Finite Group Databasebeta

← C2×#13069972 #14782303

Subgroups — C2×#13069972 #14782303

Order 2816.

1134 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66886C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic, complemented
3C2×#10622732C211yesmaximal, characteristic, complemented
4C2×#10622828C211yesmaximal, characteristic
5C22×#66896C211yesmaximal, characteristic
6#13069972C218yesmaximal, direct product factor
7C2×#10622192C211yesmaximal, characteristic, complemented
8C22×C11×#100C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×C11×#100—24no—
17C2×C11×#100C2214yes—
18#10622828—22no—
19#10622828C2214yes—
20C2×#66896—21no—
21C2×#66896—21no—
22C2×#66896—22no—
23C2×#66896—22no—
24C2×#66896C2214yes—
25C2×#66886—24no—
26C2×#66886C2214yescomplemented
27#10622734—22no—
28#10622734C2214yescomplemented
29#10622732—22no—
30#10622732C2214yescomplemented
31C2×#66882—21no—
32C2×#66881—21no—
33C2×Dic11⋊C8—22no—
34#10622192C2214yescomplemented
35C25×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11Q814yes—
45C22×D4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C2×C11×M16—21no—
49C2×C11×M16—22no—
50C2×C11×M16—21no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16D414yes—
54C2×C11×M16C2312yes—
55C2×C11×M16C2312yes—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C2×C22⋊Dic11—21no—
59#66979—21no—
60#66979—21no—
61#66979D412yes—
62#66979C2312yes—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×C4×Dic11—21no—
72C2×#4318—21no—
73C2×#4318—22no—
74C2×#4318—22no—
75C2×#4318C2312yes—
76C22×C11⋊C8—22no—
77C22×C11⋊C8—22no—
78C22×C11⋊C8—21no—
79C22×C11⋊C8D412yes—
80C22×C11⋊C8D412yes—
81C22×C11⋊C8C2312yes—
82C11×#100—28no—
83#66896—24no—
84#66896—24no—
85#66896—28no—
86#66886—28no—
87#66882—24no—
88#66881—24no—
89Dic11⋊C8—28no—
90C2×#2063—111nomaximal, Sylow
91C24×C11—24no—
92C24×C11—22no—
93C24×C11—41no—
94C24×C11—41no—
95C24×C11—42no—
96C24×C11—82no—
97C24×C11—82no—
98C24×C11#4111yescharacteristic
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11C2×Q814yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×Q812yes—
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4112yes—
125C22×C4×C11#4112yes—
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—82no—
133C11×M16—24no—
134C11×M16—22no—
135C11×M16—22no—
136C11×M16—22no—
137C11×M16—42no—
138C11×M16C2×D414yes—
139C2×C8×C11—24no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—42no—
143C22⋊Dic11—22no—
144C22⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11C2×D412yes—
152C4⋊Dic11C2×D412yes—
153C4×Dic11—22no—
154C4×Dic11—22no—
155#4318—22no—
156#4318—22no—
157#4318—42no—
158C2×C11⋊C8—24no—
159C2×C11⋊C8—24no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—42no—
164C2×C11⋊C8C2×D414yes—
165C22×#108—111no—
166C2×#428—111no—
167C2×#424—111no—
168C2×#418—111no—
169C22×#102—111no—
170C22×#100D1111yescharacteristic
171#2063—118no—
172C2×#343—111no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—24no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—44no—
179C23×C11—44no—
180C23×C11—88no—
181C23×C11—82no—
182C23×C11—82no—
183C23×C11—88no—
184C23×C11—82no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11—82no—
188C23×C11#12111yescharacteristic
189C23×C11#12111yescharacteristic
190C23×C11C22⋊Q812yes—
191C23×C11#12612yes—
192C23×C11C2×#4111yescharacteristic
193D4×C11—24no—
194D4×C11—24no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—44no—
198D4×C11—44no—
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12112yes—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11#12112yes—
205C2×C4×C11C22⋊Q812yes—
206C2×C4×C11C22⋊Q812yes—
207C2×C4×C11C22⋊Q812yes—
208C2×C4×C11C22⋊Q812yes—
209C2×C4×C11C22⋊Q812yes—
210C2×C4×C11#12612yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×Q811yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—82no—
223C2×Dic11—82no—
224C2×Dic11—82no—
225C8×C11—24no—
226C8×C11—42no—
227C11⋊C8—24no—
228C11⋊C8—42no—
229C23×D4C2×D1111yescharacteristic
230C22×M16—111no—
231C22×M16C2×D1111yescharacteristic
232C22×M16C2×D1111yescharacteristic
233C23×C8—111no—
234C2×#117—111no—
235C22×C4⋊C4—111no—
236C2×#108—114no—
237C2×#108—224no—
238#428—114no—
239#428—222no—
240C2×#107—221no—
241C2×#106—221no—
242#424—114no—
243#424—222no—
244C2×C4⋊C8—222no—
245#418—114no—
246#418—222no—
247C2×#102—114no—
248C2×#102—221no—
249C2×#102—221no—
250C2×#102—222no—
251C2×#102—222no—
252C2×#100—24no—
253C2×#100C2×D1114yes—
254#343—114no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—44no—
262C22×C11—84no—
263C22×C11—84no—
264C22×C11—88no—
265C22×C11—88no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11#39612yes—
269C22×C11#39612yes—
270C22×C11#47112yes—
271C22×C11#47212yes—
272C22×C11C2×#12111yescharacteristic
273C22×C11C2×C22⋊Q811yescharacteristic
274C22×C11C2×#12611yescharacteristic
275C4×C11#39612yes—
276C4×C11#39612yes—
277C4×C11C2×#12111yescharacteristic
278C4×C11C2×#12111yescharacteristic
279C4×C11C2×C22⋊Q811yescharacteristic
280C4×C11C2×C22⋊Q811yescharacteristic
281Dic11—42no—
282Dic11—42no—
283Dic11—82no—
284C25—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4Dic2214yes—
294C22×D4C22×D1112yes—
295C23×C4—221no—
296C23×C4C22×D1111yescharacteristic
297C2×M16—21no—
298C2×M16—22no—
299C2×M16—21no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—112no—
303C2×M16—221no—
304C2×M16—222no—
305C2×M16—222no—
306C2×M16C22⋊D1114yes—
307C2×M16C22×D1112yes—
308C2×M16C22×D1112yes—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—112no—
312C22×C8—112no—
313C22×C8—112no—
314C22×C8—222no—
315C22×C8—222no—
316C22×C8—221no—
317#117—112no—
318#117—112no—
319#117—221no—
320#117—221no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C42—221no—
331#108—228no—
332#107—224no—
333#106—224no—
334C4⋊C8—228no—
335#102—224no—
336#102—224no—
337#102—228no—
338#100—28no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—22no—
342C2×C11—84no—
343C2×C11#206314yescomplemented
344C2×C11C2×#39611yescharacteristic
345C2×C11C2×#47111yescharacteristic
346C2×C11C2×#47211yescharacteristic
347C24—24no—
348C24—22no—
349C24—42no—
350C24—41no—
351C24—41no—
352C24—82no—
353C24—82no—
354C24#433911yescharacteristic
355C2×D4—24no—
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4C2×Dic2214yes—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—222no—
376C22×C4—441no—
377C22×C4—441no—
378C22×C4—882no—
379C22×C4C2×Dic2212yes—
380C22×C4#433911yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4D4×D1111yescharacteristic
383C22×C4D4×D1111yescharacteristic
384C22×C4D4×D1111yescharacteristic
385C22×C4#434112yes—
386C22×C4#434112yes—
387C22×C4C2×C22⋊D1112yes—
388C22×C4C23×D1111yescharacteristic
389M16—24no—
390M16—22no—
391M16—22no—
392M16—22no—
393M16—42no—
394M16—222no—
395M16—222no—
396M16—442no—
397M16C2×C22⋊D1114yes—
398C2×C8—24no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—42no—
402C2×C8—114no—
403C2×C8—224no—
404C2×C8—224no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—222no—
408C2×C8—442no—
409C4⋊C4—112no—
410C4⋊C4—112no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C22⋊C4—222no—
418C22⋊C4—222no—
419C42—222no—
420C42—222no—
421C11C2×#206311yescharacteristic, complemented, Sylow
422C23—22no—
423C23—22no—
424C23—24no—
425C23—42no—
426C23—42no—
427C23—44no—
428C23—44no—
429C23—82no—
430C23—82no—
431C23—88no—
432C23—82no—
433C23—82no—
434C23—88no—
435C23—82no—
436C23—82no—
437C23#6693212yes—
438C23#6693711yescharacteristic
439C23#6693711yescharacteristic
440C23#6697712yes—
441C23C2×#433911yescharacteristic
442D4—24no—
443D4—24no—
444D4—44no—
445D4—44no—
446D4—42no—
447D4—42no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—882no—
454C2×C4—882no—
455C2×C4—882no—
456C2×C4#6693112yes—
457C2×C4#6693112yes—
458C2×C4#6693112yes—
459C2×C4#6693112yes—
460C2×C4#6693212yes—
461C2×C4#6693711yescharacteristic
462C2×C4#6693711yescharacteristic
463C2×C4#6697712yes—
464C2×C4#6699112yes—
465C2×C4#6699112yes—
466C2×C4#6699212yes—
467C2×C4#6699212yes—
468C2×C4C22×Dic2211yescharacteristic
469C2×C4C2×D4×D1111yescharacteristic
470C2×C4C2×D4×D1111yescharacteristic
471C2×C4C2×#434111yescharacteristic
472C2×C4C2×#434111yescharacteristic
473C2×C4C22×C22⋊D1111yescharacteristic
474C8—24no—
475C8—42no—
476C8—224no—
477C8—442no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—24no—
483C22—24no—
484C22—44no—
485C22—84no—
486C22—84no—
487C22—88no—
488C22—82no—
489C22—82no—
490C22—88no—
491C22#1062236112yes—
492C22#1062236212yes—
493C22#1062256112yes—
494C22#1062256112yes—
495C22C2×#6693211yescharacteristic
496C22C2×#6693711yescharacteristic
497C22C2×#6697711yescharacteristic
498C4—442no—
499C4—442no—
500C4—882no—
501C4#1062256112yes—
502C4#1062256112yes—
503C4C2×#6693111yescharacteristic
504C4C2×#6693111yescharacteristic
505C4C2×#6699111yescharacteristic
506C4C2×#6699211yescharacteristic
507C2—21no—
508C2—21no—
509C2—22no—
510C2—84no—
511C2#1306997214yesdirect product factor
512C2C2×#1062256111yescharacteristic
513C2C2×#1062236111yescharacteristic
514C2C2×#1062236211yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#100C2
socleC23×C11#121
prime radicalC23×D4×C11C22
hypercenterC22×#100D11
hypocenterC11C2×#2063
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#100

Complements

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

NH ≅ G/Ntype
1. C22×#66886C2semidirect
2. C2×#10622734C2semidirect
3. C2×#10622732C2semidirect
6. #13069972C2direct (N × H)
7. C2×#10622192C2semidirect
26. C2×#66886C22semidirect
28. #10622734C22semidirect
30. #10622732C22semidirect
34. #10622192C22semidirect
343. C2×C11#2063semidirect
421. C11C2×#2063semidirect
511. C2#13069972direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668862
C2×#106227342
C2×#106227322
C2×#106228282
C22×#668962
#130699722
C2×#106221922
C22×C11×#1002
C2×#206311