Finite Group Databasebeta

← C2×#13080847 #15630602

Subgroups — C2×#13080847 #15630602

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2#13080847C2116yesmaximal, direct product factor
3C2×#10622683C211yesmaximal, characteristic, complemented
4C2×#10622648C212yesmaximal, complemented
5C2×#10622620C211yesmaximal, characteristic, complemented
6C2×#10622655C212yesmaximal, complemented
7C2×#10622688C211yesmaximal, characteristic, complemented
8C2×#10622831C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622828C212yesmaximal, complemented
12C2×D42×C11C211yesmaximal, characteristic
13C23×D4×C11—21no—
14C23×D4×C11C2212yes—
15D42×C11—24no—
16D42×C11C2218yes—
17C2×C11×#127C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121C2212yes—
20C2×C11×#120—22no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×#66989—21no—
24C22×#4324C2211yescharacteristic
25C22×#4324C2212yescomplemented
26C2×#66979C2212yescomplemented
27C2×#66977C2212yescomplemented
28C22×#4318C2212yescomplemented
29#10623073—24no—
30#10623073C2218yescomplemented
31C2×#66940—21no—
32C2×#66932—22no—
33C2×#66922C2211yescharacteristic, complemented
34C2×C4×Dic22C2211yescharacteristic, complemented
35#10622831C22116yescomplemented
36#10622828C22116yescomplemented
37C2×#66896C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66896C2212yescomplemented
40C2×#66896C2212yescomplemented
41C2×#66896C2212yescomplemented
42C2×C22⋊(C11⋊C8)C2212yescomplemented
43#10622688C2218yescomplemented
44#10622683C2218yescomplemented
45#10622655C22116yescomplemented
46#10622648C22116yescomplemented
47C4×#4324C2218yescomplemented
48#10622625C2218yescomplemented
49#10622620C2218yescomplemented
50C2×#66874C2211yescharacteristic, complemented
51C2×#66872C2211yescharacteristic, complemented
52C2×#66871C2212yescomplemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4×C11⋊C8C2211yescharacteristic, complemented
55C25×C11—22no—
56C22×D4×C11—28no—
57C22×D4×C11—22no—
58C22×D4×C11—28no—
59C22×D4×C11—22no—
60C22×D4×C11—21no—
61C22×D4×C11—24no—
62C22×D4×C11—21no—
63C22×D4×C11—44no—
64C22×D4×C11—48no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2312yes—
67C22×D4×C11C2318yes—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11C2312yes—
71C22×Dic22—21no—
72C22×Dic22C2311yescharacteristic
73C11×#127—22no—
74C11×#127C2314yes—
75C11×#121—24no—
76C11×#121—28no—
77C11×#121C2318yes—
78C11×#120—216no—
79C4×D4×C11—22no—
80C4×D4×C11D414yes—
81C4×D4×C11C2314yes—
82C4×D4×C11C2314yes—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91#66989—28no—
92C2×#4324—24no—
93C2×#4324—44no—
94C2×#4324C2314yes—
95C2×#4324C2318yescomplemented
96#66979—24no—
97#66979C2318yescomplemented
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2312yes—
101#66977—24no—
102#66977C2318yescomplemented
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—22no—
107C2×#4318—44no—
108C2×#4318C2318yescomplemented
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112#66940—28no—
113#66932—216no—
114#66922—22no—
115#66922C2314yescomplemented
116C4×Dic22—22no—
117C4×Dic22C2314yescomplemented
118#66896C2314yes—
119#66896C2318yes—
120#66896C2318yescomplemented
121#66896C2318yescomplemented
122#66896C2318yescomplemented
123C22⋊(C11⋊C8)C2318yescomplemented
124#66874C2314yescomplemented
125#66872C2314yescomplemented
126#66871C2318yescomplemented
127C4⋊(C11⋊C8)C2314yescomplemented
128C4×C11⋊C8C2314yescomplemented
129C2×#3324—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11—22no—
132C24×C11—28no—
133C24×C11—48no—
134C24×C11—48no—
135C24×C11—84no—
136C24×C11C2×D412yes—
137C2×D4×C11—216no—
138C2×D4×C11—28no—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—28no—
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—22no—
147C2×D4×C11—24no—
148C2×D4×C11—48no—
149C2×D4×C11—416no—
150C2×D4×C11—48no—
151C2×D4×C11—432no—
152C2×D4×C11—48no—
153C2×D4×C11—44no—
154C2×D4×C11—82no—
155C2×D4×C11C2×D414yes—
156C2×D4×C11#4114yes—
157C2×D4×C11C2414yes—
158C2×D4×C11C2412yes—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—44no—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D414yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2414yes—
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C2×Dic22—21no—
174C2×Dic22—24no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—44no—
178C2×Dic22C2412yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2×D414yes—
181C11×C4⋊C4C2412yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—28no—
184C11×C22⋊C4C2×D418yes—
185C42×C11C2×D412yes—
186C42×C11C2412yes—
187C22⋊Dic11—28no—
188C22⋊Dic11—28no—
189#4324—28no—
190#4324—48no—
191C4⋊Dic11—21no—
192C4⋊Dic11—22no—
193C4⋊Dic11—24no—
194C4⋊Dic11C2414yes—
195C4⋊Dic11C2412yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—28no—
198C4×Dic11—24no—
199C4×Dic11—28no—
200#4318—48no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8C2412yes—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2414yes—
207C2×#556—111no—
208C2×D42D1111yescharacteristic
209#3324—1116no—
210C2×#486—111no—
211C2×#482—112no—
212C2×#474—111no—
213C2×#468—112no—
214C2×#460—111no—
215C2×#450—112no—
216C2×C4×SD16—111no—
217C2×#436—111no—
218C2×#418—112no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—416no—
226C23×C11—416no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—44no—
230C23×C11—44no—
231C23×C11—44no—
232C23×C11—88no—
233C23×C11—832no—
234C23×C11C22×D414yes—
235C23×C11C22×D411yescharacteristic
236D4×C11—24no—
237D4×C11—28no—
238D4×C11—24no—
239D4×C11—22no—
240D4×C11—24no—
241D4×C11—416no—
242D4×C11—416no—
243D4×C11—44no—
244D4×C11—48no—
245D4×C11—84no—
246D4×C11C2×#4114yes—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—28no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—42no—
254C2×C4×C11—48no—
255C2×C4×C11AGL(1,ℤ/8)14yes—
256C2×C4×C11C22×D414yes—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D412yes—
260C2×C4×C11C2×#4112yes—
261C2×C4×C11H(5,𝔽2)12yes—
262C2×C4×C11C2511yescharacteristic
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—42no—
267C2×Dic11—44no—
268C2×Dic11—42no—
269Dic22—22no—
270Dic22—22no—
271Dic22—42no—
272Dic22—48no—
273C11⋊C8—22no—
274C11⋊C8—22no—
275C11⋊C8—24no—
276C23×D4—21no—
277C23×D4C2×D1112yes—
278C22×SD16—111no—
279C22×SD16—112no—
280C22×M16—112no—
281#556—118no—
282#556—224no—
283D42—24no—
284D42C2×D1118yes—
285C2×C4⋊Q8—111no—
286C2×#127C2×D1111yescharacteristic
287C2×#126—222no—
288C2×#124—221no—
289C2×C22⋊Q8—112no—
290C2×#121—21no—
291C2×#121C2×D1112yes—
292C2×#120—22no—
293C2×C4×Q8—111no—
294C2×C4×Q8—221no—
295C2×C4×D4C2×D1111yescharacteristic
296C2×C4×D4C2×D1111yescharacteristic
297C2×#117—112no—
298#486—118no—
299#482—1116no—
300#474—118no—
301#468—1116no—
302#460—118no—
303#450—1116no—
304C4×SD16—118no—
305#436—118no—
306C2×#107—112no—
307C2×#106—111no—
308C2×C4⋊C8—111no—
309#418—1116no—
310C2×#103—111no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—111no—
315C2×#102—112no—
316C2×C22⋊C8—112no—
317C2×C4×C8—111no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—42no—
323C22×C11—48no—
324C22×C11—48no—
325C22×C11—42no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—832no—
330C22×C11—88no—
331C22×C11#54612yes—
332C22×C11C2×AGL(1,ℤ/8)12yes—
333C22×C11#57712yes—
334C22×C11C23×D411yescharacteristic
335C4×C11—24no—
336C4×C11—22no—
337C4×C11—42no—
338C4×C11#54612yes—
339C4×C11C2×AGL(1,ℤ/8)14yes—
340C4×C11C22×#4111yescharacteristic
341C4×C11C2×H(5,𝔽2)11yescharacteristic
342Dic11—42no—
343Dic11—44no—
344Dic11—42no—
345C25—22no—
346C22×Q8—111no—
347C22×Q8—221no—
348C22×D4—28no—
349C22×D4—22no—
350C22×D4—28no—
351C22×D4—22no—
352C22×D4—21no—
353C22×D4—24no—
354C22×D4—21no—
355C22×D4—44no—
356C22×D4—48no—
357C22×D4C22⋊D1111yescharacteristic
358C22×D4C22×D1112yes—
359C22×D4C22×D1118yes—
360C22×D4C22×D1111yescharacteristic
361C23×C4—21no—
362C23×C4C22×D1112yes—
363C2×SD16—114no—
364C2×SD16—118no—
365C2×SD16—224no—
366C2×SD16—444no—
367C2×M16—118no—
368C2×M16—444no—
369C22×C8—111no—
370C22×C8—112no—
371C22×C8—111no—
372C4⋊Q8—114no—
373C4⋊Q8—222no—
374#127—22no—
375#127C22×D1114yes—
376#126—2216no—
377#124—228no—
378C22⋊Q8—118no—
379C22⋊Q8—224no—
380#121—24no—
381#121—28no—
382#121C22×D1118yes—
383#120—216no—
384C4×Q8—114no—
385C4×Q8—228no—
386C4×Q8—222no—
387C4×D4—22no—
388C4×D4C22⋊D1114yes—
389C4×D4C22×D1114yes—
390C4×D4C22×D1114yes—
391#117—118no—
392#117—224no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—112no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4C22⋊D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4C22⋊D1112yes—
405C2×C42—222no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408#107—118no—
409#106—114no—
410C4⋊C8—114no—
411#103—114no—
412#102—114no—
413#102—118no—
414#102—118no—
415#102—118no—
416#102—118no—
417C22⋊C8—118no—
418C4×C8—114no—
419C2×C11—44no—
420C2×C11—44no—
421C2×C11—84no—
422C2×C11#332414yescomplemented
423C2×C11C2×#54611yescharacteristic
424C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C11C2×#57711yescharacteristic
426C24—21no—
427C24—22no—
428C24—28no—
429C24—48no—
430C24—48no—
431C24—84no—
432C24C2×C22⋊D1112yes—
433C2×Q8—112no—
434C2×Q8—221no—
435C2×Q8—224no—
436C2×Q8—222no—
437C2×Q8—222no—
438C2×Q8—444no—
439C2×D4—216no—
440C2×D4—28no—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—22no—
444C2×D4—24no—
445C2×D4—21no—
446C2×D4—28no—
447C2×D4—22no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—48no—
451C2×D4—416no—
452C2×D4—48no—
453C2×D4—432no—
454C2×D4—48no—
455C2×D4—44no—
456C2×D4—82no—
457C2×D4#434114yes—
458C2×D4C2×C22⋊D1114yes—
459C2×D4C23×D1114yes—
460C2×D4C23×D1112yes—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—21no—
464C22×C4—24no—
465C22×C4—44no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—221no—
469C22×C4C2×C22⋊D1114yes—
470C22×C4C2×C22⋊D1112yes—
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1114yes—
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476SD16—448no—
477M16—448no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8—114no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—224no—
484C4⋊C4—21no—
485C4⋊C4—112no—
486C4⋊C4—114no—
487C4⋊C4—221no—
488C4⋊C4—222no—
489C4⋊C4—224no—
490C4⋊C4—228no—
491C4⋊C4—224no—
492C4⋊C4C2×C22⋊D1114yes—
493C4⋊C4C23×D1112yes—
494C22⋊C4—24no—
495C22⋊C4—28no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C22⋊C4C2×C22⋊D1118yes—
499C42—228no—
500C42—224no—
501C42C2×C22⋊D1112yes—
502C42C23×D1112yes—
503C11C2×#332411yescharacteristic, complemented, Sylow
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—416no—
511C23—416no—
512C23—42no—
513C23—42no—
514C23—44no—
515C23—44no—
516C23—44no—
517C23—88no—
518C23—832no—
519C23C22×C22⋊D1114yes—
520C23C22×C22⋊D1111yescharacteristic
521Q8—222no—
522Q8—222no—
523Q8—448no—
524Q8—442no—
525D4—28no—
526D4—24no—
527D4—24no—
528D4—22no—
529D4—24no—
530D4—416no—
531D4—416no—
532D4—48no—
533D4—44no—
534D4—84no—
535D4C2×#434114yes—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—28no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—42no—
543C2×C4—48no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—444no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4#6698514yes—
551C2×C4C2×#434112yes—
552C2×C4#6703712yes—
553C2×C4C22×C22⋊D1114yes—
554C2×C4C22×C22⋊D1112yes—
555C2×C4C22×C22⋊D1112yes—
556C2×C4C22×C22⋊D1111yescharacteristic
557C2×C4C24×D1111yescharacteristic
558C8—222no—
559C8—222no—
560C8—224no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—24no—
565C22—48no—
566C22—48no—
567C22—42no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—44no—
572C22—832no—
573C22—88no—
574C22C2×#6698512yes—
575C22#1062333712yes—
576C22#1062336712yes—
577C22C23×C22⋊D1111yescharacteristic
578C4—24no—
579C4—22no—
580C4—42no—
581C4—442no—
582C4—444no—
583C4—442no—
584C4C2×#6698514yes—
585C4#1062333712yes—
586C4C22×#434111yescharacteristic
587C4C2×#6703711yescharacteristic
588C2—44no—
589C2—44no—
590C2—84no—
591C2#1308084714yesdirect product factor
592C2C2×#1062333711yescharacteristic
593C2C22×#6698511yescharacteristic
594C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×D42×C11C2
socleC23×C11C22×D4
hypercenterC2×D42D11
hypocenterC11C2×#3324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. #13080847C2direct (N × H)
3. C2×#10622683C2semidirect
4. C2×#10622648C2semidirect
5. C2×#10622620C2semidirect
6. C2×#10622655C2semidirect
7. C2×#10622688C2semidirect
8. C2×#10622831C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622828C2semidirect
25. C22×#4324C22semidirect
26. C2×#66979C22semidirect
27. C2×#66977C22semidirect
28. C22×#4318C22semidirect
30. #10623073C22semidirect
33. C2×#66922C22semidirect
34. C2×C4×Dic22C22semidirect
35. #10622831C22semidirect
36. #10622828C22semidirect
39. C2×#66896C22semidirect
40. C2×#66896C22semidirect
41. C2×#66896C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
43. #10622688C22semidirect
44. #10622683C22semidirect
45. #10622655C22semidirect
46. #10622648C22semidirect
47. C4×#4324C22semidirect
48. #10622625C22semidirect
49. #10622620C22semidirect
50. C2×#66874C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4×C11⋊C8C22semidirect
95. C2×#4324C23semidirect
97. #66979C23semidirect
102. #66977C23semidirect
108. C2×#4318C23semidirect
115. #66922C23semidirect
117. C4×Dic22C23semidirect
120. #66896C23semidirect
121. #66896C23semidirect
122. #66896C23semidirect
123. C22⋊(C11⋊C8)C23semidirect
124. #66874C23semidirect
125. #66872C23semidirect
126. #66871C23semidirect
127. C4⋊(C11⋊C8)C23semidirect
128. C4×C11⋊C8C23semidirect
422. C2×C11#3324semidirect
503. C11C2×#3324semidirect
591. C2#13080847direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130808472
C2×#106226832
C2×#106226482
C2×#106226202
C2×#106226552
C2×#106226882
C2×#106228312
C2×C4×#43242
C2×#106226252
C2×#106228282
C2×D42×C112
C2×#332411