Finite Group Databasebeta

← C2×#13070077 #14782711

Subgroups — C2×#13070077 #14782711

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622737C211yesmaximal, characteristic, complemented
2C2×#10622828C211yesmaximal, characteristic
3C22×#66897C211yesmaximal, characteristic
4#13070077C218yesmaximal, direct product factor
5C2×#10622197C211yesmaximal, characteristic, complemented
6C2×#10622171C211yesmaximal, characteristic, complemented
7C2×#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#418C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C11×#418—22no—
17C11×#418C2214yes—
18C2×C11×#102—22no—
19C2×#66897—22no—
20C2×#66897—22no—
21C2×#66897C2214yes—
22#10622828—22no—
23#10622828C2214yes—
24C2×#66896—22no—
25#10622737—22no—
26#10622737C2214yescomplemented
27C2×#66886—22no—
28#10622197C2214yescomplemented
29#10622171C2214yescomplemented
30#10622169C2214yescomplemented
31C25×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11D412yes—
44C22×D4×C11D412yes—
45C22×D4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C2×C11×M16—21no—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16C2312yes—
53C22×C8×C11—21no—
54C11×#117—21no—
55C11×#117—21no—
56C11×#117—21no—
57C11×#117C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C42×C11—21no—
61C2×C22⋊Dic11—21no—
62#66979—21no—
63#66979—21no—
64#66979—21no—
65#66979C2312yes—
66C2×C4⋊Dic11—21no—
67C2×C4×Dic11—21no—
68C2×#4318—21no—
69C2×#4318—21no—
70C2×#4318—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×#4318—21no—
82C2×#4318D412yes—
83C2×#4318C2312yes—
84C2×#4318C2312yes—
85C2×#4318C2312yes—
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8D412yes—
89C11×#102—28no—
90#66897—28no—
91#66896—28no—
92#66886—28no—
93C2×#2081—111nomaximal, Sylow
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—41no—
98C24×C11—41no—
99C24×C11—41no—
100C24×C11—41no—
101C24×C11—84no—
102C24×C11#4111yescharacteristic
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11C2×D414yes—
131C22×C4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11#4111yescharacteristic
137C22×C4×C11#4111yescharacteristic
138C22×C4×C11#4111yescharacteristic
139C22×C4×C11#4111yescharacteristic
140C22×C4×C11#4111yescharacteristic
141C22×C4×C11#4111yescharacteristic
142C22×C4×C11#4111yescharacteristic
143C22×C4×C11#4111yescharacteristic
144C22×C4×C11#4111yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—41no—
147C11×M16—22no—
148C11×M16—22no—
149C11×M16—41no—
150C11×M16—41no—
151C2×C8×C11—22no—
152C2×C8×C11—41no—
153C2×C8×C11—41no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—41no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—41no—
158C42×C11—22no—
159C42×C11—41no—
160C22⋊Dic11—22no—
161C22⋊Dic11—41no—
162C4⋊Dic11—22no—
163C4⋊Dic11—41no—
164C4×Dic11—22no—
165C4×Dic11—41no—
166#4318—22no—
167#4318—22no—
168#4318—22no—
169#4318—22no—
170#4318—22no—
171#4318—22no—
172#4318—22no—
173#4318—22no—
174#4318—41no—
175#4318—41no—
176#4318—41no—
177#4318—41no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—41no—
183C2×C11⋊C8—41no—
184C2×C11⋊C8—41no—
185C2×C11⋊C8—41no—
186C2×C11⋊C8C2×D414yes—
187C2×#430—111no—
188C2×#418—111no—
189C2×#418D1111yescharacteristic
190C22×#100—111no—
191#2081—118no—
192C2×#344—111no—
193C2×#344—111no—
194C2×H(3,ℤ/4)—111no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—84no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11—84no—
210C23×C11#12311yescharacteristic
211C23×C11#12311yescharacteristic
212C23×C11#12411yescharacteristic
213C23×C11#12411yescharacteristic
214C23×C11#12611yescharacteristic
215C23×C11#12611yescharacteristic
216C23×C11C2×#4111yescharacteristic
217D4×C11—24no—
218D4×C11—24no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—82no—
227C2×C4×C11#12111yescharacteristic
228C2×C4×C11#12111yescharacteristic
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C2×C4×C11#12311yescharacteristic
232C2×C4×C11#12311yescharacteristic
233C2×C4×C11#12311yescharacteristic
234C2×C4×C11#12311yescharacteristic
235C2×C4×C11#12311yescharacteristic
236C2×C4×C11#12311yescharacteristic
237C2×C4×C11#12311yescharacteristic
238C2×C4×C11#12311yescharacteristic
239C2×C4×C11#12311yescharacteristic
240C2×C4×C11#12311yescharacteristic
241C2×C4×C11#12411yescharacteristic
242C2×C4×C11#12411yescharacteristic
243C2×C4×C11#12611yescharacteristic
244C2×C4×C11#12611yescharacteristic
245C2×C4×C11#12611yescharacteristic
246C2×C4×C11#12611yescharacteristic
247C2×C4×C11#12611yescharacteristic
248C2×C4×C11#12611yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×Dic11—42no—
256C2×Dic11—82no—
257C8×C11—42no—
258C11⋊C8—24no—
259C11⋊C8—42no—
260C11⋊C8—42no—
261C23×D4C2×D1111yescharacteristic
262C22×M16—111no—
263C22×M16—111no—
264C22×M16—111no—
265C22×M16C2×D1111yescharacteristic
266C2×#117—111no—
267C2×#117C2×D1111yescharacteristic
268#430—114no—
269#430—222no—
270C2×#108—222no—
271#418—22no—
272#418—114no—
273#418—222no—
274#418C2×D1114yes—
275C2×#102—22no—
276C2×#102—222no—
277C2×#100—114no—
278C2×#100—222no—
279C2×#100—222no—
280#344—114no—
281#344—114no—
282H(3,ℤ/4)—114no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—44no—
291C22×C11—84no—
292C22×C11—84no—
293C22×C11—84no—
294C22×C11—84no—
295C22×C11—84no—
296C22×C11—84no—
297C22×C11—84no—
298C22×C11#39711yescharacteristic
299C22×C11#39711yescharacteristic
300C22×C11#39711yescharacteristic
301C22×C11#39711yescharacteristic
302C22×C11C2×#12311yescharacteristic
303C22×C11C2×#12411yescharacteristic
304C22×C11C2×#12611yescharacteristic
305C4×C11—82no—
306C4×C11#39711yescharacteristic
307C4×C11#39711yescharacteristic
308C4×C11#39711yescharacteristic
309C4×C11#39711yescharacteristic
310C4×C11C2×#12111yescharacteristic
311C4×C11C2×#12311yescharacteristic
312C4×C11C2×#12311yescharacteristic
313C4×C11C2×#12611yescharacteristic
314Dic11—82no—
315C25—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4C22⋊D1112yes—
328C22×D4C22⋊D1112yes—
329C22×D4C22×D1112yes—
330C23×C4C22×D1111yescharacteristic
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—112no—
337C2×M16—112no—
338C2×M16—112no—
339C2×M16—112no—
340C2×M16—221no—
341C2×M16—221no—
342C2×M16—221no—
343C2×M16—221no—
344C2×M16—221no—
345C2×M16—221no—
346C2×M16—221no—
347C2×M16—221no—
348C2×M16—221no—
349C2×M16—221no—
350C2×M16—221no—
351C2×M16—221no—
352C2×M16—221no—
353C2×M16—221no—
354C2×M16C22×D1112yes—
355C22×C8—21no—
356C22×C8—112no—
357C22×C8—221no—
358C22×C8—221no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—112no—
363#117—221no—
364#117—221no—
365#117—221no—
366#117C22×D1112yes—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—221no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—221no—
371C2×C42—21no—
372C2×C42—221no—
373#108—228no—
374#102—28no—
375#102—228no—
376#100—228no—
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—84no—
384C2×C11#208112yescomplemented
385C2×C11C2×#39711yescharacteristic
386C24—22no—
387C24—22no—
388C24—22no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—84no—
394C24#434111yescharacteristic
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4C2×C22⋊D1114yes—
423C22×C4—41no—
424C22×C4—441no—
425C22×C4#433911yescharacteristic
426C22×C4#433911yescharacteristic
427C22×C4#433911yescharacteristic
428C22×C4#433911yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4#434111yescharacteristic
432C22×C4#434111yescharacteristic
433C22×C4#434111yescharacteristic
434C22×C4#434111yescharacteristic
435C22×C4#434111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439M16—22no—
440M16—22no—
441M16—41no—
442M16—41no—
443M16—222no—
444M16—222no—
445M16—222no—
446M16—222no—
447M16—222no—
448M16—222no—
449M16—222no—
450M16—222no—
451M16—441no—
452M16—441no—
453M16—441no—
454M16—441no—
455C2×C8—22no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—114no—
459C2×C8—222no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—441no—
464C2×C8—441no—
465C2×C8—441no—
466C2×C8—441no—
467C4⋊C4—22no—
468C4⋊C4—41no—
469C4⋊C4—222no—
470C4⋊C4—441no—
471C22⋊C4—22no—
472C22⋊C4—41no—
473C22⋊C4—222no—
474C22⋊C4—441no—
475C42—22no—
476C42—41no—
477C42—222no—
478C42—441no—
479C11C2×#208111yescharacteristic, complemented, Sylow
480C23—24no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—84no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23—84no—
494C23—84no—
495C23#6693211yescharacteristic
496C23#6693211yescharacteristic
497C23#6693811yescharacteristic
498C23#6693811yescharacteristic
499C23#6698811yescharacteristic
500C23#6698811yescharacteristic
501C23C2×#434111yescharacteristic
502D4—24no—
503D4—24no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—42no—
510C2×C4—42no—
511C2×C4—82no—
512C2×C4—442no—
513C2×C4—882no—
514C2×C4#6693211yescharacteristic
515C2×C4#6693211yescharacteristic
516C2×C4#6693211yescharacteristic
517C2×C4#6693211yescharacteristic
518C2×C4#6693211yescharacteristic
519C2×C4#6693211yescharacteristic
520C2×C4#6693611yescharacteristic
521C2×C4#6693611yescharacteristic
522C2×C4#6693611yescharacteristic
523C2×C4#6693611yescharacteristic
524C2×C4#6693811yescharacteristic
525C2×C4#6693811yescharacteristic
526C2×C4#6698211yescharacteristic
527C2×C4#6698211yescharacteristic
528C2×C4#6698211yescharacteristic
529C2×C4#6698211yescharacteristic
530C2×C4#6698811yescharacteristic
531C2×C4#6698811yescharacteristic
532C2×C4#6699211yescharacteristic
533C2×C4#6699211yescharacteristic
534C2×C4#6699211yescharacteristic
535C2×C4#6699211yescharacteristic
536C2×C4C2×#433911yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4C2×#434111yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C8—42no—
543C8—224no—
544C8—442no—
545C8—442no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—44no—
554C22—84no—
555C22—84no—
556C22—84no—
557C22—84no—
558C22—84no—
559C22—84no—
560C22—84no—
561C22#1062256511yescharacteristic
562C22#1062256511yescharacteristic
563C22#1062256511yescharacteristic
564C22#1062256511yescharacteristic
565C22C2×#6693211yescharacteristic
566C22C2×#6693811yescharacteristic
567C22C2×#6698811yescharacteristic
568C4—82no—
569C4—882no—
570C4#1062256511yescharacteristic
571C4#1062256511yescharacteristic
572C4#1062256511yescharacteristic
573C4#1062256511yescharacteristic
574C4C2×#6693211yescharacteristic
575C4C2×#6693611yescharacteristic
576C4C2×#6698211yescharacteristic
577C4C2×#6699211yescharacteristic
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—84no—
585C2#1307007712yesdirect product factor
586C2C2×#1062256511yescharacteristic
subgroupG/H
centerC22#10622565
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC22×C11#397
prime radicalC23×D4×C11C22
hypercenterC2×#418D11
hypocenterC11C2×#2081
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. C2×#10622737C2semidirect
4. #13070077C2direct (N × H)
5. C2×#10622197C2semidirect
6. C2×#10622171C2semidirect
7. C2×#10622169C2semidirect
26. #10622737C22semidirect
28. #10622197C22semidirect
29. #10622171C22semidirect
30. #10622169C22semidirect
384. C2×C11#2081semidirect
479. C11C2×#2081semidirect
585. C2#13070077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227372
C2×#106228282
C22×#668972
#130700772
C2×#106221972
C2×#106221712
C2×#106221692
C2×C11×#4182
C2×#208111