Finite Group Databasebeta

← C2×#13072176 #14922023

Subgroups — C2×#13072176 #14922023

Order 2816.

3678 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic, complemented
2C22×#66999C211yesmaximal, characteristic, complemented
3C22×#66948C211yesmaximal, characteristic
4#13072176C2116yesmaximal, direct product factor
5C2×#10622607C212yesmaximal, complemented
6C2×#10622604C212yesmaximal, complemented
7C2×#10622552C211yesmaximal, characteristic, complemented
8C2×#10622552C212yesmaximal, complemented
9C2×#10622598C211yesmaximal, characteristic, complemented
10C2×#10622553C212yesmaximal, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C23×D44C2212yes—
16C23×C4×D11C2211yescharacteristic
17C2×C4×Q8×C11—28no—
18C2×C4×Q8×C11C2218yescomplemented
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C42×C11C2212yes—
23C2×#67000—28no—
24C2×#67000C2218yescomplemented
25C2×#66999—28no—
26C2×#66999C2218yescomplemented
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2212yes—
33C22×(C2×D11)⋊C4C2212yes—
34C22×(C2×D11)⋊C4C2212yes—
35C22×C4⋊Dic11C2211yescharacteristic
36C22×C4⋊Dic11C2212yes—
37C22×Dic11⋊C4C2212yes—
38C22×C4×Dic11C2211yescharacteristic
39C2×#66948—28no—
40C2×#66948C2218yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2212yes—
44#10622607C22116yescomplemented
45#10622604C22116yescomplemented
46#10622598C2218yescomplemented
47#10622553C22116yescomplemented
48#10622552C2218yescomplemented
49#10622552C22116yescomplemented
50C4×(C2×D11)⋊C4C2218yescomplemented
51C24×D11C2312yes—
52C24×D11C2311yescharacteristic
53C22×Q8×C11—24no—
54C22×Q8×C11—24no—
55C22×Q8×C11D418yescomplemented
56C22×Q8×C11C2314yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C22×D44—28no—
67C22×D44—28no—
68C22×D44—24no—
69C22×D44—24no—
70C22×D44—24no—
71C22×D44—44no—
72C22×D44C2314yes—
73C22×D44C2318yes—
74C22×C4×D11—24no—
75C22×C4×D11—24no—
76C22×C4×D11—24no—
77C22×C4×D11C2314yes—
78C4×Q8×C11—232no—
79C2×C11×C4⋊C4—28no—
80C2×C11×C4⋊C4D418yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C42×C11—28no—
84C2×C42×C11—24no—
85C2×C42×C11C2314yes—
86C2×C42×C11C2318yes—
87#67000—232no—
88#66999—232no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—28no—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4—44no—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×(C2×D11)⋊C4C2318yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×C4⋊Dic11—24no—
106C2×C4⋊Dic11—44no—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2318yes—
109C2×Dic11⋊C4—28no—
110C2×Dic11⋊C4C2318yes—
111C2×C4×Dic11—24no—
112C2×C4×Dic11C2314yes—
113#66948—232no—
114C11⋊#95C2314yes—
115C11⋊#95C2314yes—
116C11⋊#95C2318yes—
117C2×#2426—111nomaximal, Sylow
118C24×C11C2411yescharacteristic
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11#4114yes—
133C23×D11C2414yes—
134C23×D11C2412yes—
135C2×Q8×C11—232no—
136C2×Q8×C11—28no—
137C2×Q8×C11—28no—
138C2×Q8×C11C2×D4116yescomplemented
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11C2×D418yes—
149C22×C4×C11C2×D418yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11#4114yes—
153C22×C4×C11#4114yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—24no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—24no—
170C22×Dic11—22no—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C22×Dic11C2412yes—
174C22×Dic11C2414yes—
175C2×D44—216no—
176C2×D44—216no—
177C2×D44—28no—
178C2×D44—28no—
179C2×D44—28no—
180C2×D44—48no—
181C2×D44—432no—
182C2×D44—416no—
183C2×C4×D11—28no—
184C2×C4×D11—28no—
185C2×C4×D11—28no—
186C2×C4×D11—416no—
187C11×C4⋊C4—216no—
188C11×C4⋊C4C2×D4116yes—
189C42×C11—216no—
190C42×C11—28no—
191(C2×D11)⋊C4—28no—
192(C2×D11)⋊C4—216no—
193(C2×D11)⋊C4—216no—
194(C2×D11)⋊C4—216no—
195(C2×D11)⋊C4—216no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—216no—
198(C2×D11)⋊C4—48no—
199C4⋊Dic11—28no—
200C4⋊Dic11—48no—
201Dic11⋊C4—216no—
202C4×Dic11—28no—
203C22×#124—111no—
204C22×C22⋊Q8—111no—
205C22×#121—111no—
206C22×C4×Q8D1111yescharacteristic, complemented
207#2426—1116no—
208C2×#396—112no—
209C2×#394—112no—
210C2×#390—112no—
211C2×#390—111no—
212C2×#389—111no—
213C2×#388—112no—
214C2×C4×C22⋊C4—111no—
215C23×C11C22×D412yes—
216C23×C11C22×D412yes—
217C23×C11C2×#4112yes—
218C23×C11C2×#4112yes—
219C23×C11C2×#4112yes—
220C23×C11H(5,𝔽2)12yes—
221C23×C112−1+412yes—
222C23×C11C2511yescharacteristic
223C22×D11—28no—
224C22×D11—28no—
225C22×D11—28no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—44no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11—48no—
247C22×D11—48no—
248C22×D11—48no—
249C22×D11—48no—
250C22×D11C2×#4114yes—
251Q8×C11—232no—
252C2×C4×C11—216no—
253C2×C4×C11—216no—
254C2×C4×C11—28no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—44no—
265C2×C4×C11#121116yes—
266C2×C4×C11C22×D418yes—
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D418yes—
269C2×C4×C11C22×D414yes—
270C2×C4×C11C2×#4114yes—
271C2×C4×C11C2×#4114yes—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—22no—
284C2×Dic11—44no—
285C2×Dic11—44no—
286C2×Dic11—44no—
287C2×Dic11—48no—
288D44—432no—
289D44—416no—
290C4×D11—416no—
291C23×Q8C2×D1111yescharacteristic
292C23×D4—111no—
293C23×D4—112no—
294C24×C4—111no—
295C2×#124—118no—
296C2×#124—228no—
297C2×C22⋊Q8—118no—
298C2×C22⋊Q8—228no—
299C2×#121—118no—
300C2×#121—228no—
301C2×C4×Q8—28no—
302C2×C4×Q8C2×D1118yescomplemented
303C22×C4⋊C4—112no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—112no—
306C22×C4⋊C4C2×D1112yes—
307C22×C4⋊C4C2×D1111yescharacteristic
308C22×C22⋊C4—111no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4—112no—
313C22×C22⋊C4—111no—
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C42—111no—
317C22×C42C2×D1111yescharacteristic
318C22×C42C2×D1112yes—
319#396—1116no—
320#394—1116no—
321#390—118no—
322#390—1116no—
323#389—118no—
324#388—1116no—
325C4×C22⋊C4—118no—
326C2×#95—112no—
327C2×#95—111no—
328C2×#95—111no—
329C22×C11C2×#12114yes—
330C22×C11#52914yes—
331C22×C11#54214yes—
332C22×C11#54614yes—
333C22×C11#54814yes—
334C22×C11#54814yes—
335C22×C11#55014yes—
336C22×C11C23×D411yescharacteristic
337C22×C11C23×D411yescharacteristic
338C22×C11C22×#4111yescharacteristic
339C22×C11C22×#4111yescharacteristic
340C22×C11C22×#4111yescharacteristic
341C22×C11C2×H(5,𝔽2)11yescharacteristic
342C22×C11C2×2−1+411yescharacteristic
343C2×D11—24no—
344C2×D11—24no—
345C2×D11—24no—
346C2×D11—42no—
347C2×D11—416no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—816no—
359C4×C11—28no—
360C4×C11—28no—
361C4×C11—24no—
362C4×C11—42no—
363C4×C11C2×#12118yes—
364Dic11—42no—
365Dic11—42no—
366Dic11—42no—
367Dic11—44no—
368C25—111no—
369C25—112no—
370C22×Q8—24no—
371C22×Q8—24no—
372C22×Q8D4418yescomplemented
373C22×Q8C22×D1114yes—
374C22×D4—114no—
375C22×D4—118no—
376C22×D4—228no—
377C22×D4—224no—
378C22×D4—224no—
379C22×D4—228no—
380C22×D4—224no—
381C22×D4—444no—
382C23×C4—112no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—114no—
387C23×C4—224no—
388C23×C4—224no—
389C23×C4—224no—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1112yes—
392C23×C4C22×D1111yescharacteristic
393C23×C4C22×D1112yes—
394C23×C4C22×D1111yescharacteristic
395#124—2232no—
396C22⋊Q8—2232no—
397#121—2232no—
398C4×Q8—232no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—118no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—118no—
403C2×C4⋊C4—228no—
404C2×C4⋊C4—224no—
405C2×C4⋊C4—444no—
406C2×C4⋊C4C22⋊D1118yes—
407C2×C4⋊C4C22×D1118yes—
408C2×C4⋊C4C22×D1114yes—
409C2×C22⋊C4—118no—
410C2×C22⋊C4—118no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—224no—
418C2×C22⋊C4—228no—
419C2×C22⋊C4—228no—
420C2×C22⋊C4—228no—
421C2×C22⋊C4—224no—
422C2×C22⋊C4—228no—
423C2×C22⋊C4—228no—
424C2×C22⋊C4—444no—
425C2×C42—28no—
426C2×C42—24no—
427C2×C42—114no—
428C2×C42—224no—
429C2×C42C22×D1114yes—
430C2×C42C22×D1118yes—
431#95—114no—
432#95—114no—
433#95—118no—
434C2×C11#242618yescomplemented
435C2×C11C22×#12111yescharacteristic
436C2×C11C2×#52911yescharacteristic
437C2×C11C2×#54211yescharacteristic
438C2×C11C2×#54611yescharacteristic
439C2×C11C2×#54811yescharacteristic
440C2×C11C2×#54811yescharacteristic
441C2×C11C2×#55011yescharacteristic
442D11—44no—
443D11—84no—
444C24—114no—
445C24—112no—
446C24—114no—
447C24—222no—
448C24—222no—
449C24—222no—
450C24—222no—
451C24—222no—
452C24—222no—
453C24—224no—
454C24—224no—
455C24—224no—
456C24—224no—
457C24—224no—
458C24—224no—
459C24—224no—
460C24C23×D1111yescharacteristic
461C2×Q8—232no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8C2×D44116yescomplemented
465C2×D4—2216no—
466C2×D4—228no—
467C2×D4—228no—
468C2×D4—2216no—
469C2×D4—228no—
470C2×D4—448no—
471C2×D4—4432no—
472C2×D4—4416no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—224no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—224no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—224no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—228no—
499C22×C4—228no—
500C22×C4—228no—
501C22×C4—4416no—
502C22×C4C2×D4418yes—
503C22×C4C2×D4414yes—
504C22×C4#433914yes—
505C22×C4#434314yes—
506C22×C4C2×C22⋊D1118yes—
507C22×C4C2×C22⋊D1114yes—
508C22×C4C23×D1112yes—
509C22×C4C23×D1114yes—
510C22×C4C23×D1112yes—
511C22×C4C23×D1114yes—
512C22×C4C23×D1112yes—
513C4⋊C4—216no—
514C4⋊C4—2216no—
515C4⋊C4—228no—
516C4⋊C4—448no—
517C4⋊C4C2×C22⋊D11116yes—
518C22⋊C4—228no—
519C22⋊C4—2216no—
520C22⋊C4—2216no—
521C22⋊C4—2216no—
522C22⋊C4—228no—
523C22⋊C4—2216no—
524C22⋊C4—2216no—
525C22⋊C4—448no—
526C42—216no—
527C42—28no—
528C42—228no—
529C11C2×#242611yescharacteristic, complemented, Sylow
530C23—114no—
531C23—228no—
532C23—228no—
533C23—228no—
534C23—222no—
535C23—222no—
536C23—222no—
537C23—222no—
538C23—222no—
539C23—222no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—224no—
544C23—224no—
545C23—224no—
546C23—224no—
547C23—444no—
548C23—444no—
549C23—444no—
550C23—444no—
551C23—448no—
552C23—448no—
553C23—448no—
554C23—448no—
555C23—448no—
556C23—448no—
557C23—448no—
558C23C22×D4412yes—
559C23C2×#433912yes—
560C23C2×#434312yes—
561C23#6704012yes—
562C23#41×D1112yes—
563C23#6704212yes—
564C23C22×C22⋊D1112yes—
565C23C24×D1111yescharacteristic
566Q8—232no—
567D4—4432no—
568D4—4416no—
569C2×C4—216no—
570C2×C4—28no—
571C2×C4—216no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—44no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—224no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—224no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—444no—
595C2×C4—444no—
596C2×C4—444no—
597C2×C4—448no—
598C2×C4—4416no—
599C2×C4#66983116yes—
600C2×C4C22×D4418yes—
601C2×C4C22×D4414yes—
602C2×C4C2×#433914yes—
603C2×C4C2×#434314yes—
604C2×C4C22×C22⋊D1118yes—
605C2×C4C22×C22⋊D1114yes—
606C22—224no—
607C22—224no—
608C22—224no—
609C22—4416no—
610C22—442no—
611C22—442no—
612C22—442no—
613C22—442no—
614C22—444no—
615C22—444no—
616C22—444no—
617C22—444no—
618C22—444no—
619C22—444no—
620C22—444no—
621C22—8816no—
622C22#1062310714yes—
623C22#1062310814yes—
624C22#1062311114yes—
625C22#1062311314yes—
626C22C2×#6698314yes—
627C22#1062334814yes—
628C22#1062336014yes—
629C22C23×D4411yescharacteristic
630C22C22×#433911yescharacteristic
631C22C22×#434311yescharacteristic
632C22C2×#6704011yescharacteristic
633C22C2×#41×D1111yescharacteristic
634C22C2×#6704211yescharacteristic
635C22C23×C22⋊D1111yescharacteristic
636C4—28no—
637C4—24no—
638C4—28no—
639C4—42no—
640C4—442no—
641C4—442no—
642C4—442no—
643C4—444no—
644C4C2×#6698318yes—
645C2—444no—
646C2—884no—
647C2#1307217618yesdirect product factor
648C2C22×#6698311yescharacteristic
649C2C2×#1062311111yescharacteristic
650C2C2×#1062311311yescharacteristic
651C2C2×#1062336011yescharacteristic
652C2C2×#1062334811yescharacteristic
653C2C2×#1062310711yescharacteristic
654C2C2×#1062310811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×Q8×C11C2
socleC24×C11C24
prime radicalC22×#66948C2
hypercenterC22×C4×Q8D11
hypocenterC11C2×#2426
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×#66999C2semidirect
4. #13072176C2direct (N × H)
5. C2×#10622607C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622552C2semidirect
8. C2×#10622552C2semidirect
9. C2×#10622598C2semidirect
10. C2×#10622553C2semidirect
11. C2×C4×(C2×D11)⋊C4C2semidirect
12. C22×C4×Q8×C11C2semidirect
18. C2×C4×Q8×C11C22semidirect
24. C2×#67000C22semidirect
26. C2×#66999C22semidirect
44. #10622607C22semidirect
45. #10622604C22semidirect
46. #10622598C22semidirect
47. #10622553C22semidirect
48. #10622552C22semidirect
49. #10622552C22semidirect
50. C4×(C2×D11)⋊C4C22semidirect
55. C22×Q8×C11D4semidirect
138. C2×Q8×C11C2×D4semidirect
206. C22×C4×Q8D11semidirect
302. C2×C4×Q8C2×D11semidirect
372. C22×Q8D44semidirect
434. C2×C11#2426semidirect
464. C2×Q8C2×D44semidirect
529. C11C2×#2426semidirect
647. C2#13072176direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×#669992
C22×#669482
#130721762
C2×#106226072
C2×#106226042
C2×#106225522
C2×#106225982
C2×#106225532
C2×C4×(C2×D11)⋊C42
C22×C4×Q8×C112
C2×#242611