Finite Group Databasebeta

← C2×#13074410 #14920803

Subgroups — C2×#13074410 #14920803

Order 2816.

3110 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic
2C22×#66925C211yesmaximal, characteristic, complemented
3#13074410C2116yesmaximal, direct product factor
4C2×#10622605C212yesmaximal, complemented
5C2×#10622288C212yesmaximal, complemented
6C2×#10622285C212yesmaximal, complemented
7C2×#10622604C212yesmaximal, complemented
8C2×#10622552C211yesmaximal, characteristic, complemented
9C2×#10622601C211yesmaximal, characteristic, complemented
10C2×#10622586C211yesmaximal, characteristic, complemented
11C2×#10622600C211yesmaximal, characteristic, complemented
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×D44C2212yes—
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×#66948—28no—
34C2×#66948C2218yes—
35C2×#66925—28no—
36C2×#66925C2218yescomplemented
37C11×#389C2218yescomplemented
38C2×C11×#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622605C22116yescomplemented
42#10622604C22116yescomplemented
43#10622601C2218yescomplemented
44#10622600C2218yescomplemented
45#10622586C2218yescomplemented
46#10622552C2218yescomplemented
47#10622288C22116yescomplemented
48#10622285C22116yescomplemented
49C24×D11C2312yes—
50C24×D11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×D44—28no—
61C22×D44—24no—
62C22×D44—24no—
63C22×D44—24no—
64C22×D44—44no—
65C22×D44—44no—
66C22×D44C2314yes—
67C22×D44C2318yes—
68C22×C4×D11—24no—
69C22×C4×D11—24no—
70C22×C4×D11D418yes—
71C22×C4×D11C2314yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2318yes—
78C2×C42×C11—24no—
79C2×C42×C11C2314yes—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—44no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11C2314yes—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4—44no—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2318yes—
104C2×C4×Dic11—24no—
105C2×C4×Dic11C2314yes—
106#66948—232no—
107#66925—232no—
108C11×#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2624—111nomaximal, Sylow
112C24×C11C2411yescharacteristic
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11C2×D414yes—
127C23×D11C2414yes—
128C23×D11C2412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11C2×D414yes—
142C22×C4×C11#4114yes—
143C22×C4×C11#4114yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2414yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11C2×D414yes—
161C22×Dic11C2412yes—
162C22×Dic11C2414yes—
163C22×Dic11C2412yes—
164C22×Dic11C2412yes—
165C2×D44—216no—
166C2×D44—28no—
167C2×D44—28no—
168C2×D44—28no—
169C2×D44—48no—
170C2×D44—48no—
171C2×D44—432no—
172C2×D44—416no—
173C2×C4×D11—232no—
174C2×C4×D11—28no—
175C2×C4×D11—28no—
176C2×C4×D11C2×D4116yes—
177C11×C4⋊C4—28no—
178C11×C4⋊C4—28no—
179C11×C4⋊C4—48no—
180C42×C11—28no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—48no—
185(C2×D11)⋊C4—48no—
186(C2×D11)⋊C4—48no—
187(C2×D11)⋊C4—48no—
188(C2×D11)⋊C4—48no—
189C4⋊Dic11—28no—
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192Dic11⋊C4—48no—
193C4×Dic11—28no—
194C22×#121—111no—
195C22×#117—111no—
196#2624—1116no—
197C2×#399—112no—
198C2×#397—112no—
199C2×#394—112no—
200C2×#394—112no—
201C2×#390—111no—
202C2×#390—111no—
203C2×#389—111no—
204C2×#389D1111yescharacteristic, complemented
205C2×#380—111no—
206C23×C11C22×D412yes—
207C23×C11C2×#4112yes—
208C23×C11C2×#4112yes—
209C23×C11H(5,𝔽2)12yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C11H(5,𝔽2)12yes—
212C23×C112−1+412yes—
213C23×C11C2511yescharacteristic
214C22×D11—28no—
215C22×D11—28no—
216C22×D11—28no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—44no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—48no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11C22×D414yes—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—48no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—48no—
258C2×C4×C11#123116yes—
259C2×C4×C11C22×D414yes—
260C2×C4×C11C2×#4114yes—
261C2×C4×C11C2×#4114yes—
262C2×Dic11—28no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276C2×Dic11—48no—
277C2×Dic11C22×D414yes—
278D44—432no—
279D44—416no—
280C4×D11—232no—
281C23×D4—111no—
282C23×D4—112no—
283C24×C4—111no—
284C2×#121—118no—
285C2×#121—228no—
286C2×#117—118no—
287C2×#117—228no—
288C22×C4⋊C4—111no—
289C22×C4⋊C4—111no—
290C22×C4⋊C4—111no—
291C22×C4⋊C4—112no—
292C22×C4⋊C4C2×D1111yescharacteristic
293C22×C4⋊C4C2×D1111yescharacteristic
294C22×C4⋊C4C2×D1112yes—
295C22×C22⋊C4—111no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4—112no—
302C22×C22⋊C4—112no—
303C22×C42—111no—
304C22×C42C2×D1111yescharacteristic
305#399—1116no—
306#397—1116no—
307#394—1116no—
308#394—1116no—
309#390—118no—
310#390—118no—
311#389—118no—
312#389C2×D1118yescomplemented
313#380—118no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95C2×D1112yes—
317C22×C11C2×#12314yes—
318C22×C11#53514yes—
319C22×C11#53714yes—
320C22×C11#54014yes—
321C22×C11#54014yes—
322C22×C11#54214yes—
323C22×C11#54214yes—
324C22×C11C23×D411yescharacteristic
325C22×C11C22×#4111yescharacteristic
326C22×C11C22×#4111yescharacteristic
327C22×C11C2×H(5,𝔽2)11yescharacteristic
328C22×C11C2×H(5,𝔽2)11yescharacteristic
329C22×C11C2×H(5,𝔽2)11yescharacteristic
330C22×C11C2×2−1+411yescharacteristic
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—24no—
334C2×D11—416no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—816no—
347C4×C11—42no—
348C4×C11—44no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11C2×#12318yes—
352Dic11—24no—
353Dic11—42no—
354Dic11—42no—
355Dic11—44no—
356C25—111no—
357C25—112no—
358C22×D4—114no—
359C22×D4—118no—
360C22×D4—228no—
361C22×D4—224no—
362C22×D4—224no—
363C22×D4—224no—
364C22×D4—444no—
365C22×D4—444no—
366C23×C4—111no—
367C23×C4—118no—
368C23×C4—114no—
369C23×C4—111no—
370C23×C4—112no—
371C23×C4—111no—
372C23×C4—224no—
373C23×C4—224no—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1112yes—
377C23×C4C22×D1112yes—
378C23×C4C22×D1111yescharacteristic
379#121—2232no—
380#117—2232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—118no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4—224no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4—444no—
392C2×C4⋊C4C22×D1114yes—
393C2×C4⋊C4C22×D1114yes—
394C2×C4⋊C4C22×D1118yes—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—228no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4—444no—
410C2×C22⋊C4—444no—
411C2×C42—24no—
412C2×C42—114no—
413C2×C42—224no—
414C2×C42C22×D1114yes—
415#95—118no—
416#95—118no—
417#95C22×D1118yes—
418C2×C11#262418yescomplemented
419C2×C11C22×#12311yescharacteristic
420C2×C11C2×#53511yescharacteristic
421C2×C11C2×#53711yescharacteristic
422C2×C11C2×#54011yescharacteristic
423C2×C11C2×#54011yescharacteristic
424C2×C11C2×#54211yescharacteristic
425C2×C11C2×#54211yescharacteristic
426D11—44no—
427D11—84no—
428C24—114no—
429C24—112no—
430C24—114no—
431C24—222no—
432C24—222no—
433C24—222no—
434C24—222no—
435C24—222no—
436C24—222no—
437C24—224no—
438C24—224no—
439C24—224no—
440C24—224no—
441C24—224no—
442C24—224no—
443C24—224no—
444C24C23×D1111yescharacteristic
445C2×D4—2216no—
446C2×D4—228no—
447C2×D4—228no—
448C2×D4—228no—
449C2×D4—448no—
450C2×D4—448no—
451C2×D4—4432no—
452C2×D4—4416no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—114no—
466C22×C4—112no—
467C22×C4—1116no—
468C22×C4—112no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—2232no—
474C22×C4—228no—
475C22×C4—228no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—222no—
485C22×C4#433914yes—
486C22×C4D4×D1114yes—
487C22×C4#434314yes—
488C22×C4C23×D1114yes—
489C22×C4C23×D1114yes—
490C22×C4C23×D1112yes—
491C22×C4C23×D1112yes—
492C22×C4C23×D1112yes—
493C4⋊C4—28no—
494C4⋊C4—28no—
495C4⋊C4—48no—
496C4⋊C4—228no—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—448no—
500C22⋊C4—2216no—
501C22⋊C4—228no—
502C22⋊C4—228no—
503C22⋊C4—448no—
504C22⋊C4—448no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C42—28no—
509C42—228no—
510C11C2×#262411yescharacteristic, complemented, Sylow
511C23—114no—
512C23—228no—
513C23—228no—
514C23—228no—
515C23—222no—
516C23—222no—
517C23—222no—
518C23—222no—
519C23—222no—
520C23—222no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—444no—
529C23—444no—
530C23—444no—
531C23—444no—
532C23—448no—
533C23—448no—
534C23—448no—
535C23—448no—
536C23—448no—
537C23—448no—
538C23—448no—
539C23C2×#433912yes—
540C23C2×D4×D1112yes—
541C23#6703712yes—
542C23C2×#434312yes—
543C23#6704012yes—
544C23#6704212yes—
545C23#6704212yes—
546C23C24×D1111yescharacteristic
547D4—4432no—
548D4—4416no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—48no—
562C2×C4—44no—
563C2×C4—48no—
564C2×C4—44no—
565C2×C4—114no—
566C2×C4—228no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—2232no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—222no—
579C2×C4—444no—
580C2×C4—444no—
581C2×C4—448no—
582C2×C4#66947116yes—
583C2×C4C2×#433914yes—
584C2×C4C2×D4×D1114yes—
585C2×C4C2×#434314yes—
586C22—224no—
587C22—224no—
588C22—224no—
589C22—442no—
590C22—442no—
591C22—442no—
592C22—442no—
593C22—4416no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—444no—
598C22—444no—
599C22—444no—
600C22—444no—
601C22—8816no—
602C22C2×#6694714yes—
603C22#1062309314yes—
604C22#1062311314yes—
605C22#1062313814yes—
606C22#1062316014yes—
607C22#1062322914yes—
608C22#1062326414yes—
609C22C22×#433911yescharacteristic
610C22C22×D4×D1111yescharacteristic
611C22C2×#6703711yescharacteristic
612C22C22×#434311yescharacteristic
613C22C2×#6704011yescharacteristic
614C22C2×#6704211yescharacteristic
615C22C2×#6704211yescharacteristic
616C4—44no—
617C4—42no—
618C4—42no—
619C4—44no—
620C4—224no—
621C4—442no—
622C4—442no—
623C4—444no—
624C4C2×#6694718yes—
625C2—444no—
626C2—884no—
627C2#1307441018yesdirect product factor
628C2C22×#6694711yescharacteristic
629C2C2×#1062313811yescharacteristic
630C2C2×#1062316011yescharacteristic
631C2C2×#1062309311yescharacteristic
632C2C2×#1062322911yescharacteristic
633C2C2×#1062311311yescharacteristic
634C2C2×#1062326411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC22×#66948C2
hypercenterC2×#389D11
hypocenterC11C2×#2624
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#66925C2semidirect
3. #13074410C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622288C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622552C2semidirect
9. C2×#10622601C2semidirect
10. C2×#10622586C2semidirect
11. C2×#10622600C2semidirect
12. C2×C11×#389C2semidirect
36. C2×#66925C22semidirect
37. C11×#389C22semidirect
41. #10622605C22semidirect
42. #10622604C22semidirect
43. #10622601C22semidirect
44. #10622600C22semidirect
45. #10622586C22semidirect
46. #10622552C22semidirect
47. #10622288C22semidirect
48. #10622285C22semidirect
204. C2×#389D11semidirect
312. #389C2×D11semidirect
418. C2×C11#2624semidirect
510. C11C2×#2624semidirect
627. C2#13074410direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#669252
#130744102
C2×#106226052
C2×#106222882
C2×#106222852
C2×#106226042
C2×#106225522
C2×#106226012
C2×#106225862
C2×#106226002
C2×C11×#3892
C2×#262411