455C24—21no—
456C24—1222no—
457C24—1224no—
458C24—4884no—
459C24—2442no—
460C24—2441no—
461C24—2441no—
462C24#1175822211yescharacteristic
463#41—22no—
464#41—22no—
465#41—22no—
466#41—22no—
467#41—24no—
468#41—24no—
469#41—42no—
470#41—42no—
471#41—42no—
472#41—42no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—614no—
477C2×Q8—1222no—
478C2×Q8—1224no—
479C2×Q8—1222no—
480C2×Q8—1222no—
481C2×Q8—1222no—
482C2×Q8—1222no—
483C2×Q8—1224no—
484C2×Q8—1224no—
485C2×Q8—1224no—
486C2×Q8—1224no—
487C2×Q8—2442no—
488C2×Q8—2442no—
489C2×Q8—2442no—
490C2×Q8—2441no—
491C2×Q8—2441no—
492C2×Q8—2442no—
493C2×Q8—2442no—
494C2×Q8C2×D24412yes—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—614no—
503C2×D4—1222no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1224no—
509C2×D4—1224no—
510C2×D4—1224no—
511C2×D4—1224no—
512C2×D4—1224no—
513C2×D4—2442no—
514C2×D4—2442no—
515C2×D4—2442no—
516C2×D4—2441no—
517C2×D4—2441no—
518C2×D4—2442no—
519C2×D4—2442no—
520C2×D4C2×D24412yes—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—1222no—
527C22×C4—1224no—
528C22×C4—2442no—
529C22×C4—2441no—
530C22×C4—2441no—
531C22×C4C2×D24411yescharacteristic
532C22×C4C2×D24411yescharacteristic
533C22×C4#1175822211yescharacteristic
534C22×C4D4×D6112yes—
535C22×C4D4×D6112yes—
536C22×C4D4×D6112yes—
537C22×C4D4×D6112yes—
538C22×C4C2×C22⋊D6111yescharacteristic
539C22×C4C2×C22⋊D6111yescharacteristic
540C22×C4C23×D6111yescharacteristic
541Q16—12216no—
542SD16—12232no—
543SD16—12216no—
544SD16—12216no—
545D8—12216no—
546M16—22no—
547M16—22no—
548M16—42no—
549M16—614no—
550M16—614no—
551M16—1222no—
552M16—1222no—
553M16—1224no—
554M16—1224no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—22no—
560C2×C8—42no—
561C2×C8—1222no—
562C2×C8—1222no—
563C2×C8—1224no—
564C2×C8—1224no—
565C2×C8C2×C22⋊D6114yes—
566C23—24no—
567C23—22no—
568C23—44no—
569C23—42no—
570C23—1224no—
571C23—4888no—
572C23—4884no—
573C23—4888no—
574C23—4884no—
575C23—4884no—
576C23—2442no—
577C23—2442no—
578C23—2444no—
579C23—2444no—
580C23#1451975012yes—
581C23#1451975012yes—
582C23#1451975111yescharacteristic
583C23#1451975111yescharacteristic
584C23C2×#1175822211yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—42no—
588Q8—1224no—
589Q8—1224no—
590Q8—2442no—
591Q8—2442no—
592Q8—2444no—
593Q8—2444no—
594D4—22no—
595D4—22no—
596D4—42no—
597D4—42no—
598D4—44no—
599D4—42no—
600D4—1224no—
601D4—1224no—
602D4—2442no—
603D4—2442no—
604D4—2444no—
605D4—2444no—
606C2×C4—22no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—1224no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2444no—
615C2×C4—2444no—
616C2×C4#1451974512yes—
617C2×C4#1451974512yes—
618C2×C4#1451974712yes—
619C2×C4#1451974712yes—
620C2×C4#1451974712yes—
621C2×C4#1451974712yes—
622C2×C4#1451975012yes—
623C2×C4#1451975012yes—
624C2×C4#1451975111yescharacteristic
625C2×C4#1451975111yescharacteristic
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—42no—
643C22—44no—
644C22—84no—
645C22—4884no—
646C22—4884no—
647C22—4888no—
648C22—4888no—
649C22—4884no—
650C22—2444no—
651C22#1683967112yes—
652C22#1683967112yes—
653C22#1684002514yes—
654C22C2×#1451975011yescharacteristic
655C22C2×#1451975011yescharacteristic
656C22C2×#1451975111yescharacteristic
657C4—42no—
658C4—2444no—
659C4#1683967112yes—
660C4#1683967112yes—
661C4C2×#1451974511yescharacteristic
662C4C2×#1451974711yescharacteristic
663C4C2×#1451974711yescharacteristic
664C4C2×#1451977311yescharacteristic
665C2—21no—
666C2—21no—
667C2—22no—
668C2—82no—
669C2—4884no—
670C2#2144693414yesdirect product factor
671C2C2×#1683967111yescharacteristic
672C2C2×#1684002512yes—
subgroupG/H
centerC23#14519751
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#408C2
socleC23×C61#121
prime radicalC22×#14519802C2
hypercenterC2×#408D61
hypocenterC61C2×#2019
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C22×#14519807C2semidirect
3. C23×#11758190C2semidirect
4. C22×#14519695C2semidirect
5. C22×#14519693C2semidirect
6. #21446934C2direct (N × H)
7. C2×#16839527C2semidirect
8. C2×C61×#408C2semidirect
14. C2×#14519807C22semidirect
24. C22×#11758190C22semidirect
31. C2×#14519695C22semidirect
33. C2×#14519693C22semidirect
34. #16839527C22semidirect
39. C61×#408C22semidirect
334. C2×#408D61semidirect
341. C2×C61#2019semidirect
374. #408C2×D61semidirect
377. C61C2×#2019semidirect
670. C2#21446934direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198072
C22×#145198022
C23×#117581902
C22×#145196952
C22×#145196932
#214469342
C2×#168395272
C2×C61×#4082
C2×#201961