Finite Group Databasebeta

← C2×#13125658 #16733528

Subgroups — C2×#13125658 #16733528

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×#88200C211yesmaximal, characteristic
2C2×D13×C22⋊Q8C211yesmaximal, characteristic
3#13125658C2116yesmaximal, direct product factor
4C2×#11718382C211yesmaximal, characteristic, complemented
5C2×#11718466C212yesmaximal, complemented
6C2×#11718704C211yesmaximal, characteristic, complemented
7C2×#11718477C212yesmaximal, complemented
8C2×#11718850C212yesmaximal, complemented
9C2×#11718889C211yesmaximal, characteristic, complemented
10C2×#11718847C212yesmaximal, complemented
11C2×#11718387C211yesmaximal, characteristic
12C2×C13×#451C211yesmaximal, characteristic, complemented
13C23×Q8×C13C2211yescharacteristic
14C22×Q8×D13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C22×C13×Q16C2212yescomplemented
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×#88200—21no—
19C2×#88200—21no—
20C2×#88200—24no—
21C2×#88200C2218yes—
22C2×#88200C2211yescharacteristic
23C2×#88200C2212yes—
24C2×#88200C2212yes—
25C22×#6107C2212yescomplemented
26C22×#6103—21no—
27C22×C4⋊Dic13C2211yescharacteristic
28C2×#88178C2211yescharacteristic
29C22×#6101—21no—
30C22×#6094C2212yes—
31D13×C22⋊Q8—24no—
32D13×C22⋊Q8C2218yes—
33C2×#88151C2211yescharacteristic
34C2×#88150—21no—
35C2×C4⋊C4×D13—21no—
36C2×C4⋊C4×D13C2211yescharacteristic
37C2×C22⋊C4×D13—21no—
38C2×#88132—21no—
39C13×#451C2218yescomplemented
40C2×C13×#103C2212yescomplemented
41C2×C13×C22⋊C8C2211yescharacteristic
42#11718889C2218yescomplemented
43C2×#88075C2212yescomplemented
44C2×#88075C2212yescomplemented
45C2×C22⋊#1055C2211yescharacteristic
46#11718850C22116yescomplemented
47#11718847C22116yescomplemented
48C2×#88060C2212yes—
49C2×#88057C2212yescomplemented
50C2×#88056C2212yescomplemented
51#11718704C2218yescomplemented
52C2×#88048C2212yescomplemented
53#11718477C22116yescomplemented
54#11718466C22116yescomplemented
55#11718387C2218yes—
56#11718382C2218yescomplemented
57C24×D13D411yescharacteristic
58C22×Q8×C13—21no—
59C22×Q8×C13—22no—
60C22×Q8×C13—44no—
61C22×Q8×C13C2312yes—
62C22×Q8×C13C2311yescharacteristic
63C22×Q8×C13C2314yes—
64C23×C4×C13—21no—
65C23×C4×C13C2311yescharacteristic
66C23×Dic13—21no—
67C23×Dic13D411yescharacteristic
68C2×Q8×D13—22no—
69C2×Q8×D13—44no—
70C2×Q8×D13C2314yes—
71C22×C4×D13—21no—
72C22×C4×D13—21no—
73C22×C4×D13—44no—
74C22×C4×D13D411yescharacteristic
75C22×C4×D13D411yescharacteristic
76C22×C4×D13D414yes—
77C22×C4×D13C2311yescharacteristic
78C22×C4×D13C2311yescharacteristic
79C22×C4×D13C2314yes—
80C22×Dic26—21no—
81C22×Dic26C2311yescharacteristic
82C2×C13×Q16—44no—
83C2×C13×Q16C2318yescomplemented
84C22×C8×C13C2312yes—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8C2314yes—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C22⋊C4—21no—
90C2×C22⋊Dic13—21no—
91#88200—24no—
92#88200—24no—
93#88200—28no—
94#88200—28no—
95#88200—22no—
96#88200C2318yes—
97#88200C2318yes—
98#88200C2314yes—
99C2×#6107—44no—
100C2×#6107C2318yescomplemented
101C2×#6103—21no—
102C2×#6103—21no—
103C2×#6103—22no—
104C2×#6103—28no—
105C2×#6103—22no—
106C2×C4⋊Dic13—21no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—21no—
109C2×C4⋊Dic13C2311yescharacteristic
110C2×C4⋊Dic13C2314yes—
111C2×C4⋊Dic13C2312yes—
112#88178—22no—
113#88178C2314yes—
114C2×#6101—21no—
115C2×#6101—21no—
116C2×#6101—21no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—28no—
120C22×#1055C2312yes—
121C2×#6094—44no—
122C2×#6094C2318yes—
123#88151—22no—
124#88151C2314yes—
125#88150—28no—
126C4⋊C4×D13—28no—
127C4⋊C4×D13—22no—
128C4⋊C4×D13C2314yes—
129C22⋊C4×D13—28no—
130#88132—28no—
131C13×#103C2318yescomplemented
132C13×C22⋊C8C2314yes—
133#88075C2318yescomplemented
134#88075C2318yescomplemented
135C22⋊#1055C2314yes—
136#88060C2318yes—
137#88057C2318yescomplemented
138#88056C2318yescomplemented
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—24no—
149C2×Q8×C13—22no—
150C2×Q8×C13—21no—
151C2×Q8×C13—24no—
152C2×Q8×C13—24no—
153C2×Q8×C13—24no—
154C2×Q8×C13—48no—
155C2×Q8×C13—44no—
156C2×Q8×C13—48no—
157C2×Q8×C13C2412yes—
158C2×Q8×C13C2414yes—
159C22×C4×C13—24no—
160C22×C4×C13—24no—
161C22×C4×C13—22no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—44no—
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2412yes—
168C22×C4×C13C2411yescharacteristic
169C22×Dic13—21no—
170C22×Dic13—24no—
171C22×Dic13—22no—
172C22×Dic13—21no—
173C22×Dic13—42no—
174C22×Dic13—44no—
175C22×Dic13C2×D411yescharacteristic
176C22×Dic13C2×D411yescharacteristic
177C22×Dic13C2×D414yes—
178Q8×D13—48no—
179Q8×D13—48no—
180C2×C4×D13—24no—
181C2×C4×D13—24no—
182C2×C4×D13—24no—
183C2×C4×D13—24no—
184C2×C4×D13—48no—
185C2×C4×D13—48no—
186C2×C4×D13—42no—
187C2×C4×D13—42no—
188C2×C4×D13—44no—
189C2×C4×D13—44no—
190C2×C4×D13C2×D412yes—
191C2×C4×D13C2×D412yes—
192C2×C4×D13C2×D414yes—
193C2×C4×D13C2×D414yes—
194C2×C4×D13C2412yes—
195C2×C4×D13C2412yes—
196C2×Dic26—24no—
197C2×Dic26—21no—
198C2×Dic26—24no—
199C2×Dic26—44no—
200C2×Dic26C2412yes—
201C13×Q16—48no—
202C2×C8×C13—24no—
203C2×C8×C13C2414yes—
204C13×C4⋊C4—24no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4C2412yes—
207C13×C22⋊C4—24no—
208C22⋊Dic13—24no—
209#6107—48no—
210#6103—24no—
211#6103—24no—
212#6103—28no—
213#6103—28no—
214C4⋊Dic13—21no—
215C4⋊Dic13—24no—
216C4⋊Dic13—22no—
217C4⋊Dic13—24no—
218C4⋊Dic13C2412yes—
219C4⋊Dic13C2414yes—
220#6101—24no—
221#6101—24no—
222#6101—24no—
223#6101—28no—
224#6101—28no—
225C2×#1055—24no—
226C2×#1055C2414yes—
227#6094—48no—
228C22×C22⋊Q8—131no—
229C22×C22⋊Q8—131no—
230#3195—1316no—
231C2×#483—132no—
232C2×#483—131no—
233C2×#483—131no—
234C2×#470—132no—
235C2×#470—132no—
236C2×#451—131no—
237C2×#451—132no—
238C2×#451D1311yescharacteristic, complemented
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—24no—
259Q8×C13—24no—
260Q8×C13—48no—
261Q8×C13—42no—
262Q8×C13—44no—
263C2×C4×C13—22no—
264C2×C4×C13—24no—
265C2×C4×C13—24no—
266C2×C4×C13—24no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—48no—
270C2×C4×C13—42no—
271C2×C4×C13—44no—
272C2×C4×C13—42no—
273C2×C4×C13C22×D412yes—
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13H(5,𝔽2)14yes—
276C2×C4×C13C2511yescharacteristic
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—24no—
281C2×Dic13—22no—
282C2×Dic13—44no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—48no—
286C2×Dic13—44no—
287C2×Dic13C22×D412yes—
288C2×Dic13C22×D412yes—
289C4×D13—24no—
290C4×D13—24no—
291C4×D13—24no—
292C4×D13—24no—
293C4×D13—44no—
294C4×D13—44no—
295C4×D13—48no—
296C4×D13—48no—
297Dic26—24no—
298Dic26—48no—
299Dic26—42no—
300C8×C13—24no—
301#1055—24no—
302C23×Q8—131no—
303C23×Q8C2×D1311yescharacteristic
304C24×C4—131no—
305C22×Q16—132no—
306C22×Q16C2×D1312yescomplemented
307C22×M16—132no—
308C2×C22⋊Q8—132no—
309C2×C22⋊Q8—138no—
310C2×C22⋊Q8—132no—
311C2×C22⋊Q8—131no—
312C2×C22⋊Q8—131no—
313C2×C22⋊Q8—138no—
314C2×C22⋊Q8—131no—
315C2×C22⋊Q8—261no—
316C2×C22⋊Q8—261no—
317C2×C22⋊Q8—264no—
318C2×C22⋊Q8—261no—
319C2×C22⋊Q8—264no—
320C2×C22⋊Q8—261no—
321C2×C22⋊Q8C2×D1311yescharacteristic
322C22×C4⋊C4—131no—
323C22×C4⋊C4—131no—
324C22×C4⋊C4—261no—
325C22×C4⋊C4—261no—
326C22×C22⋊C4—261no—
327C22×C22⋊C4—261no—
328#483—138no—
329#483—1316no—
330#483—138no—
331#470—1316no—
332#470—1316no—
333#451—138no—
334#451—1316no—
335#451C2×D1318yescomplemented
336C2×#106—132no—
337C2×#106—132no—
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—44no—
366C4×C13—42no—
367C4×C13#53412yes—
368C4×C13C2×H(5,𝔽2)12yes—
369Dic13—22no—
370Dic13—22no—
371Dic13—42no—
372Dic13—42no—
373Dic13—44no—
374C25—131no—
375C22×Q8—22no—
376C22×Q8—21no—
377C22×Q8—44no—
378C22×Q8—134no—
379C22×Q8—131no—
380C22×Q8—261no—
381C22×Q8—262no—
382C22×Q8—524no—
383C22×Q8C22×D1312yes—
384C22×Q8C22×D1311yescharacteristic
385C22×Q8C22×D1314yes—
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—44no—
400C2×Q16—138no—
401C2×Q16—524no—
402C2×Q16C22×D1318yescomplemented
403C2×M16—138no—
404C2×M16—524no—
405C22×C8—132no—
406C22×C8C22×D1312yes—
407C22⋊Q8—22no—
408C22⋊Q8—138no—
409C22⋊Q8—134no—
410C22⋊Q8—138no—
411C22⋊Q8—134no—
412C22⋊Q8—134no—
413C22⋊Q8—268no—
414C22⋊Q8—268no—
415C22⋊Q8—262no—
416C22⋊Q8—264no—
417C22⋊Q8—262no—
418C22⋊Q8—264no—
419C22⋊Q8—268no—
420C22⋊Q8—268no—
421C22⋊Q8—262no—
422C22⋊Q8C22×D1314yes—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—132no—
425C2×C4⋊C4—131no—
426C2×C4⋊C4—134no—
427C2×C4⋊C4—134no—
428C2×C4⋊C4—262no—
429C2×C4⋊C4—268no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—268no—
432C2×C4⋊C4—261no—
433C2×C4⋊C4—262no—
434C2×C4⋊C4—262no—
435C2×C4⋊C4—261no—
436C2×C4⋊C4—262no—
437C2×C4⋊C4—261no—
438C2×C4⋊C4—261no—
439C2×C4⋊C4C22×D1311yescharacteristic
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#106—138no—
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—22no—
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—48no—
478C2×Q8—44no—
479C2×Q8—48no—
480C2×Q8—132no—
481C2×Q8—264no—
482C2×Q8—261no—
483C2×Q8—264no—
484C2×Q8—524no—
485C2×Q8—528no—
486C2×Q8—528no—
487C2×Q8C23×D1312yes—
488C2×Q8C23×D1314yes—
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—262no—
510C22×C4—261no—
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—48no—
525Q16—528no—
526M16—528no—
527C2×C8—24no—
528C2×C8—134no—
529C2×C8—264no—
530C2×C8C23×D1314yes—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—132no—
534C4⋊C4—134no—
535C4⋊C4—264no—
536C4⋊C4—264no—
537C4⋊C4—268no—
538C4⋊C4—268no—
539C4⋊C4—264no—
540C4⋊C4—264no—
541C4⋊C4—261no—
542C4⋊C4—262no—
543C4⋊C4—264no—
544C4⋊C4C23×D1312yes—
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#8817214yes—
567C23C2×D4×D1312yes—
568C23C2×D4×D1311yescharacteristic
569Q8—24no—
570Q8—24no—
571Q8—24no—
572Q8—48no—
573Q8—44no—
574Q8—42no—
575Q8—264no—
576Q8—528no—
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—42no—
586C2×C4—44no—
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—524no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4C2×D4×D1312yes—
609C2×C4C2×D4×D1311yescharacteristic
610C2×C4#8825114yes—
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#1171929412yes—
627C22C2×#8817214yes—
628C22C2×#8817212yes—
629C22D13×#13712yes—
630C22C22×D4×D1311yescharacteristic
631C4—22no—
632C4—42no—
633C4—44no—
634C4—42no—
635C4—262no—
636C4—262no—
637C4—522no—
638C4—524no—
639C4—522no—
640C4#1171929412yes—
641C4C2×#8825112yes—
642C2—24no—
643C2—264no—
644C2—522no—
645C2#1312565814yesdirect product factor
646C2C2×#1171929411yescharacteristic
647C2C2×D13×#13711yescharacteristic
648C2C22×#8817211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#451C2
socleC23×C13C22×D4
prime radicalC24×D13D4
hypercenterC2×#451D13
hypocenterC13C2×#3195
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #13125658C2direct (N × H)
4. C2×#11718382C2semidirect
5. C2×#11718466C2semidirect
6. C2×#11718704C2semidirect
7. C2×#11718477C2semidirect
8. C2×#11718850C2semidirect
9. C2×#11718889C2semidirect
10. C2×#11718847C2semidirect
12. C2×C13×#451C2semidirect
16. C22×C13×Q16C22semidirect
25. C22×#6107C22semidirect
39. C13×#451C22semidirect
40. C2×C13×#103C22semidirect
42. #11718889C22semidirect
43. C2×#88075C22semidirect
44. C2×#88075C22semidirect
46. #11718850C22semidirect
47. #11718847C22semidirect
49. C2×#88057C22semidirect
50. C2×#88056C22semidirect
51. #11718704C22semidirect
52. C2×#88048C22semidirect
53. #11718477C22semidirect
54. #11718466C22semidirect
56. #11718382C22semidirect
83. C2×C13×Q16C23semidirect
100. C2×#6107C23semidirect
131. C13×#103C23semidirect
133. #88075C23semidirect
134. #88075C23semidirect
137. #88057C23semidirect
138. #88056C23semidirect
139. #88048C23semidirect
238. C2×#451D13semidirect
306. C22×Q16C2×D13semidirect
335. #451C2×D13semidirect
341. C2×#103C2×D13semidirect
402. C2×Q16C22×D13semidirect
453. #103C22×D13semidirect
458. C2×C13#3195semidirect
551. C13C2×#3195semidirect
645. C2#13125658direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882002
C2×D13×C22⋊Q82
#131256582
C2×#117183822
C2×#117184662
C2×#117187042
C2×#117184772
C2×#117188502
C2×#117188892
C2×#117188472
C2×#117183872
C2×C13×#4512
C2×#319513