Finite Group Databasebeta

← C2×#13073495 #14923491

Subgroups — C2×#13073495 #14923491

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073495C2116yesmaximal, direct product factor
2C2×#10622273C211yesmaximal, characteristic
3C2×#10622273C211yesmaximal, characteristic
4C2×#10622271C211yesmaximal, characteristic
5C2×#10622271C211yesmaximal, characteristic
6C2×#10622260C211yesmaximal, characteristic
7C2×#10622585C211yesmaximal, characteristic
8C2×#10622594C211yesmaximal, characteristic
9C2×#10622266C211yesmaximal, characteristic
10C2×#10622267C211yesmaximal, characteristic
11C2×#10622591C211yesmaximal, characteristic
12C2×#10622591C211yesmaximal, characteristic
13C2×#10622264C211yesmaximal, characteristic
14C2×C4×Dic11⋊C4C211yesmaximal, characteristic
15C2×#10622545C211yesmaximal, characteristic
16C2×C11×#387C211yesmaximal, characteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C11×#387C2218yes—
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53#10622594C2218yes—
54#10622591C2218yes—
55#10622591C2218yes—
56#10622585C2218yes—
57#10622545C2218yes—
58C4×Dic11⋊C4C2218yes—
59#10622273C2218yes—
60#10622273C2218yes—
61#10622271C2218yes—
62#10622271C2218yes—
63#10622267C2218yes—
64#10622266C2218yes—
65#10622264C2218yes—
66#10622260C2218yes—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C42×C11—24no—
87C2×C42×C11C2314yes—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11C2314yes—
91C2×C4⋊Dic11C2314yes—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2314yes—
104C2×C4×Dic11—24no—
105C2×C4×Dic11—24no—
106C2×C4×Dic11—24no—
107C2×C4×Dic11—24no—
108C2×C4×Dic11C2314yes—
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2314yes—
112C11×#95C2314yes—
113C11×#95C2314yes—
114C11×#95C2314yes—
115C11×#95C2314yes—
116C11⋊#95C2314yes—
117C11⋊#95C2314yes—
118C11⋊#95C2314yes—
119C11⋊#95C2314yes—
120C11⋊#95C2314yes—
121C11⋊#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2314yes—
125C11⋊#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C2×#2533—111nomaximal, Sylow
133C24×C11C2411yescharacteristic
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11#4114yes—
154C22×C4×C11#4114yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2412yes—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11#4114yes—
184C22×Dic11#4114yes—
185C22×Dic11#4114yes—
186C22×Dic11C2412yes—
187C22×Dic11C2412yes—
188C22×Dic11C2412yes—
189C22×Dic11C2412yes—
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193C22×Dic11C2412yes—
194C11×C4⋊C4—28no—
195C11×C4⋊C4—28no—
196C42×C11—28no—
197C4⋊Dic11—28no—
198C4⋊Dic11—28no—
199Dic11⋊C4—28no—
200Dic11⋊C4—28no—
201Dic11⋊C4—28no—
202Dic11⋊C4—28no—
203Dic11⋊C4—28no—
204Dic11⋊C4—28no—
205C4×Dic11—28no—
206C4×Dic11—28no—
207C4×Dic11—28no—
208C4×Dic11—28no—
209#2533—1116no—
210C2×#400—111no—
211C2×#400—111no—
212C2×#400—111no—
213C2×#400—111no—
214C2×#389—111no—
215C2×#389—111no—
216C2×#387—111no—
217C2×#387—111no—
218C2×#387—111no—
219C2×#387—111no—
220C2×#387—111no—
221C2×#387D1111yescharacteristic
222C2×#383—111no—
223C2×C4×C4⋊C4—111no—
224C2×#376—111no—
225C23×C11C2×#4112yes—
226C23×C11C2×#4112yes—
227C23×C11C2×#4112yes—
228C23×C11C2×#4112yes—
229C23×C11C2×#4112yes—
230C23×C112−1+412yes—
231C23×C112−1+412yes—
232C23×C11C2511yescharacteristic
233C2×C4×C11—28no—
234C2×C4×C11—28no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C2×C4×C11—44no—
259C2×C4×C11C2×#4114yes—
260C2×C4×C11C2×#4114yes—
261C2×Dic11—28no—
262C2×Dic11—28no—
263C2×Dic11—28no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—44no—
286C2×Dic11—44no—
287C2×Dic11—44no—
288C2×Dic11—44no—
289C2×Dic11—44no—
290C2×Dic11C2×#4114yes—
291C2×Dic11C2×#4114yes—
292C2×Dic11C2×#4114yes—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—111no—
295C22×C4⋊C4—111no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—111no—
299C22×C4⋊C4—111no—
300C22×C4⋊C4—111no—
301C22×C4⋊C4C2×D1111yescharacteristic
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C42—111no—
304C22×C42—111no—
305C22×C42—111no—
306C22×C42—111no—
307C22×C42C2×D1111yescharacteristic
308#400—118no—
309#400—118no—
310#400—118no—
311#400—118no—
312#389—118no—
313#389—118no—
314#387—118no—
315#387—118no—
316#387—118no—
317#387—118no—
318#387—118no—
319#387C2×D1118yes—
320#383—118no—
321C4×C4⋊C4—118no—
322#376—118no—
323C2×#95—111no—
324C2×#95—111no—
325C2×#95—111no—
326C2×#95—111no—
327C2×#95—111no—
328C2×#95—111no—
329C2×#95—111no—
330C2×#95—111no—
331C2×#95—111no—
332C2×#95—111no—
333C2×#95—111no—
334C2×#95—111no—
335C2×#95—111no—
336C2×#95—111no—
337C2×#95—111no—
338C2×#95—111no—
339C2×#95C2×D1111yescharacteristic
340C2×#95C2×D1111yescharacteristic
341C2×#95C2×D1111yescharacteristic
342C2×#95C2×D1111yescharacteristic
343C22×C11#52914yes—
344C22×C11#52914yes—
345C22×C11#54114yes—
346C22×C11#55214yes—
347C22×C11#55214yes—
348C22×C11#55214yes—
349C22×C11#55614yes—
350C22×C11C22×#4111yescharacteristic
351C22×C11C22×#4111yescharacteristic
352C22×C11C22×#4111yescharacteristic
353C22×C11C22×#4111yescharacteristic
354C22×C11C22×#4111yescharacteristic
355C22×C11C2×2−1+411yescharacteristic
356C22×C11C2×2−1+411yescharacteristic
357C4×C11—24no—
358C4×C11—24no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—42no—
363C4×C11—42no—
364Dic11—24no—
365Dic11—24no—
366Dic11—24no—
367Dic11—42no—
368Dic11—42no—
369Dic11—42no—
370Dic11—42no—
371Dic11—42no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—114no—
391C2×C4⋊C4—114no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—114no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—114no—
396C2×C4⋊C4—114no—
397C2×C4⋊C4—224no—
398C2×C4⋊C4—224no—
399C2×C4⋊C4—224no—
400C2×C4⋊C4—224no—
401C2×C4⋊C4—224no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—224no—
404C2×C4⋊C4—224no—
405C2×C4⋊C4C22×D1114yes—
406C2×C4⋊C4C22×D1114yes—
407C2×C42—24no—
408C2×C42—114no—
409C2×C42—114no—
410C2×C42—114no—
411C2×C42—114no—
412C2×C42—224no—
413C2×C42—224no—
414C2×C42—224no—
415C2×C42—224no—
416C2×C42C22×D1114yes—
417#95—114no—
418#95—114no—
419#95—114no—
420#95—114no—
421#95—114no—
422#95—114no—
423#95—114no—
424#95—114no—
425#95—114no—
426#95—114no—
427#95—114no—
428#95—114no—
429#95—114no—
430#95—114no—
431#95—114no—
432#95—114no—
433#95C22×D1114yes—
434#95C22×D1114yes—
435#95C22×D1114yes—
436#95C22×D1114yes—
437C2×C11#253318yescomplemented
438C2×C11C2×#52911yescharacteristic
439C2×C11C2×#52911yescharacteristic
440C2×C11C2×#54111yescharacteristic
441C2×C11C2×#55211yescharacteristic
442C2×C11C2×#55211yescharacteristic
443C2×C11C2×#55211yescharacteristic
444C2×C11C2×#55611yescharacteristic
445C24C23×D1111yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4#433914yes—
498C22×C4#434114yes—
499C22×C4C23×D1112yes—
500C22×C4C23×D1112yes—
501C22×C4C23×D1112yes—
502C22×C4C23×D1112yes—
503C22×C4C23×D1112yes—
504C22×C4C23×D1112yes—
505C22×C4C23×D1112yes—
506C4⋊C4—28no—
507C4⋊C4—28no—
508C4⋊C4—228no—
509C4⋊C4—228no—
510C4⋊C4—228no—
511C4⋊C4—228no—
512C4⋊C4—228no—
513C4⋊C4—228no—
514C4⋊C4—228no—
515C4⋊C4—228no—
516C42—28no—
517C42—228no—
518C42—228no—
519C42—228no—
520C42—228no—
521C11C2×#253311yescharacteristic, complemented, Sylow
522C23C2×#433912yes—
523C23C2×#434112yes—
524C23#6704012yes—
525C23#41×D1112yes—
526C23#41×D1112yes—
527C23#41×D1112yes—
528C23#6704312yes—
529C23C24×D1111yescharacteristic
530C2×C4—28no—
531C2×C4—28no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—114no—
557C2×C4—114no—
558C2×C4—114no—
559C2×C4—228no—
560C2×C4—228no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—228no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—444no—
584C2×C4—444no—
585C2×C4—444no—
586C2×C4—444no—
587C2×C4—444no—
588C2×C4C2×#433914yes—
589C2×C4C2×#434114yes—
590C22#1062305914yes—
591C22#1062306914yes—
592C22#1062311414yes—
593C22#1062317214yes—
594C22#1062318114yes—
595C22#1062322414yes—
596C22#1062323914yes—
597C22C22×#433911yescharacteristic
598C22C22×#434111yescharacteristic
599C22C2×#6704011yescharacteristic
600C22C2×#41×D1111yescharacteristic
601C22C2×#41×D1111yescharacteristic
602C22C2×#41×D1111yescharacteristic
603C22C2×#6704311yescharacteristic
604C4—24no—
605C4—24no—
606C4—42no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—224no—
612C4—224no—
613C4—224no—
614C4—442no—
615C4—442no—
616C4—442no—
617C4—442no—
618C4—442no—
619C2#1307349518yesdirect product factor
620C2C2×#1062305911yescharacteristic
621C2C2×#1062306911yescharacteristic
622C2C2×#1062311411yescharacteristic
623C2C2×#1062322411yescharacteristic
624C2C2×#1062323911yescharacteristic
625C2C2×#1062318111yescharacteristic
626C2C2×#1062317211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#387C2
socle, prime radicalC24×C11C24
hypercenterC2×#387D11
hypocenterC11C2×#2533
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #13073495C2direct (N × H)
437. C2×C11#2533semidirect
521. C11C2×#2533semidirect
619. C2#13073495direct (N × H)

Maximal subgroups

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

subgroupindex
#130734952
C2×#106222732
C2×#106222712
C2×#106222602
C2×#106225852
C2×#106225942
C2×#106222662
C2×#106222672
C2×#106225912
C2×#106222642
C2×C4×Dic11⋊C42
C2×#106225452
C2×C11×#3872
C2×#253311