Finite Group Databasebeta

← C2×#13074496 #14920702

Subgroups — C2×#13074496 #14920702

Order 2816.

2286 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×#66942C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic
3#13074496C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic
5C2×#10622273C211yesmaximal, characteristic
6C2×#10622271C211yesmaximal, characteristic
7C2×#10622271C211yesmaximal, characteristic
8C2×#10622270C211yesmaximal, characteristic
9C2×#10622597C211yesmaximal, characteristic
10C2×#10622269C211yesmaximal, characteristic
11C2×#10622592C211yesmaximal, characteristic
12C2×#10622266C211yesmaximal, characteristic
13C2×#10622546C211yesmaximal, characteristic
14C2×#10622591C211yesmaximal, characteristic
15C2×#10622264C211yesmaximal, characteristic
16C2×C11×#387C211yesmaximal, characteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×#66942—28no—
35C2×#66942C2218yes—
36C2×C4×Dic22—28no—
37C2×C4×Dic22C2218yes—
38C11×#387C2218yes—
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
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622597C2218yes—
58#10622592C2218yes—
59#10622591C2218yes—
60#10622546C2218yes—
61#10622273C2218yes—
62#10622273C2218yes—
63#10622271C2218yes—
64#10622271C2218yes—
65#10622270C2218yes—
66#10622269C2218yes—
67#10622266C2218yes—
68#10622264C2218yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C22×Dic22—24no—
85C22×Dic22—24no—
86C22×Dic22—24no—
87C22×Dic22C2314yes—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4—24no—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C4⋊C4C2314yes—
92C2×C42×C11—24no—
93C2×C42×C11C2314yes—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11—24no—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11C2314yes—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—24no—
104C2×Dic11⋊C4—24no—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—24no—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×C4×Dic11—24no—
117C2×C4×Dic11D418yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2314yes—
120#66942—232no—
121C4×Dic22—232no—
122C11×#95C2314yes—
123C11×#95C2314yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C2×#2634—111nomaximal, Sylow
141C24×C11C2411yescharacteristic
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—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11C2×D414yes—
162C22×C4×C11#4114yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2412yes—
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—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D414yes—
193C22×Dic11#4114yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2412yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C22×Dic11C2412yes—
202C2×Dic22—232no—
203C2×Dic22—28no—
204C2×Dic22—28no—
205C2×Dic22—28no—
206C11×C4⋊C4—28no—
207C11×C4⋊C4—28no—
208C42×C11—28no—
209C4⋊Dic11—28no—
210C4⋊Dic11—28no—
211C4⋊Dic11—28no—
212Dic11⋊C4—28no—
213Dic11⋊C4—28no—
214Dic11⋊C4—28no—
215Dic11⋊C4—28no—
216Dic11⋊C4—28no—
217Dic11⋊C4—28no—
218Dic11⋊C4—28no—
219Dic11⋊C4—28no—
220C4×Dic11—28no—
221C4×Dic11C2×D4116yes—
222C22×#125—111no—
223C22×C4×Q8—111no—
224#2634—1116no—
225C2×#400—111no—
226C2×#400—111no—
227C2×#400—111no—
228C2×#400—111no—
229C2×#398—111no—
230C2×#398—111no—
231C2×#395—111no—
232C2×#395—111no—
233C2×#387—111no—
234C2×#387—111no—
235C2×#387—111no—
236C2×#387D1111yescharacteristic
237C2×#383—111no—
238C23×C11C22×D412yes—
239C23×C11C2×#4112yes—
240C23×C11C2×#4112yes—
241C23×C112−1+412yes—
242C23×C112−1+412yes—
243C23×C112−1+412yes—
244C23×C112−1+412yes—
245C23×C11C2511yescharacteristic
246C2×C4×C11—28no—
247C2×C4×C11—28no—
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—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—44no—
268C2×C4×C11—44no—
269C2×C4×C11—44no—
270C2×C4×C11—44no—
271C2×C4×C11—44no—
272C2×C4×C11C22×D414yes—
273C2×C4×C11C2×#4114yes—
274C2×Dic11—28no—
275C2×Dic11—28no—
276C2×Dic11—28no—
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—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—44no—
299C2×Dic11—44no—
300C2×Dic11—44no—
301C2×Dic11—44no—
302C2×Dic11—44no—
303C2×Dic11C22×D414yes—
304C2×Dic11C22×D414yes—
305C2×Dic11C2×#4114yes—
306Dic22—232no—
307C23×Q8—111no—
308C2×#125—118no—
309C2×#125—228no—
310C2×C4×Q8—118no—
311C2×C4×Q8—228no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4—111no—
314C22×C4⋊C4—111no—
315C22×C4⋊C4—111no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4—111no—
318C22×C4⋊C4—111no—
319C22×C4⋊C4—111no—
320C22×C4⋊C4—111no—
321C22×C4⋊C4—111no—
322C22×C4⋊C4—111no—
323C22×C4⋊C4C2×D1111yescharacteristic
324C22×C4⋊C4C2×D1111yescharacteristic
325C22×C42—111no—
326C22×C42—111no—
327C22×C42C2×D1111yescharacteristic
328#400—118no—
329#400—118no—
330#400—118no—
331#400—118no—
332#398—118no—
333#398—118no—
334#395—118no—
335#395—118no—
336#387—118no—
337#387—118no—
338#387—118no—
339#387C2×D1118yes—
340#383—118no—
341C2×#95—111no—
342C2×#95—111no—
343C2×#95—111no—
344C2×#95—111no—
345C2×#95—111no—
346C2×#95—111no—
347C2×#95—111no—
348C2×#95—111no—
349C2×#95—111no—
350C2×#95—111no—
351C2×#95—111no—
352C2×#95—111no—
353C2×#95—111no—
354C2×#95—111no—
355C2×#95C2×D1111yescharacteristic
356C2×#95C2×D1111yescharacteristic
357C2×#95C2×D1111yescharacteristic
358C2×#95C2×D1111yescharacteristic
359C22×C11#52514yes—
360C22×C11#53614yes—
361C22×C11#53614yes—
362C22×C11#54114yes—
363C22×C11#54114yes—
364C22×C11#54114yes—
365C22×C11#54114yes—
366C22×C11C23×D411yescharacteristic
367C22×C11C22×#4111yescharacteristic
368C22×C11C22×#4111yescharacteristic
369C22×C11C2×2−1+411yescharacteristic
370C22×C11C2×2−1+411yescharacteristic
371C22×C11C2×2−1+411yescharacteristic
372C22×C11C2×2−1+411yescharacteristic
373C4×C11—24no—
374C4×C11—24no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—42no—
380Dic11—24no—
381Dic11—24no—
382Dic11—24no—
383Dic11—42no—
384Dic11—42no—
385Dic11—42no—
386Dic11—42no—
387Dic11—42no—
388C22×Q8—114no—
389C22×Q8—224no—
390C22×Q8—224no—
391C22×Q8—224no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—111no—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—111no—
399C23×C4—111no—
400C23×C4C22×D1111yescharacteristic
401C23×C4C22×D1111yescharacteristic
402C23×C4C22×D1111yescharacteristic
403C23×C4C22×D1111yescharacteristic
404C23×C4C22×D1111yescharacteristic
405C23×C4C22×D1111yescharacteristic
406C23×C4C22×D1111yescharacteristic
407#125—2232no—
408C4×Q8—2232no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—114no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—114no—
415C2×C4⋊C4—114no—
416C2×C4⋊C4—114no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—114no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—114no—
421C2×C4⋊C4—114no—
422C2×C4⋊C4—224no—
423C2×C4⋊C4—224no—
424C2×C4⋊C4—224no—
425C2×C4⋊C4—224no—
426C2×C4⋊C4—224no—
427C2×C4⋊C4—224no—
428C2×C4⋊C4—224no—
429C2×C4⋊C4—224no—
430C2×C4⋊C4—224no—
431C2×C4⋊C4—224no—
432C2×C4⋊C4—224no—
433C2×C4⋊C4C22×D1114yes—
434C2×C4⋊C4C22×D1114yes—
435C2×C42—24no—
436C2×C42—118no—
437C2×C42—114no—
438C2×C42—114no—
439C2×C42—224no—
440C2×C42C22×D1114yes—
441#95—114no—
442#95—114no—
443#95—114no—
444#95—114no—
445#95—114no—
446#95—114no—
447#95—114no—
448#95—114no—
449#95—114no—
450#95—114no—
451#95—114no—
452#95—114no—
453#95—114no—
454#95—114no—
455#95C22×D1114yes—
456#95C22×D1114yes—
457#95C22×D1114yes—
458#95C22×D1114yes—
459C2×C11#263418yescomplemented
460C2×C11C2×#52511yescharacteristic
461C2×C11C2×#53611yescharacteristic
462C2×C11C2×#53611yescharacteristic
463C2×C11C2×#54111yescharacteristic
464C2×C11C2×#54111yescharacteristic
465C2×C11C2×#54111yescharacteristic
466C2×C11C2×#54111yescharacteristic
467C24C23×D1111yescharacteristic
468C2×Q8—228no—
469C2×Q8—228no—
470C2×Q8—2232no—
471C2×Q8—228no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—114no—
492C22×C4—114no—
493C22×C4—114no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4#433914yes—
524C22×C4D4×D1114yes—
525C22×C4C23×D1112yes—
526C22×C4C23×D1112yes—
527C22×C4C23×D1112yes—
528C22×C4C23×D1112yes—
529C22×C4C23×D1112yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—228no—
535C4⋊C4—228no—
536C4⋊C4—228no—
537C4⋊C4—228no—
538C4⋊C4—228no—
539C4⋊C4—228no—
540C4⋊C4—228no—
541C4⋊C4—228no—
542C4⋊C4—228no—
543C4⋊C4—228no—
544C4⋊C4—228no—
545C42—28no—
546C42—1116no—
547C42—228no—
548C11C2×#263411yescharacteristic, complemented, Sylow
549C23C2×#433912yes—
550C23C2×D4×D1112yes—
551C23#6704012yes—
552C23#41×D1112yes—
553C23#6704312yes—
554C23#6704312yes—
555C23#6704312yes—
556C23C24×D1111yescharacteristic
557Q8—2232no—
558C2×C4—28no—
559C2×C4—28no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—114no—
585C2×C4—114no—
586C2×C4—114no—
587C2×C4—228no—
588C2×C4—228no—
589C2×C4—228no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—444no—
612C2×C4—444no—
613C2×C4—444no—
614C2×C4—444no—
615C2×C4—444no—
616C2×C4C2×#433914yes—
617C2×C4C2×D4×D1114yes—
618C22#1062304914yes—
619C22#1062307814yes—
620C22#1062311414yes—
621C22#1062315914yes—
622C22#1062317914yes—
623C22#1062322714yes—
624C22#1062323214yes—
625C22C22×#433911yescharacteristic
626C22C22×D4×D1111yescharacteristic
627C22C2×#6704011yescharacteristic
628C22C2×#41×D1111yescharacteristic
629C22C2×#6704311yescharacteristic
630C22C2×#6704311yescharacteristic
631C22C2×#6704311yescharacteristic
632C4—24no—
633C4—24no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—224no—
640C4—224no—
641C4—224no—
642C4—442no—
643C4—442no—
644C4—442no—
645C4—442no—
646C4—442no—
647C2#1307449618yesdirect product factor
648C2C2×#1062307811yescharacteristic
649C2C2×#1062317911yescharacteristic
650C2C2×#1062315911yescharacteristic
651C2C2×#1062323211yescharacteristic
652C2C2×#1062311411yescharacteristic
653C2C2×#1062322711yescharacteristic
654C2C2×#1062304911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#387C2
socle, prime radicalC24×C11C24
hypercenterC2×#387D11
hypocenterC11C2×#2634
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #13074496C2direct (N × H)
459. C2×C11#2634semidirect
548. C11C2×#2634semidirect
647. C2#13074496direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669422
C22×C4×Dic222
#130744962
C2×#106222732
C2×#106222712
C2×#106222702
C2×#106225972
C2×#106222692
C2×#106225922
C2×#106222662
C2×#106225462
C2×#106225912
C2×#106222642
C2×C11×#3872
C2×#263411