Finite Group Databasebeta

← C2×#13071685 #14913378

Subgroups — C2×#13071685 #14913378

Order 2816.

3678 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66928C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3C22×C4×D44C211yesmaximal, characteristic
4#13071685C2116yesmaximal, direct product factor
5C2×#10622542C211yesmaximal, characteristic, complemented
6C2×#10622552C211yesmaximal, characteristic
7C2×#10622603C212yesmaximal, complemented
8C2×#10622282C212yesmaximal, complemented
9C2×#10622602C212yesmaximal, complemented
10C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
11C2×#10622279C212yesmaximal, complemented
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2212yes—
31C2×#66928C4116yescomplemented
32C2×#66928C2218yes—
33C2×C4×D44—28no—
34C2×C4×D44C2218yes—
35C2×C4×Dic22—28no—
36C2×C4×Dic22C2218yescomplemented
37C4×C11×C4⋊C4C2218yescomplemented
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622603C22116yescomplemented
44#10622602C22116yescomplemented
45#10622552C2218yes—
46C4×C4⋊Dic11C2218yescomplemented
47#10622542C2218yescomplemented
48#10622282C22116yescomplemented
49#10622279C22116yescomplemented
50C24×D11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C22×D44—24no—
62C22×D44—24no—
63C22×D44C2×C418yes—
64C22×D44C2314yes—
65C22×C4×D11—28no—
66C22×C4×D11—28no—
67C22×C4×D11—44no—
68C22×C4×D11C2318yes—
69C22×Dic22—24no—
70C22×Dic22—24no—
71C22×Dic22C2×C418yescomplemented
72C22×Dic22C2314yes—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C42×C11—24no—
78C2×C42×C11—24no—
79C2×C42×C11C2×C418yescomplemented
80C2×C42×C11C2314yes—
81C2×C42×C11C2314yes—
82C2×C42×C11C2314yes—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4C2×C4116yescomplemented
87C2×(C2×D11)⋊C4C2×C4116yescomplemented
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11D418yes—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2314yes—
97C2×Dic11⋊C4—28no—
98C2×Dic11⋊C4C2318yes—
99C2×C4×Dic11—28no—
100C2×C4×Dic11—44no—
101C2×C4×Dic11C2318yes—
102C2×C4×Dic11C2318yes—
103#66928C2×C4164yescomplemented
104C4×D44—232no—
105C4×Dic22—232no—
106C11×#95C2314yes—
107C11×#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2367—111nomaximal, Sylow
112C24×C11C2411yescharacteristic
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11C22×C418yes—
120C23×D11C2414yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C22×C414yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11#4114yes—
140C22×C4×C11#4114yes—
141C22×C4×C11#4114yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11C22×C418yes—
157C22×Dic11C2×D418yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C2×D44—232no—
162C2×D44—28no—
163C2×D44—28no—
164C2×D44C22×C4116yes—
165C2×C4×D11—216no—
166C2×C4×D11—216no—
167C2×C4×D11—48no—
168C2×C4×D11—432no—
169C2×Dic22—232no—
170C2×Dic22—28no—
171C2×Dic22—28no—
172C2×Dic22C22×C4116yescomplemented
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175C42×C11—28no—
176C42×C11—28no—
177C42×C11C22×C4116yescomplemented
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—216no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4C22×C4132yescomplemented
182(C2×D11)⋊C4C22×C4132yescomplemented
183C4⋊Dic11—28no—
184C4⋊Dic11C2×D4116yes—
185Dic11⋊C4—216no—
186C4×Dic11—216no—
187C4×Dic11—48no—
188C22×#124—111no—
189C22×C4×Q8—111no—
190C22×C4×D4—111no—
191#2367—1116no—
192C2×#391—111no—
193C2×#390—111no—
194C2×#388—112no—
195C2×#388—112no—
196C2×#385—112no—
197C2×C4×C4⋊C4—111no—
198C2×C4×C4⋊C4D1111yescharacteristic, complemented
199C2×C4×C22⋊C4—112no—
200C23×C11C23×C412yes—
201C23×C11C22×D412yes—
202C23×C11C2×#4112yes—
203C23×C11C2×#4112yes—
204C23×C11C2×#4112yes—
205C23×C11H(5,𝔽2)12yes—
206C23×C112−1+412yes—
207C23×C11C2511yescharacteristic
208C22×D11—216no—
209C22×D11—216no—
210C22×D11—216no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—48no—
218C22×D11—48no—
219C22×D11—48no—
220C22×D11—48no—
221C22×D11C23×C418yes—
222C2×C4×C11—28no—
223C2×C4×C11—28no—
224C2×C4×C11—28no—
225C2×C4×C11—28no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11C4×D4116yes—
243C2×C4×C11C23×C414yes—
244C2×C4×C11C23×C414yes—
245C2×C4×C11C23×C414yes—
246C2×C4×C11C22×D414yes—
247C2×C4×C11C2×#4114yes—
248C2×C4×C11C2×#4114yes—
249C2×C4×C11C2×#4114yes—
250C2×Dic11—216no—
251C2×Dic11—216no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—48no—
260C2×Dic11C23×C418yes—
261C2×Dic11C22×D418yes—
262D44—232no—
263C4×D11—432no—
264Dic22—232no—
265C23×Q8—111no—
266C23×D4—111no—
267C24×C4—112no—
268C2×#124—118no—
269C2×#124—1116no—
270C2×C4×Q8—118no—
271C2×C4×Q8—228no—
272C2×C4×D4—118no—
273C2×C4×D4—228no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—112no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4C2×D1111yescharacteristic
278C22×C4⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C42—112no—
285C22×C42—112no—
286C22×C42C2×D1111yescharacteristic
287C22×C42C2×D1111yescharacteristic
288C22×C42C2×D1111yescharacteristic
289#391—118no—
290#390—118no—
291#388—1116no—
292#388—1116no—
293#385—1116no—
294C4×C4⋊C4—118no—
295C4×C4⋊C4C2×D1118yescomplemented
296C4×C22⋊C4—1116no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95C2×D1111yescharacteristic
301C2×#95C2×D1111yescharacteristic
302C22×C11C2×C4×D414yes—
303C22×C11C4×#4114yes—
304C22×C11#52014yes—
305C22×C11#54614yes—
306C22×C11#54814yes—
307C22×C11#55614yes—
308C22×C11#55914yes—
309C22×C11C24×C411yescharacteristic
310C22×C11C23×D411yescharacteristic
311C22×C11C22×#4111yescharacteristic
312C22×C11C22×#4111yescharacteristic
313C22×C11C22×#4111yescharacteristic
314C22×C11C2×H(5,𝔽2)11yescharacteristic
315C22×C11C2×2−1+411yescharacteristic
316C2×D11—28no—
317C2×D11—28no—
318C2×D11—28no—
319C2×D11—432no—
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—44no—
324C4×C11—24no—
325C4×C11—24no—
326C4×C11—24no—
327C4×C11—24no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11C2×C4×D418yes—
331Dic11—28no—
332Dic11—28no—
333Dic11—44no—
334C25—112no—
335C22×Q8—118no—
336C22×Q8—114no—
337C22×Q8—224no—
338C22×Q8—224no—
339C22×D4—118no—
340C22×D4—114no—
341C22×D4—224no—
342C22×D4—224no—
343C23×C4—112no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4—118no—
347C23×C4—228no—
348C23×C4—228no—
349C23×C4—444no—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1111yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357#124—1164no—
358C4×Q8—2232no—
359C4×D4—2232no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—228no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4C22×D1114yes—
369C2×C4⋊C4C22×D1114yes—
370C2×C22⋊C4—1116no—
371C2×C22⋊C4—1116no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—228no—
378C2×C22⋊C4—228no—
379C2×C22⋊C4—444no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—118no—
383C2×C42—118no—
384C2×C42—228no—
385C2×C42—444no—
386C2×C42C4×D1118yescomplemented
387C2×C42C22×D1114yes—
388C2×C42C22×D1114yes—
389C2×C42C22×D1114yes—
390#95—118no—
391#95—118no—
392#95—118no—
393#95C22×D1114yes—
394#95C22×D1114yes—
395C2×C11#236718yescomplemented
396C2×C11C22×C4×D411yescharacteristic
397C2×C11C2×C4×#4111yescharacteristic
398C2×C11C2×#52011yescharacteristic
399C2×C11C2×#54611yescharacteristic
400C2×C11C2×#54811yescharacteristic
401C2×C11C2×#55611yescharacteristic
402C2×C11C2×#55911yescharacteristic
403D11—48no—
404C24—118no—
405C24—114no—
406C24—224no—
407C24—224no—
408C24—224no—
409C24—224no—
410C24—224no—
411C24—224no—
412C24C23×D1111yescharacteristic
413C2×Q8—1116no—
414C2×Q8—2232no—
415C2×Q8—228no—
416C2×Q8—228no—
417C2×D4—1116no—
418C2×D4—2232no—
419C2×D4—228no—
420C2×D4—228no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—118no—
436C22×C4—118no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—114no—
440C22×C4—2216no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—2216no—
449C22×C4—448no—
450C22×C4—4432no—
451C22×C4C2×C4×D1114yes—
452C22×C4C2×C4×D1114yes—
453C22×C4C2×C4×D1114yes—
454C22×C4#433914yes—
455C22×C4#433914yes—
456C22×C4D4×D1114yes—
457C22×C4#434314yes—
458C22×C4C23×D1112yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1112yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C22×C4C23×D1112yes—
464C22×C4C23×D1112yes—
465C4⋊C4—28no—
466C4⋊C4—28no—
467C4⋊C4—1116no—
468C4⋊C4—2216no—
469C4⋊C4—228no—
470C22⋊C4—1132no—
471C22⋊C4—1132no—
472C22⋊C4—2216no—
473C22⋊C4—2216no—
474C22⋊C4—448no—
475C42—28no—
476C42—28no—
477C42—2216no—
478C42—448no—
479C42C2×C4×D11116yescomplemented
480C11C2×#236711yescharacteristic, complemented, Sylow
481C23—118no—
482C23—2216no—
483C23—2216no—
484C23—2216no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23—224no—
489C23—224no—
490C23—224no—
491C23—448no—
492C23—448no—
493C23—448no—
494C23—448no—
495C23C22×C4×D1112yes—
496C23C2×#433912yes—
497C23C2×#433912yes—
498C23C2×D4×D1112yes—
499C23C2×#434312yes—
500C23#6704212yes—
501C23#6704312yes—
502C23C24×D1111yescharacteristic
503Q8—2232no—
504D4—2232no—
505C2×C4—28no—
506C2×C4—28no—
507C2×C4—28no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—118no—
526C2×C4—118no—
527C2×C4—2216no—
528C2×C4—2216no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—4432no—
537C2×C4—448no—
538C2×C4#66946116yes—
539C2×C4C22×C4×D1114yes—
540C2×C4C22×C4×D1114yes—
541C2×C4C22×C4×D1114yes—
542C2×C4C2×#433914yes—
543C2×C4C2×#433914yes—
544C2×C4C2×D4×D1114yes—
545C2×C4C2×#434314yes—
546C22—228no—
547C22—228no—
548C22—228no—
549C22—444no—
550C22—4432no—
551C22—444no—
552C22—444no—
553C22—444no—
554C22C4×#433914yes—
555C22C2×#6694614yes—
556C22#1062305414yes—
557C22#1062308114yes—
558C22#1062308314yes—
559C22#1062311514yes—
560C22#1062311614yes—
561C22C23×C4×D1111yescharacteristic
562C22C22×#433911yescharacteristic
563C22C22×#433911yescharacteristic
564C22C22×D4×D1111yescharacteristic
565C22C22×#434311yescharacteristic
566C22C2×#6704211yescharacteristic
567C22C2×#6704311yescharacteristic
568C4—24no—
569C4—24no—
570C4—24no—
571C4—24no—
572C4—42no—
573C4—42no—
574C4—228no—
575C4—228no—
576C4—444no—
577C4C2×#6694618yes—
578C2—448no—
579C2#1307168518yesdirect product factor
580C2C22×#6694611yescharacteristic
581C2C2×C4×#433911yescharacteristic
582C2C2×#1062305411yescharacteristic
583C2C2×#1062308111yescharacteristic
584C2C2×#1062308311yescharacteristic
585C2C2×#1062311511yescharacteristic
586C2C2×#1062311611yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC23×D44C22
cosocleC23×C11C25
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2367
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
4. #13071685C2direct (N × H)
5. C2×#10622542C2semidirect
7. C2×#10622603C2semidirect
8. C2×#10622282C2semidirect
9. C2×#10622602C2semidirect
10. C2×C4×C4⋊Dic11C2semidirect
11. C2×#10622279C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
31. C2×#66928C4semidirect
36. C2×C4×Dic22C22semidirect
37. C4×C11×C4⋊C4C22semidirect
43. #10622603C22semidirect
44. #10622602C22semidirect
46. C4×C4⋊Dic11C22semidirect
47. #10622542C22semidirect
48. #10622282C22semidirect
49. #10622279C22semidirect
71. C22×Dic22C2×C4semidirect
79. C2×C42×C11C2×C4semidirect
86. C2×(C2×D11)⋊C4C2×C4semidirect
87. C2×(C2×D11)⋊C4C2×C4semidirect
103. #66928C2×C4semidirect
172. C2×Dic22C22×C4semidirect
177. C42×C11C22×C4semidirect
181. (C2×D11)⋊C4C22×C4semidirect
182. (C2×D11)⋊C4C22×C4semidirect
198. C2×C4×C4⋊C4D11semidirect
295. C4×C4⋊C4C2×D11semidirect
386. C2×C42C4×D11semidirect
395. C2×C11#2367semidirect
479. C42C2×C4×D11semidirect
480. C11C2×#2367semidirect
579. C2#13071685direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669282
C22×C4×Dic222
C22×C4×D442
#130716852
C2×#106225422
C2×#106225522
C2×#106226032
C2×#106222822
C2×#106226022
C2×C4×C4⋊Dic112
C2×#106222792
C2×C4×C11×C4⋊C42
C2×#236711