Finite Group Databasebeta

← C2×#13117762 #16022243

Subgroups — C2×#13117762 #16022243

Order 3328.

3894 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D52C211yesmaximal, characteristic
2C22×#88146C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
4#13117762C2116yesmaximal, direct product factor
5C2×#11718330C212yesmaximal, complemented
6C2×#11718315C212yesmaximal, complemented
7C2×#11718326C212yesmaximal
8C2×#11718648C211yesmaximal, characteristic, complemented
9C2×#11718648C211yesmaximal, characteristic, complemented
10C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
11C2×#11718327C212yesmaximal, complemented
12C2×C13×#382C211yesmaximal, characteristic, complemented
13C23×D52C2211yescharacteristic
14C23×C4×D13C2212yes—
15C23×C4×D13C2211yescharacteristic
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2212yes—
29C22×C4×Dic13C2212yes—
30C22×C4×Dic13C2212yes—
31C2×#88146—28no—
32C2×#88146C2218yescomplemented
33C2×C4⋊C4×D13—28no—
34C2×C4⋊C4×D13C2218yescomplemented
35C2×C4×D52C4116yescomplemented
36C2×C4×D52C2218yes—
37C13×#382C2218yescomplemented
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×#88071C2212yes—
41C2×#88071C2212yes—
42C2×#88071C2212yes—
43#11718648C2218yescomplemented
44#11718648C2218yescomplemented
45C4×C4⋊Dic13C2218yescomplemented
46#11718330C22116yescomplemented
47#11718327C22116yescomplemented
48#11718326C22116yes—
49#11718315C22116yescomplemented
50C24×D13C2311yescharacteristic
51C24×D13C2311yescharacteristic
52C23×C4×C13C2312yes—
53C23×C4×C13C2312yes—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×Dic13C2312yes—
58C23×Dic13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2312yes—
61C22×D52—24no—
62C22×D52—24no—
63C22×D52C2×C418yes—
64C22×D52C2314yes—
65C22×C4×D13—24no—
66C22×C4×D13—24no—
67C22×C4×D13—24no—
68C22×C4×D13—24no—
69C22×C4×D13—28no—
70C22×C4×D13—28no—
71C22×C4×D13—44no—
72C22×C4×D13C2×C418yes—
73C22×C4×D13C2×C418yescomplemented
74C22×C4×D13C2318yes—
75C22×C4×D13C2314yes—
76C22×C4×D13C2314yes—
77C2×C13×C4⋊C4—24no—
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4C2314yes—
80C2×C13×C4⋊C4C2314yes—
81C2×C42×C13C2×C418yescomplemented
82C2×C42×C13C2314yes—
83C2×#6103—28no—
84C2×#6103—28no—
85C2×#6103—44no—
86C2×#6103C2×C418yes—
87C2×#6103C2×C418yescomplemented
88C2×#6103C2318yes—
89C2×#6103C2318yes—
90C2×#6103C2318yes—
91C2×#6103C2314yes—
92C2×#6103C2314yes—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13C2×C418yescomplemented
95C2×C4⋊Dic13D418yescomplemented
96C2×C4⋊Dic13C2314yes—
97C2×C4⋊Dic13C2314yes—
98C2×C4⋊Dic13C2314yes—
99C2×#6101—28no—
100C2×#6101C2318yes—
101C2×C4×Dic13—28no—
102C2×C4×Dic13—44no—
103C2×C4×Dic13C2318yes—
104C2×C4×Dic13C2318yes—
105#88146—232no—
106C4⋊C4×D13—232no—
107C4×D52C2×C4164yescomplemented
108C13×#95C2318yes—
109C13×#95C2318yes—
110#88071C2318yes—
111#88071C2318yes—
112#88071C2318yes—
113C2×#2352—131nomaximal, Sylow
114C24×C13C2411yescharacteristic
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×D13—22no—
124C23×D13—22no—
125C23×D13C22×C414yes—
126C23×D13C22×C414yes—
127C23×D13#4114yes—
128C23×D13#4114yes—
129C23×D13C2412yes—
130C23×D13C2412yes—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13—24no—
141C22×C4×C13C22×C414yes—
142C22×C4×C13C22×C414yes—
143C22×C4×C13C22×C414yes—
144C22×C4×C13C2×D414yes—
145C22×C4×C13#4114yes—
146C22×C4×C13C2414yes—
147C22×C4×C13C2414yes—
148C22×C4×C13C2412yes—
149C22×C4×C13C2412yes—
150C22×C4×C13C2412yes—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—24no—
156C22×Dic13—24no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13C22×C414yes—
161C22×Dic13C22×C414yes—
162C22×Dic13C2×D418yes—
163C22×Dic13C2414yes—
164C22×Dic13C2412yes—
165C22×Dic13C2412yes—
166C22×Dic13C2414yes—
167C2×D52—232no—
168C2×D52—28no—
169C2×D52—28no—
170C2×D52C22×C4116yes—
171C2×C4×D13—232no—
172C2×C4×D13—232no—
173C2×C4×D13—28no—
174C2×C4×D13—28no—
175C2×C4×D13—28no—
176C2×C4×D13—28no—
177C2×C4×D13—216no—
178C2×C4×D13—216no—
179C2×C4×D13—48no—
180C2×C4×D13—432no—
181C2×C4×D13C22×C4116yes—
182C2×C4×D13C22×C4116yescomplemented
183C13×C4⋊C4—28no—
184C13×C4⋊C4—28no—
185C42×C13C22×C4116yescomplemented
186#6103—216no—
187#6103—216no—
188#6103—48no—
189#6103C22×C4116yes—
190#6103C22×C4116yescomplemented
191C4⋊Dic13—28no—
192C4⋊Dic13C22×C4116yescomplemented
193C4⋊Dic13C2×D4116yescomplemented
194#6101—216no—
195C4×Dic13—216no—
196C4×Dic13—48no—
197C22×C4×D4—131no—
198C22×#117—131no—
199C23×C4⋊C4—131no—
200#2352—1316no—
201C2×#388—132no—
202C2×#387—132no—
203C2×#386—132no—
204C2×#382D1311yescharacteristic, complemented
205C2×#380—131no—
206C2×#380—131no—
207C2×C4×C4⋊C4—131no—
208C2×C4×C22⋊C4—132no—
209C23×C13C23×C412yes—
210C23×C13C22×D412yes—
211C23×C13C2×#4112yes—
212C23×C13C2×#4112yes—
213C23×C13C2×#4112yes—
214C23×C13H(5,𝔽2)12yes—
215C23×C132−1+412yes—
216C23×C13C2511yescharacteristic
217C22×D13—28no—
218C22×D13—28no—
219C22×D13—28no—
220C22×D13—28no—
221C22×D13—28no—
222C22×D13—28no—
223C22×D13—22no—
224C22×D13—22no—
225C22×D13—22no—
226C22×D13—22no—
227C22×D13—28no—
228C22×D13—28no—
229C22×D13—28no—
230C22×D13—22no—
231C22×D13—22no—
232C22×D13—22no—
233C22×D13—22no—
234C22×D13—22no—
235C22×D13—22no—
236C22×D13—44no—
237C22×D13—44no—
238C22×D13—44no—
239C22×D13—44no—
240C22×D13#117116yescomplemented
241C22×D13C23×C414yes—
242C22×D13C23×C414yes—
243C22×D13C2×#4114yes—
244C22×D13C2×#4114yes—
245C2×C4×C13—28no—
246C2×C4×C13—28no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—24no—
256C2×C4×C13—24no—
257C2×C4×C13—48no—
258C2×C4×C13—48no—
259C2×C4×C13C4×D4116yes—
260C2×C4×C13C23×C414yes—
261C2×C4×C13C23×C414yes—
262C2×C4×C13C23×C414yes—
263C2×C4×C13C22×D414yes—
264C2×C4×C13C2×#4114yes—
265C2×Dic13—28no—
266C2×Dic13—28no—
267C2×Dic13—216no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13—48no—
278C2×Dic13C23×C414yes—
279C2×Dic13C23×C414yes—
280C2×Dic13C22×D418yes—
281D52—232no—
282C4×D13—232no—
283C4×D13—232no—
284C4×D13—432no—
285C23×D4—131no—
286C24×C4—131no—
287C24×C4—131no—
288C24×C4—132no—
289C2×C4×D4—1316no—
290C2×C4×D4—138no—
291C2×#117—138no—
292C2×#117—268no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—131no—
295C22×C4⋊C4—132no—
296C22×C4⋊C4—131no—
297C22×C4⋊C4—138no—
298C22×C4⋊C4—268no—
299C22×C4⋊C4C2×D1311yescharacteristic
300C22×C4⋊C4C2×D1311yescharacteristic
301C22×C22⋊C4—131no—
302C22×C22⋊C4—131no—
303C22×C22⋊C4—132no—
304C22×C22⋊C4—132no—
305C22×C22⋊C4—132no—
306C22×C42—132no—
307C22×C42—132no—
308C22×C42C2×D1311yescharacteristic
309#388—1316no—
310#387—1316no—
311#386—1316no—
312#382C2×D1318yescomplemented
313#380—138no—
314#380—138no—
315C4×C4⋊C4—138no—
316C4×C22⋊C4—1316no—
317C2×#95—132no—
318C2×#95—132no—
319C2×#95—132no—
320C2×#95C2×D1312yes—
321C2×#95C2×D1312yes—
322C22×C13C2×#11714yes—
323C22×C13C2×C4×D414yes—
324C22×C13#52014yes—
325C22×C13#54614yes—
326C22×C13#54814yes—
327C22×C13#55214yes—
328C22×C13#55314yes—
329C22×C13C24×C411yescharacteristic
330C22×C13C23×D411yescharacteristic
331C22×C13C22×#4111yescharacteristic
332C22×C13C22×#4111yescharacteristic
333C22×C13C22×#4111yescharacteristic
334C22×C13C2×H(5,𝔽2)11yescharacteristic
335C22×C13C2×2−1+411yescharacteristic
336C2×D13—232no—
337C2×D13—24no—
338C2×D13—24no—
339C2×D13—24no—
340C2×D13—24no—
341C2×D13—24no—
342C2×D13—24no—
343C2×D13—24no—
344C2×D13—24no—
345C2×D13—24no—
346C2×D13—416no—
347C2×D13—42no—
348C2×D13—42no—
349C2×D13—42no—
350C2×D13—42no—
351C2×D13C2×#11718yescomplemented
352C4×C13—24no—
353C4×C13—24no—
354C4×C13—44no—
355C4×C13—44no—
356C4×C13C2×C4×D418yes—
357Dic13—24no—
358Dic13—24no—
359Dic13—28no—
360Dic13—44no—
361C25—131no—
362C25—131no—
363C22×D4—138no—
364C22×D4—134no—
365C22×D4—264no—
366C22×D4—264no—
367C23×C4—131no—
368C23×C4—132no—
369C23×C4—131no—
370C23×C4—138no—
371C23×C4—138no—
372C23×C4—134no—
373C23×C4—134no—
374C23×C4—132no—
375C23×C4—138no—
376C23×C4—268no—
377C23×C4—268no—
378C23×C4—264no—
379C23×C4—264no—
380C23×C4—264no—
381C23×C4—264no—
382C23×C4—524no—
383C23×C4C22×D1312yes—
384C23×C4C22×D1312yes—
385C23×C4C22×D1311yescharacteristic
386C23×C4C22×D1311yescharacteristic
387C23×C4C22×D1311yescharacteristic
388C4×D4—1364no—
389#117—2632no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—138no—
393C2×C4⋊C4—138no—
394C2×C4⋊C4—134no—
395C2×C4⋊C4—134no—
396C2×C4⋊C4—138no—
397C2×C4⋊C4—134no—
398C2×C4⋊C4—2632no—
399C2×C4⋊C4—268no—
400C2×C4⋊C4—264no—
401C2×C4⋊C4C22×D1314yes—
402C2×C4⋊C4C22×D1314yes—
403C2×C22⋊C4—138no—
404C2×C22⋊C4—138no—
405C2×C22⋊C4—134no—
406C2×C22⋊C4—134no—
407C2×C22⋊C4—138no—
408C2×C22⋊C4—138no—
409C2×C22⋊C4—138no—
410C2×C22⋊C4—268no—
411C2×C22⋊C4—268no—
412C2×C22⋊C4—524no—
413C2×C42—138no—
414C2×C42—138no—
415C2×C42—268no—
416C2×C42—524no—
417C2×C42C4×D1318yescomplemented
418C2×C42C22×D1314yes—
419#95—138no—
420#95—138no—
421#95—138no—
422#95C22×D1318yes—
423#95C22×D1318yes—
424C2×C13#235218yescomplemented
425C2×C13C22×#11711yescharacteristic
426C2×C13C22×C4×D411yescharacteristic
427C2×C13C2×#52011yescharacteristic
428C2×C13C2×#54611yescharacteristic
429C2×C13C2×#54811yescharacteristic
430C2×C13C2×#55211yescharacteristic
431C2×C13C2×#55311yescharacteristic
432D13—28no—
433D13—44no—
434C24—134no—
435C24—134no—
436C24—134no—
437C24—132no—
438C24—134no—
439C24—132no—
440C24—262no—
441C24—262no—
442C24—262no—
443C24—262no—
444C24—262no—
445C24—262no—
446C24—262no—
447C24—262no—
448C24—262no—
449C24—262no—
450C24C23×D1311yescharacteristic
451C2×D4—1316no—
452C2×D4—2632no—
453C2×D4—268no—
454C2×D4—268no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—134no—
466C22×C4—134no—
467C22×C4—138no—
468C22×C4—132no—
469C22×C4—132no—
470C22×C4—134no—
471C22×C4—1316no—
472C22×C4—1316no—
473C22×C4—134no—
474C22×C4—2616no—
475C22×C4—2616no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—264no—
481C22×C4—264no—
482C22×C4—2632no—
483C22×C4—2632no—
484C22×C4—268no—
485C22×C4—268no—
486C22×C4—268no—
487C22×C4—268no—
488C22×C4—264no—
489C22×C4—264no—
490C22×C4—264no—
491C22×C4—528no—
492C22×C4—5232no—
493C22×C4C2×C4×D1314yes—
494C22×C4C2×C4×D1314yes—
495C22×C4C2×C4×D1314yes—
496C22×C4D4×D1314yes—
497C22×C4#613114yes—
498C22×C4C23×D1314yes—
499C22×C4C23×D1314yes—
500C22×C4C23×D1312yes—
501C22×C4C23×D1312yes—
502C22×C4C23×D1312yes—
503C4⋊C4—28no—
504C4⋊C4—28no—
505C4⋊C4—1316no—
506C4⋊C4—1316no—
507C4⋊C4—2616no—
508C4⋊C4—268no—
509C22⋊C4—1316no—
510C22⋊C4—1316no—
511C22⋊C4—2616no—
512C22⋊C4—2616no—
513C22⋊C4—528no—
514C42—2616no—
515C42—528no—
516C42C2×C4×D13116yescomplemented
517C13C2×#235211yescharacteristic, complemented, Sylow
518C23—1316no—
519C23—134no—
520C23—134no—
521C23—134no—
522C23—134no—
523C23—268no—
524C23—268no—
525C23—268no—
526C23—268no—
527C23—262no—
528C23—262no—
529C23—262no—
530C23—262no—
531C23—268no—
532C23—268no—
533C23—268no—
534C23—268no—
535C23—268no—
536C23—262no—
537C23—262no—
538C23—262no—
539C23—262no—
540C23—262no—
541C23—262no—
542C23—524no—
543C23—524no—
544C23—524no—
545C23—524no—
546C23C22×C4×D1312yes—
547C23C2×D4×D1312yes—
548C23C2×#613112yes—
549C23#41×D1312yes—
550C23#41×D1312yes—
551C23#8825612yes—
552C23#8825712yes—
553C23C24×D1311yescharacteristic
554D4—2632no—
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—48no—
568C2×C4—48no—
569C2×C4—134no—
570C2×C4—134no—
571C2×C4—138no—
572C2×C4—268no—
573C2×C4—268no—
574C2×C4—2616no—
575C2×C4—262no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—262no—
579C2×C4—264no—
580C2×C4—264no—
581C2×C4—2632no—
582C2×C4—2632no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—5232no—
587C2×C4—528no—
588C2×C4#88147116yes—
589C2×C4C22×C4×D1314yes—
590C2×C4C22×C4×D1314yes—
591C2×C4C22×C4×D1314yes—
592C2×C4C2×D4×D1314yes—
593C2×C4C2×#613114yes—
594C22—138no—
595C22—2632no—
596C22—264no—
597C22—264no—
598C22—264no—
599C22—264no—
600C22—264no—
601C22—264no—
602C22—264no—
603C22—264no—
604C22—264no—
605C22—5216no—
606C22—522no—
607C22—522no—
608C22—522no—
609C22—522no—
610C22C2×#8814714yes—
611C22D13×#11714yes—
612C22#1171922814yes—
613C22#1171938114yes—
614C22#1171938214yes—
615C22#1171939914yes—
616C22#1171940014yes—
617C22C23×C4×D1311yescharacteristic
618C22C22×D4×D1311yescharacteristic
619C22C22×#613111yescharacteristic
620C22C2×#41×D1311yescharacteristic
621C22C2×#41×D1311yescharacteristic
622C22C2×#8825611yescharacteristic
623C22C2×#8825711yescharacteristic
624C4—24no—
625C4—24no—
626C4—44no—
627C4—44no—
628C4—264no—
629C4—264no—
630C4—268no—
631C4—524no—
632C4C2×#8814718yes—
633C2—268no—
634C2—524no—
635C2#1311776218yesdirect product factor
636C2C2×D13×#11711yescharacteristic
637C2C22×#8814711yescharacteristic
638C2C2×#1171922811yescharacteristic
639C2C2×#1171938111yescharacteristic
640C2C2×#1171938211yescharacteristic
641C2C2×#1171939911yescharacteristic
642C2C2×#1171940011yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#382C2
socleC24×C13C24
prime radicalC23×D52C22
cosocleC23×C13C25
hypercenterC2×#382D13
hypocenterC13C2×#2352
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. C22×#88146C2semidirect
3. C22×C4⋊C4×D13C2semidirect
4. #13117762C2direct (N × H)
5. C2×#11718330C2semidirect
6. C2×#11718315C2semidirect
8. C2×#11718648C2semidirect
9. C2×#11718648C2semidirect
10. C2×C4×C4⋊Dic13C2semidirect
11. C2×#11718327C2semidirect
12. C2×C13×#382C2semidirect
32. C2×#88146C22semidirect
34. C2×C4⋊C4×D13C22semidirect
35. C2×C4×D52C4semidirect
37. C13×#382C22semidirect
43. #11718648C22semidirect
44. #11718648C22semidirect
45. C4×C4⋊Dic13C22semidirect
46. #11718330C22semidirect
47. #11718327C22semidirect
49. #11718315C22semidirect
73. C22×C4×D13C2×C4semidirect
81. C2×C42×C13C2×C4semidirect
87. C2×#6103C2×C4semidirect
94. C2×C4⋊Dic13C2×C4semidirect
95. C2×C4⋊Dic13D4semidirect
107. C4×D52C2×C4semidirect
182. C2×C4×D13C22×C4semidirect
185. C42×C13C22×C4semidirect
190. #6103C22×C4semidirect
192. C4⋊Dic13C22×C4semidirect
193. C4⋊Dic13C2×D4semidirect
204. C2×#382D13semidirect
240. C22×D13#117semidirect
312. #382C2×D13semidirect
351. C2×D13C2×#117semidirect
417. C2×C42C4×D13semidirect
424. C2×C13#2352semidirect
516. C42C2×C4×D13semidirect
517. C13C2×#2352semidirect
635. C2#13117762direct (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×#881462
C22×C4⋊C4×D132
#131177622
C2×#117183302
C2×#117183152
C2×#117183262
C2×#117186482
C2×C4×C4⋊Dic132
C2×#117183272
C2×C13×#3822
C2×#235213