Finite Group Databasebeta

← C2×#13124649 #16730448

Subgroups — C2×#13124649 #16730448

Order 3328.

2358 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic, complemented
2C2×#11719227C211yesmaximal, characteristic
3#13124649C2116yesmaximal, direct product factor
4C2×#11718536C212yesmaximal, complemented
5C2×#11718515C212yesmaximal, complemented
6C2×#11718531C212yesmaximal, complemented
7C2×#11718551C212yesmaximal, complemented
8C2×#11718656C211yesmaximal, characteristic, complemented
9C2×#11718779C211yesmaximal, characteristic, complemented
10C2×#11718794C211yesmaximal, characteristic
11C2×#11718627C211yesmaximal, characteristic
12C2×C13×#428C211yesmaximal, characteristic, complemented
13C22×#6127C2211yescharacteristic
14C23×Dic26—21no—
15C22×C13×M16C2211yescharacteristic
16C2×C13×#117C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101—21no—
20C22×C4×Dic13C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22#11719227—24no—
23#11719227C2218yes—
24C2×#88147C2211yescharacteristic
25C2×#88147C2211yescharacteristic
26C2×#88142—24no—
27C2×#88142—21no—
28C2×#88142—21no—
29C2×#88142C2212yes—
30C2×#88142C2212yes—
31C2×#88142C2218yescomplemented
32C2×#88141C2211yescharacteristic
33C2×#88141C2211yescharacteristic
34C2×#88135—21no—
35C2×#88135—21no—
36C2×#88126—21no—
37C2×C42×D13—21no—
38C13×#428C2218yescomplemented
39C2×C13×#107C2212yes—
40C2×C13×#106C2212yes—
41#11718794C2218yes—
42#11718779C2218yescomplemented
43C2×#88061C2212yes—
44C2×#88056C2212yes—
45C2×#88054C2212yes—
46C2×#88054C2212yes—
47#11718656C2218yescomplemented
48C2×#88050C2212yes—
49#11718627C2218yes—
50C2×#88049C2212yes—
51C2×#88048C2212yes—
52C2×#88047C2212yes—
53#11718551C22116yescomplemented
54#11718536C22116yescomplemented
55#11718531C22116yescomplemented
56#11718515C22116yescomplemented
57C23×C4×C13—21no—
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13—21no—
60C23×Dic13—21no—
61C23×Dic13D411yescharacteristic
62C23×Dic13D411yescharacteristic
63C2×#6127—22no—
64C2×#6127—24no—
65C2×#6127Q818yescomplemented
66C2×#6127C2314yes—
67C22×D52C2311yescharacteristic
68C22×C4×D13—21no—
69C22×C4×D13—21no—
70C22×C4×D13—21no—
71C22×Dic26—22no—
72C22×Dic26—22no—
73C22×Dic26—28no—
74C22×Dic26—48no—
75C22×Dic26C2311yescharacteristic
76C2×C13×M16—24no—
77C2×C13×M16C2314yes—
78C22×C8×C13C2312yes—
79C13×#117—22no—
80C13×#117C2314yes—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2312yes—
86C2×C13×C4⋊C4C2314yes—
87C2×C13×C22⋊C4—21no—
88C2×C42×C13—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13C2314yes—
94C2×C4⋊Dic13C2312yes—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—28no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13D411yescharacteristic
103C2×C4×Dic13D411yescharacteristic
104C2×C4×Dic13D414yes—
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2314yes—
108C2×#6099—24no—
109C2×#6099C2314yes—
110C22×#1055C2312yes—
111#88147—22no—
112#88147—22no—
113#88147C2314yes—
114#88147C2314yes—
115#88142—24no—
116#88142—24no—
117#88142—28no—
118#88142—28no—
119#88142C2318yes—
120#88142C2318yes—
121#88141—22no—
122#88141—22no—
123#88141C2314yes—
124#88141C2314yes—
125#88135—28no—
126#88135—28no—
127#88126—28no—
128C42×D13—28no—
129C13×#107C2318yes—
130C13×#106C2318yes—
131#88061C2318yes—
132#88056C2318yes—
133#88054C2318yes—
134#88054C2318yes—
135#88050C2318yes—
136#88049C2318yes—
137#88048C2318yes—
138#88047C2318yes—
139C2×#3079—131nomaximal, Sylow
140C24×C13C2×D411yescharacteristic
141C23×D13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—24no—
145C22×C4×C13—22no—
146C22×C4×C13—44no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×Q814yes—
150C22×C4×C13#4114yes—
151C22×C4×C13C2411yescharacteristic
152C22×C4×C13C2412yes—
153C2×C22⋊D13—28no—
154C2×C22⋊D13—24no—
155C22×Dic13—21no—
156C22×Dic13—24no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—22no—
160C22×Dic13—44no—
161C22×Dic13C2×D414yes—
162C22×Dic13C2×D414yes—
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165C22×Dic13C2×D411yescharacteristic
166C22×Dic13C2×D411yescharacteristic
167#6127—216no—
168#6127—28no—
169#6127C2×Q8116yescomplemented
170C2×D52—21no—
171C2×D52—22no—
172C2×D52C2×Q814yescomplemented
173C2×D52C2412yes—
174C2×C4×D13—28no—
175C2×C4×D13—24no—
176C2×C4×D13—24no—
177C2×C4×D13—24no—
178C2×C4×D13—44no—
179C2×C4×D13—44no—
180C2×Dic26—21no—
181C2×Dic26—22no—
182C2×Dic26—28no—
183C2×Dic26—28no—
184C2×Dic26—48no—
185C2×Dic26—432no—
186C2×Dic26—48no—
187C2×Dic26C2×Q814yescomplemented
188C2×Dic26C2412yes—
189C13×M16—28no—
190C2×C8×C13—24no—
191C2×C8×C13C2414yes—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—24no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4C2412yes—
197C13×C4⋊C4C2414yes—
198C13×C4⋊C4C2412yes—
199C13×C22⋊C4—24no—
200C42×C13—24no—
201#6103—24no—
202#6103—24no—
203C4⋊Dic13—24no—
204C4⋊Dic13—22no—
205C4⋊Dic13C2414yes—
206#6101—24no—
207#6101—24no—
208#6101—28no—
209#6101—28no—
210C4×Dic13—24no—
211C4×Dic13—24no—
212C4×Dic13C2×D414yes—
213C4×Dic13C2×D414yes—
214C4×Dic13C2×D412yes—
215C4×Dic13C2×D412yes—
216C4×Dic13C2412yes—
217C4×Dic13C2412yes—
218#6099—28no—
219C2×#1055—24no—
220C2×#1055C2414yes—
221C22×C4⋊Q8—131no—
222C2×C4×#41—131no—
223#3079—1316no—
224C2×#477—132no—
225C2×#475—132no—
226C2×#476—132no—
227C2×#474—132no—
228C2×#428—131no—
229C2×#428D1311yescharacteristic, complemented
230C2×#423—131no—
231C2×#417—131no—
232C2×#417—131no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13C22⋊Q814yes—
236C23×C13C22×D412yes—
237C23×C13C22×D411yescharacteristic
238C22×D13—24no—
239C22×D13—22no—
240C22×D13—42no—
241C22×D13—42no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—24no—
245C2×C4×C13—48no—
246C2×C4×C13—44no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13C22⋊Q814yes—
250C2×C4×C13C22⋊Q818yes—
251C2×C4×C13C22×D412yes—
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C22×Q812yes—
254C2×C4×C13C22×Q814yes—
255C2×C4×C13C2×#4112yes—
256C2×C4×C13C2×#4114yes—
257C2×C4×C13C2511yescharacteristic
258C22⋊D13—216no—
259C2×Dic13—24no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—28no—
264C2×Dic13—28no—
265C2×Dic13—24no—
266C2×Dic13—48no—
267C2×Dic13—44no—
268C2×Dic13AGL(1,ℤ/8)14yes—
269C2×Dic13#13714yes—
270C2×Dic13C22×D412yes—
271C2×Dic13C22×D412yes—
272C2×Dic13C22×D412yes—
273C2×Dic13C22×D412yes—
274D52—24no—
275D52—22no—
276D52C22×Q814yescomplemented
277C4×D13—216no—
278C4×D13—48no—
279C4×D13—48no—
280Dic26—24no—
281Dic26—22no—
282Dic26—416no—
283Dic26—416no—
284Dic26C22×Q814yescomplemented
285C8×C13—24no—
286#1055—24no—
287C22×#41—131no—
288C23×Q8—261no—
289C22×M16—131no—
290C22×M16C2×D1311yescharacteristic
291C2×C4⋊Q8—132no—
292C2×C4⋊Q8—132no—
293C2×C4⋊Q8—138no—
294C2×C4⋊Q8—261no—
295C2×C4⋊Q8—264no—
296C2×C4⋊Q8—261no—
297C4×#41—138no—
298C4×#41—264no—
299C2×C4×Q8—131no—
300C2×C4×Q8—131no—
301C2×C4×D4—131no—
302C2×C4×D4—131no—
303C2×C4×D4—261no—
304C2×C4×D4—261no—
305C2×#117—261no—
306C2×#117C2×D1311yescharacteristic
307C22×C4⋊C4—131no—
308C22×C4⋊C4—261no—
309C22×C4⋊C4C2×D1311yescharacteristic
310C22×C42—131no—
311C22×C42—261no—
312#477—1316no—
313#476—1316no—
314#475—1316no—
315#474—1316no—
316#428—138no—
317#428C2×D1318yescomplemented
318C2×#107—132no—
319C2×#107C2×D1312yes—
320C2×#106—132no—
321C2×#106C2×D1312yes—
322#423—138no—
323C2×C4⋊C8—132no—
324C2×C4⋊C8—132no—
325#417—138no—
326#417—138no—
327C2×#103—132no—
328C2×#103—132no—
329C2×#102—132no—
330C2×#102—132no—
331C22×C13—28no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13C2×C22⋊Q814yes—
335C22×C13C2×C22⋊Q812yes—
336C22×C13C2×AGL(1,ℤ/8)12yes—
337C22×C13C2×#13712yes—
338C22×C13C23×D411yescharacteristic
339C2×D13—24no—
340C2×D13—48no—
341C2×D13—42no—
342C2×D13—42no—
343C4×C13—44no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13C2×C22⋊Q812yes—
347C4×C13C2×C22⋊Q814yes—
348C4×C13C23×Q811yescharacteristic
349C4×C13C22×#4111yescharacteristic
350Dic13—24no—
351Dic13—22no—
352Dic13—22no—
353Dic13—44no—
354Dic13C2×AGL(1,ℤ/8)14yes—
355Dic13C2×#13714yes—
356C2×#41—138no—
357C2×#41—134no—
358C2×#41—264no—
359C2×#41—262no—
360C22×Q8—131no—
361C22×Q8—268no—
362C22×Q8—262no—
363C22×Q8—262no—
364C22×Q8—528no—
365C22×D4—131no—
366C22×D4—261no—
367C23×C4—21no—
368C23×C4—131no—
369C23×C4—131no—
370C23×C4—261no—
371C23×C4—261no—
372C23×C4—261no—
373C23×C4—261no—
374C23×C4C22×D1311yescharacteristic
375C2×M16—24no—
376C2×M16—134no—
377C2×M16—264no—
378C2×M16C22×D1314yes—
379C22×C8—132no—
380C22×C8C22×D1312yes—
381C4⋊Q8—138no—
382C4⋊Q8—138no—
383C4⋊Q8—268no—
384C4⋊Q8—268no—
385C4⋊Q8—264no—
386C4⋊Q8—264no—
387C4×Q8—134no—
388C4×Q8—134no—
389C4×Q8—262no—
390C4×Q8—262no—
391C4×D4—134no—
392C4×D4—134no—
393C4×D4—262no—
394C4×D4—262no—
395C4×D4—268no—
396C4×D4—268no—
397#117—22no—
398#117—268no—
399#117C22×D1314yes—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—132no—
403C2×C4⋊C4—134no—
404C2×C4⋊C4—268no—
405C2×C4⋊C4—262no—
406C2×C4⋊C4—262no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—262no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4C22×D1312yes—
412C2×C4⋊C4C22×D1314yes—
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—261no—
417C2×C22⋊C4—261no—
418C2×C42—21no—
419C2×C42—131no—
420C2×C42—134no—
421C2×C42—131no—
422C2×C42—131no—
423C2×C42—131no—
424C2×C42—134no—
425C2×C42—268no—
426C2×C42—261no—
427C2×C42—261no—
428#107—138no—
429#107C22×D1318yes—
430#106—138no—
431#106C22×D1318yes—
432C4⋊C8—138no—
433C4⋊C8—138no—
434#103—138no—
435#103—138no—
436#102—138no—
437#102—138no—
438C2×C13—24no—
439C2×C13#307914yescomplemented
440C2×C13C22×C22⋊Q811yescharacteristic
441C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
442C2×C13C22×#13711yescharacteristic
443D13—44no—
444C24—261no—
445C24D4×D1311yescharacteristic
446#41—1316no—
447#41—2616no—
448#41—268no—
449C2×Q8—134no—
450C2×Q8—132no—
451C2×Q8—268no—
452C2×Q8—268no—
453C2×Q8—262no—
454C2×Q8—261no—
455C2×Q8—528no—
456C2×Q8—5232no—
457C2×Q8—528no—
458C2×D4—134no—
459C2×D4—132no—
460C2×D4—268no—
461C2×D4—264no—
462C2×D4—262no—
463C2×D4—261no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—44no—
469C22×C4—131no—
470C22×C4—131no—
471C22×C4—134no—
472C22×C4—134no—
473C22×C4—131no—
474C22×C4—131no—
475C22×C4—264no—
476C22×C4—264no—
477C22×C4—264no—
478C22×C4—264no—
479C22×C4—261no—
480C22×C4—268no—
481C22×C4—264no—
482C22×C4—264no—
483C22×C4—262no—
484C22×C4—524no—
485C22×C4—524no—
486C22×C4—524no—
487C22×C4#612714yes—
488C22×C4D4×D1312yes—
489C22×C4D4×D1311yescharacteristic
490C22×C4Q8×D1314yes—
491C22×C4C23×D1312yes—
492C22×C4C23×D1311yescharacteristic
493M16—28no—
494M16—268no—
495C2×C8—24no—
496C2×C8—134no—
497C2×C8—264no—
498C2×C8C23×D1314yes—
499C4⋊C4—24no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—134no—
504C4⋊C4—268no—
505C4⋊C4—268no—
506C4⋊C4—264no—
507C4⋊C4—264no—
508C4⋊C4—264no—
509C4⋊C4—262no—
510C4⋊C4C23×D1314yes—
511C4⋊C4C23×D1312yes—
512C4⋊C4C23×D1312yes—
513C22⋊C4—24no—
514C22⋊C4—264no—
515C22⋊C4—264no—
516C42—24no—
517C42—134no—
518C42—134no—
519C42—132no—
520C42—132no—
521C42—132no—
522C42—132no—
523C42—264no—
524C42—264no—
525C13C2×#307911yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—264no—
529C23—262no—
530C23—522no—
531C23—522no—
532C23#8815014yes—
533C23C2×D4×D1312yes—
534C23C2×D4×D1311yescharacteristic
535Q8—134no—
536Q8—264no—
537Q8—262no—
538Q8—5216no—
539Q8—5216no—
540D4—134no—
541D4—2616no—
542D4—264no—
543D4—262no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—48no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—134no—
552C2×C4—134no—
553C2×C4—132no—
554C2×C4—132no—
555C2×C4—132no—
556C2×C4—132no—
557C2×C4—268no—
558C2×C4—268no—
559C2×C4—264no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—2616no—
564C2×C4—264no—
565C2×C4—528no—
566C2×C4—528no—
567C2×C4—528no—
568C2×C4—524no—
569C2×C4#8815014yes—
570C2×C4#8815018yes—
571C2×C4C2×#612712yes—
572C2×C4C2×#612714yes—
573C2×C4C2×D4×D1312yes—
574C2×C4C2×D4×D1311yescharacteristic
575C2×C4C2×Q8×D1312yes—
576C2×C4C2×Q8×D1314yes—
577C2×C4C24×D1311yescharacteristic
578C8—24no—
579C8—264no—
580C22—28no—
581C22—22no—
582C22—22no—
583C22—264no—
584C22—528no—
585C22—522no—
586C22—522no—
587C22C2×#8815014yes—
588C22C2×#8815012yes—
589C22D13×AGL(1,ℤ/8)12yes—
590C22D13×#13712yes—
591C22C22×D4×D1311yescharacteristic
592C4—44no—
593C4—42no—
594C4—42no—
595C4—134no—
596C4—134no—
597C4—262no—
598C4—262no—
599C4—264no—
600C4—524no—
601C4C2×#8815014yes—
602C4C2×#8815012yes—
603C4C22×#612711yescharacteristic
604C4C22×Q8×D1311yescharacteristic
605C2—24no—
606C2—524no—
607C2#1312464914yesdirect product factor
608C2C22×#8815011yescharacteristic
609C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
610C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#428C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
hypercenterC2×#428D13
hypocenterC13C2×#3079
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C22×#88142C2semidirect
3. #13124649C2direct (N × H)
4. C2×#11718536C2semidirect
5. C2×#11718515C2semidirect
6. C2×#11718531C2semidirect
7. C2×#11718551C2semidirect
8. C2×#11718656C2semidirect
9. C2×#11718779C2semidirect
12. C2×C13×#428C2semidirect
31. C2×#88142C22semidirect
38. C13×#428C22semidirect
42. #11718779C22semidirect
47. #11718656C22semidirect
53. #11718551C22semidirect
54. #11718536C22semidirect
55. #11718531C22semidirect
56. #11718515C22semidirect
65. C2×#6127Q8semidirect
169. #6127C2×Q8semidirect
172. C2×D52C2×Q8semidirect
187. C2×Dic26C2×Q8semidirect
229. C2×#428D13semidirect
276. D52C22×Q8semidirect
284. Dic26C22×Q8semidirect
317. #428C2×D13semidirect
439. C2×C13#3079semidirect
525. C13C2×#3079semidirect
607. C2#13124649direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881422
C2×#117192272
#131246492
C2×#117185362
C2×#117185152
C2×#117185312
C2×#117185512
C2×#117186562
C2×#117187792
C2×#117187942
C2×#117186272
C2×C13×#4282
C2×#307913