Finite Group Databasebeta

← C2×#13118285 #16030874

Subgroups — C2×#13118285 #16030874

Order 3328.

3830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic, complemented
2C22×#88151C211yesmaximal, characteristic, complemented
3C22×C4×D52C211yesmaximal, characteristic
4C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
5#13118285C2116yesmaximal, direct product factor
6C2×#11718322C212yesmaximal, complemented
7C2×#11718655C212yesmaximal, complemented
8C2×#11718590C211yesmaximal, characteristic, complemented
9C2×#11718326C212yesmaximal
10C2×#11718648C211yesmaximal, characteristic, complemented
11C2×#11718648C212yesmaximal, complemented
12C2×C13×#389C211yesmaximal, characteristic, complemented
13C23×D52C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
15C23×C4×D13C2212yes—
16C23×C4×D13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×#6103C2212yes—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2212yes—
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2212yes—
31C22×#6101C2212yes—
32C2×#88151—28no—
33C2×#88151—28no—
34C2×#88151C2218yescomplemented
35C2×#88151C2218yescomplemented
36C2×C4⋊C4×D13—28no—
37C2×C4⋊C4×D13C2218yescomplemented
38C2×C4×D52—28no—
39C2×C4×D52C2218yes—
40C13×#389C2218yescomplemented
41C2×C13×#95C2212yes—
42C2×#88071C2212yes—
43C2×#88071C2212yes—
44C2×#88071C2212yes—
45#11718655C22116yescomplemented
46#11718648C2218yescomplemented
47#11718648C22116yescomplemented
48#11718590C2218yescomplemented
49#11718326C22116yes—
50#11718322C22116yescomplemented
51C24×D13C2311yescharacteristic
52C24×D13C2311yescharacteristic
53C23×C4×C13C2312yes—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×Dic13C2312yes—
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2312yes—
61C23×Dic13C2311yescharacteristic
62C22×D52—24no—
63C22×D52—24no—
64C22×D52Q818yescomplemented
65C22×D52C2314yes—
66C22×C4×D13—24no—
67C22×C4×D13—24no—
68C22×C4×D13—28no—
69C22×C4×D13—24no—
70C22×C4×D13—28no—
71C22×C4×D13—24no—
72C22×C4×D13—24no—
73C22×C4×D13—44no—
74C22×C4×D13D418yes—
75C22×C4×D13C2314yes—
76C22×C4×D13C2318yes—
77C22×C4×D13C2314yes—
78C22×Dic26—24no—
79C22×Dic26—24no—
80C22×Dic26—24no—
81C22×Dic26C2314yes—
82C2×C13×C4⋊C4—24no—
83C2×C13×C4⋊C4—44no—
84C2×C13×C4⋊C4D418yescomplemented
85C2×C13×C4⋊C4C2314yes—
86C2×C13×C4⋊C4C2318yes—
87C2×C13×C4⋊C4C2314yes—
88C2×C42×C13—24no—
89C2×C42×C13C2314yes—
90C2×#6103—24no—
91C2×#6103—28no—
92C2×#6103—28no—
93C2×#6103—24no—
94C2×#6103—44no—
95C2×#6103C2314yes—
96C2×#6103C2314yes—
97C2×#6103C2318yes—
98C2×#6103C2318yes—
99C2×#6103C2318yes—
100C2×C4⋊Dic13—24no—
101C2×C4⋊Dic13—28no—
102C2×C4⋊Dic13—24no—
103C2×C4⋊Dic13—28no—
104C2×C4⋊Dic13C2314yes—
105C2×C4⋊Dic13C2314yes—
106C2×C4⋊Dic13C2318yes—
107C2×C4⋊Dic13C2318yes—
108C2×#6101—28no—
109C2×#6101C2318yes—
110#88151—232no—
111#88151—232no—
112C4⋊C4×D13—232no—
113C4×D52—232no—
114C13×#95C2318yes—
115#88071C2318yes—
116#88071C2318yes—
117#88071C2318yes—
118C2×#2417—131nomaximal, Sylow
119C24×C13C2411yescharacteristic
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13—22no—
128C23×D13—22no—
129C23×D13—22no—
130C23×D13C2×D414yes—
131C23×D13C2×Q814yes—
132C23×D13C2×Q814yes—
133C23×D13#4114yes—
134C23×D13C2412yes—
135C23×D13C2412yes—
136C22×C4×C13—22no—
137C22×C4×C13—24no—
138C22×C4×C13—22no—
139C22×C4×C13—24no—
140C22×C4×C13—24no—
141C22×C4×C13—22no—
142C22×C4×C13—24no—
143C22×C4×C13—22no—
144C22×C4×C13—24no—
145C22×C4×C13—22no—
146C22×C4×C13C2×D418yes—
147C22×C4×C13C2×D414yes—
148C22×C4×C13C2×D414yes—
149C22×C4×C13C2×Q814yes—
150C22×C4×C13#4114yes—
151C22×C4×C13C2412yes—
152C22×C4×C13C2414yes—
153C22×C4×C13C2414yes—
154C22×C4×C13C2412yes—
155C22×C4×C13C2412yes—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—24no—
159C22×Dic13—22no—
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13—22no—
163C22×Dic13—24no—
164C22×Dic13—22no—
165C22×Dic13—24no—
166C22×Dic13—24no—
167C22×Dic13C2×D414yes—
168C22×Dic13C2414yes—
169C22×Dic13C2412yes—
170C22×Dic13C2414yes—
171C22×Dic13C2412yes—
172C2×D52—232no—
173C2×D52—28no—
174C2×D52—28no—
175C2×D52C2×Q8116yescomplemented
176C2×C4×D13—232no—
177C2×C4×D13—28no—
178C2×C4×D13—28no—
179C2×C4×D13—216no—
180C2×C4×D13—28no—
181C2×C4×D13—216no—
182C2×C4×D13—28no—
183C2×C4×D13—28no—
184C2×C4×D13—48no—
185C2×C4×D13—432no—
186C2×C4×D13—416no—
187C2×C4×D13C2×D4116yes—
188C2×Dic26—28no—
189C2×Dic26—28no—
190C2×Dic26—28no—
191C2×Dic26—416no—
192C13×C4⋊C4—28no—
193C13×C4⋊C4—48no—
194C13×C4⋊C4C2×D4116yescomplemented
195C42×C13—28no—
196#6103—28no—
197#6103—216no—
198#6103—216no—
199#6103—28no—
200#6103—48no—
201C4⋊Dic13—28no—
202C4⋊Dic13—216no—
203C4⋊Dic13—28no—
204C4⋊Dic13—216no—
205#6101—216no—
206C22×C22⋊Q8—131no—
207C22×C22⋊Q8—131no—
208C22×C4×D4—131no—
209C23×C4⋊C4—131no—
210#2417—1316no—
211C2×#398—132no—
212C2×#396—132no—
213C2×#391—131no—
214C2×#389D1311yescharacteristic, complemented
215C2×#386—132no—
216C2×#380—132no—
217C2×#380—131no—
218C23×C13C22×D412yes—
219C23×C13C22×D412yes—
220C23×C13C22×Q812yes—
221C23×C13C2×#4112yes—
222C23×C13C2×#4112yes—
223C23×C13H(5,𝔽2)12yes—
224C23×C132−1+412yes—
225C23×C13C2511yescharacteristic
226C22×D13—28no—
227C22×D13—28no—
228C22×D13—28no—
229C22×D13—28no—
230C22×D13—28no—
231C22×D13—28no—
232C22×D13—22no—
233C22×D13—22no—
234C22×D13—22no—
235C22×D13—22no—
236C22×D13—28no—
237C22×D13—28no—
238C22×D13—28no—
239C22×D13—22no—
240C22×D13—22no—
241C22×D13—22no—
242C22×D13—22no—
243C22×D13—22no—
244C22×D13—22no—
245C22×D13—44no—
246C22×D13—44no—
247C22×D13—44no—
248C22×D13—44no—
249C22×D13C22⋊Q8116yescomplemented
250C22×D13C22×D414yes—
251C22×D13C22×Q814yes—
252C22×D13C22×Q814yes—
253C22×D13C2×#4114yes—
254C2×C4×C13—28no—
255C2×C4×C13—216no—
256C2×C4×C13—22no—
257C2×C4×C13—24no—
258C2×C4×C13—22no—
259C2×C4×C13—24no—
260C2×C4×C13—24no—
261C2×C4×C13—22no—
262C2×C4×C13—24no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—24no—
266C2×C4×C13—48no—
267C2×C4×C13—44no—
268C2×C4×C13#121116yes—
269C2×C4×C13C22×D418yes—
270C2×C4×C13C22×D414yes—
271C2×C4×C13C22×D414yes—
272C2×C4×C13C22×Q814yes—
273C2×C4×C13C2×#4114yes—
274C2×Dic13—28no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—24no—
278C2×Dic13—22no—
279C2×Dic13—24no—
280C2×Dic13—24no—
281C2×Dic13—22no—
282C2×Dic13—24no—
283C2×Dic13—22no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—48no—
287C2×Dic13—44no—
288C2×Dic13—48no—
289C2×Dic13C22×D414yes—
290D52—232no—
291C4×D13—232no—
292C4×D13—432no—
293C4×D13—416no—
294Dic26—416no—
295C23×Q8—131no—
296C23×D4—131no—
297C24×C4—131no—
298C24×C4—131no—
299C24×C4—132no—
300C2×C22⋊Q8—138no—
301C2×C22⋊Q8—138no—
302C2×C22⋊Q8—268no—
303C2×C22⋊Q8—268no—
304C2×C4×D4—138no—
305C2×C4×D4—268no—
306C22×C4⋊C4—132no—
307C22×C4⋊C4—132no—
308C22×C4⋊C4—131no—
309C22×C4⋊C4—132no—
310C22×C4⋊C4—131no—
311C22×C4⋊C4—138no—
312C22×C4⋊C4—268no—
313C22×C4⋊C4C2×D1311yescharacteristic
314C22×C4⋊C4C2×D1312yes—
315C22×C4⋊C4C2×D1311yescharacteristic
316C22×C22⋊C4—131no—
317C22×C22⋊C4—132no—
318C22×C22⋊C4—131no—
319C22×C22⋊C4—132no—
320C22×C22⋊C4—132no—
321C22×C42C2×D1311yescharacteristic
322#398—1316no—
323#396—1316no—
324#391—138no—
325#389C2×D1318yescomplemented
326#386—1316no—
327#380—138no—
328#380—1316no—
329C2×#95—132no—
330C2×#95—132no—
331C2×#95—132no—
332C2×#95C2×D1312yes—
333C22×C13C2×#12114yes—
334C22×C13C2×C22⋊Q814yes—
335C22×C13#53714yes—
336C22×C13#54614yes—
337C22×C13D4×Q814yes—
338C22×C13#55214yes—
339C22×C13#55414yes—
340C22×C13C23×D411yescharacteristic
341C22×C13C23×D411yescharacteristic
342C22×C13C23×Q811yescharacteristic
343C22×C13C22×#4111yescharacteristic
344C22×C13C22×#4111yescharacteristic
345C22×C13C2×H(5,𝔽2)11yescharacteristic
346C22×C13C2×2−1+411yescharacteristic
347C2×D13—24no—
348C2×D13—232no—
349C2×D13—24no—
350C2×D13—24no—
351C2×D13—24no—
352C2×D13—24no—
353C2×D13—24no—
354C2×D13—24no—
355C2×D13—24no—
356C2×D13—24no—
357C2×D13—42no—
358C2×D13—416no—
359C2×D13—42no—
360C2×D13—42no—
361C2×D13—42no—
362C2×D13C2×C22⋊Q818yescomplemented
363C4×C13—24no—
364C4×C13—28no—
365C4×C13—44no—
366C4×C13—42no—
367C4×C13C2×#12118yes—
368Dic13—24no—
369Dic13—44no—
370Dic13—42no—
371Dic13—44no—
372C25—131no—
373C25—131no—
374C22×Q8—134no—
375C22×Q8—264no—
376C22×Q8—264no—
377C22×Q8—264no—
378C22×D4—138no—
379C22×D4—134no—
380C22×D4—264no—
381C22×D4—264no—
382C23×C4—131no—
383C23×C4—138no—
384C23×C4—134no—
385C23×C4—132no—
386C23×C4—131no—
387C23×C4—132no—
388C23×C4—134no—
389C23×C4—138no—
390C23×C4—268no—
391C23×C4—264no—
392C23×C4—264no—
393C23×C4—268no—
394C23×C4—264no—
395C23×C4—264no—
396C23×C4—264no—
397C23×C4—524no—
398C23×C4C22×D1312yes—
399C23×C4C22×D1311yescharacteristic
400C23×C4C22×D1312yes—
401C23×C4C22×D1311yescharacteristic
402C23×C4C22×D1311yescharacteristic
403C22⋊Q8—2632no—
404C22⋊Q8—2632no—
405C4×D4—2632no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—138no—
409C2×C4⋊C4—134no—
410C2×C4⋊C4—134no—
411C2×C4⋊C4—138no—
412C2×C4⋊C4—138no—
413C2×C4⋊C4—264no—
414C2×C4⋊C4—268no—
415C2×C4⋊C4—268no—
416C2×C4⋊C4—264no—
417C2×C4⋊C4—268no—
418C2×C4⋊C4—2632no—
419C2×C4⋊C4D5218yescomplemented
420C2×C4⋊C4C22×D1314yes—
421C2×C4⋊C4C22×D1318yes—
422C2×C4⋊C4C22×D1314yes—
423C2×C22⋊C4—134no—
424C2×C22⋊C4—134no—
425C2×C22⋊C4—138no—
426C2×C22⋊C4—138no—
427C2×C22⋊C4—138no—
428C2×C22⋊C4—264no—
429C2×C22⋊C4—264no—
430C2×C22⋊C4—268no—
431C2×C22⋊C4—268no—
432C2×C22⋊C4—524no—
433C2×C42—24no—
434C2×C42C22×D1314yes—
435#95—138no—
436#95—138no—
437#95—138no—
438#95C22×D1318yes—
439C2×C13#241718yescomplemented
440C2×C13C22×#12111yescharacteristic
441C2×C13C22×C22⋊Q811yescharacteristic
442C2×C13C2×#53711yescharacteristic
443C2×C13C2×#54611yescharacteristic
444C2×C13C2×D4×Q811yescharacteristic
445C2×C13C2×#55211yescharacteristic
446C2×C13C2×#55411yescharacteristic
447D13—28no—
448D13—44no—
449C24—134no—
450C24—134no—
451C24—134no—
452C24—132no—
453C24—134no—
454C24—132no—
455C24—262no—
456C24—262no—
457C24—262no—
458C24—262no—
459C24—262no—
460C24—262no—
461C24—262no—
462C24—262no—
463C24—262no—
464C24—262no—
465C24C23×D1311yescharacteristic
466C2×Q8—268no—
467C2×Q8—268no—
468C2×Q8—268no—
469C2×Q8—5216no—
470C2×D4—1316no—
471C2×D4—268no—
472C2×D4—2632no—
473C2×D4—268no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—134no—
485C22×C4—132no—
486C22×C4—1316no—
487C22×C4—134no—
488C22×C4—134no—
489C22×C4—132no—
490C22×C4—2616no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—2632no—
494C22×C4—268no—
495C22×C4—268no—
496C22×C4—264no—
497C22×C4—262no—
498C22×C4—264no—
499C22×C4—262no—
500C22×C4—264no—
501C22×C4—264no—
502C22×C4—262no—
503C22×C4—264no—
504C22×C4—264no—
505C22×C4—2616no—
506C22×C4—268no—
507C22×C4—268no—
508C22×C4—268no—
509C22×C4—528no—
510C22×C4—5232no—
511C22×C4—5216no—
512C22×C4C2×D5218yes—
513C22×C4C2×D5214yes—
514C22×C4D4×D1314yes—
515C22×C4Q8×D1314yes—
516C22×C4#613114yes—
517C22×C4C23×D1312yes—
518C22×C4C23×D1314yes—
519C22×C4C23×D1314yes—
520C22×C4C23×D1312yes—
521C22×C4C23×D1312yes—
522C4⋊C4—28no—
523C4⋊C4—48no—
524C4⋊C4—268no—
525C4⋊C4—2616no—
526C4⋊C4—2616no—
527C4⋊C4—268no—
528C4⋊C4—2616no—
529C4⋊C4C2×D52116yescomplemented
530C22⋊C4—268no—
531C22⋊C4—268no—
532C22⋊C4—2616no—
533C22⋊C4—2616no—
534C22⋊C4—528no—
535C42—28no—
536C13C2×#241711yescharacteristic, complemented, Sylow
537C23—1316no—
538C23—134no—
539C23—134no—
540C23—134no—
541C23—134no—
542C23—268no—
543C23—268no—
544C23—268no—
545C23—268no—
546C23—268no—
547C23—262no—
548C23—262no—
549C23—262no—
550C23—262no—
551C23—268no—
552C23—268no—
553C23—268no—
554C23—268no—
555C23—262no—
556C23—262no—
557C23—262no—
558C23—262no—
559C23—262no—
560C23—262no—
561C23—524no—
562C23—524no—
563C23—524no—
564C23—524no—
565C23C22×D5212yes—
566C23C2×D4×D1312yes—
567C23#8825112yes—
568C23C2×Q8×D1312yes—
569C23C2×#613112yes—
570C23#41×D1312yes—
571C23#8825712yes—
572C23C24×D1311yescharacteristic
573Q8—5216no—
574D4—2632no—
575C2×C4—216no—
576C2×C4—28no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—44no—
588C2×C4—48no—
589C2×C4—134no—
590C2×C4—268no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—2632no—
594C2×C4—264no—
595C2×C4—264no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—264no—
599C2×C4—264no—
600C2×C4—262no—
601C2×C4—264no—
602C2×C4—264no—
603C2×C4—5232no—
604C2×C4—524no—
605C2×C4—528no—
606C2×C4—528no—
607C2×C4—5216no—
608C2×C4#88149116yes—
609C2×C4C22×D5218yes—
610C2×C4C22×D5214yes—
611C2×C4C2×D4×D1314yes—
612C2×C4C2×Q8×D1314yes—
613C2×C4C2×#613114yes—
614C22—138no—
615C22—2632no—
616C22—264no—
617C22—264no—
618C22—264no—
619C22—264no—
620C22—264no—
621C22—264no—
622C22—264no—
623C22—264no—
624C22—264no—
625C22—5216no—
626C22—522no—
627C22—522no—
628C22—522no—
629C22—522no—
630C22C2×#8814914yes—
631C22#1171925914yes—
632C22Q8×D5214yes—
633C22#1171931314yes—
634C22D13×C22⋊Q814yes—
635C22#1171939914yes—
636C22#1171943514yes—
637C22C23×D5211yescharacteristic
638C22C22×D4×D1311yescharacteristic
639C22C2×#8825111yescharacteristic
640C22C22×Q8×D1311yescharacteristic
641C22C22×#613111yescharacteristic
642C22C2×#41×D1311yescharacteristic
643C22C2×#8825711yescharacteristic
644C4—28no—
645C4—24no—
646C4—42no—
647C4—44no—
648C4—264no—
649C4—524no—
650C4—522no—
651C4—524no—
652C4C2×#8814918yes—
653C2—268no—
654C2—524no—
655C2#1311828518yesdirect product factor
656C2C22×#8814911yescharacteristic
657C2C2×D13×C22⋊Q811yescharacteristic
658C2C2×#1171931311yescharacteristic
659C2C2×#1171925911yescharacteristic
660C2C2×Q8×D5211yescharacteristic
661C2C2×#1171939911yescharacteristic
662C2C2×#1171943511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#389C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#389D13
hypocenterC13C2×#2417
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#88151C2semidirect
2. C22×#88151C2semidirect
4. C22×C4⋊C4×D13C2semidirect
5. #13118285C2direct (N × H)
6. C2×#11718322C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718590C2semidirect
10. C2×#11718648C2semidirect
11. C2×#11718648C2semidirect
12. C2×C13×#389C2semidirect
34. C2×#88151C22semidirect
35. C2×#88151C22semidirect
37. C2×C4⋊C4×D13C22semidirect
40. C13×#389C22semidirect
45. #11718655C22semidirect
46. #11718648C22semidirect
47. #11718648C22semidirect
48. #11718590C22semidirect
50. #11718322C22semidirect
64. C22×D52Q8semidirect
84. C2×C13×C4⋊C4D4semidirect
175. C2×D52C2×Q8semidirect
194. C13×C4⋊C4C2×D4semidirect
214. C2×#389D13semidirect
249. C22×D13C22⋊Q8semidirect
325. #389C2×D13semidirect
362. C2×D13C2×C22⋊Q8semidirect
419. C2×C4⋊C4D52semidirect
439. C2×C13#2417semidirect
529. C4⋊C4C2×D52semidirect
536. C13C2×#2417semidirect
655. C2#13118285direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881512
C22×C4×D522
C22×C4⋊C4×D132
#131182852
C2×#117183222
C2×#117186552
C2×#117185902
C2×#117183262
C2×#117186482
C2×C13×#3892
C2×#241713