Finite Group Databasebeta

← C2×#13113341 #15830060

Subgroups — C2×#13113341 #15830060

Order 3328.

1834 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2C22×#88071C211yesmaximal, characteristic, complemented
3#13113341C218yesmaximal, direct product factor
4C2×#11718059C212yesmaximal, complemented
5C2×#11718062C212yesmaximal, complemented
6C2×C13×#407C211yesmaximal, characteristic, complemented
7C24×C4×C13C2211yescharacteristic
8C24×Dic13—21no—
9C22×#6127C411yescharacteristic, complemented
10C22×C13×M16—21no—
11C2×#88207—21no—
12#11719496—22no—
13#11719496—22no—
14#11719496C414yescomplemented
15#11719496C2214yes—
16C2×#88184C411yescharacteristic, complemented
17C2×#88184C2211yescharacteristic
18C2×#88183—21no—
19C2×C4×C22⋊D13—21no—
20C2×C4×C22⋊D13—21no—
21C2×#88180C411yescharacteristic, complemented
22C2×#88178C411yescharacteristic, complemented
23C2×#88178C2211yescharacteristic
24C13×#407—22no—
25C13×#407C2214yescomplemented
26C2×C13×C22⋊C8—21no—
27C2×C13×C22⋊C8C2212yes—
28C2×#88071—22no—
29C2×#88071—21no—
30C2×#88071C2212yes—
31C2×#88071C2214yescomplemented
32#11718062C2218yescomplemented
33#11718059C2218yescomplemented
34C25×C13D411yescharacteristic
35C23×C4×C13—44no—
36C23×C4×C13C2×C411yescharacteristic
37C23×C4×C13C2×C411yescharacteristic
38C23×C4×C13C2×C412yes—
39C23×C4×C13D411yescharacteristic
40C23×C4×C13D412yes—
41C23×C4×C13D411yescharacteristic
42C23×C4×C13D411yescharacteristic
43C23×C4×C13D412yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C22×C22⋊D13—21no—
47C22×C22⋊D13—21no—
48C22×C22⋊D13—21no—
49C23×Dic13—28no—
50C23×Dic13—22no—
51C23×Dic13—24no—
52C23×Dic13—44no—
53C23×Dic13—44no—
54C2×#6127—22no—
55C2×#6127—44no—
56C2×#6127C2×C414yescomplemented
57C22×D52C2×C411yescharacteristic, complemented
58C22×C4×D13—21no—
59C22×Dic26C2×C411yescharacteristic, complemented
60C2×C13×M16—24no—
61C2×C13×M16—44no—
62C22×C8×C13—22no—
63#88207—24no—
64#88207—24no—
65C2×C22⋊Dic13—21no—
66C2×C22⋊Dic13—21no—
67C2×C22⋊Dic13—21no—
68#88184—22no—
69#88184—21no—
70#88184—21no—
71#88184C2×C414yescomplemented
72#88184C2×C412yescomplemented
73#88184C2312yes—
74#88183—24no—
75#88183—24no—
76C4×C22⋊D13—24no—
77C4×C22⋊D13—24no—
78C4×C22⋊D13—24no—
79C4×C22⋊D13—24no—
80C2×#6103—21no—
81C2×#6103—21no—
82#88180—22no—
83#88180C2×C414yescomplemented
84C2×C4⋊Dic13C2×C411yescharacteristic, complemented
85C2×C4⋊Dic13C2×C411yescharacteristic, complemented
86#88178—22no—
87#88178—21no—
88#88178—21no—
89#88178C2×C414yescomplemented
90#88178C2×C412yescomplemented
91#88178C2312yes—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C13×C22⋊C8—24no—
96C13×C22⋊C8—22no—
97C13×C22⋊C8C2314yes—
98#88071—22no—
99#88071—24no—
100#88071C2314yes—
101C2×#1504—131nomaximal, Sylow
102C24×C13—24no—
103C24×C13—24no—
104C24×C13—22no—
105C24×C13—22no—
106C24×C13C22⋊C412yes—
107C24×C13C22⋊C411yescharacteristic
108C24×C13C22⋊C411yescharacteristic
109C24×C13C2×D412yes—
110C24×C13C2×D411yescharacteristic
111C23×D13—21no—
112C22×C4×C13—24no—
113C22×C4×C13—24no—
114C22×C4×C13—42no—
115C22×C4×C13—44no—
116C22×C4×C13—42no—
117C22×C4×C13—44no—
118C22×C4×C13—42no—
119C22×C4×C13—44no—
120C22×C4×C13—42no—
121C22×C4×C13—44no—
122C22×C4×C13C22⋊C411yescharacteristic
123C22×C4×C13C22⋊C411yescharacteristic
124C22×C4×C13C22⋊C412yes—
125C22×C4×C13C22⋊C412yes—
126C22×C4×C13C22⋊C412yes—
127C22×C4×C13C22⋊C412yes—
128C22×C4×C13C22⋊C412yes—
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C22×C412yes—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2411yescharacteristic
140C2×C22⋊D13—22no—
141C2×C22⋊D13—24no—
142C2×C22⋊D13—24no—
143C2×C22⋊D13—22no—
144C2×C22⋊D13—44no—
145C2×C22⋊D13—44no—
146C2×C22⋊D13—42no—
147C2×C22⋊D13—42no—
148C22×Dic13—28no—
149C22×Dic13—216no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—24no—
154C22×Dic13—432no—
155C22×Dic13—44no—
156C22×Dic13—48no—
157C22×Dic13—48no—
158C22×Dic13—44no—
159#6127—48no—
160#6127—48no—
161C2×D52—21no—
162C2×D52—42no—
163C2×D52C22×C412yescomplemented
164C2×C4×D13—24no—
165C2×C4×D13—44no—
166C2×Dic26—21no—
167C2×Dic26—42no—
168C2×Dic26C22×C412yescomplemented
169C13×M16—48no—
170C2×C8×C13—24no—
171C2×C8×C13—44no—
172C22⋊Dic13—22no—
173C22⋊Dic13—24no—
174C22⋊Dic13—24no—
175C22⋊Dic13—22no—
176#6103—24no—
177#6103—22no—
178#6103—22no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13C22×C412yescomplemented
182C4⋊Dic13C22×C412yescomplemented
183#6101—24no—
184#6101—22no—
185#6101—22no—
186C4×Dic13—24no—
187C2×#525—131no—
188C2×#407D1311yescharacteristic, complemented
189C22×#95—131no—
190#1504—138no—
191C2×#328—132no—
192C2×#327—132no—
193C23×C13—216no—
194C23×C13—216no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—24no—
198C23×C13—22no—
199C23×C13—24no—
200C23×C13—22no—
201C23×C13—24no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—24no—
205C23×C13—22no—
206C23×C13—24no—
207C23×C13—22no—
208C23×C13#9914yes—
209C23×C13#10414yes—
210C23×C13C2×C22⋊C412yes—
211C23×C13C2×C22⋊C411yescharacteristic
212C23×C13C2×C22⋊C412yes—
213C23×C13C2×C22⋊C411yescharacteristic
214C23×C13AGL(1,ℤ/8)12yes—
215C23×C13#13712yes—
216C23×C13C22×D411yescharacteristic
217C22×D13—22no—
218C22×D13—42no—
219C22×D13—42no—
220C22×D13—42no—
221C2×C4×C13—22no—
222C2×C4×C13—24no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—22no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—41no—
233C2×C4×C13—42no—
234C2×C4×C13—41no—
235C2×C4×C13—42no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—41no—
239C2×C4×C13C2×C22⋊C412yes—
240C2×C4×C13C2×C22⋊C412yes—
241C2×C4×C13C2×C22⋊C411yescharacteristic
242C2×C4×C13C2×C22⋊C411yescharacteristic
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C22⋊D13—42no—
246C22⋊D13—42no—
247C22⋊D13—48no—
248C22⋊D13—44no—
249C22⋊D13—48no—
250C2×Dic13—28no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—432no—
255C2×Dic13—44no—
256C2×Dic13—416no—
257C2×Dic13—44no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261D52—42no—
262D52—42no—
263C4×D13—48no—
264Dic26—42no—
265Dic26—42no—
266C8×C13—44no—
267C22×#41—131no—
268C24×C4—261no—
269C24×C4C2×D1311yescharacteristic
270C22×M16—21no—
271#525—134no—
272#525—134no—
273#525—262no—
274#525—262no—
275C2×#123—261no—
276C2×C22⋊Q8—131no—
277C2×C22⋊Q8—131no—
278C2×#121—131no—
279C2×#121—131no—
280C2×#120—261no—
281C2×C4×D4—261no—
282C2×C4×D4—261no—
283C2×#117—131no—
284#407—22no—
285#407C2×D1314yescomplemented
286C2×C22⋊C8—21no—
287C2×C22⋊C8C2×D1312yes—
288C2×#95—132no—
289C2×#95—134no—
290C2×#95—261no—
291C2×#95—262no—
292#328—138no—
293#327—138no—
294C22×C13—28no—
295C22×C13—28no—
296C22×C13—216no—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—22no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13—21no—
303C22×C13—22no—
304C22×C13—21no—
305C22×C13—24no—
306C22×C13—28no—
307C22×C13—28no—
308C22×C13—24no—
309C22×C13C2×#9914yes—
310C22×C13C2×#9912yes—
311C22×C13#41712yes—
312C22×C13#41712yes—
313C22×C13C2×#10414yes—
314C22×C13C2×#10412yes—
315C22×C13C22×C22⋊C411yescharacteristic
316C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
317C22×C13C2×#13711yescharacteristic
318C2×D13—42no—
319C2×D13—42no—
320C2×D13—42no—
321C2×D13—84no—
322C4×C13—21no—
323C4×C13—21no—
324C4×C13—21no—
325C4×C13—22no—
326C4×C13—21no—
327C4×C13—22no—
328Dic13—48no—
329Dic13—42no—
330Dic13—42no—
331Dic13—42no—
332C25D5211yescharacteristic
333C2×#41—134no—
334C2×#41—262no—
335C2×#41—524no—
336C22×Q8—131no—
337C22×D4—131no—
338C22×D4—261no—
339C22×D4—261no—
340C22×D4—261no—
341C23×C4—44no—
342C23×C4—268no—
343C23×C4—264no—
344C23×C4—262no—
345C23×C4—261no—
346C23×C4—524no—
347C23×C4—524no—
348C23×C4C4×D1311yescharacteristic
349C23×C4C4×D1311yescharacteristic
350C23×C4C4×D1312yes—
351C23×C4D5211yescharacteristic
352C23×C4D5212yes—
353C23×C4C22⋊D1311yescharacteristic
354C23×C4C22⋊D1311yescharacteristic
355C23×C4C22⋊D1312yes—
356C23×C4C22×D1311yescharacteristic
357C23×C4C22×D1312yes—
358C2×M16—24no—
359C2×M16—44no—
360C22×C8—22no—
361#123—264no—
362#123—264no—
363C22⋊Q8—134no—
364C22⋊Q8—132no—
365C22⋊Q8—132no—
366C22⋊Q8—262no—
367C22⋊Q8—261no—
368C22⋊Q8—261no—
369#121—134no—
370#121—132no—
371#121—132no—
372#121—262no—
373#121—261no—
374#121—261no—
375#120—264no—
376#120—264no—
377C4×D4—264no—
378C4×D4—264no—
379C4×D4—264no—
380C4×D4—264no—
381#117—134no—
382#117—262no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C42—261no—
393C22⋊C8—24no—
394C22⋊C8—22no—
395C22⋊C8C22×D1314yes—
396#95—134no—
397#95—264no—
398#95—262no—
399C2×C13—21no—
400C2×C13—21no—
401C2×C13—24no—
402C2×C13—22no—
403C2×C13—24no—
404C2×C13#150414yescomplemented
405C2×C13C22×#9911yescharacteristic
406C2×C13C2×#41711yescharacteristic
407C2×C13C22×#10411yescharacteristic
408D13—82no—
409C24—24no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—261no—
414C24#610312yes—
415C24#610311yescharacteristic
416C24#610311yescharacteristic
417C24C2×D5212yes—
418C24C2×D5211yescharacteristic
419#41—528no—
420#41—528no—
421C2×Q8—132no—
422C2×Q8—261no—
423C2×Q8—522no—
424C2×D4—132no—
425C2×D4—262no—
426C2×D4—264no—
427C2×D4—264no—
428C2×D4—262no—
429C2×D4—261no—
430C2×D4—522no—
431C2×D4—524no—
432C2×D4—522no—
433C2×D4—522no—
434C2×D4—524no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—42no—
438C22×C4—44no—
439C22×C4—42no—
440C22×C4—44no—
441C22×C4—42no—
442C22×C4—44no—
443C22×C4—42no—
444C22×C4—44no—
445C22×C4—2616no—
446C22×C4—268no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—264no—
451C22×C4—264no—
452C22×C4—524no—
453C22×C4—5232no—
454C22×C4—528no—
455C22×C4—524no—
456C22×C4—528no—
457C22×C4—524no—
458C22×C4#610312yes—
459C22×C4#610312yes—
460C22×C4#610311yescharacteristic
461C22×C4#610311yescharacteristic
462C22×C4#610312yes—
463C22×C4#610312yes—
464C22×C4#610312yes—
465C22×C4C2×C4×D1312yes—
466C22×C4C2×C4×D1311yescharacteristic
467C22×C4C2×C4×D1311yescharacteristic
468C22×C4C2×C4×D1312yes—
469C22×C4C2×D5212yes—
470C22×C4C2×D5211yescharacteristic
471C22×C4C2×C22⋊D1312yes—
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1312yes—
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C23×D1311yescharacteristic
476M16—48no—
477C2×C8—24no—
478C2×C8—44no—
479C4⋊C4—132no—
480C4⋊C4—132no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—264no—
484C4⋊C4—262no—
485C4⋊C4—262no—
486C22⋊C4—264no—
487C22⋊C4—262no—
488C22⋊C4—264no—
489C22⋊C4—262no—
490C22⋊C4—264no—
491C22⋊C4—262no—
492C22⋊C4—262no—
493C42—264no—
494C13C2×#150411yescharacteristic, complemented, Sylow
495C23—216no—
496C23—216no—
497C23—22no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—22no—
502C23—24no—
503C23—22no—
504C23—24no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—24no—
509C23—22no—
510C23—262no—
511C23—522no—
512C23—522no—
513C23—522no—
514C23#8804614yes—
515C23#8806514yes—
516C23#8816212yes—
517C23#8816312yes—
518C23C2×#610311yescharacteristic
519C23C2×#610312yes—
520C23C2×#610312yes—
521C23C2×#610311yescharacteristic
522C23C22×D5211yescharacteristic
523Q8—522no—
524Q8—522no—
525D4—522no—
526D4—522no—
527D4—522no—
528D4—522no—
529D4—524no—
530D4—528no—
531D4—528no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—268no—
551C2×C4—262no—
552C2×C4—262no—
553C2×C4—262no—
554C2×C4—528no—
555C2×C4—5232no—
556C2×C4—524no—
557C2×C4—5216no—
558C2×C4—524no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4C2×#610312yes—
563C2×C4C2×#610311yescharacteristic
564C2×C4C2×#610312yes—
565C2×C4C2×#610311yescharacteristic
566C2×C4C22×C4×D1311yescharacteristic
567C2×C4C22×C22⋊D1311yescharacteristic
568C8—44no—
569C22—28no—
570C22—28no—
571C22—216no—
572C22—22no—
573C22—22no—
574C22—21no—
575C22—21no—
576C22—22no—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—24no—
581C22—28no—
582C22—24no—
583C22—28no—
584C22—522no—
585C22—522no—
586C22—522no—
587C22—1044no—
588C22C2×#8804614yes—
589C22C2×#8804612yes—
590C22#1171879412yes—
591C22#1171879412yes—
592C22C2×#8806514yes—
593C22C2×#8806512yes—
594C22C2×#8816211yescharacteristic
595C22C2×#8816311yescharacteristic
596C22C22×#610311yescharacteristic
597C4—21no—
598C4—22no—
599C4—21no—
600C4—22no—
601C4—21no—
602C4—21no—
603C4—528no—
604C4—522no—
605C4—522no—
606C4—522no—
607C2—21no—
608C2—21no—
609C2—22no—
610C2—24no—
611C2—24no—
612C2—1042no—
613C2#1311334114yesdirect product factor
614C2C22×#8804611yescharacteristic
615C2C2×#1171879411yescharacteristic
616C2C22×#8806511yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#407C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenterC2×#407D13
hypocenterC13C2×#1504
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×#88071C2semidirect
3. #13113341C2direct (N × H)
4. C2×#11718059C2semidirect
5. C2×#11718062C2semidirect
6. C2×C13×#407C2semidirect
9. C22×#6127C4semidirect
14. #11719496C4semidirect
16. C2×#88184C4semidirect
21. C2×#88180C4semidirect
22. C2×#88178C4semidirect
25. C13×#407C22semidirect
31. C2×#88071C22semidirect
32. #11718062C22semidirect
33. #11718059C22semidirect
56. C2×#6127C2×C4semidirect
57. C22×D52C2×C4semidirect
59. C22×Dic26C2×C4semidirect
71. #88184C2×C4semidirect
72. #88184C2×C4semidirect
83. #88180C2×C4semidirect
84. C2×C4⋊Dic13C2×C4semidirect
85. C2×C4⋊Dic13C2×C4semidirect
89. #88178C2×C4semidirect
90. #88178C2×C4semidirect
163. C2×D52C22×C4semidirect
168. C2×Dic26C22×C4semidirect
181. C4⋊Dic13C22×C4semidirect
182. C4⋊Dic13C22×C4semidirect
188. C2×#407D13semidirect
285. #407C2×D13semidirect
404. C2×C13#1504semidirect
494. C13C2×#1504semidirect
613. C2#13113341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194962
C22×#880712
#131133412
C2×#117180592
C2×#117180622
C2×C13×#4072
C2×#150413