Finite Group Databasebeta

← C2×#13130021 #16791684

Subgroups — C2×#13130021 #16791684

Order 3328.

3246 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊#261C211yesmaximal, characteristic
2C22×(C2×#261)⋊C4C212yesmaximal
3C22×(C2×#261)⋊C4C211yesmaximal, characteristic
4C22×(C2×#261)⋊C4C212yesmaximal
5#13130021C218yesmaximal, direct product factor
6C22×C4⋊C4×D13C211yesmaximal, characteristic
7C24×#261C2212yes—
8C24×#261C2212yes—
9C23×C4×D13C2211yescharacteristic
10C23×C4×D13C2211yescharacteristic
11C23×C4×D13C2211yescharacteristic
12C22×C4⋊#261—28no—
13C22×C4⋊#261—24no—
14C22×C4⋊#261C2214yes—
15C22×C13×C4⋊C4C411yescharacteristic, complemented
16C22×C4⋊Dic13C411yescharacteristic, complemented
17C22×#6101C411yescharacteristic, complemented
18C22×#6101C411yescharacteristic, complemented
19C2×C4⋊C4×D13—24no—
20C2×C4⋊C4×D13—24no—
21C2×C4⋊C4×D13C414yescomplemented
22C2×C4⋊C4×D13C2214yes—
23C2×(C2×#261)⋊C4—28no—
24C2×(C2×#261)⋊C4—24no—
25C2×(C2×#261)⋊C4—28no—
26C2×(C2×#261)⋊C4C2218yes—
27C2×(C2×#261)⋊C4C2214yes—
28C2×(C2×#261)⋊C4C2218yes—
29C24×D13C2311yescharacteristic
30C23×#261—24no—
31C23×#261—24no—
32C23×#261—24no—
33C23×#261—24no—
34C23×#261—24no—
35C23×#261—24no—
36C23×#261—24no—
37C23×#261—24no—
38C23×#261—24no—
39C23×#261—24no—
40C23×#261—24no—
41C23×#261—24no—
42C23×#261D418yes—
43C23×#261Q818yes—
44C23×#261C2314yes—
45C23×#261C2314yes—
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×C4×C13C2×C411yescharacteristic
49C23×Dic13C2×C411yescharacteristic
50C23×Dic13C2×C411yescharacteristic
51C23×Dic13C2×C411yescharacteristic
52C22×C4×D13—22no—
53C22×C4×D13—22no—
54C22×C4×D13—24no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—24no—
58C22×C4×D13—22no—
59C22×C4×D13—22no—
60C22×C4×D13—24no—
61C22×C4×D13—24no—
62C22×C4×D13C2×C412yes—
63C22×C4×D13C2×C412yes—
64C22×C4×D13C2×C412yes—
65C22×C4×D13D414yes—
66C22×C4×D13D414yes—
67C22×C4×D13D414yes—
68C22×C4×D13Q814yes—
69C22×C4×D13C2312yes—
70C22×C4×D13C2312yes—
71C22×C4×D13C2312yes—
72C2×C4⋊#261—232no—
73C2×C4⋊#261—216no—
74C2×C4⋊#261—28no—
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4C2×C414yescomplemented
77C2×C4⋊Dic13—24no—
78C2×C4⋊Dic13C2×C414yescomplemented
79C2×#6101—24no—
80C2×#6101—24no—
81C2×#6101C2×C414yescomplemented
82C2×#6101C2×C414yescomplemented
83C4⋊C4×D13—216no—
84C4⋊C4×D13—28no—
85C4⋊C4×D13—28no—
86(C2×#261)⋊C4—216no—
87(C2×#261)⋊C4—28no—
88(C2×#261)⋊C4—216no—
89C2×#1441—131nomaximal, Sylow
90C24×C13C22×C411yescharacteristic
91C23×D13C22×C411yescharacteristic
92C23×D13C2×D412yes—
93C23×D13C2×D412yes—
94C23×D13C2×D412yes—
95C23×D13C2×D414yes—
96C23×D13C2×Q812yes—
97C23×D13C2×Q814yes—
98C23×D13#4112yes—
99C23×D13#4112yes—
100C23×D13#4114yes—
101C23×D13#4114yes—
102C23×D13C2411yescharacteristic
103C22×#261—216no—
104C22×#261—216no—
105C22×#261—216no—
106C22×#261—216no—
107C22×#261—216no—
108C22×#261—216no—
109C22×#261—24no—
110C22×#261—24no—
111C22×#261—24no—
112C22×#261—24no—
113C22×#261—24no—
114C22×#261—24no—
115C22×#261—24no—
116C22×#261—24no—
117C22×#261—24no—
118C22×#261—24no—
119C22×#261—24no—
120C22×#261—24no—
121C22×#261—48no—
122C22×#261—48no—
123C22×#261—48no—
124C22×#261—48no—
125C22×#261—48no—
126C22×#261—48no—
127C22×#261—48no—
128C22×#261—48no—
129C22×#261C2×D418yes—
130C22×#261C2×Q818yes—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—24no—
134C22×C4×C13—22no—
135C22×C4×C13—24no—
136C22×C4×C13C22⋊C414yes—
137C22×C4×C13C4⋊C414yescomplemented
138C22×C4×C13C22×C412yes—
139C22×C4×C13C22×C412yes—
140C22×C4×C13C22×C412yes—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—24no—
144C22×Dic13—22no—
145C22×Dic13—24no—
146C22×Dic13C22⋊C414yes—
147C22×Dic13C4⋊C414yescomplemented
148C22×Dic13C22×C412yes—
149C22×Dic13C22×C412yes—
150C22×Dic13C22×C412yes—
151C2×C4×D13—24no—
152C2×C4×D13—24no—
153C2×C4×D13—28no—
154C2×C4×D13—28no—
155C2×C4×D13—28no—
156C2×C4×D13—28no—
157C2×C4×D13—216no—
158C2×C4×D13—28no—
159C2×C4×D13—28no—
160C2×C4×D13—28no—
161C2×C4×D13—22no—
162C2×C4×D13—22no—
163C2×C4×D13—24no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—24no—
167C2×C4×D13—24no—
168C2×C4×D13—28no—
169C2×C4×D13—24no—
170C2×C4×D13—22no—
171C2×C4×D13—22no—
172C2×C4×D13—24no—
173C2×C4×D13—44no—
174C2×C4×D13—48no—
175C2×C4×D13—44no—
176C2×C4×D13C22⋊C418yes—
177C2×C4×D13C4⋊C418yescomplemented
178C2×C4×D13C2×D414yes—
179C2×C4×D13C2×D414yes—
180C2×C4×D13C2×D414yes—
181C2×C4×D13C2×Q814yes—
182C4⋊#261—232no—
183C13×C4⋊C4—28no—
184C4⋊Dic13—28no—
185#6101—28no—
186#6101—28no—
187C23×C4⋊C4—131no—
188C23×C4⋊C4—131no—
189C22×#95—131no—
190C22×#95—132no—
191C22×#95—132no—
192#1441—138no—
193C23×C13C2×C22⋊C412yes—
194C23×C13C2×C4⋊C412yes—
195C23×C13#11712yes—
196C23×C13C4×D414yes—
197C23×C13C4×Q814yes—
198C23×C13C23×C411yescharacteristic
199C22×D13C2×C22⋊C412yes—
200C22×D13C2×C4⋊C412yes—
201C22×D13#11712yes—
202C22×D13C4×D414yes—
203C22×D13C4×Q814yes—
204C22×D13#12014yes—
205C22×D13#12114yes—
206C22×D13#12114yes—
207C22×D13#12118yes—
208C22×D13#12118yes—
209C22×D13C22⋊Q814yes—
210C22×D13C22⋊Q814yes—
211C22×D13C22⋊Q818yes—
212C22×D13C22⋊Q818yes—
213C22×D13C22⋊Q818yes—
214C22×D13#12314yes—
215C22×D13#12318yes—
216C22×D13#12414yes—
217C22×D13#12518yes—
218C22×D13#12518yes—
219C22×D13#12618yes—
220C22×D13C4⋊Q818yes—
221C22×D13C4⋊Q814yes—
222C22×D13C22×D412yes—
223C22×D13C22×D411yescharacteristic
224C22×D13C22×D411yescharacteristic
225C22×D13C22×D411yescharacteristic
226C22×D13C22×Q812yes—
227C22×D13C22×Q811yescharacteristic
228C22×D13C2×#4111yescharacteristic
229C22×D13C2×#4111yescharacteristic
230C22×D13C2×#4112yes—
231C22×D13C2×#4112yes—
232C2×#261—28no—
233C2×#261—28no—
234C2×#261—28no—
235C2×#261—28no—
236C2×#261—28no—
237C2×#261—28no—
238C2×#261—44no—
239C2×#261—44no—
240C2×#261—44no—
241C2×#261—44no—
242C2×#261—44no—
243C2×#261—44no—
244C2×#261—44no—
245C2×#261—44no—
246C2×#261—432no—
247C2×#261—432no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—24no—
251C2×C4×C13—28no—
252C2×C4×C13—28no—
253C2×C4×C13—22no—
254C2×C4×C13—24no—
255C2×C4×C13—44no—
256C2×C4×C13C2×C22⋊C414yes—
257C2×C4×C13C2×C4⋊C414yescomplemented
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—28no—
262C2×Dic13—28no—
263C2×Dic13—22no—
264C2×Dic13—24no—
265C2×Dic13—44no—
266C2×Dic13C2×C22⋊C414yes—
267C2×Dic13C2×C4⋊C414yescomplemented
268C4×D13—24no—
269C4×D13—24no—
270C4×D13—24no—
271C4×D13—28no—
272C4×D13—24no—
273C4×D13—24no—
274C4×D13—24no—
275C4×D13—216no—
276C4×D13—216no—
277C4×D13—42no—
278C4×D13—44no—
279C4×D13—42no—
280C4×D13—48no—
281C24×C4—131no—
282C24×C4—131no—
283C24×C4—132no—
284C24×C4—132no—
285C24×C4—131no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—131no—
288C22×C4⋊C4—131no—
289C22×C4⋊C4—134no—
290C22×C4⋊C4—134no—
291C22×C4⋊C4—134no—
292C22×C4⋊C4—264no—
293C22×C4⋊C4—264no—
294C22×C4⋊C4—264no—
295C22×C4⋊C4—268no—
296C22×C4⋊C4#26111yescharacteristic, complemented
297C2×#95—134no—
298C2×#95—138no—
299C2×#95—138no—
300C2×#95—268no—
301C2×#95—264no—
302C2×#95—268no—
303C22×C13#38014yes—
304C22×C13#38614yes—
305C22×C13#38718yes—
306C22×C13#38918yes—
307C22×C13#39114yes—
308C22×C13C22×C22⋊C411yescharacteristic
309C22×C13C22×C4⋊C411yescharacteristic
310C22×C13C2×#11711yescharacteristic
311C22×C13C2×C4×D412yes—
312C22×C13C2×C4×Q812yes—
313C2×D13#38014yes—
314C2×D13#38614yes—
315C2×D13#38718yes—
316C2×D13#38918yes—
317C2×D13#39114yes—
318C2×D13#39418yes—
319C2×D13#39518yes—
320C2×D13#396116yes—
321C2×D13#39818yes—
322C2×D13#398116yes—
323C2×D13#40018yes—
324C2×D13C2×#12011yescharacteristic
325C2×D13C2×#12112yes—
326C2×D13C2×#12111yescharacteristic
327C2×D13C2×#12111yescharacteristic
328C2×D13C2×#12112yes—
329C2×D13C2×C22⋊Q812yes—
330C2×D13C2×C22⋊Q811yescharacteristic
331C2×D13C2×C22⋊Q812yes—
332C2×D13C2×C22⋊Q812yes—
333C2×D13C2×C22⋊Q811yescharacteristic
334C2×D13C2×#12312yes—
335C2×D13C2×#12311yescharacteristic
336C2×D13C2×#12411yescharacteristic
337C2×D13C2×#12512yes—
338C2×D13C2×#12512yes—
339C2×D13C2×#12612yes—
340C2×D13C2×C4⋊Q812yes—
341C2×D13C2×C4⋊Q811yescharacteristic
342#261—48no—
343#261—48no—
344C4×C13—24no—
345C4×C13—24no—
346C4×C13—42no—
347Dic13—24no—
348Dic13—24no—
349Dic13—42no—
350C25—131no—
351C23×C4—131no—
352C23×C4—131no—
353C23×C4—134no—
354C23×C4—134no—
355C23×C4—134no—
356C23×C4—134no—
357C23×C4—132no—
358C23×C4—132no—
359C23×C4—132no—
360C23×C4—132no—
361C23×C4—134no—
362C23×C4—138no—
363C23×C4—134no—
364C23×C4—138no—
365C23×C4—131no—
366C23×C4—132no—
367C23×C4—132no—
368C23×C4—264no—
369C23×C4—262no—
370C23×C4—262no—
371C23×C4—262no—
372C23×C4—262no—
373C23×C4—264no—
374C23×C4—262no—
375C23×C4—262no—
376C23×C4—264no—
377C23×C4—264no—
378C23×C4—264no—
379C23×C4—264no—
380C23×C4—264no—
381C23×C4—264no—
382C23×C4—264no—
383C23×C4—264no—
384C23×C4—264no—
385C23×C4—264no—
386C23×C4—264no—
387C23×C4—264no—
388C23×C4—264no—
389C23×C4—264no—
390C23×C4C2×#26111yescharacteristic
391C23×C4C2×#26111yescharacteristic
392C23×C4C2×#26111yescharacteristic
393C2×C4⋊C4—24no—
394C2×C4⋊C4—134no—
395C2×C4⋊C4—134no—
396C2×C4⋊C4—134no—
397C2×C4⋊C4—268no—
398C2×C4⋊C4—268no—
399C2×C4⋊C4—2616no—
400C2×C4⋊C4—264no—
401C2×C4⋊C4—264no—
402C2×C4⋊C4—268no—
403C2×C4⋊C4—2616no—
404C2×C4⋊C4—2632no—
405C2×C4⋊C4—264no—
406C2×C4⋊C4C2×#26114yescomplemented
407#95—2616no—
408#95—268no—
409#95—2616no—
410C2×C13#144118yescomplemented
411C2×C13C2×#38011yescharacteristic
412C2×C13C2×#38611yescharacteristic
413C2×C13C2×#38712yes—
414C2×C13C2×#38912yes—
415C2×C13C2×#39111yescharacteristic
416D13#144118yescomplemented
417D13C2×#39411yescharacteristic
418D13C2×#39511yescharacteristic
419D13C2×#39612yes—
420D13C2×#39811yescharacteristic
421D13C2×#39812yes—
422D13C2×#40011yescharacteristic
423C24—132no—
424C24—132no—
425C24—132no—
426C24—132no—
427C24—134no—
428C24—134no—
429C24—134no—
430C24—134no—
431C24—132no—
432C24—132no—
433C24—131no—
434C24—131no—
435C24C22×#26111yescharacteristic
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—134no—
442C22×C4—134no—
443C22×C4—132no—
444C22×C4—132no—
445C22×C4—134no—
446C22×C4—138no—
447C22×C4—134no—
448C22×C4—134no—
449C22×C4—134no—
450C22×C4—138no—
451C22×C4—138no—
452C22×C4—138no—
453C22×C4—132no—
454C22×C4—264no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—264no—
458C22×C4—268no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—264no—
462C22×C4—264no—
463C22×C4—268no—
464C22×C4—268no—
465C22×C4—268no—
466C22×C4—268no—
467C22×C4—268no—
468C22×C4—2616no—
469C22×C4—268no—
470C22×C4—264no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—264no—
474C22×C4—264no—
475C22×C4—268no—
476C22×C4—262no—
477C22×C4—264no—
478C22×C4—262no—
479C22×C4—264no—
480C22×C4—264no—
481C22×C4—264no—
482C22×C4—264no—
483C22×C4—264no—
484C22×C4—264no—
485C22×C4—2616no—
486C22×C4—2616no—
487C22×C4—2616no—
488C22×C4—2616no—
489C22×C4—2616no—
490C22×C4—264no—
491C22×C4—264no—
492C22×C4—264no—
493C22×C4—264no—
494C22×C4—264no—
495C22×C4—264no—
496C22×C4—2616no—
497C22×C4—264no—
498C22×C4—262no—
499C22×C4—524no—
500C22×C4—528no—
501C22×C4—524no—
502C22×C4—528no—
503C22×C4—528no—
504C22×C4—528no—
505C22×C4—528no—
506C22×C4—528no—
507C22×C4—528no—
508C22×C4—528no—
509C22×C4—528no—
510C22×C4C4⋊#26114yescomplemented
511C22×C4C22⋊#26114yes—
512C22×C4C22×#26112yes—
513C22×C4C22×#26112yes—
514C22×C4C22×#26112yes—
515C4⋊C4—28no—
516C4⋊C4—268no—
517C4⋊C4—268no—
518C4⋊C4—2632no—
519C4⋊C4—268no—
520C13C2×#144111yescharacteristic, complemented, Sylow
521C23—138no—
522C23—138no—
523C23—138no—
524C23—138no—
525C23—138no—
526C23—138no—
527C23—138no—
528C23—138no—
529C23—131no—
530C23—132no—
531C23—131no—
532C23—131no—
533C23—131no—
534C23—132no—
535C23—132no—
536C23—132no—
537C23—134no—
538C23—132no—
539C23—132no—
540C23—134no—
541C23—131no—
542C23—131no—
543C23—132no—
544C23—134no—
545C23—134no—
546C23—134no—
547C23—134no—
548C23—134no—
549C23—138no—
550C23—134no—
551C23—138no—
552C23—134no—
553C23—134no—
554C23C2×C4⋊#26112yes—
555C23#8823712yes—
556C23D4×#26114yes—
557C23Q8×#26114yes—
558C23C2×C22⋊#26112yes—
559C23C23×#26111yescharacteristic
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—28no—
564C2×C4—28no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—44no—
568C2×C4—134no—
569C2×C4—134no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—2616no—
576C2×C4—268no—
577C2×C4—264no—
578C2×C4—2616no—
579C2×C4—262no—
580C2×C4—264no—
581C2×C4—262no—
582C2×C4—268no—
583C2×C4—268no—
584C2×C4—268no—
585C2×C4—268no—
586C2×C4—268no—
587C2×C4—268no—
588C2×C4—268no—
589C2×C4—268no—
590C2×C4—264no—
591C2×C4—262no—
592C2×C4—522no—
593C2×C4—524no—
594C2×C4—522no—
595C2×C4—528no—
596C2×C4—524no—
597C2×C4—524no—
598C2×C4—524no—
599C2×C4—524no—
600C2×C4—524no—
601C2×C4—524no—
602C2×C4—524no—
603C2×C4—524no—
604C2×C4—5232no—
605C2×C4—5232no—
606C2×C4—524no—
607C2×C4C2×C4⋊#26114yescomplemented
608C2×C4C2×C22⋊#26114yes—
609C22—131no—
610C22—131no—
611C22—131no—
612C22—131no—
613C22—134no—
614C22—131no—
615C22—132no—
616C22—131no—
617C22—134no—
618C22—132no—
619C22—132no—
620C22—132no—
621C22—132no—
622C22—138no—
623C22—132no—
624C22—132no—
625C22—132no—
626C22—132no—
627C22—138no—
628C22—132no—
629C22—131no—
630C22—131no—
631C22—134no—
632C22—138no—
633C22—138no—
634C22—1316no—
635C22—1316no—
636C22—138no—
637C22—138no—
638C22#1171908218yes—
639C22#1171908318yes—
640C22#1171913614yes—
641C22#1171915014yes—
642C22(C2×#261)⋊Q814yes—
643C22C22×C4⋊#26111yescharacteristic
644C22C2×#8823711yescharacteristic
645C22C2×D4×#26112yes—
646C22C2×Q8×#26112yes—
647C22C22×C22⋊#26111yescharacteristic
648C4—24no—
649C4—24no—
650C4—42no—
651C4—264no—
652C4—264no—
653C4—528no—
654C4—528no—
655C4—522no—
656C2—131no—
657C2—132no—
658C2—131no—
659C2—131no—
660C2—132no—
661C2—131no—
662C2—138no—
663C2#1313002118yesdirect product factor
664C2C2×#1171913611yescharacteristic
665C2C2×#1171915011yescharacteristic
666C2C2×#1171908212yes—
667C2C2×#1171908312yes—
668C2C2×(C2×#261)⋊Q811yescharacteristic
subgroupG/H
centerC24C22×#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC22×C13×C4⋊C4C4
socleC24×C13C22×C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#1441
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #13130021C2direct (N × H)
15. C22×C13×C4⋊C4C4semidirect
16. C22×C4⋊Dic13C4semidirect
17. C22×#6101C4semidirect
18. C22×#6101C4semidirect
21. C2×C4⋊C4×D13C4semidirect
76. C2×C13×C4⋊C4C2×C4semidirect
78. C2×C4⋊Dic13C2×C4semidirect
81. C2×#6101C2×C4semidirect
82. C2×#6101C2×C4semidirect
137. C22×C4×C13C4⋊C4semidirect
147. C22×Dic13C4⋊C4semidirect
177. C2×C4×D13C4⋊C4semidirect
257. C2×C4×C13C2×C4⋊C4semidirect
267. C2×Dic13C2×C4⋊C4semidirect
296. C22×C4⋊C4#261semidirect
406. C2×C4⋊C4C2×#261semidirect
410. C2×C13#1441semidirect
416. D13#1441semidirect
510. C22×C4C4⋊#261semidirect
520. C13C2×#1441semidirect
607. C2×C4C2×C4⋊#261semidirect
663. C2#13130021direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊#2612
C22×(C2×#261)⋊C42
#131300212
C22×C4⋊C4×D132
C2×#144113