Finite Group Databasebeta

← C2×#13069990 #14782357

Subgroups — C2×#13069990 #14782357

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66872C211yesmaximal, characteristic, complemented
2C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic
4C22×#66896C211yesmaximal, characteristic
5C2×#10622541C211yesmaximal, characteristic, complemented
6#13069990C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C2×C11×#390C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4—21no—
12C22×C11×C22⋊C4—21no—
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4—21no—
17C23×C11⋊C8C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C11×#390—22no—
20C11×#390C2214yes—
21C2×#66896—24no—
22C2×#66896—24no—
23C2×#66896C2214yes—
24C2×#66896C2214yes—
25C2×C11⋊#95—21no—
26C2×#66872—24no—
27C2×#66872C2214yescomplemented
28#10622541—22no—
29#10622541C2214yescomplemented
30C2×C4⋊(C11⋊C8)—24no—
31C2×C4⋊(C11⋊C8)C2214yescomplemented
32#10622167C2214yescomplemented
33C25×C11—21no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11Q814yes—
41C22×D4×C11C2312yes—
42C23×C4×C11—21no—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C22⋊C4—24no—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—44no—
55C2×C11×C22⋊C4—44no—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11D412yes—
59C2×C42×C11C2312yes—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D414yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—44no—
70C22×C11⋊C8—22no—
71C22×C11⋊C8—22no—
72C22×C11⋊C8—22no—
73C22×C11⋊C8—22no—
74C22×C11⋊C8—22no—
75C22×C11⋊C8D414yes—
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2312yes—
78#66896—28no—
79#66896—28no—
80C11⋊#95—24no—
81#66872—28no—
82C4⋊(C11⋊C8)—28no—
83C2×#2065—111nomaximal, Sylow
84C24×C11—24no—
85C24×C11—22no—
86C24×C11—42no—
87C24×C11—42no—
88C24×C11—42no—
89C24×C11—42no—
90C24×C11—42no—
91C24×C11—42no—
92C24×C11C2×D411yescharacteristic
93C2×D4×C11—28no—
94C2×D4×C11—28no—
95C2×D4×C11—24no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—44no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C2×D4×C11—44no—
105C2×D4×C11C2×Q814yes—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11SD1614yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×Q812yes—
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—24no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—42no—
130C22×Dic11—42no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—42no—
137C11×C22⋊C4—48no—
138C11×C22⋊C4—48no—
139C42×C11—24no—
140C42×C11—22no—
141C42×C11—22no—
142C4⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—42no—
147C4⋊Dic11C2×D414yes—
148Dic11⋊C4—48no—
149C2×C11⋊C8—28no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—44no—
156C2×C11⋊C8C2×D414yes—
157C22×#106—111no—
158C22×C4⋊C8—111no—
159C22×#102—111no—
160C22×#102—111no—
161C2×#390D1111yescharacteristic
162C2×#389—111no—
163#2065—118no—
164C2×#340—111no—
165C23×C11—24no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—48no—
173C23×C11—48no—
174C23×C11—48no—
175C23×C11—84no—
176C23×C11—84no—
177C23×C11—84no—
178C23×C11—84no—
179C23×C11#12112yes—
180C23×C11#12112yes—
181C23×C11C22⋊Q812yes—
182C23×C11C2×SD1612yes—
183C23×C11#13512yes—
184C23×C11AGL(1,ℤ/8)12yes—
185C23×C11AGL(1,ℤ/8)12yes—
186C23×C11C22×D411yescharacteristic
187D4×C11—24no—
188D4×C11—24no—
189D4×C11—42no—
190D4×C11—42no—
191D4×C11—48no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—28no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—84no—
203C2×C4×C11#12114yes—
204C2×C4×C11#12112yes—
205C2×C4×C11#12112yes—
206C2×C4×C11C22⋊Q814yes—
207C2×C4×C11C22⋊Q814yes—
208C2×C4×C11C22⋊Q812yes—
209C2×C4×C11#12614yes—
210C2×C4×C11C2×SD1614yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×Q811yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×Dic11—24no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—48no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—84no—
225C11⋊C8—24no—
226C11⋊C8—42no—
227C23×D4C2×D1111yescharacteristic
228C23×C8—111no—
229C23×C8—111no—
230C22×C4⋊C4—111no—
231C22×C4⋊C4—111no—
232C22×C4⋊C4—221no—
233C22×C4⋊C4C2×D1111yescharacteristic
234C22×C22⋊C4—21no—
235C22×C22⋊C4—21no—
236C22×C42C2×D1111yescharacteristic
237C2×#106—114no—
238C2×#106—224no—
239C2×C4⋊C8—114no—
240C2×C4⋊C8—224no—
241C2×#102—114no—
242C2×#102—114no—
243C2×#102—224no—
244C2×#102—224no—
245#390—22no—
246#390C2×D1114yes—
247#389—114no—
248#389—222no—
249C2×#95—221no—
250#340—114no—
251C22×C11—44no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—816no—
255C22×C11—82no—
256C22×C11—82no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11#39614yes—
260C22×C11#46014yes—
261C22×C11#46314yes—
262C22×C11#46514yes—
263C22×C11#46914yes—
264C22×C11#47614yes—
265C22×C11#47814yes—
266C22×C11C2×#12111yescharacteristic
267C22×C11C2×#12111yescharacteristic
268C22×C11C2×C22⋊Q811yescharacteristic
269C22×C11C22×SD1611yescharacteristic
270C22×C11C2×#13511yescharacteristic
271C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C4×C11—24no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11#39614yes—
277C4×C11C2×#12111yescharacteristic
278C4×C11C2×C22⋊Q811yescharacteristic
279C4×C11C2×C22⋊Q811yescharacteristic
280C4×C11C2×#12611yescharacteristic
281Dic11—44no—
282Dic11—82no—
283C25—21no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4Dic2214yes—
291C22×D4C22×D1112yes—
292C23×C4—21no—
293C23×C4—221no—
294C23×C4—221no—
295C23×C4C22⋊D1111yescharacteristic
296C23×C4C22⋊D1111yescharacteristic
297C23×C4C22×D1111yescharacteristic
298C22×C8—114no—
299C22×C8—112no—
300C22×C8—112no—
301C22×C8—222no—
302C22×C8—222no—
303C22×C8—222no—
304C22×C8—222no—
305C22×C8—222no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—114no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4—444no—
319C2×C4⋊C4C22×D1112yes—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42C22⋊D1112yes—
327C2×C42C22×D1112yes—
328#106—228no—
329C4⋊C8—228no—
330#102—228no—
331#102—228no—
332#95—224no—
333C2×C11—84no—
334C2×C11#206518yescomplemented
335C2×C11C2×#39611yescharacteristic
336C2×C11C2×#46311yescharacteristic
337C2×C11C2×#46011yescharacteristic
338C2×C11C2×#46511yescharacteristic
339C2×C11C2×#46911yescharacteristic
340C2×C11C2×#47611yescharacteristic
341C2×C11C2×#47811yescharacteristic
342C24—24no—
343C24—22no—
344C24—42no—
345C24—42no—
346C24—42no—
347C24—42no—
348C24—42no—
349C24—42no—
350C24C2×C22⋊D1111yescharacteristic
351C2×D4—28no—
352C2×D4—28no—
353C2×D4—24no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—44no—
360C2×D4—44no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4C2×Dic2214yes—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—224no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4—442no—
380C22×C4—442no—
381C22×C4#432414yes—
382C22×C4C2×Dic2212yes—
383C22×C4#433912yes—
384C22×C4D4×D1112yes—
385C22×C4D4×D1112yes—
386C22×C4#434112yes—
387C22×C4#434112yes—
388C22×C4C2×C22⋊D1112yes—
389C22×C4C2×C22⋊D1112yes—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392C2×C8—114no—
393C2×C8—228no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—444no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—114no—
404C4⋊C4—224no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—448no—
409C4⋊C4—442no—
410C22⋊C4—48no—
411C22⋊C4—48no—
412C42—24no—
413C42—22no—
414C42—22no—
415C11C2×#206511yescharacteristic, complemented, Sylow
416C23—24no—
417C23—42no—
418C23—42no—
419C23—48no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—48no—
425C23—48no—
426C23—84no—
427C23—84no—
428C23—84no—
429C23—84no—
430C23#6697712yes—
431C23#6698512yes—
432C23C2×#432412yes—
433C23#6699112yes—
434C23#6699212yes—
435C23#6700212yes—
436C23#6700312yes—
437C23C22×C22⋊D1111yescharacteristic
438D4—24no—
439D4—24no—
440D4—42no—
441D4—42no—
442D4—48no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—28no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—84no—
454C2×C4—224no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—448no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—884no—
462C2×C4#6693114yes—
463C2×C4#6693114yes—
464C2×C4#6693214yes—
465C2×C4#6693714yes—
466C2×C4#6697712yes—
467C2×C4C2×#432414yes—
468C2×C4#6699112yes—
469C2×C4#6699212yes—
470C2×C4C22×Dic2211yescharacteristic
471C2×C4C2×#433911yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4C2×#434111yescharacteristic
475C2×C4C2×#434111yescharacteristic
476C8—224no—
477C8—442no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—816no—
485C22—82no—
486C22#1062256114yes—
487C22#1062262114yes—
488C22#1062262214yes—
489C22#1062265214yes—
490C22#1062265414yes—
491C22#1062267014yes—
492C22#1062268814yes—
493C22C2×#6697711yescharacteristic
494C22C2×#6698511yescharacteristic
495C22C22×#432411yescharacteristic
496C22C2×#6699111yescharacteristic
497C22C2×#6699211yescharacteristic
498C22C2×#6700211yescharacteristic
499C22C2×#6700311yescharacteristic
500C4—24no—
501C4—42no—
502C4—82no—
503C4—444no—
504C4—882no—
505C4#1062256114yes—
506C4C2×#6693111yescharacteristic
507C4C2×#6693111yescharacteristic
508C4C2×#6693211yescharacteristic
509C4C2×#6693711yescharacteristic
510C2—84no—
511C2#1306999018yesdirect product factor
512C2C2×#1062256111yescharacteristic
513C2C2×#1062267011yescharacteristic
514C2C2×#1062268811yescharacteristic
515C2C2×#1062265411yescharacteristic
516C2C2×#1062265211yescharacteristic
517C2C2×#1062262111yescharacteristic
518C2C2×#1062262211yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#390C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11C2×#2065
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66872C2semidirect
2. C22×C4⋊(C11⋊C8)C2semidirect
5. C2×#10622541C2semidirect
6. #13069990C2direct (N × H)
7. C2×#10622167C2semidirect
27. C2×#66872C22semidirect
29. #10622541C22semidirect
31. C2×C4⋊(C11⋊C8)C22semidirect
32. #10622167C22semidirect
334. C2×C11#2065semidirect
415. C11C2×#2065semidirect
511. C2#13069990direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668722
C22×C4⋊(C11⋊C8)2
C22×#668962
C2×#106225412
#130699902
C2×#106221672
C2×C11×#3902
C2×#206511