Finite Group Databasebeta

← C2×#13071617 #14913286

Subgroups — C2×#13071617 #14913286

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic
3#13071617C2116yesmaximal, direct product factor
4C2×#10622843C211yesmaximal, characteristic, complemented
5C2×#10622541C211yesmaximal, characteristic, complemented
6C2×#10622585C212yesmaximal, complemented
7C2×#10622546C212yesmaximal, complemented
8C2×#10622602C212yesmaximal
9C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
11C2×C4×(C2×D11)⋊C4C212yesmaximal
12C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C2×C4×Q8×C11—28no—
17C2×C4×Q8×C11C2218yescomplemented
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2212yes—
21C22×C42×C11C2211yescharacteristic
22C2×#66999C4116yescomplemented
23C2×#66999C2218yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2212yes—
34C2×C4⋊C4×D11—28no—
35C2×C4⋊C4×D11C2218yes—
36#10622843C2218yescomplemented
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622602C22116yes—
44C4⋊C4×Dic11C2218yescomplemented
45#10622585C22116yescomplemented
46C4×(C2×D11)⋊C4C22116yes—
47C4×(C2×D11)⋊C4C2218yes—
48#10622546C22116yescomplemented
49#10622541C2218yescomplemented
50C24×D11C2311yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—24no—
53C22×Q8×C11C2×C418yescomplemented
54C22×Q8×C11C2314yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C22×C4×D11—24no—
66C22×C4×D11—24no—
67C22×C4×D11—28no—
68C22×C4×D11—28no—
69C22×C4×D11—44no—
70C22×C4×D11C2×C418yes—
71C22×C4×D11C2318yes—
72C22×C4×D11C2314yes—
73C4×Q8×C11—232no—
74C2×C11×C4⋊C4—28no—
75C2×C11×C4⋊C4D418yes—
76C2×C11×C4⋊C4C2318yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C42×C11—28no—
79C2×C42×C11—24no—
80C2×C42×C11C2314yes—
81C2×C42×C11C2318yes—
82#66999C2×C4164yescomplemented
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4C2×C4116yes—
85C2×(C2×D11)⋊C4Q818yescomplemented
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11C2×C418yescomplemented
91C2×C4⋊Dic11C2314yes—
92C2×C4⋊Dic11C2314yes—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4—44no—
95C2×Dic11⋊C4C2×C4116yescomplemented
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98C2×Dic11⋊C4C2318yes—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—44no—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2318yes—
103C4⋊C4×D11—232no—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2314yes—
109C11⋊#95C2318yes—
110C2×#2360—111nomaximal, Sylow
111C24×C11C2411yescharacteristic
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11C22×C414yes—
117C23×D11C2×Q814yes—
118C23×D11#4114yes—
119C23×D11C2412yes—
120C2×Q8×C11—232no—
121C2×Q8×C11—28no—
122C2×Q8×C11—28no—
123C2×Q8×C11C22×C4116yescomplemented
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C418yes—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C2×D418yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×Q814yes—
138C22×C4×C11#4114yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11C22×C414yes—
157C22×Dic11C22×C418yes—
158C22×Dic11C2×Q814yes—
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2414yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164C2×C4×D11—216no—
165C2×C4×D11—232no—
166C2×C4×D11—28no—
167C2×C4×D11—216no—
168C2×C4×D11—28no—
169C2×C4×D11—48no—
170C2×C4×D11—432no—
171C2×C4×D11C22×C4116yes—
172C11×C4⋊C4—216no—
173C11×C4⋊C4C2×D4116yes—
174C42×C11—216no—
175C42×C11—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4C22×C4132yes—
178(C2×D11)⋊C4C2×Q8116yescomplemented
179C4⋊Dic11—28no—
180C4⋊Dic11C22×C4116yescomplemented
181Dic11⋊C4—216no—
182Dic11⋊C4—48no—
183Dic11⋊C4C22×C4132yescomplemented
184C4×Dic11—28no—
185C4×Dic11—48no—
186C22×C22⋊Q8—111no—
187C22×C4×Q8D1111yescharacteristic, complemented
188C23×C4⋊C4—111no—
189#2360—1116no—
190C2×#391—111no—
191C2×#389—111no—
192C2×#389—112no—
193C2×#387—112no—
194C2×#385—112no—
195C2×C4×C4⋊C4—111no—
196C2×C4×C22⋊C4—112no—
197C2×C4×C22⋊C4—111no—
198C23×C11C23×C412yes—
199C23×C11C22×D412yes—
200C23×C11C22×Q812yes—
201C23×C11C2×#4112yes—
202C23×C11C2×#4112yes—
203C23×C11H(5,𝔽2)12yes—
204C23×C112−1+412yes—
205C23×C11C2511yescharacteristic
206C22×D11—28no—
207C22×D11—28no—
208C22×D11—28no—
209C22×D11—28no—
210C22×D11—28no—
211C22×D11—28no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11C4×Q8116yescomplemented
217C22×D11C23×C414yes—
218C22×D11C22×Q814yes—
219C22×D11C2×#4114yes—
220Q8×C11—232no—
221C2×C4×C11—216no—
222C2×C4×C11—216no—
223C2×C4×C11—28no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—44no—
234C2×C4×C11C4×D4116yes—
235C2×C4×C11C23×C418yes—
236C2×C4×C11C23×C414yes—
237C2×C4×C11C22×D418yes—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×Q814yes—
240C2×C4×C11C2×#4114yes—
241C2×Dic11—28no—
242C2×Dic11—216no—
243C2×Dic11—28no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—48no—
257C2×Dic11—44no—
258C2×Dic11C23×C414yes—
259C2×Dic11C23×C418yes—
260C2×Dic11C22×Q814yes—
261C4×D11—232no—
262C4×D11—432no—
263C23×Q8C2×D1111yescharacteristic
264C24×C4—111no—
265C24×C4—112no—
266C2×C22⋊Q8—118no—
267C2×C22⋊Q8—1116no—
268C2×C4×Q8—28no—
269C2×C4×Q8C2×D1118yescomplemented
270C22×C4⋊C4—112no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4—112no—
275C22×C4⋊C4—118no—
276C22×C4⋊C4—228no—
277C22×C4⋊C4C2×D1112yes—
278C22×C4⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4—112no—
280C22×C22⋊C4—111no—
281C22×C22⋊C4—111no—
282C22×C42—111no—
283C22×C42—112no—
284C22×C42C2×D1112yes—
285C22×C42C2×D1111yescharacteristic
286#391—118no—
287#389—1116no—
288#389—118no—
289#387—1116no—
290#385—1116no—
291C4×C4⋊C4—118no—
292C4×C22⋊C4—118no—
293C4×C22⋊C4—1116no—
294C2×#95—111no—
295C2×#95—112no—
296C2×#95—111no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C22×C11C2×C4×D414yes—
301C22×C11C2×C4×Q814yes—
302C22×C11#52014yes—
303C22×C11#54614yes—
304C22×C11D4×Q814yes—
305C22×C11#55214yes—
306C22×C11#55414yes—
307C22×C11C24×C411yescharacteristic
308C22×C11C23×D411yescharacteristic
309C22×C11C23×Q811yescharacteristic
310C22×C11C22×#4111yescharacteristic
311C22×C11C22×#4111yescharacteristic
312C22×C11C2×H(5,𝔽2)11yescharacteristic
313C22×C11C2×2−1+411yescharacteristic
314C2×D11—232no—
315C2×D11—24no—
316C2×D11—24no—
317C2×D11—24no—
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—24no—
321C2×D11C2×C4×Q818yescomplemented
322C4×C11—28no—
323C4×C11—28no—
324C4×C11—24no—
325C4×C11—42no—
326C4×C11C2×C4×D418yes—
327Dic11—24no—
328Dic11—28no—
329Dic11—24no—
330Dic11—44no—
331Dic11—42no—
332C25—111no—
333C22×Q8—24no—
334C22×Q8—24no—
335C22×Q8C4×D1118yescomplemented
336C22×Q8C22×D1114yes—
337C23×C4—112no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—118no—
341C23×C4—114no—
342C23×C4—111no—
343C23×C4—112no—
344C23×C4—118no—
345C23×C4—228no—
346C23×C4—224no—
347C23×C4—224no—
348C23×C4—228no—
349C23×C4—444no—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1112yes—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1112yes—
354C23×C4C22×D1111yescharacteristic
355C22⋊Q8—1164no—
356C4×Q8—232no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—1116no—
359C2×C4⋊C4—118no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—118no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—228no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—2232no—
368C2×C4⋊C4—444no—
369C2×C4⋊C4C22⋊D1118yes—
370C2×C4⋊C4C22×D1118yes—
371C2×C4⋊C4C22×D1114yes—
372C2×C22⋊C4—1116no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—224no—
378C2×C42—28no—
379C2×C42—24no—
380C2×C42—114no—
381C2×C42—118no—
382C2×C42—224no—
383C2×C42—444no—
384C2×C42C22×D1118yes—
385C2×C42C22×D1114yes—
386#95—114no—
387#95—118no—
388#95—114no—
389#95—118no—
390#95—118no—
391#95—118no—
392C2×C11#236018yescomplemented
393C2×C11C22×C4×D411yescharacteristic
394C2×C11C22×C4×Q811yescharacteristic
395C2×C11C2×#52011yescharacteristic
396C2×C11C2×#54611yescharacteristic
397C2×C11C2×D4×Q811yescharacteristic
398C2×C11C2×#55211yescharacteristic
399C2×C11C2×#55411yescharacteristic
400D11—28no—
401C24—114no—
402C24—114no—
403C24—114no—
404C24—112no—
405C24—222no—
406C24—222no—
407C24—222no—
408C24—222no—
409C24C23×D1111yescharacteristic
410C2×Q8—232no—
411C2×Q8—28no—
412C2×Q8—28no—
413C2×Q8C2×C4×D11116yescomplemented
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—118no—
424C22×C4—114no—
425C22×C4—114no—
426C22×C4—112no—
427C22×C4—114no—
428C22×C4—112no—
429C22×C4—1116no—
430C22×C4—112no—
431C22×C4—114no—
432C22×C4—2216no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—224no—
436C22×C4—222no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—2232no—
440C22×C4—228no—
441C22×C4—228no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—2216no—
449C22×C4—448no—
450C22×C4—4432no—
451C22×C4C2×C4×D1118yes—
452C22×C4C2×C4×D1114yes—
453C22×C4#433914yes—
454C22×C4Q8×D1114yes—
455C22×C4C2×C22⋊D1118yes—
456C22×C4C2×C22⋊D1114yes—
457C22×C4C23×D1112yes—
458C22×C4C23×D1114yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1114yes—
461C22×C4C23×D1112yes—
462C4⋊C4—216no—
463C4⋊C4—1132no—
464C4⋊C4—1116no—
465C4⋊C4—2216no—
466C4⋊C4—228no—
467C4⋊C4—448no—
468C4⋊C4C2×C22⋊D11116yes—
469C22⋊C4—1132no—
470C22⋊C4—1116no—
471C22⋊C4—228no—
472C42—216no—
473C42—28no—
474C42—228no—
475C42—448no—
476C11C2×#236011yescharacteristic, complemented, Sylow
477C23—1116no—
478C23—114no—
479C23—114no—
480C23—114no—
481C23—228no—
482C23—228no—
483C23—228no—
484C23—228no—
485C23—228no—
486C23—228no—
487C23—222no—
488C23—222no—
489C23—222no—
490C23—222no—
491C23C22×C4×D1112yes—
492C23C2×#433912yes—
493C23C2×Q8×D1112yes—
494C23#6704012yes—
495C23#41×D1112yes—
496C23#6704212yes—
497C23C22×C22⋊D1112yes—
498C23C24×D1111yescharacteristic
499Q8—232no—
500C2×C4—216no—
501C2×C4—28no—
502C2×C4—216no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—44no—
513C2×C4—118no—
514C2×C4—114no—
515C2×C4—114no—
516C2×C4—228no—
517C2×C4—2216no—
518C2×C4—228no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—222no—
525C2×C4—2232no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—4432no—
533C2×C4—448no—
534C2×C4—444no—
535C2×C4C4×C22⋊D11116yes—
536C2×C4C22×C4×D1118yes—
537C2×C4C22×C4×D1114yes—
538C2×C4C2×#433914yes—
539C2×C4C2×Q8×D1114yes—
540C2×C4C22×C22⋊D1118yes—
541C2×C4C22×C22⋊D1114yes—
542C22—118no—
543C22—2232no—
544C22—224no—
545C22—224no—
546C22—224no—
547C22—224no—
548C22—224no—
549C22—224no—
550C22C4×Q8×D1114yes—
551C22#1062310514yes—
552C22#1062311014yes—
553C22#1062311214yes—
554C22C2×C4×C22⋊D1114yes—
555C22Q8×C22⋊D1114yes—
556C22#1062336014yes—
557C22C23×C4×D1111yescharacteristic
558C22C22×#433911yescharacteristic
559C22C22×Q8×D1111yescharacteristic
560C22C2×#6704011yescharacteristic
561C22C2×#41×D1111yescharacteristic
562C22C2×#6704211yescharacteristic
563C22C23×C22⋊D1111yescharacteristic
564C4—28no—
565C4—28no—
566C4—24no—
567C4—42no—
568C4—224no—
569C4—224no—
570C4—228no—
571C4—442no—
572C4—444no—
573C4C2×C4×C22⋊D1118yes—
574C2—228no—
575C2#1307161718yesdirect product factor
576C2C22×C4×C22⋊D1111yescharacteristic
577C2C2×C4×Q8×D1111yescharacteristic
578C2C2×#1062310511yescharacteristic
579C2C2×#1062336011yescharacteristic
580C2C2×Q8×C22⋊D1111yescharacteristic
581C2C2×#1062311211yescharacteristic
582C2C2×#1062311011yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C4×Q8×C11C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC22×C4×Q8D11
hypocenterC11C2×#2360
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #13071617C2direct (N × H)
4. C2×#10622843C2semidirect
5. C2×#10622541C2semidirect
6. C2×#10622585C2semidirect
7. C2×#10622546C2semidirect
9. C2×C4⋊C4×Dic11C2semidirect
12. C22×C4×Q8×C11C2semidirect
17. C2×C4×Q8×C11C22semidirect
22. C2×#66999C4semidirect
36. #10622843C22semidirect
44. C4⋊C4×Dic11C22semidirect
45. #10622585C22semidirect
48. #10622546C22semidirect
49. #10622541C22semidirect
53. C22×Q8×C11C2×C4semidirect
82. #66999C2×C4semidirect
85. C2×(C2×D11)⋊C4Q8semidirect
90. C2×C4⋊Dic11C2×C4semidirect
95. C2×Dic11⋊C4C2×C4semidirect
123. C2×Q8×C11C22×C4semidirect
178. (C2×D11)⋊C4C2×Q8semidirect
180. C4⋊Dic11C22×C4semidirect
183. Dic11⋊C4C22×C4semidirect
187. C22×C4×Q8D11semidirect
216. C22×D11C4×Q8semidirect
269. C2×C4×Q8C2×D11semidirect
321. C2×D11C2×C4×Q8semidirect
335. C22×Q8C4×D11semidirect
392. C2×C11#2360semidirect
413. C2×Q8C2×C4×D11semidirect
476. C11C2×#2360semidirect
575. C2#13071617direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×C4⋊C4×D112
#130716172
C2×#106228432
C2×#106225412
C2×#106225852
C2×#106225462
C2×#106226022
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C22×C4×Q8×C112
C2×#236011