Finite Group Databasebeta

← C2×#13070066 #14782691

Subgroups — C2×#13070066 #14782691

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622612C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic
3C2×#10622850C211yesmaximal, characteristic
4#13070066C218yesmaximal, direct product factor
5C2×#10622194C211yesmaximal, characteristic, complemented
6C2×#10622196C211yesmaximal, characteristic, complemented
7C2×#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#421C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C11×#421—22no—
17C11×#421C2214yes—
18C2×C11×#104—22no—
19#10622850—22no—
20#10622850C2214yes—
21#10622846—22no—
22#10622846C2214yes—
23C2×#66900—21no—
24C2×#66899—21no—
25C2×#66897—21no—
26C2×#66896—21no—
27#10622612—22no—
28#10622612C2214yescomplemented
29C2×C4⋊(C11⋊C8)—22no—
30#10622196C2214yescomplemented
31#10622194C2214yescomplemented
32#10622169C2214yescomplemented
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41D412yes—
44C2×C11×#41C2312yes—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16C2312yes—
56C22×C8×C11—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117D412yes—
60C11×#117C2312yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C42×C11D412yes—
64C2×C22⋊Dic11—21no—
65#66979—21no—
66#66979—21no—
67#66979—21no—
68#66979C2312yes—
69C2×C4⋊Dic11—21no—
70C2×C4×Dic11—21no—
71C2×#4318—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×#4318C2312yes—
82C2×#4318C2312yes—
83C22×C11⋊C8—21no—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90C22×C11⋊C8—21no—
91C22×C11⋊C8C2312yes—
92C11×#104—28no—
93#66900—24no—
94#66899—24no—
95#66897—24no—
96#66896—24no—
97C4⋊(C11⋊C8)—28no—
98C2×#2080—111nomaximal, Sylow
99C24×C11—21no—
100C24×C11#4111yescharacteristic
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—41no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—41no—
161C11×M16—41no—
162C2×C8×C11—22no—
163C2×C8×C11—41no—
164C2×C8×C11—41no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C42×C11—22no—
170C42×C11C2×D414yes—
171C22⋊Dic11—22no—
172C22⋊Dic11—41no—
173C4⋊Dic11—22no—
174C4⋊Dic11—41no—
175C4×Dic11—22no—
176C4×Dic11—41no—
177#4318—22no—
178#4318—22no—
179#4318—22no—
180#4318—22no—
181#4318—41no—
182#4318—41no—
183#4318—41no—
184#4318—41no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—41no—
191C2×C11⋊C8—41no—
192C2×C11⋊C8—41no—
193C2×C11⋊C8—41no—
194C2×C11⋊C8—41no—
195C2×C11⋊C8—41no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×#424—111no—
199C2×#421D1111yescharacteristic
200C2×#416—111no—
201C2×#413—111no—
202#2080—118no—
203C2×#344—111no—
204C2×#341—111no—
205C2×H(3,ℤ/4)—111no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—82no—
211C23×C11#12311yescharacteristic
212C23×C11#12311yescharacteristic
213C23×C11#12311yescharacteristic
214C23×C11#12311yescharacteristic
215C23×C11#12611yescharacteristic
216C23×C11#12611yescharacteristic
217C23×C11C2×#4111yescharacteristic
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—41no—
229D4×C11—41no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—44no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12311yescharacteristic
244C2×C4×C11#12311yescharacteristic
245C2×C4×C11#12311yescharacteristic
246C2×C4×C11#12311yescharacteristic
247C2×C4×C11#12311yescharacteristic
248C2×C4×C11#12311yescharacteristic
249C2×C4×C11#12311yescharacteristic
250C2×C4×C11#12311yescharacteristic
251C2×C4×C11#12411yescharacteristic
252C2×C4×C11#12411yescharacteristic
253C2×C4×C11#12411yescharacteristic
254C2×C4×C11#12411yescharacteristic
255C2×C4×C11#12611yescharacteristic
256C2×C4×C11#12611yescharacteristic
257C2×C4×C11#12611yescharacteristic
258C2×C4×C11#12611yescharacteristic
259C2×C4×C11#12611yescharacteristic
260C2×C4×C11#12611yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×Dic11—42no—
268C2×Dic11—82no—
269C8×C11—42no—
270C11⋊C8—42no—
271C11⋊C8—42no—
272C11⋊C8—42no—
273C22×#41C2×D1111yescharacteristic
274C22×M16—111no—
275C22×M16—111no—
276C22×M16C2×D1111yescharacteristic
277C23×C8—111no—
278C2×#117—111no—
279C2×#117C2×D1111yescharacteristic
280#424—114no—
281#424—222no—
282C2×C4⋊C8—222no—
283#421—22no—
284#421C2×D1114yes—
285C2×#104—22no—
286#416—114no—
287#416—222no—
288C2×#103—221no—
289C2×#102—221no—
290#413—114no—
291#413—222no—
292C2×#101—221no—
293C2×#100—221no—
294#344—114no—
295#341—114no—
296H(3,ℤ/4)—114no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—42no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11#39711yescharacteristic
309C22×C11#39711yescharacteristic
310C22×C11#39711yescharacteristic
311C22×C11#39711yescharacteristic
312C22×C11C2×#12311yescharacteristic
313C22×C11C2×#12311yescharacteristic
314C22×C11C2×#12611yescharacteristic
315C4×C11—44no—
316C4×C11—42no—
317C4×C11#39711yescharacteristic
318C4×C11#39711yescharacteristic
319C4×C11#39711yescharacteristic
320C4×C11#39711yescharacteristic
321C4×C11C2×#12111yescharacteristic
322C4×C11C2×#12311yescharacteristic
323C4×C11C2×#12411yescharacteristic
324C4×C11C2×#12611yescharacteristic
325Dic11—82no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41D4412yes—
337C2×#41C22×D1112yes—
338C22×Q8D4411yescharacteristic
339C22×D4—21no—
340C22×D4D4411yescharacteristic
341C23×C4—21no—
342C23×C4C22×D1111yescharacteristic
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—112no—
349C2×M16—112no—
350C2×M16—221no—
351C2×M16—221no—
352C2×M16—221no—
353C2×M16—221no—
354C2×M16—221no—
355C2×M16—221no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16—221no—
359C2×M16—221no—
360C2×M16C22×D1112yes—
361C22×C8—21no—
362C22×C8—112no—
363C22×C8—221no—
364C22×C8—221no—
365C22×C8—221no—
366C22×C8—221no—
367C22×C8—221no—
368C22×C8—221no—
369C22×C8—221no—
370C22×C8—221no—
371#117—21no—
372#117—21no—
373#117—112no—
374#117—221no—
375#117—221no—
376#117—221no—
377#117C22⋊D1112yes—
378#117C22×D1112yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—221no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—221no—
383C2×C42—221no—
384C2×C42C22⋊D1112yes—
385C4⋊C8—228no—
386#104—28no—
387#103—224no—
388#102—224no—
389#101—224no—
390#100—224no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—82no—
398C2×C11#208012yescomplemented
399C2×C11C2×#39711yescharacteristic
400C24—21no—
401C24#434111yescharacteristic
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8C2×D4412yes—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4C2×D4412yes—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—441no—
445C22×C4C2×D4411yescharacteristic
446C22×C4C2×D4411yescharacteristic
447C22×C4#433911yescharacteristic
448C22×C4#433911yescharacteristic
449C22×C4#434111yescharacteristic
450C22×C4#434111yescharacteristic
451C22×C4#434111yescharacteristic
452C22×C4#434111yescharacteristic
453C22×C4#434111yescharacteristic
454C22×C4#434111yescharacteristic
455C22×C4#434111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459M16—22no—
460M16—22no—
461M16—41no—
462M16—41no—
463M16—222no—
464M16—222no—
465M16—222no—
466M16—222no—
467M16—441no—
468M16—441no—
469M16—441no—
470M16—441no—
471C2×C8—22no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8—441no—
480C2×C8—441no—
481C2×C8—441no—
482C2×C8—441no—
483C2×C8—441no—
484C2×C8—441no—
485C2×C8—441no—
486C2×C8—441no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—222no—
490C4⋊C4—441no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—222no—
494C22⋊C4—441no—
495C42—22no—
496C42—222no—
497C42—441no—
498C42C2×C22⋊D1114yes—
499C11C2×#208011yescharacteristic, complemented, Sylow
500C23—22no—
501C23—42no—
502C23—41no—
503C23—41no—
504C23—82no—
505C23#6693211yescharacteristic
506C23#6693211yescharacteristic
507C23#6693911yescharacteristic
508C23#6693911yescharacteristic
509C23#6698811yescharacteristic
510C23#6698811yescharacteristic
511C23C2×#434111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—41no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—442no—
534C2×C4—882no—
535C2×C4#6693211yescharacteristic
536C2×C4#6693211yescharacteristic
537C2×C4#6693211yescharacteristic
538C2×C4#6693211yescharacteristic
539C2×C4#6693211yescharacteristic
540C2×C4#6693211yescharacteristic
541C2×C4#6693911yescharacteristic
542C2×C4#6693911yescharacteristic
543C2×C4#6693911yescharacteristic
544C2×C4#6693911yescharacteristic
545C2×C4#6693911yescharacteristic
546C2×C4#6693911yescharacteristic
547C2×C4#6698311yescharacteristic
548C2×C4#6698311yescharacteristic
549C2×C4#6698311yescharacteristic
550C2×C4#6698311yescharacteristic
551C2×C4#6698811yescharacteristic
552C2×C4#6698811yescharacteristic
553C2×C4#6698911yescharacteristic
554C2×C4#6698911yescharacteristic
555C2×C4#6698911yescharacteristic
556C2×C4#6698911yescharacteristic
557C2×C4C22×D4411yescharacteristic
558C2×C4C2×#433911yescharacteristic
559C2×C4C2×#434111yescharacteristic
560C2×C4C2×#434111yescharacteristic
561C2×C4C2×#434111yescharacteristic
562C2×C4C22×C22⋊D1111yescharacteristic
563C8—42no—
564C8—442no—
565C8—442no—
566C8—442no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22#1062256611yescharacteristic
579C22#1062256611yescharacteristic
580C22#1062256611yescharacteristic
581C22#1062256611yescharacteristic
582C22C2×#6693211yescharacteristic
583C22C2×#6693911yescharacteristic
584C22C2×#6698811yescharacteristic
585C4—44no—
586C4—42no—
587C4—882no—
588C4#1062256611yescharacteristic
589C4#1062256611yescharacteristic
590C4#1062256611yescharacteristic
591C4#1062256611yescharacteristic
592C4C2×#6693211yescharacteristic
593C4C2×#6693911yescharacteristic
594C4C2×#6698311yescharacteristic
595C4C2×#6698911yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—82no—
603C2#1307006612yesdirect product factor
604C2C2×#1062256611yescharacteristic
subgroupG/H
centerC2×C4#66989
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#421C2
socleC22×C11#397
prime radicalC22×C11×#41C22
hypercenterC2×#421D11
hypocenterC11C2×#2080
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#10622612C2semidirect
4. #13070066C2direct (N × H)
5. C2×#10622194C2semidirect
6. C2×#10622196C2semidirect
7. C2×#10622169C2semidirect
28. #10622612C22semidirect
30. #10622196C22semidirect
31. #10622194C22semidirect
32. #10622169C22semidirect
398. C2×C11#2080semidirect
499. C11C2×#2080semidirect
603. C2#13070066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226122
C2×#106228462
C2×#106228502
#130700662
C2×#106221942
C2×#106221962
C2×#106221692
C2×C11×#4212
C2×#208011