Finite Group Databasebeta

← C2×#13119760 #16034692

Subgroups — C2×#13119760 #16034692

Order 3328.

3614 conjugacy classes of subgroups.

The subgroup lattice has 660 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×#88141C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D13C211yesmaximal, characteristic
5#13119760C2116yesmaximal, direct product factor
6C2×#11718337C212yesmaximal, complemented
7C2×#11718609C212yesmaximal, complemented
8C2×#11718618C212yesmaximal
9C2×#11718308C212yesmaximal, complemented
10C2×#11718637C211yesmaximal, characteristic, complemented
11C2×#11718648C211yesmaximal, characteristic, complemented
12C2×C13×#380C211yesmaximal, characteristic, complemented
13C24×C4×C13C2211yescharacteristic
14C23×C22⋊D13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C23×Dic26C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2212yes—
22C2×C4×C22⋊D13—28no—
23C2×C4×C22⋊D13C2218yes—
24C22×#6103C2211yescharacteristic
25C22×#6103C2212yes—
26C22×#6103C2212yes—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2212yes—
29C2×#88178—28no—
30C2×#88178C2218yescomplemented
31C22×#6101C2212yes—
32C22×#6101C2211yescharacteristic
33C22×#6101C2212yes—
34C22×#6101C2212yes—
35C22×#6101C2212yes—
36C22×C4×Dic13C2212yes—
37C22×C4×Dic13C2211yescharacteristic
38C2×#88151—28no—
39C2×#88151C2218yescomplemented
40C2×#88141—28no—
41C2×#88141C2218yescomplemented
42C13×#380C2218yescomplemented
43C2×C13×#95C2212yes—
44C2×#88071C2212yes—
45#11718648C2218yescomplemented
46#11718637C2218yescomplemented
47#11718618C22116yes—
48#11718609C22116yescomplemented
49#11718337C22116yescomplemented
50#11718308C22116yescomplemented
51C25×C13C2311yescharacteristic
52C24×D13C2311yescharacteristic
53C23×C4×C13—24no—
54C23×C4×C13—24no—
55C23×C4×C13—24no—
56C23×C4×C13C2314yes—
57C23×C4×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C22×C22⋊D13—24no—
62C22×C22⋊D13—24no—
63C22×C22⋊D13Q818yescomplemented
64C22×C22⋊D13C2314yes—
65C23×Dic13C2312yes—
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2312yes—
69C23×Dic13C2311yescharacteristic
70C22×C4×D13—24no—
71C22×C4×D13—24no—
72C22×C4×D13—24no—
73C22×C4×D13C2314yes—
74C22×Dic26—24no—
75C22×Dic26—24no—
76C22×Dic26D418yescomplemented
77C22×Dic26C2314yes—
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4—24no—
80C2×C13×C4⋊C4C2314yes—
81C2×C13×C4⋊C4C2314yes—
82C2×C13×C22⋊C4—44no—
83C2×C13×C22⋊C4C2318yes—
84C2×C22⋊Dic13—28no—
85C2×C22⋊Dic13—24no—
86C2×C22⋊Dic13C2318yes—
87C2×C22⋊Dic13C2314yes—
88C4×C22⋊D13—232no—
89C2×#6103—28no—
90C2×#6103—24no—
91C2×#6103—44no—
92C2×#6103C2318yes—
93C2×#6103C2314yes—
94C2×#6103C2318yes—
95C2×C4⋊Dic13—24no—
96C2×C4⋊Dic13—28no—
97C2×C4⋊Dic13C2318yes—
98C2×C4⋊Dic13C2314yes—
99#88178—232no—
100C2×#6101—28no—
101C2×#6101—28no—
102C2×#6101—24no—
103C2×#6101—28no—
104C2×#6101—44no—
105C2×#6101C2318yes—
106C2×#6101C2318yes—
107C2×#6101C2314yes—
108C2×#6101C2318yes—
109C2×#6101C2318yes—
110C2×C4×Dic13—28no—
111C2×C4×Dic13D418yes—
112C2×C4×Dic13C2318yes—
113C2×C4×Dic13C2314yes—
114#88151—232no—
115#88141—232no—
116C13×#95C2318yes—
117#88071C2318yes—
118C2×#2538—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×D13—22no—
133C23×D13—22no—
134C23×D13C2×Q814yes—
135C23×D13C2412yes—
136C22×C4×C13—24no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
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×C13C2412yes—
154C22×C4×C13C2414yes—
155C22×C4×C13C2412yes—
156C2×C22⋊D13—232no—
157C2×C22⋊D13—28no—
158C2×C22⋊D13—28no—
159C2×C22⋊D13C2×Q8116yescomplemented
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—24no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—24no—
168C22×Dic13—22no—
169C22×Dic13—24no—
170C22×Dic13C2×D414yes—
171C22×Dic13C2×D418yes—
172C22×Dic13C2×D414yes—
173C22×Dic13C2×Q814yes—
174C22×Dic13#4114yes—
175C22×Dic13C2412yes—
176C22×Dic13C2414yes—
177C22×Dic13C2412yes—
178C22×Dic13C2414yes—
179C22×Dic13C2412yes—
180C2×C4×D13—28no—
181C2×C4×D13—28no—
182C2×C4×D13—28no—
183C2×C4×D13—416no—
184C2×Dic26—232no—
185C2×Dic26—28no—
186C2×Dic26—28no—
187C2×Dic26C2×D4116yescomplemented
188C13×C4⋊C4—28no—
189C13×C4⋊C4—28no—
190C13×C22⋊C4—48no—
191C22⋊Dic13—216no—
192C22⋊Dic13—28no—
193#6103—216no—
194#6103—28no—
195#6103—48no—
196C4⋊Dic13—28no—
197C4⋊Dic13—216no—
198#6101—216no—
199#6101—216no—
200#6101—28no—
201#6101—216no—
202#6101—48no—
203C4×Dic13—216no—
204C4×Dic13C2×D4116yes—
205C22×C22⋊Q8—131no—
206C22×C22⋊Q8—131no—
207C22×C4×Q8—131no—
208C22×C4×D4—131no—
209#2538—1316no—
210C2×#396—132no—
211C2×#396—132no—
212C2×#390—132no—
213C2×#389—132no—
214C2×#384—131no—
215C2×#380—131no—
216C2×#380D1311yescharacteristic, complemented
217C23×C13—28no—
218C23×C13—28no—
219C23×C13—28no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—44no—
227C23×C13—44no—
228C23×C13—44no—
229C23×C13—44no—
230C23×C13C22×D412yes—
231C23×C13C22×D412yes—
232C23×C13C22×Q814yes—
233C23×C13C22×Q812yes—
234C23×C13C2×#4112yes—
235C23×C13C2×#4112yes—
236C23×C13H(5,𝔽2)12yes—
237C23×C132−1+412yes—
238C23×C13C2511yescharacteristic
239C22×D13—28no—
240C22×D13—28no—
241C22×D13—28no—
242C22×D13—22no—
243C22×D13—22no—
244C22×D13—22no—
245C22×D13—22no—
246C22×D13—22no—
247C22×D13—22no—
248C22×D13—44no—
249C22×D13—44no—
250C22×D13—44no—
251C22×D13—44no—
252C22×D13C22×Q814yes—
253C2×C4×C13—24no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—24no—
257C2×C4×C13—24no—
258C2×C4×C13—22no—
259C2×C4×C13—24no—
260C2×C4×C13—24no—
261C2×C4×C13—24no—
262C2×C4×C13—44no—
263C2×C4×C13—48no—
264C2×C4×C13—48no—
265C2×C4×C13—416no—
266C2×C4×C13#121116yes—
267C2×C4×C13C22×D414yes—
268C2×C4×C13C22×D414yes—
269C2×C4×C13C2×#4114yes—
270C22⋊D13—232no—
271C2×Dic13—216no—
272C2×Dic13—28no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—24no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—24no—
281C2×Dic13—22no—
282C2×Dic13—24no—
283C2×Dic13—44no—
284C2×Dic13—48no—
285C2×Dic13C22⋊Q8116yescomplemented
286C2×Dic13C22×D414yes—
287C2×Dic13C22×D418yes—
288C2×Dic13C22×D414yes—
289C2×Dic13C22×Q814yes—
290C2×Dic13C2×#4114yes—
291C4×D13—416no—
292Dic26—232no—
293C23×Q8—131no—
294C23×D4—131no—
295C24×C4—131no—
296C24×C4C2×D1311yescharacteristic
297C2×C22⋊Q8—138no—
298C2×C22⋊Q8—138no—
299C2×C22⋊Q8—268no—
300C2×C22⋊Q8—268no—
301C2×C4×Q8—138no—
302C2×C4×Q8—268no—
303C2×C4×D4—138no—
304C2×C4×D4—268no—
305C22×C4⋊C4—132no—
306C22×C4⋊C4—132no—
307C22×C4⋊C4—131no—
308C22×C4⋊C4—132no—
309C22×C4⋊C4—132no—
310C22×C4⋊C4—131no—
311C22×C4⋊C4—132no—
312C22×C4⋊C4C2×D1311yescharacteristic
313C22×C4⋊C4C2×D1311yescharacteristic
314C22×C22⋊C4—131no—
315C22×C22⋊C4—132no—
316C22×C22⋊C4—131no—
317C22×C22⋊C4—132no—
318C22×C22⋊C4—132no—
319C22×C22⋊C4C2×D1312yes—
320C22×C42—131no—
321C22×C42—132no—
322#396—1316no—
323#396—1316no—
324#390—1316no—
325#389—1316no—
326#384—138no—
327#380—138no—
328#380C2×D1318yescomplemented
329C2×#95—132no—
330C2×#95C2×D1312yes—
331C22×C13—24no—
332C22×C13—24no—
333C22×C13—24no—
334C22×C13—42no—
335C22×C13—42no—
336C22×C13—42no—
337C22×C13—42no—
338C22×C13—416no—
339C22×C13C2×#12114yes—
340C22×C13C2×C22⋊Q814yes—
341C22×C13#53714yes—
342C22×C13D4×Q814yes—
343C22×C13#55014yes—
344C22×C13#55414yes—
345C22×C13#55614yes—
346C22×C13C23×D411yescharacteristic
347C22×C13C23×D411yescharacteristic
348C22×C13C23×Q811yescharacteristic
349C22×C13C22×#4111yescharacteristic
350C22×C13C22×#4111yescharacteristic
351C22×C13C2×H(5,𝔽2)11yescharacteristic
352C22×C13C2×2−1+411yescharacteristic
353C2×D13—24no—
354C2×D13—24no—
355C2×D13—24no—
356C2×D13—42no—
357C2×D13—42no—
358C2×D13—42no—
359C2×D13—42no—
360C2×D13—416no—
361C4×C13—42no—
362C4×C13—44no—
363C4×C13—44no—
364C4×C13C2×#12118yes—
365Dic13—28no—
366Dic13—24no—
367Dic13—42no—
368Dic13—44no—
369Dic13C2×C22⋊Q818yescomplemented
370C25—131no—
371C25C22×D1311yescharacteristic
372C22×Q8—138no—
373C22×Q8—134no—
374C22×Q8—264no—
375C22×Q8—264no—
376C22×D4—138no—
377C22×D4—134no—
378C22×D4—264no—
379C22×D4—264no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—131no—
384C23×C4—131no—
385C23×C4—132no—
386C23×C4—132no—
387C23×C4—131no—
388C23×C4—134no—
389C23×C4—264no—
390C23×C4—264no—
391C23×C4—264no—
392C23×C4C22×D1314yes—
393C23×C4C22×D1312yes—
394C23×C4C22×D1312yes—
395C23×C4C22×D1311yescharacteristic
396C23×C4C22×D1311yescharacteristic
397C22⋊Q8—2632no—
398C22⋊Q8—2632no—
399C4×Q8—2632no—
400C4×D4—2632no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—134no—
404C2×C4⋊C4—138no—
405C2×C4⋊C4—138no—
406C2×C4⋊C4—134no—
407C2×C4⋊C4—138no—
408C2×C4⋊C4—138no—
409C2×C4⋊C4—138no—
410C2×C4⋊C4—264no—
411C2×C4⋊C4—268no—
412C2×C4⋊C4—268no—
413C2×C4⋊C4—268no—
414C2×C4⋊C4—268no—
415C2×C4⋊C4—264no—
416C2×C4⋊C4—524no—
417C2×C4⋊C4C22×D1314yes—
418C2×C4⋊C4C22×D1314yes—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—134no—
421C2×C22⋊C4—138no—
422C2×C22⋊C4—134no—
423C2×C22⋊C4—138no—
424C2×C22⋊C4—138no—
425C2×C22⋊C4—264no—
426C2×C22⋊C4—268no—
427C2×C22⋊C4—264no—
428C2×C22⋊C4—268no—
429C2×C22⋊C4—524no—
430C2×C22⋊C4C22×D1318yes—
431C2×C42—138no—
432C2×C42—134no—
433C2×C42—138no—
434C2×C42—268no—
435#95—138no—
436#95C22×D1318yes—
437C2×C13—44no—
438C2×C13#253818yescomplemented
439C2×C13C22×#12111yescharacteristic
440C2×C13C22×C22⋊Q811yescharacteristic
441C2×C13C2×#53711yescharacteristic
442C2×C13C2×D4×Q811yescharacteristic
443C2×C13C2×#55011yescharacteristic
444C2×C13C2×#55411yescharacteristic
445C2×C13C2×#55611yescharacteristic
446D13—44no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—134no—
454C24—132no—
455C24—262no—
456C24—262no—
457C24—262no—
458C24—262no—
459C24—262no—
460C24—262no—
461C24Q8×D1314yes—
462C24C23×D1312yes—
463C24C23×D1311yescharacteristic
464C2×Q8—1316no—
465C2×Q8—2632no—
466C2×Q8—268no—
467C2×Q8—268no—
468C2×D4—1316no—
469C2×D4—268no—
470C2×D4—2632no—
471C2×D4—268no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—416no—
485C22×C4—134no—
486C22×C4—134no—
487C22×C4—134no—
488C22×C4—132no—
489C22×C4—134no—
490C22×C4—138no—
491C22×C4—132no—
492C22×C4—134no—
493C22×C4—132no—
494C22×C4—134no—
495C22×C4—264no—
496C22×C4—264no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—264no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—264no—
504C22×C4—264no—
505C22×C4—268no—
506C22×C4—268no—
507C22×C4—268no—
508C22×C4—5216no—
509C22×C4#612714yes—
510C22×C4D4×D1314yes—
511C22×C4D4×D1314yes—
512C22×C4C23×D1314yes—
513C22×C4C23×D1312yes—
514C22×C4C23×D1314yes—
515C22×C4C23×D1312yes—
516C4⋊C4—28no—
517C4⋊C4—28no—
518C4⋊C4—268no—
519C4⋊C4—2616no—
520C4⋊C4—2616no—
521C4⋊C4—2616no—
522C4⋊C4—2616no—
523C4⋊C4—268no—
524C4⋊C4—528no—
525C22⋊C4—48no—
526C22⋊C4—268no—
527C22⋊C4—2616no—
528C22⋊C4—268no—
529C22⋊C4—2616no—
530C22⋊C4—528no—
531C42—1316no—
532C42—2616no—
533C13C2×#253811yescharacteristic, complemented, Sylow
534C23—28no—
535C23—28no—
536C23—28no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23—134no—
548C23—268no—
549C23—268no—
550C23—268no—
551C23—262no—
552C23—262no—
553C23—262no—
554C23—262no—
555C23—262no—
556C23—262no—
557C23—524no—
558C23—524no—
559C23—524no—
560C23—524no—
561C23C2×#612712yes—
562C23C2×D4×D1312yes—
563C23C2×D4×D1312yes—
564C23#8825112yes—
565C23C2×Q8×D1314yes—
566C23C2×Q8×D1312yes—
567C23#41×D1312yes—
568C23#8825712yes—
569C23C24×D1311yescharacteristic
570Q8—2632no—
571D4—2632no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—44no—
582C2×C4—48no—
583C2×C4—48no—
584C2×C4—416no—
585C2×C4—1316no—
586C2×C4—134no—
587C2×C4—134no—
588C2×C4—134no—
589C2×C4—134no—
590C2×C4—138no—
591C2×C4—2616no—
592C2×C4—268no—
593C2×C4—264no—
594C2×C4—264no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—264no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—264no—
602C2×C4—264no—
603C2×C4—524no—
604C2×C4—528no—
605C2×C4—5216no—
606C2×C4#88138116yes—
607C2×C4C2×#612714yes—
608C2×C4C2×D4×D1314yes—
609C2×C4C2×D4×D1314yes—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—416no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—264no—
619C22—264no—
620C22—264no—
621C22—5216no—
622C22—522no—
623C22—522no—
624C22—522no—
625C22—522no—
626C22C2×#8813814yes—
627C22#1171921614yes—
628C22#1171923814yes—
629C22#1171930414yes—
630C22#1171931314yes—
631C22D13×C22⋊Q814yes—
632C22#1171933714yes—
633C22C22×#612711yescharacteristic
634C22C22×D4×D1311yescharacteristic
635C22C22×D4×D1311yescharacteristic
636C22C2×#8825111yescharacteristic
637C22C22×Q8×D1311yescharacteristic
638C22C2×#41×D1311yescharacteristic
639C22C2×#8825711yescharacteristic
640C4—42no—
641C4—44no—
642C4—44no—
643C4—138no—
644C4—268no—
645C4—264no—
646C4—522no—
647C4—524no—
648C4C2×#8813818yes—
649C2—44no—
650C2—524no—
651C2#1311976018yesdirect product factor
652C2C22×#8813811yescharacteristic
653C2C2×D13×C22⋊Q811yescharacteristic
654C2C2×#1171931311yescharacteristic
655C2C2×#1171933711yescharacteristic
656C2C2×#1171930411yescharacteristic
657C2C2×#1171921611yescharacteristic
658C2C2×#1171923811yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#380D13
hypocenterC13C2×#2538
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
3. C22×#88141C2semidirect
5. #13119760C2direct (N × H)
6. C2×#11718337C2semidirect
7. C2×#11718609C2semidirect
9. C2×#11718308C2semidirect
10. C2×#11718637C2semidirect
11. C2×#11718648C2semidirect
12. C2×C13×#380C2semidirect
30. C2×#88178C22semidirect
39. C2×#88151C22semidirect
41. C2×#88141C22semidirect
42. C13×#380C22semidirect
45. #11718648C22semidirect
46. #11718637C22semidirect
48. #11718609C22semidirect
49. #11718337C22semidirect
50. #11718308C22semidirect
63. C22×C22⋊D13Q8semidirect
76. C22×Dic26D4semidirect
159. C2×C22⋊D13C2×Q8semidirect
187. C2×Dic26C2×D4semidirect
216. C2×#380D13semidirect
285. C2×Dic13C22⋊Q8semidirect
328. #380C2×D13semidirect
369. Dic13C2×C22⋊Q8semidirect
438. C2×C13#2538semidirect
533. C13C2×#2538semidirect
651. C2#13119760direct (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×#881412
C22×C4×C22⋊D132
#131197602
C2×#117183372
C2×#117186092
C2×#117186182
C2×#117183082
C2×#117186372
C2×#117186482
C2×C13×#3802
C2×#253813