Finite Group Databasebeta

← C2×#13078740 #15621969

Subgroups — C2×#13078740 #15621969

Order 2816.

2398 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3#13078740C2116yesmaximal, direct product factor
4C2×#10622495C212yesmaximal, complemented
5C2×#10622704C211yesmaximal, characteristic, complemented
6C2×#10622461C211yesmaximal, characteristic, complemented
7C2×#10622640C211yesmaximal, characteristic, complemented
8C2×#10622419C212yesmaximal, complemented
9C2×#10622430C212yesmaximal, complemented
10C2×#10622502C212yesmaximal, complemented
11C2×#10622448C211yesmaximal, characteristic, complemented
12C2×C11×#477C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C22×Q8×D11C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#67000—21no—
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2212yes—
20C22×#4314C2212yes—
21#10623256—24no—
22#10623256C2218yes—
23C4×Q8×D11—24no—
24C4×Q8×D11C2218yescomplemented
25C2×#66948—21no—
26C2×#66948C2212yes—
27C2×#66946—21no—
28C2×#66946C2212yes—
29C2×C4⋊C4×D11—21no—
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×#66940—21no—
32C2×#66940C2211yescharacteristic
33C2×#66927C2211yescharacteristic
34C2×C42×D11—21no—
35C2×C42×D11C2211yescharacteristic
36C2×C4×Dic22—21no—
37C2×C4×Dic22C2211yescharacteristic
38C11×#477C2218yescomplemented
39C2×C11×#107C2212yes—
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#103C2212yes—
42C2×#66885C2212yes—
43C2×(C2×D11)⋊C8C2212yes—
44C2×#66879C2212yes—
45#10622704C2218yescomplemented
46#10622640C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66873C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622502C22116yescomplemented
52#10622495C22116yescomplemented
53#10622461C2218yescomplemented
54#10622448C2218yescomplemented
55#10622430C22116yescomplemented
56#10622419C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C2×#4343—28no—
60C2×#4343—48no—
61C2×Q8×D11—24no—
62C2×Q8×D11—22no—
63C2×Q8×D11—24no—
64C2×Q8×D11C2314yes—
65C22×D44—22no—
66C22×D44—21no—
67C22×D44—21no—
68C22×D44C2312yes—
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11—22no—
72C22×C4×D11D411yescharacteristic
73C22×C4×D11D411yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×Dic22—21no—
76C22×Dic22C2311yescharacteristic
77C22×C8×C11C2312yes—
78C11×C4⋊Q8—22no—
79C11×C4⋊Q8C2314yes—
80C4×Q8×C11—22no—
81C4×Q8×C11C2314yes—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88#67000—28no—
89Q8×Dic11—22no—
90Q8×Dic11C2314yes—
91C2×#4325—28no—
92C2×#4325C2318yes—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C2×#4314—28no—
108C2×#4314C2318yes—
109#66948—24no—
110#66948—28no—
111#66948C2318yes—
112#66946—24no—
113#66946—28no—
114#66946C2318yes—
115C4⋊C4×D11—28no—
116C4⋊C4×D11—22no—
117C4⋊C4×D11C2314yes—
118#66940—28no—
119#66940—22no—
120#66940C2314yes—
121#66927—22no—
122#66927C2314yes—
123C42×D11—28no—
124C42×D11D414yes—
125C42×D11C2314yes—
126C4×Dic22—22no—
127C4×Dic22—28no—
128C4×Dic22C2314yes—
129C11×#107C2318yes—
130C11×C4⋊C8C2314yes—
131C11×#103C2318yes—
132#66885C2318yes—
133(C2×D11)⋊C8C2318yes—
134#66879C2318yes—
135#66874C2318yes—
136#66873C2318yes—
137#66871C2318yes—
138C4⋊(C11⋊C8)C2314yes—
139C2×#3112—111nomaximal, Sylow
140C23×D11—22no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—24no—
144C2×Q8×C11—22no—
145C2×Q8×C11—44no—
146C2×Q8×C11#4114yescomplemented
147C2×Q8×C11C2412yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159#4343—432no—
160Q8×D11—216no—
161Q8×D11—28no—
162Q8×D11—28no—
163C2×D44—28no—
164C2×D44—22no—
165C2×D44—24no—
166C2×D44—24no—
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—44no—
170C2×D44—48no—
171C2×D44—44no—
172C2×D44C2414yes—
173C2×C4×D11—28no—
174C2×C4×D11—28no—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—22no—
180C2×C4×D11—22no—
181C2×C4×D11—48no—
182C2×C4×D11—44no—
183C2×C4×D11C2×D414yes—
184C2×C4×D11C2×D412yes—
185C2×C4×D11C2×D414yes—
186C2×C4×D11C2412yes—
187C2×Dic22—28no—
188C2×Dic22—24no—
189C2×Dic22—21no—
190C2×Dic22—22no—
191C2×Dic22#4114yescomplemented
192C2×Dic22C2412yes—
193C2×C8×C11—24no—
194C2×C8×C11C2414yes—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4C2414yes—
200C11×C4⋊C4C2412yes—
201C42×C11—24no—
202C42×C11C2×D412yes—
203C42×C11C2412yes—
204#4325—216no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—28no—
207C4⋊Dic11—24no—
208C4⋊Dic11—21no—
209C4⋊Dic11C2412yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213C4×Dic11—24no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C4×Dic11C2×D414yes—
217C4×Dic11C2×D412yes—
218C4×Dic11C2×D414yes—
219C4×Dic11C2412yes—
220C2×C11⋊C8—24no—
221C2×C11⋊C8C2414yes—
222#4314—216no—
223C2×#532—111no—
224C22×C4×Q8—111no—
225#3112—1116no—
226C2×#480—112no—
227C2×#477—111no—
228C2×#477D1111yescharacteristic, complemented
229C2×#460—111no—
230C2×#460—111no—
231C2×#448—112no—
232C2×#440—112no—
233C2×#440—112no—
234C2×#432—111no—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—24no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11AGL(1,ℤ/8)14yes—
243C22×D11C22×D412yes—
244Q8×C11—24no—
245Q8×C11—22no—
246Q8×C11—48no—
247Q8×C11C2×#4114yescomplemented
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—44no—
254C2×C4×C11—42no—
255C2×C4×C11#13714yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D412yes—
259C2×C4×C11C2×#4112yes—
260C2×C4×C11C2×#4112yes—
261C2×C4×C11C2511yescharacteristic
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—42no—
269C2×Dic11C22×D412yes—
270C2×Dic11C22×D412yes—
271C2×Dic11C22×D412yes—
272D44—24no—
273D44—24no—
274D44—48no—
275D44—416no—
276D44—44no—
277D44—48no—
278C4×D11—216no—
279C4×D11—28no—
280C4×D11—24no—
281C4×D11—28no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—416no—
285C4×D11—48no—
286Dic22—216no—
287Dic22—24no—
288Dic22—22no—
289Dic22C2×#4114yescomplemented
290C8×C11—24no—
291C11⋊C8—24no—
292C22×#41—221no—
293C23×Q8—111no—
294C22×SD16—112no—
295C22×SD16—112no—
296#532—118no—
297#532—224no—
298C2×C4⋊Q8C2×D1111yescharacteristic
299C2×#127—111no—
300C2×#124—221no—
301C2×#121—112no—
302C2×#121—221no—
303C2×C4×Q8—111no—
304C2×C4×Q8—118no—
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8—221no—
308C2×C4×Q8—221no—
309C2×C4×Q8—224no—
310C2×C4×Q8C2×D1111yescharacteristic
311C2×C4×D4—112no—
312C2×C4×D4—221no—
313C22×C4⋊C4—111no—
314C22×C4⋊C4—221no—
315C22×C42—111no—
316C22×C42—221no—
317#480—1116no—
318#477—118no—
319#477C2×D1118yescomplemented
320#460—118no—
321#460—118no—
322#448—1116no—
323#440—1116no—
324#440—1116no—
325#432—118no—
326C2×#107—112no—
327C2×#107C2×D1112yes—
328C2×C4⋊C8—111no—
329C2×C4⋊C8C2×D1111yescharacteristic
330C2×#103—112no—
331C2×#103C2×D1112yes—
332C2×#102—112no—
333C2×#102—112no—
334C2×C22⋊C8—112no—
335C2×#97—112no—
336C22×C11#52512yes—
337C22×C11C2×AGL(1,ℤ/8)12yes—
338C22×C11C2×#13712yes—
339C22×C11C23×D411yescharacteristic
340C2×D11—28no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—88no—
347C2×D11C2×AGL(1,ℤ/8)14yes—
348C4×C11—24no—
349C4×C11—22no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11#52512yes—
353C4×C11C2×#13714yes—
354C4×C11C22×#4111yescharacteristic
355C4×C11C22×#4111yescharacteristic
356Dic11—22no—
357Dic11—24no—
358Dic11—22no—
359Dic11—22no—
360Dic11—42no—
361C2×#41—228no—
362C2×#41—448no—
363C22×Q8—21no—
364C22×Q8—114no—
365C22×Q8—111no—
366C22×Q8—221no—
367C22×Q8—222no—
368C22×Q8—224no—
369C22×Q8—224no—
370C22×Q8C22×D1111yescharacteristic
371C22×D4—112no—
372C22×D4—222no—
373C22×D4—221no—
374C22×D4—221no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—222no—
379C23×C4—221no—
380C23×C4—221no—
381C2×SD16—118no—
382C2×SD16—118no—
383C2×SD16—228no—
384C2×SD16—228no—
385C22×C8—112no—
386C22×C8C22×D1112yes—
387C4⋊Q8—22no—
388C4⋊Q8C22×D1114yes—
389#127—114no—
390#127—222no—
391#124—228no—
392#121—118no—
393#121—224no—
394#121—228no—
395C4×Q8—22no—
396C4×Q8—114no—
397C4×Q8—114no—
398C4×Q8—114no—
399C4×Q8—228no—
400C4×Q8—222no—
401C4×Q8—228no—
402C4×Q8—222no—
403C4×Q8—222no—
404C4×Q8C22×D1114yes—
405C4×D4—118no—
406C4×D4—224no—
407C4×D4—228no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—228no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1112yes—
420C2×C22⋊C4—222no—
421C2×C22⋊C4—222no—
422C2×C42—21no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—114no—
427C2×C42—114no—
428C2×C42—228no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42C22×D1111yescharacteristic
433#107—118no—
434#107C22×D1118yes—
435C4⋊C8—114no—
436C4⋊C8C22×D1114yes—
437#103—118no—
438#103C22×D1118yes—
439#102—118no—
440#102—118no—
441C22⋊C8—118no—
442#97—118no—
443C2×C11#311214yescomplemented
444C2×C11C2×#52511yescharacteristic
445C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
446C2×C11C22×#13711yescharacteristic
447D11—24no—
448D11—84no—
449C24—111no—
450C24—222no—
451#41—4432no—
452C2×Q8—21no—
453C2×Q8—24no—
454C2×Q8—22no—
455C2×Q8—44no—
456C2×Q8—114no—
457C2×Q8—112no—
458C2×Q8—224no—
459C2×Q8—228no—
460C2×Q8—228no—
461C2×Q8—2216no—
462C2×Q8—228no—
463C2×Q8—221no—
464C2×Q8—222no—
465C2×Q8#434314yescomplemented
466C2×Q8C23×D1112yes—
467C2×D4—114no—
468C2×D4—228no—
469C2×D4—224no—
470C2×D4—222no—
471C2×D4—224no—
472C2×D4—224no—
473C2×D4—224no—
474C2×D4—444no—
475C2×D4—448no—
476C2×D4—444no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—114no—
484C22×C4—114no—
485C22×C4—112no—
486C22×C4—112no—
487C22×C4—228no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—228no—
491C22×C4—224no—
492C22×C4—221no—
493C22×C4—224no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—448no—
498C22×C4—444no—
499C22×C4D4×D1111yescharacteristic
500C22×C4D4×D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502SD16—2216no—
503SD16—2216no—
504C2×C8—24no—
505C2×C8—114no—
506C2×C8—224no—
507C2×C8C23×D1114yes—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—112no—
513C4⋊C4—224no—
514C4⋊C4—224no—
515C4⋊C4—224no—
516C4⋊C4—221no—
517C4⋊C4—224no—
518C4⋊C4C23×D1112yes—
519C4⋊C4C23×D1114yes—
520C22⋊C4—228no—
521C22⋊C4—228no—
522C42—24no—
523C42—112no—
524C42—114no—
525C42—114no—
526C42—112no—
527C42—224no—
528C42—224no—
529C42—224no—
530C42D4×D1112yes—
531C42C23×D1112yes—
532C11C2×#311211yescharacteristic, complemented, Sylow
533C23—114no—
534C23—112no—
535C23—222no—
536C23—222no—
537C23—224no—
538C23—444no—
539C23—444no—
540C23—444no—
541C23C2×D4×D1111yescharacteristic
542Q8—24no—
543Q8—22no—
544Q8—48no—
545Q8—114no—
546Q8—2216no—
547Q8—224no—
548Q8—222no—
549Q8C2×#434314yescomplemented
550D4—224no—
551D4—224no—
552D4—448no—
553D4—4416no—
554D4—448no—
555D4—444no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—228no—
567C2×C4—2216no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—224no—
572C2×C4—222no—
573C2×C4—228no—
574C2×C4—224no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—4416no—
579C2×C4—448no—
580C2×C4—442no—
581C2×C4#6697114yes—
582C2×C4C2×D4×D1112yes—
583C2×C4C2×D4×D1112yes—
584C2×C4C2×D4×D1111yescharacteristic
585C2×C4C2×#434312yes—
586C2×C4#41×D1112yes—
587C2×C4C24×D1111yescharacteristic
588C8—24no—
589C8—224no—
590C22—114no—
591C22—222no—
592C22—228no—
593C22—222no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—888no—
598C22#1062315812yes—
599C22C2×#6697112yes—
600C22D11×AGL(1,ℤ/8)12yes—
601C22C22×D4×D1111yescharacteristic
602C4—24no—
603C4—22no—
604C4—44no—
605C4—42no—
606C4—222no—
607C4—224no—
608C4—222no—
609C4—222no—
610C4—442no—
611C4#1062315812yes—
612C4C2×#6697114yes—
613C4C22×#434311yescharacteristic
614C4C2×#41×D1111yescharacteristic
615C2—224no—
616C2—884no—
617C2#1307874014yesdirect product factor
618C2C2×#1062315811yescharacteristic
619C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
620C2C22×#6697111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenterC2×#477D11
hypocenterC11C2×#3112
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
3. #13078740C2direct (N × H)
4. C2×#10622495C2semidirect
5. C2×#10622704C2semidirect
6. C2×#10622461C2semidirect
7. C2×#10622640C2semidirect
8. C2×#10622419C2semidirect
9. C2×#10622430C2semidirect
10. C2×#10622502C2semidirect
11. C2×#10622448C2semidirect
12. C2×C11×#477C2semidirect
24. C4×Q8×D11C22semidirect
38. C11×#477C22semidirect
45. #10622704C22semidirect
46. #10622640C22semidirect
51. #10622502C22semidirect
52. #10622495C22semidirect
53. #10622461C22semidirect
54. #10622448C22semidirect
55. #10622430C22semidirect
56. #10622419C22semidirect
146. C2×Q8×C11#41semidirect
191. C2×Dic22#41semidirect
228. C2×#477D11semidirect
247. Q8×C11C2×#41semidirect
289. Dic22C2×#41semidirect
319. #477C2×D11semidirect
443. C2×C11#3112semidirect
465. C2×Q8#4343semidirect
532. C11C2×#3112semidirect
549. Q8C2×#4343semidirect
617. C2#13078740direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×C4×Q8×D112
#130787402
C2×#106224952
C2×#106227042
C2×#106224612
C2×#106226402
C2×#106224192
C2×#106224302
C2×#106225022
C2×#106224482
C2×C11×#4772
C2×#311211