Finite Group Databasebeta

← C2×#13073537 #14925544

Subgroups — C2×#13073537 #14925544

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C212yesmaximal, complemented
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic
4#13073537C2116yesmaximal, direct product factor
5C2×#10622289C212yesmaximal, complemented
6C2×#10622607C212yesmaximal, complemented
7C2×#10622552C211yesmaximal, characteristic
8C2×#10622601C211yesmaximal, characteristic
9C2×#10622586C211yesmaximal, characteristic, complemented
10C2×#10622589C211yesmaximal, characteristic, complemented
11C2×#10622280C212yesmaximal, complemented
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
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×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×#66949—216no—
35C2×#66949C22116yescomplemented
36C2×#66946—28no—
37C2×#66946C2218yes—
38C2×C4×Dic22—28no—
39C2×C4×Dic22C2218yescomplemented
40C11×#389C2218yescomplemented
41C2×C11×#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622607C22116yescomplemented
44#10622601C2218yes—
45#10622589C2218yescomplemented
46#10622586C2218yescomplemented
47#10622552C2218yes—
48#10622289C22116yescomplemented
49#10622280C22116yescomplemented
50C24×D11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
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—28no—
68C22×C4×D11C2318yes—
69C22×Dic22—24no—
70C22×Dic22—24no—
71C22×Dic22D418yescomplemented
72C22×Dic22C2314yes—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—28no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2318yes—
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—44no—
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—24no—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2314yes—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—28no—
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4—44no—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2318yes—
103C2×Dic11⋊C4C2318yes—
104C2×Dic11⋊C4C2318yes—
105C2×C4×Dic11—24no—
106C2×C4×Dic11D418yes—
107C2×C4×Dic11C2314yes—
108C2×C4×Dic11C2314yes—
109#66949—264no—
110#66946—232no—
111C4×Dic22—232no—
112C11×#95C2318yes—
113C11⋊#95C2318yes—
114C2×#2538—111nomaximal, Sylow
115C24×C11C2411yescharacteristic
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11C2×Q818yes—
123C23×D11C2414yes—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×Q814yes—
138C22×C4×C11#4114yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2412yes—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11C2×D414yes—
155C22×Dic11C2×D414yes—
156C22×Dic11C2×D414yes—
157C22×Dic11C2×D414yes—
158C22×Dic11#4114yes—
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164C2×D44—232no—
165C2×D44—28no—
166C2×D44—28no—
167C2×D44C2×Q8116yescomplemented
168C2×C4×D11—216no—
169C2×C4×D11—216no—
170C2×C4×D11—216no—
171C2×C4×D11—432no—
172C2×Dic22—232no—
173C2×Dic22—28no—
174C2×Dic22—28no—
175C2×Dic22C2×D4116yescomplemented
176C11×C4⋊C4—28no—
177C11×C4⋊C4—216no—
178C11×C4⋊C4—28no—
179C42×C11—28no—
180(C2×D11)⋊C4—216no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—48no—
184(C2×D11)⋊C4—48no—
185C4⋊Dic11—28no—
186C4⋊Dic11—28no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189Dic11⋊C4—216no—
190Dic11⋊C4—216no—
191Dic11⋊C4—48no—
192C4×Dic11—28no—
193C4×Dic11C2×D4116yes—
194C22×C22⋊Q8—112no—
195C22×C4×Q8—111no—
196C22×C4×D4—111no—
197#2538—1116no—
198C2×#396—112no—
199C2×#396—112no—
200C2×#390—111no—
201C2×#390—111no—
202C2×#389—111no—
203C2×#389D1111yescharacteristic, complemented
204C2×#384—111no—
205C2×#380—112no—
206C23×C11C22×D412yes—
207C23×C11C22×D412yes—
208C23×C11C22×Q812yes—
209C23×C11C2×#4112yes—
210C23×C11C2×#4112yes—
211C23×C11H(5,𝔽2)12yes—
212C23×C112−1+412yes—
213C23×C11C2511yescharacteristic
214C22×D11—216no—
215C22×D11—216no—
216C22×D11—216no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—48no—
224C22×D11—48no—
225C22×D11—48no—
226C22×D11—48no—
227C22×D11C22×Q818yes—
228C2×C4×C11—28no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—48no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11C22⋊Q8116yescomplemented
244C2×C4×C11C22×D414yes—
245C2×C4×C11C22×D414yes—
246C2×C4×C11C22×Q814yes—
247C2×C4×C11C2×#4114yes—
248C2×Dic11—28no—
249C2×Dic11—28no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—44no—
261C2×Dic11—48no—
262C2×Dic11#121116yes—
263C2×Dic11C22×D414yes—
264C2×Dic11C22×D414yes—
265C2×Dic11C22×D414yes—
266C2×Dic11C22×D414yes—
267C2×Dic11C2×#4114yes—
268D44—232no—
269C4×D11—432no—
270Dic22—232no—
271C23×Q8—111no—
272C23×D4—111no—
273C24×C4—112no—
274C2×C22⋊Q8—1116no—
275C2×C22⋊Q8—2216no—
276C2×C4×Q8—118no—
277C2×C4×Q8—228no—
278C2×C4×D4—118no—
279C2×C4×D4—228no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4C2×D1112yes—
288C22×C4⋊C4C2×D1111yescharacteristic
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C42—111no—
296C22×C42—111no—
297C22×C42C2×D1111yescharacteristic
298#396—1116no—
299#396—1116no—
300#390—118no—
301#390—118no—
302#389—118no—
303#389C2×D1118yescomplemented
304#384—118no—
305#380—1116no—
306C2×#95—112no—
307C2×#95C2×D1112yes—
308C22×C11C2×#12114yes—
309C22×C11C2×C22⋊Q814yes—
310C22×C11#53714yes—
311C22×C11D4×Q814yes—
312C22×C11#55014yes—
313C22×C11#55414yes—
314C22×C11#55614yes—
315C22×C11C23×D411yescharacteristic
316C22×C11C23×D411yescharacteristic
317C22×C11C23×Q811yescharacteristic
318C22×C11C22×#4111yescharacteristic
319C22×C11C22×#4111yescharacteristic
320C22×C11C2×H(5,𝔽2)11yescharacteristic
321C22×C11C2×2−1+411yescharacteristic
322C2×D11—28no—
323C2×D11—28no—
324C2×D11—28no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—432no—
330C4×C11—24no—
331C4×C11—44no—
332C4×C11—42no—
333C4×C11—44no—
334C4×C11C2×C22⋊Q818yescomplemented
335Dic11—24no—
336Dic11—24no—
337Dic11—42no—
338Dic11—44no—
339Dic11C2×#12118yes—
340C25—112no—
341C22×Q8—118no—
342C22×Q8—114no—
343C22×Q8—224no—
344C22×Q8—224no—
345C22×D4—118no—
346C22×D4—114no—
347C22×D4—224no—
348C22×D4—224no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—112no—
353C23×C4—111no—
354C23×C4—118no—
355C23×C4—228no—
356C23×C4—228no—
357C23×C4—228no—
358C23×C4C22×D1112yes—
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1112yes—
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C22⋊Q8—2264no—
364C4×Q8—2232no—
365C4×D4—2232no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—118no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—118no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—228no—
380C2×C4⋊C4—228no—
381C2×C4⋊C4—224no—
382C2×C4⋊C4—444no—
383C2×C4⋊C4C22×D1114yes—
384C2×C4⋊C4C22×D1118yes—
385C2×C4⋊C4C22×D1114yes—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—228no—
392C2×C22⋊C4—228no—
393C2×C22⋊C4—228no—
394C2×C22⋊C4—444no—
395C2×C22⋊C4—444no—
396C2×C42—24no—
397C2×C42—118no—
398C2×C42—114no—
399C2×C42—114no—
400C2×C42—224no—
401C2×C42C22×D1114yes—
402#95—118no—
403#95C22×D1118yes—
404C2×C11#253818yescomplemented
405C2×C11C22×#12111yescharacteristic
406C2×C11C22×C22⋊Q811yescharacteristic
407C2×C11C2×#53711yescharacteristic
408C2×C11C2×D4×Q811yescharacteristic
409C2×C11C2×#55011yescharacteristic
410C2×C11C2×#55411yescharacteristic
411C2×C11C2×#55611yescharacteristic
412D11—48no—
413C24—118no—
414C24—114no—
415C24—224no—
416C24—224no—
417C24—224no—
418C24—224no—
419C24—224no—
420C24—224no—
421C24C23×D1111yescharacteristic
422C2×Q8—1116no—
423C2×Q8—228no—
424C2×Q8—2232no—
425C2×Q8—228no—
426C2×D4—1116no—
427C2×D4—2232no—
428C2×D4—228no—
429C2×D4—228no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—114no—
451C22×C4—2216no—
452C22×C4—2216no—
453C22×C4—2216no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—224no—
459C22×C4—222no—
460C22×C4—224no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—224no—
464C22×C4—4432no—
465C22×C4#433914yes—
466C22×C4D4×D1114yes—
467C22×C4D4×D1114yes—
468C22×C4Q8×D1114yes—
469C22×C4C23×D1114yes—
470C22×C4C23×D1112yes—
471C22×C4C23×D1114yes—
472C22×C4C23×D1112yes—
473C22×C4C23×D1112yes—
474C4⋊C4—28no—
475C4⋊C4—28no—
476C4⋊C4—216no—
477C4⋊C4—228no—
478C4⋊C4—228no—
479C4⋊C4—228no—
480C4⋊C4—2216no—
481C4⋊C4—2216no—
482C4⋊C4—228no—
483C4⋊C4—448no—
484C22⋊C4—2216no—
485C22⋊C4—2216no—
486C22⋊C4—2216no—
487C22⋊C4—448no—
488C22⋊C4—448no—
489C42—28no—
490C42—1116no—
491C42—228no—
492C11C2×#253811yescharacteristic, complemented, Sylow
493C23—118no—
494C23—2216no—
495C23—2216no—
496C23—224no—
497C23—224no—
498C23—224no—
499C23—224no—
500C23—224no—
501C23—224no—
502C23—2216no—
503C23—448no—
504C23—448no—
505C23—448no—
506C23—448no—
507C23C2×#433912yes—
508C23C2×D4×D1112yes—
509C23C2×D4×D1112yes—
510C23C2×Q8×D1112yes—
511C23#6704012yes—
512C23#41×D1112yes—
513C23#6704212yes—
514C23C24×D1111yescharacteristic
515Q8—2232no—
516D4—2232no—
517C2×C4—28no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—48no—
530C2×C4—48no—
531C2×C4—44no—
532C2×C4—1116no—
533C2×C4—114no—
534C2×C4—114no—
535C2×C4—114no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—228no—
539C2×C4—228no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—224no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—224no—
550C2×C4—4432no—
551C2×C4—448no—
552C2×C4—444no—
553C2×C4#66949116yescomplemented
554C2×C4C2×#433914yes—
555C2×C4C2×D4×D1114yes—
556C2×C4C2×D4×D1114yes—
557C2×C4C2×Q8×D1114yes—
558C22—228no—
559C22—228no—
560C22—228no—
561C22—444no—
562C22—444no—
563C22—4432no—
564C22—444no—
565C22—444no—
566C22C2×#6694914yes—
567C22#1062308414yes—
568C22#1062309914yes—
569C22D11×#12114yes—
570C22#1062316014yes—
571C22#1062322114yes—
572C22#1062325814yes—
573C22C22×#433911yescharacteristic
574C22C22×D4×D1111yescharacteristic
575C22C22×D4×D1111yescharacteristic
576C22C22×Q8×D1111yescharacteristic
577C22C2×#6704011yescharacteristic
578C22C2×#41×D1111yescharacteristic
579C22C2×#6704211yescharacteristic
580C4—24no—
581C4—42no—
582C4—44no—
583C4—44no—
584C4—118no—
585C4—224no—
586C4—224no—
587C4—442no—
588C4—444no—
589C4C2×#6694918yescomplemented
590C2—448no—
591C2#1307353718yesdirect product factor
592C2C2×D11×#12111yescharacteristic
593C2C22×#6694911yescharacteristic
594C2C2×#1062316011yescharacteristic
595C2C2×#1062325811yescharacteristic
596C2C2×#1062308411yescharacteristic
597C2C2×#1062322111yescharacteristic
598C2C2×#1062309911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11C2×#2538
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
2. C22×C4×Dic22C2semidirect
4. #13073537C2direct (N × H)
5. C2×#10622289C2semidirect
6. C2×#10622607C2semidirect
9. C2×#10622586C2semidirect
10. C2×#10622589C2semidirect
11. C2×#10622280C2semidirect
12. C2×C11×#389C2semidirect
35. C2×#66949C22semidirect
39. C2×C4×Dic22C22semidirect
40. C11×#389C22semidirect
43. #10622607C22semidirect
45. #10622589C22semidirect
46. #10622586C22semidirect
48. #10622289C22semidirect
49. #10622280C22semidirect
63. C22×D44Q8semidirect
71. C22×Dic22D4semidirect
167. C2×D44C2×Q8semidirect
175. C2×Dic22C2×D4semidirect
203. C2×#389D11semidirect
243. C2×C4×C11C22⋊Q8semidirect
303. #389C2×D11semidirect
334. C4×C11C2×C22⋊Q8semidirect
404. C2×C11#2538semidirect
492. C11C2×#2538semidirect
553. C2×C4#66949semidirect
589. C4C2×#66949semidirect
591. C2#13073537direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×C4×Dic222
C22×#669462
#130735372
C2×#106222892
C2×#106226072
C2×#106225522
C2×#106226012
C2×#106225862
C2×#106225892
C2×#106222802
C2×C11×#3892
C2×#253811