Finite Group Databasebeta

← C2×#13118289 #16030876

Subgroups — C2×#13118289 #16030876

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×#88178C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D13C211yesmaximal, characteristic
4C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
5#13118289C2116yesmaximal, direct product factor
6C2×#11718318C212yesmaximal, complemented
7C2×#11718609C212yesmaximal, complemented
8C2×#11718635C211yesmaximal, characteristic, complemented
9C2×#11718634C211yesmaximal, characteristic, complemented
10C2×#11718617C212yesmaximal
11C2×#11718328C212yesmaximal, complemented
12C2×C13×#380C211yesmaximal, characteristic, complemented
13C24×C4×C13C2211yescharacteristic
14C23×C22⋊D13C2211yescharacteristic
15C23×C4×D13C2212yes—
16C23×C4×D13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2212yes—
21C22×C22⋊Dic13C2212yes—
22C22×C22⋊Dic13C2211yescharacteristic
23C2×C4×C22⋊D13—28no—
24C2×C4×C22⋊D13C2218yes—
25C22×#6103C2211yescharacteristic
26C22×#6103C2212yes—
27C22×C4⋊Dic13C2212yes—
28C22×C4⋊Dic13C2211yescharacteristic
29C2×#88178—28no—
30C2×#88178C2218yescomplemented
31C22×#6101C2212yes—
32C22×#6101C2212yes—
33C22×#6101C2211yescharacteristic
34C22×#6101C2212yes—
35C22×C4×Dic13C2211yescharacteristic
36C2×#88151—28no—
37C2×#88151C2218yescomplemented
38C2×C4⋊C4×D13—28no—
39C2×C4⋊C4×D13C2218yescomplemented
40C13×#380C2218yescomplemented
41C2×C13×#95C2212yes—
42C2×#88071C2212yes—
43C2×#88071C2212yes—
44C2×#88071C2212yes—
45#11718635C2218yescomplemented
46#11718634C2218yescomplemented
47#11718617C22116yes—
48#11718609C22116yescomplemented
49#11718328C22116yescomplemented
50#11718318C22116yescomplemented
51C25×C13C2311yescharacteristic
52C24×D13C2311yescharacteristic
53C23×C4×C13—24no—
54C23×C4×C13—24no—
55C23×C4×C13—24no—
56C23×C4×C13C2314yes—
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2312yes—
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C22×C22⋊D13—24no—
62C22×C22⋊D13—24no—
63C22×C22⋊D13Q818yescomplemented
64C22×C22⋊D13C2314yes—
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2312yes—
69C23×Dic13C2311yescharacteristic
70C22×C4×D13—24no—
71C22×C4×D13—24no—
72C22×C4×D13—28no—
73C22×C4×D13—28no—
74C22×C4×D13—44no—
75C22×C4×D13D418yes—
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—24no—
84C2×C13×C4⋊C4C2314yes—
85C2×C13×C4⋊C4C2314yes—
86C2×C13×C22⋊C4—44no—
87C2×C13×C22⋊C4C2318yes—
88C2×C22⋊Dic13—28no—
89C2×C22⋊Dic13—24no—
90C2×C22⋊Dic13C2318yes—
91C2×C22⋊Dic13C2314yes—
92C4×C22⋊D13—232no—
93C2×#6103—28no—
94C2×#6103—24no—
95C2×#6103C2318yes—
96C2×#6103C2314yes—
97C2×C4⋊Dic13—28no—
98C2×C4⋊Dic13D418yescomplemented
99C2×C4⋊Dic13C2318yes—
100C2×C4⋊Dic13C2314yes—
101#88178—232no—
102C2×#6101—28no—
103C2×#6101—28no—
104C2×#6101—24no—
105C2×#6101—44no—
106C2×#6101C2318yes—
107C2×#6101C2318yes—
108C2×#6101C2314yes—
109C2×#6101C2318yes—
110C2×C4×Dic13—24no—
111C2×C4×Dic13C2314yes—
112#88151—232no—
113C4⋊C4×D13—232no—
114C13×#95C2318yes—
115#88071C2318yes—
116#88071C2318yes—
117#88071C2318yes—
118C2×#2417—131nomaximal, Sylow
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—22no—
122C24×C13—22no—
123C24×C13—22no—
124C24×C13—22no—
125C24×C13C2×Q814yes—
126C24×C13C2412yes—
127C24×C13C2411yescharacteristic
128C23×D13—22no—
129C23×D13—22no—
130C23×D13—22no—
131C23×D13—22no—
132C23×D13C2×D414yes—
133C23×D13C2×Q814yes—
134C23×D13#4114yes—
135C23×D13C2412yes—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13—24no—
141C22×C4×C13—22no—
142C22×C4×C13—24no—
143C22×C4×C13—24no—
144C22×C4×C13—24no—
145C22×C4×C13—28no—
146C22×C4×C13—28no—
147C22×C4×C13—28no—
148C22×C4×C13—416no—
149C22×C4×C13C2×D414yes—
150C22×C4×C13C2×D414yes—
151C22×C4×C13#4114yes—
152C22×C4×C13C2414yes—
153C22×C4×C13C2414yes—
154C22×C4×C13C2412yes—
155C22×C4×C13C2412yes—
156C2×C22⋊D13—232no—
157C2×C22⋊D13—28no—
158C2×C22⋊D13—28no—
159C2×C22⋊D13C2×Q8116yescomplemented
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—24no—
164C22×Dic13—22no—
165C22×Dic13—24no—
166C22×Dic13—22no—
167C22×Dic13—24no—
168C22×Dic13—24no—
169C22×Dic13—24no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13C2×D418yes—
173C22×Dic13C2×D414yes—
174C22×Dic13C2×Q814yes—
175C22×Dic13C2412yes—
176C22×Dic13C2414yes—
177C22×Dic13C2414yes—
178C22×Dic13C2412yes—
179C22×Dic13C2412yes—
180C2×C4×D13—232no—
181C2×C4×D13—28no—
182C2×C4×D13—28no—
183C2×C4×D13—216no—
184C2×C4×D13—216no—
185C2×C4×D13—48no—
186C2×C4×D13—432no—
187C2×C4×D13C2×D4116yes—
188C2×Dic26—28no—
189C2×Dic26—28no—
190C2×Dic26—28no—
191C2×Dic26—416no—
192C13×C4⋊C4—28no—
193C13×C4⋊C4—28no—
194C13×C22⋊C4—48no—
195C22⋊Dic13—216no—
196C22⋊Dic13—28no—
197#6103—216no—
198#6103—28no—
199C4⋊Dic13—216no—
200C4⋊Dic13C2×D4116yescomplemented
201#6101—216no—
202#6101—216no—
203#6101—28no—
204#6101—48no—
205C4×Dic13—28no—
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×#389—131no—
215C2×#386—132no—
216C2×#380—132no—
217C2×#380D1311yescharacteristic, complemented
218C23×C13—28no—
219C23×C13—28no—
220C23×C13—28no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—44no—
228C23×C13—44no—
229C23×C13—44no—
230C23×C13—44no—
231C23×C13C22×D412yes—
232C23×C13C22×D412yes—
233C23×C13C22×Q814yes—
234C23×C13C22×Q812yes—
235C23×C13C2×#4112yes—
236C23×C13C2×#4112yes—
237C23×C13H(5,𝔽2)12yes—
238C23×C132−1+412yes—
239C23×C13C2511yescharacteristic
240C22×D13—28no—
241C22×D13—28no—
242C22×D13—28no—
243C22×D13—28no—
244C22×D13—28no—
245C22×D13—28no—
246C22×D13—22no—
247C22×D13—22no—
248C22×D13—22no—
249C22×D13—22no—
250C22×D13C22⋊Q8116yescomplemented
251C22×D13C22×D414yes—
252C22×D13C22×Q814yes—
253C22×D13C2×#4114yes—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—24no—
257C2×C4×C13—24no—
258C2×C4×C13—24no—
259C2×C4×C13—22no—
260C2×C4×C13—24no—
261C2×C4×C13—24no—
262C2×C4×C13—24no—
263C2×C4×C13—44no—
264C2×C4×C13—48no—
265C2×C4×C13—48no—
266C2×C4×C13—416no—
267C2×C4×C13#121116yes—
268C2×C4×C13C22×D414yes—
269C2×C4×C13C22×D414yes—
270C2×C4×C13C2×#4114yes—
271C22⋊D13—232no—
272C2×Dic13—28no—
273C2×Dic13—28no—
274C2×Dic13—216no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—24no—
279C2×Dic13—22no—
280C2×Dic13—24no—
281C2×Dic13—22no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—22no—
286C2×Dic13—22no—
287C2×Dic13—48no—
288C2×Dic13—44no—
289C2×Dic13C22×D418yes—
290C2×Dic13C22×D414yes—
291C2×Dic13C22×Q814yes—
292C4×D13—232no—
293C4×D13—432no—
294Dic26—416no—
295C23×Q8—131no—
296C23×D4—131no—
297C24×C4—131no—
298C24×C4—132no—
299C24×C4C2×D1311yescharacteristic
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—131no—
307C22×C4⋊C4—132no—
308C22×C4⋊C4—131no—
309C22×C4⋊C4—132no—
310C22×C4⋊C4—132no—
311C22×C4⋊C4—132no—
312C22×C4⋊C4—138no—
313C22×C4⋊C4—268no—
314C22×C4⋊C4C2×D1311yescharacteristic
315C22×C4⋊C4C2×D1311yescharacteristic
316C22×C22⋊C4—131no—
317C22×C22⋊C4—132no—
318C22×C22⋊C4—131no—
319C22×C22⋊C4—132no—
320C22×C22⋊C4C2×D1312yes—
321C22×C42—131no—
322#398—1316no—
323#396—1316no—
324#391—138no—
325#389—138no—
326#386—1316no—
327#380—1316no—
328#380C2×D1318yescomplemented
329C2×#95—132no—
330C2×#95—132no—
331C2×#95—132no—
332C2×#95C2×D1312yes—
333C22×C13—24no—
334C22×C13—24no—
335C22×C13—24no—
336C22×C13—42no—
337C22×C13—416no—
338C22×C13—42no—
339C22×C13—42no—
340C22×C13—42no—
341C22×C13C2×#12114yes—
342C22×C13C2×C22⋊Q814yes—
343C22×C13#53714yes—
344C22×C13#54614yes—
345C22×C13D4×Q814yes—
346C22×C13#55214yes—
347C22×C13#55414yes—
348C22×C13C23×D411yescharacteristic
349C22×C13C23×D411yescharacteristic
350C22×C13C23×Q811yescharacteristic
351C22×C13C22×#4111yescharacteristic
352C22×C13C22×#4111yescharacteristic
353C22×C13C2×H(5,𝔽2)11yescharacteristic
354C22×C13C2×2−1+411yescharacteristic
355C2×D13—24no—
356C2×D13—232no—
357C2×D13—24no—
358C2×D13—24no—
359C2×D13—24no—
360C2×D13—24no—
361C2×D13—24no—
362C2×D13C2×C22⋊Q818yescomplemented
363C4×C13—42no—
364C4×C13—44no—
365C4×C13—44no—
366C4×C13C2×#12118yes—
367Dic13—24no—
368Dic13—24no—
369Dic13—28no—
370Dic13—44no—
371Dic13—42no—
372C25—131no—
373C25C22×D1311yescharacteristic
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—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—131no—
386C23×C4—132no—
387C23×C4—131no—
388C23×C4—138no—
389C23×C4—134no—
390C23×C4—132no—
391C23×C4—131no—
392C23×C4—138no—
393C23×C4—268no—
394C23×C4—268no—
395C23×C4—264no—
396C23×C4—264no—
397C23×C4—524no—
398C23×C4C22×D1314yes—
399C23×C4C22×D1312yes—
400C23×C4C22×D1311yescharacteristic
401C23×C4C22×D1312yes—
402C23×C4C22×D1311yescharacteristic
403C22⋊Q8—2632no—
404C22⋊Q8—2632no—
405C4×D4—2632no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—138no—
409C2×C4⋊C4—134no—
410C2×C4⋊C4—138no—
411C2×C4⋊C4—134no—
412C2×C4⋊C4—138no—
413C2×C4⋊C4—138no—
414C2×C4⋊C4—138no—
415C2×C4⋊C4—2632no—
416C2×C4⋊C4—268no—
417C2×C4⋊C4—264no—
418C2×C4⋊C4—268no—
419C2×C4⋊C4—268no—
420C2×C4⋊C4—524no—
421C2×C4⋊C4C22×D1314yes—
422C2×C4⋊C4C22×D1314yes—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—134no—
425C2×C22⋊C4—138no—
426C2×C22⋊C4—134no—
427C2×C22⋊C4—138no—
428C2×C22⋊C4—264no—
429C2×C22⋊C4—268no—
430C2×C22⋊C4—264no—
431C2×C22⋊C4—268no—
432C2×C22⋊C4C22×D1318yes—
433C2×C42—134no—
434C2×C42—264no—
435#95—138no—
436#95—138no—
437#95—138no—
438#95C22×D1318yes—
439C2×C13—44no—
440C2×C13#241718yescomplemented
441C2×C13C22×#12111yescharacteristic
442C2×C13C22×C22⋊Q811yescharacteristic
443C2×C13C2×#53711yescharacteristic
444C2×C13C2×#54611yescharacteristic
445C2×C13C2×D4×Q811yescharacteristic
446C2×C13C2×#55211yescharacteristic
447C2×C13C2×#55411yescharacteristic
448D13—28no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—134no—
456C24—134no—
457C24—134no—
458C24—132no—
459C24—262no—
460C24—262no—
461C24—262no—
462C24—262no—
463C24Q8×D1314yes—
464C24C23×D1312yes—
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—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—416no—
487C22×C4—138no—
488C22×C4—134no—
489C22×C4—134no—
490C22×C4—132no—
491C22×C4—134no—
492C22×C4—132no—
493C22×C4—1316no—
494C22×C4—132no—
495C22×C4—134no—
496C22×C4—2616no—
497C22×C4—2616no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—264no—
502C22×C4—264no—
503C22×C4—262no—
504C22×C4—2632no—
505C22×C4—268no—
506C22×C4—268no—
507C22×C4—264no—
508C22×C4—262no—
509C22×C4—264no—
510C22×C4—264no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—528no—
514C22×C4—5232no—
515C22×C4#612714yes—
516C22×C4D4×D1314yes—
517C22×C4D4×D1314yes—
518C22×C4C23×D1314yes—
519C22×C4C23×D1314yes—
520C22×C4C23×D1312yes—
521C22×C4C23×D1312yes—
522C4⋊C4—28no—
523C4⋊C4—28no—
524C4⋊C4—1316no—
525C4⋊C4—2616no—
526C4⋊C4—268no—
527C4⋊C4—2616no—
528C4⋊C4—2616no—
529C4⋊C4—528no—
530C22⋊C4—48no—
531C22⋊C4—268no—
532C22⋊C4—2616no—
533C22⋊C4—268no—
534C22⋊C4—2616no—
535C42—268no—
536C13C2×#241711yescharacteristic, complemented, Sylow
537C23—28no—
538C23—28no—
539C23—28no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—44no—
547C23—44no—
548C23—44no—
549C23—44no—
550C23—1316no—
551C23—134no—
552C23—134no—
553C23—134no—
554C23—268no—
555C23—268no—
556C23—268no—
557C23—268no—
558C23—268no—
559C23—268no—
560C23—262no—
561C23—262no—
562C23—262no—
563C23—262no—
564C23C2×#612712yes—
565C23C2×D4×D1312yes—
566C23C2×D4×D1312yes—
567C23#8825112yes—
568C23C2×Q8×D1314yes—
569C23C2×Q8×D1312yes—
570C23#41×D1312yes—
571C23#8825712yes—
572C23C24×D1311yescharacteristic
573Q8—5216no—
574D4—2632no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—48no—
586C2×C4—48no—
587C2×C4—416no—
588C2×C4—138no—
589C2×C4—134no—
590C2×C4—134no—
591C2×C4—268no—
592C2×C4—2616no—
593C2×C4—268no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—264no—
598C2×C4—264no—
599C2×C4—262no—
600C2×C4—2632no—
601C2×C4—264no—
602C2×C4—262no—
603C2×C4—264no—
604C2×C4—264no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—5232no—
608C2×C4—528no—
609C2×C4—524no—
610C2×C4#88138116yes—
611C2×C4C2×#612714yes—
612C2×C4C2×D4×D1314yes—
613C2×C4C2×D4×D1314yes—
614C22—24no—
615C22—24no—
616C22—24no—
617C22—416no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—138no—
623C22—2632no—
624C22—264no—
625C22—264no—
626C22—264no—
627C22—264no—
628C22—264no—
629C22—264no—
630C22C2×#8813814yes—
631C22#1171921614yes—
632C22#1171923414yes—
633C22#1171931314yes—
634C22#1171931714yes—
635C22D13×C22⋊Q814yes—
636C22#1171933714yes—
637C22C22×#612711yescharacteristic
638C22C22×D4×D1311yescharacteristic
639C22C22×D4×D1311yescharacteristic
640C22C2×#8825111yescharacteristic
641C22C22×Q8×D1311yescharacteristic
642C22C2×#41×D1311yescharacteristic
643C22C2×#8825711yescharacteristic
644C4—44no—
645C4—42no—
646C4—44no—
647C4—268no—
648C4—264no—
649C4—264no—
650C4—524no—
651C4—522no—
652C4C2×#8813818yes—
653C2—44no—
654C2—268no—
655C2#1311828918yesdirect product factor
656C2C22×#8813811yescharacteristic
657C2C2×D13×C22⋊Q811yescharacteristic
658C2C2×#1171931311yescharacteristic
659C2C2×#1171931711yescharacteristic
660C2C2×#1171933711yescharacteristic
661C2C2×#1171923411yescharacteristic
662C2C2×#1171921611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#380D13
hypocenterC13C2×#2417
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#88151C2semidirect
2. C22×#88178C2semidirect
4. C22×C4⋊C4×D13C2semidirect
5. #13118289C2direct (N × H)
6. C2×#11718318C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718635C2semidirect
9. C2×#11718634C2semidirect
11. C2×#11718328C2semidirect
12. C2×C13×#380C2semidirect
30. C2×#88178C22semidirect
37. C2×#88151C22semidirect
39. C2×C4⋊C4×D13C22semidirect
40. C13×#380C22semidirect
45. #11718635C22semidirect
46. #11718634C22semidirect
48. #11718609C22semidirect
49. #11718328C22semidirect
50. #11718318C22semidirect
63. C22×C22⋊D13Q8semidirect
98. C2×C4⋊Dic13D4semidirect
159. C2×C22⋊D13C2×Q8semidirect
200. C4⋊Dic13C2×D4semidirect
217. C2×#380D13semidirect
250. C22×D13C22⋊Q8semidirect
328. #380C2×D13semidirect
362. C2×D13C2×C22⋊Q8semidirect
440. C2×C13#2417semidirect
536. C13C2×#2417semidirect
655. C2#13118289direct (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×#881782
C22×C4×C22⋊D132
C22×C4⋊C4×D132
#131182892
C2×#117183182
C2×#117186092
C2×#117186352
C2×#117186342
C2×#117186172
C2×#117183282
C2×C13×#3802
C2×#241713