Finite Group Databasebeta

← C2×#13073306 #14922985

Subgroups — C2×#13073306 #14922985

Order 2816.

2030 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073306C2116yesmaximal, direct product factor
2C2×#10622272C211yesmaximal, characteristic
3C2×#10622597C211yesmaximal, characteristic
4C2×#10622596C211yesmaximal, characteristic
5C2×#10622269C211yesmaximal, characteristic
6C2×#10622259C211yesmaximal, characteristic
7C2×#10622259C211yesmaximal, characteristic
8C2×#10622594C211yesmaximal, characteristic
9C2×#10622267C211yesmaximal, characteristic
10C2×#10622265C211yesmaximal, characteristic
11C2×#10622265C211yesmaximal, characteristic
12C2×#10622591C211yesmaximal, characteristic
13C2×#10622263C211yesmaximal, characteristic
14C2×C4×Dic11⋊C4C211yesmaximal, characteristic
15C2×C4×C4⋊Dic11C211yesmaximal, 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×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C11×#387C2218yes—
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#10622597C2218yes—
54#10622596C2218yes—
55#10622594C2218yes—
56#10622591C2218yes—
57C4×C4⋊Dic11C2218yes—
58C4×Dic11⋊C4C2218yes—
59#10622272C2218yes—
60#10622269C2218yes—
61#10622267C2218yes—
62#10622265C2218yes—
63#10622265C2218yes—
64#10622263C2218yes—
65#10622259C2218yes—
66#10622259C2218yes—
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
82C22×Dic22—24no—
83C22×Dic22—24no—
84C22×Dic22—42no—
85C22×Dic22C2314yes—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C42×C11—24no—
91C2×C42×C11C2314yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2314yes—
97C2×C4⋊Dic11C2314yes—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4—42no—
101C2×Dic11⋊C4—42no—
102C2×Dic11⋊C4—42no—
103C2×Dic11⋊C4Q818yescomplemented
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—24no—
112C2×C4×Dic11—42no—
113C2×C4×Dic11—42no—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2314yes—
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—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C2×#2520—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—
198C2×Dic22—28no—
199C2×Dic22—28no—
200C2×Dic22—44no—
201C2×Dic22—416no—
202C11×C4⋊C4—28no—
203C11×C4⋊C4—28no—
204C42×C11—28no—
205C4⋊Dic11—28no—
206C4⋊Dic11—28no—
207C4⋊Dic11—28no—
208Dic11⋊C4—28no—
209Dic11⋊C4—28no—
210Dic11⋊C4—44no—
211Dic11⋊C4—44no—
212Dic11⋊C4—44no—
213Dic11⋊C4C2×Q8116yescomplemented
214C4×Dic11—28no—
215C4×Dic11—28no—
216C4×Dic11—44no—
217C4×Dic11—44no—
218#2520—1116no—
219C2×#400—111no—
220C2×#398—111no—
221C2×#398—111no—
222C2×#395—111no—
223C2×#391—111no—
224C2×#391—111no—
225C2×#387—111no—
226C2×#387—111no—
227C2×#387—111no—
228C2×#387—111no—
229C2×#387—111no—
230C2×#387D1111yescharacteristic
231C2×#382—111no—
232C2×C4×C4⋊C4—111no—
233C2×C4×C4⋊C4—111no—
234C23×C11C22×Q812yes—
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11C2×#4112yes—
238C23×C11C2×#4112yes—
239C23×C11H(5,𝔽2)12yes—
240C23×C112−1+412yes—
241C23×C11C2511yescharacteristic
242C2×C4×C11—28no—
243C2×C4×C11—28no—
244C2×C4×C11—28no—
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—22no—
263C2×C4×C11—44no—
264C2×C4×C11—44no—
265C2×C4×C11—44no—
266C2×C4×C11—44no—
267C2×C4×C11C22×Q814yes—
268C2×C4×C11C2×#4114yes—
269C2×C4×C11C2×#4114yes—
270C2×Dic11—28no—
271C2×Dic11—28no—
272C2×Dic11—28no—
273C2×Dic11—28no—
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—22no—
294C2×Dic11—44no—
295C2×Dic11—44no—
296C2×Dic11—44no—
297C2×Dic11—44no—
298C2×Dic11C22×Q814yes—
299C2×Dic11C22×Q814yes—
300C2×Dic11C2×#4114yes—
301C2×Dic11C2×#4114yes—
302Dic22—416no—
303C23×Q8—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#395—118no—
324#391—118no—
325#391—118no—
326#387—118no—
327#387—118no—
328#387—118no—
329#387—118no—
330#387—118no—
331#387C2×D1118yes—
332#382—118no—
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×#95—111no—
348C2×#95—111no—
349C2×#95C2×D1111yescharacteristic
350C2×#95C2×D1111yescharacteristic
351C2×#95C2×D1111yescharacteristic
352C2×#95C2×D1111yescharacteristic
353C22×C11#52914yes—
354C22×C11#53314yes—
355C22×C11#54214yes—
356C22×C11#55114yes—
357C22×C11#55214yes—
358C22×C11#55414yes—
359C22×C11#55714yes—
360C22×C11C23×Q811yescharacteristic
361C22×C11C22×#4111yescharacteristic
362C22×C11C22×#4111yescharacteristic
363C22×C11C22×#4111yescharacteristic
364C22×C11C22×#4111yescharacteristic
365C22×C11C2×H(5,𝔽2)11yescharacteristic
366C22×C11C2×2−1+411yescharacteristic
367C4×C11—24no—
368C4×C11—24no—
369C4×C11—24no—
370C4×C11—42no—
371C4×C11—42no—
372C4×C11—42no—
373C4×C11—42no—
374Dic11—24no—
375Dic11—24no—
376Dic11—24no—
377Dic11—24no—
378Dic11—42no—
379Dic11—42no—
380Dic11—42no—
381Dic11—42no—
382C22×Q8—114no—
383C22×Q8—224no—
384C22×Q8—224no—
385C22×Q8—442no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4C22×D1111yescharacteristic
395C23×C4C22×D1111yescharacteristic
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—118no—
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—114no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—114no—
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—224no—
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#95—114no—
446#95—114no—
447#95C22×D1114yes—
448#95C22×D1114yes—
449#95C22×D1114yes—
450#95C22×D1114yes—
451C2×C11#252018yescomplemented
452C2×C11C2×#52911yescharacteristic
453C2×C11C2×#53311yescharacteristic
454C2×C11C2×#54211yescharacteristic
455C2×C11C2×#55111yescharacteristic
456C2×C11C2×#55211yescharacteristic
457C2×C11C2×#55411yescharacteristic
458C2×C11C2×#55711yescharacteristic
459C24C23×D1111yescharacteristic
460C2×Q8—228no—
461C2×Q8—228no—
462C2×Q8—444no—
463C2×Q8—4416no—
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—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4—114no—
485C22×C4—114no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—112no—
491C22×C4—112no—
492C22×C4—112no—
493C22×C4—112no—
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—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4#433914yes—
515C22×C4#434114yes—
516C22×C4Q8×D1114yes—
517C22×C4C23×D1112yes—
518C22×C4C23×D1112yes—
519C22×C4C23×D1112yes—
520C22×C4C23×D1112yes—
521C22×C4C23×D1112yes—
522C22×C4C23×D1112yes—
523C22×C4C23×D1112yes—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—1116no—
527C4⋊C4—228no—
528C4⋊C4—228no—
529C4⋊C4—228no—
530C4⋊C4—228no—
531C4⋊C4—228no—
532C4⋊C4—444no—
533C4⋊C4—444no—
534C4⋊C4—444no—
535C42—28no—
536C42—228no—
537C42—228no—
538C42—444no—
539C42—444no—
540C11C2×#252011yescharacteristic, complemented, Sylow
541C23C2×#433912yes—
542C23C2×#434112yes—
543C23C2×Q8×D1112yes—
544C23#41×D1112yes—
545C23#41×D1112yes—
546C23#6704212yes—
547C23#6704312yes—
548C23C24×D1111yescharacteristic
549Q8—4416no—
550C2×C4—28no—
551C2×C4—28no—
552C2×C4—28no—
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—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—114no—
576C2×C4—114no—
577C2×C4—114no—
578C2×C4—114no—
579C2×C4—228no—
580C2×C4—228no—
581C2×C4—228no—
582C2×C4—228no—
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—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—444no—
604C2×C4—444no—
605C2×C4—444no—
606C2×C4—444no—
607C2×C4C2×#433914yes—
608C2×C4C2×#434114yes—
609C2×C4C2×Q8×D1114yes—
610C22#1062306514yes—
611C22#1062306914yes—
612C22#1062310914yes—
613C22#1062316614yes—
614C22#1062318114yes—
615C22#1062321614yes—
616C22#1062323614yes—
617C22C22×#433911yescharacteristic
618C22C22×#434111yescharacteristic
619C22C22×Q8×D1111yescharacteristic
620C22C2×#41×D1111yescharacteristic
621C22C2×#41×D1111yescharacteristic
622C22C2×#6704211yescharacteristic
623C22C2×#6704311yescharacteristic
624C4—24no—
625C4—24no—
626C4—24no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—42no—
631C4—224no—
632C4—224no—
633C4—224no—
634C4—224no—
635C4—442no—
636C4—442no—
637C4—442no—
638C4—442no—
639C2#1307330618yesdirect product factor
640C2C2×#1062306911yescharacteristic
641C2C2×#1062310911yescharacteristic
642C2C2×#1062306511yescharacteristic
643C2C2×#1062323611yescharacteristic
644C2C2×#1062318111yescharacteristic
645C2C2×#1062316611yescharacteristic
646C2C2×#1062321611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#387C2
socle, prime radicalC24×C11C24
hypercenterC2×#387D11
hypocenterC11C2×#2520
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #13073306C2direct (N × H)
103. C2×Dic11⋊C4Q8semidirect
213. Dic11⋊C4C2×Q8semidirect
451. C2×C11#2520semidirect
540. C11C2×#2520semidirect
639. C2#13073306direct (N × H)

Maximal subgroups

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

subgroupindex
#130733062
C2×#106222722
C2×#106225972
C2×#106225962
C2×#106222692
C2×#106222592
C2×#106225942
C2×#106222672
C2×#106222652
C2×#106225912
C2×#106222632
C2×C4×Dic11⋊C42
C2×C4×C4⋊Dic112
C2×C11×#3872
C2×#252011