Finite Group Databasebeta

← C2×#13120482 #16033586

Subgroups — C2×#13120482 #16033586

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120482C2116yesmaximal, direct product factor
2C2×#11718320C211yesmaximal, characteristic
3C2×#11718643C211yesmaximal, characteristic
4C2×#11718317C211yesmaximal, characteristic
5C2×#11718890C211yesmaximal, characteristic
6C2×#11718891C211yesmaximal, characteristic
7C2×#11718590C211yesmaximal, characteristic
8C2×#11718307C211yesmaximal, characteristic
9C2×#11718316C211yesmaximal, characteristic
10C2×#11718642C211yesmaximal, characteristic
11C2×#11718314C211yesmaximal, characteristic
12C2×#11718315C211yesmaximal, characteristic
13C2×#11718312C211yesmaximal, characteristic
14C2×C4×#6101C211yesmaximal, characteristic
15C2×#11718309C211yesmaximal, characteristic
16C2×C13×#391C211yesmaximal, characteristic
17C23×Q8×C13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C13×#391C2218yes—
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37#11718891C2218yes—
38#11718890C2218yes—
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718643C2218yes—
56#11718642C2218yes—
57C4×#6101C2218yes—
58#11718590C2218yes—
59#11718320C2218yes—
60#11718317C2218yes—
61#11718316C2218yes—
62#11718315C2218yes—
63#11718314C2218yes—
64#11718312C2218yes—
65#11718309C2218yes—
66#11718307C2218yes—
67C22×Q8×C13—24no—
68C22×Q8×C13—24no—
69C22×Q8×C13—42no—
70C22×Q8×C13C2314yes—
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C22×Dic26—24no—
87C22×Dic26—24no—
88C22×Dic26—42no—
89C22×Dic26C2314yes—
90C2×C13×C4⋊C4—24no—
91C2×C13×C4⋊C4C2314yes—
92C2×C42×C13—42no—
93C2×C42×C13C2314yes—
94C2×C4⋊Dic13—24no—
95C2×C4⋊Dic13—24no—
96C2×C4⋊Dic13—42no—
97C2×C4⋊Dic13C2314yes—
98C2×C4⋊Dic13C2314yes—
99C2×C4⋊Dic13C2314yes—
100C2×#6101—24no—
101C2×#6101—24no—
102C2×#6101—24no—
103C2×#6101—42no—
104C2×#6101C2314yes—
105C2×#6101C2314yes—
106C2×#6101C2314yes—
107C2×#6101C2314yes—
108C2×C4×Dic13—24no—
109C2×C4×Dic13—24no—
110C2×C4×Dic13—42no—
111C2×C4×Dic13Q818yescomplemented
112C2×C4×Dic13C2314yes—
113C2×C4×Dic13C2314yes—
114C2×C4×Dic13C2314yes—
115C2×C4×Dic13C2314yes—
116C13×#95C2314yes—
117C13×#95C2314yes—
118C13×#95C2314yes—
119C13×#95C2314yes—
120#88071C2314yes—
121#88071C2314yes—
122#88071C2314yes—
123#88071C2314yes—
124#88071C2314yes—
125#88071C2314yes—
126#88071C2314yes—
127#88071C2314yes—
128#88071C2314yes—
129#88071C2314yes—
130#88071C2314yes—
131#88071C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136C2×#2605—131nomaximal, Sylow
137C24×C13C2411yescharacteristic
138C2×Q8×C13—28no—
139C2×Q8×C13—28no—
140C2×Q8×C13—44no—
141C2×Q8×C13—416no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13C2×Q814yes—
160C22×C4×C13#4114yes—
161C22×C4×C13#4114yes—
162C22×C4×C13#4114yes—
163C22×C4×C13C2412yes—
164C22×C4×C13C2412yes—
165C22×C4×C13C2412yes—
166C22×C4×C13C2412yes—
167C22×C4×C13C2412yes—
168C22×C4×C13C2412yes—
169C22×C4×C13C2412yes—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13C2×Q814yes—
192C22×Dic13C2×Q814yes—
193C22×Dic13#4114yes—
194C22×Dic13C2412yes—
195C22×Dic13C2412yes—
196C22×Dic13C2412yes—
197C22×Dic13C2412yes—
198C22×Dic13C2412yes—
199C22×Dic13C2412yes—
200C22×Dic13C2412yes—
201C22×Dic13C2412yes—
202C2×Dic26—28no—
203C2×Dic26—28no—
204C2×Dic26—44no—
205C2×Dic26—416no—
206C13×C4⋊C4—28no—
207C42×C13—44no—
208C4⋊Dic13—28no—
209C4⋊Dic13—28no—
210C4⋊Dic13—44no—
211#6101—28no—
212#6101—28no—
213#6101—28no—
214#6101—44no—
215C4×Dic13—28no—
216C4×Dic13—28no—
217C4×Dic13—44no—
218C4×Dic13C2×Q8116yescomplemented
219#2605—1316no—
220C2×#400—131no—
221C2×#400—131no—
222C2×#395—131no—
223C2×#395—131no—
224C2×#391—131no—
225C2×#391—131no—
226C2×#391—131no—
227C2×#391D1311yescharacteristic
228C2×#387—131no—
229C2×#387—131no—
230C2×#387—131no—
231C2×#387—131no—
232C2×#383—131no—
233C2×C4×C4⋊C4—131no—
234C2×#376—131no—
235C23×C13C22×Q812yes—
236C23×C13C2×#4112yes—
237C23×C13C2×#4112yes—
238C23×C13C2×#4112yes—
239C23×C13C2×#4112yes—
240C23×C13H(5,𝔽2)12yes—
241C23×C132−1+412yes—
242C23×C13C2511yescharacteristic
243Q8×C13—416no—
244C2×C4×C13—28no—
245C2×C4×C13—28no—
246C2×C4×C13—28no—
247C2×C4×C13—28no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—44no—
266C2×C4×C13—44no—
267C2×C4×C13—44no—
268C2×C4×C13C22×Q814yes—
269C2×C4×C13C2×#4114yes—
270C2×C4×C13C2×#4114yes—
271C2×C4×C13C2×#4114yes—
272C2×Dic13—28no—
273C2×Dic13—28no—
274C2×Dic13—28no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—22no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—22no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—22no—
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—22no—
296C2×Dic13—44no—
297C2×Dic13—44no—
298C2×Dic13—44no—
299C2×Dic13—44no—
300C2×Dic13—44no—
301C2×Dic13C22×Q814yes—
302C2×Dic13C22×Q814yes—
303C2×Dic13C2×#4114yes—
304Dic26—416no—
305C23×Q8—131no—
306C23×Q8C2×D1311yescharacteristic
307C22×C4⋊C4—131no—
308C22×C4⋊C4—131no—
309C22×C4⋊C4—131no—
310C22×C4⋊C4—131no—
311C22×C4⋊C4—131no—
312C22×C4⋊C4—131no—
313C22×C4⋊C4—131no—
314C22×C4⋊C4C2×D1311yescharacteristic
315C22×C42—131no—
316C22×C42—131no—
317C22×C42—131no—
318C22×C42—131no—
319C22×C42C2×D1311yescharacteristic
320#400—138no—
321#400—138no—
322#395—138no—
323#395—138no—
324#391—138no—
325#391—138no—
326#391—138no—
327#391C2×D1318yes—
328#387—138no—
329#387—138no—
330#387—138no—
331#387—138no—
332#383—138no—
333C4×C4⋊C4—138no—
334#376—138no—
335C2×#95—131no—
336C2×#95—131no—
337C2×#95—131no—
338C2×#95—131no—
339C2×#95—131no—
340C2×#95—131no—
341C2×#95—131no—
342C2×#95—131no—
343C2×#95—131no—
344C2×#95—131no—
345C2×#95—131no—
346C2×#95—131no—
347C2×#95—131no—
348C2×#95—131no—
349C2×#95—131no—
350C2×#95—131no—
351C2×#95C2×D1311yescharacteristic
352C2×#95C2×D1311yescharacteristic
353C2×#95C2×D1311yescharacteristic
354C2×#95C2×D1311yescharacteristic
355C22×C13#53314yes—
356C22×C13#53314yes—
357C22×C13#54414yes—
358C22×C13#55114yes—
359C22×C13#55114yes—
360C22×C13#55614yes—
361C22×C13#55614yes—
362C22×C13C23×Q811yescharacteristic
363C22×C13C22×#4111yescharacteristic
364C22×C13C22×#4111yescharacteristic
365C22×C13C22×#4111yescharacteristic
366C22×C13C22×#4111yescharacteristic
367C22×C13C2×H(5,𝔽2)11yescharacteristic
368C22×C13C2×2−1+411yescharacteristic
369C4×C13—24no—
370C4×C13—24no—
371C4×C13—24no—
372C4×C13—24no—
373C4×C13—42no—
374C4×C13—42no—
375C4×C13—42no—
376Dic13—24no—
377Dic13—24no—
378Dic13—24no—
379Dic13—42no—
380Dic13—42no—
381Dic13—42no—
382Dic13—42no—
383Dic13—42no—
384C22×Q8—24no—
385C22×Q8—24no—
386C22×Q8—42no—
387C22×Q8—134no—
388C22×Q8—264no—
389C22×Q8—264no—
390C22×Q8—522no—
391C22×Q8C22×D1314yes—
392C23×C4—131no—
393C23×C4—131no—
394C23×C4—131no—
395C23×C4—131no—
396C23×C4—131no—
397C23×C4—131no—
398C23×C4—131no—
399C23×C4—131no—
400C23×C4C22×D1311yescharacteristic
401C23×C4C22×D1311yescharacteristic
402C23×C4C22×D1311yescharacteristic
403C23×C4C22×D1311yescharacteristic
404C23×C4C22×D1311yescharacteristic
405C23×C4C22×D1311yescharacteristic
406C23×C4C22×D1311yescharacteristic
407C2×C4⋊C4—24no—
408C2×C4⋊C4—134no—
409C2×C4⋊C4—134no—
410C2×C4⋊C4—134no—
411C2×C4⋊C4—134no—
412C2×C4⋊C4—134no—
413C2×C4⋊C4—134no—
414C2×C4⋊C4—134no—
415C2×C4⋊C4—264no—
416C2×C4⋊C4—264no—
417C2×C4⋊C4—264no—
418C2×C4⋊C4—264no—
419C2×C4⋊C4—264no—
420C2×C4⋊C4—522no—
421C2×C4⋊C4—522no—
422C2×C4⋊C4C22×D1314yes—
423C2×C42—42no—
424C2×C42—138no—
425C2×C42—134no—
426C2×C42—134no—
427C2×C42—134no—
428C2×C42—134no—
429C2×C42—264no—
430C2×C42—264no—
431C2×C42—522no—
432C2×C42C22×D1314yes—
433#95—134no—
434#95—134no—
435#95—134no—
436#95—134no—
437#95—134no—
438#95—134no—
439#95—134no—
440#95—134no—
441#95—134no—
442#95—134no—
443#95—134no—
444#95—134no—
445#95—134no—
446#95—134no—
447#95—134no—
448#95—134no—
449#95C22×D1314yes—
450#95C22×D1314yes—
451#95C22×D1314yes—
452#95C22×D1314yes—
453C2×C13#260518yescomplemented
454C2×C13C2×#53311yescharacteristic
455C2×C13C2×#53311yescharacteristic
456C2×C13C2×#54411yescharacteristic
457C2×C13C2×#55111yescharacteristic
458C2×C13C2×#55111yescharacteristic
459C2×C13C2×#55611yescharacteristic
460C2×C13C2×#55611yescharacteristic
461C24C23×D1311yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—44no—
465C2×Q8—416no—
466C2×Q8—268no—
467C2×Q8—268no—
468C2×Q8—524no—
469C2×Q8—5216no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—134no—
488C22×C4—134no—
489C22×C4—134no—
490C22×C4—132no—
491C22×C4—132no—
492C22×C4—132no—
493C22×C4—132no—
494C22×C4—132no—
495C22×C4—132no—
496C22×C4—132no—
497C22×C4—132no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—262no—
517C22×C4—262no—
518C22×C4—262no—
519C22×C4#612714yes—
520C22×C4#612914yes—
521C22×C4Q8×D1314yes—
522C22×C4#613114yes—
523C22×C4C23×D1312yes—
524C22×C4C23×D1312yes—
525C22×C4C23×D1312yes—
526C22×C4C23×D1312yes—
527C22×C4C23×D1312yes—
528C22×C4C23×D1312yes—
529C22×C4C23×D1312yes—
530C4⋊C4—28no—
531C4⋊C4—268no—
532C4⋊C4—268no—
533C4⋊C4—268no—
534C4⋊C4—268no—
535C4⋊C4—268no—
536C4⋊C4—524no—
537C4⋊C4—524no—
538C42—44no—
539C42—1316no—
540C42—268no—
541C42—268no—
542C42—524no—
543C13C2×#260511yescharacteristic, complemented, Sylow
544C23C2×#612712yes—
545C23C2×#612912yes—
546C23#8825112yes—
547C23C2×Q8×D1312yes—
548C23C2×#613112yes—
549C23#41×D1312yes—
550C23#8825712yes—
551C23C24×D1311yescharacteristic
552Q8—416no—
553Q8—5216no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—28no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—134no—
579C2×C4—134no—
580C2×C4—134no—
581C2×C4—268no—
582C2×C4—268no—
583C2×C4—268no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—262no—
588C2×C4—262no—
589C2×C4—262no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—524no—
606C2×C4—524no—
607C2×C4—524no—
608C2×C4—524no—
609C2×C4—524no—
610C2×C4C2×#612714yes—
611C2×C4C2×#612914yes—
612C2×C4C2×Q8×D1314yes—
613C2×C4C2×#613114yes—
614C22#1171920014yes—
615C22#1171928314yes—
616C22#1171928914yes—
617C22#1171932814yes—
618C22#1171934214yes—
619C22#1171937614yes—
620C22#1171943314yes—
621C22C22×#612711yescharacteristic
622C22C22×#612911yescharacteristic
623C22C2×#8825111yescharacteristic
624C22C22×Q8×D1311yescharacteristic
625C22C22×#613111yescharacteristic
626C22C2×#41×D1311yescharacteristic
627C22C2×#8825711yescharacteristic
628C4—24no—
629C4—24no—
630C4—24no—
631C4—24no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—264no—
636C4—264no—
637C4—264no—
638C4—522no—
639C4—522no—
640C4—522no—
641C4—522no—
642C4—522no—
643C2#1312048218yesdirect product factor
644C2C2×#1171928311yescharacteristic
645C2C2×#1171943311yescharacteristic
646C2C2×#1171932811yescharacteristic
647C2C2×#1171920011yescharacteristic
648C2C2×#1171934211yescharacteristic
649C2C2×#1171937611yescharacteristic
650C2C2×#1171928911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#391C2
socle, prime radicalC24×C13C24
hypercenterC2×#391D13
hypocenterC13C2×#2605
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. #13120482C2direct (N × H)
111. C2×C4×Dic13Q8semidirect
218. C4×Dic13C2×Q8semidirect
453. C2×C13#2605semidirect
543. C13C2×#2605semidirect
643. C2#13120482direct (N × H)

Maximal subgroups

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

subgroupindex
#131204822
C2×#117183202
C2×#117186432
C2×#117183172
C2×#117188902
C2×#117188912
C2×#117185902
C2×#117183072
C2×#117183162
C2×#117186422
C2×#117183142
C2×#117183152
C2×#117183122
C2×C4×#61012
C2×#117183092
C2×C13×#3912
C2×#260513