Finite Group Databasebeta

← C2×#21447375 #29709898

Subgroups — C2×#21447375 #29709898

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839810C211yesmaximal, characteristic, complemented
2C2×#16839788C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic
4C2×#16839778C211yesmaximal, characteristic
5C2×#16839728C211yesmaximal, characteristic
6#21447375C218yesmaximal, direct product factor
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×#424C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12C2×#14519736C2211yescharacteristic
13#16839810—22no—
14#16839810C2214yescomplemented
15C2×#14519712—22no—
16#16839788—22no—
17#16839788C2214yescomplemented
18C2×#14519706—22no—
19#16839780—22no—
20#16839780C2214yes—
21#16839778—22no—
22#16839778C2214yes—
23C2×#14519705—22no—
24C2×#14519703—22no—
25#16839728—22no—
26#16839728C2214yes—
27C2×#14519689—22no—
28#16839518C2214yescomplemented
29C22×M16×C61C2211yescharacteristic
30C23×C8×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic
32C61×#424—22no—
33C61×#424C2214yescomplemented
34C2×C4⋊C8×C61—22no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222Q812yes—
46C2×#11758222C2312yes—
47C22×Dic122Q811yescharacteristic
48C22×D244Q811yescharacteristic
49C22×C22⋊D61—21no—
50C22×C4×D61—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194D412yes—
61C2×#11758194C2312yes—
62C2×#11758194C2312yes—
63C22×#92418—21no—
64C22×#92418D412yes—
65#14519736—21no—
66#14519736—21no—
67#14519736D412yes—
68#14519736C2312yes—
69C2×C4⋊Dic61—21no—
70C2×C22⋊Dic61—21no—
71C2×C4×Dic61D412yes—
72#14519712—28no—
73#14519706—28no—
74#14519705—28no—
75#14519703—28no—
76#14519689—28no—
77C23×C4×C61C2311yescharacteristic
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61C2312yes—
84C22×C8×C61—21no—
85C22×C8×C61—21no—
86C22×C8×C61—21no—
87C22×C8×C61—21no—
88C22×C8×C61—21no—
89C22×C8×C61—21no—
90C22×C8×C61—21no—
91C22×C8×C61C2312yes—
92#117×C61—21no—
93#117×C61—21no—
94#117×C61D412yes—
95#117×C61C2312yes—
96C2×C4⋊C4×C61—21no—
97C2×C22⋊C4×C61—21no—
98C2×C42×C61D412yes—
99C4⋊C8×C61—28no—
100C24×C61#4111yescharacteristic
101C23×D61—21no—
102C22×C4×C61—22no—
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×Q811yescharacteristic
110C22×C4×C61C2×Q811yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×C4×C61C2411yescharacteristic
117C2×C22⋊D61—22no—
118C2×C22⋊D61—22no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C22×Dic61—21no—
124C22×Dic61—22no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139#11758222—41no—
140#11758222—41no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244C2×Q812yes—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122C2×Q812yes—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—41no—
162M16×C61—41no—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61—22no—
167C2×C8×C61—41no—
168C2×C8×C61—41no—
169C2×C8×C61—41no—
170C2×C8×C61—41no—
171C2×C8×C61—41no—
172C2×C8×C61—41no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176C22⋊C4×C61—22no—
177C42×C61—22no—
178C42×C61C2×D414yes—
179C22⋊Dic61—22no—
180C22⋊Dic61—22no—
181C4⋊Dic61—22no—
182C4⋊Dic61—22no—
183C4×Dic61—22no—
184C4×Dic61C2×D414yes—
185#11758194—22no—
186#11758194—22no—
187#11758194—22no—
188#11758194—22no—
189#11758194—22no—
190#11758194—22no—
191#11758194—41no—
192#11758194—41no—
193C2×#92418—22no—
194C2×#92418—22no—
195C2×#92418—22no—
196C2×#92418—41no—
197C2×#92418—41no—
198C2×#92418C2×D414yes—
199C23×C61—42no—
200C23×C61C22⋊Q811yescharacteristic
201C23×C61C22⋊Q811yescharacteristic
202C23×C61#12311yescharacteristic
203C23×C61#12311yescharacteristic
204C23×C61#12311yescharacteristic
205C23×C61#12311yescharacteristic
206C23×C61C2×#4111yescharacteristic
207C22×D61—22no—
208C22×D61—44no—
209C22×D61—41no—
210C22×D61—41no—
211C2×C4×C61—24no—
212C2×C4×C61—44no—
213C2×C4×C61C22⋊Q811yescharacteristic
214C2×C4×C61C22⋊Q811yescharacteristic
215C2×C4×C61C22⋊Q811yescharacteristic
216C2×C4×C61C22⋊Q811yescharacteristic
217C2×C4×C61C22⋊Q811yescharacteristic
218C2×C4×C61C22⋊Q811yescharacteristic
219C2×C4×C61C22⋊Q811yescharacteristic
220C2×C4×C61C22⋊Q811yescharacteristic
221C2×C4×C61C22⋊Q811yescharacteristic
222C2×C4×C61C22⋊Q811yescharacteristic
223C2×C4×C61#12311yescharacteristic
224C2×C4×C61#12311yescharacteristic
225C2×C4×C61#12311yescharacteristic
226C2×C4×C61#12311yescharacteristic
227C2×C4×C61#12311yescharacteristic
228C2×C4×C61#12311yescharacteristic
229C2×C4×C61#12311yescharacteristic
230C2×C4×C61#12311yescharacteristic
231C2×C4×C61#12711yescharacteristic
232C2×C4×C61#12711yescharacteristic
233C2×C4×C61#12711yescharacteristic
234C2×C4×C61#12711yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×Q811yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C22⋊D61—42no—
242C22⋊D61—42no—
243C22⋊D61—42no—
244C22⋊D61—42no—
245C2×Dic61—22no—
246C2×Dic61—24no—
247C2×Dic61—44no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250D244—22no—
251D244—22no—
252D244—41no—
253D244—41no—
254C4×D61—42no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—42no—
258Dic122—22no—
259Dic122—22no—
260Dic122—41no—
261Dic122—41no—
262C8×C61—42no—
263C8×C61—42no—
264#92418—24no—
265#92418—42no—
266C2×#2098—611nomaximal, Sylow
267C22×C61—22no—
268C22×C61—22no—
269C22×C61—22no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61#39911yescharacteristic
275C22×C61#39911yescharacteristic
276C22×C61#39911yescharacteristic
277C22×C61#39911yescharacteristic
278C22×C61C2×C22⋊Q811yescharacteristic
279C22×C61C2×#12311yescharacteristic
280C22×C61C2×#12311yescharacteristic
281C2×D61—44no—
282C2×D61—42no—
283C2×D61—82no—
284C2×D61—82no—
285C4×C61—44no—
286C4×C61#39911yescharacteristic
287C4×C61#39911yescharacteristic
288C4×C61#39911yescharacteristic
289C4×C61#39911yescharacteristic
290C4×C61C2×C22⋊Q811yescharacteristic
291C4×C61C2×C22⋊Q811yescharacteristic
292C4×C61C2×#12311yescharacteristic
293C4×C61C2×#12711yescharacteristic
294Dic61—44no—
295Dic61—42no—
296C2×#430—611no—
297C2×#424—611no—
298C2×#424D6111yescharacteristic, complemented
299C2×#421—611no—
300C2×#421—611no—
301C2×#408—611no—
302#2098—618no—
303C2×H(3,ℤ/4)—611no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61—21no—
309C2×C61—21no—
310C2×C61#209812yescomplemented
311C2×C61C2×#39911yescharacteristic
312D61—82no—
313C22×#41—611no—
314C22×M16—611no—
315C22×M16—611no—
316C22×M16C2×D6111yescharacteristic
317C23×C8C2×D6111yescharacteristic
318C2×#117—611no—
319C2×#117C2×D6111yescharacteristic
320#430—614no—
321#430—1222no—
322C2×#108—1222no—
323#424—22no—
324#424—614no—
325#424—1222no—
326#424C2×D6114yescomplemented
327C2×C4⋊C8—22no—
328C2×C4⋊C8—1222no—
329#421—614no—
330#421—614no—
331#421—1222no—
332#421—1222no—
333C2×#104—1222no—
334C2×#104—1222no—
335#408—614no—
336#408—1222no—
337C2×C22⋊C8—1222no—
338H(3,ℤ/4)—614no—
339C61C2×#209811yescharacteristic, complemented, Sylow
340C2×#41—612no—
341C2×#41—612no—
342C2×#41—1221no—
343C2×#41—1221no—
344C2×#41—1221no—
345C2×#41—1221no—
346C2×#41—1221no—
347C2×#41—1221no—
348C2×#41—1221no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1221no—
352C22×Q8—611no—
353C22×D4—611no—
354C22×D4—1221no—
355C23×C4—1221no—
356C23×C4C22×D6111yescharacteristic
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—612no—
363C2×M16—612no—
364C2×M16—612no—
365C2×M16—1221no—
366C2×M16—1221no—
367C2×M16—1221no—
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16—1221no—
372C2×M16—1221no—
373C2×M16—1221no—
374C2×M16C22×D6112yes—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—612no—
383C22×C8—1221no—
384C22×C8C22×D6112yes—
385#117—21no—
386#117—21no—
387#117—612no—
388#117—612no—
389#117—1221no—
390#117—1221no—
391#117C22⋊D6112yes—
392#117C22×D6112yes—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—1221no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—1221no—
397C2×C42—612no—
398C2×C42C22⋊D6112yes—
399#108—1228no—
400C4⋊C8—28no—
401C4⋊C8—1228no—
402#104—1228no—
403#104—1228no—
404C22⋊C8—1228no—
405C24—1221no—
406C24#1175822211yescharacteristic
407#41—1222no—
408#41—1222no—
409#41—1222no—
410#41—1222no—
411#41—1222no—
412#41—1222no—
413#41—1222no—
414#41—1222no—
415#41—2441no—
416#41—2441no—
417#41—2441no—
418#41—2441no—
419#41—2441no—
420#41—2441no—
421#41—2441no—
422#41—2441no—
423C2×Q8—612no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×D4—612no—
430C2×D4—1222no—
431C2×D4—1222no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—1221no—
436C2×D4—1221no—
437C2×D4—2441no—
438C2×D4—2441no—
439C2×D4—2441no—
440C2×D4—2441no—
441C22×C4—22no—
442C22×C4—1221no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—1222no—
446C22×C4—2441no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4#1175822211yescharacteristic
451C22×C4#1175822211yescharacteristic
452C22×C4#1175822211yescharacteristic
453C22×C4D4×D6111yescharacteristic
454C22×C4D4×D6111yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4Q8×D6111yescharacteristic
458C22×C4Q8×D6111yescharacteristic
459C22×C4#1175822611yescharacteristic
460C22×C4#1175822611yescharacteristic
461C22×C4C2×C22⋊D6111yescharacteristic
462C22×C4C2×C22⋊D6111yescharacteristic
463C22×C4C23×D6111yescharacteristic
464M16—22no—
465M16—22no—
466M16—41no—
467M16—41no—
468M16—1222no—
469M16—1222no—
470M16—1222no—
471M16—1222no—
472M16—1222no—
473M16—1222no—
474M16—2441no—
475M16—2441no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—614no—
487C2×C8—1222no—
488C2×C8—1222no—
489C2×C8—1222no—
490C2×C8—2441no—
491C2×C8—2441no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C42—22no—
501C42—614no—
502C42—1222no—
503C42C2×C22⋊D6114yes—
504C23—42no—
505C23—1222no—
506C23—2444no—
507C23—2441no—
508C23—2441no—
509C23#1451975511yescharacteristic
510C23#1451975511yescharacteristic
511C23#1451976011yescharacteristic
512C23#1451976011yescharacteristic
513C23#1451976211yescharacteristic
514C23#1451976211yescharacteristic
515C23C2×#1175822211yescharacteristic
516Q8—1222no—
517Q8—1222no—
518Q8—2441no—
519Q8—2441no—
520D4—1222no—
521D4—1222no—
522D4—2442no—
523D4—2442no—
524D4—2442no—
525D4—2442no—
526D4—2441no—
527D4—2441no—
528C2×C4—24no—
529C2×C4—44no—
530C2×C4—1222no—
531C2×C4—1224no—
532C2×C4—2444no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4—2442no—
539C2×C4#1451975311yescharacteristic
540C2×C4#1451975311yescharacteristic
541C2×C4#1451975311yescharacteristic
542C2×C4#1451975311yescharacteristic
543C2×C4#1451975511yescharacteristic
544C2×C4#1451975511yescharacteristic
545C2×C4#1451975511yescharacteristic
546C2×C4#1451975511yescharacteristic
547C2×C4#1451975511yescharacteristic
548C2×C4#1451975511yescharacteristic
549C2×C4#1451976011yescharacteristic
550C2×C4#1451976011yescharacteristic
551C2×C4#1451976211yescharacteristic
552C2×C4#1451976211yescharacteristic
553C2×C4#1451976211yescharacteristic
554C2×C4#1451976211yescharacteristic
555C2×C4#1451976211yescharacteristic
556C2×C4#1451976211yescharacteristic
557C2×C4#1451977311yescharacteristic
558C2×C4#1451977311yescharacteristic
559C2×C4#1451977311yescharacteristic
560C2×C4#1451977311yescharacteristic
561C2×C4C2×D4×D6111yescharacteristic
562C2×C4C2×D4×D6111yescharacteristic
563C2×C4C22×C22⋊D6111yescharacteristic
564C2×C4C2×Q8×D6111yescharacteristic
565C2×C4C2×#1175822211yescharacteristic
566C2×C4C2×#1175822611yescharacteristic
567C8—42no—
568C8—42no—
569C8—1224no—
570C8—2442no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—4882no—
579C22—4882no—
580C22—2444no—
581C22—2442no—
582C22#1683969711yescharacteristic
583C22#1683969711yescharacteristic
584C22#1683969711yescharacteristic
585C22#1683969711yescharacteristic
586C22C2×#1451975511yescharacteristic
587C22C2×#1451976011yescharacteristic
588C22C2×#1451976211yescharacteristic
589C4—44no—
590C4—2444no—
591C4—2442no—
592C4#1683969711yescharacteristic
593C4#1683969711yescharacteristic
594C4#1683969711yescharacteristic
595C4#1683969711yescharacteristic
596C4C2×#1451975311yescharacteristic
597C4C2×#1451975511yescharacteristic
598C4C2×#1451976211yescharacteristic
599C4C2×#1451977311yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—4882no—
607C2#2144737512yesdirect product factor
608C2C2×#1683969711yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#424C2
socleC22×C61#399
prime radicalC22×#11758222C22
hypercenterC2×#424D61
hypocenterC61C2×#2098
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#16839810C2semidirect
2. C2×#16839788C2semidirect
6. #21447375C2direct (N × H)
7. C2×#16839518C2semidirect
8. C2×C61×#424C2semidirect
14. #16839810C22semidirect
17. #16839788C22semidirect
28. #16839518C22semidirect
33. C61×#424C22semidirect
298. C2×#424D61semidirect
310. C2×C61#2098semidirect
326. #424C2×D61semidirect
339. C61C2×#2098semidirect
607. C2#21447375direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168398102
C2×#168397882
C2×#168397802
C2×#168397782
C2×#168397282
#214473752
C2×#168395182
C2×C61×#4242
C2×#209861