Finite Group Databasebeta

← C2×#13072379 #14921671

Subgroups — C2×#13072379 #14921671

Order 2816.

4110 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C22×#66939C212yesmaximal, complemented
3C22×D4×Dic11C211yesmaximal, characteristic, complemented
4#13072379C2116yesmaximal, direct product factor
5C2×#10622574C212yesmaximal, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622552C211yesmaximal, characteristic, complemented
8C2×#10622601C211yesmaximal, characteristic, complemented
9C2×#10622598C211yesmaximal, characteristic, complemented
10C2×#10622571C212yesmaximal, complemented
11C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#390C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C24×Dic11C2212yes—
17C23×D44C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C2×#66993—28no—
24C2×#66993C2218yes—
25C2×D4×Dic11—28no—
26C2×D4×Dic11C2218yescomplemented
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2212yes—
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×#66939—216no—
38C2×#66939C22116yescomplemented
39C11×#390C2218yescomplemented
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43#10622601C2218yescomplemented
44#10622598C2218yescomplemented
45#10622574C22116yescomplemented
46#10622574C22116yescomplemented
47#10622571C22116yescomplemented
48#10622552C2218yescomplemented
49C4×C4⋊Dic11C2218yescomplemented
50C25×C11C2312yes—
51C24×D11C2312yes—
52C22×D4×C11—24no—
53C22×D4×C11—24no—
54C22×D4×C11D418yes—
55C22×D4×C11C2314yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—28no—
61C22×C22⋊D11—28no—
62C22×C22⋊D11—28no—
63C22×C22⋊D11—28no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11C2318yes—
67C22×C22⋊D11C2318yes—
68C23×Dic11—28no—
69C23×Dic11—28no—
70C23×Dic11—44no—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C23×Dic11C2318yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C22×D44—24no—
78C22×D44—24no—
79C22×D44—24no—
80C22×D44C2314yes—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C22⋊C4—28no—
84C2×C11×C22⋊C4—44no—
85C2×C11×C22⋊C4C2318yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C42×C11—24no—
88C2×C42×C11C2314yes—
89C2×C22⋊Dic11—28no—
90C2×C22⋊Dic11C2318yes—
91#66993—232no—
92D4×Dic11—232no—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4—28no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4—44no—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×C4⋊Dic11—24no—
102C2×C4⋊Dic11—28no—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11D418yescomplemented
105C2×C4⋊Dic11C2318yes—
106C2×C4⋊Dic11C2314yes—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2314yes—
109C2×C4×Dic11—24no—
110C2×C4×Dic11—24no—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2314yes—
113#66939—264no—
114C11⋊#95C2314yes—
115C11⋊#95C2314yes—
116C11⋊#95C2318yes—
117C2×#2445—111nomaximal, Sylow
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11C2×D418yes—
125C24×C11C2414yes—
126C24×C11C2411yescharacteristic
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11—24no—
134C23×D11C2414yes—
135C2×D4×C11—232no—
136C2×D4×C11—28no—
137C2×D4×C11—28no—
138C2×D4×C11C2×D4116yes—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11#4114yes—
150C22×C4×C11#4114yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C2×C22⋊D11—216no—
156C2×C22⋊D11—216no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—432no—
162C2×C22⋊D11—432no—
163C22×Dic11—216no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—216no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—24no—
177C22×Dic11—48no—
178C22×Dic11—432no—
179C22×Dic11C2×D414yes—
180C22×Dic11C2×D414yes—
181C22×Dic11#4114yes—
182C22×Dic11C2412yes—
183C22×Dic11C2414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C22×Dic11C2412yes—
187C2×D44—28no—
188C2×D44—28no—
189C2×D44—28no—
190C2×D44—416no—
191C11×C4⋊C4—28no—
192C11×C22⋊C4—216no—
193C11×C22⋊C4—48no—
194C42×C11—28no—
195C22⋊Dic11—216no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—216no—
198(C2×D11)⋊C4—48no—
199(C2×D11)⋊C4—48no—
200C4⋊Dic11—216no—
201C4⋊Dic11—28no—
202C4⋊Dic11—28no—
203C4⋊Dic11C2×D4116yescomplemented
204C4×Dic11—28no—
205C4×Dic11—28no—
206C22×#127—111no—
207C22×#123—112no—
208C22×C4×D4—111no—
209#2445—1116no—
210C2×#394—112no—
211C2×#394—112no—
212C2×#390—111no—
213C2×#390—111no—
214C2×#390D1111yescharacteristic, complemented
215C2×#389—111no—
216C2×#386—112no—
217C2×C4×C4⋊C4—111no—
218C23×C11—216no—
219C23×C11—216no—
220C23×C11—216no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11—48no—
231C23×C11C22×D418yes—
232C23×C11C22×D412yes—
233C23×C11C22×D412yes—
234C23×C11C2×#4112yes—
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11H(5,𝔽2)12yes—
238C23×C11H(5,𝔽2)12yes—
239C23×C11C2511yescharacteristic
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—48no—
248C22×D11—48no—
249C22×D11—48no—
250C22×D11—48no—
251C22×D11—48no—
252C22×D11—48no—
253C22×D11—48no—
254D4×C11—232no—
255C2×C4×C11—28no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—44no—
265C2×C4×C11—48no—
266C2×C4×C11#123116yescomplemented
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D414yes—
269C2×C4×C11C2×#4114yes—
270C2×C4×C11C2×#4114yes—
271C22⋊D11—432no—
272C22⋊D11—432no—
273C2×Dic11—28no—
274C2×Dic11—28no—
275C2×Dic11—28no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—432no—
289C2×Dic11—48no—
290C2×Dic11—44no—
291C2×Dic11C22×D414yes—
292C2×Dic11C22×D414yes—
293C2×Dic11C2×#4114yes—
294D44—416no—
295C23×D4—112no—
296C23×D4—112no—
297C23×D4—111no—
298C23×D4C2×D1111yescharacteristic
299C24×C4—112no—
300C2×#127—118no—
301C2×#127—228no—
302C2×#123—1116no—
303C2×#123—2216no—
304C2×C4×D4—118no—
305C2×C4×D4—228no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—112no—
309C22×C4⋊C4—111no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4—112no—
312C22×C22⋊C4—112no—
313C22×C22⋊C4—112no—
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4C2×D1112yes—
317C22×C22⋊C4C2×D1112yes—
318C22×C42—111no—
319C22×C42—111no—
320C22×C42C2×D1111yescharacteristic
321#394—1116no—
322#394—1116no—
323#390—118no—
324#390—118no—
325#390C2×D1118yescomplemented
326#389—118no—
327#386—1116no—
328C4×C4⋊C4—118no—
329C2×#95—111no—
330C2×#95—112no—
331C2×#95—111no—
332C22×C11—28no—
333C22×C11—28no—
334C22×C11—28no—
335C22×C11—44no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—432no—
339C22×C11—44no—
340C22×C11C2×#12314yes—
341C22×C11#53214yes—
342C22×C11#54014yes—
343C22×C11D4214yes—
344C22×C11#54614yes—
345C22×C11#55014yes—
346C22×C11#55914yes—
347C22×C11C23×D411yescharacteristic
348C22×C11C23×D411yescharacteristic
349C22×C11C22×#4111yescharacteristic
350C22×C11C22×#4111yescharacteristic
351C22×C11C22×#4111yescharacteristic
352C22×C11C2×H(5,𝔽2)11yescharacteristic
353C22×C11C2×H(5,𝔽2)11yescharacteristic
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—44no—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—816no—
362C4×C11—24no—
363C4×C11—42no—
364C4×C11—44no—
365C4×C11C2×#12318yescomplemented
366Dic11—24no—
367Dic11—24no—
368Dic11—24no—
369Dic11—44no—
370Dic11—42no—
371C25—112no—
372C25C22×D1112yes—
373C22×D4—24no—
374C22×D4—24no—
375C22×D4—118no—
376C22×D4—118no—
377C22×D4—114no—
378C22×D4—228no—
379C22×D4—228no—
380C22×D4—228no—
381C22×D4—228no—
382C22×D4—224no—
383C22×D4—224no—
384C22×D4—224no—
385C22×D4—444no—
386C22×D4—444no—
387C22×D4D4418yes—
388C22×D4C22×D1114yes—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—112no—
394C23×C4—118no—
395C23×C4—228no—
396C23×C4—228no—
397C23×C4—444no—
398C23×C4C22×D1112yes—
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C23×C4C22×D1111yescharacteristic
402#127—2232no—
403#123—2264no—
404C4×D4—2232no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—118no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4—118no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4—228no—
412C2×C4⋊C4—224no—
413C2×C4⋊C4—224no—
414C2×C4⋊C4C22×D1114yes—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—118no—
419C2×C22⋊C4—118no—
420C2×C22⋊C4—118no—
421C2×C22⋊C4—118no—
422C2×C22⋊C4—228no—
423C2×C22⋊C4—228no—
424C2×C22⋊C4—228no—
425C2×C22⋊C4—444no—
426C2×C22⋊C4—444no—
427C2×C22⋊C4C22×D1118yes—
428C2×C22⋊C4C22×D1118yes—
429C2×C42—24no—
430C2×C42—114no—
431C2×C42—114no—
432C2×C42—224no—
433C2×C42—224no—
434C2×C42C22×D1114yes—
435#95—114no—
436#95—114no—
437#95—118no—
438C2×C11—48no—
439C2×C11#244518yescomplemented
440C2×C11C22×#12311yescharacteristic
441C2×C11C2×#53211yescharacteristic
442C2×C11C2×#54011yescharacteristic
443C2×C11C2×D4211yescharacteristic
444C2×C11C2×#54611yescharacteristic
445C2×C11C2×#55011yescharacteristic
446C2×C11C2×#55911yescharacteristic
447D11—84no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—114no—
455C24—224no—
456C24—224no—
457C24—224no—
458C24—224no—
459C24—224no—
460C24—224no—
461C24—224no—
462C24C2×D4418yes—
463C24C23×D1114yes—
464C24C23×D1111yescharacteristic
465C2×D4—232no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—2216no—
469C2×D4—2216no—
470C2×D4—2216no—
471C2×D4—2216no—
472C2×D4—228no—
473C2×D4—228no—
474C2×D4—228no—
475C2×D4—448no—
476C2×D4—448no—
477C2×D4—4432no—
478C2×D4—4432no—
479C2×D4—4416no—
480C2×D4C2×D44116yes—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—114no—
490C22×C4—114no—
491C22×C4—114no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—114no—
497C22×C4—2216no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—224no—
506C22×C4—2216no—
507C22×C4—224no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—224no—
511C22×C4—448no—
512C22×C4—4432no—
513C22×C4C2×D4414yes—
514C22×C4D4×D1114yes—
515C22×C4#434114yes—
516C22×C4#434114yes—
517C22×C4C23×D1112yes—
518C22×C4C23×D1114yes—
519C22×C4C23×D1112yes—
520C22×C4C23×D1112yes—
521C4⋊C4—28no—
522C4⋊C4—1116no—
523C4⋊C4—2216no—
524C4⋊C4—228no—
525C4⋊C4—228no—
526C22⋊C4—216no—
527C22⋊C4—48no—
528C22⋊C4—2216no—
529C22⋊C4—2216no—
530C22⋊C4—2216no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C42—28no—
534C42—228no—
535C42—228no—
536C11C2×#244511yescharacteristic, complemented, Sylow
537C23—216no—
538C23—216no—
539C23—216no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—48no—
547C23—48no—
548C23—48no—
549C23—48no—
550C23—224no—
551C23—224no—
552C23—224no—
553C23—224no—
554C23—224no—
555C23—224no—
556C23—224no—
557C23—448no—
558C23—448no—
559C23—448no—
560C23—448no—
561C23—448no—
562C23—448no—
563C23—448no—
564C23C22×D4418yes—
565C23C22×D4412yes—
566C23C2×D4×D1112yes—
567C23C2×#434112yes—
568C23C2×#434112yes—
569C23#6703712yes—
570C23#41×D1112yes—
571C23#6704212yes—
572C23C24×D1111yescharacteristic
573D4—232no—
574D4—4432no—
575D4—4432no—
576D4—4416no—
577C2×C4—28no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—48no—
587C2×C4—44no—
588C2×C4—114no—
589C2×C4—114no—
590C2×C4—114no—
591C2×C4—228no—
592C2×C4—228no—
593C2×C4—228no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—4432no—
607C2×C4—448no—
608C2×C4—444no—
609C2×C4#66939116yescomplemented
610C2×C4C22×D4414yes—
611C2×C4C2×D4×D1114yes—
612C2×C4C2×#434114yes—
613C2×C4C2×#434114yes—
614C22—28no—
615C22—28no—
616C22—28no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—432no—
622C22—444no—
623C22—444no—
624C22—444no—
625C22—444no—
626C22—444no—
627C22—444no—
628C22—444no—
629C22—8816no—
630C22C2×#6693914yes—
631C22D4×D4414yes—
632C22#1062308514yes—
633C22#1062312714yes—
634C22#1062315014yes—
635C22#1062321214yes—
636C22#1062324914yes—
637C22C23×D4411yescharacteristic
638C22C22×D4×D1111yescharacteristic
639C22C22×#434111yescharacteristic
640C22C22×#434111yescharacteristic
641C22C2×#6703711yescharacteristic
642C22C2×#41×D1111yescharacteristic
643C22C2×#6704211yescharacteristic
644C4—24no—
645C4—42no—
646C4—44no—
647C4—224no—
648C4—224no—
649C4—224no—
650C4—444no—
651C4—442no—
652C4C2×#6693918yescomplemented
653C2—48no—
654C2—884no—
655C2#1307237918yesdirect product factor
656C2C22×#6693911yescharacteristic
657C2C2×#1062312711yescharacteristic
658C2C2×#1062315011yescharacteristic
659C2C2×D4×D4411yescharacteristic
660C2C2×#1062308511yescharacteristic
661C2C2×#1062324911yescharacteristic
662C2C2×#1062321211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC22×#66993C2
hypercenterC2×#390D11
hypocenterC11C2×#2445
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×#66939C2semidirect
3. C22×D4×Dic11C2semidirect
4. #13072379C2direct (N × H)
5. C2×#10622574C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622552C2semidirect
8. C2×#10622601C2semidirect
9. C2×#10622598C2semidirect
10. C2×#10622571C2semidirect
11. C2×C4×C4⋊Dic11C2semidirect
12. C2×C11×#390C2semidirect
26. C2×D4×Dic11C22semidirect
38. C2×#66939C22semidirect
39. C11×#390C22semidirect
43. #10622601C22semidirect
44. #10622598C22semidirect
45. #10622574C22semidirect
46. #10622574C22semidirect
47. #10622571C22semidirect
48. #10622552C22semidirect
49. C4×C4⋊Dic11C22semidirect
104. C2×C4⋊Dic11D4semidirect
203. C4⋊Dic11C2×D4semidirect
214. C2×#390D11semidirect
266. C2×C4×C11#123semidirect
325. #390C2×D11semidirect
365. C4×C11C2×#123semidirect
439. C2×C11#2445semidirect
536. C11C2×#2445semidirect
609. C2×C4#66939semidirect
652. C4C2×#66939semidirect
655. C2#13072379direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
C22×#669392
C22×D4×Dic112
#130723792
C2×#106225742
C2×#106225522
C2×#106226012
C2×#106225982
C2×#106225712
C2×C4×C4⋊Dic112
C2×C11×#3902
C2×#244511