Finite Group Databasebeta

← C2×#13071096 #14912152

Subgroups — C2×#13071096 #14912152

Order 2816.

3854 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C22×#66925C211yesmaximal, characteristic
3C22×C42×D11C211yesmaximal, characteristic
4#13071096C2116yesmaximal, direct product factor
5C2×#10622260C212yesmaximal, complemented
6C2×#10622585C212yesmaximal, complemented
7C2×#10622281C212yesmaximal
8C2×#10622602C212yesmaximal
9C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
10C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C23×C4×D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2212yes—
31C22×C4×Dic11C2211yescharacteristic
32C2×#66925—28no—
33C2×#66925C4116yescomplemented
34C2×#66925C2218yes—
35C2×#66925C2218yes—
36C2×C42×D11—28no—
37C2×C42×D11C2218yes—
38C4×C11×C4⋊C4C2218yescomplemented
39C2×C11×#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622602C22116yes—
44#10622585C22116yescomplemented
45C4×C4⋊Dic11C2218yescomplemented
46C4×Dic11⋊C4C2218yescomplemented
47C4×Dic11⋊C4C2218yescomplemented
48#10622281C22116yes—
49#10622260C22116yescomplemented
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C22×C4×D11—28no—
62C22×C4×D11—28no—
63C22×C4×D11—28no—
64C22×C4×D11C2×C418yes—
65C22×C4×D11D418yes—
66C22×C4×D11Q818yes—
67C22×C4×D11C2318yes—
68C22×C4×D11C2314yes—
69C2×C11×C4⋊C4—28no—
70C2×C11×C4⋊C4C2318yes—
71C2×C42×C11—24no—
72C2×C42×C11—24no—
73C2×C42×C11C2×C418yescomplemented
74C2×C42×C11C2314yes—
75C2×C42×C11C2314yes—
76C2×C42×C11C2314yes—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4C2×C418yes—
79C2×(C2×D11)⋊C4C2×C418yes—
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×C4⋊Dic11—28no—
84C2×C4⋊Dic11C2318yes—
85C2×Dic11⋊C4—28no—
86C2×Dic11⋊C4—28no—
87C2×Dic11⋊C4—28no—
88C2×Dic11⋊C4C2×C418yescomplemented
89C2×Dic11⋊C4C2×C418yescomplemented
90C2×Dic11⋊C4C2318yes—
91C2×Dic11⋊C4C2318yes—
92C2×Dic11⋊C4C2318yes—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2314yes—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—28no—
98C2×C4×Dic11C2×C418yescomplemented
99C2×C4×Dic11C2318yes—
100C2×C4×Dic11C2314yes—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2314yes—
103#66925—232no—
104#66925C2×C4164yescomplemented
105C42×D11—232no—
106C11×#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C2×#2296—111nomaximal, Sylow
111C24×C11C2411yescharacteristic
112C23×D11—24no—
113C23×D11—24no—
114C23×D11C22×C414yes—
115C23×D11C2×D414yes—
116C23×D11C2×Q814yes—
117C23×D11C2412yes—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11C22×C414yes—
126C22×C4×C11C22×C414yes—
127C22×C4×C11C22×C414yes—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×Q814yes—
130C22×C4×C11#4118yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2412yes—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11C22×C414yes—
144C22×Dic11C22×C414yes—
145C22×Dic11C22×C414yes—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×Q814yes—
148C22×Dic11#4118yes—
149C22×Dic11C2414yes—
150C22×Dic11C2412yes—
151C22×Dic11C2412yes—
152C22×Dic11C2414yes—
153C22×Dic11C2412yes—
154C2×C4×D11—264no—
155C2×C4×D11—216no—
156C2×C4×D11—216no—
157C2×C4×D11—216no—
158C2×C4×D11C4⋊C4164yescomplemented
159C2×C4×D11C22×C4116yes—
160C2×C4×D11C2×D4116yes—
161C2×C4×D11C2×Q8116yes—
162C11×C4⋊C4—216no—
163C42×C11—28no—
164C42×C11—28no—
165C42×C11C22×C4116yescomplemented
166(C2×D11)⋊C4—216no—
167(C2×D11)⋊C4C22×C4116yes—
168(C2×D11)⋊C4C22×C4116yes—
169C4⋊Dic11—216no—
170Dic11⋊C4—216no—
171Dic11⋊C4—216no—
172Dic11⋊C4—216no—
173Dic11⋊C4C22×C4116yescomplemented
174Dic11⋊C4C22×C4116yescomplemented
175C4×Dic11—216no—
176C4×Dic11—28no—
177C4×Dic11—28no—
178C4×Dic11C22×C4116yescomplemented
179C22×#117—111no—
180C22×#117—111no—
181C23×C42—111no—
182#2296—1116no—
183C2×#389—112no—
184C2×#389—112no—
185C2×#385—112no—
186C2×#385—112no—
187C2×C4×C4⋊C4—111no—
188C2×C4×C4⋊C4—111no—
189C2×C4×C4⋊C4—111no—
190C2×C4×C4⋊C4D1111yescharacteristic, complemented
191C23×C11C23×C412yes—
192C23×C11C22×D412yes—
193C23×C11C22×Q812yes—
194C23×C11C2×#4114yes—
195C23×C11C2×#4114yes—
196C23×C11C2511yescharacteristic
197C22×D11—28no—
198C22×D11—28no—
199C22×D11—216no—
200C22×D11—216no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11C2×C4⋊C4116yes—
204C22×D11C23×C414yes—
205C22×D11C22×D414yes—
206C22×D11C22×Q814yes—
207C2×C4×C11—28no—
208C2×C4×C11—28no—
209C2×C4×C11—216no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—48no—
218C2×C4×C11C2×C4⋊C4116yes—
219C2×C4×C11C23×C414yes—
220C2×C4×C11C23×C414yes—
221C2×C4×C11C23×C414yes—
222C2×C4×C11C22×D414yes—
223C2×C4×C11C22×Q814yes—
224C2×C4×C11C2×#4118yes—
225C2×Dic11—28no—
226C2×Dic11—28no—
227C2×Dic11—216no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—48no—
236C2×Dic11C2×C4⋊C4116yes—
237C2×Dic11C23×C414yes—
238C2×Dic11C23×C414yes—
239C2×Dic11C23×C414yes—
240C2×Dic11C22×D414yes—
241C2×Dic11C22×Q814yes—
242C2×Dic11C2×#4118yes—
243C4×D11—264no—
244C4×D11C2×C4⋊C4164yescomplemented
245C24×C4—111no—
246C24×C4—112no—
247C2×#117—118no—
248C2×#117—118no—
249C2×#117—1116no—
250C2×#117—228no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4—112no—
254C22×C4⋊C4—112no—
255C22×C4⋊C4—112no—
256C22×C4⋊C4—112no—
257C22×C4⋊C4C2×D1112yes—
258C22×C22⋊C4—111no—
259C22×C22⋊C4—111no—
260C22×C22⋊C4—112no—
261C22×C42—111no—
262C22×C42—112no—
263C22×C42—111no—
264C22×C42—111no—
265C22×C42—118no—
266C22×C42—228no—
267C22×C42C2×D1111yescharacteristic
268C22×C42C2×D1111yescharacteristic
269C22×C42C2×D1111yescharacteristic
270#389—1116no—
271#389—1116no—
272#385—1116no—
273#385—1116no—
274C4×C4⋊C4—118no—
275C4×C4⋊C4—118no—
276C4×C4⋊C4—118no—
277C4×C4⋊C4C2×D1118yescomplemented
278C2×#95—112no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95C2×D1112yes—
282C22×C11C22×C4⋊C414yes—
283C22×C11C4×#4114yes—
284C22×C11C4×#4114yes—
285C22×C11#52518yes—
286C22×C11#53318yes—
287C22×C11C24×C411yescharacteristic
288C22×C11C23×D411yescharacteristic
289C22×C11C23×Q811yescharacteristic
290C22×C11C22×#4112yes—
291C22×C11C22×#4112yes—
292C2×D11—24no—
293C2×D11—24no—
294C2×D11—28no—
295C2×D11—28no—
296C2×D11—232no—
297C2×D11C22×C4⋊C418yes—
298C4×C11—24no—
299C4×C11—24no—
300C4×C11—28no—
301C4×C11—44no—
302C4×C11C22×C4⋊C418yes—
303Dic11—24no—
304Dic11—24no—
305Dic11—28no—
306Dic11—44no—
307Dic11C22×C4⋊C418yes—
308C25—111no—
309C23×C4—111no—
310C23×C4—118no—
311C23×C4—118no—
312C23×C4—118no—
313C23×C4—114no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—112no—
317C23×C4—112no—
318C23×C4—118no—
319C23×C4—228no—
320C23×C4—228no—
321C23×C4—228no—
322C23×C4C22×D1112yes—
323C23×C4C22×D1111yescharacteristic
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1112yes—
326C23×C4C22×D1111yescharacteristic
327#117—1164no—
328#117—2232no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—118no—
331C2×C4⋊C4—118no—
332C2×C4⋊C4—114no—
333C2×C4⋊C4—114no—
334C2×C4⋊C4—118no—
335C2×C4⋊C4—118no—
336C2×C4⋊C4—118no—
337C2×C4⋊C4—118no—
338C2×C4⋊C4—228no—
339C2×C4⋊C4—228no—
340C2×C4⋊C4—228no—
341C2×C4⋊C4—228no—
342C2×C4⋊C4C22×D1118yes—
343C2×C22⋊C4—118no—
344C2×C22⋊C4—118no—
345C2×C22⋊C4—114no—
346C2×C22⋊C4—114no—
347C2×C22⋊C4—118no—
348C2×C22⋊C4—228no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—118no—
352C2×C42—114no—
353C2×C42—114no—
354C2×C42—114no—
355C2×C42—118no—
356C2×C42—2232no—
357C2×C42—228no—
358C2×C42—224no—
359C2×C42—224no—
360C2×C42C4×D1118yescomplemented
361C2×C42C22×D1114yes—
362C2×C42C22×D1114yes—
363C2×C42C22×D1114yes—
364#95—118no—
365#95—118no—
366#95—118no—
367#95C22×D1118yes—
368C2×C11#229618yescomplemented
369C2×C11C23×C4⋊C411yescharacteristic
370C2×C11C2×C4×#4111yescharacteristic
371C2×C11C2×C4×#4111yescharacteristic
372C2×C11C2×#52512yes—
373C2×C11C2×#53312yes—
374D11—28no—
375C24—114no—
376C24—114no—
377C24—114no—
378C24—112no—
379C24—224no—
380C24—224no—
381C24C23×D1111yescharacteristic
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—114no—
392C22×C4—112no—
393C22×C4—1164no—
394C22×C4—1116no—
395C22×C4—1116no—
396C22×C4—1116no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—118no—
400C22×C4—114no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—114no—
404C22×C4—2216no—
405C22×C4—2216no—
406C22×C4—2264no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—224no—
411C22×C4—2216no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4C2×C4×D1114yes—
416C22×C4C2×C4×D1114yes—
417C22×C4C2×C4×D1114yes—
418C22×C4#433918yes—
419C22×C4D4×D1114yes—
420C22×C4Q8×D1114yes—
421C22×C4C23×D1114yes—
422C22×C4C23×D1112yes—
423C22×C4C23×D1112yes—
424C22×C4C23×D1114yes—
425C22×C4C23×D1112yes—
426C4⋊C4—216no—
427C4⋊C4—1116no—
428C4⋊C4—1116no—
429C4⋊C4—2216no—
430C4⋊C4—2216no—
431C4⋊C4—2216no—
432C4⋊C4—2216no—
433C22⋊C4—1116no—
434C22⋊C4—1116no—
435C22⋊C4—2216no—
436C42—28no—
437C42—28no—
438C42—1116no—
439C42—2216no—
440C42—228no—
441C42—228no—
442C42C2×C4×D11116yescomplemented
443C11C2×#229611yescharacteristic, complemented, Sylow
444C23—1116no—
445C23—114no—
446C23—114no—
447C23—114no—
448C23—228no—
449C23—228no—
450C23—2216no—
451C23—2216no—
452C23—224no—
453C23—224no—
454C23C22×C4×D1112yes—
455C23C2×#433914yes—
456C23C2×D4×D1112yes—
457C23C2×Q8×D1112yes—
458C23#41×D1114yes—
459C23C24×D1111yescharacteristic
460C2×C4—28no—
461C2×C4—28no—
462C2×C4—216no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—48no—
471C2×C4—1116no—
472C2×C4—114no—
473C2×C4—114no—
474C2×C4—114no—
475C2×C4—1164no—
476C2×C4—114no—
477C2×C4—114no—
478C2×C4—118no—
479C2×C4—2264no—
480C2×C4—228no—
481C2×C4—228no—
482C2×C4—2216no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—448no—
491C2×C4C4⋊C4×D11116yes—
492C2×C4C22×C4×D1114yes—
493C2×C4C22×C4×D1114yes—
494C2×C4C22×C4×D1114yes—
495C2×C4C2×#433918yes—
496C2×C4C2×D4×D1114yes—
497C2×C4C2×Q8×D1114yes—
498C22—118no—
499C22—228no—
500C22—228no—
501C22—224no—
502C22—224no—
503C22—2232no—
504C22C4×#433914yes—
505C22C2×C4⋊C4×D1114yes—
506C22#1062305314yes—
507C22#1062307818yes—
508C22#1062310918yes—
509C22C23×C4×D1111yescharacteristic
510C22C22×#433912yes—
511C22C22×D4×D1111yescharacteristic
512C22C22×Q8×D1111yescharacteristic
513C22C2×#41×D1112yes—
514C4—28no—
515C4—24no—
516C4—24no—
517C4—44no—
518C4—118no—
519C4—228no—
520C4—224no—
521C4—224no—
522C4—444no—
523C4C2×C4⋊C4×D1118yes—
524C2—228no—
525C2#1307109618yesdirect product factor
526C2C22×C4⋊C4×D1111yescharacteristic
527C2C2×#1062305311yescharacteristic
528C2C2×C4×#433911yescharacteristic
529C2C2×#1062307812yes—
530C2C2×#1062310912yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2296
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #13071096C2direct (N × H)
5. C2×#10622260C2semidirect
6. C2×#10622585C2semidirect
9. C2×C4×Dic11⋊C4C2semidirect
10. C2×C4×Dic11⋊C4C2semidirect
11. C2×C4×C4⋊Dic11C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
33. C2×#66925C4semidirect
38. C4×C11×C4⋊C4C22semidirect
44. #10622585C22semidirect
45. C4×C4⋊Dic11C22semidirect
46. C4×Dic11⋊C4C22semidirect
47. C4×Dic11⋊C4C22semidirect
49. #10622260C22semidirect
73. C2×C42×C11C2×C4semidirect
88. C2×Dic11⋊C4C2×C4semidirect
89. C2×Dic11⋊C4C2×C4semidirect
98. C2×C4×Dic11C2×C4semidirect
104. #66925C2×C4semidirect
158. C2×C4×D11C4⋊C4semidirect
165. C42×C11C22×C4semidirect
173. Dic11⋊C4C22×C4semidirect
174. Dic11⋊C4C22×C4semidirect
178. C4×Dic11C22×C4semidirect
190. C2×C4×C4⋊C4D11semidirect
244. C4×D11C2×C4⋊C4semidirect
277. C4×C4⋊C4C2×D11semidirect
360. C2×C42C4×D11semidirect
368. C2×C11#2296semidirect
442. C42C2×C4×D11semidirect
443. C11C2×#2296semidirect
525. C2#13071096direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669252
C22×C42×D112
#130710962
C2×#106222602
C2×#106225852
C2×#106222812
C2×#106226022
C2×C4×Dic11⋊C42
C2×C4×C4⋊Dic112
C2×C4×C11×C4⋊C42
C2×#229611