Finite Group Databasebeta

← C2×#13078737 #15621966

Subgroups — C2×#13078737 #15621966

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×#10623247C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3#13078737C2116yesmaximal, direct product factor
4C2×#10622387C212yesmaximal, complemented
5C2×#10622463C211yesmaximal, characteristic, complemented
6C2×#10622634C211yesmaximal, characteristic, complemented
7C2×#10622688C211yesmaximal, characteristic, complemented
8C2×#10622783C212yesmaximal, complemented
9C2×#10622777C212yesmaximal, complemented
10C2×#10622370C212yesmaximal, complemented
11C2×#10622448C211yesmaximal, characteristic, complemented
12C2×C11×#460C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2211yescharacteristic
14C22×#4341—21no—
15C22×C11×SD16C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66991—21no—
20C2×#66991C2212yes—
21C2×#66989—21no—
22C2×D4×Dic11—21no—
23C2×D4×Dic11C2212yes—
24C22×#4324C2212yes—
25#10623247—24no—
26#10623247C2218yes—
27C4×Q8×D11—24no—
28C4×Q8×D11C2218yescomplemented
29C2×C4⋊C4×D11—21no—
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×#66940—21no—
32C2×#66940C2211yescharacteristic
33C2×C42×D11—21no—
34C2×C42×D11C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22—21no—
37C2×C4×Dic22C2211yescharacteristic
38C11×#460C2218yescomplemented
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#102C2212yes—
41C2×#66899C2212yes—
42C2×#66896C2212yes—
43#10622783C22116yescomplemented
44#10622777C22116yescomplemented
45C2×(C2×D11)⋊C8C2212yes—
46C2×#66882C2212yes—
47C2×#66880C2212yes—
48C2×#66879C2212yes—
49#10622688C2218yescomplemented
50#10622634C2218yescomplemented
51C2×#66871C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622463C2218yescomplemented
54#10622448C2218yescomplemented
55#10622387C22116yescomplemented
56#10622370C22116yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11C2312yes—
61C22×C22⋊D11—22no—
62C23×Dic11—22no—
63C2×Q8×D11—24no—
64C2×Q8×D11—22no—
65C2×Q8×D11—24no—
66C2×Q8×D11C2314yes—
67C2×#4341—28no—
68C2×#4341—48no—
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11D411yescharacteristic
72C22×C4×D11D411yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×Dic22—21no—
75C22×Dic22—21no—
76C22×Dic22C2311yescharacteristic
77C2×C11×SD16—28no—
78C2×C11×SD16C2318yes—
79C22×C8×C11C2312yes—
80C11×#127—22no—
81C11×#127C2314yes—
82C4×Q8×C11—22no—
83C4×Q8×C11C2314yes—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90Q8×Dic11—22no—
91Q8×Dic11C2314yes—
92#66991—24no—
93#66991—28no—
94#66991C2318yes—
95#66989—28no—
96D4×Dic11—24no—
97D4×Dic11—28no—
98D4×Dic11C2318yes—
99C2×#4324—28no—
100C2×#4324C2318yes—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2312yes—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11D411yescharacteristic
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2312yes—
115C4⋊C4×D11—28no—
116C4⋊C4×D11—22no—
117C4⋊C4×D11C2314yes—
118#66940—28no—
119#66940—22no—
120#66940C2314yes—
121C42×D11—28no—
122C42×D11D414yes—
123C42×D11C2314yes—
124#66922—22no—
125#66922C2314yes—
126C4×Dic22—22no—
127C4×Dic22—28no—
128C4×Dic22C2314yes—
129C11×C4⋊C8C2314yes—
130C11×#102C2318yes—
131#66899C2318yes—
132#66896C2318yes—
133(C2×D11)⋊C8C2318yes—
134#66882C2318yes—
135#66880C2318yes—
136#66879C2318yes—
137#66871C2318yes—
138C4⋊(C11⋊C8)C2314yes—
139C2×#3112—111nomaximal, Sylow
140C24×C11—22no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11#4114yescomplemented
145C2×Q8×C11C2412yes—
146C2×D4×C11—22no—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—44no—
152C2×D4×C11—44no—
153C2×D4×C11C2414yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—28no—
160C2×C22⋊D11—48no—
161C22×Dic11—28no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—48no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169Q8×D11—216no—
170Q8×D11—28no—
171Q8×D11—28no—
172#4341—432no—
173C2×C4×D11—28no—
174C2×C4×D11—24no—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—44no—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2×D412yes—
183C2×C4×D11C2×D414yes—
184C2×C4×D11C2412yes—
185C2×Dic22—28no—
186C2×Dic22—24no—
187C2×Dic22—21no—
188C2×Dic22—24no—
189C2×Dic22—22no—
190C2×Dic22—44no—
191C2×Dic22#4114yescomplemented
192C2×Dic22C2412yes—
193C11×SD16—216no—
194C2×C8×C11—24no—
195C2×C8×C11C2414yes—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4C2412yes—
199C42×C11—24no—
200C42×C11C2×D412yes—
201C42×C11C2412yes—
202C22⋊Dic11—28no—
203C22⋊Dic11—28no—
204#4324—216no—
205C4⋊Dic11—24no—
206C4⋊Dic11—21no—
207C4⋊Dic11—22no—
208C4⋊Dic11—24no—
209C4⋊Dic11C2414yes—
210C4⋊Dic11C2412yes—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C4×Dic11—24no—
217C4×Dic11C2×D414yes—
218C4×Dic11C2×D412yes—
219C4×Dic11C2×D414yes—
220C4×Dic11C2412yes—
221C2×C11⋊C8—24no—
222C2×C11⋊C8C2414yes—
223C2×#532—111no—
224C22×C4×Q8—111no—
225#3112—1116no—
226C2×#480—112no—
227C2×#477—111no—
228C2×#477—111no—
229C2×#460—111no—
230C2×#460D1111yescharacteristic, complemented
231C2×#448—112no—
232C2×#440—112no—
233C2×#440—112no—
234C2×#432—111no—
235C23×C11—24no—
236C23×C11—44no—
237C23×C11—44no—
238C23×C11—44no—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—22no—
242C22×D11AGL(1,ℤ/8)14yes—
243C22×D11C22×D412yes—
244Q8×C11—24no—
245Q8×C11—22no—
246Q8×C11C2×#4114yescomplemented
247D4×C11—24no—
248D4×C11—24no—
249D4×C11—48no—
250D4×C11—44no—
251D4×C11—48no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—42no—
257C2×C4×C11#13714yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D412yes—
261C2×C4×C11C2×#4112yes—
262C2×C4×C11C2×#4112yes—
263C2×C4×C11C2511yescharacteristic
264C22⋊D11—416no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—416no—
273C2×Dic11—44no—
274C2×Dic11—42no—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×D412yes—
277C2×Dic11C22×D412yes—
278C4×D11—216no—
279C4×D11—28no—
280C4×D11—24no—
281C4×D11—28no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—48no—
285Dic22—216no—
286Dic22—24no—
287Dic22—22no—
288Dic22—48no—
289Dic22C2×#4114yescomplemented
290C8×C11—24no—
291C11⋊C8—24no—
292C22×#41—221no—
293C23×Q8—111no—
294C22×SD16—112no—
295C22×SD16C2×D1112yes—
296#532—118no—
297#532—224no—
298C2×C4⋊Q8—111no—
299C2×#127C2×D1111yescharacteristic
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#477—118no—
320#460—118no—
321#460C2×D1118yescomplemented
322#448—1116no—
323#440—1116no—
324#440—1116no—
325#432—118no—
326C2×#107—112no—
327C2×#107—112no—
328C2×C4⋊C8—111no—
329C2×C4⋊C8C2×D1111yescharacteristic
330C2×#103—112no—
331C2×#103—112no—
332C2×#102—112no—
333C2×#102C2×D1112yes—
334C2×C22⋊C8—112no—
335C2×#97—112no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—44no—
339C22×C11—88no—
340C22×C11#52512yes—
341C22×C11C2×AGL(1,ℤ/8)12yes—
342C22×C11C2×#13712yes—
343C22×C11C23×D411yescharacteristic
344C2×D11—28no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11C2×AGL(1,ℤ/8)14yes—
348C4×C11—24no—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11#52512yes—
352C4×C11C2×#13714yes—
353C4×C11C22×#4111yescharacteristic
354C4×C11C22×#4111yescharacteristic
355Dic11—22no—
356Dic11—24no—
357Dic11—22no—
358Dic11—22no—
359Dic11—44no—
360Dic11—42no—
361C2×#41—228no—
362C2×#41—448no—
363C22×Q8—114no—
364C22×Q8—111no—
365C22×Q8—221no—
366C22×Q8—222no—
367C22×Q8—224no—
368C22×Q8—224no—
369C22×Q8—221no—
370C22×Q8C22×D1111yescharacteristic
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—222no—
374C22×D4C22×D1112yes—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—221no—
379C23×C4—221no—
380C23×C4—222no—
381C2×SD16—28no—
382C2×SD16—118no—
383C2×SD16—228no—
384C2×SD16C22×D1118yes—
385C22×C8—112no—
386C22×C8C22×D1112yes—
387C4⋊Q8—114no—
388C4⋊Q8—222no—
389#127—22no—
390#127C22×D1114yes—
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—111no—
410C2×C4⋊C4—112no—
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⋊C4—221no—
419C2×C4⋊C4C22×D1111yescharacteristic
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#107—118no—
435C4⋊C8—114no—
436C4⋊C8C22×D1114yes—
437#103—118no—
438#103—118no—
439#102—118no—
440#102C22×D1118yes—
441C22⋊C8—118no—
442#97—118no—
443C2×C11—84no—
444C2×C11#311214yescomplemented
445C2×C11C2×#52511yescharacteristic
446C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
447C2×C11C22×#13711yescharacteristic
448D11—24no—
449C24—22no—
450C24—111no—
451#41—4432no—
452C2×Q8—21no—
453C2×Q8—22no—
454C2×Q8—114no—
455C2×Q8—112no—
456C2×Q8—224no—
457C2×Q8—228no—
458C2×Q8—228no—
459C2×Q8—2216no—
460C2×Q8—228no—
461C2×Q8—221no—
462C2×Q8—224no—
463C2×Q8—222no—
464C2×Q8—444no—
465C2×Q8#434114yescomplemented
466C2×Q8C23×D1112yes—
467C2×D4—22no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—228no—
475C2×D4—448no—
476C2×D4C23×D1114yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—228no—
489C22×C4—224no—
490C22×C4—228no—
491C22×C4—221no—
492C22×C4—224no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—444no—
498C22×C4—448no—
499C22×C4D4×D1111yescharacteristic
500C22×C4D4×D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502SD16—216no—
503SD16—2216no—
504C2×C8—24no—
505C2×C8—114no—
506C2×C8—224no—
507C2×C8C23×D1114yes—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—112no—
511C4⋊C4—114no—
512C4⋊C4—224no—
513C4⋊C4—224no—
514C4⋊C4—224no—
515C4⋊C4—221no—
516C4⋊C4—222no—
517C4⋊C4—224no—
518C4⋊C4—224no—
519C4⋊C4C23×D1112yes—
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—24no—
534C23—44no—
535C23—44no—
536C23—44no—
537C23—114no—
538C23—112no—
539C23—222no—
540C23—222no—
541C23C2×D4×D1111yescharacteristic
542Q8—24no—
543Q8—22no—
544Q8—114no—
545Q8—2216no—
546Q8—224no—
547Q8—222no—
548Q8—448no—
549Q8C2×#434114yescomplemented
550D4—24no—
551D4—24no—
552D4—48no—
553D4—48no—
554D4—44no—
555D4—4416no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—42no—
561C2×C4—112no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—228no—
565C2×C4—2216no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—222no—
571C2×C4—228no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—448no—
578C2×C4—4416no—
579C2×C4—444no—
580C2×C4—442no—
581C2×C4#6696814yes—
582C2×C4C2×D4×D1112yes—
583C2×C4C2×D4×D1112yes—
584C2×C4C2×D4×D1111yescharacteristic
585C2×C4C2×#434112yes—
586C2×C4#41×D1112yes—
587C2×C4C24×D1111yescharacteristic
588C8—24no—
589C8—224no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—88no—
594C22—114no—
595C22—222no—
596C22—228no—
597C22—222no—
598C22#1062313712yes—
599C22C2×#6696812yes—
600C22D11×AGL(1,ℤ/8)12yes—
601C22C22×D4×D1111yescharacteristic
602C4—24no—
603C4—22no—
604C4—42no—
605C4—222no—
606C4—224no—
607C4—222no—
608C4—222no—
609C4—444no—
610C4—442no—
611C4#1062313712yes—
612C4C2×#6696814yes—
613C4C22×#434111yescharacteristic
614C4C2×#41×D1111yescharacteristic
615C2—84no—
616C2—224no—
617C2#1307873714yesdirect product factor
618C2C2×#1062313711yescharacteristic
619C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
620C2C22×#6696811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
prime radicalC2×#10623247C2
hypercenterC2×#460D11
hypocenterC11C2×#3112
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
3. #13078737C2direct (N × H)
4. C2×#10622387C2semidirect
5. C2×#10622463C2semidirect
6. C2×#10622634C2semidirect
7. C2×#10622688C2semidirect
8. C2×#10622783C2semidirect
9. C2×#10622777C2semidirect
10. C2×#10622370C2semidirect
11. C2×#10622448C2semidirect
12. C2×C11×#460C2semidirect
28. C4×Q8×D11C22semidirect
38. C11×#460C22semidirect
43. #10622783C22semidirect
44. #10622777C22semidirect
49. #10622688C22semidirect
50. #10622634C22semidirect
53. #10622463C22semidirect
54. #10622448C22semidirect
55. #10622387C22semidirect
56. #10622370C22semidirect
144. C2×Q8×C11#41semidirect
191. C2×Dic22#41semidirect
230. C2×#460D11semidirect
246. Q8×C11C2×#41semidirect
289. Dic22C2×#41semidirect
321. #460C2×D11semidirect
444. C2×C11#3112semidirect
465. C2×Q8#4341semidirect
532. C11C2×#3112semidirect
549. Q8C2×#4341semidirect
617. C2#13078737direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232472
C2×C4×Q8×D112
#130787372
C2×#106223872
C2×#106224632
C2×#106226342
C2×#106226882
C2×#106227832
C2×#106227772
C2×#106223702
C2×#106224482
C2×C11×#4602
C2×#311211