Finite Group Databasebeta

← C2×#13073771 #14924145

Subgroups — C2×#13073771 #14924145

Order 2816.

4166 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic11C211yesmaximal, characteristic
3#13073771C2116yesmaximal, direct product factor
4C2×#10622565C212yesmaximal, complemented
5C2×#10622560C212yesmaximal, complemented
6C2×#10622564C212yesmaximal, complemented
7C2×#10622557C212yesmaximal, complemented
8C2×#10622556C211yesmaximal, characteristic, complemented
9C2×#10622556C211yesmaximal, characteristic, complemented
10C2×#10622860C211yesmaximal, characteristic
11C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#379C211yesmaximal, characteristic
13C26×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×Dic22C2211yescharacteristic, complemented
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11—28no—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2218yes—
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2212yes—
28C22×C22⋊Dic11C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic, complemented
30C22×Dic11⋊C4C2211yescharacteristic, complemented
31C22×Dic11⋊C4C2211yescharacteristic, complemented
32C22×C4×Dic11C2212yescomplemented
33C2×#66931—28no—
34C2×#66931C2218yescomplemented
35C11×#379C2218yes—
36#10622860C2218yes—
37C2×C11⋊#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2212yescomplemented
42#10622565C22116yescomplemented
43#10622564C22116yescomplemented
44#10622560C22116yescomplemented
45#10622557C22116yescomplemented
46#10622556C2218yescomplemented
47#10622556C2218yescomplemented
48C22⋊C4×Dic11C2218yescomplemented
49C25×C11—24no—
50C25×C11—28no—
51C25×C11—24no—
52C25×C11—24no—
53C25×C11—44no—
54C25×C11C2312yes—
55C25×C11C2314yes—
56C25×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—24no—
61C23×Dic11—24no—
62C23×Dic11—24no—
63C23×Dic11—44no—
64C23×Dic11D418yes—
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2314yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2314yes—
73C22×Dic22—24no—
74C22×Dic22—44no—
75C22×Dic22C2314yescomplemented
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—28no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—44no—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C11×C22⋊C4C2318yes—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11—28no—
88C2×C22⋊Dic11—28no—
89C2×C22⋊Dic11—232no—
90C2×C22⋊Dic11—44no—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2318yes—
96C2×C22⋊Dic11C2318yes—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2314yescomplemented
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4C2314yescomplemented
102C2×Dic11⋊C4C2314yescomplemented
103C2×C4×Dic11—44no—
104C2×C4×Dic11C2318yescomplemented
105#66931—232no—
106C11⋊#95C2318yescomplemented
107C11⋊#95C2318yescomplemented
108C11⋊#95C2318yescomplemented
109C11⋊#95C2318yescomplemented
110C11⋊#95C2318yescomplemented
111C2×#2561—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—232no—
115C24×C11—28no—
116C24×C11—24no—
117C24×C11—216no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—28no—
124C24×C11—28no—
125C24×C11—48no—
126C24×C11—432no—
127C24×C11—432no—
128C24×C11—416no—
129C24×C11—416no—
130C24×C11C2×D414yes—
131C24×C11#4118yes—
132C24×C11#4114yes—
133C24×C11#4114yes—
134C24×C11C2414yes—
135C24×C11C2412yes—
136C24×C11C2411yescharacteristic
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—28no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—28no—
155C22×Dic11—24no—
156C22×Dic11—28no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—416no—
163C22×Dic11—48no—
164C22×Dic11—416no—
165C22×Dic11C2×D414yes—
166C22×Dic11C2×D414yes—
167C22×Dic11C2×D4116yes—
168C22×Dic11C2414yes—
169C22×Dic11C2414yes—
170C22×Dic11C2412yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C22×Dic11C2412yes—
174C2×Dic22—28no—
175C2×Dic22—48no—
176C2×Dic22—416no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—216no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—48no—
181C22⋊Dic11—216no—
182C22⋊Dic11—216no—
183C22⋊Dic11—28no—
184C22⋊Dic11—28no—
185C22⋊Dic11—216no—
186C22⋊Dic11—48no—
187C4⋊Dic11—28no—
188Dic11⋊C4—28no—
189Dic11⋊C4—28no—
190C4×Dic11—48no—
191C22×C22⋊Q8—111no—
192C23×C22⋊C4—111no—
193#2561—1116no—
194C2×#397—112no—
195C2×#393—112no—
196C2×#388—112no—
197C2×#388—112no—
198C2×#381—111no—
199C2×#381—111no—
200C2×#379—111no—
201C2×#379D1111yescharacteristic
202C2×C4×C22⋊C4—111no—
203C23×C11—28no—
204C23×C11—28no—
205C23×C11—216no—
206C23×C11—216no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—232no—
210C23×C11—216no—
211C23×C11—216no—
212C23×C11—216no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—432no—
220C23×C11—432no—
221C23×C11—4128no—
222C23×C11—416no—
223C23×C11—416no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11#124116yes—
229C23×C11C22×D414yes—
230C23×C11C22×D412yes—
231C23×C11C2×#4114yes—
232C23×C11C2×#4112yes—
233C23×C11C2×#4118yes—
234C23×C11C2×#4114yes—
235C23×C11C2×#4114yes—
236C23×C11C2×#4112yes—
237C23×C11H(5,𝔽2)14yes—
238C23×C11C2511yescharacteristic
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—48no—
249C2×Dic11—28no—
250C2×Dic11—28no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—416no—
264C2×Dic11—44no—
265C2×Dic11—416no—
266C2×Dic11—48no—
267C2×Dic11—44no—
268C2×Dic11—48no—
269C2×Dic11C22×D414yes—
270C2×Dic11C22×D414yes—
271Dic22—416no—
272C26C2×D1111yescharacteristic
273C23×Q8—111no—
274C24×C4—111no—
275C24×C4—111no—
276C2×C22⋊Q8—118no—
277C2×C22⋊Q8—228no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4—111no—
280C22×C4⋊C4—111no—
281C22×C22⋊C4—118no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4—111no—
286C22×C22⋊C4—111no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—228no—
289C22×C22⋊C4C2×D1112yes—
290C22×C22⋊C4C2×D1111yescharacteristic
291C22×C22⋊C4C2×D1111yescharacteristic
292C22×C22⋊C4C2×D1112yes—
293C22×C42—112no—
294#397—1116no—
295#393—1116no—
296#388—1116no—
297#388—1116no—
298#381—118no—
299#381—118no—
300#379—118no—
301#379C2×D1118yes—
302C4×C22⋊C4—118no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—112no—
308C22×C11—232no—
309C22×C11—24no—
310C22×C11—24no—
311C22×C11—28no—
312C22×C11—28no—
313C22×C11—28no—
314C22×C11—28no—
315C22×C11—28no—
316C22×C11—464no—
317C22×C11—432no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11#52514yes—
323C22×C11C2×#12418yes—
324C22×C11C2×#12414yes—
325C22×C11#53414yes—
326C22×C11#55118yes—
327C22×C11#55118yes—
328C22×C11C23×D411yescharacteristic
329C22×C11C22×#4111yescharacteristic
330C22×C11C22×#4112yes—
331C22×C11C22×#4111yescharacteristic
332C22×C11C2×H(5,𝔽2)12yes—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—44no—
336Dic11—24no—
337Dic11—24no—
338Dic11—42no—
339Dic11—44no—
340Dic11—42no—
341Dic11—44no—
342C25—24no—
343C25—28no—
344C25—24no—
345C25—24no—
346C25—44no—
347C25C22×D1112yes—
348C25C22×D1114yes—
349C25C22×D1111yescharacteristic
350C22×Q8—114no—
351C22×Q8—224no—
352C22×Q8—444no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—118no—
356C23×C4—114no—
357C23×C4—114no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—112no—
361C23×C4—112no—
362C23×C4—224no—
363C23×C4—224no—
364C23×C4—224no—
365C23×C4—444no—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1112yes—
369C22⋊Q8—2232no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—224no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4—114no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—228no—
387C2×C22⋊C4—228no—
388C2×C22⋊C4—2232no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—228no—
392C2×C22⋊C4—444no—
393C2×C22⋊C4C22×D1114yes—
394C2×C22⋊C4C22×D1114yes—
395C2×C22⋊C4C22×D1118yes—
396C2×C22⋊C4C22×D1118yes—
397C2×C42—118no—
398C2×C42—444no—
399#95—118no—
400#95—118no—
401#95—118no—
402#95—118no—
403#95—118no—
404C2×C11—28no—
405C2×C11—48no—
406C2×C11#256118yescomplemented
407C2×C11C2×#52511yescharacteristic
408C2×C11C22×#12411yescharacteristic
409C2×C11C2×#53411yescharacteristic
410C2×C11C2×#55112yes—
411C2×C11C2×#55112yes—
412C24—24no—
413C24—24no—
414C24—232no—
415C24—24no—
416C24—28no—
417C24—24no—
418C24—216no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—28no—
424C24—28no—
425C24—48no—
426C24—432no—
427C24—432no—
428C24—416no—
429C24—416no—
430C24#433914yes—
431C24D4×D1114yes—
432C24#434118yes—
433C24#434114yes—
434C24C23×D1114yes—
435C24C23×D1112yes—
436C24C23×D1111yescharacteristic
437C2×Q8—228no—
438C2×Q8—448no—
439C2×Q8—4416no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—114no—
448C22×C4—114no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—1116no—
452C22×C4—114no—
453C22×C4—114no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—228no—
460C22×C4—224no—
461C22×C4—228no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—228no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—4416no—
472C22×C4—448no—
473C22×C4—4416no—
474C22×C4C23×D1114yes—
475C22×C4C23×D1112yes—
476C22×C4C23×D1112yes—
477C4⋊C4—228no—
478C4⋊C4—228no—
479C4⋊C4—228no—
480C22⋊C4—28no—
481C22⋊C4—216no—
482C22⋊C4—28no—
483C22⋊C4—48no—
484C22⋊C4—2216no—
485C22⋊C4—2216no—
486C22⋊C4—228no—
487C22⋊C4—228no—
488C22⋊C4—2216no—
489C22⋊C4—448no—
490C42—448no—
491C11C2×#256111yescharacteristic, complemented, Sylow
492C23—216no—
493C23—28no—
494C23—216no—
495C23—28no—
496C23—24no—
497C23—24no—
498C23—232no—
499C23—216no—
500C23—216no—
501C23—216no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—432no—
509C23—432no—
510C23—416no—
511C23—4128no—
512C23—416no—
513C23—48no—
514C23—48no—
515C23—48no—
516C23—48no—
517C23#66938116yes—
518C23C2×#433914yes—
519C23C2×#433912yes—
520C23C2×D4×D1114yes—
521C23C2×D4×D1112yes—
522C23C2×#434118yes—
523C23C2×#434114yes—
524C23C2×#434112yes—
525C23C2×#434114yes—
526C23#6703714yes—
527C23C24×D1111yescharacteristic
528Q8—4416no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—44no—
537C2×C4—48no—
538C2×C4—44no—
539C2×C4—114no—
540C2×C4—114no—
541C2×C4—228no—
542C2×C4—228no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—4416no—
556C2×C4—4416no—
557C2×C4—448no—
558C2×C4—448no—
559C2×C4—444no—
560C2×C4—444no—
561C22—28no—
562C22—28no—
563C22—24no—
564C22—232no—
565C22—24no—
566C22—28no—
567C22—28no—
568C22—28no—
569C22—464no—
570C22—44no—
571C22—44no—
572C22—44no—
573C22—44no—
574C22—432no—
575C22C2×#6693818yes—
576C22C2×#6693814yes—
577C22#1062302618yes—
578C22#1062311714yes—
579C22#1062311818yes—
580C22#1062312014yes—
581C22C22×#433911yescharacteristic
582C22C22×D4×D1111yescharacteristic
583C22C22×#434112yes—
584C22C22×#434111yescharacteristic
585C22C2×#6703712yes—
586C4—44no—
587C4—42no—
588C4—42no—
589C4—224no—
590C4—224no—
591C4—444no—
592C4—444no—
593C4—442no—
594C4—442no—
595C2—28no—
596C2—48no—
597C2#1307377118yesdirect product factor
598C2C2×#1062311711yescharacteristic
599C2C22×#6693811yescharacteristic
600C2C2×#1062312011yescharacteristic
601C2C2×#1062302612yes—
602C2C2×#1062311812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#379C2
socleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11C2×#2561
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
3. #13073771C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622560C2semidirect
6. C2×#10622564C2semidirect
7. C2×#10622557C2semidirect
8. C2×#10622556C2semidirect
9. C2×#10622556C2semidirect
11. C2×C22⋊C4×Dic11C2semidirect
16. C23×Dic22C22semidirect
29. C22×C4⋊Dic11C22semidirect
30. C22×Dic11⋊C4C22semidirect
31. C22×Dic11⋊C4C22semidirect
32. C22×C4×Dic11C22semidirect
34. C2×#66931C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
42. #10622565C22semidirect
43. #10622564C22semidirect
44. #10622560C22semidirect
45. #10622557C22semidirect
46. #10622556C22semidirect
47. #10622556C22semidirect
48. C22⋊C4×Dic11C22semidirect
75. C22×Dic22C23semidirect
98. C2×C4⋊Dic11C23semidirect
101. C2×Dic11⋊C4C23semidirect
102. C2×Dic11⋊C4C23semidirect
104. C2×C4×Dic11C23semidirect
106. C11⋊#95C23semidirect
107. C11⋊#95C23semidirect
108. C11⋊#95C23semidirect
109. C11⋊#95C23semidirect
110. C11⋊#95C23semidirect
406. C2×C11#2561semidirect
491. C11C2×#2561semidirect
597. C2#13073771direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C23×C22⋊Dic112
#130737712
C2×#106225652
C2×#106225602
C2×#106225642
C2×#106225572
C2×#106225562
C2×#106228602
C2×C22⋊C4×Dic112
C2×C11×#3792
C2×#256111