Finite Group Databasebeta

← C2×#13070074 #14782708

Subgroups — C2×#13070074 #14782708

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×#10622744C211yesmaximal, characteristic
2C2×#10622744C211yesmaximal, characteristic
3C22×#66887C211yesmaximal, characteristic
4#13070074C218yesmaximal, direct product factor
5C2×#10622197C211yesmaximal, characteristic, complemented
6C2×#10622194C211yesmaximal, characteristic, complemented
7C2×#10622195C211yesmaximal, characteristic, complemented
8C2×C11×#430C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C11×#430—22no—
17C11×#430C2214yescomplemented
18C2×C11×#108—22no—
19#10622744—22no—
20#10622744—22no—
21#10622744C2214yes—
22#10622744C2214yes—
23C2×#66887—22no—
24C2×#66887—22no—
25C2×#66887C2214yes—
26C2×#66885—22no—
27C2×#66885—22no—
28#10622197C2214yescomplemented
29#10622195C2214yescomplemented
30#10622194C2214yescomplemented
31C24×D11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×D44—21no—
34C22×D44—21no—
35C22×D44—21no—
36C22×D44—21no—
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44D412yes—
45C22×D44D412yes—
46C22×D44C2312yes—
47C2×C11×M16—21no—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
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×M16D412yes—
62C2×C11×M16C2312yes—
63C2×C11×M16C2312yes—
64C2×C11×M16C2312yes—
65C22×C8×C11—21no—
66C22×C8×C11—21no—
67C22×C8×C11D412yes—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70#66979—21no—
71#66979—21no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979C2312yes—
77#66979C2312yes—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318C2312yes—
88C22×C11⋊C8—21no—
89C11×#108—28no—
90#66887—28no—
91#66885—28no—
92#66885—28no—
93C2×#2081—111nomaximal, Sylow
94C24×C11#4111yescharacteristic
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—41no—
99C23×D11—41no—
100C23×D11—41no—
101C23×D11—41no—
102C23×D11—84no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—41no—
118C22×Dic11—41no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
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—41no—
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×D44C2×D414yes—
147C11×M16—22no—
148C11×M16—22no—
149C11×M16—22no—
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—41no—
156C11×M16—41no—
157C11×M16—41no—
158C11×M16—41no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—41no—
164C2×C8×C11—41no—
165C2×C8×C11—41no—
166C2×C8×C11—41no—
167C2×C8×C11C2×D414yes—
168C22⋊Dic11—22no—
169C22⋊Dic11—22no—
170C22⋊Dic11—41no—
171C22⋊Dic11—41no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—41no—
175C4⋊Dic11—41no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11—41no—
179C4×Dic11—41no—
180#4318—22no—
181#4318—22no—
182#4318—41no—
183#4318—41no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—41no—
186C2×C11⋊C8—41no—
187C2×#430D1111yescharacteristic, complemented
188C2×#418—111no—
189C2×#418—111no—
190C22×#100—111no—
191#2081—118no—
192C2×#344—111no—
193C2×#344—111no—
194C2×H(3,ℤ/4)—111no—
195C23×C11—42no—
196C23×C11#12311yescharacteristic
197C23×C11#12311yescharacteristic
198C23×C11#12411yescharacteristic
199C23×C11#12411yescharacteristic
200C23×C11#12611yescharacteristic
201C23×C11#12611yescharacteristic
202C23×C11C2×#4111yescharacteristic
203C22×D11—24no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—84no—
211C22×D11—84no—
212C22×D11—84no—
213C22×D11—84no—
214C22×D11—84no—
215C22×D11—84no—
216C22×D11—84no—
217C2×C4×C11#12111yescharacteristic
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11#12311yescharacteristic
222C2×C4×C11#12311yescharacteristic
223C2×C4×C11#12311yescharacteristic
224C2×C4×C11#12311yescharacteristic
225C2×C4×C11#12311yescharacteristic
226C2×C4×C11#12311yescharacteristic
227C2×C4×C11#12311yescharacteristic
228C2×C4×C11#12311yescharacteristic
229C2×C4×C11#12311yescharacteristic
230C2×C4×C11#12311yescharacteristic
231C2×C4×C11#12411yescharacteristic
232C2×C4×C11#12411yescharacteristic
233C2×C4×C11#12611yescharacteristic
234C2×C4×C11#12611yescharacteristic
235C2×C4×C11#12611yescharacteristic
236C2×C4×C11#12611yescharacteristic
237C2×C4×C11#12611yescharacteristic
238C2×C4×C11#12611yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—82no—
248C2×Dic11—82no—
249D44—24no—
250D44—24no—
251D44—42no—
252D44—42no—
253D44—42no—
254D44—42no—
255D44—42no—
256D44—42no—
257C8×C11—24no—
258C8×C11—42no—
259C8×C11—42no—
260C11⋊C8—42no—
261C23×D4—111no—
262C22×M16—111no—
263C22×M16C2×D1111yescharacteristic
264C22×M16C2×D1111yescharacteristic
265C22×M16C2×D1111yescharacteristic
266C2×#117—111no—
267C2×#117—111no—
268#430—22no—
269#430C2×D1114yescomplemented
270C2×#108—22no—
271#418—114no—
272#418—114no—
273#418—222no—
274#418—222no—
275C2×#102—222no—
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#39711yescharacteristic
291C22×C11#39711yescharacteristic
292C22×C11#39711yescharacteristic
293C22×C11#39711yescharacteristic
294C22×C11C2×#12311yescharacteristic
295C22×C11C2×#12411yescharacteristic
296C22×C11C2×#12611yescharacteristic
297C2×D11—44no—
298C2×D11—84no—
299C2×D11—84no—
300C2×D11—84no—
301C2×D11—84no—
302C2×D11—84no—
303C2×D11—84no—
304C2×D11—84no—
305C4×C11#39711yescharacteristic
306C4×C11#39711yescharacteristic
307C4×C11#39711yescharacteristic
308C4×C11#39711yescharacteristic
309C4×C11C2×#12111yescharacteristic
310C4×C11C2×#12311yescharacteristic
311C4×C11C2×#12311yescharacteristic
312C4×C11C2×#12611yescharacteristic
313Dic11—82no—
314Dic11—82no—
315C25—221no—
316C22×D4—112no—
317C22×D4—112no—
318C22×D4—112no—
319C22×D4—221no—
320C22×D4—221no—
321C22×D4—221no—
322C22×D4—221no—
323C22×D4—221no—
324C22×D4—221no—
325C22×D4—221no—
326C22×D4—221no—
327C22×D4—221no—
328C22×D4—221no—
329C22×D4—221no—
330C23×C4C22×D1111yescharacteristic
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
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—112no—
346C2×M16—221no—
347C2×M16—221no—
348C2×M16—221no—
349C2×M16—221no—
350C2×M16—221no—
351C2×M16C22⋊D1112yes—
352C2×M16C22×D1112yes—
353C2×M16C22×D1112yes—
354C2×M16C22×D1112yes—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—221no—
358C22×C8C22⋊D1112yes—
359#117—112no—
360#117—112no—
361#117—221no—
362#117—221no—
363#117—221no—
364#117—221no—
365#117—221no—
366#117—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C42—221no—
372C2×C42—221no—
373#108—28no—
374#102—228no—
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#208112yescomplemented
384C2×C11C2×#39711yescharacteristic
385D11—84no—
386C24—222no—
387C24—222no—
388C24—222no—
389C24—441no—
390C24—441no—
391C24—441no—
392C24—441no—
393C24—884no—
394C24#434311yescharacteristic
395C2×D4—114no—
396C2×D4—222no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
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—441no—
412C2×D4—441no—
413C2×D4—441no—
414C2×D4—441no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—441no—
421C2×D4—441no—
422C2×D4—441no—
423C22×C4—441no—
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#434311yescharacteristic
434C22×C4#434311yescharacteristic
435C22×C4#434311yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439M16—22no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—22no—
445M16—22no—
446M16—22no—
447M16—41no—
448M16—41no—
449M16—41no—
450M16—41no—
451M16—222no—
452M16—222no—
453M16—441no—
454M16—441no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—222no—
464C2×C8—441no—
465C2×C8—441no—
466C2×C8C2×C22⋊D1114yes—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—441no—
470C4⋊C4—441no—
471C22⋊C4—222no—
472C22⋊C4—222no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C42—222no—
476C42—222no—
477C42—441no—
478C42—441no—
479C11C2×#208111yescharacteristic, complemented, Sylow
480C23—42no—
481C23—224no—
482C23—442no—
483C23—442no—
484C23—442no—
485C23—442no—
486C23—442no—
487C23—442no—
488C23—884no—
489C23—884no—
490C23—884no—
491C23—884no—
492C23—884no—
493C23—884no—
494C23—884no—
495C23#6694711yescharacteristic
496C23#6694711yescharacteristic
497C23#6695111yescharacteristic
498C23#6695111yescharacteristic
499C23#6700011yescharacteristic
500C23#6700011yescharacteristic
501C23C2×#434311yescharacteristic
502D4—224no—
503D4—224no—
504D4—442no—
505D4—442no—
506D4—442no—
507D4—442no—
508D4—442no—
509D4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—882no—
513C2×C4—882no—
514C2×C4#6694711yescharacteristic
515C2×C4#6694711yescharacteristic
516C2×C4#6694711yescharacteristic
517C2×C4#6694711yescharacteristic
518C2×C4#6694711yescharacteristic
519C2×C4#6694711yescharacteristic
520C2×C4#6695111yescharacteristic
521C2×C4#6695111yescharacteristic
522C2×C4#6695111yescharacteristic
523C2×C4#6695111yescharacteristic
524C2×C4#6695111yescharacteristic
525C2×C4#6695111yescharacteristic
526C2×C4#6698211yescharacteristic
527C2×C4#6698211yescharacteristic
528C2×C4#6698211yescharacteristic
529C2×C4#6698211yescharacteristic
530C2×C4#6699111yescharacteristic
531C2×C4#6699111yescharacteristic
532C2×C4#6699111yescharacteristic
533C2×C4#6699111yescharacteristic
534C2×C4#6700011yescharacteristic
535C2×C4#6700011yescharacteristic
536C2×C4C2×#433911yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4C2×#434311yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C8—24no—
543C8—42no—
544C8—42no—
545C8—442no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—444no—
554C22—884no—
555C22—884no—
556C22—884no—
557C22—884no—
558C22—884no—
559C22—884no—
560C22—884no—
561C22#1062260611yescharacteristic
562C22#1062260611yescharacteristic
563C22#1062260611yescharacteristic
564C22#1062260611yescharacteristic
565C22C2×#6694711yescharacteristic
566C22C2×#6695111yescharacteristic
567C22C2×#6700011yescharacteristic
568C4—882no—
569C4—882no—
570C4#1062260611yescharacteristic
571C4#1062260611yescharacteristic
572C4#1062260611yescharacteristic
573C4#1062260611yescharacteristic
574C4C2×#6694711yescharacteristic
575C4C2×#6695111yescharacteristic
576C4C2×#6698211yescharacteristic
577C4C2×#6699111yescharacteristic
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—884no—
585C2#1307007412yesdirect product factor
586C2C2×#1062260611yescharacteristic
subgroupG/H
centerC22#10622606
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#430C2
socleC22×C11#397
prime radicalC23×D44C22
hypercenterC2×#430D11
hypocenterC11C2×#2081
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
4. #13070074C2direct (N × H)
5. C2×#10622197C2semidirect
6. C2×#10622194C2semidirect
7. C2×#10622195C2semidirect
8. C2×C11×#430C2semidirect
17. C11×#430C22semidirect
28. #10622197C22semidirect
29. #10622195C22semidirect
30. #10622194C22semidirect
187. C2×#430D11semidirect
269. #430C2×D11semidirect
383. C2×C11#2081semidirect
479. C11C2×#2081semidirect
585. C2#13070074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227442
C22×#668872
#130700742
C2×#106221972
C2×#106221942
C2×#106221952
C2×C11×#4302
C2×#208111