Finite Group Databasebeta

← C2×#20275890 #27411519

Subgroups — C2×#20275890 #27411519

Order 13568.

1234 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
1C2×#16811176C211yesmaximal, characteristic, complemented
2C2×#16810639C211yesmaximal, characteristic
3C22×#13133143C211yesmaximal, characteristic
4C2×#16810596C211yesmaximal, characteristic
5#20275890C218yesmaximal, direct product factor
6C2×#16810384C211yesmaximal, characteristic, complemented
7C2×#16810380C211yesmaximal, characteristic, complemented
8C2×C53×#344C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10#16811176—22no—
11#16811176—22no—
12#16811176—22no—
13#16811176C2214yescomplemented
14C2×#13133216—21no—
15C2×#13133208—21no—
16C2×#13133194—22no—
17C2×C4×Dic106—22no—
18C2×#13133176C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20C22×C4×Dic53C2211yescharacteristic
21#16810639—22no—
22#16810639C2214yes—
23C2×#13133143—21no—
24C2×#13133143—21no—
25C2×#13133143—22no—
26C2×#13133143—22no—
27C2×#13133143C2214yes—
28#16810596—22no—
29#16810596C2214yes—
30C2×#13133131—22no—
31#16810384C2214yescomplemented
32#16810380C2214yescomplemented
33C22×M16×C53C2211yescharacteristic
34C22×M16×C53C2211yescharacteristic
35C2×#117×C53C2211yescharacteristic
36C53×#344C2214yescomplemented
37C2×#11719945—21no—
38C2×#11719945—21no—
39C2×#11719945—21no—
40C2×#11719945—21no—
41C2×#11719945—21no—
42C2×#11719945—21no—
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945Q812yescomplemented
48C2×#11719945C2312yes—
49C22×Dic106—22no—
50C22×Dic106Q811yescharacteristic, complemented
51C22×D212Q811yescharacteristic, complemented
52C22×C22⋊D53—21no—
53C23×Dic53—21no—
54C22×C4×D53—21no—
55#13133216—24no—
56#13133216—24no—
57#13133208—24no—
58#13133208—24no—
59#13133194—28no—
60#13133194—28no—
61C4×Dic106—28no—
62C4×Dic106—28no—
63#13133176—21no—
64#13133176—21no—
65#13133176—21no—
66#13133176—21no—
67#13133176—21no—
68#13133176D412yes—
69#13133176C2312yes—
70#13133176C2312yes—
71C2×C4⋊Dic53—22no—
72C2×C4⋊Dic53—21no—
73C2×C4⋊Dic53—21no—
74C2×#11719919—22no—
75C2×#11719919—22no—
76C2×C22⋊Dic53—21no—
77C2×C22⋊Dic53—21no—
78C2×C4×Dic53—21no—
79C2×C4×Dic53—21no—
80C2×C4×Dic53—21no—
81C2×C4×Dic53—21no—
82C2×C4×Dic53D411yescharacteristic
83C2×C4×Dic53D411yescharacteristic
84C2×C4×Dic53D412yes—
85C2×C4×Dic53D412yes—
86C2×C4×Dic53C2312yes—
87#13133143—24no—
88#13133143—24no—
89#13133143—28no—
90#13133131—28no—
91C23×C4×C53C2311yescharacteristic
92C2×M16×C53—21no—
93C2×M16×C53—21no—
94C2×M16×C53—21no—
95C2×M16×C53—21no—
96C2×M16×C53—21no—
97C2×M16×C53—21no—
98C2×M16×C53—21no—
99C2×M16×C53—21no—
100C2×M16×C53—21no—
101C2×M16×C53—21no—
102C2×M16×C53C2312yes—
103C2×M16×C53C2312yes—
104C22×C8×C53—21no—
105C22×C8×C53—21no—
106#117×C53—21no—
107#117×C53—21no—
108#117×C53D412yes—
109#117×C53C2312yes—
110C2×C4⋊C4×C53—21no—
111C2×C22⋊C4×C53D412yes—
112C2×C42×C53—21no—
113C24×C53C2×D411yescharacteristic
114C23×D53—21no—
115C22×C4×C53—22no—
116C22×C4×C53C2×D411yescharacteristic
117C22×C4×C53C2×D411yescharacteristic
118C22×C4×C53C2×D411yescharacteristic
119C22×C4×C53C2×D411yescharacteristic
120C22×C4×C53C2×D411yescharacteristic
121C22×C4×C53C2×Q811yescharacteristic
122C22×C4×C53C2×Q811yescharacteristic
123C22×C4×C53#4111yescharacteristic
124C22×C4×C53#4111yescharacteristic
125C22×C4×C53#4111yescharacteristic
126C22×C4×C53#4111yescharacteristic
127C22×C4×C53#4111yescharacteristic
128C22×C4×C53#4111yescharacteristic
129C22×C4×C53C2411yescharacteristic
130C2×C22⋊D53—22no—
131C2×C22⋊D53—22no—
132C2×C22⋊D53—41no—
133C2×C22⋊D53—41no—
134C2×C22⋊D53—41no—
135C2×C22⋊D53—41no—
136C22×Dic53—21no—
137C22×Dic53—21no—
138C22×Dic53—22no—
139C22×Dic53—22no—
140C22×Dic53—21no—
141C22×Dic53—22no—
142C22×Dic53—44no—
143C22×Dic53—41no—
144#11719945—22no—
145#11719945—22no—
146#11719945—22no—
147#11719945—22no—
148#11719945—22no—
149#11719945—22no—
150#11719945—22no—
151#11719945—22no—
152#11719945—41no—
153#11719945—41no—
154#11719945—41no—
155#11719945—41no—
156#11719945—41no—
157#11719945—41no—
158#11719945—41no—
159#11719945—41no—
160C2×D212—21no—
161C2×D212—21no—
162C2×D212—21no—
163C2×D212—21no—
164C2×D212—21no—
165C2×D212C2×Q812yescomplemented
166C2×C4×D53—22no—
167C2×C4×D53—22no—
168C2×C4×D53—41no—
169C2×C4×D53—41no—
170C2×C4×D53—41no—
171C2×C4×D53—41no—
172C2×Dic106—21no—
173C2×Dic106—21no—
174C2×Dic106—21no—
175C2×Dic106—21no—
176C2×Dic106—28no—
177C2×Dic106—21no—
178C2×Dic106—48no—
179C2×Dic106C2×Q812yescomplemented
180M16×C53—22no—
181M16×C53—22no—
182M16×C53—22no—
183M16×C53—22no—
184M16×C53—41no—
185M16×C53—41no—
186M16×C53—41no—
187M16×C53—41no—
188C2×C8×C53—22no—
189C2×C8×C53—22no—
190C2×C8×C53—41no—
191C2×C8×C53—41no—
192C2×C8×C53—41no—
193C2×C8×C53—41no—
194C4⋊C4×C53—22no—
195C4⋊C4×C53—22no—
196C22⋊C4×C53—22no—
197C22⋊C4×C53C2×D414yes—
198C42×C53—22no—
199C42×C53—22no—
200C22⋊Dic53—22no—
201C22⋊Dic53—22no—
202C22⋊Dic53—22no—
203C22⋊Dic53—41no—
204C4⋊Dic53—28no—
205C4⋊Dic53—22no—
206C4⋊Dic53—22no—
207C4⋊Dic53—22no—
208C4⋊Dic53—41no—
209#11719919—28no—
210#11719919—28no—
211C4×Dic53—22no—
212C4×Dic53—21no—
213C4×Dic53—21no—
214C4×Dic53—22no—
215C4×Dic53—22no—
216C4×Dic53—22no—
217C4×Dic53—41no—
218C4×Dic53C2×D412yes—
219C4×Dic53C2×D412yes—
220C4×Dic53C2×D414yes—
221C23×C53—42no—
222C23×C53#12011yescharacteristic
223C23×C53#12011yescharacteristic
224C23×C53C22⋊Q811yescharacteristic
225C23×C53C22⋊Q811yescharacteristic
226C23×C53#12411yescharacteristic
227C23×C53#12411yescharacteristic
228C23×C53C22×D411yescharacteristic
229C22×D53—22no—
230C22×D53—41no—
231C22×D53—41no—
232C22×D53—82no—
233C2×C4×C53—24no—
234C2×C4×C53—44no—
235C2×C4×C53#12011yescharacteristic
236C2×C4×C53#12011yescharacteristic
237C2×C4×C53C22⋊Q811yescharacteristic
238C2×C4×C53C22⋊Q811yescharacteristic
239C2×C4×C53C22⋊Q811yescharacteristic
240C2×C4×C53C22⋊Q811yescharacteristic
241C2×C4×C53C22⋊Q811yescharacteristic
242C2×C4×C53C22⋊Q811yescharacteristic
243C2×C4×C53C22⋊Q811yescharacteristic
244C2×C4×C53C22⋊Q811yescharacteristic
245C2×C4×C53C22⋊Q811yescharacteristic
246C2×C4×C53C22⋊Q811yescharacteristic
247C2×C4×C53#12411yescharacteristic
248C2×C4×C53#12411yescharacteristic
249C2×C4×C53#12411yescharacteristic
250C2×C4×C53#12411yescharacteristic
251C2×C4×C53#12411yescharacteristic
252C2×C4×C53#12411yescharacteristic
253C2×C4×C53#12411yescharacteristic
254C2×C4×C53#12411yescharacteristic
255C2×C4×C53#12411yescharacteristic
256C2×C4×C53#12411yescharacteristic
257C2×C4×C53C22×D411yescharacteristic
258C2×C4×C53C22×D411yescharacteristic
259C2×C4×C53C22×Q811yescharacteristic
260C2×C4×C53C2×#4111yescharacteristic
261C2×C4×C53C2×#4111yescharacteristic
262C2×C4×C53C2×#4111yescharacteristic
263C22⋊D53—42no—
264C22⋊D53—42no—
265C22⋊D53—42no—
266C22⋊D53—42no—
267C2×Dic53—24no—
268C2×Dic53—22no—
269C2×Dic53—24no—
270C2×Dic53—22no—
271C2×Dic53—22no—
272C2×Dic53—44no—
273C2×Dic53—44no—
274C2×Dic53—44no—
275C2×Dic53—42no—
276C2×Dic53—41no—
277C2×Dic53—41no—
278C2×Dic53—42no—
279C2×Dic53—82no—
280D212—22no—
281D212—22no—
282D212—41no—
283D212—41no—
284C4×D53—42no—
285C4×D53—42no—
286C4×D53—42no—
287C4×D53—42no—
288Dic106—22no—
289Dic106—22no—
290Dic106—416no—
291Dic106—41no—
292Dic106—41no—
293C8×C53—42no—
294C8×C53—42no—
295C2×#2031—531nomaximal, Sylow
296C22×C53—22no—
297C22×C53—22no—
298C22×C53—22no—
299C22×C53—41no—
300C22×C53—41no—
301C22×C53—41no—
302C22×C53—41no—
303C22×C53#39311yescharacteristic
304C22×C53#39311yescharacteristic
305C22×C53#39311yescharacteristic
306C22×C53#39311yescharacteristic
307C22×C53C2×#12011yescharacteristic
308C22×C53C2×C22⋊Q811yescharacteristic
309C22×C53C2×#12411yescharacteristic
310C2×D53—42no—
311C2×D53—82no—
312C2×D53—82no—
313C2×D53—82no—
314C4×C53—44no—
315C4×C53#39311yescharacteristic
316C4×C53#39311yescharacteristic
317C4×C53#39311yescharacteristic
318C4×C53#39311yescharacteristic
319C4×C53C2×C22⋊Q811yescharacteristic
320C4×C53C2×C22⋊Q811yescharacteristic
321C4×C53C2×#12411yescharacteristic
322C4×C53C2×#12411yescharacteristic
323Dic53—24no—
324Dic53—44no—
325Dic53—42no—
326Dic53—42no—
327Dic53—82no—
328C2×#533—531no—
329C2×#421—531no—
330C22×#104—531no—
331C2×#410—531no—
332#2031—538no—
333C2×#344D5311yescharacteristic, complemented
334C2×#339—531no—
335C2×H(3,ℤ/4)—531no—
336C2×C53—21no—
337C2×C53—21no—
338C2×C53—21no—
339C2×C53—21no—
340C2×C53—21no—
341C2×C53—21no—
342C2×C53#203112yescomplemented
343C2×C53C2×#39311yescharacteristic
344D53—82no—
345C22×#41—531no—
346C22×M16C2×D5311yescharacteristic
347C22×M16C2×D5311yescharacteristic
348#533—534no—
349#533—1062no—
350#533—1062no—
351#533—1062no—
352C2×C4⋊Q8—1061no—
353C2×#125—1061no—
354C2×C22⋊Q8—1062no—
355C2×C4×Q8—1062no—
356C2×#117—531no—
357C2×#117—531no—
358C2×#117C2×D5311yescharacteristic
359C22×C42—531no—
360#421—534no—
361#421—1062no—
362C2×#104—534no—
363C2×#104—1061no—
364C2×#104—1061no—
365C2×#104—1062no—
366C2×#104—1062no—
367#410—534no—
368#410—1062no—
369C2×#99—1062no—
370#344C2×D5314yescomplemented
371#339—534no—
372H(3,ℤ/4)—534no—
373C53C2×#203111yescharacteristic, complemented, Sylow
374C2×#41—532no—
375C2×#41—532no—
376C2×#41—1061no—
377C2×#41—1061no—
378C2×#41—1061no—
379C2×#41—1061no—
380C2×#41—1061no—
381C2×#41—1061no—
382C2×#41—1061no—
383C2×#41—1061no—
384C2×#41—1061no—
385C2×#41—1061no—
386C22×Q8—531no—
387C22×Q8—1062no—
388C22×D4—531no—
389C22×D4—1061no—
390C23×C4—1061no—
391C23×C4—1061no—
392C23×C4C22×D5311yescharacteristic
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—21no—
397C2×M16—21no—
398C2×M16—21no—
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16C22×D5312yes—
404C2×M16C22×D5312yes—
405C22×C8—21no—
406C22×C8—21no—
407C4⋊Q8—1064no—
408C4⋊Q8—1064no—
409#125—1064no—
410#125—1064no—
411C22⋊Q8—1068no—
412C22⋊Q8—1068no—
413C4×Q8—1068no—
414C4×Q8—1068no—
415#117—21no—
416#117—21no—
417#117—532no—
418#117—532no—
419#117—532no—
420#117—1061no—
421#117—1061no—
422#117—1061no—
423#117—1061no—
424#117—1061no—
425#117D21212yes—
426#117C22×D5312yes—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—1062no—
429C2×C4⋊C4—1062no—
430C2×C4⋊C4—1062no—
431C2×C4⋊C4—1061no—
432C2×C4⋊C4—1061no—
433C2×C22⋊C4—1061no—
434C2×C22⋊C4—1061no—
435C2×C22⋊C4D21212yes—
436C2×C42—21no—
437C2×C42—532no—
438C2×C42—531no—
439C2×C42—531no—
440C2×C42—532no—
441C2×C42—532no—
442C2×C42—1061no—
443C2×C42—1061no—
444C2×C42—1061no—
445C2×C42—1061no—
446#104—1064no—
447#104—1064no—
448#104—1068no—
449#99—1068no—
450C24—1061no—
451C24C2×D21211yescharacteristic
452#41—1062no—
453#41—1062no—
454#41—1062no—
455#41—1062no—
456#41—1062no—
457#41—1062no—
458#41—1062no—
459#41—1062no—
460#41—2121no—
461#41—2121no—
462#41—2121no—
463#41—2121no—
464#41—2121no—
465#41—2121no—
466#41—2121no—
467#41—2121no—
468C2×Q8—532no—
469C2×Q8—1068no—
470C2×Q8—1061no—
471C2×Q8—1061no—
472C2×Q8—1061no—
473C2×Q8—1061no—
474C2×Q8—1061no—
475C2×Q8—2128no—
476C2×D4—532no—
477C2×D4—1062no—
478C2×D4—1062no—
479C2×D4—1061no—
480C2×D4—1061no—
481C2×D4—1061no—
482C2×D4—1061no—
483C2×D4—1061no—
484C2×D4—2121no—
485C2×D4—2121no—
486C2×D4—2121no—
487C2×D4—2121no—
488C22×C4—22no—
489C22×C4—1061no—
490C22×C4—1061no—
491C22×C4—1062no—
492C22×C4—1062no—
493C22×C4—1061no—
494C22×C4—1062no—
495C22×C4—1062no—
496C22×C4—1062no—
497C22×C4—2124no—
498C22×C4—2121no—
499C22×C4—2121no—
500C22×C4—2121no—
501C22×C4—2121no—
502C22×C4—2121no—
503C22×C4C2×D21211yescharacteristic
504C22×C4#1171994511yescharacteristic
505C22×C4#1171994511yescharacteristic
506C22×C4#1171994511yescharacteristic
507C22×C4#1171994511yescharacteristic
508C22×C4D4×D5311yescharacteristic
509C22×C4D4×D5311yescharacteristic
510C22×C4D4×D5311yescharacteristic
511C22×C4D4×D5311yescharacteristic
512C22×C4#1171994711yescharacteristic
513C22×C4#1171994711yescharacteristic
514C22×C4Q8×D5311yescharacteristic
515C22×C4Q8×D5311yescharacteristic
516C22×C4C23×D5311yescharacteristic
517M16—22no—
518M16—22no—
519M16—22no—
520M16—22no—
521M16—41no—
522M16—41no—
523M16—41no—
524M16—41no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—1068no—
534C4⋊C4—1068no—
535C4⋊C4—1068no—
536C4⋊C4—1062no—
537C4⋊C4—1062no—
538C4⋊C4—1062no—
539C4⋊C4—2121no—
540C22⋊C4—22no—
541C22⋊C4—1062no—
542C22⋊C4—1062no—
543C22⋊C4—1062no—
544C22⋊C4—2121no—
545C22⋊C4C2×D21214yes—
546C42—22no—
547C42—22no—
548C42—532no—
549C42—532no—
550C42—534no—
551C42—1062no—
552C42—1061no—
553C42—1061no—
554C42—1062no—
555C42—1062no—
556C42—1062no—
557C42—2121no—
558C23—42no—
559C23—1062no—
560C23—4242no—
561C23—2121no—
562C23—2121no—
563C23#1313318711yescharacteristic
564C23#1313318711yescharacteristic
565C23#1313319711yescharacteristic
566C23#1313319711yescharacteristic
567C23#1313320511yescharacteristic
568C23#1313320511yescharacteristic
569C23C22×D21211yescharacteristic
570Q8—1062no—
571Q8—1062no—
572Q8—21216no—
573Q8—2121no—
574Q8—2121no—
575D4—1062no—
576D4—1062no—
577D4—2122no—
578D4—2122no—
579D4—2122no—
580D4—2122no—
581D4—2121no—
582D4—2121no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—1064no—
586C2×C4—1062no—
587C2×C4—1062no—
588C2×C4—1064no—
589C2×C4—1062no—
590C2×C4—4242no—
591C2×C4—2124no—
592C2×C4—2124no—
593C2×C4—2122no—
594C2×C4—2122no—
595C2×C4—2124no—
596C2×C4—2121no—
597C2×C4—2121no—
598C2×C4—2122no—
599C2×C4—2122no—
600C2×C4—2122no—
601C2×C4—2122no—
602C2×C4#1313318711yescharacteristic
603C2×C4#1313318711yescharacteristic
604C2×C4#1313319511yescharacteristic
605C2×C4#1313319511yescharacteristic
606C2×C4#1313319511yescharacteristic
607C2×C4#1313319511yescharacteristic
608C2×C4#1313319511yescharacteristic
609C2×C4#1313319511yescharacteristic
610C2×C4#1313319511yescharacteristic
611C2×C4#1313319511yescharacteristic
612C2×C4#1313319711yescharacteristic
613C2×C4#1313319711yescharacteristic
614C2×C4#1313320311yescharacteristic
615C2×C4#1313320311yescharacteristic
616C2×C4#1313320311yescharacteristic
617C2×C4#1313320311yescharacteristic
618C2×C4#1313320311yescharacteristic
619C2×C4#1313320311yescharacteristic
620C2×C4#1313320311yescharacteristic
621C2×C4#1313320311yescharacteristic
622C2×C4#1313320511yescharacteristic
623C2×C4#1313320511yescharacteristic
624C2×C4C2×D4×D5311yescharacteristic
625C2×C4C2×D4×D5311yescharacteristic
626C2×C4C2×Q8×D5311yescharacteristic
627C2×C4C2×#1171994711yescharacteristic
628C2×C4C2×#1171994511yescharacteristic
629C2×C4C2×#1171994511yescharacteristic
630C8—42no—
631C8—42no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—4242no—
640C22—4242no—
641C22—4242no—
642C22—2122no—
643C22#1681053611yescharacteristic
644C22#1681053611yescharacteristic
645C22#1681053611yescharacteristic
646C22#1681053611yescharacteristic
647C22C2×#1313318711yescharacteristic
648C22C2×#1313319711yescharacteristic
649C22C2×#1313320511yescharacteristic
650C4—44no—
651C4—1064no—
652C4—4242no—
653C4—2122no—
654C4—2124no—
655C4—2122no—
656C4#1681053611yescharacteristic
657C4#1681053611yescharacteristic
658C4#1681053611yescharacteristic
659C4#1681053611yescharacteristic
660C4C2×#1313319511yescharacteristic
661C4C2×#1313319511yescharacteristic
662C4C2×#1313320311yescharacteristic
663C4C2×#1313320311yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—4242no—
671C2#2027589012yesdirect product factor
672C2C2×#1681053611yescharacteristic
subgroupG/H
centerC2×C4#13133203
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C53×#344C2
socleC22×C53#393
prime radicalC22×#11719945C22
hypercenterC2×#344D53
hypocenterC53C2×#2031
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#16811176C2semidirect
5. #20275890C2direct (N × H)
6. C2×#16810384C2semidirect
7. C2×#16810380C2semidirect
8. C2×C53×#344C2semidirect
13. #16811176C22semidirect
31. #16810384C22semidirect
32. #16810380C22semidirect
36. C53×#344C22semidirect
47. C2×#11719945Q8semidirect
50. C22×Dic106Q8semidirect
51. C22×D212Q8semidirect
165. C2×D212C2×Q8semidirect
179. C2×Dic106C2×Q8semidirect
333. C2×#344D53semidirect
342. C2×C53#2031semidirect
370. #344C2×D53semidirect
373. C53C2×#2031semidirect
671. C2#20275890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111762
C2×#168106392
C22×#131331432
C2×#168105962
#202758902
C2×#168103842
C2×#168103802
C2×C53×#3442
C2×#203153