Finite Group Databasebeta

← C4×#11718654 #15784743

Subgroups — C4×#11718654 #15784743

Order 3328.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718654C211yesmaximal, characteristic
2C2×C4×#6103C212yesmaximal
3C2×C4×#6103C211yesmaximal, characteristic
4#13113104C211yesmaximal, characteristic, complemented
5#13113097C212yesmaximal, complemented
6#13113095C211yesmaximal, characteristic, complemented
7#13113084C212yesmaximal
8#13113078C211yesmaximal, characteristic
9C4×#88071C212yesmaximal, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2212yes—
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2212yes—
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C4×C13×C4⋊C4—24no—
24C2×C13×#95C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36#11718654C418yesdirect product factor
37C4×#6103—28no—
38C4×#6103—24no—
39C24×D13C2311yescharacteristic
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C22×C4×D13—22no—
51C22×C4×D13—24no—
52C22×C4×D13—22no—
53C22×C4×D13—24no—
54C22×C4×D13D414yes—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4C2×C414yescomplemented
60C2×C42×C13—24no—
61C2×C42×C13—24no—
62C2×C42×C13—24no—
63C2×C42×C13—24no—
64C2×C42×C13D414yes—
65C2×#6103—24no—
66C2×#6103—24no—
67C2×#6103—22no—
68C2×#6103—24no—
69C2×#6103—22no—
70C2×#6103—22no—
71C2×#6103—24no—
72C2×#6103—22no—
73C2×#6103—24no—
74C2×#6103—22no—
75C2×#6103C2×C418yes—
76C2×#6103C2×C414yes—
77C2×C4×Dic13—24no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C13×#95—24no—
83#88071—22no—
84#88071—22no—
85#88071—24no—
86#88071—22no—
87#88071—24no—
88#88071—24no—
89#88071—24no—
90#88071—24no—
91#88071—24no—
92#88071C2×C418yescomplemented
93#88071C2×C414yescomplemented
94C4×#397—131nomaximal, Sylow
95C24×C13C2411yescharacteristic
96C23×D13—21no—
97C23×D13—21no—
98C23×D13—22no—
99C23×D13—22no—
100C23×D13—21no—
101C23×D13—22no—
102C23×D13—21no—
103C23×D13—22no—
104C23×D13C22×C412yes—
105C23×D13C2×D412yes—
106C23×D13#4112yes—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13C22×C414yes—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×D412yes—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×D412yes—
131C22×C4×C13#4114yes—
132C22×C4×C13#4112yes—
133C22×C4×C13#4114yes—
134C22×C4×C13#4112yes—
135C22×C4×C13#4114yes—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—21no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13C22×C414yes—
161C22×Dic13C22×C412yes—
162C22×Dic13C2×D412yes—
163C22×Dic13#4114yes—
164C22×Dic13#4112yes—
165C2×C4×D13—28no—
166C2×C4×D13—216no—
167C2×C4×D13—44no—
168C2×C4×D13—44no—
169C2×C4×D13—48no—
170C13×C4⋊C4—28no—
171C13×C4⋊C4—28no—
172C42×C13—28no—
173C42×C13—48no—
174#6103—28no—
175#6103—216no—
176#6103—216no—
177#6103—28no—
178C4×Dic13—48no—
179C4×Dic13—44no—
180C2×#397—131no—
181C2×C4×C4⋊C4D1311yescharacteristic, complemented
182C2×C4×C22⋊C4—131no—
183C2×C4×C22⋊C4—132no—
184#1445—131no—
185#1443—132no—
186#1442—131no—
187#1440—132no—
188#1439—131no—
189C4×#95—131no—
190C4×#95—132no—
191C23×C13C23×C411yescharacteristic
192C23×C13C22×D411yescharacteristic
193C23×C13C22×D411yescharacteristic
194C23×C13C2×#4111yescharacteristic
195C23×C13C2×#4111yescharacteristic
196C23×C13C2×#4111yescharacteristic
197C23×C13C2×#4112yes—
198C23×C13C2×#4112yes—
199C23×C13C2×#4112yes—
200C23×C13C2×#4111yescharacteristic
201C23×C13C2×#4112yes—
202C22×D13—22no—
203C22×D13—22no—
204C22×D13—24no—
205C22×D13—24no—
206C22×D13—22no—
207C22×D13—24no—
208C22×D13—24no—
209C22×D13—22no—
210C22×D13—22no—
211C22×D13—24no—
212C22×D13—24no—
213C22×D13—22no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—42no—
218C22×D13—42no—
219C22×D13—42no—
220C22×D13—42no—
221C22×D13—42no—
222C22×D13—42no—
223C22×D13—41no—
224C22×D13C4×D414yes—
225C2×C4×C13—24no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13C4×D414yes—
249C2×C4×C13#12114yes—
250C2×C4×C13#12318yes—
251C2×C4×C13#12314yes—
252C2×C4×C13#12414yes—
253C2×C4×C13#12618yes—
254C2×Dic13—24no—
255C2×Dic13—22no—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—24no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—24no—
262C2×Dic13—22no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—42no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—41no—
283C4×D13—416no—
284C24×C4—131no—
285C22×C4⋊C4C2×D1311yescharacteristic
286C22×C4⋊C4C2×D1311yescharacteristic
287C22×C22⋊C4—131no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4—132no—
290C22×C22⋊C4—131no—
291C22×C42—132no—
292C22×C42—131no—
293C22×C42C2×D1312yes—
294C22×C42C2×D1311yescharacteristic
295#397—138no—
296C4×C4⋊C4—24no—
297C4×C22⋊C4—268no—
298C4×C22⋊C4—264no—
299C2×#95—131no—
300C2×#95—132no—
301C2×#95—132no—
302C2×#95—131no—
303C2×#95—132no—
304C2×#95—132no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—131no—
308C2×#95—131no—
309C2×#95—132no—
310C2×#95C2×D1312yes—
311C22×C13C2×C4×D411yescharacteristic
312C22×C13C2×C4×D411yescharacteristic
313C22×C13C4×#4112yes—
314C22×C13C4×#4111yescharacteristic
315C22×C13C4×#4112yes—
316C22×C13C2×#12111yescharacteristic
317C22×C13C2×#12312yes—
318C22×C13C2×#12311yescharacteristic
319C22×C13#52511yescharacteristic
320C22×C13#52512yes—
321C22×C13#52511yescharacteristic
322C22×C13C2×#12411yescharacteristic
323C22×C13C2×#12612yes—
324C22×C13#52912yes—
325C22×C13#52912yes—
326C22×C13#52912yes—
327C22×C13#52912yes—
328C22×C13#52911yescharacteristic
329C22×C13#52912yes—
330C22×C13#52912yes—
331C22×C13#52912yes—
332C22×C13#53211yescharacteristic
333C22×C13#53211yescharacteristic
334C2×D13—24no—
335C2×D13—28no—
336C2×D13—44no—
337C2×D13—42no—
338C2×D13—42no—
339C2×D13—42no—
340C2×D13—44no—
341C2×D13—42no—
342C2×D13—44no—
343C2×D13—42no—
344C2×D13—42no—
345C4×C13—24no—
346C4×C13—44no—
347C4×C13—42no—
348C4×C13—44no—
349C4×C13#39718yescomplemented
350Dic13—42no—
351Dic13—44no—
352Dic13—42no—
353Dic13—44no—
354Dic13—42no—
355C25—131no—
356C23×C4—132no—
357C23×C4—131no—
358C23×C4—131no—
359C23×C4—132no—
360C23×C4—131no—
361C23×C4—134no—
362C23×C4—264no—
363C23×C4—262no—
364C23×C4—264no—
365C23×C4—262no—
366C23×C4C22×D1312yes—
367C23×C4C22×D1312yes—
368C23×C4C22×D1311yescharacteristic
369C23×C4C22×D1311yescharacteristic
370C23×C4C22×D1311yescharacteristic
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4C4×D1314yescomplemented
376C2×C22⋊C4—138no—
377C2×C22⋊C4—134no—
378C2×C22⋊C4—264no—
379C2×C22⋊C4—262no—
380C2×C22⋊C4—264no—
381C2×C22⋊C4—262no—
382C2×C22⋊C4—264no—
383C2×C22⋊C4—264no—
384C2×C22⋊C4—264no—
385C2×C22⋊C4—262no—
386C2×C22⋊C4—262no—
387C2×C22⋊C4—262no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—264no—
393C2×C42—264no—
394C2×C42—264no—
395C2×C42—264no—
396C2×C42—262no—
397C2×C42C22⋊D1314yes—
398#95—24no—
399#95—138no—
400#95—134no—
401#95—264no—
402#95—264no—
403#95—264no—
404#95—264no—
405#95—264no—
406#95—264no—
407#95—262no—
408#95—262no—
409#95—262no—
410C2×C13C4×#12111yescharacteristic
411C2×C13C4×#12311yescharacteristic
412C2×C13C4×#12312yes—
413C2×C13C4×#12411yescharacteristic
414C2×C13C4×#12612yes—
415C2×C13C2×#39711yescharacteristic
416C2×C13#239211yescharacteristic
417C2×C13#239511yescharacteristic
418C2×C13#239512yes—
419C2×C13#239811yescharacteristic
420C2×C13#240112yes—
421D13—44no—
422C24—132no—
423C24—132no—
424C24—132no—
425C24—262no—
426C24—261no—
427C24—262no—
428C24—261no—
429C24—262no—
430C24—262no—
431C24—261no—
432C24—261no—
433C24C23×D1311yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—134no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—134no—
456C22×C4—132no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—261no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—261no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—2616no—
482C22×C4—268no—
483C22×C4—528no—
484C22×C4—524no—
485C22×C4—524no—
486C22×C4C2×C4×D1314yes—
487C22×C4C2×C4×D1312yes—
488C22×C4#612714yes—
489C22×C4#612712yes—
490C22×C4#612714yes—
491C22×C4D4×D1312yes—
492C22×C4#612912yes—
493C22×C4#613114yes—
494C22×C4C2×C22⋊D1312yes—
495C22×C4C2×C22⋊D1312yes—
496C22×C4C2×C22⋊D1312yes—
497C4⋊C4—28no—
498C4⋊C4—28no—
499C22⋊C4—2616no—
500C22⋊C4—2616no—
501C22⋊C4—268no—
502C22⋊C4—268no—
503C42—28no—
504C42—48no—
505C42—528no—
506C42—524no—
507C13C4×#39711yescharacteristic, complemented, Sylow
508C23—134no—
509C23—264no—
510C23—264no—
511C23—264no—
512C23—262no—
513C23—262no—
514C23—262no—
515C23—264no—
516C23—262no—
517C23—262no—
518C23—262no—
519C23—264no—
520C23—264no—
521C23—522no—
522C23—522no—
523C23—522no—
524C23—521no—
525C23—521no—
526C23—522no—
527C23—521no—
528C23—521no—
529C23—522no—
530C23—522no—
531C23C22×C4×D1311yescharacteristic
532C23C2×#612712yes—
533C23C2×#612712yes—
534C23C2×#612711yescharacteristic
535C23C2×D4×D1311yescharacteristic
536C23C2×#612911yescharacteristic
537C23C2×#613112yes—
538C23#41×D1311yescharacteristic
539C23#41×D1312yes—
540C23#41×D1311yescharacteristic
541C23C22×C22⋊D1311yescharacteristic
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—264no—
566C2×C4—264no—
567C2×C4—264no—
568C2×C4—262no—
569C2×C4—264no—
570C2×C4—262no—
571C2×C4—264no—
572C2×C4—262no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—264no—
576C2×C4—264no—
577C2×C4—522no—
578C2×C4—522no—
579C2×C4—522no—
580C2×C4—522no—
581C2×C4—522no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—522no—
585C2×C4—522no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—5216no—
595C2×C4#8814818yes—
596C2×C4#8815218yes—
597C2×C4C4×C22⋊D1314yes—
598C2×C4#8818314yes—
599C2×C4#8819214yes—
600C2×C4#8820114yes—
601C22—264no—
602C22—268no—
603C22—522no—
604C22—522no—
605C22—522no—
606C22—524no—
607C22—522no—
608C22—522no—
609C22—524no—
610C22—522no—
611C22—524no—
612C22C4×#612712yes—
613C22#1171918412yes—
614C22C2×#8814812yes—
615C22C2×#8815212yes—
616C22#1171923312yes—
617C22#1171923312yes—
618C22C4×#612911yescharacteristic
619C22#1171924312yes—
620C22C4×D4×D1311yescharacteristic
621C22#1171925212yes—
622C22#1171925311yescharacteristic
623C22#1171926211yescharacteristic
624C22C4×#613112yes—
625C22#1171928512yes—
626C22#1171928512yes—
627C22#1171928512yes—
628C22C2×C4×C22⋊D1311yescharacteristic
629C22C2×#8818311yescharacteristic
630C22#1171949611yescharacteristic
631C22C2×#8819211yescharacteristic
632C22C2×#8820111yescharacteristic
633C22#1171953311yescharacteristic
634C22#1171953711yescharacteristic
635C4—24no—
636C4—44no—
637C4—42no—
638C4—44no—
639C4—522no—
640C4—524no—
641C4—522no—
642C4—524no—
643C4—522no—
644C4#1171865418yesdirect product factor
645C2—524no—
646C2C4×#8819211yescharacteristic
647C2C4×#8818311yescharacteristic
648C2C4×#8814812yes—
649C2C4×#8820111yescharacteristic
650C2C4×#8815212yes—
651C2C2×#1171865411yescharacteristic
652C2#1311807411yescharacteristic
653C2#1311809311yescharacteristic
654C2#1311809912yes—
655C2#1311811911yescharacteristic
656C2#1311813712yes—
subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C4×#397
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #13113104C2semidirect
5. #13113097C2semidirect
6. #13113095C2semidirect
9. C4×#88071C2semidirect
10. C4×#88071C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
36. #11718654C4direct (N × H)
59. C2×C13×C4⋊C4C2×C4semidirect
92. #88071C2×C4semidirect
93. #88071C2×C4semidirect
181. C2×C4×C4⋊C4D13semidirect
349. C4×C13#397semidirect
375. C2×C4⋊C4C4×D13semidirect
507. C13C4×#397semidirect
644. C4#11718654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186542
C2×C4×#61032
#131131042
#131130972
#131130952
#131130842
#131130782
C4×#880712
C2×C4×C13×C4⋊C42
C4×#39713