Finite Group Databasebeta

← C2×#13119151 #16032092

Subgroups — C2×#13119151 #16032092

Order 3328.

3374 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D52C211yesmaximal, characteristic
2C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
3#13119151C2116yesmaximal, direct product factor
4C2×#11718321C212yesmaximal, complemented
5C2×#11718653C212yesmaximal, complemented
6C2×#11718589C211yesmaximal, characteristic, complemented
7C2×#11718326C212yesmaximal
8C2×#11718650C212yesmaximal, complemented
9C2×#11718648C211yesmaximal, characteristic, complemented
10C2×#11718648C211yesmaximal, characteristic, complemented
11C2×#11718648C211yesmaximal, characteristic, complemented
12C2×C13×#389C211yesmaximal, characteristic, complemented
13C23×D52C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
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×#6103C2211yescharacteristic
24C22×#6103C2212yes—
25C22×#6103C2212yes—
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2212yes—
30C22×#6101C2212yes—
31C2×C4⋊C4×D13—28no—
32C2×C4⋊C4×D13C2218yescomplemented
33C2×C4×D52—28no—
34C2×C4×D52C2218yes—
35C13×#389C2218yescomplemented
36C2×C13×#95C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41#11718653C22116yescomplemented
42#11718650C22116yescomplemented
43#11718648C2218yescomplemented
44#11718648C2218yescomplemented
45#11718648C2218yescomplemented
46#11718589C2218yescomplemented
47#11718326C22116yes—
48#11718321C22116yescomplemented
49C24×D13C2311yescharacteristic
50C24×D13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2312yes—
53C23×C4×C13C2312yes—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×Dic13C2312yes—
57C23×Dic13C2312yes—
58C23×Dic13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C22×D52—24no—
61C22×D52—24no—
62C22×D52Q818yes—
63C22×D52C2314yes—
64C22×C4×D13—24no—
65C22×C4×D13—24no—
66C22×C4×D13—28no—
67C22×C4×D13—24no—
68C22×C4×D13—24no—
69C22×C4×D13—24no—
70C22×C4×D13—44no—
71C22×C4×D13—44no—
72C22×C4×D13D418yes—
73C22×C4×D13C2314yes—
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—24no—
85C2×#6103—28no—
86C2×#6103—24no—
87C2×#6103—44no—
88C2×#6103—44no—
89C2×#6103C2314yes—
90C2×#6103C2314yes—
91C2×#6103C2318yes—
92C2×#6103C2318yes—
93C2×#6103C2318yes—
94C2×C4⋊Dic13—24no—
95C2×C4⋊Dic13—24no—
96C2×C4⋊Dic13—24no—
97C2×C4⋊Dic13C2314yes—
98C2×C4⋊Dic13C2314yes—
99C2×C4⋊Dic13C2314yes—
100C2×#6101—28no—
101C2×#6101—44no—
102C2×#6101C2318yes—
103C2×#6101C2318yes—
104C4⋊C4×D13—232no—
105C4×D52—232no—
106C13×#95C2318yes—
107#88071C2318yes—
108#88071C2318yes—
109#88071C2318yes—
110#88071C2318yes—
111C2×#2487—131nomaximal, Sylow
112C24×C13C2411yescharacteristic
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—22no—
116C23×D13—22no—
117C23×D13—22no—
118C23×D13—22no—
119C23×D13—22no—
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13C2×D414yes—
124C23×D13C2×Q814yes—
125C23×D13C2×Q814yes—
126C23×D13#4114yes—
127C23×D13C2412yes—
128C23×D13C2412yes—
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—22no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13—22no—
139C22×C4×C13—24no—
140C22×C4×C13C2×D414yes—
141C22×C4×C13C2×Q814yes—
142C22×C4×C13#4114yes—
143C22×C4×C13#4114yes—
144C22×C4×C13C2414yes—
145C22×C4×C13C2414yes—
146C22×C4×C13C2412yes—
147C22×C4×C13C2412yes—
148C22×C4×C13C2412yes—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—24no—
152C22×Dic13—22no—
153C22×Dic13—24no—
154C22×Dic13—24no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13C2×D414yes—
161C22×Dic13C2412yes—
162C22×Dic13C2414yes—
163C22×Dic13C2414yes—
164C22×Dic13C2412yes—
165C2×D52—232no—
166C2×D52—28no—
167C2×D52—28no—
168C2×D52C2×Q8116yes—
169C2×C4×D13—232no—
170C2×C4×D13—28no—
171C2×C4×D13—28no—
172C2×C4×D13—216no—
173C2×C4×D13—28no—
174C2×C4×D13—28no—
175C2×C4×D13—28no—
176C2×C4×D13—48no—
177C2×C4×D13—48no—
178C2×C4×D13—432no—
179C2×C4×D13—416no—
180C2×C4×D13C2×D4116yes—
181C13×C4⋊C4—28no—
182C13×C4⋊C4—28no—
183C13×C4⋊C4—48no—
184C42×C13—28no—
185#6103—28no—
186#6103—216no—
187#6103—28no—
188#6103—48no—
189#6103—48no—
190C4⋊Dic13—28no—
191C4⋊Dic13—28no—
192C4⋊Dic13—28no—
193#6101—216no—
194#6101—48no—
195C22×C4×D4—131no—
196C23×C4⋊C4—131no—
197#2487—1316no—
198C2×#400—132no—
199C2×#399—132no—
200C2×#389—131no—
201C2×#389D1311yescharacteristic, complemented
202C2×#386—132no—
203C2×#385—132no—
204C2×#380—131no—
205C2×#380—131no—
206C2×#380—131no—
207C23×C13C22×D412yes—
208C23×C13C22×Q812yes—
209C23×C13C2×#4112yes—
210C23×C13C2×#4112yes—
211C23×C13C2×#4112yes—
212C23×C13H(5,𝔽2)12yes—
213C23×C13H(5,𝔽2)12yes—
214C23×C13C2511yescharacteristic
215C22×D13—28no—
216C22×D13—28no—
217C22×D13—28no—
218C22×D13—28no—
219C22×D13—28no—
220C22×D13—28no—
221C22×D13—22no—
222C22×D13—22no—
223C22×D13—22no—
224C22×D13—22no—
225C22×D13—28no—
226C22×D13—28no—
227C22×D13—28no—
228C22×D13—22no—
229C22×D13—22no—
230C22×D13—22no—
231C22×D13—22no—
232C22×D13—22no—
233C22×D13—22no—
234C22×D13—44no—
235C22×D13—44no—
236C22×D13—44no—
237C22×D13—44no—
238C22×D13C22⋊Q8116yes—
239C22×D13C22×D414yes—
240C22×D13C22×Q814yes—
241C22×D13C22×Q814yes—
242C22×D13C2×#4114yes—
243C2×C4×C13—28no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—22no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—22no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—22no—
254C2×C4×C13—24no—
255C2×C4×C13—48no—
256C2×C4×C13—44no—
257C2×C4×C13—48no—
258C2×C4×C13#123116yes—
259C2×C4×C13C22×D414yes—
260C2×C4×C13C22×Q814yes—
261C2×C4×C13C2×#4114yes—
262C2×C4×C13C2×#4114yes—
263C2×Dic13—28no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—24no—
267C2×Dic13—22no—
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—44no—
276C2×Dic13—48no—
277C2×Dic13—48no—
278C2×Dic13C22×D414yes—
279D52—232no—
280C4×D13—232no—
281C4×D13—432no—
282C4×D13—416no—
283C23×D4—131no—
284C24×C4—131no—
285C24×C4—131no—
286C24×C4—132no—
287C2×C4×D4—138no—
288C2×C4×D4—268no—
289C22×C4⋊C4—132no—
290C22×C4⋊C4—131no—
291C22×C4⋊C4—131no—
292C22×C4⋊C4—131no—
293C22×C4⋊C4—132no—
294C22×C4⋊C4—138no—
295C22×C4⋊C4—268no—
296C22×C4⋊C4C2×D1311yescharacteristic
297C22×C4⋊C4C2×D1311yescharacteristic
298C22×C4⋊C4C2×D1312yes—
299C22×C22⋊C4—131no—
300C22×C22⋊C4—131no—
301C22×C22⋊C4—132no—
302C22×C22⋊C4—132no—
303C22×C22⋊C4—132no—
304C22×C42C2×D1311yescharacteristic
305#400—1316no—
306#399—1316no—
307#389—138no—
308#389C2×D1318yescomplemented
309#386—1316no—
310#385—1316no—
311#380—138no—
312#380—138no—
313#380—138no—
314C2×#95—132no—
315C2×#95—132no—
316C2×#95—132no—
317C2×#95—132no—
318C2×#95C2×D1312yes—
319C22×C13C2×C22⋊Q814yes—
320C22×C13C2×#12314yes—
321C22×C13#53514yes—
322C22×C13#55314yes—
323C22×C13#55314yes—
324C22×C13#55414yes—
325C22×C13#55414yes—
326C22×C13C23×D411yescharacteristic
327C22×C13C23×Q811yescharacteristic
328C22×C13C22×#4111yescharacteristic
329C22×C13C22×#4111yescharacteristic
330C22×C13C22×#4111yescharacteristic
331C22×C13C2×H(5,𝔽2)11yescharacteristic
332C22×C13C2×H(5,𝔽2)11yescharacteristic
333C2×D13—24no—
334C2×D13—24no—
335C2×D13—24no—
336C2×D13—24no—
337C2×D13—24no—
338C2×D13—24no—
339C2×D13—232no—
340C2×D13—24no—
341C2×D13—24no—
342C2×D13—24no—
343C2×D13—42no—
344C2×D13—42no—
345C2×D13—42no—
346C2×D13—42no—
347C2×D13—416no—
348C2×D13C2×C22⋊Q818yes—
349C4×C13—24no—
350C4×C13—44no—
351C4×C13—42no—
352C4×C13—44no—
353C4×C13C2×#12318yes—
354Dic13—24no—
355Dic13—42no—
356Dic13—44no—
357Dic13—44no—
358C25—131no—
359C25—131no—
360C22×D4—138no—
361C22×D4—134no—
362C22×D4—264no—
363C22×D4—264no—
364C23×C4—131no—
365C23×C4—138no—
366C23×C4—134no—
367C23×C4—132no—
368C23×C4—132no—
369C23×C4—131no—
370C23×C4—134no—
371C23×C4—138no—
372C23×C4—268no—
373C23×C4—264no—
374C23×C4—264no—
375C23×C4—264no—
376C23×C4—264no—
377C23×C4—264no—
378C23×C4—524no—
379C23×C4—524no—
380C23×C4C22×D1311yescharacteristic
381C23×C4C22×D1312yes—
382C23×C4C22×D1312yes—
383C23×C4C22×D1311yescharacteristic
384C23×C4C22×D1311yescharacteristic
385C4×D4—2632no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—138no—
390C2×C4⋊C4—134no—
391C2×C4⋊C4—134no—
392C2×C4⋊C4—134no—
393C2×C4⋊C4—138no—
394C2×C4⋊C4—2632no—
395C2×C4⋊C4—268no—
396C2×C4⋊C4—264no—
397C2×C4⋊C4—264no—
398C2×C4⋊C4—264no—
399C2×C4⋊C4—524no—
400C2×C4⋊C4C22×D1314yes—
401C2×C4⋊C4C22×D1314yes—
402C2×C4⋊C4C22×D1318yes—
403C2×C22⋊C4—134no—
404C2×C22⋊C4—134no—
405C2×C22⋊C4—138no—
406C2×C22⋊C4—138no—
407C2×C22⋊C4—138no—
408C2×C22⋊C4—264no—
409C2×C22⋊C4—264no—
410C2×C22⋊C4—268no—
411C2×C22⋊C4—524no—
412C2×C22⋊C4—524no—
413C2×C42—24no—
414C2×C42C22×D1314yes—
415#95—138no—
416#95—138no—
417#95—138no—
418#95—138no—
419#95C22×D1318yes—
420C2×C13#248718yescomplemented
421C2×C13C22×C22⋊Q811yescharacteristic
422C2×C13C22×#12311yescharacteristic
423C2×C13C2×#53511yescharacteristic
424C2×C13C2×#55311yescharacteristic
425C2×C13C2×#55311yescharacteristic
426C2×C13C2×#55411yescharacteristic
427C2×C13C2×#55411yescharacteristic
428D13—28no—
429D13—44no—
430C24—134no—
431C24—134no—
432C24—134no—
433C24—132no—
434C24—134no—
435C24—132no—
436C24—262no—
437C24—262no—
438C24—262no—
439C24—262no—
440C24—262no—
441C24—262no—
442C24—262no—
443C24—262no—
444C24—262no—
445C24—262no—
446C24C23×D1311yescharacteristic
447C2×D4—1316no—
448C2×D4—268no—
449C2×D4—2632no—
450C2×D4—268no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—134no—
463C22×C4—132no—
464C22×C4—1316no—
465C22×C4—132no—
466C22×C4—134no—
467C22×C4—134no—
468C22×C4—2616no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—2632no—
472C22×C4—268no—
473C22×C4—268no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—264no—
477C22×C4—264no—
478C22×C4—264no—
479C22×C4—262no—
480C22×C4—264no—
481C22×C4—264no—
482C22×C4—264no—
483C22×C4—268no—
484C22×C4—268no—
485C22×C4—268no—
486C22×C4—528no—
487C22×C4—528no—
488C22×C4—5232no—
489C22×C4—5216no—
490C22×C4#612714yes—
491C22×C4D4×D1314yes—
492C22×C4Q8×D1314yes—
493C22×C4#613114yes—
494C22×C4C23×D1314yes—
495C22×C4C23×D1314yes—
496C22×C4C23×D1312yes—
497C22×C4C23×D1312yes—
498C22×C4C23×D1312yes—
499C4⋊C4—28no—
500C4⋊C4—28no—
501C4⋊C4—48no—
502C4⋊C4—2616no—
503C4⋊C4—268no—
504C4⋊C4—268no—
505C4⋊C4—268no—
506C4⋊C4—528no—
507C22⋊C4—268no—
508C22⋊C4—268no—
509C22⋊C4—2616no—
510C22⋊C4—528no—
511C22⋊C4—528no—
512C42—28no—
513C13C2×#248711yescharacteristic, complemented, Sylow
514C23—1316no—
515C23—134no—
516C23—134no—
517C23—134no—
518C23—134no—
519C23—268no—
520C23—268no—
521C23—268no—
522C23—268no—
523C23—268no—
524C23—262no—
525C23—262no—
526C23—262no—
527C23—262no—
528C23—268no—
529C23—268no—
530C23—268no—
531C23—268no—
532C23—262no—
533C23—262no—
534C23—262no—
535C23—262no—
536C23—262no—
537C23—262no—
538C23—524no—
539C23—524no—
540C23—524no—
541C23—524no—
542C23C2×#612712yes—
543C23C2×D4×D1312yes—
544C23#8825112yes—
545C23C2×Q8×D1312yes—
546C23C2×#613112yes—
547C23#41×D1312yes—
548C23#8825612yes—
549C23C24×D1311yescharacteristic
550D4—2632no—
551C2×C4—28no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—48no—
564C2×C4—48no—
565C2×C4—44no—
566C2×C4—134no—
567C2×C4—268no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—2632no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—264no—
576C2×C4—262no—
577C2×C4—264no—
578C2×C4—264no—
579C2×C4—264no—
580C2×C4—5232no—
581C2×C4—524no—
582C2×C4—528no—
583C2×C4—528no—
584C2×C4—5216no—
585C2×C4#88148116yes—
586C2×C4C2×#612714yes—
587C2×C4C2×D4×D1314yes—
588C2×C4C2×Q8×D1314yes—
589C2×C4C2×#613114yes—
590C22—138no—
591C22—264no—
592C22—264no—
593C22—264no—
594C22—2632no—
595C22—264no—
596C22—264no—
597C22—264no—
598C22—264no—
599C22—264no—
600C22—264no—
601C22—522no—
602C22—522no—
603C22—522no—
604C22—5216no—
605C22—522no—
606C22C2×#8814814yes—
607C22#1171926314yes—
608C22#1171928414yes—
609C22#1171931214yes—
610C22D13×C22⋊Q814yes—
611C22#1171940014yes—
612C22#1171943514yes—
613C22C22×#612711yescharacteristic
614C22C22×D4×D1311yescharacteristic
615C22C2×#8825111yescharacteristic
616C22C22×Q8×D1311yescharacteristic
617C22C22×#613111yescharacteristic
618C22C2×#41×D1311yescharacteristic
619C22C2×#8825611yescharacteristic
620C4—24no—
621C4—44no—
622C4—42no—
623C4—44no—
624C4—264no—
625C4—522no—
626C4—524no—
627C4—524no—
628C4C2×#8814818yes—
629C2—268no—
630C2—524no—
631C2#1311915118yesdirect product factor
632C2C2×D13×C22⋊Q811yescharacteristic
633C2C22×#8814811yescharacteristic
634C2C2×#1171931211yescharacteristic
635C2C2×#1171926311yescharacteristic
636C2C2×#1171940011yescharacteristic
637C2C2×#1171928411yescharacteristic
638C2C2×#1171943511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#389C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#389D13
hypocenterC13C2×#2487
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⋊C4×D13C2semidirect
3. #13119151C2direct (N × H)
4. C2×#11718321C2semidirect
5. C2×#11718653C2semidirect
6. C2×#11718589C2semidirect
8. C2×#11718650C2semidirect
9. C2×#11718648C2semidirect
10. C2×#11718648C2semidirect
11. C2×#11718648C2semidirect
12. C2×C13×#389C2semidirect
32. C2×C4⋊C4×D13C22semidirect
35. C13×#389C22semidirect
41. #11718653C22semidirect
42. #11718650C22semidirect
43. #11718648C22semidirect
44. #11718648C22semidirect
45. #11718648C22semidirect
46. #11718589C22semidirect
48. #11718321C22semidirect
201. C2×#389D13semidirect
308. #389C2×D13semidirect
420. C2×C13#2487semidirect
513. C13C2×#2487semidirect
631. C2#13119151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D522
C22×C4⋊C4×D132
#131191512
C2×#117183212
C2×#117186532
C2×#117185892
C2×#117183262
C2×#117186502
C2×#117186482
C2×C13×#3892
C2×#248713