Finite Group Databasebeta

← C2×#13125659 #16733529

Subgroups — C2×#13125659 #16733529

Order 3328.

2322 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic
2C2×D13×C22⋊Q8C211yesmaximal, characteristic
3#13125659C2116yesmaximal, direct product factor
4C2×#11718523C212yesmaximal, complemented
5C2×#11718632C211yesmaximal, characteristic, complemented
6C2×#11718529C212yesmaximal, complemented
7C2×#11718477C212yesmaximal, complemented
8C2×#11718400C211yesmaximal, characteristic, complemented
9C2×#11718469C212yesmaximal, complemented
10C2×#11718711C211yesmaximal, characteristic, complemented
11C2×#11718387C211yesmaximal, characteristic
12C2×C13×#483C211yesmaximal, characteristic, complemented
13C22×Q8×D13C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
15C23×Dic26C2211yescharacteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C2×#88200C2211yescharacteristic
19C22×#6107C2212yescomplemented
20C22×#6103—21no—
21C22×C4⋊Dic13—21no—
22C2×#88178C2211yescharacteristic
23C22×Dic52C2212yescomplemented
24C22×#6094C2212yes—
25D13×C22⋊Q8—24no—
26D13×C22⋊Q8C2218yes—
27C2×#88151—21no—
28C2×#88151—21no—
29C2×#88151—24no—
30C2×#88151C2218yes—
31C2×#88151C2212yes—
32C2×#88151C2211yescharacteristic
33C2×#88151C2212yes—
34C2×#88150—21no—
35C2×C4⋊C4×D13—21no—
36C2×C4⋊C4×D13C2211yescharacteristic
37C2×C22⋊C4×D13—21no—
38C2×#88132—21no—
39C13×#483C2218yescomplemented
40C2×C13×#106C2212yescomplemented
41C2×C13×#103C2212yescomplemented
42C2×C13×C22⋊C8C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44C2×#88060C2212yes—
45C2×#88056C2212yescomplemented
46#11718711C2218yescomplemented
47#11718632C2218yescomplemented
48C2×#88050C2212yescomplemented
49C2×#88050C2212yescomplemented
50C2×#88048C2212yescomplemented
51#11718529C22116yescomplemented
52#11718523C22116yescomplemented
53#11718477C22116yescomplemented
54#11718469C22116yescomplemented
55#11718400C2218yescomplemented
56#11718387C2218yes—
57C24×D13D411yescharacteristic
58C22×Q8×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C23×Dic13D411yescharacteristic
63C2×Q8×D13—22no—
64C2×Q8×D13—44no—
65C2×Q8×D13C2314yes—
66C22×C4×D13—21no—
67C22×C4×D13—21no—
68C22×C4×D13—44no—
69C22×C4×D13D411yescharacteristic
70C22×C4×D13D411yescharacteristic
71C22×C4×D13D414yes—
72C22×C4×D13C2311yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C22×C4×D13C2314yes—
75C22×Dic26—21no—
76C22×Dic26—22no—
77C22×Dic26—21no—
78C22×Dic26—44no—
79C22×Dic26C2311yescharacteristic
80C22×Dic26C2312yes—
81C22×Dic26C2314yes—
82C22×C8×C13C2312yes—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8C2314yes—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4C2312yes—
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C4⋊C4C2314yes—
91C2×C13×C22⋊C4—21no—
92C2×C22⋊Dic13—21no—
93#88200—22no—
94#88200C2314yes—
95C2×#6107—44no—
96C2×#6107C2318yescomplemented
97C2×#6103—21no—
98C2×#6103—21no—
99C2×#6103—22no—
100C2×#6103—28no—
101C2×#6103—22no—
102C2×C4⋊Dic13—21no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—28no—
106C2×C4⋊Dic13C2311yescharacteristic
107#88178—22no—
108#88178C2314yes—
109C2×#6101—21no—
110C2×#6101—21no—
111C2×#6101—21no—
112C22×#1055C2312yes—
113C2×Dic52—44no—
114C2×Dic52C2318yescomplemented
115C2×#6094—44no—
116C2×#6094C2318yes—
117#88151—24no—
118#88151—24no—
119#88151—28no—
120#88151—28no—
121#88151—22no—
122#88151C2318yes—
123#88151C2318yes—
124#88151C2314yes—
125#88150—28no—
126C4⋊C4×D13—28no—
127C4⋊C4×D13—22no—
128C4⋊C4×D13C2314yes—
129C22⋊C4×D13—28no—
130#88132—28no—
131C13×#106C2318yescomplemented
132C13×#103C2318yescomplemented
133C13×C22⋊C8C2314yes—
134C22⋊#1055C2314yes—
135#88060C2318yes—
136#88056C2318yescomplemented
137#88050C2318yescomplemented
138#88050C2318yescomplemented
139#88048C2318yescomplemented
140C2×#3195—131nomaximal, Sylow
141C24×C13C2×D411yescharacteristic
142C23×D13—24no—
143C23×D13—24no—
144C23×D13—42no—
145C23×D13C2×D411yescharacteristic
146C23×D13C2×D414yes—
147C23×D13C2×D411yescharacteristic
148C2×Q8×C13—21no—
149C2×Q8×C13—24no—
150C2×Q8×C13C2412yes—
151C22×C4×C13—24no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—24no—
155C22×C4×C13—22no—
156C22×C4×C13—44no—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2412yes—
160C22×C4×C13C2411yescharacteristic
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—24no—
164C22×Dic13—22no—
165C22×Dic13—42no—
166C22×Dic13—44no—
167C22×Dic13C2×D411yescharacteristic
168C22×Dic13C2×D411yescharacteristic
169C22×Dic13C2×D414yes—
170Q8×D13—48no—
171Q8×D13—48no—
172C2×C4×D13—24no—
173C2×C4×D13—24no—
174C2×C4×D13—24no—
175C2×C4×D13—24no—
176C2×C4×D13—48no—
177C2×C4×D13—48no—
178C2×C4×D13—42no—
179C2×C4×D13—42no—
180C2×C4×D13—44no—
181C2×C4×D13—44no—
182C2×C4×D13C2×D412yes—
183C2×C4×D13C2×D412yes—
184C2×C4×D13C2×D414yes—
185C2×C4×D13C2×D414yes—
186C2×C4×D13C2412yes—
187C2×C4×D13C2412yes—
188C2×Dic26—24no—
189C2×Dic26—24no—
190C2×Dic26—24no—
191C2×Dic26—24no—
192C2×Dic26—22no—
193C2×Dic26—21no—
194C2×Dic26—24no—
195C2×Dic26—48no—
196C2×Dic26—44no—
197C2×Dic26—44no—
198C2×Dic26—48no—
199C2×Dic26C2414yes—
200C2×Dic26C2412yes—
201C2×C8×C13—24no—
202C2×C8×C13C2414yes—
203C13×C4⋊C4—24no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—24no—
206C13×C4⋊C4—22no—
207C13×C4⋊C4C2414yes—
208C13×C4⋊C4C2412yes—
209C13×C22⋊C4—24no—
210C22⋊Dic13—24no—
211#6107—48no—
212#6103—24no—
213#6103—24no—
214#6103—28no—
215#6103—28no—
216C4⋊Dic13—21no—
217C4⋊Dic13—24no—
218C4⋊Dic13—28no—
219C4⋊Dic13—28no—
220C4⋊Dic13C2412yes—
221#6101—24no—
222#6101—24no—
223#6101—24no—
224C2×#1055—24no—
225C2×#1055C2414yes—
226Dic52—48no—
227#6094—48no—
228C22×C22⋊Q8—131no—
229C22×C22⋊Q8—131no—
230#3195—1316no—
231C2×#483—132no—
232C2×#483—131no—
233C2×#483D1311yescharacteristic, complemented
234C2×#470—132no—
235C2×#470—132no—
236C2×#451—132no—
237C2×#451—131no—
238C2×#451—131no—
239C2×#407—131no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13#13714yes—
243C23×C13C22×D412yes—
244C23×C13C22×D411yescharacteristic
245C22×D13—22no—
246C22×D13—22no—
247C22×D13—22no—
248C22×D13—28no—
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—28no—
252C22×D13—44no—
253C22×D13—416no—
254C22×D13#13714yes—
255C22×D13C22×D412yes—
256C22×D13C22×D412yes—
257Q8×C13—24no—
258Q8×C13—42no—
259C2×C4×C13—22no—
260C2×C4×C13—24no—
261C2×C4×C13—24no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—24no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—48no—
268C2×C4×C13—44no—
269C2×C4×C13C22×D412yes—
270C2×C4×C13C22×D411yescharacteristic
271C2×C4×C13H(5,𝔽2)14yes—
272C2×C4×C13C2511yescharacteristic
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—24no—
278C2×Dic13—44no—
279C2×Dic13—48no—
280C2×Dic13—42no—
281C2×Dic13—44no—
282C2×Dic13—42no—
283C2×Dic13C22×D412yes—
284C2×Dic13C22×D412yes—
285C4×D13—24no—
286C4×D13—24no—
287C4×D13—24no—
288C4×D13—24no—
289C4×D13—44no—
290C4×D13—44no—
291C4×D13—48no—
292C4×D13—48no—
293Dic26—24no—
294Dic26—24no—
295Dic26—24no—
296Dic26—48no—
297Dic26—48no—
298Dic26—44no—
299Dic26—42no—
300C8×C13—24no—
301#1055—24no—
302C23×Q8—131no—
303C23×Q8—131no—
304C24×C4—131no—
305C22×Q16—132no—
306C22×Q16—132no—
307C22×M16—132no—
308C2×C22⋊Q8—131no—
309C2×C22⋊Q8—131no—
310C2×C22⋊Q8—138no—
311C2×C22⋊Q8—132no—
312C2×C22⋊Q8—138no—
313C2×C22⋊Q8—131no—
314C2×C22⋊Q8—132no—
315C2×C22⋊Q8—261no—
316C2×C22⋊Q8—261no—
317C2×C22⋊Q8—261no—
318C2×C22⋊Q8—264no—
319C2×C22⋊Q8—261no—
320C2×C22⋊Q8—264no—
321C2×C22⋊Q8C2×D1311yescharacteristic
322C22×C4⋊C4—131no—
323C22×C4⋊C4—261no—
324C22×C4⋊C4—261no—
325C22×C4⋊C4C2×D1311yescharacteristic
326C22×C22⋊C4—261no—
327C22×C22⋊C4—261no—
328#483—138no—
329#483—1316no—
330#483C2×D1318yescomplemented
331#470—1316no—
332#470—1316no—
333#451—138no—
334#451—1316no—
335#451—138no—
336C2×#106—132no—
337C2×#106C2×D1312yescomplemented
338C2×#103—132no—
339C2×#103—132no—
340C2×#103—132no—
341C2×#103C2×D1312yescomplemented
342#407—138no—
343C2×C22⋊C8—131no—
344C2×C22⋊C8—132no—
345C2×C22⋊C8C2×D1311yescharacteristic
346C22×C13—22no—
347C22×C13—28no—
348C22×C13—22no—
349C22×C13#53412yes—
350C22×C13C2×#13714yes—
351C22×C13C2×#13712yes—
352C22×C13C2×#13712yes—
353C22×C13C23×D411yescharacteristic
354C2×D13—22no—
355C2×D13—28no—
356C2×D13—22no—
357C2×D13—22no—
358C2×D13—22no—
359C2×D13—22no—
360C2×D13—416no—
361C2×D13—44no—
362C2×D13C2×#13714yes—
363C4×C13—22no—
364C4×C13—42no—
365C4×C13—42no—
366C4×C13—44no—
367C4×C13#53412yes—
368C4×C13C2×H(5,𝔽2)12yes—
369Dic13—22no—
370Dic13—22no—
371Dic13—42no—
372Dic13—44no—
373Dic13—42no—
374C25—131no—
375C22×Q8—134no—
376C22×Q8—131no—
377C22×Q8—132no—
378C22×Q8—134no—
379C22×Q8—261no—
380C22×Q8—262no—
381C22×Q8—262no—
382C22×Q8—261no—
383C22×Q8—524no—
384C22×Q8—524no—
385C22×Q8C22×D1311yescharacteristic
386C23×C4—21no—
387C23×C4—131no—
388C23×C4—131no—
389C23×C4—131no—
390C23×C4—131no—
391C23×C4—131no—
392C23×C4—134no—
393C23×C4—134no—
394C23×C4—261no—
395C23×C4—261no—
396C23×C4—261no—
397C23×C4—524no—
398C23×C4C22×D1311yescharacteristic
399C2×Q16—138no—
400C2×Q16—138no—
401C2×Q16—524no—
402C2×Q16—524no—
403C2×M16—138no—
404C2×M16—524no—
405C22×C8—132no—
406C22×C8C22×D1312yes—
407C22⋊Q8—22no—
408C22⋊Q8—134no—
409C22⋊Q8—134no—
410C22⋊Q8—138no—
411C22⋊Q8—134no—
412C22⋊Q8—138no—
413C22⋊Q8—268no—
414C22⋊Q8—268no—
415C22⋊Q8—264no—
416C22⋊Q8—264no—
417C22⋊Q8—268no—
418C22⋊Q8—268no—
419C22⋊Q8—262no—
420C22⋊Q8—262no—
421C22⋊Q8—262no—
422C22⋊Q8C22×D1314yes—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—131no—
427C2×C4⋊C4—134no—
428C2×C4⋊C4—262no—
429C2×C4⋊C4—268no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—261no—
432C2×C4⋊C4—268no—
433C2×C4⋊C4—261no—
434C2×C4⋊C4—262no—
435C2×C4⋊C4—262no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4C22×D1311yescharacteristic
438C2×C4⋊C4C22×D1312yes—
439C2×C4⋊C4C22×D1314yes—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—268no—
442C2×C22⋊C4—268no—
443C2×C22⋊C4—261no—
444C2×C22⋊C4—261no—
445C2×C22⋊C4—262no—
446C2×C22⋊C4—262no—
447C2×C22⋊C4—261no—
448#106—138no—
449#106C22×D1318yescomplemented
450#103—138no—
451#103—138no—
452#103—138no—
453#103C22×D1318yescomplemented
454C22⋊C8—134no—
455C22⋊C8—138no—
456C22⋊C8C22×D1314yes—
457C2×C13—24no—
458C2×C13#319514yescomplemented
459C2×C13C2×#53411yescharacteristic
460C2×C13C22×#13711yescharacteristic
461C2×C13C22×#13711yescharacteristic
462D13—24no—
463D13—42no—
464C24—131no—
465C24—131no—
466C24—134no—
467C24—264no—
468C24—264no—
469C24—522no—
470C24D4×D1311yescharacteristic
471C2×Q8—21no—
472C2×Q8—24no—
473C2×Q8—134no—
474C2×Q8—132no—
475C2×Q8—264no—
476C2×Q8—264no—
477C2×Q8—262no—
478C2×Q8—261no—
479C2×Q8—264no—
480C2×Q8—264no—
481C2×Q8—264no—
482C2×Q8—528no—
483C2×Q8—524no—
484C2×Q8—528no—
485C2×Q8—524no—
486C2×Q8—528no—
487C2×Q8—528no—
488C2×Q8C23×D1312yes—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—44no—
495C22×C4—131no—
496C22×C4—131no—
497C22×C4—134no—
498C22×C4—132no—
499C22×C4—132no—
500C22×C4—132no—
501C22×C4—132no—
502C22×C4—134no—
503C22×C4—134no—
504C22×C4—264no—
505C22×C4—264no—
506C22×C4—264no—
507C22×C4—264no—
508C22×C4—264no—
509C22×C4—261no—
510C22×C4—262no—
511C22×C4—261no—
512C22×C4—528no—
513C22×C4—528no—
514C22×C4—522no—
515C22×C4—522no—
516C22×C4—524no—
517C22×C4—524no—
518C22×C4—522no—
519C22×C4—524no—
520C22×C4D4×D1312yes—
521C22×C4D4×D1311yescharacteristic
522C22×C4C23×D1312yes—
523C22×C4C23×D1311yescharacteristic
524Q16—528no—
525Q16—528no—
526M16—528no—
527C2×C8—24no—
528C2×C8—134no—
529C2×C8—264no—
530C2×C8C23×D1314yes—
531C4⋊C4—24no—
532C4⋊C4—22no—
533C4⋊C4—24no—
534C4⋊C4—21no—
535C4⋊C4—132no—
536C4⋊C4—264no—
537C4⋊C4—264no—
538C4⋊C4—264no—
539C4⋊C4—268no—
540C4⋊C4—268no—
541C4⋊C4—261no—
542C4⋊C4—264no—
543C4⋊C4C23×D1312yes—
544C4⋊C4C23×D1314yes—
545C22⋊C4—24no—
546C22⋊C4—264no—
547C22⋊C4—264no—
548C22⋊C4—268no—
549C22⋊C4—268no—
550C22⋊C4—264no—
551C13C2×#319511yescharacteristic, complemented, Sylow
552C23—22no—
553C23—22no—
554C23—134no—
555C23—132no—
556C23—132no—
557C23—268no—
558C23—262no—
559C23—262no—
560C23—268no—
561C23—262no—
562C23—262no—
563C23—262no—
564C23—524no—
565C23—5216no—
566C23#8816914yes—
567C23C2×D4×D1312yes—
568C23C2×D4×D1311yescharacteristic
569Q8—24no—
570Q8—42no—
571Q8—264no—
572Q8—264no—
573Q8—264no—
574Q8—528no—
575Q8—528no—
576Q8—524no—
577Q8—522no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—48no—
585C2×C4—44no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—132no—
589C2×C4—132no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—264no—
593C2×C4—264no—
594C2×C4—264no—
595C2×C4—264no—
596C2×C4—262no—
597C2×C4—264no—
598C2×C4—262no—
599C2×C4—524no—
600C2×C4—524no—
601C2×C4—528no—
602C2×C4—528no—
603C2×C4—524no—
604C2×C4—528no—
605C2×C4—522no—
606C2×C4—522no—
607C2×C4—524no—
608C2×C4C2×D4×D1312yes—
609C2×C4C2×D4×D1311yescharacteristic
610C2×C4#8825614yes—
611C2×C4C24×D1311yescharacteristic
612C8—24no—
613C8—264no—
614C22—28no—
615C22—22no—
616C22—22no—
617C22—134no—
618C22—268no—
619C22—262no—
620C22—262no—
621C22—262no—
622C22—262no—
623C22—262no—
624C22—5216no—
625C22—524no—
626C22#1171935812yes—
627C22C2×#8816914yes—
628C22C2×#8816912yes—
629C22D13×#13712yes—
630C22C22×D4×D1311yescharacteristic
631C4—22no—
632C4—42no—
633C4—44no—
634C4—42no—
635C4—262no—
636C4—262no—
637C4—522no—
638C4—522no—
639C4—524no—
640C4#1171935812yes—
641C4C2×#8825612yes—
642C2—24no—
643C2—264no—
644C2—522no—
645C2#1312565914yesdirect product factor
646C2C2×#1171935811yescharacteristic
647C2C2×D13×#13711yescharacteristic
648C2C22×#8816911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#483C2
socleC23×C13C22×D4
prime radicalC24×D13D4
hypercenterC2×#483D13
hypocenterC13C2×#3195
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #13125659C2direct (N × H)
4. C2×#11718523C2semidirect
5. C2×#11718632C2semidirect
6. C2×#11718529C2semidirect
7. C2×#11718477C2semidirect
8. C2×#11718400C2semidirect
9. C2×#11718469C2semidirect
10. C2×#11718711C2semidirect
12. C2×C13×#483C2semidirect
19. C22×#6107C22semidirect
23. C22×Dic52C22semidirect
39. C13×#483C22semidirect
40. C2×C13×#106C22semidirect
41. C2×C13×#103C22semidirect
45. C2×#88056C22semidirect
46. #11718711C22semidirect
47. #11718632C22semidirect
48. C2×#88050C22semidirect
49. C2×#88050C22semidirect
50. C2×#88048C22semidirect
51. #11718529C22semidirect
52. #11718523C22semidirect
53. #11718477C22semidirect
54. #11718469C22semidirect
55. #11718400C22semidirect
96. C2×#6107C23semidirect
114. C2×Dic52C23semidirect
131. C13×#106C23semidirect
132. C13×#103C23semidirect
136. #88056C23semidirect
137. #88050C23semidirect
138. #88050C23semidirect
139. #88048C23semidirect
233. C2×#483D13semidirect
330. #483C2×D13semidirect
337. C2×#106C2×D13semidirect
341. C2×#103C2×D13semidirect
449. #106C22×D13semidirect
453. #103C22×D13semidirect
458. C2×C13#3195semidirect
551. C13C2×#3195semidirect
645. C2#13125659direct (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×C22⋊Q82
#131256592
C2×#117185232
C2×#117186322
C2×#117185292
C2×#117184772
C2×#117184002
C2×#117184692
C2×#117187112
C2×#117183872
C2×C13×#4832
C2×#319513