Finite Group Databasebeta

← C2×#13070013 #14782489

Subgroups — C2×#13070013 #14782489

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622738C211yesmaximal, characteristic, complemented
2C2×#10622737C211yesmaximal, characteristic, complemented
3C22×#66887C211yesmaximal, characteristic
4C22×#66887C211yesmaximal, characteristic
5C22×#66887C211yesmaximal, characteristic
6#13070013C218yesmaximal, direct product factor
7C2×C11⋊#338C211yesmaximal, characteristic, complemented
8C2×C11×#430C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C11×#430—22no—
17C11×#430C2214yescomplemented
18C2×C11×#108—22no—
19C2×#66887—22no—
20C2×#66887—22no—
21C2×#66887—22no—
22C2×#66887—22no—
23C2×#66887—22no—
24C2×#66887—22no—
25C2×#66887C2214yes—
26C2×#66887C2214yes—
27C2×#66887C2214yes—
28#10622738—22no—
29#10622738C2214yescomplemented
30#10622737—22no—
31#10622737C2214yescomplemented
32C2×#66886—22no—
33C2×#66883—22no—
34C11⋊#338C2214yescomplemented
35C24×D11Q812yes—
36C23×C4×C11C2311yescharacteristic
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44—21no—
48C22×D44—21no—
49C22×D44Q812yes—
50C22×D44C2312yes—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16D412yes—
63C2×C11×M16D412yes—
64C2×C11×M16D412yes—
65C2×C11×M16D412yes—
66C2×C11×M16C2312yes—
67C2×C11×M16C2312yes—
68C2×C11×M16C2312yes—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C2×#4318—21no—
73C2×#4318—21no—
74C2×#4318—21no—
75C2×#4318—21no—
76C2×#4318—21no—
77C2×#4318—21no—
78C2×#4318—21no—
79C2×#4318—21no—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318D412yes—
86C2×#4318D412yes—
87C2×#4318C2312yes—
88C2×#4318C2312yes—
89C2×#4318C2312yes—
90C22×C11⋊C8—21no—
91C22×C11⋊C8—21no—
92C22×C11⋊C8—21no—
93C11×#108—28no—
94#66887—28no—
95#66887—28no—
96#66887—28no—
97#66886—28no—
98#66883—28no—
99C2×#2069—111nomaximal, Sylow
100C24×C11C2×Q811yescharacteristic
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—84no—
108C23×D11C2×Q814yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×Q811yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—41no—
136C2×D44—41no—
137C2×D44—41no—
138C2×D44—41no—
139C2×D44—41no—
140C2×D44—41no—
141C2×D44—41no—
142C2×D44—41no—
143C2×D44—41no—
144C2×D44—41no—
145C2×D44—41no—
146C2×D44—41no—
147C2×D44—41no—
148C2×D44—41no—
149C2×D44—41no—
150C2×D44—41no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—22no—
156C11×M16—22no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—41no—
160C11×M16—41no—
161C11×M16C2×D414yes—
162C11×M16C2×D414yes—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172#4318—22no—
173#4318—22no—
174#4318—22no—
175#4318—22no—
176#4318—22no—
177#4318—22no—
178#4318—22no—
179#4318—41no—
180#4318—41no—
181#4318—41no—
182#4318—41no—
183#4318C2×D414yes—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—41no—
190C2×C11⋊C8—41no—
191C2×C11⋊C8—41no—
192C2×C11⋊C8—41no—
193C2×#430—111no—
194C2×#430—111no—
195C2×#430D1111yescharacteristic, complemented
196C22×#100—111no—
197C22×#100—111no—
198C22×#100—111no—
199#2069—118no—
200C2×#338—111no—
201C23×C11—42no—
202C23×C11C22⋊Q811yescharacteristic
203C23×C11C22⋊Q811yescharacteristic
204C23×C11C22⋊Q811yescharacteristic
205C23×C11C22⋊Q811yescharacteristic
206C23×C11C22⋊Q811yescharacteristic
207C23×C11C22⋊Q811yescharacteristic
208C23×C11C22×Q811yescharacteristic
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—84no—
217C22×D11—84no—
218C22×D11—84no—
219C22×D11—84no—
220C22×D11—84no—
221C22×D11—84no—
222C22×D11—84no—
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11#12111yescharacteristic
228C2×C4×C11#12111yescharacteristic
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C2×C4×C11#12111yescharacteristic
232C2×C4×C11#12111yescharacteristic
233C2×C4×C11#12111yescharacteristic
234C2×C4×C11#12111yescharacteristic
235C2×C4×C11C22⋊Q811yescharacteristic
236C2×C4×C11C22⋊Q811yescharacteristic
237C2×C4×C11C22⋊Q811yescharacteristic
238C2×C4×C11C22⋊Q811yescharacteristic
239C2×C4×C11C22⋊Q811yescharacteristic
240C2×C4×C11C22⋊Q811yescharacteristic
241C2×C4×C11#12611yescharacteristic
242C2×C4×C11#12611yescharacteristic
243C2×C4×C11#12611yescharacteristic
244C2×C4×C11#12611yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251D44—42no—
252D44—42no—
253D44—42no—
254D44—42no—
255D44—42no—
256D44—42no—
257D44—42no—
258D44—42no—
259C8×C11—24no—
260C8×C11—24no—
261C8×C11—42no—
262C11⋊C8—24no—
263C11⋊C8—42no—
264C11⋊C8—42no—
265C23×D4—111no—
266C22×M16—111no—
267C22×M16—111no—
268C22×M16—111no—
269C22×M16C2×D1111yescharacteristic
270C22×M16C2×D1111yescharacteristic
271C22×M16C2×D1111yescharacteristic
272#430—22no—
273#430—114no—
274#430—114no—
275#430—222no—
276#430—222no—
277#430C2×D1114yescomplemented
278C2×#108—22no—
279C2×#108—222no—
280C2×#108—222no—
281C2×#100—114no—
282C2×#100—114no—
283C2×#100—114no—
284C2×#100—222no—
285C2×#100—222no—
286C2×#100—222no—
287C2×#100—222no—
288C2×#100—222no—
289C2×#100—222no—
290#338—114no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11#39611yescharacteristic
299C22×C11#39611yescharacteristic
300C22×C11#39611yescharacteristic
301C22×C11#39611yescharacteristic
302C22×C11C2×C22⋊Q811yescharacteristic
303C22×C11C2×C22⋊Q811yescharacteristic
304C22×C11C2×C22⋊Q811yescharacteristic
305C2×D11—44no—
306C2×D11—84no—
307C2×D11—84no—
308C2×D11—84no—
309C2×D11—84no—
310C2×D11—84no—
311C2×D11—84no—
312C2×D11—84no—
313C4×C11#39611yescharacteristic
314C4×C11#39611yescharacteristic
315C4×C11#39611yescharacteristic
316C4×C11#39611yescharacteristic
317C4×C11C2×#12111yescharacteristic
318C4×C11C2×#12111yescharacteristic
319C4×C11C2×#12111yescharacteristic
320C4×C11C2×#12611yescharacteristic
321C25—112no—
322C22×D4—112no—
323C22×D4—112no—
324C22×D4—221no—
325C22×D4—221no—
326C22×D4—221no—
327C22×D4—221no—
328C22×D4—221no—
329C22×D4—221no—
330C22×D4—221no—
331C22×D4—221no—
332C22×D4—221no—
333C22×D4—221no—
334C22×D4—221no—
335C22×D4—221no—
336C23×C4C22×D1111yescharacteristic
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—112no—
349C2×M16—112no—
350C2×M16—112no—
351C2×M16—112no—
352C2×M16—112no—
353C2×M16—221no—
354C2×M16—221no—
355C2×M16—221no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16—221no—
359C2×M16—221no—
360C2×M16—221no—
361C2×M16—221no—
362C2×M16—221no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16D4412yes—
367C2×M16D4412yes—
368C2×M16C22⋊D1112yes—
369C2×M16C22⋊D1112yes—
370C2×M16C22×D1112yes—
371C2×M16C22×D1112yes—
372C2×M16C22×D1112yes—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—221no—
377C22×C8—221no—
378C22×C8—221no—
379#108—28no—
380#108—228no—
381#108—228no—
382#100—228no—
383#100—228no—
384#100—228no—
385C2×C11—21no—
386C2×C11—21no—
387C2×C11—21no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11#206912yescomplemented
392C2×C11C2×#39611yescharacteristic
393D11—84no—
394C24—114no—
395C24—222no—
396C24—222no—
397C24—222no—
398C24—222no—
399C24—222no—
400C24—222no—
401C24—884no—
402C24Q8×D1111yescharacteristic
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—222no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—222no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—441no—
421C2×D4—441no—
422C2×D4—441no—
423C2×D4—441no—
424C2×D4—441no—
425C2×D4—441no—
426C2×D4—441no—
427C2×D4—441no—
428C2×D4—441no—
429C2×D4—441no—
430C2×D4—441no—
431C22×C4C2×D4411yescharacteristic
432C22×C4C2×D4411yescharacteristic
433C22×C4#433911yescharacteristic
434C22×C4#433911yescharacteristic
435C22×C4D4×D1111yescharacteristic
436C22×C4D4×D1111yescharacteristic
437C22×C4#434111yescharacteristic
438C22×C4#434111yescharacteristic
439C22×C4Q8×D1111yescharacteristic
440C22×C4#434311yescharacteristic
441C22×C4#434311yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445M16—22no—
446M16—22no—
447M16—22no—
448M16—22no—
449M16—22no—
450M16—22no—
451M16—22no—
452M16—22no—
453M16—41no—
454M16—41no—
455M16—114no—
456M16—222no—
457M16—222no—
458M16—222no—
459M16—222no—
460M16—222no—
461M16—222no—
462M16—222no—
463M16—441no—
464M16—441no—
465M16—441no—
466M16—441no—
467M16C2×D4414yes—
468M16C2×C22⋊D1114yes—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—441no—
484C2×C8—441no—
485C2×C8—441no—
486C2×C8—441no—
487C11C2×#206911yescharacteristic, complemented, Sylow
488C23—42no—
489C23—224no—
490C23—224no—
491C23—224no—
492C23—442no—
493C23—442no—
494C23—442no—
495C23—442no—
496C23—884no—
497C23—884no—
498C23—884no—
499C23—884no—
500C23—884no—
501C23—884no—
502C23—884no—
503C23#6694911yescharacteristic
504C23#6694911yescharacteristic
505C23#6695011yescharacteristic
506C23#6695011yescharacteristic
507C23#6699911yescharacteristic
508C23#6699911yescharacteristic
509C23C2×Q8×D1111yescharacteristic
510D4—442no—
511D4—442no—
512D4—442no—
513D4—442no—
514D4—442no—
515D4—442no—
516D4—442no—
517D4—442no—
518C2×C4#6694811yescharacteristic
519C2×C4#6694811yescharacteristic
520C2×C4#6694811yescharacteristic
521C2×C4#6694811yescharacteristic
522C2×C4#6694911yescharacteristic
523C2×C4#6694911yescharacteristic
524C2×C4#6695011yescharacteristic
525C2×C4#6695011yescharacteristic
526C2×C4#6695111yescharacteristic
527C2×C4#6695111yescharacteristic
528C2×C4#6695111yescharacteristic
529C2×C4#6695111yescharacteristic
530C2×C4#6698311yescharacteristic
531C2×C4#6698311yescharacteristic
532C2×C4#6698311yescharacteristic
533C2×C4#6698311yescharacteristic
534C2×C4#6699211yescharacteristic
535C2×C4#6699211yescharacteristic
536C2×C4#6699211yescharacteristic
537C2×C4#6699211yescharacteristic
538C2×C4#6699911yescharacteristic
539C2×C4#6699911yescharacteristic
540C2×C4C22×D4411yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4C2×#434311yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—24no—
547C8—24no—
548C8—42no—
549C8—224no—
550C8—442no—
551C8—442no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—444no—
560C22—884no—
561C22—884no—
562C22—884no—
563C22—884no—
564C22—884no—
565C22—884no—
566C22—884no—
567C22#1062260711yescharacteristic
568C22#1062260711yescharacteristic
569C22#1062260711yescharacteristic
570C22#1062260711yescharacteristic
571C22C2×#6694911yescharacteristic
572C22C2×#6695011yescharacteristic
573C22C2×#6699911yescharacteristic
574C4#1062260711yescharacteristic
575C4#1062260711yescharacteristic
576C4#1062260711yescharacteristic
577C4#1062260711yescharacteristic
578C4C2×#6694811yescharacteristic
579C4C2×#6695111yescharacteristic
580C4C2×#6698311yescharacteristic
581C4C2×#6699211yescharacteristic
582C2—21no—
583C2—21no—
584C2—21no—
585C2—21no—
586C2—21no—
587C2—21no—
588C2—884no—
589C2#1307001312yesdirect product factor
590C2C2×#1062260711yescharacteristic
subgroupG/H
centerC22#10622607
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#430C2
socleC22×C11#396
prime radicalC23×D44C22
hypercenterC2×#430D11
hypocenterC11C2×#2069
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
1. C2×#10622738C2semidirect
2. C2×#10622737C2semidirect
6. #13070013C2direct (N × H)
7. C2×C11⋊#338C2semidirect
8. C2×C11×#430C2semidirect
17. C11×#430C22semidirect
29. #10622738C22semidirect
31. #10622737C22semidirect
34. C11⋊#338C22semidirect
195. C2×#430D11semidirect
277. #430C2×D11semidirect
391. C2×C11#2069semidirect
487. C11C2×#2069semidirect
589. C2#13070013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227382
C2×#106227372
C22×#668872
#130700132
C2×C11⋊#3382
C2×C11×#4302
C2×#206911