Finite Group Databasebeta

← C2×#13072482 #14921936

Subgroups — C2×#13072482 #14921936

Order 2816.

3094 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic, complemented
2#13072482C2116yesmaximal, direct product factor
3C2×#10622562C212yesmaximal, complemented
4C2×#10622561C212yesmaximal, complemented
5C2×#10622834C211yesmaximal, characteristic
6C2×#10622834C211yesmaximal, characteristic
7C2×#10622598C211yesmaximal, characteristic, complemented
8C2×#10622541C211yesmaximal, characteristic, complemented
9C2×#10622823C212yesmaximal, complemented
10C2×#10622825C212yesmaximal, complemented
11C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2212yes—
15C2×C4×D4×C11—28no—
16C2×C4×D4×C11C2218yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C4⋊Dic11C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×#66943—28no—
35C2×#66943C2218yescomplemented
36#10622834C2218yes—
37#10622834C2218yes—
38#10622825C22116yescomplemented
39#10622823C22116yescomplemented
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622598C2218yescomplemented
45#10622562C22116yescomplemented
46#10622561C22116yescomplemented
47C4×Dic11⋊C4C2218yescomplemented
48#10622541C2218yescomplemented
49C25×C11C2312yes—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11Q818yes—
53C22×D4×C11C2314yes—
54C23×C4×C11—28no—
55C23×C4×C11—28no—
56C23×C4×C11—44no—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2318yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C4×D4×C11—232no—
69C2×C11×C4⋊C4D418yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C22⋊C4—28no—
72C2×C11×C22⋊C4C2318yes—
73C2×C42×C11—24no—
74C2×C42×C11C2314yes—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11—44no—
77C2×C22⋊Dic11—44no—
78C2×C22⋊Dic11—44no—
79C2×C22⋊Dic11C2318yes—
80C2×C22⋊Dic11C2318yes—
81C2×C22⋊Dic11C2318yes—
82C2×C22⋊Dic11C2318yes—
83C2×C4⋊Dic11—28no—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11—44no—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2318yes—
89C2×C4⋊Dic11C2314yes—
90C2×C4⋊Dic11C2318yes—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—44no—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2318yes—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—24no—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2314yes—
103#66943—232no—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C2×#2454—111nomaximal, Sylow
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11C2×Q818yes—
116C24×C11C2414yes—
117C24×C11C2411yescharacteristic
118C2×D4×C11—232no—
119C2×D4×C11—28no—
120C2×D4×C11—28no—
121C2×D4×C11C2×Q8116yes—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—216no—
130C22×C4×C11—216no—
131C22×C4×C11—48no—
132C22×C4×C11—432no—
133C22×C4×C11C2×D418yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×Q814yes—
136C22×C4×C11#4114yes—
137C22×C4×C11#4114yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11#4114yes—
160C22×Dic11C2412yes—
161C22×Dic11C2414yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164C22×Dic11C2414yes—
165C22×Dic11C2412yes—
166C11×C4⋊C4C2×D4116yes—
167C11×C22⋊C4—216no—
168C42×C11—28no—
169C22⋊Dic11—216no—
170C22⋊Dic11—48no—
171C22⋊Dic11—48no—
172C22⋊Dic11—48no—
173C4⋊Dic11—216no—
174C4⋊Dic11—28no—
175C4⋊Dic11—28no—
176C4⋊Dic11—48no—
177Dic11⋊C4—28no—
178Dic11⋊C4—216no—
179Dic11⋊C4—28no—
180Dic11⋊C4—48no—
181C4×Dic11—28no—
182C4×Dic11—28no—
183C22×#125—111no—
184C22×C4×D4D1111yescharacteristic
185#2454—1116no—
186C2×#399—112no—
187C2×#396—112no—
188C2×#390—111no—
189C2×#390—111no—
190C2×#389—111no—
191C2×#389—111no—
192C2×#385—112no—
193C2×#380—112no—
194C2×C4×C4⋊C4—111no—
195C23×C11—216no—
196C23×C11—216no—
197C23×C11—216no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11C22×D412yes—
209C23×C11C22×Q818yes—
210C23×C11C22×Q812yes—
211C23×C11C2×#4112yes—
212C23×C11C2×#4112yes—
213C23×C11C2×#4112yes—
214C23×C11H(5,𝔽2)12yes—
215C23×C11H(5,𝔽2)12yes—
216C23×C11C2511yescharacteristic
217D4×C11—232no—
218C2×C4×C11—28no—
219C2×C4×C11—216no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—432no—
228C2×C4×C11—44no—
229C2×C4×C11C22⋊Q8116yes—
230C2×C4×C11C22×D418yes—
231C2×C4×C11C22×D414yes—
232C2×C4×C11C22×Q814yes—
233C2×C4×C11C2×#4114yes—
234C2×C4×C11C2×#4114yes—
235C2×Dic11—28no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—44no—
254C2×Dic11—48no—
255C2×Dic11—44no—
256C2×Dic11—44no—
257C2×Dic11—48no—
258C2×Dic11C2×#4114yes—
259C23×D4C2×D1111yescharacteristic
260C24×C4C2×D1112yes—
261C2×#125—118no—
262C2×#125—228no—
263C2×C4×D4—28no—
264C2×C4×D4C2×D1118yes—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4—112no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4C2×D1112yes—
279C22×C42—111no—
280C22×C42—111no—
281C22×C42C2×D1111yescharacteristic
282#399—1116no—
283#396—1116no—
284#390—118no—
285#390—118no—
286#389—118no—
287#389—118no—
288#385—1116no—
289#380—1116no—
290C4×C4⋊C4—118no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—111no—
294C2×#95—112no—
295C22×C11—28no—
296C22×C11—28no—
297C22×C11—28no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—432no—
303C22×C11C2×C22⋊Q814yes—
304C22×C11#52914yes—
305C22×C11#54014yes—
306C22×C11#54614yes—
307C22×C11#55014yes—
308C22×C11#55414yes—
309C22×C11#55414yes—
310C22×C11C23×D411yescharacteristic
311C22×C11C23×Q811yescharacteristic
312C22×C11C22×#4111yescharacteristic
313C22×C11C22×#4111yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C2×H(5,𝔽2)11yescharacteristic
316C22×C11C2×H(5,𝔽2)11yescharacteristic
317C4×C11—24no—
318C4×C11—28no—
319C4×C11—42no—
320C4×C11C2×C22⋊Q818yes—
321Dic11—24no—
322Dic11—42no—
323Dic11—44no—
324Dic11—42no—
325Dic11—42no—
326Dic11—44no—
327C25C22×D1112yes—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4Dic2218yes—
331C22×D4C22×D1114yes—
332C23×C4—28no—
333C23×C4—28no—
334C23×C4—44no—
335C23×C4—111no—
336C23×C4—112no—
337C23×C4—112no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4C22×D1111yescharacteristic
342C23×C4C22×D1118yes—
343C23×C4C22×D1111yescharacteristic
344C23×C4C22×D1112yes—
345C23×C4C22×D1111yescharacteristic
346#125—2232no—
347C4×D4—232no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—114no—
351C2×C4⋊C4—114no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—118no—
355C2×C4⋊C4—118no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—228no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—444no—
363C2×C4⋊C4—444no—
364C2×C4⋊C4C22⋊D1118yes—
365C2×C4⋊C4C22×D1114yes—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—228no—
372C2×C22⋊C4—444no—
373C2×C22⋊C4—444no—
374C2×C22⋊C4—444no—
375C2×C22⋊C4C22×D1118yes—
376C2×C42—24no—
377C2×C42—114no—
378C2×C42—114no—
379C2×C42—224no—
380C2×C42—224no—
381C2×C42C22×D1114yes—
382#95—114no—
383#95—114no—
384#95—118no—
385#95—118no—
386C2×C11—48no—
387C2×C11#245418yescomplemented
388C2×C11C22×C22⋊Q811yescharacteristic
389C2×C11C2×#52911yescharacteristic
390C2×C11C2×#54011yescharacteristic
391C2×C11C2×#54611yescharacteristic
392C2×C11C2×#55011yescharacteristic
393C2×C11C2×#55411yescharacteristic
394C2×C11C2×#55411yescharacteristic
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24C2×Dic2218yes—
402C24C23×D1114yes—
403C24C23×D1111yescharacteristic
404C2×D4—232no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4C2×Dic22116yes—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—216no—
416C22×C4—216no—
417C22×C4—48no—
418C22×C4—432no—
419C22×C4—114no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—114no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4—224no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—224no—
443C22×C4C2×Dic2214yes—
444C22×C4#433914yes—
445C22×C4#434114yes—
446C22×C4C2×C22⋊D1118yes—
447C22×C4C2×C22⋊D1114yes—
448C22×C4C23×D1112yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1114yes—
451C22×C4C23×D1112yes—
452C4⋊C4—228no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—2216no—
456C4⋊C4—2216no—
457C4⋊C4—228no—
458C4⋊C4—448no—
459C4⋊C4—448no—
460C4⋊C4C2×C22⋊D11116yes—
461C22⋊C4—216no—
462C22⋊C4—2216no—
463C22⋊C4—448no—
464C22⋊C4—448no—
465C22⋊C4—448no—
466C42—28no—
467C42—228no—
468C42—228no—
469C11C2×#245411yescharacteristic, complemented, Sylow
470C23—216no—
471C23—216no—
472C23—216no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—48no—
483C23C22×Dic2218yes—
484C23C22×Dic2212yes—
485C23C2×#433912yes—
486C23C2×#434112yes—
487C23#6703712yes—
488C23#41×D1112yes—
489C23#6704212yes—
490C23C22×C22⋊D1112yes—
491C23C24×D1111yescharacteristic
492D4—232no—
493C2×C4—28no—
494C2×C4—216no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—432no—
503C2×C4—44no—
504C2×C4—114no—
505C2×C4—228no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—224no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—444no—
524C2×C4—444no—
525C2×C4—448no—
526C2×C4—448no—
527C2×C4—444no—
528C2×C4#66977116yes—
529C2×C4C22×Dic2214yes—
530C2×C4C2×#433914yes—
531C2×C4C2×#434114yes—
532C2×C4C22×C22⋊D1118yes—
533C2×C4C22×C22⋊D1114yes—
534C22—28no—
535C22—28no—
536C22—28no—
537C22—44no—
538C22—432no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22#1062307014yes—
543C22#1062307414yes—
544C22#1062308814yes—
545C22#1062309314yes—
546C22C2×#6697714yes—
547C22#1062333714yes—
548C22#1062336514yes—
549C22C23×Dic2211yescharacteristic
550C22C22×#433911yescharacteristic
551C22C22×#434111yescharacteristic
552C22C2×#6703711yescharacteristic
553C22C2×#41×D1111yescharacteristic
554C22C2×#6704211yescharacteristic
555C22C23×C22⋊D1111yescharacteristic
556C4—24no—
557C4—28no—
558C4—42no—
559C4—224no—
560C4—442no—
561C4—444no—
562C4—442no—
563C4—444no—
564C4—442no—
565C4C2×#6697718yes—
566C2—48no—
567C2#1307248218yesdirect product factor
568C2C22×#6697711yescharacteristic
569C2C2×#1062308811yescharacteristic
570C2C2×#1062309311yescharacteristic
571C2C2×#1062333711yescharacteristic
572C2C2×#1062336511yescharacteristic
573C2C2×#1062307411yescharacteristic
574C2C2×#1062307011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11C2×#2454
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
2. #13072482C2direct (N × H)
3. C2×#10622562C2semidirect
4. C2×#10622561C2semidirect
7. C2×#10622598C2semidirect
8. C2×#10622541C2semidirect
9. C2×#10622823C2semidirect
10. C2×#10622825C2semidirect
11. C2×C4×Dic11⋊C4C2semidirect
35. C2×#66943C22semidirect
38. #10622825C22semidirect
39. #10622823C22semidirect
44. #10622598C22semidirect
45. #10622562C22semidirect
46. #10622561C22semidirect
47. C4×Dic11⋊C4C22semidirect
48. #10622541C22semidirect
387. C2×C11#2454semidirect
469. C11C2×#2454semidirect
567. C2#13072482direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669432
#130724822
C2×#106225622
C2×#106225612
C2×#106228342
C2×#106225982
C2×#106225412
C2×#106228232
C2×#106228252
C2×C4×Dic11⋊C42
C22×C4×D4×C112
C2×#245411