Finite Group Databasebeta

← C2×#13074017 #14924028

Subgroups — C2×#13074017 #14924028

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074017C2116yesmaximal, direct product factor
2C2×#10622271C211yesmaximal, characteristic
3C2×#10622270C211yesmaximal, characteristic
4C2×#10622597C211yesmaximal, characteristic
5C2×#10622596C211yesmaximal, characteristic
6C2×#10622598C211yesmaximal, characteristic
7C2×#10622260C211yesmaximal, characteristic
8C2×#10622260C211yesmaximal, characteristic
9C2×#10622266C211yesmaximal, characteristic
10C2×#10622546C211yesmaximal, characteristic
11C2×#10622267C211yesmaximal, characteristic
12C2×#10622265C211yesmaximal, characteristic
13C2×#10622591C211yesmaximal, characteristic
14C2×C4×C4⋊Dic11C211yesmaximal, characteristic
15C2×#10622262C211yesmaximal, characteristic
16C2×C11×#387C211yesmaximal, characteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
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
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C11×#387C2218yes—
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#10622598C2218yes—
54#10622597C2218yes—
55#10622596C2218yes—
56#10622591C2218yes—
57C4×C4⋊Dic11C2218yes—
58#10622546C2218yes—
59#10622271C2218yes—
60#10622270C2218yes—
61#10622267C2218yes—
62#10622266C2218yes—
63#10622265C2218yes—
64#10622262C2218yes—
65#10622260C2218yes—
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⋊Dic11—24no—
91C2×C4⋊Dic11—24no—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2314yes—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4—42no—
101C2×Dic11⋊C4—42no—
102C2×Dic11⋊C4—42no—
103C2×Dic11⋊C4Q818yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×C4×Dic11—24no—
113C2×C4×Dic11—42no—
114C2×C4×Dic11—42no—
115C2×C4×Dic11—42no—
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2314yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2314yes—
120C11×#95C2314yes—
121C11×#95C2314yes—
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—
136C2×#2585—111nomaximal, Sylow
137C24×C11C2411yescharacteristic
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—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11C2×Q814yes—
157C22×C4×C11#4114yes—
158C22×C4×C11#4114yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
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—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11C2×Q814yes—
187C22×Dic11C2×Q814yes—
188C22×Dic11#4114yes—
189C22×Dic11#4114yes—
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193C22×Dic11C2412yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C11×C4⋊C4—28no—
199C11×C4⋊C4—28no—
200C42×C11—28no—
201C4⋊Dic11—28no—
202C4⋊Dic11—28no—
203C4⋊Dic11—28no—
204C4⋊Dic11—28no—
205Dic11⋊C4—28no—
206Dic11⋊C4—28no—
207Dic11⋊C4—28no—
208Dic11⋊C4—28no—
209Dic11⋊C4—44no—
210Dic11⋊C4—44no—
211Dic11⋊C4—44no—
212Dic11⋊C4C2×Q8116yes—
213C4×Dic11—28no—
214C4×Dic11—44no—
215C4×Dic11—44no—
216C4×Dic11—44no—
217#2585—1116no—
218C2×#400—111no—
219C2×#398—111no—
220C2×#398—111no—
221C2×#398—111no—
222C2×#389—111no—
223C2×#389—111no—
224C2×#389—111no—
225C2×#387—111no—
226C2×#387—111no—
227C2×#387—111no—
228C2×#387—111no—
229C2×#387—111no—
230C2×#387D1111yescharacteristic
231C2×C4×C4⋊C4—111no—
232C2×C4×C4⋊C4—111no—
233C23×C11C22×Q812yes—
234C23×C11C2×#4112yes—
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11C2×#4112yes—
238C23×C11H(5,𝔽2)12yes—
239C23×C112−1+412yes—
240C23×C11C2511yescharacteristic
241C2×C4×C11—28no—
242C2×C4×C11—28no—
243C2×C4×C11—28no—
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—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—44no—
263C2×C4×C11—44no—
264C2×C4×C11—44no—
265C2×C4×C11—44no—
266C2×C4×C11C22×Q814yes—
267C2×C4×C11C2×#4114yes—
268C2×C4×C11C2×#4114yes—
269C2×Dic11—28no—
270C2×Dic11—28no—
271C2×Dic11—28no—
272C2×Dic11—28no—
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—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—44no—
294C2×Dic11—44no—
295C2×Dic11—44no—
296C2×Dic11—44no—
297C2×Dic11C22×Q814yes—
298C2×Dic11C22×Q814yes—
299C2×Dic11C2×#4114yes—
300C2×Dic11C2×#4114yes—
301C22×C4⋊C4—111no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—111no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—111no—
310C22×C4⋊C4—111no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4C2×D1111yescharacteristic
314C22×C4⋊C4C2×D1111yescharacteristic
315C22×C42—111no—
316C22×C42—111no—
317C22×C42—111no—
318C22×C42—111no—
319C22×C42C2×D1111yescharacteristic
320#400—118no—
321#398—118no—
322#398—118no—
323#398—118no—
324#389—118no—
325#389—118no—
326#389—118no—
327#387—118no—
328#387—118no—
329#387—118no—
330#387—118no—
331#387—118no—
332#387C2×D1118yes—
333C4×C4⋊C4—118no—
334C4×C4⋊C4—118no—
335C2×#95—111no—
336C2×#95—111no—
337C2×#95—111no—
338C2×#95—111no—
339C2×#95—111no—
340C2×#95—111no—
341C2×#95—111no—
342C2×#95—111no—
343C2×#95—111no—
344C2×#95—111no—
345C2×#95—111no—
346C2×#95—111no—
347C2×#95C2×D1111yescharacteristic
348C2×#95C2×D1111yescharacteristic
349C2×#95C2×D1111yescharacteristic
350C2×#95C2×D1111yescharacteristic
351C22×C11#52914yes—
352C22×C11#53314yes—
353C22×C11#53914yes—
354C22×C11#55214yes—
355C22×C11#55314yes—
356C22×C11#55414yes—
357C22×C11#55714yes—
358C22×C11C23×Q811yescharacteristic
359C22×C11C22×#4111yescharacteristic
360C22×C11C22×#4111yescharacteristic
361C22×C11C22×#4111yescharacteristic
362C22×C11C22×#4111yescharacteristic
363C22×C11C2×H(5,𝔽2)11yescharacteristic
364C22×C11C2×2−1+411yescharacteristic
365C4×C11—24no—
366C4×C11—24no—
367C4×C11—24no—
368C4×C11—42no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11—42no—
372Dic11—24no—
373Dic11—24no—
374Dic11—24no—
375Dic11—24no—
376Dic11—42no—
377Dic11—42no—
378Dic11—42no—
379Dic11—42no—
380C23×C4—111no—
381C23×C4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C23×C4C22×D1111yescharacteristic
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1111yescharacteristic
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—118no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—224no—
411C2×C4⋊C4—224no—
412C2×C4⋊C4—224no—
413C2×C4⋊C4—224no—
414C2×C4⋊C4—224no—
415C2×C4⋊C4—224no—
416C2×C4⋊C4—224no—
417C2×C4⋊C4—224no—
418C2×C4⋊C4—442no—
419C2×C4⋊C4—442no—
420C2×C4⋊C4—442no—
421C2×C4⋊C4C22×D1114yes—
422C2×C4⋊C4C22×D1114yes—
423C2×C42—24no—
424C2×C42—114no—
425C2×C42—114no—
426C2×C42—114no—
427C2×C42—114no—
428C2×C42—224no—
429C2×C42—442no—
430C2×C42—442no—
431C2×C42—442no—
432C2×C42C22×D1114yes—
433#95—114no—
434#95—114no—
435#95—114no—
436#95—114no—
437#95—114no—
438#95—114no—
439#95—114no—
440#95—114no—
441#95—114no—
442#95—114no—
443#95—114no—
444#95—114no—
445#95C22×D1114yes—
446#95C22×D1114yes—
447#95C22×D1114yes—
448#95C22×D1114yes—
449C2×C11#258518yescomplemented
450C2×C11C2×#52911yescharacteristic
451C2×C11C2×#53311yescharacteristic
452C2×C11C2×#53911yescharacteristic
453C2×C11C2×#55211yescharacteristic
454C2×C11C2×#55311yescharacteristic
455C2×C11C2×#55411yescharacteristic
456C2×C11C2×#55711yescharacteristic
457C24C23×D1111yescharacteristic
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—114no—
479C22×C4—114no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—112no—
487C22×C4—112no—
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—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4#433914yes—
509C22×C4#434114yes—
510C22×C4Q8×D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C22×C4C23×D1112yes—
514C22×C4C23×D1112yes—
515C22×C4C23×D1112yes—
516C22×C4C23×D1112yes—
517C22×C4C23×D1112yes—
518C4⋊C4—28no—
519C4⋊C4—28no—
520C4⋊C4—1116no—
521C4⋊C4—228no—
522C4⋊C4—228no—
523C4⋊C4—228no—
524C4⋊C4—228no—
525C4⋊C4—228no—
526C4⋊C4—228no—
527C4⋊C4—228no—
528C4⋊C4—228no—
529C4⋊C4—444no—
530C4⋊C4—444no—
531C4⋊C4—444no—
532C42—28no—
533C42—228no—
534C42—444no—
535C42—444no—
536C42—444no—
537C11C2×#258511yescharacteristic, complemented, Sylow
538C23C2×#433912yes—
539C23C2×#434112yes—
540C23C2×Q8×D1112yes—
541C23#41×D1112yes—
542C23#41×D1112yes—
543C23#6704212yes—
544C23#6704312yes—
545C23C24×D1111yescharacteristic
546C2×C4—28no—
547C2×C4—28no—
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—114no—
572C2×C4—114no—
573C2×C4—114no—
574C2×C4—114no—
575C2×C4—228no—
576C2×C4—228no—
577C2×C4—228no—
578C2×C4—228no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
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—444no—
600C2×C4—444no—
601C2×C4—444no—
602C2×C4—444no—
603C2×C4C2×#433914yes—
604C2×C4C2×#434114yes—
605C2×C4C2×Q8×D1114yes—
606C22#1062306114yes—
607C22#1062307214yes—
608C22#1062310914yes—
609C22#1062316614yes—
610C22#1062318014yes—
611C22#1062321614yes—
612C22#1062323814yes—
613C22C22×#433911yescharacteristic
614C22C22×#434111yescharacteristic
615C22C22×Q8×D1111yescharacteristic
616C22C2×#41×D1111yescharacteristic
617C22C2×#41×D1111yescharacteristic
618C22C2×#6704211yescharacteristic
619C22C2×#6704311yescharacteristic
620C4—24no—
621C4—24no—
622C4—24no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—224no—
628C4—224no—
629C4—224no—
630C4—224no—
631C4—442no—
632C4—442no—
633C4—442no—
634C4—442no—
635C2#1307401718yesdirect product factor
636C2C2×#1062318011yescharacteristic
637C2C2×#1062310911yescharacteristic
638C2C2×#1062323811yescharacteristic
639C2C2×#1062307211yescharacteristic
640C2C2×#1062306111yescharacteristic
641C2C2×#1062316611yescharacteristic
642C2C2×#1062321611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#387C2
socle, prime radicalC24×C11C24
hypercenterC2×#387D11
hypocenterC11C2×#2585
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #13074017C2direct (N × H)
449. C2×C11#2585semidirect
537. C11C2×#2585semidirect
635. C2#13074017direct (N × H)

Maximal subgroups

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

subgroupindex
#130740172
C2×#106222712
C2×#106222702
C2×#106225972
C2×#106225962
C2×#106225982
C2×#106222602
C2×#106222662
C2×#106225462
C2×#106222672
C2×#106222652
C2×#106225912
C2×C4×C4⋊Dic112
C2×#106222622
C2×C11×#3872
C2×#258511