Finite Group Databasebeta

← C2×#13067017 #14720271

Subgroups — C2×#13067017 #14720271

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic
3C2×D11×C4⋊C8C211yesmaximal, characteristic
4#13067017C218yesmaximal, direct product factor
5C2×#10622094C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622122C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66999C411yescharacteristic
11C2×#66997C411yescharacteristic
12C22×C8×D11—21no—
13#10623109—22no—
14#10623109—22no—
15#10623109C414yes—
16#10623109C2214yes—
17C2×#66950C411yescharacteristic
18C2×#66949—21no—
19C2×#66942—21no—
20C2×#66941C411yescharacteristic
21C2×#66925—21no—
22C2×C42×D11C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×(C2×D11)⋊C8—21no—
28C2×Dic11⋊C8—21no—
29C2×Dic11⋊C8—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32D11×C4⋊C8—22no—
33D11×C4⋊C8C2214yes—
34#10622298—22no—
35#10622298C2214yes—
36C11×Q8⋊C8C2214yescomplemented
37Q8⋊(C11⋊C8)C2214yescomplemented
38#10622122C2214yescomplemented
39#10622094C2214yescomplemented
40C22×Q8×C11C2×C411yescharacteristic
41C22×C4×D11C2×C411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×C4×D11D411yescharacteristic
44C22×Dic22—21no—
45C22×Dic22C2×C411yescharacteristic
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11C2×C412yes—
51C4×Q8×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2×C411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56#66999—22no—
57#66999C2×C414yes—
58#66997—22no—
59#66997C2×C414yes—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11C2×C411yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11C2×C411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11D411yescharacteristic
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75C2×C8×D11—24no—
76C2×C8×D11—44no—
77#66950—22no—
78#66950C2×C414yes—
79#66949—24no—
80#66949—24no—
81#66942—24no—
82#66942—24no—
83#66941—22no—
84#66941C2×C414yes—
85#66925—24no—
86#66925—24no—
87C42×D11C2×C412yes—
88C42×D11D412yes—
89C42×D11D412yes—
90C42×D11C2312yes—
91C4×Dic22—21no—
92C4×Dic22—21no—
93C4×Dic22—24no—
94C4×Dic22—24no—
95C4×Dic22C2×C412yes—
96C4×Dic22C2312yes—
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2312yes—
99C4×C8×C11—21no—
100C4×C8×C11C2312yes—
101(C2×D11)⋊C8—24no—
102Dic11⋊C8—24no—
103Dic11⋊C8—24no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4×C11⋊C8—21no—
107C4×C11⋊C8C2312yes—
108C2×#1481—111nomaximal, Sylow
109C23×D11C22⋊C411yescharacteristic
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11C22×C412yes—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11C22⋊C411yescharacteristic
122C22×Dic11C22⋊C411yescharacteristic
123C22×Dic11C22⋊C411yescharacteristic
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—42no—
127C2×C4×D11C22⋊C412yes—
128C2×C4×D11C22⋊C412yes—
129C2×C4×D11C22⋊C412yes—
130C2×C4×D11SD1614yes—
131C2×C4×D11Q1614yes—
132C2×C4×D11C22×C412yes—
133C2×C4×D11C2×D412yes—
134C2×C4×D11C2×D412yes—
135C2×Dic22—24no—
136C2×Dic22—21no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—44no—
140C2×Dic22C22×C412yes—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—42no—
144C2×C8×C11—42no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4C22×C412yes—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11C22×C411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2411yescharacteristic
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—24no—
157C4⋊Dic11—24no—
158C4⋊Dic11—21no—
159C4⋊Dic11C22×C412yes—
160Dic11⋊C4—24no—
161Dic11⋊C4—24no—
162Dic11⋊C4—24no—
163Dic11⋊C4—24no—
164Dic11⋊C4—22no—
165Dic11⋊C4—22no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C4×Dic11C22⋊C412yes—
169C4×Dic11C22⋊C412yes—
170C4×Dic11C22⋊C412yes—
171C4×Dic11C22×C412yes—
172C4×Dic11C2×D412yes—
173C4×Dic11C2×D412yes—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—42no—
177C2×C11⋊C8—42no—
178C8×D11—48no—
179C2×#533—111no—
180C2×#431—111no—
181C22×C4⋊C8—111no—
182#1481—118no—
183C2×Q8⋊C8—111no—
184C2×Q8⋊C8—111no—
185C2×Q8⋊C8—111no—
186C2×Q8⋊C8D1111yescharacteristic, complemented
187C23×C11C2×C22⋊C411yescharacteristic
188C22×D11—22no—
189C22×D11—22no—
190C22×D11#10314yes—
191C22×D11C2×C22⋊C412yes—
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—42no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11C2×C22⋊C411yescharacteristic
201C2×C4×C11C2×C22⋊C411yescharacteristic
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11#13112yes—
204C2×C4×C11#13112yes—
205C2×C4×C11C2×SD1612yes—
206C2×C4×C11C2×Q1612yes—
207C2×C4×C11C23×C411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11#10314yes—
217C2×Dic11C2×C22⋊C412yes—
218C2×Dic11C2×C22⋊C412yes—
219C2×Dic11C2×C22⋊C412yes—
220C4×D11—22no—
221C4×D11—22no—
222C4×D11—24no—
223C4×D11—42no—
224C4×D11—42no—
225C4×D11#10318yes—
226C4×D11C2×SD1614yes—
227C4×D11C2×Q1614yes—
228Dic22—22no—
229Dic22—22no—
230Dic22—48no—
231Dic22—42no—
232C8×C11—42no—
233C8×C11—42no—
234C11⋊C8—42no—
235C11⋊C8—42no—
236C23×C8—221no—
237#533—114no—
238#533—114no—
239#533—222no—
240#533—222no—
241C2×C4⋊Q8—111no—
242C2×C4⋊Q8—111no—
243C2×#125—221no—
244C2×C22⋊Q8—111no—
245C2×C22⋊Q8—111no—
246C2×C22⋊Q8—221no—
247C2×C4×Q8—111no—
248C2×C4×Q8—221no—
249C2×C4×Q8C2×D1111yescharacteristic
250C2×#117—221no—
251C22×C42—111no—
252#431—114no—
253#431—222no—
254C2×C4⋊C8—111no—
255C2×C4⋊C8—114no—
256C2×C4⋊C8—222no—
257C2×C4⋊C8—221no—
258C2×C4⋊C8—221no—
259C2×C4⋊C8C2×D1111yescharacteristic
260C2×C22⋊C8—221no—
261C2×C4×C8—111no—
262C2×C4×C8C2×D1111yescharacteristic
263Q8⋊C8—114no—
264Q8⋊C8—114no—
265Q8⋊C8—114no—
266Q8⋊C8C2×D1114yescomplemented
267C22×C11#40812yes—
268C22×C11C2×#10312yes—
269C22×C11#42112yes—
270C22×C11C22×C22⋊C411yescharacteristic
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—28no—
274C2×D11C2×#10314yes—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11#40812yes—
280C4×C11C2×#10312yes—
281C4×C11C2×#13111yescharacteristic
282C4×C11C2×#13111yescharacteristic
283C4×C11C22×SD1611yescharacteristic
284C4×C11C22×Q1611yescharacteristic
285Dic11—22no—
286Dic11—22no—
287Dic11—42no—
288Dic11—42no—
289Dic11C2×#10314yes—
290C22×Q8—111no—
291C22×Q8—221no—
292C22×Q8C4×D1111yescharacteristic
293C23×C4—111no—
294C23×C4—111no—
295C23×C4—111no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—224no—
299C22×C8—221no—
300C22×C8—221no—
301C22×C8—444no—
302C4⋊Q8—114no—
303C4⋊Q8—114no—
304C4⋊Q8—222no—
305C4⋊Q8—222no—
306#125—224no—
307#125—224no—
308C22⋊Q8—114no—
309C22⋊Q8—114no—
310C22⋊Q8—222no—
311C22⋊Q8—224no—
312C22⋊Q8—224no—
313C22⋊Q8—222no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—112no—
317C4×Q8—112no—
318C4×Q8—224no—
319C4×Q8—224no—
320C4×Q8—221no—
321C4×Q8—221no—
322C4×Q8C4×D1112yes—
323C4×Q8C22×D1112yes—
324#117—224no—
325#117—224no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C4×D1111yescharacteristic
335C2×C22⋊C4—221no—
336C2×C22⋊C4—221no—
337C2×C42—21no—
338C2×C42—111no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—112no—
342C2×C42—112no—
343C2×C42—112no—
344C2×C42—112no—
345C2×C42—221no—
346C2×C42C22×D1111yescharacteristic
347C4⋊C8—21no—
348C4⋊C8—112no—
349C4⋊C8—224no—
350C4⋊C8—224no—
351C4⋊C8—221no—
352C4⋊C8C22×D1112yes—
353C22⋊C8—224no—
354C4×C8—21no—
355C4×C8—112no—
356C4×C8—221no—
357C4×C8C22×D1112yes—
358C2×C11#148114yescomplemented
359C2×C11C2×#40811yescharacteristic
360C2×C11C22×#10311yescharacteristic
361C2×C11C2×#42111yescharacteristic
362D11—24no—
363C24—111no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—112no—
368C2×Q8—224no—
369C2×Q8—221no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—444no—
373C2×Q8C2×C4×D1112yes—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—111no—
377C22×C4—112no—
378C22×C4—114no—
379C22×C4—114no—
380C22×C4—112no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—112no—
384C22×C4—112no—
385C22×C4—112no—
386C22×C4—112no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—442no—
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4D4×D1111yescharacteristic
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—42no—
398C2×C8—42no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—448no—
402C2×C8—442no—
403C2×C8—442no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—112no—
408C4⋊C4—224no—
409C4⋊C4—224no—
410C4⋊C4—224no—
411C4⋊C4—224no—
412C4⋊C4—224no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4C2×C4×D1112yes—
417C22⋊C4—224no—
418C22⋊C4—224no—
419C42—22no—
420C42—22no—
421C42—112no—
422C42—112no—
423C42—112no—
424C42—112no—
425C42—112no—
426C42—112no—
427C42—222no—
428C42—222no—
429C42C2×C4×D1111yescharacteristic
430C42D4×D1111yescharacteristic
431C42D4×D1111yescharacteristic
432C42C23×D1111yescharacteristic
433C11C2×#148111yescharacteristic, complemented, Sylow
434C23—112no—
435C23—114no—
436C23—222no—
437C23—222no—
438C23C22⋊C4×D1111yescharacteristic
439Q8—22no—
440Q8—22no—
441Q8—42no—
442Q8—222no—
443Q8—222no—
444Q8—448no—
445Q8—442no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—112no—
452C2×C4—114no—
453C2×C4—114no—
454C2×C4—114no—
455C2×C4—118no—
456C2×C4—112no—
457C2×C4—112no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—224no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4C22⋊C4×D1111yescharacteristic
470C2×C4C22⋊C4×D1111yescharacteristic
471C2×C4C22⋊C4×D1111yescharacteristic
472C2×C4#6695412yes—
473C2×C4#6696012yes—
474C2×C4SD16×D1112yes—
475C2×C4Q16×D1112yes—
476C2×C4C22×C4×D1111yescharacteristic
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C8—42no—
480C8—42no—
481C8—442no—
482C8—442no—
483C22—114no—
484C22—228no—
485C22—222no—
486C22—222no—
487C22#1062234012yes—
488C22D11×#10312yes—
489C22#1062243412yes—
490C22C2×C22⋊C4×D1111yescharacteristic
491C4—21no—
492C4—21no—
493C4—42no—
494C4—42no—
495C4—114no—
496C4—222no—
497C4—222no—
498C4—442no—
499C4—442no—
500C4#1062234012yes—
501C4D11×#10312yes—
502C4C2×#6695411yescharacteristic
503C4C2×#6696011yescharacteristic
504C4C2×SD16×D1111yescharacteristic
505C4C2×Q16×D1111yescharacteristic
506C2—224no—
507C2#1306701714yesdirect product factor
508C2C2×#1062234011yescharacteristic
509C2C2×D11×#10311yescharacteristic
510C2C2×#1062243411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1481
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #13067017C2direct (N × H)
5. C2×#10622094C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
7. C2×#10622122C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
36. C11×Q8⋊C8C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. #10622122C22semidirect
39. #10622094C22semidirect
186. C2×Q8⋊C8D11semidirect
266. Q8⋊C8C2×D11semidirect
358. C2×C11#1481semidirect
433. C11C2×#1481semidirect
507. C2#13067017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106222982
C2×D11×C4⋊C82
#130670172
C2×#106220942
C2×Q8⋊(C11⋊C8)2
C2×#106221222
C2×C11×Q8⋊C82
C2×#148111