Finite Group Databasebeta

← C4×#11718653 #15784746

Subgroups — C4×#11718653 #15784746

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718653C211yesmaximal, characteristic
2C2×C4×#6101C212yesmaximal, complemented
3C2×C4×#6103C211yesmaximal, characteristic
4C2×C4×#6103C212yesmaximal
5#13113104C211yesmaximal, characteristic, complemented
6#13113102C212yesmaximal, complemented
7#13113099C211yesmaximal, characteristic, complemented
8#13113080C212yesmaximal
9#13113078C211yesmaximal, characteristic
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×#6101C2212yes—
22C22×#6101C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2212yes—
25C4×C13×C4⋊C4—24no—
26C2×C13×#95C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36#11718653C418yesdirect product factor
37C4×#6103—24no—
38C4×#6103—28no—
39C4×#6101—28no—
40C24×D13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C22×C4×D13—24no—
52C22×C4×D13—22no—
53C22×C4×D13—24no—
54C22×C4×D13—22no—
55C22×C4×D13Q814yes—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—24no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4C2×C414yescomplemented
61C2×C42×C13—24no—
62C2×C42×C13—24no—
63C2×C42×C13—24no—
64C2×C42×C13—24no—
65C2×C42×C13D414yes—
66C2×#6103—24no—
67C2×#6103—22no—
68C2×#6103—22no—
69C2×#6103—22no—
70C2×#6103—24no—
71C2×#6103—22no—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—22no—
75C2×#6103—24no—
76C2×#6103C2×C414yes—
77C2×#6103C2×C418yes—
78C2×#6101—24no—
79C2×#6101—24no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×#6101C2×C418yescomplemented
84C2×C4×Dic13—24no—
85C2×C4×Dic13—24no—
86C2×C4×Dic13—24no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13D418yes—
89C13×#95—24no—
90#88071—22no—
91#88071—22no—
92#88071—22no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071C2×C414yescomplemented
99C4×#399—131nomaximal, Sylow
100C24×C13C2411yescharacteristic
101C23×D13—22no—
102C23×D13—21no—
103C23×D13—21no—
104C23×D13—22no—
105C23×D13—22no—
106C23×D13—21no—
107C23×D13—22no—
108C23×D13—21no—
109C23×D13C22×C412yes—
110C23×D13C2×Q812yes—
111C23×D13#4112yes—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13C22×C414yes—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C2×D414yes—
133C22×C4×C13C2×D412yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×Q812yes—
137C22×C4×C13#4114yes—
138C22×C4×C13#4112yes—
139C22×C4×C13#4114yes—
140C22×C4×C13#4112yes—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—21no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13C22×C412yes—
164C22×Dic13C22×C414yes—
165C22×Dic13C2×D414yes—
166C22×Dic13C2×D414yes—
167C22×Dic13C2×Q812yes—
168C22×Dic13#4112yes—
169C22×Dic13#4114yes—
170C2×C4×D13—216no—
171C2×C4×D13—28no—
172C2×C4×D13—48no—
173C2×C4×D13—44no—
174C2×C4×D13—44no—
175C13×C4⋊C4—28no—
176C13×C4⋊C4—28no—
177C42×C13—28no—
178C42×C13—48no—
179#6103—216no—
180#6103—28no—
181#6103—28no—
182#6103—216no—
183#6101—216no—
184#6101—216no—
185C4×Dic13—216no—
186C4×Dic13—44no—
187C2×#399—131no—
188C2×C4×C4⋊C4—132no—
189C2×C4×C4⋊C4D1311yescharacteristic, complemented
190C2×C4×C22⋊C4—132no—
191C2×C4×C22⋊C4—131no—
192#1445—132no—
193#1445—131no—
194#1444—131no—
195#1439—132no—
196#1439—131no—
197C4×#95—131no—
198C23×C13C23×C411yescharacteristic
199C23×C13C22×D412yes—
200C23×C13C22×D411yescharacteristic
201C23×C13C22×Q811yescharacteristic
202C23×C13C2×#4111yescharacteristic
203C23×C13C2×#4112yes—
204C23×C13C2×#4111yescharacteristic
205C23×C13C2×#4112yes—
206C23×C13C2×#4111yescharacteristic
207C23×C13C2×#4112yes—
208C23×C13C2×#4111yescharacteristic
209C22×D13—22no—
210C22×D13—24no—
211C22×D13—24no—
212C22×D13—22no—
213C22×D13—24no—
214C22×D13—22no—
215C22×D13—24no—
216C22×D13—22no—
217C22×D13—24no—
218C22×D13—22no—
219C22×D13—22no—
220C22×D13—24no—
221C22×D13—42no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13—42no—
227C22×D13—42no—
228C22×D13—41no—
229C22×D13—42no—
230C22×D13—41no—
231C22×D13C4×Q814yes—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—22no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13C4×D414yes—
256C2×C4×C13C22⋊Q818yes—
257C2×C4×C13C22⋊Q814yes—
258C2×C4×C13#12318yes—
259C2×C4×C13#12314yes—
260C2×C4×C13#12714yes—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—22no—
269C2×Dic13—24no—
270C2×Dic13—22no—
271C2×Dic13—24no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—22no—
275C2×Dic13—24no—
276C2×Dic13—42no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—42no—
288C2×Dic13—41no—
289C2×Dic13C4×D418yes—
290C4×D13—416no—
291C24×C4—131no—
292C22×C4⋊C4—132no—
293C22×C4⋊C4—132no—
294C22×C4⋊C4C2×D1311yescharacteristic
295C22×C4⋊C4C2×D1311yescharacteristic
296C22×C22⋊C4—132no—
297C22×C22⋊C4—131no—
298C22×C22⋊C4—131no—
299C22×C22⋊C4—132no—
300C22×C42—132no—
301C22×C42—131no—
302C22×C42C2×D1312yes—
303C22×C42C2×D1311yescharacteristic
304#399—138no—
305C4×C4⋊C4—24no—
306C4×C4⋊C4—268no—
307C4×C22⋊C4—268no—
308C4×C22⋊C4—264no—
309C2×#95—131no—
310C2×#95—132no—
311C2×#95—131no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95—132no—
315C2×#95—131no—
316C2×#95—132no—
317C2×#95—131no—
318C2×#95C2×D1312yes—
319C22×C13C2×C4×D411yescharacteristic
320C22×C13C2×C4×D412yes—
321C22×C13C2×C4×Q811yescharacteristic
322C22×C13C4×#4112yes—
323C22×C13C4×#4111yescharacteristic
324C22×C13C2×C22⋊Q812yes—
325C22×C13C2×C22⋊Q811yescharacteristic
326C22×C13C2×#12312yes—
327C22×C13C2×#12311yescharacteristic
328C22×C13#52511yescharacteristic
329C22×C13#52512yes—
330C22×C13#52512yes—
331C22×C13#52511yescharacteristic
332C22×C13#52912yes—
333C22×C13#52912yes—
334C22×C13#52912yes—
335C22×C13#52911yescharacteristic
336C22×C13#52912yes—
337C22×C13C2×#12711yescharacteristic
338C22×C13#53212yes—
339C22×C13#53211yescharacteristic
340C22×C13#53312yes—
341C22×C13#53311yescharacteristic
342C2×D13—24no—
343C2×D13—28no—
344C2×D13—42no—
345C2×D13—42no—
346C2×D13—42no—
347C2×D13—44no—
348C2×D13—42no—
349C2×D13—44no—
350C2×D13—42no—
351C2×D13—42no—
352C2×D13—44no—
353C4×C13—24no—
354C4×C13—44no—
355C4×C13—42no—
356C4×C13—44no—
357C4×C13#39918yescomplemented
358Dic13—28no—
359Dic13—42no—
360Dic13—42no—
361Dic13—44no—
362Dic13—42no—
363C25—131no—
364C23×C4—132no—
365C23×C4—131no—
366C23×C4—131no—
367C23×C4—132no—
368C23×C4—131no—
369C23×C4—134no—
370C23×C4—264no—
371C23×C4—264no—
372C23×C4—262no—
373C23×C4—262no—
374C23×C4C22×D1312yes—
375C23×C4C22×D1312yes—
376C23×C4C22×D1311yescharacteristic
377C23×C4C22×D1311yescharacteristic
378C23×C4C22×D1311yescharacteristic
379C2×C4⋊C4—24no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—138no—
384C2×C4⋊C4—264no—
385C2×C4⋊C4—264no—
386C2×C4⋊C4—264no—
387C2×C4⋊C4—264no—
388C2×C4⋊C4—264no—
389C2×C4⋊C4C4×D1314yescomplemented
390C2×C22⋊C4—138no—
391C2×C22⋊C4—134no—
392C2×C22⋊C4—264no—
393C2×C22⋊C4—262no—
394C2×C22⋊C4—264no—
395C2×C22⋊C4—264no—
396C2×C22⋊C4—264no—
397C2×C22⋊C4—262no—
398C2×C22⋊C4—264no—
399C2×C22⋊C4—262no—
400C2×C22⋊C4—262no—
401C2×C22⋊C4—262no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—138no—
407C2×C42—264no—
408C2×C42—264no—
409C2×C42—264no—
410C2×C42—262no—
411C2×C42C22⋊D1314yes—
412#95—24no—
413#95—134no—
414#95—264no—
415#95—264no—
416#95—264no—
417#95—264no—
418#95—264no—
419#95—262no—
420#95—262no—
421#95—262no—
422C2×C13C4×#12311yescharacteristic
423C2×C13C4×#12312yes—
424C2×C13C4×C22⋊Q811yescharacteristic
425C2×C13C4×C22⋊Q812yes—
426C2×C13C4×#12711yescharacteristic
427C2×C13C2×#39911yescharacteristic
428C2×C13#239511yescharacteristic
429C2×C13#239512yes—
430C2×C13#239611yescharacteristic
431C2×C13#239612yes—
432C2×C13#239711yescharacteristic
433D13—44no—
434C24—132no—
435C24—132no—
436C24—132no—
437C24—262no—
438C24—261no—
439C24—262no—
440C24—262no—
441C24—261no—
442C24—262no—
443C24—261no—
444C24—261no—
445C24C23×D1311yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
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—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—134no—
465C22×C4—134no—
466C22×C4—134no—
467C22×C4—132no—
468C22×C4—134no—
469C22×C4—132no—
470C22×C4—132no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—261no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—261no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—261no—
489C22×C4—262no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—2616no—
494C22×C4—268no—
495C22×C4—528no—
496C22×C4—524no—
497C22×C4—524no—
498C22×C4C2×C4×D1314yes—
499C22×C4C2×C4×D1312yes—
500C22×C4#612714yes—
501C22×C4#612712yes—
502C22×C4#612714yes—
503C22×C4D4×D1314yes—
504C22×C4Q8×D1312yes—
505C22×C4#613112yes—
506C22×C4C2×C22⋊D1312yes—
507C22×C4C2×C22⋊D1312yes—
508C22×C4C2×C22⋊D1312yes—
509C4⋊C4—28no—
510C4⋊C4—28no—
511C4⋊C4—2616no—
512C4⋊C4—2616no—
513C22⋊C4—2616no—
514C22⋊C4—2616no—
515C22⋊C4—268no—
516C22⋊C4—268no—
517C42—28no—
518C42—48no—
519C42—2616no—
520C42—524no—
521C13C4×#39911yescharacteristic, complemented, Sylow
522C23—134no—
523C23—264no—
524C23—264no—
525C23—264no—
526C23—262no—
527C23—264no—
528C23—264no—
529C23—262no—
530C23—262no—
531C23—262no—
532C23—262no—
533C23—264no—
534C23—262no—
535C23—522no—
536C23—522no—
537C23—522no—
538C23—521no—
539C23—521no—
540C23—522no—
541C23—521no—
542C23—522no—
543C23—521no—
544C23—522no—
545C23C22×C4×D1311yescharacteristic
546C23C2×#612712yes—
547C23C2×#612712yes—
548C23C2×#612711yescharacteristic
549C23C2×D4×D1312yes—
550C23C2×Q8×D1311yescharacteristic
551C23C2×#613111yescharacteristic
552C23#41×D1312yes—
553C23#41×D1311yescharacteristic
554C23#41×D1311yescharacteristic
555C23C22×C22⋊D1311yescharacteristic
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—138no—
580C2×C4—264no—
581C2×C4—264no—
582C2×C4—264no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—264no—
588C2×C4—262no—
589C2×C4—264no—
590C2×C4—264no—
591C2×C4—264no—
592C2×C4—264no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—522no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—522no—
605C2×C4—521no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4—5216no—
609C2×C4#8814818yes—
610C2×C4#8815018yes—
611C2×C4C4×C22⋊D1314yes—
612C2×C4#8818314yes—
613C2×C4#8819414yes—
614C2×C4#8820014yes—
615C22—264no—
616C22—268no—
617C22—522no—
618C22—522no—
619C22—524no—
620C22—522no—
621C22—524no—
622C22—522no—
623C22—522no—
624C22—524no—
625C22—522no—
626C22C4×#612712yes—
627C22#1171918412yes—
628C22C2×#8814812yes—
629C22C2×#8815012yes—
630C22#1171923312yes—
631C22#1171923312yes—
632C22C4×D4×D1312yes—
633C22#1171925212yes—
634C22#1171925212yes—
635C22#1171925312yes—
636C22C4×Q8×D1311yescharacteristic
637C22C4×#613111yescharacteristic
638C22#1171928312yes—
639C22#1171928311yescharacteristic
640C22#1171928511yescharacteristic
641C22#1171928512yes—
642C22C2×C4×C22⋊D1311yescharacteristic
643C22C2×#8818311yescharacteristic
644C22#1171949611yescharacteristic
645C22C2×#8819411yescharacteristic
646C22C2×#8820011yescharacteristic
647C22#1171953311yescharacteristic
648C22#1171953711yescharacteristic
649C4—24no—
650C4—42no—
651C4—44no—
652C4—44no—
653C4—268no—
654C4—522no—
655C4—524no—
656C4—522no—
657C4—522no—
658C4#1171865318yesdirect product factor
659C2—524no—
660C2C4×#8818311yescharacteristic
661C2C4×#8814812yes—
662C2C4×#8820011yescharacteristic
663C2C4×#8815012yes—
664C2C4×#8819411yescharacteristic
665C2C2×#1171865311yescharacteristic
666C2#1311809311yescharacteristic
667C2#1311809912yes—
668C2#1311810611yescharacteristic
669C2#1311811212yes—
670C2#1311811511yescharacteristic
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×#399
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
2. C2×C4×#6101C2semidirect
5. #13113104C2semidirect
6. #13113102C2semidirect
7. #13113099C2semidirect
10. C4×#88071C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
36. #11718653C4direct (N × H)
60. C2×C13×C4⋊C4C2×C4semidirect
83. C2×#6101C2×C4semidirect
98. #88071C2×C4semidirect
189. C2×C4×C4⋊C4D13semidirect
357. C4×C13#399semidirect
389. C2×C4⋊C4C4×D13semidirect
521. C13C4×#399semidirect
658. C4#11718653direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186532
C2×C4×#61012
C2×C4×#61032
#131131042
#131131022
#131130992
#131130802
#131130782
C4×#880712
C2×C4×C13×C4⋊C42
C4×#39913