Finite Group Databasebeta

← C4×#11719281 #16022748

Subgroups — C4×#11719281 #16022748

Order 3328.

3232 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719281C211yesmaximal, characteristic
2C2×C4×#6131C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D13C211yesmaximal, characteristic, complemented
4#13117907C213yesmaximal, complemented
5#13117865C213yesmaximal, complemented
6#13117854C213yesmaximal, complemented
7#13117768C213yesmaximal, complemented
8#13117757C211yesmaximal, characteristic, complemented
9#13117674C211yesmaximal, characteristic, complemented
10Q8×#6103C211yesmaximal, characteristic, complemented
11C4×#88129C213yesmaximal, complemented
12C4×#88151C213yesmaximal, complemented
13C4×#88149C213yesmaximal, complemented
14C42×D52C213yesmaximal, complemented
15C42×Q8×C13C211yesmaximal, characteristic, complemented
16C22×#6131C2211yescharacteristic
17C22×Q8×D13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×Q8×Dic13C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23#11719281C4116yesdirect product factor
24C4×#6131—28no—
25C4×Q8×D13—28no—
26C2×#88151C2213yes—
27C2×#88149C2213yes—
28C2×#88147C2213yes—
29C2×#88146C2213yes—
30C2×C4⋊C4×D13C2213yes—
31C2×#88141C2213yes—
32C2×#88129C2213yes—
33C2×C4×D52C2213yes—
34C2×C4×D52C2213yes—
35C2×C4×D52C2213yes—
36C2×C4×D52C2213yes—
37C2×C42×D13C2213yes—
38C2×C42×D13C2213yes—
39C2×C4×Dic26C2213yes—
40C4×C13×C4⋊C4C2213yes—
41C4×C13×C4⋊C4C2213yes—
42C4×C13×C4⋊C4C2213yes—
43C43×C13C2213yes—
44#11718649C2213yes—
45#11718648C2213yes—
46#11718648C2213yes—
47#11718646C2213yes—
48#11718646C2213yes—
49#11718635C2213yes—
50#11718601C2216yes—
51#11718601C2216yes—
52#11718600C2213yes—
53C4×#6103C2211yescharacteristic
54C4×#6103C2213yes—
55C4×#6103C2213yes—
56C4×#6103C2213yes—
57C4×#6103C2213yes—
58C4×#6103C2213yes—
59C4×#6103C2216yes—
60#11718597C2213yes—
61C4×C4⋊Dic13C2213yes—
62C4×C4⋊Dic13C2213yes—
63C4×C4⋊Dic13C2213yes—
64#11718590C2213yes—
65#11718331C2216yes—
66#11718329C2216yes—
67#11718326C2216yes—
68#11718314C2216yes—
69C22×Q8×C13C2311yescharacteristic
70C2×#6131—24no—
71C2×#6131—24no—
72C2×#6131C2×C418yescomplemented
73C2×Q8×D13—24no—
74C2×Q8×D13—24no—
75C2×Q8×D13C2×C418yescomplemented
76C22×D52C2313yes—
77C22×D52C2313yes—
78C22×C4×D13C2313yes—
79C22×C4×D13C2313yes—
80C22×C4×D13C2313yes—
81C22×C4×D13C2313yes—
82C22×C4×D13C2313yes—
83C22×C4×D13C2311yescharacteristic
84C22×Dic26C2313yes—
85C4×Q8×C13—24no—
86C4×Q8×C13C2×C418yescomplemented
87C4×Q8×C13D418yescomplemented
88C2×C13×C4⋊C4C2313yes—
89C2×C13×C4⋊C4C2313yes—
90C2×C13×C4⋊C4C2313yes—
91C2×C42×C13C2313yes—
92C2×C42×C13C2313yes—
93C2×C42×C13C2313yes—
94C2×C42×C13C2311yescharacteristic
95C2×C42×C13C2313yes—
96C2×C42×C13C2313yes—
97C2×C42×C13C2313yes—
98Q8×Dic13—24no—
99Q8×Dic13—24no—
100C2×#6103C2316yes—
101C2×#6103C2313yes—
102C2×#6103C2313yes—
103C2×#6103C2313yes—
104C2×#6103C2316yes—
105C2×#6103C2311yescharacteristic
106C2×#6103C2313yes—
107C2×#6103C2316yes—
108C2×#6103C2311yescharacteristic
109C2×C4⋊Dic13C2313yes—
110C2×C4⋊Dic13C2313yes—
111C2×C4⋊Dic13C2313yes—
112C2×C4⋊Dic13C2313yes—
113C2×C4⋊Dic13C2313yes—
114C2×#6101C2316yes—
115C2×C4×Dic13C2313yes—
116C2×C4×Dic13C2311yescharacteristic
117C2×C4×Dic13C2313yes—
118C2×C4×Dic13C2313yes—
119C2×C4×Dic13C2313yes—
120C2×C4×Dic13C2313yes—
121#88151C2×C4124yescomplemented
122#88149C2×C4124yescomplemented
123#88147—212no—
124#88146—212no—
125C4⋊C4×D13—212no—
126#88141—212no—
127#88129C2×C4124yescomplemented
128C4×D52—212no—
129C4×D52—212no—
130C4×D52—212no—
131C4×D52C2×C4124yescomplemented
132C42×D13—212no—
133C42×D13—212no—
134C4×Dic26—212no—
135C13×#95C2316yes—
136#88071C2313yes—
137#88071C2316yes—
138#88071C2316yes—
139#88071C2313yes—
140#88071C2313yes—
141#88071C2311yescharacteristic
142#88071C2311yescharacteristic
143#88071C2313yes—
144C4×#548—131nomaximal, Sylow
145C23×D13C2413yes—
146C23×D13C2411yescharacteristic
147C2×Q8×C13C22×C414yes—
148C2×Q8×C13C2×D414yes—
149C2×Q8×C13#4114yes—
150C22×C4×C13C2413yes—
151C22×C4×C13C2411yescharacteristic
152C22×C4×C13C2413yes—
153C22×C4×C13C2413yes—
154C22×C4×C13C2411yescharacteristic
155C22×C4×C13C2413yes—
156C22×C4×C13C2411yescharacteristic
157C22×Dic13C2413yes—
158C22×Dic13C2413yes—
159C22×Dic13C2411yescharacteristic
160C22×Dic13C2413yes—
161C22×Dic13C2411yescharacteristic
162C22×Dic13C2411yescharacteristic
163#6131—232no—
164Q8×D13—232no—
165C2×D52—26no—
166C2×D52—26no—
167C2×D52—26no—
168C2×D52—26no—
169C2×D52C22×C4112yes—
170C2×D52C22×C4112yes—
171C2×C4×D13—22no—
172C2×C4×D13—26no—
173C2×C4×D13—26no—
174C2×C4×D13—26no—
175C2×C4×D13—26no—
176C2×C4×D13—22no—
177C2×C4×D13—26no—
178C2×C4×D13—26no—
179C2×C4×D13—26no—
180C2×C4×D13—26no—
181C2×C4×D13—26no—
182C2×C4×D13—26no—
183C2×C4×D13—26no—
184C2×C4×D13—43no—
185C2×C4×D13—43no—
186C2×C4×D13C22×C4112yes—
187C2×C4×D13C22×C4112yes—
188C2×C4×D13#4114yescomplemented
189C2×Dic26—26no—
190C2×Dic26—26no—
191C2×Dic26C22×C4112yes—
192C13×C4⋊C4—26no—
193C13×C4⋊C4C22×C4112yes—
194C13×C4⋊C4C2×D4112yes—
195C42×C13—26no—
196C42×C13—26no—
197C42×C13—26no—
198C42×C13—22no—
199C42×C13—43no—
200C42×C13C22×C4112yes—
201C42×C13C2×D4112yes—
202#6103—26no—
203#6103—212no—
204#6103—26no—
205#6103—26no—
206#6103—46no—
207#6103C22×C414yes—
208#6103C22×C4112yes—
209#6103C22×C4124yes—
210#6103#4114yescomplemented
211C4⋊Dic13—26no—
212C4⋊Dic13—26no—
213C4⋊Dic13—26no—
214C4⋊Dic13—26no—
215C4⋊Dic13C22×C4112yes—
216#6101—212no—
217C4×Dic13—26no—
218C4×Dic13—22no—
219C4×Dic13—26no—
220C4×Dic13—26no—
221C4×Dic13—26no—
222C4×Dic13—26no—
223C2×#548—131no—
224C2×C4×#41—131no—
225C22×C4×Q8—131no—
226#2367—133no—
227#2362—133no—
228#2361—133no—
229#2352—133no—
230#2351—131no—
231#2341—131no—
232Q8×C22⋊C4—131no—
233C4×#124—133no—
234C4×C22⋊Q8—133no—
235C4×#121—133no—
236C42×Q8D1311yescharacteristic, complemented
237C42×D4—133no—
238C23×C13C2511yescharacteristic
239C22×D13—21no—
240C22×D13—21no—
241C22×D13—21no—
242C22×D13—21no—
243C22×D13—23no—
244C22×D13—23no—
245C22×D13—23no—
246C22×D13—23no—
247C22×D13—23no—
248C22×D13—23no—
249C22×D13C23×C416yes—
250C22×D13C23×C412yes—
251C22×D13C2×#4112yes—
252C22×D13C2×#4112yes—
253Q8×C13C4×D4116yescomplemented
254C2×C4×C13—23no—
255C2×C4×C13—23no—
256C2×C4×C13—21no—
257C2×C4×C13—23no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—23no—
262C2×C4×C13—23no—
263C2×C4×C13—23no—
264C2×C4×C13—23no—
265C2×C4×C13C23×C416yes—
266C2×C4×C13C23×C412yes—
267C2×C4×C13C23×C416yes—
268C2×C4×C13C22×D416yes—
269C2×C4×C13C22×D416yes—
270C2×C4×C13C22×D412yes—
271C2×C4×C13C2×#4112yes—
272C2×C4×C13C2×#4116yes—
273C2×C4×C13C2×#4112yes—
274C2×C4×C132−1+412yes—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—23no—
279C2×Dic13—23no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—23no—
284C2×Dic13—23no—
285C2×Dic13—23no—
286C2×Dic13—23no—
287C2×Dic13—23no—
288C2×Dic13—23no—
289C2×Dic13C23×C412yes—
290C2×Dic13C23×C416yes—
291C2×Dic13C2×#4112yes—
292C2×Dic13C2×#4112yes—
293D52—224no—
294D52—224no—
295C4×D13—224no—
296C4×D13—224no—
297C4×D13—28no—
298C4×D13—412no—
299C4×D13—412no—
300C4×D13—412no—
301Dic26—224no—
302C22×#41—131no—
303C23×Q8—131no—
304#548—1316no—
305C2×#124—133no—
306C2×C22⋊Q8—133no—
307C2×#121—133no—
308C4×#41—268no—
309C2×C4×Q8—131no—
310C2×C4×Q8—131no—
311C2×C4×Q8—133no—
312C2×C4×Q8—133no—
313C2×C4×Q8—268no—
314C2×C4×Q8C2×D1311yescharacteristic
315C2×C4×Q8C2×D1311yescharacteristic
316C2×C4×Q8C2×D1311yescharacteristic
317C2×C4×D4—133no—
318C2×C4×D4—133no—
319C2×C4×D4—133no—
320C2×C4×D4—133no—
321C2×C4×D4—133no—
322C2×#117—133no—
323C22×C4⋊C4—133no—
324C22×C42—133no—
325C22×C42—133no—
326#391—133no—
327#391—133no—
328#390—133no—
329#390—133no—
330#389—133no—
331#389—133no—
332#388—136no—
333#388—136no—
334#388—136no—
335#387—136no—
336#386—136no—
337#385—136no—
338#382—133no—
339#380—133no—
340#380—133no—
341C4×C4⋊C4—133no—
342C4×C4⋊C4—133no—
343C4×C4⋊C4—133no—
344C4×C4⋊C4C2×D1313yes—
345C4×C4⋊C4C2×D1313yes—
346C4×C4⋊C4C2×D1313yes—
347C4×C22⋊C4—133no—
348C4×C22⋊C4—133no—
349C4×C22⋊C4—133no—
350C4×C22⋊C4—133no—
351C4×C22⋊C4—131no—
352C4×C22⋊C4—133no—
353C4×C22⋊C4—136no—
354C43C2×D1313yes—
355C22×C13C24×C411yescharacteristic
356C22×C13C23×D411yescharacteristic
357C22×C13C22×#4111yescharacteristic
358C22×C13C22×#4111yescharacteristic
359C22×C13C22×#4111yescharacteristic
360C22×C13C2×2−1+411yescharacteristic
361C22×C13#58511yescharacteristic
362C2×D13—22no—
363C2×D13—22no—
364C2×D13—22no—
365C2×D13—22no—
366C2×D13—22no—
367C2×D13—22no—
368C2×D13—26no—
369C2×D13—26no—
370C2×D13—26no—
371C2×D13—43no—
372C2×D13—43no—
373C2×D13—43no—
374C2×D13—43no—
375C2×D13C4×#4114yescomplemented
376C4×C13—26no—
377C4×C13—22no—
378C4×C13—26no—
379C4×C13—22no—
380C4×C13—43no—
381C4×C13C2×C4×D4112yes—
382C4×C13#54814yescomplemented
383Dic13—26no—
384Dic13—22no—
385Dic13—22no—
386Dic13—22no—
387Dic13—43no—
388Dic13—43no—
389C2×#41—138no—
390C2×#41—264no—
391C2×#41—264no—
392C22×Q8—138no—
393C22×Q8—133no—
394C22×Q8—264no—
395C22×Q8—264no—
396C22×Q8C22×D1311yescharacteristic
397C22×D4—133no—
398C22×D4—133no—
399C23×C4—133no—
400C23×C4—133no—
401C23×C4—131no—
402C23×C4—133no—
403C23×C4—133no—
404C23×C4—133no—
405#124—1324no—
406C22⋊Q8—1324no—
407#121—1324no—
408C4×Q8—24no—
409C4×Q8—264no—
410C4×Q8—264no—
411C4×Q8—2612no—
412C4×Q8—2612no—
413C4×Q8C4×D1318yescomplemented
414C4×Q8D5218yescomplemented
415C4×D4—1324no—
416C4×D4—2612no—
417C4×D4—2612no—
418C4×D4—2612no—
419C4×D4—2612no—
420#117—2612no—
421C2×C4⋊C4—133no—
422C2×C4⋊C4—136no—
423C2×C4⋊C4—133no—
424C2×C4⋊C4—133no—
425C2×C4⋊C4—133no—
426C2×C4⋊C4—133no—
427C2×C4⋊C4—2612no—
428C2×C4⋊C4C22×D1313yes—
429C2×C4⋊C4C22×D1313yes—
430C2×C4⋊C4C22×D1313yes—
431C2×C22⋊C4—131no—
432C2×C22⋊C4—131no—
433C2×C22⋊C4—133no—
434C2×C22⋊C4—136no—
435C2×C22⋊C4—136no—
436C2×C22⋊C4—133no—
437C2×C22⋊C4—133no—
438C2×C22⋊C4—133no—
439C2×C22⋊C4—136no—
440C2×C42—133no—
441C2×C42—133no—
442C2×C42—133no—
443C2×C42—133no—
444C2×C42—133no—
445C2×C42—131no—
446C2×C42—2612no—
447C2×C42—2612no—
448C2×C42C22×D1313yes—
449C2×C42C22×D1313yes—
450C2×C42C22×D1313yes—
451C2×C42C22×D1311yescharacteristic
452C2×C42C22×D1313yes—
453C2×C42C22×D1313yes—
454C2×C42C22×D1313yes—
455#95—131no—
456#95—131no—
457#95—133no—
458#95—133no—
459#95—133no—
460#95—133no—
461#95—136no—
462#95—136no—
463#95C22×D1316yes—
464C2×C13C22×C4×D411yescharacteristic
465C2×C13C2×C4×#4111yescharacteristic
466C2×C13C4×2−1+411yescharacteristic
467C2×C13C2×#54811yescharacteristic
468C2×C13D4×#4111yescharacteristic
469C2×C13#348011yescharacteristic
470C2×C13#348211yescharacteristic
471D13—24no—
472D13—46no—
473C24—131no—
474C24—133no—
475#41—2632no—
476C2×Q8—1312no—
477C2×Q8—2632no—
478C2×Q8—266no—
479C2×Q8—266no—
480C2×Q8C2×C4×D1314yes—
481C2×Q8C2×D5214yes—
482C2×Q8#612714yes—
483C2×D4—1312no—
484C2×D4—1312no—
485C2×D4—266no—
486C2×D4—266no—
487C2×D4—266no—
488C2×D4—266no—
489C22×C4—131no—
490C22×C4—131no—
491C22×C4—133no—
492C22×C4—131no—
493C22×C4—1312no—
494C22×C4—1312no—
495C22×C4—134no—
496C22×C4—133no—
497C22×C4—133no—
498C22×C4—266no—
499C22×C4—266no—
500C22×C4—262no—
501C22×C4—266no—
502C22×C4—266no—
503C22×C4—266no—
504C22×C4—266no—
505C22×C4—262no—
506C22×C4—266no—
507C22×C4—266no—
508C22×C4—266no—
509C22×C4—266no—
510C22×C4—266no—
511C22×C4—523no—
512C22×C4—523no—
513C22×C4C23×D1313yes—
514C22×C4C23×D1311yescharacteristic
515C22×C4C23×D1313yes—
516C22×C4C23×D1313yes—
517C22×C4C23×D1311yescharacteristic
518C22×C4C23×D1313yes—
519C22×C4C23×D1311yescharacteristic
520C4⋊C4—26no—
521C4⋊C4—1312no—
522C4⋊C4—266no—
523C4⋊C4—266no—
524C4⋊C4—2612no—
525C4⋊C4—266no—
526C4⋊C4—266no—
527C4⋊C4C2×C4×D13112yes—
528C4⋊C4C2×D52112yes—
529C22⋊C4—134no—
530C22⋊C4—1312no—
531C22⋊C4—1324no—
532C22⋊C4—134no—
533C22⋊C4—266no—
534C22⋊C4—266no—
535C22⋊C4—2612no—
536C22⋊C4—266no—
537C22⋊C4—526no—
538C42—26no—
539C42—22no—
540C42—26no—
541C42—26no—
542C42—43no—
543C42—262no—
544C42—266no—
545C42—266no—
546C42—266no—
547C42—266no—
548C42—266no—
549C42C2×C4×D13112yes—
550C42C2×D52112yes—
551C13C4×#54811yescharacteristic, complemented, Sylow
552C23—132no—
553C23—132no—
554C23—132no—
555C23—136no—
556C23—261no—
557C23—261no—
558C23—261no—
559C23—261no—
560C23—263no—
561C23—263no—
562C23—263no—
563C23—263no—
564C23—263no—
565C23—263no—
566C23C24×D1311yescharacteristic
567Q8—2624no—
568Q8C4×D52116yescomplemented
569D4—2624no—
570D4—2624no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—23no—
576C2×C4—23no—
577C2×C4—21no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—136no—
583C2×C4—132no—
584C2×C4—132no—
585C2×C4—132no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—263no—
590C2×C4—261no—
591C2×C4—263no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—2624no—
595C2×C4—2624no—
596C2×C4—268no—
597C2×C4—263no—
598C2×C4—263no—
599C2×C4—263no—
600C2×C4—263no—
601C2×C4—263no—
602C2×C4—263no—
603C2×C4—5212no—
604C2×C4—5212no—
605C2×C4—5212no—
606C2×C4C22×C4×D1312yes—
607C2×C4C22×C4×D1316yes—
608C2×C4C22×C4×D1316yes—
609C2×C4C22×D5216yes—
610C2×C4C22×D5216yes—
611C2×C4C22×D5212yes—
612C2×C4C2×#612716yes—
613C2×C4#8825412yes—
614C2×C4#41×D1312yes—
615C2×C4#41×D1312yes—
616C22—134no—
617C22—262no—
618C22—262no—
619C22—262no—
620C22—262no—
621C22—262no—
622C22—262no—
623C22—266no—
624C22—266no—
625C22—266no—
626C22—523no—
627C22—523no—
628C22—523no—
629C22—523no—
630C22C23×C4×D1311yescharacteristic
631C22C23×D5211yescharacteristic
632C22C22×#612711yescharacteristic
633C22C2×#8825411yescharacteristic
634C22C2×#41×D1311yescharacteristic
635C22C2×#41×D1311yescharacteristic
636C22#1171964811yescharacteristic
637C4—22no—
638C4—26no—
639C4—22no—
640C4—26no—
641C4—43no—
642C4—262no—
643C4—266no—
644C4—262no—
645C4—262no—
646C4—523no—
647C4—523no—
648C4C2×C4×D52112yes—
649C4#1171928114yesdirect product factor
650C2—264no—
651C2—526no—
652C2C22×C4×D5211yescharacteristic
653C2C4×#41×D1311yescharacteristic
654C2C4×#8825411yescharacteristic
655C2C2×#1171928111yescharacteristic
656C2#41×D5211yescharacteristic
657C2#1312843411yescharacteristic
658C2#1312845311yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC42×Q8×C13C2
socle, cosocleC23×C13C25
prime radicalC2×#11719281C2
hypercenterC42×Q8D13
hypocenterC13C4×#548
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6131C2semidirect
3. C2×C4×Q8×D13C2semidirect
4. #13117907C2semidirect
5. #13117865C2semidirect
6. #13117854C2semidirect
7. #13117768C2semidirect
8. #13117757C2semidirect
9. #13117674C2semidirect
10. Q8×#6103C2semidirect
11. C4×#88129C2semidirect
12. C4×#88151C2semidirect
13. C4×#88149C2semidirect
14. C42×D52C2semidirect
15. C42×Q8×C13C2semidirect
23. #11719281C4direct (N × H)
72. C2×#6131C2×C4semidirect
75. C2×Q8×D13C2×C4semidirect
86. C4×Q8×C13C2×C4semidirect
87. C4×Q8×C13D4semidirect
121. #88151C2×C4semidirect
122. #88149C2×C4semidirect
127. #88129C2×C4semidirect
131. C4×D52C2×C4semidirect
188. C2×C4×D13#41semidirect
210. #6103#41semidirect
236. C42×Q8D13semidirect
253. Q8×C13C4×D4semidirect
375. C2×D13C4×#41semidirect
382. C4×C13#548semidirect
413. C4×Q8C4×D13semidirect
414. C4×Q8D52semidirect
551. C13C4×#548semidirect
568. Q8C4×D52semidirect
649. C4#11719281direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192812
C2×C4×#61312
C2×C4×Q8×D132
#131179072
#131178652
#131178542
#131177682
#131177572
#131176742
Q8×#61032
C4×#881292
C4×#881512
C4×#881492
C42×D522
C42×Q8×C132
C4×#54813