Finite Group Databasebeta

← C2×#13079813 #15625915

Subgroups — C2×#13079813 #15625915

Order 2816.

2038 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×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623079C211yesmaximal, characteristic
3#13079813C2116yesmaximal, direct product factor
4C2×#10622489C212yesmaximal, complemented
5C2×#10622377C212yesmaximal, complemented
6C2×#10622498C212yesmaximal, complemented
7C2×#10622392C212yesmaximal, complemented
8C2×#10622455C211yesmaximal, characteristic, complemented
9C2×#10622621C211yesmaximal, characteristic, complemented
10C2×#10622700C211yesmaximal, characteristic, complemented
11C2×#10622448C211yesmaximal, characteristic, complemented
12C2×C11×#474C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66999—21no—
17C2×Q8×Dic11—21no—
18C2×#66993C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21#10623259—24no—
22#10623259C2218yescomplemented
23#10623079—24no—
24#10623079C2218yes—
25C2×#66950—21no—
26C2×#66948C2211yescharacteristic
27C2×#66945C2212yes—
28C2×#66943C2212yes—
29C2×#66941C2211yescharacteristic
30C2×#66940—21no—
31C2×#66938—21no—
32C2×#66937—21no—
33C2×C4×D44C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C11×#474C2218yescomplemented
37C2×C11×#107C2212yes—
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#102C2212yes—
40C2×#66896C2212yes—
41C2×#66885C2212yes—
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66881C2212yes—
44C2×#66879C2212yes—
45#10622700C2218yescomplemented
46#10622621C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622498C22116yescomplemented
52#10622489C22116yescomplemented
53#10622455C2218yescomplemented
54#10622448C2218yescomplemented
55#10622392C22116yescomplemented
56#10622377C22116yescomplemented
57C22×Q8×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C2×#4339—28no—
64C2×#4339—48no—
65C22×D44—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C22×Dic22—21no—
73C22×C8×C11C2312yes—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8C2314yes—
76C4×D4×C11—22no—
77C4×D4×C11C2314yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84#66999—28no—
85Q8×Dic11—28no—
86#66993—22no—
87#66993C2314yes—
88#66991—22no—
89#66991C2314yes—
90C4×C22⋊D11—28no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11D411yescharacteristic
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2312yes—
105#66950—28no—
106#66948—22no—
107#66948C2314yes—
108#66945—24no—
109#66945C2318yes—
110#66943—24no—
111#66943C2318yes—
112#66941—22no—
113#66941C2314yes—
114#66940—28no—
115#66938—28no—
116#66937—28no—
117C4×D44—22no—
118C4×D44C2314yes—
119C42×D11D414yes—
120C42×D11C2314yes—
121#66922—22no—
122#66922C2314yes—
123C11×#107C2318yes—
124C11×C4⋊C8C2314yes—
125C11×#102C2318yes—
126#66896C2318yes—
127#66885C2318yes—
128(C2×D11)⋊C8C2318yes—
129#66881C2318yes—
130#66879C2318yes—
131#66873C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134C4⋊(C11⋊C8)C2314yes—
135C2×#3235—111nomaximal, Sylow
136C24×C11—21no—
137C23×D11—21no—
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—24no—
140C2×Q8×C11—44no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11C2412yes—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—44no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—24no—
153C2×C22⋊D11—24no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11—44no—
156C2×C22⋊D11—44no—
157C2×C22⋊D11—44no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163#4339—432no—
164C2×D44—24no—
165C2×D44—21no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—44no—
169C2×D44C2412yes—
170C2×C4×D11—24no—
171C2×C4×D11—24no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—42no—
175C2×C4×D11—44no—
176C2×C4×D11C2×D412yes—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2×D414yes—
179C2×C4×D11C2412yes—
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—44no—
183C2×Dic22—44no—
184C2×C8×C11—24no—
185C2×C8×C11C2414yes—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2414yes—
190C11×C4⋊C4C2412yes—
191C11×C22⋊C4—24no—
192C42×C11C2×D412yes—
193C42×C11C2412yes—
194C22⋊Dic11—24no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—24no—
198C4⋊Dic11—28no—
199C4⋊Dic11—22no—
200C4⋊Dic11—24no—
201C4⋊Dic11—21no—
202C4⋊Dic11C2412yes—
203C4⋊Dic11C2414yes—
204Dic11⋊C4—24no—
205Dic11⋊C4—28no—
206C4×Dic11—28no—
207C4×Dic11C2×D412yes—
208C4×Dic11C2×D414yes—
209C4×Dic11C2×D414yes—
210C4×Dic11C2412yes—
211C2×C11⋊C8—24no—
212C2×C11⋊C8C2414yes—
213C2×#533—111no—
214C2×#532—111no—
215#3235—1116no—
216C2×#501—112no—
217C2×#490—112no—
218C2×#482—112no—
219C2×#482—112no—
220C2×#476—111no—
221C2×#476—111no—
222C2×#474—111no—
223C2×#474D1111yescharacteristic, complemented
224C2×#432—111no—
225C23×C11—22no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11C22×D412yes—
238Q8×C11—48no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—42no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—42no—
246C2×C4×C11—44no—
247C2×C4×C11—48no—
248C2×C4×C11AGL(1,ℤ/8)14yes—
249C2×C4×C11C22×D412yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D412yes—
252C2×C4×C112−1+412yes—
253C2×C4×C112−1+412yes—
254C2×C4×C11C2511yescharacteristic
255C22⋊D11—48no—
256C22⋊D11—48no—
257C22⋊D11—48no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—42no—
264C2×Dic11—44no—
265C2×Dic11C22×D412yes—
266C2×Dic11C22×D412yes—
267C2×Dic11C22×D412yes—
268D44—22no—
269D44—22no—
270D44—48no—
271D44—42no—
272C4×D11—24no—
273C4×D11—28no—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—44no—
277C4×D11—48no—
278Dic22—48no—
279Dic22—48no—
280C8×C11—24no—
281C11⋊C8—24no—
282C22×#41—221no—
283#533—118no—
284#533—224no—
285#532—118no—
286#532—224no—
287C2×C4⋊Q8—111no—
288C2×C4⋊Q8—111no—
289C2×C4⋊Q8C2×D1111yescharacteristic
290C2×#127—111no—
291C2×#125—112no—
292C2×#124—221no—
293C2×C22⋊Q8—221no—
294C2×C22⋊Q8—221no—
295C2×#121—111no—
296C2×#121—111no—
297C2×#121—221no—
298C2×C4×Q8—221no—
299C2×C4×Q8—221no—
300C2×C4×D4—111no—
301C2×C4×D4—221no—
302C2×C4×D4C2×D1111yescharacteristic
303C2×#117—112no—
304C22×C42—111no—
305#501—1116no—
306#490—1116no—
307#482—1116no—
308#482—1116no—
309#476—118no—
310#476—118no—
311#474—118no—
312#474C2×D1118yescomplemented
313#432—118no—
314C2×#107—112no—
315C2×#107C2×D1112yes—
316C2×#106—112no—
317C2×#106—112no—
318C2×C4⋊C8—111no—
319C2×C4⋊C8C2×D1111yescharacteristic
320C2×#102—112no—
321C2×#102—112no—
322C2×#102—112no—
323C2×#102C2×D1112yes—
324C2×C22⋊C8—112no—
325C2×#97—112no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—84no—
330C22×C11#53612yes—
331C22×C11C2×AGL(1,ℤ/8)12yes—
332C22×C11#57512yes—
333C22×C11C23×D411yescharacteristic
334C2×D11—22no—
335C2×D11—22no—
336C2×D11—22no—
337C2×D11—44no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—84no—
342C4×C11—22no—
343C4×C11—42no—
344C4×C11—44no—
345C4×C11#53612yes—
346C4×C11C2×AGL(1,ℤ/8)14yes—
347C4×C11C2×2−1+411yescharacteristic
348C4×C11C2×2−1+411yescharacteristic
349Dic11—22no—
350Dic11—22no—
351Dic11—22no—
352Dic11—42no—
353Dic11—44no—
354C2×#41—228no—
355C2×#41—448no—
356C22×Q8—21no—
357C22×Q8—221no—
358C22×Q8—221no—
359C22×D4—111no—
360C22×D4—221no—
361C22×D4—221no—
362C22×D4—221no—
363C22×D4—221no—
364C22×D4C22×D1111yescharacteristic
365C23×C4—21no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—111no—
369C23×C4—221no—
370C22×C8—112no—
371C22×C8C22×D1112yes—
372C4⋊Q8—22no—
373C4⋊Q8—114no—
374C4⋊Q8—114no—
375C4⋊Q8—222no—
376C4⋊Q8—222no—
377C4⋊Q8C22×D1114yes—
378#127—114no—
379#127—222no—
380#125—118no—
381#125—224no—
382#124—228no—
383C22⋊Q8—228no—
384C22⋊Q8—228no—
385#121—114no—
386#121—114no—
387#121—228no—
388#121—222no—
389#121—222no—
390C4×Q8—228no—
391C4×Q8—228no—
392C4×D4—22no—
393C4×D4—114no—
394C4×D4—228no—
395C4×D4—222no—
396C4×D4C22×D1114yes—
397#117—118no—
398#117—224no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22×D1112yes—
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—222no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—114no—
417C2×C42—114no—
418C2×C42—222no—
419C2×C42C22×D1111yescharacteristic
420#107—118no—
421#107C22×D1118yes—
422#106—118no—
423#106—118no—
424C4⋊C8—114no—
425C4⋊C8C22×D1114yes—
426#102—118no—
427#102—118no—
428#102—118no—
429#102C22×D1118yes—
430C22⋊C8—118no—
431#97—118no—
432C2×C11—82no—
433C2×C11#323514yescomplemented
434C2×C11C2×#53611yescharacteristic
435C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
436C2×C11C2×#57511yescharacteristic
437D11—42no—
438D11—82no—
439C24—21no—
440C24—111no—
441C24—221no—
442#41—4432no—
443C2×Q8—24no—
444C2×Q8—44no—
445C2×Q8—224no—
446C2×Q8—224no—
447C2×Q8—444no—
448C2×Q8—444no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—112no—
453C2×D4—224no—
454C2×D4—224no—
455C2×D4—224no—
456C2×D4—224no—
457C2×D4—221no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—444no—
461C2×D4—444no—
462C2×D4—444no—
463C2×D4—444no—
464C2×D4C23×D1112yes—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—44no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—112no—
473C22×C4—114no—
474C22×C4—112no—
475C22×C4—114no—
476C22×C4—224no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—221no—
481C22×C4—224no—
482C22×C4—442no—
483C22×C4—444no—
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487C2×C8—24no—
488C2×C8—114no—
489C2×C8—224no—
490C2×C8C23×D1114yes—
491C4⋊C4—24no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—114no—
495C4⋊C4—112no—
496C4⋊C4—224no—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—222no—
500C4⋊C4—221no—
501C4⋊C4—224no—
502C4⋊C4C23×D1114yes—
503C4⋊C4C23×D1112yes—
504C22⋊C4—24no—
505C22⋊C4—224no—
506C22⋊C4—228no—
507C22⋊C4—224no—
508C22⋊C4—224no—
509C42—114no—
510C42—114no—
511C42—112no—
512C42—112no—
513C42—228no—
514C42D4×D1112yes—
515C42C23×D1112yes—
516C11C2×#323511yescharacteristic, complemented, Sylow
517C23—22no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—112no—
522C23—222no—
523C23—222no—
524C23—222no—
525C23—222no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23C2×D4×D1111yescharacteristic
530Q8—48no—
531Q8—448no—
532Q8—448no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—222no—
537D4—222no—
538D4—448no—
539D4—448no—
540D4—448no—
541D4—448no—
542D4—442no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—48no—
549C2×C4—112no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—228no—
556C2×C4—224no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—224no—
560C2×C4—222no—
561C2×C4—444no—
562C2×C4—442no—
563C2×C4—444no—
564C2×C4—448no—
565C2×C4#6696414yes—
566C2×C4C2×D4×D1112yes—
567C2×C4C2×D4×D1112yes—
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4#6704012yes—
570C2×C4#6704312yes—
571C2×C4C24×D1111yescharacteristic
572C8—24no—
573C8—224no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—84no—
578C22—222no—
579C22—222no—
580C22—222no—
581C22—444no—
582C22—442no—
583C22—442no—
584C22—442no—
585C22—884no—
586C22#1062315912yes—
587C22C2×#6696412yes—
588C22#1062330812yes—
589C22C22×D4×D1111yescharacteristic
590C4—22no—
591C4—42no—
592C4—44no—
593C4—222no—
594C4—222no—
595C4—222no—
596C4—442no—
597C4—444no—
598C4#1062315912yes—
599C4C2×#6696414yes—
600C4C2×#6704011yescharacteristic
601C4C2×#6704311yescharacteristic
602C2—82no—
603C2—442no—
604C2—882no—
605C2#1307981314yesdirect product factor
606C2C2×#1062315911yescharacteristic
607C2C22×#6696411yescharacteristic
608C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC2×#10623079C2
hypercenterC2×#474D11
hypocenterC11C2×#3235
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079813C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622377C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622392C2semidirect
8. C2×#10622455C2semidirect
9. C2×#10622621C2semidirect
10. C2×#10622700C2semidirect
11. C2×#10622448C2semidirect
12. C2×C11×#474C2semidirect
22. #10623259C22semidirect
36. C11×#474C22semidirect
45. #10622700C22semidirect
46. #10622621C22semidirect
51. #10622498C22semidirect
52. #10622489C22semidirect
53. #10622455C22semidirect
54. #10622448C22semidirect
55. #10622392C22semidirect
56. #10622377C22semidirect
223. C2×#474D11semidirect
312. #474C2×D11semidirect
433. C2×C11#3235semidirect
516. C11C2×#3235semidirect
605. C2#13079813direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106230792
#130798132
C2×#106224892
C2×#106223772
C2×#106224982
C2×#106223922
C2×#106224552
C2×#106226212
C2×#106227002
C2×#106224482
C2×C11×#4742
C2×#323511