Finite Group Databasebeta

← C2×#13124786 #16730727

Subgroups — C2×#13124786 #16730727

Order 3328.

2326 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic
2C2×D13×#117C211yesmaximal, characteristic
3#13124786C2116yesmaximal, direct product factor
4C2×#11718545C212yesmaximal, complemented
5C2×#11718528C212yesmaximal, complemented
6C2×#11718549C212yesmaximal, complemented
7C2×#11718523C212yesmaximal, complemented
8C2×#11718625C211yesmaximal, characteristic, complemented
9C2×#11718781C211yesmaximal, characteristic, complemented
10C2×#11718665C211yesmaximal, characteristic, complemented
11C2×#11718787C211yesmaximal, characteristic
12C2×C13×#428C211yesmaximal, characteristic, complemented
13C23×C4×D13C2211yescharacteristic
14C23×Dic26C2211yescharacteristic
15C22×C13×M16C2211yescharacteristic
16C2×C13×#117C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×#6103—21no—
19C2×#88180C2211yescharacteristic
20C22×C4⋊Dic13—21no—
21C22×#6099C2211yescharacteristic
22D13×#117—24no—
23D13×#117C2218yes—
24C2×#88151—21no—
25C2×#88151—21no—
26C2×#88151—24no—
27C2×#88151C2212yes—
28C2×#88151C2212yes—
29C2×#88151C2218yes—
30C2×#88146C2211yescharacteristic
31C2×#88146C2211yescharacteristic
32C2×C4⋊C4×D13C2211yescharacteristic
33C2×C4⋊C4×D13C2211yescharacteristic
34C2×C22⋊C4×D13—21no—
35C2×#88131—21no—
36C2×#88126—21no—
37C2×C42×D13—21no—
38C13×#428C2218yescomplemented
39C2×C13×#107C2212yescomplemented
40C2×C13×#106C2212yescomplemented
41#11718787C2218yes—
42#11718781C2218yescomplemented
43C2×#88060C2212yes—
44C2×#88060C2212yes—
45C2×#88056C2212yescomplemented
46C2×#88056C2212yescomplemented
47#11718665C2218yescomplemented
48C2×#88050C2212yescomplemented
49C2×#88050C2212yescomplemented
50#11718625C2218yescomplemented
51C2×#88048C2212yescomplemented
52C2×#88047C2212yescomplemented
53#11718549C22116yescomplemented
54#11718545C22116yescomplemented
55#11718528C22116yescomplemented
56#11718523C22116yescomplemented
57C24×D13D411yescharacteristic
58C23×C4×C13—21no—
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C23×Dic13D411yescharacteristic
62C22×C4×D13—24no—
63C22×C4×D13—24no—
64C22×C4×D13—21no—
65C22×C4×D13—21no—
66C22×C4×D13D411yescharacteristic
67C22×C4×D13D411yescharacteristic
68C22×C4×D13D414yes—
69C22×C4×D13C2311yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C22×C4×D13C2314yes—
72C22×Dic26—24no—
73C22×Dic26—24no—
74C22×Dic26—21no—
75C22×Dic26—22no—
76C22×Dic26C2314yes—
77C22×Dic26C2312yes—
78C2×C13×M16—24no—
79C2×C13×M16C2314yes—
80C22×C8×C13C2312yes—
81C13×#117—22no—
82C13×#117C2314yes—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C4⋊C4C2312yes—
88C2×C13×C4⋊C4C2314yes—
89C2×C13×C22⋊C4—21no—
90C2×C42×C13—21no—
91C2×C22⋊Dic13—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×#6103—22no—
95C2×#6103—28no—
96C2×#6103—22no—
97#88180—22no—
98#88180C2314yes—
99C2×C4⋊Dic13—28no—
100C2×C4⋊Dic13—22no—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13C2311yescharacteristic
103C2×C4⋊Dic13C2311yescharacteristic
104C2×#6101—21no—
105C2×#6101—21no—
106C2×C4×Dic13—21no—
107C2×C4×Dic13—21no—
108C2×C4×Dic13—21no—
109C2×#6099—24no—
110C2×#6099C2314yes—
111C22×#1055C2312yes—
112#88151—28no—
113#88151—28no—
114#88151—24no—
115#88151—24no—
116#88151C2318yes—
117#88151C2318yes—
118#88146—22no—
119#88146—22no—
120#88146C2314yes—
121#88146C2314yes—
122C4⋊C4×D13—22no—
123C4⋊C4×D13—22no—
124C4⋊C4×D13C2314yes—
125C4⋊C4×D13C2314yes—
126C22⋊C4×D13—28no—
127#88131—28no—
128#88126—28no—
129C42×D13—28no—
130C13×#107C2318yescomplemented
131C13×#106C2318yescomplemented
132#88060C2318yes—
133#88060C2318yes—
134#88056C2318yescomplemented
135#88056C2318yescomplemented
136#88050C2318yescomplemented
137#88050C2318yescomplemented
138#88048C2318yescomplemented
139#88047C2318yescomplemented
140C2×#3095—131nomaximal, Sylow
141C24×C13C2×D411yescharacteristic
142C23×D13—24no—
143C23×D13—24no—
144C23×D13—42no—
145C23×D13C2×D411yescharacteristic
146C23×D13C2×D414yes—
147C23×D13C2×D411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—24no—
151C22×C4×C13—22no—
152C22×C4×C13—44no—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D412yes—
155C22×C4×C13#4114yes—
156C22×C4×C13#4114yes—
157C22×C4×C13C2411yescharacteristic
158C22×C4×C13C2412yes—
159C22×Dic13—24no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—24no—
163C22×Dic13—22no—
164C22×Dic13—44no—
165C22×Dic13C2×D414yes—
166C22×Dic13C2×D411yescharacteristic
167C22×Dic13C2×D411yescharacteristic
168C2×C4×D13—24no—
169C2×C4×D13—24no—
170C2×C4×D13—216no—
171C2×C4×D13—22no—
172C2×C4×D13—22no—
173C2×C4×D13—28no—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×C4×D13—28no—
177C2×C4×D13—24no—
178C2×C4×D13—24no—
179C2×C4×D13—44no—
180C2×C4×D13—44no—
181C2×C4×D13C2×D414yes—
182C2×C4×D13C2×D414yes—
183C2×C4×D13C2×D412yes—
184C2×C4×D13C2×D412yes—
185C2×C4×D13C2412yes—
186C2×C4×D13C2412yes—
187C2×Dic26—24no—
188C2×Dic26—28no—
189C2×Dic26—24no—
190C2×Dic26—28no—
191C2×Dic26—24no—
192C2×Dic26—22no—
193C2×Dic26—48no—
194C2×Dic26—44no—
195C2×Dic26C2414yes—
196C13×M16—28no—
197C2×C8×C13—24no—
198C2×C8×C13C2414yes—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—24no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4C2412yes—
204C13×C4⋊C4C2414yes—
205C13×C4⋊C4C2412yes—
206C13×C22⋊C4—24no—
207C42×C13—24no—
208C22⋊Dic13—24no—
209#6103—24no—
210#6103—24no—
211#6103—28no—
212#6103—28no—
213C4⋊Dic13—21no—
214C4⋊Dic13—21no—
215C4⋊Dic13—28no—
216C4⋊Dic13—28no—
217C4⋊Dic13C2412yes—
218C4⋊Dic13C2412yes—
219#6101—24no—
220#6101—24no—
221C4×Dic13—24no—
222C4×Dic13—24no—
223C4×Dic13—24no—
224#6099—28no—
225C2×#1055—24no—
226C2×#1055C2414yes—
227C22×C22⋊Q8—131no—
228C22×#117—131no—
229#3095—1316no—
230C2×#484—132no—
231C2×#485—132no—
232C2×#485—132no—
233C2×#483—132no—
234C2×#428—131no—
235C2×#428D1311yescharacteristic, complemented
236C2×#419—131no—
237C2×#419—131no—
238C2×#407—131no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13#12314yes—
242C23×C13C22×D412yes—
243C23×C13C22×D411yescharacteristic
244C22×D13—22no—
245C22×D13—22no—
246C22×D13—28no—
247C22×D13—22no—
248C22×D13—22no—
249C22×D13—22no—
250C22×D13—28no—
251C22×D13—44no—
252C22×D13—416no—
253C22×D13#13714yes—
254C22×D13C22×D412yes—
255C22×D13C22×D412yes—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—24no—
259C2×C4×C13—48no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—44no—
263C2×C4×C13#12318yes—
264C2×C4×C13#12314yes—
265C2×C4×C13C22×D412yes—
266C2×C4×C13C22×D411yescharacteristic
267C2×C4×C13C2×#4112yes—
268C2×C4×C13C2×#4114yes—
269C2×C4×C13C2×#4112yes—
270C2×C4×C13C2×#4114yes—
271C2×C4×C13C2511yescharacteristic
272C2×Dic13—28no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—24no—
278C2×Dic13—48no—
279C2×Dic13—44no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13C22×D412yes—
283C2×Dic13C22×D412yes—
284C4×D13—28no—
285C4×D13—24no—
286C4×D13—28no—
287C4×D13—24no—
288C4×D13—22no—
289C4×D13—22no—
290C4×D13—22no—
291C4×D13—22no—
292C4×D13—48no—
293C4×D13—48no—
294Dic26—24no—
295Dic26—24no—
296Dic26—48no—
297Dic26—44no—
298C8×C13—24no—
299#1055—24no—
300C23×Q8—131no—
301C24×C4—131no—
302C22×M16—131no—
303C22×M16C2×D1311yescharacteristic
304C2×C22⋊Q8—132no—
305C2×C22⋊Q8—132no—
306C2×C22⋊Q8—138no—
307C2×C22⋊Q8—264no—
308C2×C22⋊Q8—261no—
309C2×C22⋊Q8—261no—
310C2×#117—131no—
311C2×#117—138no—
312C2×#117—131no—
313C2×#117—131no—
314C2×#117—261no—
315C2×#117—261no—
316C2×#117—264no—
317C2×#117C2×D1311yescharacteristic
318C22×C4⋊C4—131no—
319C22×C4⋊C4—131no—
320C22×C4⋊C4—261no—
321C22×C4⋊C4C2×D1311yescharacteristic
322C22×C22⋊C4—261no—
323C22×C22⋊C4—261no—
324C22×C42—261no—
325#485—1316no—
326#485—1316no—
327#484—1316no—
328#483—1316no—
329#428—138no—
330#428C2×D1318yescomplemented
331C2×#107—132no—
332C2×#107C2×D1312yescomplemented
333C2×#106—132no—
334C2×#106C2×D1312yescomplemented
335#419—138no—
336#419—138no—
337C2×#103—132no—
338C2×#103—132no—
339C2×#103—132no—
340C2×#103—132no—
341#407—138no—
342C2×C22⋊C8—132no—
343C2×C22⋊C8—132no—
344C22×C13—28no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13C2×#12314yes—
348C22×C13C2×#12312yes—
349C22×C13C2×#13712yes—
350C22×C13#57512yes—
351C22×C13C23×D411yescharacteristic
352C2×D13—28no—
353C2×D13—22no—
354C2×D13—22no—
355C2×D13—22no—
356C2×D13—22no—
357C2×D13—22no—
358C2×D13—416no—
359C2×D13—44no—
360C2×D13C2×#13714yes—
361C4×C13—42no—
362C4×C13—42no—
363C4×C13—44no—
364C4×C13C2×#12314yes—
365C4×C13C2×#12312yes—
366C4×C13C22×#4111yescharacteristic
367C4×C13C22×#4111yescharacteristic
368Dic13—22no—
369Dic13—22no—
370Dic13—44no—
371Dic13—42no—
372Dic13—42no—
373C25—131no—
374C22×Q8—132no—
375C22×Q8—134no—
376C22×Q8—262no—
377C22×Q8—261no—
378C22×Q8—264no—
379C22×Q8—264no—
380C23×C4—21no—
381C23×C4—131no—
382C23×C4—134no—
383C23×C4—131no—
384C23×C4—131no—
385C23×C4—131no—
386C23×C4—131no—
387C23×C4—134no—
388C23×C4—261no—
389C23×C4—261no—
390C23×C4—264no—
391C23×C4—264no—
392C23×C4—261no—
393C23×C4C22×D1311yescharacteristic
394C2×M16—24no—
395C2×M16—134no—
396C2×M16—264no—
397C2×M16C22×D1314yes—
398C22×C8—132no—
399C22×C8C22×D1312yes—
400C22⋊Q8—138no—
401C22⋊Q8—138no—
402C22⋊Q8—268no—
403C22⋊Q8—264no—
404C22⋊Q8—264no—
405C22⋊Q8—268no—
406#117—22no—
407#117—134no—
408#117—134no—
409#117—134no—
410#117—268no—
411#117—268no—
412#117—262no—
413#117—262no—
414#117—262no—
415#117C22×D1314yes—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—134no—
421C2×C4⋊C4—134no—
422C2×C4⋊C4—262no—
423C2×C4⋊C4—262no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—268no—
427C2×C4⋊C4—262no—
428C2×C4⋊C4—262no—
429C2×C4⋊C4C22×D1311yescharacteristic
430C2×C4⋊C4C22×D1311yescharacteristic
431C2×C4⋊C4C22×D1312yes—
432C2×C4⋊C4C22×D1314yes—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—268no—
435C2×C22⋊C4—261no—
436C2×C22⋊C4—261no—
437C2×C22⋊C4—268no—
438C2×C22⋊C4—262no—
439C2×C22⋊C4—262no—
440C2×C22⋊C4—261no—
441C2×C42—21no—
442C2×C42—268no—
443C2×C42—261no—
444C2×C42—261no—
445C2×C42—261no—
446#107—138no—
447#107C22×D1318yescomplemented
448#106—138no—
449#106C22×D1318yescomplemented
450#103—138no—
451#103—138no—
452#103—138no—
453#103—138no—
454C22⋊C8—138no—
455C22⋊C8—138no—
456C2×C13—24no—
457C2×C13#309514yescomplemented
458C2×C13C22×#12311yescharacteristic
459C2×C13C22×#13711yescharacteristic
460C2×C13C2×#57511yescharacteristic
461D13—24no—
462D13—42no—
463C24—131no—
464C24—131no—
465C24—134no—
466C24—264no—
467C24—264no—
468C24—522no—
469C24D4×D1311yescharacteristic
470C2×Q8—134no—
471C2×Q8—264no—
472C2×Q8—262no—
473C2×Q8—264no—
474C2×Q8—268no—
475C2×Q8—264no—
476C2×Q8—268no—
477C2×Q8—528no—
478C2×Q8—524no—
479C22×C4—24no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—44no—
484C22×C4—134no—
485C22×C4—131no—
486C22×C4—131no—
487C22×C4—134no—
488C22×C4—132no—
489C22×C4—132no—
490C22×C4—134no—
491C22×C4—132no—
492C22×C4—132no—
493C22×C4—264no—
494C22×C4—264no—
495C22×C4—264no—
496C22×C4—264no—
497C22×C4—2616no—
498C22×C4—264no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—268no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—268no—
505C22×C4—264no—
506C22×C4—261no—
507C22×C4—261no—
508C22×C4—262no—
509C22×C4—524no—
510C22×C4—524no—
511C22×C4—524no—
512C22×C4#612714yes—
513C22×C4D4×D1312yes—
514C22×C4D4×D1311yescharacteristic
515C22×C4#613114yes—
516C22×C4C23×D1312yes—
517C22×C4C23×D1311yescharacteristic
518M16—28no—
519M16—268no—
520C2×C8—24no—
521C2×C8—134no—
522C2×C8—264no—
523C2×C8C23×D1314yes—
524C4⋊C4—24no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—132no—
529C4⋊C4—132no—
530C4⋊C4—264no—
531C4⋊C4—264no—
532C4⋊C4—268no—
533C4⋊C4—268no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C4⋊C4C23×D1312yes—
537C4⋊C4C23×D1312yes—
538C4⋊C4C23×D1314yes—
539C22⋊C4—24no—
540C22⋊C4—264no—
541C22⋊C4—264no—
542C22⋊C4—268no—
543C22⋊C4—268no—
544C22⋊C4—264no—
545C42—24no—
546C42—264no—
547C42—264no—
548C42—264no—
549C13C2×#309511yescharacteristic, complemented, Sylow
550C23—22no—
551C23—22no—
552C23—134no—
553C23—132no—
554C23—132no—
555C23—268no—
556C23—262no—
557C23—262no—
558C23—268no—
559C23—262no—
560C23—262no—
561C23—262no—
562C23—524no—
563C23—5216no—
564C23#8814814yes—
565C23C2×D4×D1312yes—
566C23C2×D4×D1311yescharacteristic
567Q8—264no—
568Q8—264no—
569Q8—524no—
570Q8—528no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—48no—
575C2×C4—44no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—132no—
579C2×C4—132no—
580C2×C4—268no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—268no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—268no—
587C2×C4—262no—
588C2×C4—262no—
589C2×C4—262no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—264no—
594C2×C4—528no—
595C2×C4—528no—
596C2×C4—528no—
597C2×C4—524no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4#8814818yes—
601C2×C4#8814814yes—
602C2×C4C2×#612712yes—
603C2×C4C2×#612714yes—
604C2×C4C2×D4×D1312yes—
605C2×C4C2×D4×D1311yescharacteristic
606C2×C4C2×#613112yes—
607C2×C4C2×#613114yes—
608C2×C4C24×D1311yescharacteristic
609C8—24no—
610C8—264no—
611C22—22no—
612C22—22no—
613C22—28no—
614C22—134no—
615C22—262no—
616C22—262no—
617C22—268no—
618C22—262no—
619C22—262no—
620C22—262no—
621C22—5216no—
622C22—524no—
623C22C2×#8814814yes—
624C22C2×#8814812yes—
625C22#1171947812yes—
626C22D13×#13712yes—
627C22C22×D4×D1311yescharacteristic
628C4—42no—
629C4—44no—
630C4—42no—
631C4—262no—
632C4—262no—
633C4—522no—
634C4—522no—
635C4—524no—
636C4C2×#8814812yes—
637C4C2×#8814814yes—
638C4C22×#612711yescharacteristic
639C4C22×#613111yescharacteristic
640C2—24no—
641C2—264no—
642C2—522no—
643C2#1312478614yesdirect product factor
644C2C22×#8814811yescharacteristic
645C2C2×D13×#13711yescharacteristic
646C2C2×#1171947811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#428C2
socleC23×C13C22×D4
prime radicalC24×D13D4
hypercenterC2×#428D13
hypocenterC13C2×#3095
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
3. #13124786C2direct (N × H)
4. C2×#11718545C2semidirect
5. C2×#11718528C2semidirect
6. C2×#11718549C2semidirect
7. C2×#11718523C2semidirect
8. C2×#11718625C2semidirect
9. C2×#11718781C2semidirect
10. C2×#11718665C2semidirect
12. C2×C13×#428C2semidirect
38. C13×#428C22semidirect
39. C2×C13×#107C22semidirect
40. C2×C13×#106C22semidirect
42. #11718781C22semidirect
45. C2×#88056C22semidirect
46. C2×#88056C22semidirect
47. #11718665C22semidirect
48. C2×#88050C22semidirect
49. C2×#88050C22semidirect
50. #11718625C22semidirect
51. C2×#88048C22semidirect
52. C2×#88047C22semidirect
53. #11718549C22semidirect
54. #11718545C22semidirect
55. #11718528C22semidirect
56. #11718523C22semidirect
130. C13×#107C23semidirect
131. C13×#106C23semidirect
134. #88056C23semidirect
135. #88056C23semidirect
136. #88050C23semidirect
137. #88050C23semidirect
138. #88048C23semidirect
139. #88047C23semidirect
235. C2×#428D13semidirect
330. #428C2×D13semidirect
332. C2×#107C2×D13semidirect
334. C2×#106C2×D13semidirect
447. #107C22×D13semidirect
449. #106C22×D13semidirect
457. C2×C13#3095semidirect
549. C13C2×#3095semidirect
643. C2#13124786direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881512
C2×D13×#1172
#131247862
C2×#117185452
C2×#117185282
C2×#117185492
C2×#117185232
C2×#117186252
C2×#117187812
C2×#117186652
C2×#117187872
C2×C13×#4282
C2×#309513