Finite Group Databasebeta

← C2×#13130015 #16791529

Subgroups — C2×#13130015 #16791529

Order 3328.

3550 conjugacy classes of subgroups.

The subgroup lattice has 630 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#13130015C218yesmaximal, 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)⋊C4C4116yescomplemented
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×#261C2×C418yes—
41C23×#261C2×C418yes—
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—24no—
56C22×C4×D13—24no—
57C22×C4×D13—22no—
58C22×C4×D13—22no—
59C22×C4×D13—24no—
60C22×C4×D13—24no—
61C22×C4×D13C2×C412yes—
62C22×C4×D13C2×C412yes—
63C22×C4×D13C2×C418yes—
64C22×C4×D13C2×C412yes—
65C22×C4×D13D414yes—
66C22×C4×D13D414yes—
67C22×C4×D13C2312yes—
68C22×C4×D13C2312yes—
69C22×C4×D13C2312yes—
70C2×C4×#261—232no—
71C2×C4×#261—216no—
72C2×C4×#261—28no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4C2×C414yescomplemented
75C2×C4⋊Dic13—24no—
76C2×C4⋊Dic13C2×C414yescomplemented
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101C2×C414yescomplemented
80C2×#6101C2×C414yescomplemented
81C4⋊C4×D13—216no—
82C4⋊C4×D13—28no—
83C4⋊C4×D13—28no—
84(C2×#261)⋊C4—216no—
85(C2×#261)⋊C4—28no—
86(C2×#261)⋊C4C2×C4132yescomplemented
87C2×#1436—131nomaximal, Sylow
88C24×C13C22×C411yescharacteristic
89C23×D13C22×C411yescharacteristic
90C23×D13C22×C414yes—
91C23×D13C2×D412yes—
92C23×D13C2×D412yes—
93C23×D13C2×D414yes—
94C23×D13C2×Q814yes—
95C23×D13#4114yes—
96C23×D13#4114yes—
97C23×D13#4114yes—
98C23×D13C2411yescharacteristic
99C22×#261—216no—
100C22×#261—216no—
101C22×#261—216no—
102C22×#261—216no—
103C22×#261—216no—
104C22×#261—216no—
105C22×#261—24no—
106C22×#261—24no—
107C22×#261—24no—
108C22×#261—24no—
109C22×#261—216no—
110C22×#261—216no—
111C22×#261—216no—
112C22×#261—24no—
113C22×#261—24no—
114C22×#261—24no—
115C22×#261—24no—
116C22×#261—24no—
117C22×#261—24no—
118C22×#261—48no—
119C22×#261—48no—
120C22×#261—48no—
121C22×#261—48no—
122C22×#261C4⋊C4132yescomplemented
123C22×#261C22×C418yes—
124C22×#261C22×C418yes—
125C22×#261C2×D418yes—
126C22×#261C2×Q818yes—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—24no—
130C22×C4×C13—22no—
131C22×C4×C13—24no—
132C22×C4×C13C4214yescomplemented
133C22×C4×C13C22⋊C414yes—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C22×C412yes—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—24no—
140C22×Dic13—22no—
141C22×Dic13—24no—
142C22×Dic13C4214yescomplemented
143C22×Dic13C22⋊C414yes—
144C22×Dic13C22×C412yes—
145C22×Dic13C22×C412yes—
146C22×Dic13C22×C412yes—
147C2×C4×D13—24no—
148C2×C4×D13—24no—
149C2×C4×D13—216no—
150C2×C4×D13—216no—
151C2×C4×D13—28no—
152C2×C4×D13—28no—
153C2×C4×D13—216no—
154C2×C4×D13—28no—
155C2×C4×D13—22no—
156C2×C4×D13—22no—
157C2×C4×D13—24no—
158C2×C4×D13—24no—
159C2×C4×D13—24no—
160C2×C4×D13—24no—
161C2×C4×D13—28no—
162C2×C4×D13—24no—
163C2×C4×D13—22no—
164C2×C4×D13—22no—
165C2×C4×D13—24no—
166C2×C4×D13—44no—
167C2×C4×D13—48no—
168C2×C4×D13—44no—
169C2×C4×D13C4218yescomplemented
170C2×C4×D13C22⋊C418yes—
171C2×C4×D13C22×C418yes—
172C2×C4×D13C2×D414yes—
173C2×C4×D13C2×D414yes—
174C4×#261—232no—
175C13×C4⋊C4—28no—
176C4⋊Dic13—28no—
177#6101—28no—
178#6101—28no—
179C23×C4⋊C4—131no—
180C23×C42—131no—
181C22×#95—132no—
182C22×#95—132no—
183C22×#95—131no—
184#1436—138no—
185C23×C13C2×C4212yes—
186C23×C13C2×C22⋊C412yes—
187C23×C13#11712yes—
188C23×C13C4×D414yes—
189C23×C13C4×Q814yes—
190C23×C13C23×C411yescharacteristic
191C22×D13C2×C4212yes—
192C22×D13C2×C22⋊C412yes—
193C22×D13C2×C4⋊C418yes—
194C22×D13#11718yes—
195C22×D13#11712yes—
196C22×D13C4×D418yes—
197C22×D13C4×D418yes—
198C22×D13C4×D418yes—
199C22×D13C4×D414yes—
200C22×D13C4×Q818yes—
201C22×D13C4×Q814yes—
202C22×D13#12014yes—
203C22×D13#12118yes—
204C22×D13C22⋊Q818yes—
205C22×D13C22⋊Q818yes—
206C22×D13#12318yes—
207C22×D13#12314yes—
208C22×D13#12414yes—
209C22×D13#12518yes—
210C22×D13#12618yes—
211C22×D13C4⋊Q814yes—
212C22×D13C23×C412yes—
213C22×D13C22×D412yes—
214C22×D13C22×D411yescharacteristic
215C22×D13C22×D411yescharacteristic
216C22×D13C22×Q812yes—
217C22×D13C2×#4112yes—
218C22×D13C2×#4112yes—
219C22×D13C2×#4112yes—
220C2×#261—28no—
221C2×#261—28no—
222C2×#261—28no—
223C2×#261—28no—
224C2×#261—28no—
225C2×#261—28no—
226C2×#261—264no—
227C2×#261—28no—
228C2×#261—28no—
229C2×#261—28no—
230C2×#261—44no—
231C2×#261—44no—
232C2×#261—44no—
233C2×#261—44no—
234C2×#261—432no—
235C2×#261C2×C4⋊C4116yescomplemented
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—28no—
240C2×C4×C13—28no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—44no—
244C2×C4×C13C2×C4214yescomplemented
245C2×C4×C13C2×C22⋊C414yes—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—24no—
249C2×Dic13—28no—
250C2×Dic13—28no—
251C2×Dic13—22no—
252C2×Dic13—24no—
253C2×Dic13—44no—
254C2×Dic13C2×C4214yescomplemented
255C2×Dic13C2×C22⋊C414yes—
256C4×D13—28no—
257C4×D13—28no—
258C4×D13—24no—
259C4×D13—28no—
260C4×D13—24no—
261C4×D13—216no—
262C4×D13—216no—
263C4×D13—42no—
264C4×D13—44no—
265C4×D13—42no—
266C4×D13—48no—
267C24×C4—132no—
268C24×C4—131no—
269C24×C4—131no—
270C24×C4—132no—
271C24×C4—131no—
272C22×C4⋊C4—131no—
273C22×C4⋊C4—131no—
274C22×C4⋊C4—131no—
275C22×C4⋊C4—134no—
276C22×C4⋊C4—134no—
277C22×C4⋊C4—264no—
278C22×C4⋊C4—264no—
279C22×C4⋊C4#26111yescharacteristic, complemented
280C22×C42—134no—
281C22×C42—268no—
282C22×C42—264no—
283C2×#95—138no—
284C2×#95—1316no—
285C2×#95—138no—
286C2×#95—134no—
287C2×#95—268no—
288C2×#95—264no—
289C22×C13C4×C22⋊C414yes—
290C22×C13C4×C4⋊C418yes—
291C22×C13#38614yes—
292C22×C13#38718yes—
293C22×C13#39114yes—
294C22×C13C22×C4211yescharacteristic
295C22×C13C22×C22⋊C411yescharacteristic
296C22×C13C2×#11711yescharacteristic
297C22×C13C2×C4×D412yes—
298C22×C13C2×C4×Q812yes—
299C2×D13C4×C22⋊C414yes—
300C2×D13C4×C4⋊C418yes—
301C2×D13#385116yes—
302C2×D13#38614yes—
303C2×D13#38718yes—
304C2×D13#387116yes—
305C2×D13#388116yes—
306C2×D13#389116yes—
307C2×D13#39114yes—
308C2×D13C22×C4⋊C412yes—
309C2×D13C2×#11712yes—
310C2×D13C2×C4×D412yes—
311C2×D13C2×C4×D412yes—
312C2×D13C2×C4×D412yes—
313C2×D13C2×C4×Q812yes—
314C2×D13C2×#12011yescharacteristic
315C2×D13C2×#12112yes—
316C2×D13C2×C22⋊Q812yes—
317C2×D13C2×C22⋊Q812yes—
318C2×D13C2×#12312yes—
319C2×D13C2×#12311yescharacteristic
320C2×D13C2×#12411yescharacteristic
321C2×D13C2×#12512yes—
322C2×D13C2×#12612yes—
323C2×D13C2×C4⋊Q811yescharacteristic
324#261—216no—
325#261—48no—
326C4×C13—24no—
327C4×C13—24no—
328C4×C13—42no—
329Dic13—24no—
330Dic13—24no—
331Dic13—42no—
332C25—131no—
333C23×C4—134no—
334C23×C4—138no—
335C23×C4—138no—
336C23×C4—138no—
337C23×C4—131no—
338C23×C4—131no—
339C23×C4—138no—
340C23×C4—134no—
341C23×C4—134no—
342C23×C4—132no—
343C23×C4—132no—
344C23×C4—132no—
345C23×C4—132no—
346C23×C4—134no—
347C23×C4—138no—
348C23×C4—131no—
349C23×C4—132no—
350C23×C4—132no—
351C23×C4—262no—
352C23×C4—262no—
353C23×C4—264no—
354C23×C4—264no—
355C23×C4—264no—
356C23×C4—262no—
357C23×C4—262no—
358C23×C4—264no—
359C23×C4—264no—
360C23×C4—264no—
361C23×C4—264no—
362C23×C4—264no—
363C23×C4—264no—
364C23×C4—264no—
365C23×C4—264no—
366C23×C4—264no—
367C23×C4—264no—
368C23×C4—264no—
369C23×C4—264no—
370C23×C4C2×#26111yescharacteristic
371C23×C4C2×#26111yescharacteristic
372C23×C4C2×#26111yescharacteristic
373C2×C4⋊C4—24no—
374C2×C4⋊C4—134no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—134no—
377C2×C4⋊C4—268no—
378C2×C4⋊C4—268no—
379C2×C4⋊C4—2616no—
380C2×C4⋊C4—264no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—264no—
383C2×C4⋊C4C2×#26114yescomplemented
384C2×C42—2616no—
385C2×C42—268no—
386C2×C42—2632no—
387#95—1332no—
388#95—2616no—
389#95—268no—
390C2×C13#143618yescomplemented
391C2×C13C2×C4×C22⋊C411yescharacteristic
392C2×C13C2×C4×C4⋊C412yes—
393C2×C13C2×#38611yescharacteristic
394C2×C13C2×#38712yes—
395C2×C13C2×#39111yescharacteristic
396D13#143618yescomplemented
397D13C2×#38512yes—
398D13C2×#38712yes—
399D13C2×#38812yes—
400D13C2×#38912yes—
401C24—134no—
402C24—134no—
403C24—134no—
404C24—134no—
405C24—134no—
406C24—134no—
407C24—132no—
408C24—132no—
409C24—131no—
410C24—131no—
411C24C22×#26111yescharacteristic
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—138no—
418C22×C4—138no—
419C22×C4—1332no—
420C22×C4—138no—
421C22×C4—134no—
422C22×C4—134no—
423C22×C4—132no—
424C22×C4—132no—
425C22×C4—138no—
426C22×C4—138no—
427C22×C4—134no—
428C22×C4—134no—
429C22×C4—138no—
430C22×C4—138no—
431C22×C4—132no—
432C22×C4—264no—
433C22×C4—268no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—264no—
437C22×C4—264no—
438C22×C4—264no—
439C22×C4—264no—
440C22×C4—268no—
441C22×C4—2616no—
442C22×C4—2616no—
443C22×C4—2616no—
444C22×C4—268no—
445C22×C4—264no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—264no—
449C22×C4—264no—
450C22×C4—268no—
451C22×C4—264no—
452C22×C4—264no—
453C22×C4—2616no—
454C22×C4—2616no—
455C22×C4—2616no—
456C22×C4—2616no—
457C22×C4—264no—
458C22×C4—264no—
459C22×C4—2616no—
460C22×C4—2616no—
461C22×C4—262no—
462C22×C4—264no—
463C22×C4—262no—
464C22×C4—264no—
465C22×C4—264no—
466C22×C4—2616no—
467C22×C4—2616no—
468C22×C4—264no—
469C22×C4—264no—
470C22×C4—264no—
471C22×C4—264no—
472C22×C4—2616no—
473C22×C4—264no—
474C22×C4—262no—
475C22×C4—524no—
476C22×C4—528no—
477C22×C4—524no—
478C22×C4—528no—
479C22×C4—528no—
480C22×C4—528no—
481C22×C4—528no—
482C22×C4C4×#26114yescomplemented
483C22×C4C22⋊#26114yes—
484C22×C4C22×#26112yes—
485C22×C4C22×#26112yes—
486C22×C4C22×#26112yes—
487C4⋊C4—28no—
488C4⋊C4—268no—
489C4⋊C4—268no—
490C4⋊C4—268no—
491C42—2632no—
492C13C2×#143611yescharacteristic, complemented, Sylow
493C23—138no—
494C23—138no—
495C23—138no—
496C23—138no—
497C23—138no—
498C23—138no—
499C23—138no—
500C23—138no—
501C23—132no—
502C23—132no—
503C23—132no—
504C23—132no—
505C23—132no—
506C23—132no—
507C23—134no—
508C23—132no—
509C23—132no—
510C23—134no—
511C23—131no—
512C23—131no—
513C23—132no—
514C23—138no—
515C23—138no—
516C23—134no—
517C23—138no—
518C23—134no—
519C23—138no—
520C23—134no—
521C23—134no—
522C23C2×C4×#26112yes—
523C23#8823712yes—
524C23D4×#26114yes—
525C23Q8×#26114yes—
526C23C2×C22⋊#26112yes—
527C23C23×#26111yescharacteristic
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—28no—
532C2×C4—28no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—44no—
536C2×C4—1316no—
537C2×C4—134no—
538C2×C4—134no—
539C2×C4—264no—
540C2×C4—268no—
541C2×C4—268no—
542C2×C4—2616no—
543C2×C4—268no—
544C2×C4—264no—
545C2×C4—2616no—
546C2×C4—268no—
547C2×C4—268no—
548C2×C4—268no—
549C2×C4—268no—
550C2×C4—268no—
551C2×C4—268no—
552C2×C4—2664no—
553C2×C4—262no—
554C2×C4—264no—
555C2×C4—262no—
556C2×C4—268no—
557C2×C4—268no—
558C2×C4—268no—
559C2×C4—268no—
560C2×C4—268no—
561C2×C4—264no—
562C2×C4—262no—
563C2×C4—522no—
564C2×C4—524no—
565C2×C4—522no—
566C2×C4—528no—
567C2×C4—524no—
568C2×C4—524no—
569C2×C4—524no—
570C2×C4—524no—
571C2×C4—5232no—
572C2×C4—524no—
573C2×C4C2×C4×#26114yescomplemented
574C2×C4C2×C22⋊#26114yes—
575C22—132no—
576C22—132no—
577C22—134no—
578C22—132no—
579C22—132no—
580C22—132no—
581C22—132no—
582C22—138no—
583C22—131no—
584C22—132no—
585C22—131no—
586C22—134no—
587C22—132no—
588C22—132no—
589C22—132no—
590C22—132no—
591C22—138no—
592C22—132no—
593C22—131no—
594C22—131no—
595C22—134no—
596C22—1316no—
597C22—1316no—
598C22—1316no—
599C22—1316no—
600C22C4⋊C4×#26118yes—
601C22#1171908218yes—
602C22C4×C22⋊#26114yes—
603C22#1171915014yes—
604C22(C2×#261)⋊Q814yes—
605C22C22×C4×#26111yescharacteristic
606C22C2×#8823711yescharacteristic
607C22C2×D4×#26112yes—
608C22C2×Q8×#26112yes—
609C22C22×C22⋊#26111yescharacteristic
610C4—24no—
611C4—24no—
612C4—42no—
613C4—2616no—
614C4—264no—
615C4—264no—
616C4—528no—
617C4—522no—
618C2—132no—
619C2—132no—
620C2—138no—
621C2—132no—
622C2—132no—
623C2#1313001518yesdirect product factor
624C2C2×C4×C22⋊#26111yescharacteristic
625C2C2×C4⋊C4×#26112yes—
626C2C2×#1171915011yescharacteristic
627C2C2×#1171908212yes—
628C2C2×(C2×#261)⋊Q811yescharacteristic
subgroupG/H
centerC24C22×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC22×C13×C4⋊C4C4
socleC24×C13C22×C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#1436
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #13130015C2direct (N × H)
15. C22×C13×C4⋊C4C4semidirect
16. C22×C4⋊Dic13C4semidirect
17. C22×#6101C4semidirect
18. C22×#6101C4semidirect
21. C2×C4⋊C4×D13C4semidirect
25. C2×(C2×#261)⋊C4C4semidirect
74. C2×C13×C4⋊C4C2×C4semidirect
76. C2×C4⋊Dic13C2×C4semidirect
79. C2×#6101C2×C4semidirect
80. C2×#6101C2×C4semidirect
86. (C2×#261)⋊C4C2×C4semidirect
122. C22×#261C4⋊C4semidirect
132. C22×C4×C13C42semidirect
142. C22×Dic13C42semidirect
169. C2×C4×D13C42semidirect
235. C2×#261C2×C4⋊C4semidirect
244. C2×C4×C13C2×C42semidirect
254. C2×Dic13C2×C42semidirect
279. C22×C4⋊C4#261semidirect
383. C2×C4⋊C4C2×#261semidirect
390. C2×C13#1436semidirect
396. D13#1436semidirect
482. C22×C4C4×#261semidirect
492. C13C2×#1436semidirect
573. C2×C4C2×C4×#261semidirect
623. C2#13130015direct (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
#131300152
C22×C4⋊C4×D132
C2×#143613