Finite Group Databasebeta

← C2×#13069314 #14756404

Subgroups — C2×#13069314 #14756404

Order 2816.

1422 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×#66885C211yesmaximal, characteristic
2C22×#66873C211yesmaximal, characteristic
3C22×#66879C211yesmaximal, characteristic, complemented
4C2×#10622601C211yesmaximal, characteristic
5C2×#10622598C211yesmaximal, characteristic, complemented
6#13069314C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C2×C11×#340C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4—21no—
14C22×(C2×D11)⋊C4—21no—
15C22×C4⋊Dic11—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×C11⋊#95—21no—
20C2×#66885—24no—
21C2×#66885C2214yes—
22C2×#66879—24no—
23C2×#66879C2214yescomplemented
24#10622601—22no—
25#10622601C2214yes—
26#10622598—22no—
27#10622598C2214yescomplemented
28C2×#66873C418yescomplemented
29C2×#66873C2214yes—
30C11×#340C2214yescomplemented
31#10622167C2214yescomplemented
32C24×D11—21no—
33C23×C4×C11—21no—
34C23×C4×C11—21no—
35C23×C4×C11C2311yescharacteristic
36C23×Dic11—21no—
37C23×Dic11D411yescharacteristic
38C23×Dic11D411yescharacteristic
39C22×D44—22no—
40C22×D44—22no—
41C22×D44—22no—
42C22×D44—22no—
43C22×D44—21no—
44C22×D44—22no—
45C22×D44C2×C414yes—
46C22×D44C2312yes—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11D414yes—
50C22×C8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—44no—
62C2×(C2×D11)⋊C4—44no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—44no—
68C2×C4⋊Dic11C2312yes—
69C2×C4×Dic11—22no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11D412yes—
72C2×C4×Dic11C2312yes—
73C22×C11⋊C8—22no—
74C22×C11⋊C8—22no—
75C22×C11⋊C8C2×C414yes—
76C22×C11⋊C8C2312yes—
77C11⋊#95—24no—
78#66885—28no—
79#66879—28no—
80#66873C2×C4116yescomplemented
81C2×#1936—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C23×D11—24no—
84C23×D11—22no—
85C23×D11—42no—
86C23×D11—42no—
87C23×D11—42no—
88C23×D11—42no—
89C23×D11—42no—
90C23×D11—42no—
91C22×C4×C11—24no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11#4112yes—
103C22×C4×C11#4112yes—
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—42no—
115C22×Dic11—42no—
116C22×Dic11—42no—
117C22×Dic11C2×D412yes—
118C22×Dic11C2×D412yes—
119C2×D44—28no—
120C2×D44—24no—
121C2×D44—28no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—42no—
128C2×D44—44no—
129C2×D44—42no—
130C2×D44—44no—
131C2×D44C22×C414yes—
132C2×C8×C11—28no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11C2×D414yes—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4C22×C414yes—
142(C2×D11)⋊C4—48no—
143(C2×D11)⋊C4—48no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—48no—
147C4⋊Dic11—42no—
148C4×Dic11—24no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C2×C11⋊C8—28no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8C22×C414yes—
155C22×#102—111no—
156C22×#102—111no—
157C22×#97—111no—
158C2×#390—111no—
159C2×#389—111no—
160#1936—118no—
161C2×#340—111no—
162C2×#340D1111yescharacteristic, complemented
163C23×C11C4×D412yes—
164C23×C11#12112yes—
165C23×C11#12412yes—
166C23×C11AGL(1,ℤ/8)12yes—
167C23×C11AGL(1,ℤ/8)12yes—
168C23×C11AGL(1,ℤ/8)12yes—
169C23×C11#13712yes—
170C23×C11C22×D411yescharacteristic
171C22×D11—24no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—48no—
179C22×D11—48no—
180C22×D11—48no—
181C22×D11—84no—
182C22×D11—84no—
183C22×D11—84no—
184C22×D11—84no—
185C2×C4×C11—24no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—48no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—84no—
193C2×C4×C11#11714yes—
194C2×C4×C11C4×D414yes—
195C2×C4×C11C4×D412yes—
196C2×C4×C11#12112yes—
197C2×C4×C11#12314yes—
198C2×C4×C11#12412yes—
199C2×C4×C11#12614yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—44no—
213C2×Dic11—44no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—84no—
218D44—24no—
219D44—24no—
220D44—42no—
221D44—42no—
222D44—48no—
223C8×C11—24no—
224C11⋊C8—24no—
225C23×D4—111no—
226C23×C8—111no—
227C23×C8C2×D1111yescharacteristic
228C22×C4⋊C4—111no—
229C22×C4⋊C4—221no—
230C22×C4⋊C4C2×D1111yescharacteristic
231C22×C4⋊C4C2×D1111yescharacteristic
232C22×C22⋊C4—221no—
233C22×C22⋊C4—221no—
234C22×C42—111no—
235C2×#102—114no—
236C2×#102—118no—
237C2×#102—114no—
238C2×#102—224no—
239C2×#97—114no—
240C2×#97—224no—
241#390—114no—
242#390—222no—
243#389—114no—
244#389—222no—
245C2×#95—221no—
246#340—114no—
247#340C2×D1114yescomplemented
248C22×C11#38814yes—
249C22×C11#44014yes—
250C22×C11#44214yes—
251C22×C11#46814yes—
252C22×C11#46914yes—
253C22×C11#48914yes—
254C22×C11#49014yes—
255C22×C11C2×C4×D411yescharacteristic
256C22×C11C2×#12111yescharacteristic
257C22×C11C2×#12411yescharacteristic
258C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C11C2×#13711yescharacteristic
262C2×D11—44no—
263C2×D11—44no—
264C2×D11—44no—
265C2×D11—82no—
266C2×D11—82no—
267C2×D11—816no—
268C2×D11—82no—
269C2×D11—82no—
270C4×C11—44no—
271C4×C11—82no—
272C4×C11#38814yes—
273C4×C11C2×#11711yescharacteristic
274C4×C11C2×C4×D411yescharacteristic
275C4×C11C2×#12311yescharacteristic
276C4×C11C2×#12611yescharacteristic
277Dic11—42no—
278Dic11—42no—
279Dic11—82no—
280C25—221no—
281C22×D4—114no—
282C22×D4—112no—
283C22×D4—222no—
284C22×D4—222no—
285C22×D4—221no—
286C22×D4—222no—
287C22×D4—222no—
288C22×D4—222no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—111no—
292C23×C4—111no—
293C23×C4—221no—
294C23×C4C22×D1111yescharacteristic
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—114no—
298C22×C8—112no—
299C22×C8—222no—
300C22×C8—222no—
301C22×C8D4414yes—
302C22×C8C22×D1112yes—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—224no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—444no—
314C2×C4⋊C4C4×D1114yes—
315C2×C4⋊C4C22×D1112yes—
316C2×C4⋊C4C22×D1112yes—
317C2×C22⋊C4—224no—
318C2×C22⋊C4—224no—
319C2×C22⋊C4—444no—
320C2×C22⋊C4—444no—
321C2×C42—112no—
322C2×C42—112no—
323C2×C42—222no—
324C2×C42—222no—
325#102—1116no—
326#102—228no—
327#97—228no—
328#95—224no—
329C2×C11#193618yescomplemented
330C2×C11C2×#38811yescharacteristic
331C2×C11C2×#44011yescharacteristic
332C2×C11C2×#44211yescharacteristic
333C2×C11C2×#46811yescharacteristic
334C2×C11C2×#46911yescharacteristic
335C2×C11C2×#48911yescharacteristic
336C2×C11C2×#49011yescharacteristic
337D11—84no—
338C24—224no—
339C24—222no—
340C24—442no—
341C24—442no—
342C24—442no—
343C24—442no—
344C24—442no—
345C24—442no—
346C24D4×D1111yescharacteristic
347C2×D4—114no—
348C2×D4—228no—
349C2×D4—224no—
350C2×D4—228no—
351C2×D4—222no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—442no—
357C2×D4—444no—
358C2×D4—442no—
359C2×D4—444no—
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—112no—
369C22×C4—112no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4—442no—
380C22×C4C2×C4×D1112yes—
381C22×C4C2×D4412yes—
382C22×C4#433912yes—
383C22×C4D4×D1111yescharacteristic
384C22×C4#434112yes—
385C22×C4#434112yes—
386C22×C4#434312yes—
387C22×C4C23×D1111yescharacteristic
388C2×C8—28no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—114no—
392C2×C8—228no—
393C2×C8—222no—
394C2×C8—222no—
395C2×C8C2×D4414yes—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—42no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4—448no—
404C4⋊C4—442no—
405C4⋊C4C2×C4×D1114yes—
406C22⋊C4—448no—
407C22⋊C4—448no—
408C42—224no—
409C42—222no—
410C42—222no—
411C11C2×#193611yescharacteristic, complemented, Sylow
412C23—224no—
413C23—442no—
414C23—442no—
415C23—442no—
416C23—442no—
417C23—442no—
418C23—442no—
419C23—448no—
420C23—448no—
421C23—448no—
422C23—884no—
423C23—884no—
424C23—884no—
425C23—884no—
426C23(C22⋊D11)⋊C412yes—
427C23#6693812yes—
428C23#6694812yes—
429C23#6696412yes—
430C23#6696712yes—
431C23#6696712yes—
432C23#6697112yes—
433C23C2×D4×D1111yescharacteristic
434D4—224no—
435D4—224no—
436D4—442no—
437D4—442no—
438D4—448no—
439C2×C4—24no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—48no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—84no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—444no—
454C2×C4—444no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—884no—
459C2×C4C4×D4414yes—
460C2×C4(C22⋊D11)⋊C412yes—
461C2×C4#6693812yes—
462C2×C4#6693914yes—
463C2×C4#6694514yes—
464C2×C4#6694812yes—
465C2×C4#6695114yes—
466C2×C4C22×C4×D1111yescharacteristic
467C2×C4C22×D4411yescharacteristic
468C2×C4C2×#433911yescharacteristic
469C2×C4C2×#434111yescharacteristic
470C2×C4C2×#434111yescharacteristic
471C2×C4C2×#434311yescharacteristic
472C8—24no—
473C8—224no—
474C22—444no—
475C22—444no—
476C22—444no—
477C22—8816no—
478C22—882no—
479C22—882no—
480C22—882no—
481C22—882no—
482C22#1062228314yes—
483C22#1062237714yes—
484C22#1062239814yes—
485C22#1062240814yes—
486C22#1062243014yes—
487C22#1062247814yes—
488C22#1062249914yes—
489C22C2×(C22⋊D11)⋊C411yescharacteristic
490C22C2×#6693811yescharacteristic
491C22C2×#6694811yescharacteristic
492C22C2×#6696411yescharacteristic
493C22C2×#6696711yescharacteristic
494C22C2×#6696711yescharacteristic
495C22C2×#6697111yescharacteristic
496C4—44no—
497C4—82no—
498C4—442no—
499C4—442no—
500C4—882no—
501C4#1062228314yes—
502C4C2×C4×D4411yescharacteristic
503C4C2×#6693911yescharacteristic
504C4C2×#6694511yescharacteristic
505C4C2×#6695111yescharacteristic
506C2—884no—
507C2#1306931418yesdirect product factor
508C2C2×#1062228311yescharacteristic
509C2C2×#1062243011yescharacteristic
510C2C2×#1062239811yescharacteristic
511C2C2×#1062249911yescharacteristic
512C2C2×#1062247811yescharacteristic
513C2C2×#1062240811yescharacteristic
514C2C2×#1062237711yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterC2×#340D11
hypocenterC11C2×#1936
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. C22×#66879C2semidirect
5. C2×#10622598C2semidirect
6. #13069314C2direct (N × H)
7. C2×#10622167C2semidirect
8. C2×C11×#340C2semidirect
23. C2×#66879C22semidirect
27. #10622598C22semidirect
28. C2×#66873C4semidirect
30. C11×#340C22semidirect
31. #10622167C22semidirect
80. #66873C2×C4semidirect
162. C2×#340D11semidirect
247. #340C2×D11semidirect
329. C2×C11#1936semidirect
411. C11C2×#1936semidirect
507. C2#13069314direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668852
C22×#668732
C22×#668792
C2×#106226012
C2×#106225982
#130693142
C2×#106221672
C2×C11×#3402
C2×#193611