Finite Group Databasebeta

← C2×#13072464 #14921683

Subgroups — C2×#13072464 #14921683

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C22×#66950C212yesmaximal, complemented
3C22×#66946C211yesmaximal, characteristic
4#13072464C2116yesmaximal, direct product factor
5C2×#10622607C212yesmaximal, complemented
6C2×#10622286C212yesmaximal, complemented
7C2×#10622552C211yesmaximal, characteristic
8C2×#10622601C211yesmaximal, characteristic
9C2×#10622598C211yesmaximal, characteristic, complemented
10C2×#10622281C212yesmaximal, complemented
11C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×Dic22C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C2×#66950—216no—
33C2×#66950C22116yescomplemented
34C2×#66946—28no—
35C2×#66946C2218yes—
36C2×#66941—28no—
37C2×#66941C2218yescomplemented
38C11×#389C2218yescomplemented
39C2×C11×#95C2212yes—
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43#10622607C22116yescomplemented
44#10622601C2218yes—
45#10622598C2218yescomplemented
46#10622552C2218yes—
47C4×C4⋊Dic11C2218yescomplemented
48#10622286C22116yescomplemented
49#10622281C22116yescomplemented
50C24×D11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C22×D44—24no—
62C22×D44—24no—
63C22×D44Q818yescomplemented
64C22×D44C2314yes—
65C22×C4×D11—28no—
66C22×C4×D11—28no—
67C22×C4×D11—44no—
68C22×C4×D11C2318yes—
69C22×Dic22—28no—
70C22×Dic22—28no—
71C22×Dic22—44no—
72C22×Dic22C2318yes—
73C2×C11×C4⋊C4—28no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4D418yes—
76C2×C11×C4⋊C4C2318yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C42×C11—24no—
80C2×C42×C11C2314yes—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×C4⋊Dic11—24no—
92C2×C4⋊Dic11—28no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11D418yescomplemented
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2318yes—
97C2×C4⋊Dic11C2314yes—
98C2×C4⋊Dic11C2314yes—
99C2×Dic11⋊C4—28no—
100C2×Dic11⋊C4C2318yes—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11C2314yes—
104C2×C4×Dic11C2314yes—
105#66950—264no—
106#66946—232no—
107#66941—232no—
108C11×#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2318yes—
112C2×#2452—111nomaximal, Sylow
113C24×C11C2411yescharacteristic
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11C2×Q818yes—
121C23×D11C2414yes—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11C2×D418yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×Q814yes—
136C22×C4×C11#4114yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11C2×D414yes—
155C22×Dic11C2×D414yes—
156C22×Dic11#4114yes—
157C22×Dic11C2412yes—
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C2×D44—232no—
163C2×D44—28no—
164C2×D44—28no—
165C2×D44C2×Q8116yescomplemented
166C2×C4×D11—216no—
167C2×C4×D11—216no—
168C2×C4×D11—48no—
169C2×C4×D11—432no—
170C2×Dic22—216no—
171C2×Dic22—216no—
172C2×Dic22—48no—
173C2×Dic22—432no—
174C11×C4⋊C4—216no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4C2×D4116yes—
177C42×C11—28no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—216no—
180(C2×D11)⋊C4—216no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—48no—
183C4⋊Dic11—216no—
184C4⋊Dic11—28no—
185C4⋊Dic11—28no—
186C4⋊Dic11C2×D4116yescomplemented
187Dic11⋊C4—216no—
188C4×Dic11—28no—
189C4×Dic11—28no—
190C22×C4⋊Q8—111no—
191C22×C22⋊Q8—112no—
192C22×C4×D4—111no—
193#2452—1116no—
194C2×#396—112no—
195C2×#393—112no—
196C2×#390—111no—
197C2×#390—111no—
198C2×#389—111no—
199C2×#389D1111yescharacteristic, complemented
200C2×#385—112no—
201C2×C4×C4⋊C4—111no—
202C23×C11C22×D412yes—
203C23×C11C22×D412yes—
204C23×C11C22×Q812yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4112yes—
207C23×C11H(5,𝔽2)12yes—
208C23×C112−1+412yes—
209C23×C11C2511yescharacteristic
210C22×D11—216no—
211C22×D11—216no—
212C22×D11—216no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—48no—
220C22×D11—48no—
221C22×D11—48no—
222C22×D11—48no—
223C22×D11C22×Q818yes—
224C2×C4×C11—28no—
225C2×C4×C11—216no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—48no—
237C2×C4×C11—44no—
238C2×C4×C11C22⋊Q8116yescomplemented
239C2×C4×C11C22×D418yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C22×D414yes—
242C2×C4×C11C22×Q814yes—
243C2×C4×C11C2×#4114yes—
244C2×Dic11—28no—
245C2×Dic11—28no—
246C2×Dic11—28no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—48no—
260C2×Dic11—44no—
261C2×Dic11C22×D414yes—
262C2×Dic11C22×D414yes—
263C2×Dic11C2×#4114yes—
264D44—232no—
265C4×D11—432no—
266Dic22—432no—
267C23×Q8—112no—
268C23×D4—111no—
269C24×C4—112no—
270C2×C4⋊Q8—118no—
271C2×C4⋊Q8—228no—
272C2×C22⋊Q8—1116no—
273C2×C22⋊Q8—2216no—
274C2×C4×D4—118no—
275C2×C4×D4—228no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—112no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4C2×D1112yes—
282C22×C4⋊C4C2×D1111yescharacteristic
283C22×C4⋊C4C2×D1111yescharacteristic
284C22×C22⋊C4—112no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C42—111no—
290C22×C42—111no—
291C22×C42C2×D1111yescharacteristic
292#396—1116no—
293#393—1116no—
294#390—118no—
295#390—118no—
296#389—118no—
297#389C2×D1118yescomplemented
298#385—1116no—
299C4×C4⋊C4—118no—
300C2×#95—111no—
301C2×#95—112no—
302C2×#95—111no—
303C2×#95C2×D1112yes—
304C22×C11C2×C22⋊Q814yes—
305C22×C11#53214yes—
306C22×C11#54214yes—
307C22×C11D4214yes—
308C22×C11#54814yes—
309C22×C11D4×Q814yes—
310C22×C11#55414yes—
311C22×C11C23×D411yescharacteristic
312C22×C11C23×D411yescharacteristic
313C22×C11C23×Q811yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C22×#4111yescharacteristic
316C22×C11C2×H(5,𝔽2)11yescharacteristic
317C22×C11C2×2−1+411yescharacteristic
318C2×D11—28no—
319C2×D11—28no—
320C2×D11—28no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—432no—
326C4×C11—24no—
327C4×C11—28no—
328C4×C11—44no—
329C4×C11—42no—
330C4×C11C2×C22⋊Q818yescomplemented
331Dic11—24no—
332Dic11—24no—
333Dic11—24no—
334Dic11—44no—
335Dic11—42no—
336C25—112no—
337C22×Q8—118no—
338C22×Q8—228no—
339C22×Q8—228no—
340C22×Q8—444no—
341C22×D4—118no—
342C22×D4—114no—
343C22×D4—224no—
344C22×D4—224no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—112no—
349C23×C4—111no—
350C23×C4—118no—
351C23×C4—228no—
352C23×C4—228no—
353C23×C4—444no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1112yes—
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C4⋊Q8—2232no—
360C22⋊Q8—2264no—
361C4×D4—2232no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—118no—
367C2×C4⋊C4—118no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—228no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4—228no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4D4418yes—
375C2×C4⋊C4C22×D1118yes—
376C2×C4⋊C4C22×D1114yes—
377C2×C4⋊C4C22×D1114yes—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—228no—
384C2×C22⋊C4—228no—
385C2×C22⋊C4—228no—
386C2×C22⋊C4—228no—
387C2×C22⋊C4—444no—
388C2×C42—24no—
389C2×C42—114no—
390C2×C42—114no—
391C2×C42—224no—
392C2×C42—224no—
393C2×C42C22×D1114yes—
394#95—114no—
395#95—114no—
396#95—118no—
397#95C22×D1118yes—
398C2×C11#245218yescomplemented
399C2×C11C22×C22⋊Q811yescharacteristic
400C2×C11C2×#53211yescharacteristic
401C2×C11C2×#54211yescharacteristic
402C2×C11C2×D4211yescharacteristic
403C2×C11C2×#54811yescharacteristic
404C2×C11C2×D4×Q811yescharacteristic
405C2×C11C2×#55411yescharacteristic
406D11—48no—
407C24—118no—
408C24—114no—
409C24—224no—
410C24—224no—
411C24—224no—
412C24—224no—
413C24—224no—
414C24—224no—
415C24C23×D1111yescharacteristic
416C2×Q8—2216no—
417C2×Q8—2216no—
418C2×Q8—448no—
419C2×Q8—4432no—
420C2×D4—1116no—
421C2×D4—2232no—
422C2×D4—228no—
423C2×D4—228no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—114no—
437C22×C4—112no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—114no—
442C22×C4—2216no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—224no—
455C22×C4—2216no—
456C22×C4—448no—
457C22×C4—4432no—
458C22×C4C2×D4418yes—
459C22×C4C2×D4414yes—
460C22×C4D4×D1114yes—
461C22×C4#434114yes—
462C22×C4Q8×D1114yes—
463C22×C4C23×D1112yes—
464C22×C4C23×D1114yes—
465C22×C4C23×D1114yes—
466C22×C4C23×D1112yes—
467C22×C4C23×D1112yes—
468C4⋊C4—216no—
469C4⋊C4—28no—
470C4⋊C4—1116no—
471C4⋊C4—2216no—
472C4⋊C4—228no—
473C4⋊C4—2216no—
474C4⋊C4—228no—
475C4⋊C4C2×D44116yes—
476C22⋊C4—2216no—
477C22⋊C4—2216no—
478C22⋊C4—2216no—
479C22⋊C4—2216no—
480C22⋊C4—448no—
481C42—28no—
482C42—228no—
483C42—228no—
484C11C2×#245211yescharacteristic, complemented, Sylow
485C23—118no—
486C23—2216no—
487C23—2216no—
488C23—224no—
489C23—224no—
490C23—224no—
491C23—224no—
492C23—224no—
493C23—224no—
494C23—2216no—
495C23—448no—
496C23—448no—
497C23—448no—
498C23—448no—
499C23C22×D4412yes—
500C23C2×D4×D1112yes—
501C23C2×#434112yes—
502C23C2×Q8×D1112yes—
503C23#6704012yes—
504C23#41×D1112yes—
505C23#6704212yes—
506C23C24×D1111yescharacteristic
507Q8—4432no—
508D4—2232no—
509C2×C4—216no—
510C2×C4—28no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—48no—
522C2×C4—44no—
523C2×C4—114no—
524C2×C4—114no—
525C2×C4—114no—
526C2×C4—228no—
527C2×C4—228no—
528C2×C4—228no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—4432no—
542C2×C4—448no—
543C2×C4—444no—
544C2×C4#66950116yescomplemented
545C2×C4C22×D4418yes—
546C2×C4C22×D4414yes—
547C2×C4C2×D4×D1114yes—
548C2×C4C2×#434114yes—
549C2×C4C2×Q8×D1114yes—
550C22—228no—
551C22—228no—
552C22—228no—
553C22—444no—
554C22—4432no—
555C22—444no—
556C22—444no—
557C22—444no—
558C22C2×#6695014yes—
559C22D4×D4414yes—
560C22#1062310714yes—
561C22#1062312714yes—
562C22#1062317414yes—
563C22#1062322114yes—
564C22#1062325814yes—
565C22C23×D4411yescharacteristic
566C22C22×D4×D1111yescharacteristic
567C22C22×#434111yescharacteristic
568C22C22×Q8×D1111yescharacteristic
569C22C2×#6704011yescharacteristic
570C22C2×#41×D1111yescharacteristic
571C22C2×#6704211yescharacteristic
572C4—24no—
573C4—28no—
574C4—44no—
575C4—42no—
576C4—224no—
577C4—224no—
578C4—224no—
579C4—444no—
580C4—442no—
581C4C2×#6695018yescomplemented
582C2—448no—
583C2#1307246418yesdirect product factor
584C2C22×#6695011yescharacteristic
585C2C2×#1062312711yescharacteristic
586C2C2×#1062317411yescharacteristic
587C2C2×D4×D4411yescharacteristic
588C2C2×#1062310711yescharacteristic
589C2C2×#1062325811yescharacteristic
590C2C2×#1062322111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11C2×#2452
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C22×#66950C2semidirect
4. #13072464C2direct (N × H)
5. C2×#10622607C2semidirect
6. C2×#10622286C2semidirect
9. C2×#10622598C2semidirect
10. C2×#10622281C2semidirect
11. C2×C4×C4⋊Dic11C2semidirect
12. C2×C11×#389C2semidirect
33. C2×#66950C22semidirect
37. C2×#66941C22semidirect
38. C11×#389C22semidirect
43. #10622607C22semidirect
45. #10622598C22semidirect
47. C4×C4⋊Dic11C22semidirect
48. #10622286C22semidirect
49. #10622281C22semidirect
63. C22×D44Q8semidirect
94. C2×C4⋊Dic11D4semidirect
165. C2×D44C2×Q8semidirect
186. C4⋊Dic11C2×D4semidirect
199. C2×#389D11semidirect
238. C2×C4×C11C22⋊Q8semidirect
297. #389C2×D11semidirect
330. C4×C11C2×C22⋊Q8semidirect
398. C2×C11#2452semidirect
484. C11C2×#2452semidirect
544. C2×C4#66950semidirect
581. C4C2×#66950semidirect
583. C2#13072464direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
C22×#669502
C22×#669462
#130724642
C2×#106226072
C2×#106222862
C2×#106225522
C2×#106226012
C2×#106225982
C2×#106222812
C2×C4×C4⋊Dic112
C2×C11×#3892
C2×#245211