Finite Group Databasebeta

← C2×#13125956 #16734931

Subgroups — C2×#13125956 #16734931

Order 3328.

2286 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719253C211yesmaximal, characteristic
2C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
3#13125956C2116yesmaximal, direct product factor
4C2×#11718535C212yesmaximal, complemented
5C2×#11718421C212yesmaximal, complemented
6C2×#11718543C212yesmaximal, complemented
7C2×#11718435C212yesmaximal, complemented
8C2×#11718507C211yesmaximal, characteristic, complemented
9C2×#11718668C211yesmaximal, characteristic, complemented
10C2×#11718748C211yesmaximal, characteristic, complemented
11C2×#11718494C211yesmaximal, characteristic, complemented
12C2×C13×#474C211yesmaximal, characteristic, complemented
13C22×Q8×D13—21no—
14C22×#6127—21no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×#88198—21no—
18C2×#88194C2211yescharacteristic
19C2×#88192C2211yescharacteristic
20C2×C4×C22⋊D13—21no—
21D13×C4⋊Q8—24no—
22D13×C4⋊Q8C2218yescomplemented
23#11719253—24no—
24#11719253C2218yes—
25C2×#88149C2211yescharacteristic
26C2×C4⋊C4×D13—21no—
27C2×C4⋊C4×D13C2212yes—
28C2×#88142—21no—
29C2×#88142C2212yes—
30C2×#88142C2211yescharacteristic
31C2×#88139—21no—
32C2×#88138—21no—
33C2×C4×D52C2211yescharacteristic
34C2×C42×D13C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C13×#474C2218yescomplemented
37C2×C13×#107C2212yes—
38C2×C13×C4⋊C8C2211yescharacteristic
39C2×C13×#102C2212yes—
40C2×#88072C2212yes—
41C2×#88061C2212yes—
42C2×#88060C2212yes—
43C2×#88058C2212yes—
44C2×C8×Dic13C2212yes—
45#11718748C2218yescomplemented
46#11718668C2218yescomplemented
47C2×#88049C2212yes—
48C2×#88047C2212yes—
49C2×#88047C2212yes—
50C2×C4⋊#1055C2211yescharacteristic
51#11718543C22116yescomplemented
52#11718535C22116yescomplemented
53#11718507C2218yescomplemented
54#11718494C2218yescomplemented
55#11718435C22116yescomplemented
56#11718421C22116yescomplemented
57C22×Q8×C13—21no—
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C22×C22⋊D13—21no—
61C22×C22⋊D13—21no—
62C22×C22⋊D13—21no—
63C2×Q8×D13—28no—
64C2×Q8×D13—48no—
65C2×#6127—28no—
66C2×#6127—48no—
67C22×D52—21no—
68C22×D52C2311yescharacteristic
69C22×C4×D13—22no—
70C22×C4×D13—21no—
71C22×C4×D13D411yescharacteristic
72C22×C4×D13D411yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C22×Dic26—21no—
75C22×Dic26—21no—
76C22×Dic26—22no—
77C22×C8×C13C2312yes—
78C13×C4⋊Q8—22no—
79C13×C4⋊Q8C2314yes—
80C4×D4×C13—22no—
81C4×D4×C13C2314yes—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4C2312yes—
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88#88198—28no—
89#88194—22no—
90#88194C2314yes—
91#88192—22no—
92#88192C2314yes—
93C4×C22⋊D13—28no—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13C2312yes—
98C2×C4⋊Dic13C2311yescharacteristic
99C2×#6101—21no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×C4×Dic13D411yescharacteristic
103C2×C4×Dic13D411yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C22×#1055C2312yes—
106#88149—22no—
107#88149C2314yes—
108C4⋊C4×D13—24no—
109C4⋊C4×D13—28no—
110C4⋊C4×D13C2318yes—
111#88142—24no—
112#88142—28no—
113#88142—22no—
114#88142C2318yes—
115#88142C2314yes—
116#88139—28no—
117#88138—28no—
118C4×D52—22no—
119C4×D52C2314yes—
120C42×D13D414yes—
121C42×D13C2314yes—
122#88123—22no—
123#88123C2314yes—
124C13×#107C2318yes—
125C13×C4⋊C8C2314yes—
126C13×#102C2318yes—
127#88072C2318yes—
128#88061C2318yes—
129#88060C2318yes—
130#88058C2318yes—
131C8×Dic13C2318yes—
132#88049C2318yes—
133#88047C2318yes—
134#88047C2318yes—
135C4⋊#1055C2314yes—
136C2×#3226—131nomaximal, Sylow
137C24×C13—21no—
138C23×D13—21no—
139C23×D13C2×D411yescharacteristic
140C2×Q8×C13—24no—
141C2×Q8×C13—44no—
142C2×D4×C13—21no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13C2412yes—
146C22×C4×C13—22no—
147C22×C4×C13—21no—
148C22×C4×C13—24no—
149C22×C4×C13—44no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C2×C22⋊D13—24no—
154C2×C22⋊D13—24no—
155C2×C22⋊D13—24no—
156C2×C22⋊D13—44no—
157C2×C22⋊D13—44no—
158C2×C22⋊D13—44no—
159C22×Dic13—22no—
160C22×Dic13—21no—
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164Q8×D13—432no—
165#6127—432no—
166C2×D52—22no—
167C2×D52—22no—
168C2×D52—24no—
169C2×D52—21no—
170C2×D52—44no—
171C2×D52C2412yes—
172C2×C4×D13—22no—
173C2×C4×D13—22no—
174C2×C4×D13—24no—
175C2×C4×D13—28no—
176C2×C4×D13—24no—
177C2×C4×D13—48no—
178C2×C4×D13—44no—
179C2×C4×D13D818yes—
180C2×C4×D13C2×D412yes—
181C2×C4×D13C2×D414yes—
182C2×C4×D13C2×D414yes—
183C2×C4×D13C2412yes—
184C2×Dic26—24no—
185C2×Dic26—24no—
186C2×Dic26—28no—
187C2×Dic26—44no—
188C2×Dic26—44no—
189C2×Dic26—48no—
190C2×C8×C13—24no—
191C2×C8×C13C2414yes—
192C13×C4⋊C4—24no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4C2414yes—
196C13×C4⋊C4C2412yes—
197C13×C22⋊C4—24no—
198C42×C13C2×D412yes—
199C42×C13C2412yes—
200C22⋊Dic13—24no—
201#6103—24no—
202#6103—24no—
203C4⋊Dic13—22no—
204C4⋊Dic13—24no—
205C4⋊Dic13—21no—
206C4⋊Dic13C2414yes—
207C4⋊Dic13C2412yes—
208#6101—24no—
209#6101—28no—
210#6101—28no—
211C4×Dic13C2×D412yes—
212C4×Dic13C2×D414yes—
213C4×Dic13C2×D414yes—
214C4×Dic13C2412yes—
215C2×#1055—24no—
216C2×#1055C2414yes—
217C2×#532—131no—
218C22×C4⋊Q8—131no—
219#3226—1316no—
220C2×#500—132no—
221C2×#486—132no—
222C2×#480—132no—
223C2×#480—132no—
224C2×#474—131no—
225C2×#474—131no—
226C2×#474—131no—
227C2×#474D1311yescharacteristic, complemented
228C2×#431—131no—
229C23×C13—22no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13—42no—
233C23×C13C22×D411yescharacteristic
234C22×D13—22no—
235C22×D13—22no—
236C22×D13—22no—
237C22×D13—42no—
238C22×D13—42no—
239C22×D13—42no—
240C22×D13C2×D814yes—
241C22×D13C22×D412yes—
242Q8×C13—48no—
243D4×C13—22no—
244D4×C13—22no—
245D4×C13—42no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—44no—
250C2×C4×C13—42no—
251C2×C4×C13—48no—
252C2×C4×C13C2×D814yes—
253C2×C4×C13C22×D412yes—
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D412yes—
256C2×C4×C132−1+412yes—
257C2×C4×C132−1+412yes—
258C2×C4×C13C2511yescharacteristic
259C22⋊D13—48no—
260C22⋊D13—48no—
261C22⋊D13—48no—
262C2×Dic13—22no—
263C2×Dic13—24no—
264C2×Dic13—22no—
265C2×Dic13—44no—
266C2×Dic13—42no—
267C2×Dic13C2×D814yes—
268C2×Dic13#13714yes—
269C2×Dic13C22×D412yes—
270C2×Dic13C22×D412yes—
271C2×Dic13C22×D412yes—
272D52—22no—
273D52—22no—
274D52—48no—
275D52—42no—
276C4×D13—24no—
277C4×D13—22no—
278C4×D13—22no—
279C4×D13—28no—
280C4×D13—416no—
281C4×D13—48no—
282C4×D13C2×D8116yes—
283Dic26—48no—
284Dic26—48no—
285Dic26—416no—
286C8×C13—24no—
287#1055—24no—
288C22×#41—261no—
289C23×Q8—261no—
290#532—138no—
291#532—264no—
292C2×C4⋊Q8—138no—
293C2×C4⋊Q8—132no—
294C2×C4⋊Q8—131no—
295C2×C4⋊Q8—131no—
296C2×C4⋊Q8—261no—
297C2×C4⋊Q8—264no—
298C2×C4⋊Q8—261no—
299C2×C4⋊Q8C2×D1311yescharacteristic
300C2×#127—131no—
301C2×#124—261no—
302C2×#121—131no—
303C2×#121—131no—
304C2×#121—261no—
305C2×C4×D4—131no—
306C2×C4×D4—261no—
307C2×C4×D4C2×D1311yescharacteristic
308C22×C4⋊C4—132no—
309C22×C4⋊C4—261no—
310C22×C42—131no—
311#500—1316no—
312#486—1316no—
313#480—1316no—
314#480—1316no—
315#474—138no—
316#474—138no—
317#474—138no—
318#474C2×D1318yescomplemented
319#431—138no—
320C2×#107—132no—
321C2×#107—132no—
322C2×#107—132no—
323C2×#107C2×D1312yes—
324C2×C4⋊C8—131no—
325C2×C4⋊C8C2×D1311yescharacteristic
326C2×#102—132no—
327C2×#102—132no—
328C2×#102—132no—
329C2×#102C2×D1312yes—
330C2×C22⋊C8—132no—
331C2×C4×C8—132no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—42no—
335C22×C13—84no—
336C22×C13#53612yes—
337C22×C13C22×D812yes—
338C22×C13C2×#13712yes—
339C22×C13C23×D411yescharacteristic
340C2×D13—22no—
341C2×D13—28no—
342C2×D13—22no—
343C2×D13—42no—
344C2×D13—42no—
345C2×D13—42no—
346C2×D13—84no—
347C2×D13C22×D814yes—
348C4×C13—22no—
349C4×C13—44no—
350C4×C13—42no—
351C4×C13#53612yes—
352C4×C13C22×D814yes—
353C4×C13C2×2−1+411yescharacteristic
354C4×C13C2×2−1+411yescharacteristic
355Dic13—22no—
356Dic13—44no—
357Dic13—42no—
358Dic13C22×D814yes—
359Dic13C2×#13714yes—
360C2×#41—268no—
361C2×#41—528no—
362C22×Q8—21no—
363C22×Q8—261no—
364C22×Q8—262no—
365C22×Q8—268no—
366C22×Q8—261no—
367C22×Q8—528no—
368C22×D4—131no—
369C22×D4—261no—
370C22×D4—261no—
371C22×D4—261no—
372C22×D4—261no—
373C22×D4C22×D1311yescharacteristic
374C23×C4—21no—
375C23×C4—131no—
376C23×C4—131no—
377C23×C4—131no—
378C23×C4—262no—
379C23×C4—261no—
380C22×C8—132no—
381C22×C8C22×D1312yes—
382C4⋊Q8—22no—
383C4⋊Q8—138no—
384C4⋊Q8—134no—
385C4⋊Q8—134no—
386C4⋊Q8—268no—
387C4⋊Q8—264no—
388C4⋊Q8—262no—
389C4⋊Q8—268no—
390C4⋊Q8—262no—
391C4⋊Q8C22×D1314yes—
392#127—134no—
393#127—262no—
394#124—268no—
395#121—134no—
396#121—134no—
397#121—268no—
398#121—262no—
399#121—262no—
400C4×D4—22no—
401C4×D4—134no—
402C4×D4—268no—
403C4×D4—262no—
404C4×D4C22×D1314yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—132no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—138no—
409C2×C4⋊C4—264no—
410C2×C4⋊C4—268no—
411C2×C4⋊C4—262no—
412C2×C4⋊C4—262no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4C22×D1312yes—
416C2×C4⋊C4C22×D1311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—261no—
419C2×C22⋊C4—261no—
420C2×C22⋊C4—261no—
421C2×C42—131no—
422C2×C42—131no—
423C2×C42—131no—
424C2×C42—134no—
425C2×C42—134no—
426C2×C42C22×D1311yescharacteristic
427#107—138no—
428#107—138no—
429#107—138no—
430#107C22×D1318yes—
431C4⋊C8—134no—
432C4⋊C8C22×D1314yes—
433#102—138no—
434#102—138no—
435#102—138no—
436#102C22×D1318yes—
437C22⋊C8—138no—
438C4×C8—138no—
439C2×C13—82no—
440C2×C13#322614yescomplemented
441C2×C13C2×#53611yescharacteristic
442C2×C13C23×D811yescharacteristic
443C2×C13C22×#13711yescharacteristic
444D13—24no—
445D13—82no—
446C24—21no—
447C24—131no—
448C24—261no—
449#41—5232no—
450C2×Q8—24no—
451C2×Q8—44no—
452C2×Q8—264no—
453C2×Q8—268no—
454C2×Q8—264no—
455C2×Q8—528no—
456C2×Q8—524no—
457C2×Q8—5232no—
458C2×Q8—524no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—132no—
463C2×D4—264no—
464C2×D4—264no—
465C2×D4—264no—
466C2×D4—264no—
467C2×D4—261no—
468C2×D4—262no—
469C2×D4—262no—
470C2×D4—524no—
471C2×D4—524no—
472C2×D4—524no—
473C2×D4—524no—
474C2×D4C23×D1312yes—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—44no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—138no—
482C22×C4—134no—
483C22×C4—131no—
484C22×C4—134no—
485C22×C4—132no—
486C22×C4—132no—
487C22×C4—264no—
488C22×C4—268no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—261no—
492C22×C4—262no—
493C22×C4—264no—
494C22×C4—528no—
495C22×C4—524no—
496C22×C4D4×D1311yescharacteristic
497C22×C4D4×D1311yescharacteristic
498C22×C4C23×D1311yescharacteristic
499C2×C8—24no—
500C2×C8—134no—
501C2×C8—264no—
502C2×C8C23×D1314yes—
503C4⋊C4—24no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—134no—
507C4⋊C4—132no—
508C4⋊C4—268no—
509C4⋊C4—268no—
510C4⋊C4—264no—
511C4⋊C4—262no—
512C4⋊C4—261no—
513C4⋊C4—264no—
514C4⋊C4C23×D1314yes—
515C4⋊C4C23×D1312yes—
516C22⋊C4—24no—
517C22⋊C4—264no—
518C22⋊C4—264no—
519C22⋊C4—264no—
520C42—134no—
521C42—134no—
522C42—132no—
523C42—132no—
524C42D4×D1312yes—
525C42C23×D1312yes—
526C13C2×#322611yescharacteristic, complemented, Sylow
527C23—22no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—134no—
532C23—132no—
533C23—262no—
534C23—262no—
535C23—262no—
536C23—522no—
537C23—522no—
538C23—522no—
539C23C2×D4×D1311yescharacteristic
540Q8—48no—
541Q8—5216no—
542Q8—528no—
543Q8—528no—
544D4—22no—
545D4—22no—
546D4—42no—
547D4—262no—
548D4—262no—
549D4—528no—
550D4—528no—
551D4—528no—
552D4—528no—
553D4—522no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—48no—
560C2×C4—134no—
561C2×C4—134no—
562C2×C4—132no—
563C2×C4—132no—
564C2×C4—1316no—
565C2×C4—132no—
566C2×C4—268no—
567C2×C4—262no—
568C2×C4—264no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—264no—
573C2×C4—5216no—
574C2×C4—522no—
575C2×C4—524no—
576C2×C4—528no—
577C2×C4D8×D1314yes—
578C2×C4C2×D4×D1312yes—
579C2×C4C2×D4×D1312yes—
580C2×C4C2×D4×D1311yescharacteristic
581C2×C4#8825412yes—
582C2×C4#8825712yes—
583C2×C4C24×D1311yescharacteristic
584C8—24no—
585C8—264no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—84no—
590C22—134no—
591C22—268no—
592C22—262no—
593C22—262no—
594C22—522no—
595C22—522no—
596C22—522no—
597C22—1044no—
598C22#1171933312yes—
599C22C2×D8×D1312yes—
600C22D13×#13712yes—
601C22C22×D4×D1311yescharacteristic
602C4—22no—
603C4—42no—
604C4—44no—
605C4—134no—
606C4—134no—
607C4—262no—
608C4—522no—
609C4—524no—
610C4#1171933312yes—
611C4C2×D8×D1314yes—
612C4C2×#8825411yescharacteristic
613C4C2×#8825711yescharacteristic
614C2—82no—
615C2—264no—
616C2—1042no—
617C2#1312595614yesdirect product factor
618C2C2×#1171933311yescharacteristic
619C2C22×D8×D1311yescharacteristic
620C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#474C2
socleC23×C13C22×D4
prime radicalC2×#11719253C2
hypercenterC2×#474D13
hypocenterC13C2×#3226
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
2. C2×D13×C4⋊Q8C2semidirect
3. #13125956C2direct (N × H)
4. C2×#11718535C2semidirect
5. C2×#11718421C2semidirect
6. C2×#11718543C2semidirect
7. C2×#11718435C2semidirect
8. C2×#11718507C2semidirect
9. C2×#11718668C2semidirect
10. C2×#11718748C2semidirect
11. C2×#11718494C2semidirect
12. C2×C13×#474C2semidirect
22. D13×C4⋊Q8C22semidirect
36. C13×#474C22semidirect
45. #11718748C22semidirect
46. #11718668C22semidirect
51. #11718543C22semidirect
52. #11718535C22semidirect
53. #11718507C22semidirect
54. #11718494C22semidirect
55. #11718435C22semidirect
56. #11718421C22semidirect
227. C2×#474D13semidirect
318. #474C2×D13semidirect
440. C2×C13#3226semidirect
526. C13C2×#3226semidirect
617. C2#13125956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192532
C2×D13×C4⋊Q82
#131259562
C2×#117185352
C2×#117184212
C2×#117185432
C2×#117184352
C2×#117185072
C2×#117186682
C2×#117187482
C2×#117184942
C2×C13×#4742
C2×#322613