Finite Group Databasebeta

← C2×#13070022 #14782505

Subgroups — C2×#13070022 #14782505

Order 2816.

1366 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×#66896C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622589C211yesmaximal, characteristic, complemented
4#13070022C218yesmaximal, direct product factor
5C2×#10622189C211yesmaximal, characteristic, complemented
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C22⋊Dic11—21no—
13C22×C22⋊Dic11—21no—
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4—21no—
17C22×Dic11⋊C4—21no—
18C22×C4×Dic11C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×C11×#102—24no—
21C2×C11×#102C2214yes—
22#10622834—22no—
23#10622834C2214yes—
24C2×#66896—24no—
25C2×#66896C2214yes—
26#10622589—22no—
27#10622589C2214yescomplemented
28#10622189C2214yescomplemented
29#10622188C2214yescomplemented
30#10622167C2214yescomplemented
31C25×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—22no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11D414yes—
39C22×D4×C11C2312yes—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C23×Dic11—21no—
44C23×Dic11D411yescharacteristic
45C23×Dic11D411yescharacteristic
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—44no—
57C2×C22⋊Dic11—44no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—24no—
67C2×Dic11⋊C4—24no—
68C2×Dic11⋊C4—44no—
69C2×Dic11⋊C4—44no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11D412yes—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—22no—
76C22×C11⋊C8—22no—
77C22×C11⋊C8C2312yes—
78C11×#102—28no—
79#66896—28no—
80C2×#2071—111nomaximal, Sylow
81C24×C11—24no—
82C24×C11—22no—
83C24×C11—42no—
84C24×C11—42no—
85C24×C11—42no—
86C24×C11—42no—
87C24×C11—42no—
88C24×C11—42no—
89C24×C11C2×D411yescharacteristic
90C2×D4×C11—24no—
91C2×D4×C11—28no—
92C2×D4×C11—28no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—44no—
101C2×D4×C11—44no—
102C2×D4×C11C2×D414yes—
103C22×C4×C11—22no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×C4×C11#4112yes—
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—42no—
122C22×Dic11—42no—
123C22×Dic11—42no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11D814yes—
128C22×Dic11SD1614yes—
129C22×Dic11C2×D412yes—
130C22×Dic11C2×D412yes—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—44no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—42no—
138C22⋊Dic11—48no—
139C22⋊Dic11—48no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—42no—
145C4⋊Dic11—42no—
146Dic11⋊C4—48no—
147Dic11⋊C4—48no—
148C4×Dic11—24no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—44no—
155C22×#102—111no—
156C22×#102D1111yescharacteristic
157C2×#390—111no—
158C2×#384—111no—
159#2071—118no—
160C2×#340—111no—
161C2×#340—111no—
162C2×#336—111no—
163C23×C11—24no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—48no—
171C23×C11—48no—
172C23×C11—48no—
173C23×C11—84no—
174C23×C11—84no—
175C23×C11—84no—
176C23×C11—84no—
177C23×C11#12112yes—
178C23×C11#12312yes—
179C23×C11#12412yes—
180C23×C11C2×D812yes—
181C23×C11C2×SD1612yes—
182C23×C11AGL(1,ℤ/8)12yes—
183C23×C11#13712yes—
184C23×C11C22×D411yescharacteristic
185D4×C11—24no—
186D4×C11—24no—
187D4×C11—42no—
188D4×C11—42no—
189D4×C11—48no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—84no—
194C2×C4×C11#12112yes—
195C2×C4×C11#12312yes—
196C2×C4×C11#12314yes—
197C2×C4×C11#12314yes—
198C2×C4×C11#12412yes—
199C2×C4×C11#12614yes—
200C2×C4×C11#12614yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—28no—
212C2×Dic11—28no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—84no—
220C2×Dic11—84no—
221C2×Dic11C2×D814yes—
222C2×Dic11C2×SD1614yes—
223C8×C11—42no—
224C11⋊C8—42no—
225C23×D4C2×D1111yescharacteristic
226C23×C8—111no—
227C23×C8C2×D1111yescharacteristic
228C22×C4⋊C4—111no—
229C22×C4⋊C4—111no—
230C22×C4⋊C4—221no—
231C22×C4⋊C4—221no—
232C22×C4⋊C4C2×D1111yescharacteristic
233C22×C22⋊C4—221no—
234C22×C22⋊C4—221no—
235C22×C42—111no—
236C2×#102—24no—
237C2×#102—114no—
238C2×#102—224no—
239C2×#102C2×D1114yes—
240#390—114no—
241#390—222no—
242#384—114no—
243#384—222no—
244#340—114no—
245#340—114no—
246#336—114no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11—44no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—816no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11#39714yes—
256C22×C11#45914yes—
257C22×C11#46114yes—
258C22×C11#48014yes—
259C22×C11#48114yes—
260C22×C11#48614yes—
261C22×C11#48914yes—
262C22×C11C2×#12111yescharacteristic
263C22×C11C2×#12311yescharacteristic
264C22×C11C2×#12411yescharacteristic
265C22×C11C22×D811yescharacteristic
266C22×C11C22×SD1611yescharacteristic
267C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C11C2×#13711yescharacteristic
269C4×C11—82no—
270C4×C11#39714yes—
271C4×C11C2×#12311yescharacteristic
272C4×C11C2×#12311yescharacteristic
273C4×C11C2×#12611yescharacteristic
274C4×C11C2×#12611yescharacteristic
275Dic11—24no—
276Dic11—24no—
277Dic11—82no—
278Dic11—82no—
279C25—21no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—21no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4C22⋊D1114yes—
287C22×D4C22×D1112yes—
288C23×C4—21no—
289C23×C4—111no—
290C23×C4—111no—
291C23×C4—221no—
292C23×C4—221no—
293C23×C4C22×D1111yescharacteristic
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—112no—
298C22×C8—222no—
299C22×C8—222no—
300C22×C8—222no—
301C22×C8C22×D1112yes—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—224no—
312C2×C4⋊C4—224no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—444no—
316C2×C4⋊C4—444no—
317C2×C4⋊C4C22×D1112yes—
318C2×C22⋊C4—224no—
319C2×C22⋊C4—224no—
320C2×C22⋊C4—444no—
321C2×C22⋊C4—444no—
322C2×C42—112no—
323C2×C42—112no—
324C2×C42—222no—
325C2×C42—222no—
326#102—28no—
327#102—228no—
328C2×C11—84no—
329C2×C11#207118yescomplemented
330C2×C11C2×#39711yescharacteristic
331C2×C11C2×#45911yescharacteristic
332C2×C11C2×#46111yescharacteristic
333C2×C11C2×#48011yescharacteristic
334C2×C11C2×#48111yescharacteristic
335C2×C11C2×#48611yescharacteristic
336C2×C11C2×#48911yescharacteristic
337C24—24no—
338C24—22no—
339C24—42no—
340C24—42no—
341C24—42no—
342C24—42no—
343C24—42no—
344C24—42no—
345C24D4×D1111yescharacteristic
346C2×D4—28no—
347C2×D4—28no—
348C2×D4—24no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—44no—
355C2×D4—44no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4C2×C22⋊D1114yes—
359C22×C4—22no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—114no—
364C22×C4—114no—
365C22×C4—112no—
366C22×C4—112no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—442no—
374C22×C4—442no—
375C22×C4—442no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4#433912yes—
380C22×C4#433912yes—
381C22×C4D4×D1111yescharacteristic
382C22×C4#434112yes—
383C22×C4#434112yes—
384C22×C4#434112yes—
385C22×C4C2×C22⋊D1112yes—
386C22×C4C23×D1111yescharacteristic
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—44no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C2×C8—444no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—42no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4—448no—
403C4⋊C4—448no—
404C4⋊C4—442no—
405C4⋊C4—442no—
406C22⋊C4—448no—
407C22⋊C4—448no—
408C42—224no—
409C42—222no—
410C42—222no—
411C11C2×#207111yescharacteristic, complemented, Sylow
412C23—24no—
413C23—48no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—48no—
419C23—42no—
420C23—42no—
421C23—48no—
422C23—84no—
423C23—84no—
424C23—84no—
425C23—84no—
426C23#6693612yes—
427C23#6693812yes—
428C23D8×D1112yes—
429C23#6696412yes—
430C23SD16×D1112yes—
431C23#6696812yes—
432C23#6699212yes—
433C23C2×D4×D1111yescharacteristic
434D4—24no—
435D4—24no—
436D4—42no—
437D4—42no—
438D4—48no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—84no—
443C2×C4—114no—
444C2×C4—114no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—228no—
450C2×C4—228no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—884no—
458C2×C4—884no—
459C2×C4#6693214yes—
460C2×C4#6693214yes—
461C2×C4#6693612yes—
462C2×C4#6693812yes—
463C2×C4#6698214yes—
464C2×C4#6698814yes—
465C2×C4#6699212yes—
466C2×C4C2×#433911yescharacteristic
467C2×C4C2×#433911yescharacteristic
468C2×C4C2×#434111yescharacteristic
469C2×C4C2×#434111yescharacteristic
470C2×C4C2×#434111yescharacteristic
471C2×C4C22×C22⋊D1111yescharacteristic
472C8—42no—
473C8—442no—
474C22—44no—
475C22—44no—
476C22—44no—
477C22—82no—
478C22—82no—
479C22—816no—
480C22—82no—
481C22—82no—
482C22#1062237314yes—
483C22#1062237814yes—
484C22#1062238714yes—
485C22#1062239014yes—
486C22#1062256514yes—
487C22#1062276314yes—
488C22#1062277514yes—
489C22C2×#6693611yescharacteristic
490C22C2×#6693811yescharacteristic
491C22C2×D8×D1111yescharacteristic
492C22C2×#6696411yescharacteristic
493C22C2×SD16×D1111yescharacteristic
494C22C2×#6696811yescharacteristic
495C22C2×#6699211yescharacteristic
496C4—82no—
497C4—224no—
498C4—224no—
499C4—882no—
500C4—882no—
501C4#1062256514yes—
502C4C2×#6693211yescharacteristic
503C4C2×#6693211yescharacteristic
504C4C2×#6698211yescharacteristic
505C4C2×#6698811yescharacteristic
506C2—84no—
507C2#1307002218yesdirect product factor
508C2C2×#1062256511yescharacteristic
509C2C2×#1062276311yescharacteristic
510C2C2×#1062277511yescharacteristic
511C2C2×#1062238711yescharacteristic
512C2C2×#1062239011yescharacteristic
513C2C2×#1062237311yescharacteristic
514C2C2×#1062237811yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC22×#102D11
hypocenterC11C2×#2071
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
3. C2×#10622589C2semidirect
4. #13070022C2direct (N × H)
5. C2×#10622189C2semidirect
6. C2×#10622167C2semidirect
7. C2×#10622188C2semidirect
27. #10622589C22semidirect
28. #10622189C22semidirect
29. #10622188C22semidirect
30. #10622167C22semidirect
329. C2×C11#2071semidirect
411. C11C2×#2071semidirect
507. C2#13070022direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668962
C2×#106228342
C2×#106225892
#130700222
C2×#106221892
C2×#106221672
C2×#106221882
C22×C11×#1022
C2×#207111