Finite Group Databasebeta

← C2×#13072968 #14923219

Subgroups — C2×#13072968 #14923219

Order 2816.

3158 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic
3#13072968C2116yesmaximal, direct product factor
4C2×#10622288C212yesmaximal, complemented
5C2×#10622572C212yesmaximal, complemented
6C2×#10622552C211yesmaximal, characteristic, complemented
7C2×#10622552C211yesmaximal, characteristic, complemented
8C2×#10622570C212yesmaximal, complemented
9C2×#10622282C212yesmaximal, complemented
10C2×#10622825C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×D44C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C2×#66983—28no—
22C2×#66983C2218yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×Dic11⋊C4C2212yes—
33C22×C4×Dic11C2212yes—
34C2×#66923—28no—
35C2×#66923C2218yescomplemented
36C4×C11×C22⋊C4C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39#10622825C2218yescomplemented
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622572C22116yescomplemented
43#10622570C22116yescomplemented
44#10622552C2218yescomplemented
45#10622552C2218yescomplemented
46C4×C4⋊Dic11C2218yescomplemented
47#10622288C22116yescomplemented
48#10622282C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2312yes—
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11—24no—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2314yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—28no—
62C22×C22⋊D11—28no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11C2318yes—
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C22×D44—24no—
69C22×D44—24no—
70C22×D44—24no—
71C22×D44C2314yes—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4C2314yes—
75C2×C11×C22⋊C4C2314yes—
76C2×C42×C11—24no—
77C2×C42×C11—24no—
78C2×C42×C11C2314yes—
79C2×C42×C11C2314yes—
80C2×C22⋊Dic11—44no—
81C2×C22⋊Dic11C2318yes—
82#66983—232no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11D418yes—
96C2×C4⋊Dic11C2314yes—
97C2×C4⋊Dic11C2314yes—
98C2×C4⋊Dic11C2314yes—
99C2×Dic11⋊C4—28no—
100C2×Dic11⋊C4—28no—
101C2×Dic11⋊C4C2318yes—
102C2×Dic11⋊C4C2318yes—
103C2×C4×Dic11—44no—
104C2×C4×Dic11C2318yes—
105#66923—232no—
106C11×#95C2314yes—
107C11×#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C2×#2490—111nomaximal, Sylow
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11#4114yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11C2414yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—28no—
143C22×C4×C11—28no—
144C22×C4×C11—28no—
145C22×C4×C11—416no—
146C22×C4×C11C2×D414yes—
147C22×C4×C11#4114yes—
148C22×C4×C11#4114yes—
149C22×C4×C11#4114yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C2×C22⋊D11—216no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—432no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11C2×D418yes—
169C22×Dic11C2414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2414yes—
172C2×D44—28no—
173C2×D44—28no—
174C2×D44—28no—
175C2×D44—416no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—28no—
178C42×C11—28no—
179C42×C11—28no—
180C22⋊Dic11—48no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—48no—
184(C2×D11)⋊C4—48no—
185(C2×D11)⋊C4—48no—
186C4⋊Dic11—28no—
187C4⋊Dic11—28no—
188C4⋊Dic11C2×D4116yes—
189Dic11⋊C4—216no—
190Dic11⋊C4—216no—
191C4×Dic11—48no—
192C22×#125—111no—
193C22×#121—111no—
194#2490—1116no—
195C2×#397—112no—
196C2×#394—112no—
197C2×#390—111no—
198C2×#390—111no—
199C2×#390—112no—
200C2×#388—112no—
201C2×#380—111no—
202C2×C4×C4⋊C4—111no—
203C2×C4×C22⋊C4D1111yescharacteristic, complemented
204C23×C11—28no—
205C23×C11—28no—
206C23×C11—28no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—44no—
217C23×C11C22×D412yes—
218C23×C11C2×#4114yes—
219C23×C11C2×#4112yes—
220C23×C11C2×#4112yes—
221C23×C11C2×#4112yes—
222C23×C11C2×#4112yes—
223C23×C11H(5,𝔽2)12yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11C2511yescharacteristic
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—48no—
234C22×D11—48no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C2×C4×C11—28no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
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—44no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C2×C4×C11—44no—
259C2×C4×C11—416no—
260C2×C4×C11#124116yes—
261C2×C4×C11C22×D414yes—
262C2×C4×C11C2×#4114yes—
263C2×C4×C11C2×#4114yes—
264C2×C4×C11C2×#4114yes—
265C22⋊D11—432no—
266C2×Dic11—216no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—48no—
276C2×Dic11—48no—
277C2×Dic11C22×D418yes—
278D44—416no—
279C23×D4—112no—
280C23×D4—111no—
281C24×C4C2×D1111yescharacteristic
282C2×#125—118no—
283C2×#125—228no—
284C2×#121—118no—
285C2×#121—228no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—112no—
288C22×C4⋊C4—112no—
289C22×C4⋊C4—111no—
290C22×C4⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4C2×D1111yescharacteristic
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C42—112no—
300C22×C42C2×D1111yescharacteristic
301C22×C42C2×D1111yescharacteristic
302#397—1116no—
303#394—1116no—
304#390—1116no—
305#390—118no—
306#390—118no—
307#388—1116no—
308#380—118no—
309C4×C4⋊C4—118no—
310C4×C22⋊C4C2×D1118yescomplemented
311C2×#95—112no—
312C2×#95—112no—
313C2×#95C2×D1111yescharacteristic
314C2×#95C2×D1111yescharacteristic
315C22×C11—24no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—416no—
323C22×C11C2×#12414yes—
324C22×C11#52914yes—
325C22×C11#54014yes—
326C22×C11#54614yes—
327C22×C11#55014yes—
328C22×C11#55314yes—
329C22×C11#55314yes—
330C22×C11C23×D411yescharacteristic
331C22×C11C22×#4111yescharacteristic
332C22×C11C22×#4111yescharacteristic
333C22×C11C22×#4111yescharacteristic
334C22×C11C22×#4111yescharacteristic
335C22×C11C2×H(5,𝔽2)11yescharacteristic
336C22×C11C2×H(5,𝔽2)11yescharacteristic
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—816no—
345C4×C11—24no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11C2×#12418yes—
351Dic11—28no—
352Dic11—44no—
353Dic11—44no—
354C25—112no—
355C25C22×D1111yescharacteristic
356C22×D4—118no—
357C22×D4—114no—
358C22×D4—228no—
359C22×D4—228no—
360C22×D4—224no—
361C22×D4—224no—
362C22×D4—224no—
363C22×D4—444no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—112no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4C22×D1114yes—
371C23×C4C22×D1111yescharacteristic
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1111yescharacteristic
377#125—2232no—
378#121—2232no—
379C2×C4⋊C4—118no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—118no—
383C2×C4⋊C4—118no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—228no—
386C2×C4⋊C4—228no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—224no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—228no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4—444no—
400C2×C22⋊C4—444no—
401C2×C22⋊C4—444no—
402C2×C22⋊C4—444no—
403C2×C22⋊C4C22×D1114yes—
404C2×C22⋊C4C22×D1114yes—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—118no—
408C2×C42—444no—
409C2×C42C22×D1114yes—
410C2×C42C22×D1114yes—
411#95—118no—
412#95—118no—
413#95C22×D1114yes—
414#95C22×D1114yes—
415C2×C11—44no—
416C2×C11#249018yescomplemented
417C2×C11C22×#12411yescharacteristic
418C2×C11C2×#52911yescharacteristic
419C2×C11C2×#54011yescharacteristic
420C2×C11C2×#54611yescharacteristic
421C2×C11C2×#55011yescharacteristic
422C2×C11C2×#55311yescharacteristic
423C2×C11C2×#55311yescharacteristic
424D11—84no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—114no—
432C24—224no—
433C24—224no—
434C24—224no—
435C24—224no—
436C24—224no—
437C24—224no—
438C24—224no—
439C24#433914yes—
440C24C23×D1112yes—
441C24C23×D1111yescharacteristic
442C2×D4—2216no—
443C2×D4—2216no—
444C2×D4—228no—
445C2×D4—228no—
446C2×D4—228no—
447C2×D4—448no—
448C2×D4—4432no—
449C2×D4—4416no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—416no—
468C22×C4—118no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4#433914yes—
481C22×C4#433914yes—
482C22×C4D4×D1114yes—
483C22×C4#434114yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C22×C4C23×D1112yes—
489C22×C4C23×D1112yes—
490C4⋊C4—1116no—
491C4⋊C4—2216no—
492C4⋊C4—2216no—
493C4⋊C4—228no—
494C4⋊C4—228no—
495C22⋊C4—28no—
496C22⋊C4—28no—
497C22⋊C4—2216no—
498C22⋊C4—2216no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C22⋊C4—448no—
502C22⋊C4—448no—
503C42—28no—
504C42—28no—
505C42—448no—
506C11C2×#249011yescharacteristic, complemented, Sylow
507C23—28no—
508C23—28no—
509C23—28no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—44no—
517C23—44no—
518C23—44no—
519C23—44no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—448no—
528C23—448no—
529C23—448no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—448no—
534C23C2×#433914yes—
535C23C2×#433912yes—
536C23C2×#433912yes—
537C23C2×#433912yes—
538C23C2×D4×D1112yes—
539C23C2×#434112yes—
540C23#6704212yes—
541C23#6704212yes—
542C23C24×D1111yescharacteristic
543D4—4432no—
544D4—4416no—
545C2×C4—28no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
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—44no—
561C2×C4—44no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—416no—
565C2×C4—118no—
566C2×C4—2216no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—448no—
576C2×C4—448no—
577C2×C4#66938116yes—
578C2×C4C2×#433914yes—
579C2×C4C2×#433914yes—
580C2×C4C2×D4×D1114yes—
581C2×C4C2×#434114yes—
582C22—24no—
583C22—24no—
584C22—24no—
585C22—42no—
586C22—42no—
587C22—416no—
588C22—42no—
589C22—42no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—8816no—
598C22#1062301014yes—
599C22C2×#6693814yes—
600C22#1062306614yes—
601C22#1062308114yes—
602C22#1062308414yes—
603C22#1062309614yes—
604C22#1062309614yes—
605C22C22×#433911yescharacteristic
606C22C22×#433911yescharacteristic
607C22C22×#433911yescharacteristic
608C22C22×D4×D1111yescharacteristic
609C22C22×#434111yescharacteristic
610C22C2×#6704211yescharacteristic
611C22C2×#6704211yescharacteristic
612C4—24no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4—42no—
617C4—228no—
618C4—444no—
619C4—444no—
620C4C2×#6693818yes—
621C2—44no—
622C2—884no—
623C2#1307296818yesdirect product factor
624C2C22×#6693811yescharacteristic
625C2C2×#1062301011yescharacteristic
626C2C2×#1062306611yescharacteristic
627C2C2×#1062308111yescharacteristic
628C2C2×#1062308411yescharacteristic
629C2C2×#1062309611yescharacteristic
630C2C2×#1062309611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC22×#66983C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2490
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66923C2semidirect
3. #13072968C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622572C2semidirect
6. C2×#10622552C2semidirect
7. C2×#10622552C2semidirect
8. C2×#10622570C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622825C2semidirect
11. C2×C4×C4⋊Dic11C2semidirect
12. C2×C4×C11×C22⋊C4C2semidirect
35. C2×#66923C22semidirect
36. C4×C11×C22⋊C4C22semidirect
39. #10622825C22semidirect
42. #10622572C22semidirect
43. #10622570C22semidirect
44. #10622552C22semidirect
45. #10622552C22semidirect
46. C4×C4⋊Dic11C22semidirect
47. #10622288C22semidirect
48. #10622282C22semidirect
203. C2×C4×C22⋊C4D11semidirect
310. C4×C22⋊C4C2×D11semidirect
416. C2×C11#2490semidirect
506. C11C2×#2490semidirect
623. C2#13072968direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
C22×#669832
#130729682
C2×#106222882
C2×#106225722
C2×#106225522
C2×#106225702
C2×#106222822
C2×#106228252
C2×C4×C4⋊Dic112
C2×C4×C11×C22⋊C42
C2×#249011