Finite Group Databasebeta

← C2×#13118329 #16031052

Subgroups — C2×#13118329 #16031052

Order 3328.

3438 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88149C211yesmaximal, characteristic
2C22×C4×D52C211yesmaximal, characteristic, complemented
3#13118329C2116yesmaximal, direct product factor
4C2×#11718654C212yesmaximal, complemented
5C2×#11718652C212yesmaximal, complemented
6C2×#11718649C211yesmaximal, characteristic, complemented
7C2×#11718326C212yesmaximal, complemented
8C2×#11718638C211yesmaximal, characteristic, complemented
9C2×#11718325C212yesmaximal, complemented
10C2×#11718648C211yesmaximal, characteristic, complemented
11C2×C4×#6103C211yesmaximal, characteristic, complemented
12C2×C13×#389C211yesmaximal, characteristic, complemented
13C23×D52C2212yes—
14C23×D52C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C23×C4×D13C2212yes—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2212yes—
20C22×C42×C13C2211yescharacteristic
21C22×#6103C2212yes—
22C22×#6103C2211yescharacteristic
23C22×#6103C2212yes—
24C22×#6103C2211yescharacteristic
25C22×#6103C2212yes—
26C22×#6103C2212yes—
27C22×#6103C2212yes—
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C2×#88149—28no—
31C2×#88149C2218yes—
32C2×C4×D52—28no—
33C2×C4×D52C2218yescomplemented
34C13×#389C2218yescomplemented
35C2×C13×#95C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2211yescharacteristic
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2211yescharacteristic
41#11718654C22116yescomplemented
42#11718652C22116yescomplemented
43#11718649C2218yescomplemented
44#11718648C2218yescomplemented
45#11718638C2218yescomplemented
46C4×#6103C2218yescomplemented
47#11718326C22116yescomplemented
48#11718325C22116yescomplemented
49C24×D13C2312yes—
50C24×D13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2312yes—
53C23×C4×C13C2312yes—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×Dic13C2311yescharacteristic
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2312yes—
59C23×Dic13C2311yescharacteristic
60C22×D52—24no—
61C22×D52—24no—
62C22×D52—28no—
63C22×D52—28no—
64C22×D52—44no—
65C22×D52D418yes—
66C22×D52C2318yes—
67C22×D52C2314yes—
68C22×C4×D13—28no—
69C22×C4×D13—24no—
70C22×C4×D13—24no—
71C22×C4×D13—28no—
72C22×C4×D13—24no—
73C22×C4×D13—44no—
74C22×C4×D13C2314yes—
75C22×C4×D13C2318yes—
76C2×C13×C4⋊C4—24no—
77C2×C13×C4⋊C4—24no—
78C2×C13×C4⋊C4—44no—
79C2×C13×C4⋊C4C2314yes—
80C2×C13×C4⋊C4C2314yes—
81C2×C13×C4⋊C4C2318yes—
82C2×C42×C13—24no—
83C2×C42×C13C2314yes—
84C2×#6103—28no—
85C2×#6103—28no—
86C2×#6103—24no—
87C2×#6103—24no—
88C2×#6103—44no—
89C2×#6103—44no—
90C2×#6103—44no—
91C2×#6103C2318yes—
92C2×#6103C2318yes—
93C2×#6103C2314yes—
94C2×#6103C2314yes—
95C2×#6103C2318yes—
96C2×#6103C2318yes—
97C2×#6103C2318yes—
98C2×C4⋊Dic13—24no—
99C2×C4⋊Dic13C2314yes—
100C2×C4×Dic13—24no—
101C2×C4×Dic13C2314yes—
102#88149—232no—
103C4×D52—232no—
104C13×#95C2318yes—
105#88071C2314yes—
106#88071C2318yes—
107#88071C2318yes—
108#88071C2318yes—
109#88071C2314yes—
110C2×#2420—131nomaximal, Sylow
111C24×C13C2411yescharacteristic
112C23×D13—22no—
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—24no—
116C23×D13—22no—
117C23×D13—24no—
118C23×D13—24no—
119C23×D13—24no—
120C23×D13—22no—
121C23×D13—24no—
122C23×D13—24no—
123C23×D13—22no—
124C23×D13C2×D418yes—
125C23×D13#4114yes—
126C23×D13C2414yes—
127C23×D13C2412yes—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—24no—
132C22×C4×C13—22no—
133C22×C4×C13—24no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—22no—
138C22×C4×C13—24no—
139C22×C4×C13C2×D414yes—
140C22×C4×C13#4114yes—
141C22×C4×C13#4114yes—
142C22×C4×C13#4114yes—
143C22×C4×C13C2414yes—
144C22×C4×C13C2414yes—
145C22×C4×C13C2412yes—
146C22×C4×C13C2412yes—
147C22×C4×C13C2412yes—
148C22×Dic13—24no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—24no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—24no—
160C22×Dic13C2412yes—
161C22×Dic13C2412yes—
162C22×Dic13C2412yes—
163C22×Dic13C2414yes—
164C2×D52—232no—
165C2×D52—28no—
166C2×D52—28no—
167C2×D52—216no—
168C2×D52—216no—
169C2×D52—48no—
170C2×D52—432no—
171C2×D52C2×D4116yes—
172C2×C4×D13—216no—
173C2×C4×D13—28no—
174C2×C4×D13—216no—
175C2×C4×D13—28no—
176C2×C4×D13—28no—
177C2×C4×D13—48no—
178C2×C4×D13—432no—
179C2×C4×D13—416no—
180C13×C4⋊C4—28no—
181C13×C4⋊C4—28no—
182C13×C4⋊C4—48no—
183C42×C13—28no—
184#6103—216no—
185#6103—216no—
186#6103—28no—
187#6103—28no—
188#6103—48no—
189#6103—48no—
190#6103—48no—
191C4⋊Dic13—28no—
192C4×Dic13—28no—
193C22×#121—131no—
194C22×C4×D4—131no—
195#2420—1316no—
196C2×#397—132no—
197C2×#394—132no—
198C2×#390—131no—
199C2×#389D1311yescharacteristic, complemented
200C2×#386—132no—
201C2×#382—131no—
202C2×#381—132no—
203C2×#380—131no—
204C2×C4×C22⋊C4—131no—
205C23×C13C22×D412yes—
206C23×C13C2×#4112yes—
207C23×C13C2×#4112yes—
208C23×C13C2×#4112yes—
209C23×C13C2×#4112yes—
210C23×C13H(5,𝔽2)12yes—
211C23×C13H(5,𝔽2)12yes—
212C23×C13C2511yescharacteristic
213C22×D13—216no—
214C22×D13—28no—
215C22×D13—216no—
216C22×D13—28no—
217C22×D13—216no—
218C22×D13—28no—
219C22×D13—22no—
220C22×D13—22no—
221C22×D13—22no—
222C22×D13—24no—
223C22×D13—22no—
224C22×D13—24no—
225C22×D13—24no—
226C22×D13—24no—
227C22×D13—22no—
228C22×D13—24no—
229C22×D13—24no—
230C22×D13—22no—
231C22×D13—44no—
232C22×D13—48no—
233C22×D13—44no—
234C22×D13—48no—
235C22×D13—44no—
236C22×D13—48no—
237C22×D13—44no—
238C22×D13—48no—
239C22×D13C22×D418yes—
240C22×D13C2×#4114yes—
241C2×C4×C13—28no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—24no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—22no—
252C2×C4×C13—24no—
253C2×C4×C13—48no—
254C2×C4×C13—48no—
255C2×C4×C13—44no—
256C2×C4×C13#123116yes—
257C2×C4×C13C22×D414yes—
258C2×C4×C13C2×#4114yes—
259C2×C4×C13C2×#4114yes—
260C2×C4×C13C2×#4114yes—
261C2×Dic13—24no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—24no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—24no—
273C2×Dic13—44no—
274C2×Dic13—48no—
275C2×Dic13—44no—
276C2×Dic13—44no—
277D52—232no—
278D52—432no—
279C4×D13—432no—
280C4×D13—416no—
281C23×D4—131no—
282C23×D4—132no—
283C24×C4—131no—
284C24×C4—132no—
285C2×#121—138no—
286C2×#121—268no—
287C2×C4×D4—138no—
288C2×C4×D4—268no—
289C22×C4⋊C4—131no—
290C22×C4⋊C4C2×D1311yescharacteristic
291C22×C4⋊C4C2×D1311yescharacteristic
292C22×C4⋊C4C2×D1312yes—
293C22×C22⋊C4—131no—
294C22×C22⋊C4—132no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4—131no—
297C22×C22⋊C4—132no—
298C22×C22⋊C4—132no—
299C22×C22⋊C4—132no—
300C22×C42—131no—
301C22×C42C2×D1311yescharacteristic
302#397—1316no—
303#394—1316no—
304#390—138no—
305#389C2×D1318yescomplemented
306#386—1316no—
307#382—138no—
308#381—1316no—
309#380—138no—
310C4×C22⋊C4—138no—
311C2×#95—132no—
312C2×#95—131no—
313C2×#95—132no—
314C2×#95—132no—
315C2×#95—131no—
316C2×#95C2×D1312yes—
317C22×C13C2×#12314yes—
318C22×C13#52914yes—
319C22×C13#54014yes—
320C22×C13#54614yes—
321C22×C13#54614yes—
322C22×C13#55314yes—
323C22×C13#55514yes—
324C22×C13C23×D411yescharacteristic
325C22×C13C22×#4111yescharacteristic
326C22×C13C22×#4111yescharacteristic
327C22×C13C22×#4111yescharacteristic
328C22×C13C22×#4111yescharacteristic
329C22×C13C2×H(5,𝔽2)11yescharacteristic
330C22×C13C2×H(5,𝔽2)11yescharacteristic
331C2×D13—28no—
332C2×D13—24no—
333C2×D13—28no—
334C2×D13—24no—
335C2×D13—28no—
336C2×D13—24no—
337C2×D13—42no—
338C2×D13—44no—
339C2×D13—432no—
340C2×D13—416no—
341C2×D13—42no—
342C2×D13—44no—
343C2×D13—42no—
344C2×D13—44no—
345C2×D13—42no—
346C2×D13—44no—
347C4×C13—24no—
348C4×C13—44no—
349C4×C13—44no—
350C4×C13—42no—
351C4×C13C2×#12318yes—
352Dic13—42no—
353Dic13—44no—
354Dic13—42no—
355Dic13—42no—
356C25—132no—
357C25—131no—
358C22×D4—138no—
359C22×D4—134no—
360C22×D4—138no—
361C22×D4—268no—
362C22×D4—268no—
363C22×D4—264no—
364C22×D4—264no—
365C22×D4—524no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4—132no—
369C23×C4—131no—
370C23×C4—134no—
371C23×C4—138no—
372C23×C4—268no—
373C23×C4—264no—
374C23×C4—264no—
375C23×C4—268no—
376C23×C4—264no—
377C23×C4—524no—
378C23×C4C22×D1312yes—
379C23×C4C22×D1311yescharacteristic
380C23×C4C22×D1312yes—
381C23×C4C22×D1311yescharacteristic
382C23×C4C22×D1311yescharacteristic
383#121—2632no—
384C4×D4—2632no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—134no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4C22×D1314yes—
391C2×C4⋊C4C22×D1314yes—
392C2×C4⋊C4C22×D1318yes—
393C2×C22⋊C4—138no—
394C2×C22⋊C4—138no—
395C2×C22⋊C4—134no—
396C2×C22⋊C4—134no—
397C2×C22⋊C4—138no—
398C2×C22⋊C4—138no—
399C2×C22⋊C4—138no—
400C2×C22⋊C4—268no—
401C2×C22⋊C4—268no—
402C2×C22⋊C4—264no—
403C2×C22⋊C4—264no—
404C2×C22⋊C4—524no—
405C2×C22⋊C4—524no—
406C2×C22⋊C4—524no—
407C2×C42—24no—
408C2×C42—134no—
409C2×C42—264no—
410C2×C42C22×D1314yes—
411#95—134no—
412#95—134no—
413#95—138no—
414#95—138no—
415#95—138no—
416#95C22×D1318yes—
417C2×C13#242018yescomplemented
418C2×C13C22×#12311yescharacteristic
419C2×C13C2×#52911yescharacteristic
420C2×C13C2×#54011yescharacteristic
421C2×C13C2×#54611yescharacteristic
422C2×C13C2×#54611yescharacteristic
423C2×C13C2×#55311yescharacteristic
424C2×C13C2×#55511yescharacteristic
425D13—48no—
426D13—44no—
427C24—138no—
428C24—134no—
429C24—134no—
430C24—132no—
431C24—262no—
432C24—264no—
433C24—262no—
434C24—264no—
435C24—262no—
436C24—262no—
437C24—264no—
438C24—262no—
439C24—264no—
440C24—264no—
441C24—262no—
442C24—264no—
443C24C23×D1311yescharacteristic
444C2×D4—1316no—
445C2×D4—2616no—
446C2×D4—2616no—
447C2×D4—2632no—
448C2×D4—268no—
449C2×D4—268no—
450C2×D4—528no—
451C2×D4—5232no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—132no—
464C22×C4—132no—
465C22×C4—132no—
466C22×C4—134no—
467C22×C4—2616no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—264no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—264no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—264no—
480C22×C4—268no—
481C22×C4—268no—
482C22×C4—2616no—
483C22×C4—268no—
484C22×C4—528no—
485C22×C4—5232no—
486C22×C4—5216no—
487C22×C4#612714yes—
488C22×C4D4×D1314yes—
489C22×C4#613114yes—
490C22×C4#613114yes—
491C22×C4C23×D1314yes—
492C22×C4C23×D1314yes—
493C22×C4C23×D1312yes—
494C22×C4C23×D1312yes—
495C22×C4C23×D1312yes—
496C4⋊C4—28no—
497C4⋊C4—28no—
498C4⋊C4—48no—
499C4⋊C4—268no—
500C22⋊C4—2616no—
501C22⋊C4—2616no—
502C22⋊C4—268no—
503C22⋊C4—268no—
504C22⋊C4—528no—
505C22⋊C4—528no—
506C22⋊C4—528no—
507C42—28no—
508C42—268no—
509C13C2×#242011yescharacteristic, complemented, Sylow
510C23—138no—
511C23—134no—
512C23—2616no—
513C23—268no—
514C23—268no—
515C23—2616no—
516C23—2616no—
517C23—262no—
518C23—264no—
519C23—262no—
520C23—264no—
521C23—262no—
522C23—262no—
523C23—264no—
524C23—262no—
525C23—264no—
526C23—264no—
527C23—262no—
528C23—264no—
529C23—268no—
530C23—528no—
531C23—524no—
532C23—524no—
533C23—524no—
534C23—528no—
535C23—528no—
536C23—524no—
537C23—528no—
538C23C2×#612712yes—
539C23C2×D4×D1312yes—
540C23#8825112yes—
541C23C2×#613112yes—
542C23C2×#613112yes—
543C23#41×D1312yes—
544C23#8825612yes—
545C23C24×D1311yescharacteristic
546D4—2632no—
547D4—5232no—
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—48no—
561C2×C4—48no—
562C2×C4—44no—
563C2×C4—262no—
564C2×C4—262no—
565C2×C4—264no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—264no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—262no—
574C2×C4—264no—
575C2×C4—5232no—
576C2×C4—524no—
577C2×C4—524no—
578C2×C4—528no—
579C2×C4—524no—
580C2×C4—5216no—
581C2×C4#88148116yes—
582C2×C4C2×#612714yes—
583C2×C4C2×D4×D1314yes—
584C2×C4C2×#613114yes—
585C2×C4C2×#613114yes—
586C22—268no—
587C22—264no—
588C22—268no—
589C22—268no—
590C22—264no—
591C22—264no—
592C22—522no—
593C22—524no—
594C22—522no—
595C22—5232no—
596C22—5216no—
597C22—522no—
598C22—524no—
599C22—524no—
600C22—524no—
601C22—522no—
602C22C2×#8814814yes—
603C22#1171926714yes—
604C22#1171928514yes—
605C22#1171931714yes—
606C22#1171933514yes—
607C22#1171940014yes—
608C22#1171943914yes—
609C22C22×#612711yescharacteristic
610C22C22×D4×D1311yescharacteristic
611C22C2×#8825111yescharacteristic
612C22C22×#613111yescharacteristic
613C22C22×#613111yescharacteristic
614C22C2×#41×D1311yescharacteristic
615C22C2×#8825611yescharacteristic
616C4—24no—
617C4—44no—
618C4—42no—
619C4—44no—
620C4—524no—
621C4—522no—
622C4—522no—
623C4—522no—
624C4C2×#8814818yes—
625C2—528no—
626C2—524no—
627C2#1311832918yesdirect product factor
628C2C22×#8814811yescharacteristic
629C2C2×#1171928511yescharacteristic
630C2C2×#1171926711yescharacteristic
631C2C2×#1171933511yescharacteristic
632C2C2×#1171931711yescharacteristic
633C2C2×#1171940011yescharacteristic
634C2C2×#1171943911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#389C2
socleC24×C13C24
prime radicalC22×#88149C2
hypercenterC2×#389D13
hypocenterC13C2×#2420
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×C4×D52C2semidirect
3. #13118329C2direct (N × H)
4. C2×#11718654C2semidirect
5. C2×#11718652C2semidirect
6. C2×#11718649C2semidirect
7. C2×#11718326C2semidirect
8. C2×#11718638C2semidirect
9. C2×#11718325C2semidirect
10. C2×#11718648C2semidirect
11. C2×C4×#6103C2semidirect
12. C2×C13×#389C2semidirect
33. C2×C4×D52C22semidirect
34. C13×#389C22semidirect
41. #11718654C22semidirect
42. #11718652C22semidirect
43. #11718649C22semidirect
44. #11718648C22semidirect
45. #11718638C22semidirect
46. C4×#6103C22semidirect
47. #11718326C22semidirect
48. #11718325C22semidirect
199. C2×#389D13semidirect
305. #389C2×D13semidirect
417. C2×C13#2420semidirect
509. C13C2×#2420semidirect
627. C2#13118329direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881492
C22×C4×D522
#131183292
C2×#117186542
C2×#117186522
C2×#117186492
C2×#117183262
C2×#117186382
C2×#117183252
C2×#117186482
C2×C4×#61032
C2×C13×#3892
C2×#242013