Finite Group Databasebeta

← C2×C13×#2036 #15709817

Subgroups — C2×C13×#2036 #15709817

Order 3328.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic
2C22×C13×#107C211yesmaximal, characteristic, complemented
3C22×C13×#103C211yesmaximal, characteristic, complemented
4C22×C13×#103C211yesmaximal, characteristic, complemented
5C22×C13×C22⋊C8C211yesmaximal, characteristic
6C2×C13×#380C211yesmaximal, characteristic
7C13×#2036C218yesmaximal, direct product factor
8C2×C13×#340C211yesmaximal, characteristic, complemented
9C23×Q8×C13C2211yescharacteristic
10C24×C4×C13C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C23×C8×C13C2211yescharacteristic
13C2×C13×C22⋊Q8—24no—
14C2×C13×C22⋊Q8—22no—
15C2×C13×C22⋊Q8—24no—
16C2×C13×C22⋊Q8C2214yes—
17C22×C13×C4⋊C4—21no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4—21no—
22C22×C13×C22⋊C4—21no—
23C2×C13×#107—24no—
24C2×C13×#107C2214yescomplemented
25C2×C13×#103—24no—
26C2×C13×#103—24no—
27C2×C13×#103C2214yescomplemented
28C2×C13×#103C2214yescomplemented
29C2×C13×C22⋊C8—24no—
30C2×C13×C22⋊C8C2214yes—
31C13×#380—22no—
32C13×#380C2214yes—
33C2×C13×#95—21no—
34C13×#340C2214yescomplemented
35C25×C13D411yescharacteristic
36C22×Q8×C13—22no—
37C22×Q8×C13—21no—
38C22×Q8×C13—22no—
39C22×Q8×C13—22no—
40C22×Q8×C13—22no—
41C22×Q8×C13—22no—
42C22×Q8×C13D414yes—
43C22×Q8×C13C2312yes—
44C23×C4×C13—21no—
45C23×C4×C13—21no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—22no—
50C23×C4×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13—21no—
53C23×C4×C13—21no—
54C23×C4×C13D412yes—
55C23×C4×C13D411yescharacteristic
56C23×C4×C13C2312yes—
57C23×C4×C13C2311yescharacteristic
58C22×C8×C13—22no—
59C22×C8×C13—22no—
60C22×C8×C13—22no—
61C22×C8×C13—22no—
62C22×C8×C13—22no—
63C22×C8×C13D414yes—
64C22×C8×C13C2312yes—
65C22×C8×C13C2312yes—
66C13×C22⋊Q8—216no—
67C13×C22⋊Q8—28no—
68C13×C22⋊Q8—28no—
69C2×C13×C4⋊C4—28no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4D414yes—
80C2×C13×C4⋊C4C2312yes—
81C2×C13×C4⋊C4C2312yes—
82C2×C13×C4⋊C4C2312yes—
83C2×C13×C22⋊C4—28no—
84C2×C13×C22⋊C4—24no—
85C2×C13×C22⋊C4—24no—
86C2×C13×C22⋊C4—44no—
87C13×#107—28no—
88C13×#103—28no—
89C13×#103—28no—
90C13×C22⋊C8—28no—
91C13×#95—24no—
92C2×#2036C1311yesmaximal, characteristic, direct product factor, Sylow
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13Q1614yes—
100C24×C13C2×D412yes—
101C24×C13C2×D411yescharacteristic
102C2×Q8×C13—24no—
103C2×Q8×C13—22no—
104C2×Q8×C13—28no—
105C2×Q8×C13—28no—
106C2×Q8×C13—22no—
107C2×Q8×C13—22no—
108C2×Q8×C13—22no—
109C2×Q8×C13—22no—
110C2×Q8×C13—42no—
111C2×Q8×C13—44no—
112C2×Q8×C13—42no—
113C2×Q8×C13—44no—
114C2×Q8×C13C2×D414yes—
115C22×C4×C13—24no—
116C22×C4×C13—24no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—24no—
123C22×C4×C13—24no—
124C22×C4×C13—24no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13—44no—
138C22×C4×C13—44no—
139C22×C4×C13—44no—
140C22×C4×C13—44no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13C2411yescharacteristic
156C2×C8×C13—28no—
157C2×C8×C13—22no—
158C2×C8×C13—22no—
159C2×C8×C13—22no—
160C2×C8×C13—22no—
161C2×C8×C13—22no—
162C2×C8×C13—44no—
163C2×C8×C13C2×D414yes—
164C13×C4⋊C4—216no—
165C13×C4⋊C4—24no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4C2×D414yes—
174C13×C22⋊C4—216no—
175C13×C22⋊C4—48no—
176C22×C22⋊Q8C2×C1311yescharacteristic
177C22×#107C2×C1311yescharacteristic, complemented
178C22×#103C2×C1311yescharacteristic, complemented
179C22×#103C2×C1311yescharacteristic, complemented
180C22×C22⋊C8C2×C1311yescharacteristic
181C2×#380C2×C1311yescharacteristic
182#2036C2×C1318yesdirect product factor
183C2×#340C2×C1311yescharacteristic, complemented
184C23×C13—22no—
185C23×C13—22no—
186C23×C13—22no—
187C23×C13—22no—
188C23×C13—22no—
189C23×C13—22no—
190C23×C13—28no—
191C23×C13—28no—
192C23×C13—28no—
193C23×C13—44no—
194C23×C13—44no—
195C23×C13—44no—
196C23×C13—44no—
197C23×C13#12012yes—
198C23×C13#12112yes—
199C23×C13#12312yes—
200C23×C13C2×Q1614yes—
201C23×C13C2×Q1612yes—
202C23×C13#13512yes—
203C23×C13AGL(1,ℤ/8)12yes—
204C23×C13#13712yes—
205C23×C13C22×D411yescharacteristic
206Q8×C13—24no—
207Q8×C13—24no—
208Q8×C13—42no—
209Q8×C13—42no—
210Q8×C13—48no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—44no—
221C2×C4×C13—48no—
222C2×C4×C13—48no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—48no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—84no—
235C2×C4×C13—84no—
236C2×C4×C13#12012yes—
237C2×C4×C13#12114yes—
238C2×C4×C13#12114yes—
239C2×C4×C13#12112yes—
240C2×C4×C13#12314yes—
241C2×C4×C13#12312yes—
242C2×C4×C13#12414yes—
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C8×C13—24no—
250C8×C13—42no—
251C23×Q8C22×C1311yescharacteristic
252C24×C4C22×C1311yescharacteristic
253C23×C8C22×C1311yescharacteristic
254C23×C8C22×C1311yescharacteristic
255C2×C22⋊Q8—24no—
256C2×C22⋊Q8—22no—
257C2×C22⋊Q8—24no—
258C2×C22⋊Q8C22×C1314yes—
259C22×C4⋊C4—21no—
260C22×C4⋊C4C22×C1311yescharacteristic
261C22×C4⋊C4C22×C1311yescharacteristic
262C22×C4⋊C4C22×C1311yescharacteristic
263C22×C22⋊C4—21no—
264C22×C22⋊C4—21no—
265C2×#107—24no—
266C2×#107C22×C1314yescomplemented
267C2×#103—24no—
268C2×#103—24no—
269C2×#103C22×C1314yescomplemented
270C2×#103C22×C1314yescomplemented
271C2×C22⋊C8—24no—
272C2×C22⋊C8C22×C1314yes—
273#380—22no—
274#380C22×C1314yes—
275C2×#95—21no—
276#340C22×C1314yescomplemented
277C22×C13—24no—
278C22×C13—24no—
279C22×C13—24no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—416no—
285C22×C13#39414yes—
286C22×C13#44914yes—
287C22×C13#45114yes—
288C22×C13#46714yes—
289C22×C13#46814yes—
290C22×C13#48414yes—
291C22×C13#48514yes—
292C22×C13C2×#12011yescharacteristic
293C22×C13C2×#12111yescharacteristic
294C22×C13C2×#12311yescharacteristic
295C22×C13C22×Q1611yescharacteristic
296C22×C13C2×#13511yescharacteristic
297C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C13C2×#13711yescharacteristic
299C4×C13—42no—
300C4×C13—44no—
301C4×C13—44no—
302C4×C13—82no—
303C4×C13—82no—
304C4×C13#39414yes—
305C4×C13C2×#12111yescharacteristic
306C4×C13C2×#12111yescharacteristic
307C4×C13C2×#12311yescharacteristic
308C4×C13C2×#12411yescharacteristic
309C25D4×C1311yescharacteristic
310C22×Q8—22no—
311C22×Q8—21no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8D4×C1314yes—
317C22×Q8C23×C1312yes—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4D4×C1311yescharacteristic
329C23×C4D4×C1312yes—
330C23×C4C23×C1312yes—
331C23×C4C23×C1311yescharacteristic
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8D4×C1314yes—
338C22×C8C23×C1312yes—
339C22×C8C23×C1312yes—
340C22⋊Q8—216no—
341C22⋊Q8—28no—
342C22⋊Q8—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4D4×C1314yes—
354C2×C4⋊C4C23×C1312yes—
355C2×C4⋊C4C23×C1312yes—
356C2×C4⋊C4C23×C1312yes—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—44no—
361#107—28no—
362#103—28no—
363#103—28no—
364C22⋊C8—28no—
365#95—24no—
366C2×C13—44no—
367C2×C13#203618yesdirect product factor
368C2×C13C2×#39411yescharacteristic
369C2×C13C2×#45111yescharacteristic
370C2×C13C2×#44911yescharacteristic
371C2×C13C2×#46711yescharacteristic
372C2×C13C2×#46811yescharacteristic
373C2×C13C2×#48511yescharacteristic
374C2×C13C2×#48411yescharacteristic
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24C13×Q1614yes—
382C24C2×D4×C1312yes—
383C24C2×D4×C1311yescharacteristic
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—28no—
387C2×Q8—28no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—44no—
393C2×Q8—42no—
394C2×Q8—42no—
395C2×Q8—44no—
396C2×Q8C2×D4×C1314yes—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4C2×D4×C1312yes—
430C22×C4C2×D4×C1311yescharacteristic
431C22×C4C2×D4×C1312yes—
432C22×C4C2×D4×C1312yes—
433C22×C4C2×D4×C1312yes—
434C22×C4C13×#4112yes—
435C22×C4C13×#4112yes—
436C22×C4C13×#4112yes—
437C22×C4C24×C1311yescharacteristic
438C2×C8—28no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—44no—
445C2×C8C2×D4×C1314yes—
446C4⋊C4—216no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—42no—
454C4⋊C4—42no—
455C4⋊C4C2×D4×C1314yes—
456C22⋊C4—216no—
457C22⋊C4—48no—
458C13C2×#203611yescharacteristic, direct product factor, Sylow
459C23—28no—
460C23—28no—
461C23—28no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23C13×#12012yes—
473C23C13×#12112yes—
474C23C13×#12312yes—
475C23C2×C13×Q1614yes—
476C23C2×C13×Q1612yes—
477C23C13×#13512yes—
478C23C13×AGL(1,ℤ/8)12yes—
479C23C13×#13712yes—
480C23C22×D4×C1311yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—48no—
484Q8—42no—
485Q8—42no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—44no—
492C2×C4—48no—
493C2×C4—48no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—48no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—84no—
510C2×C4—84no—
511C2×C4C13×#12012yes—
512C2×C4C13×#12112yes—
513C2×C4C13×#12114yes—
514C2×C4C13×#12114yes—
515C2×C4C13×#12312yes—
516C2×C4C13×#12314yes—
517C2×C4C13×#12414yes—
518C2×C4C22×D4×C1311yescharacteristic
519C2×C4C22×D4×C1311yescharacteristic
520C2×C4C22×D4×C1311yescharacteristic
521C2×C4C2×C13×#4111yescharacteristic
522C2×C4C2×C13×#4111yescharacteristic
523C2×C4C2×C13×#4111yescharacteristic
524C8—24no—
525C8—42no—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—42no—
530C22—416no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22C13×#39414yes—
535C22C13×#44914yes—
536C22C13×#45114yes—
537C22C13×#46714yes—
538C22C13×#46814yes—
539C22C13×#48414yes—
540C22C13×#48514yes—
541C22C2×C13×#12011yescharacteristic
542C22C2×C13×#12111yescharacteristic
543C22C2×C13×#12311yescharacteristic
544C22C22×C13×Q1611yescharacteristic
545C22C2×C13×#13511yescharacteristic
546C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
547C22C2×C13×#13711yescharacteristic
548C4—42no—
549C4—44no—
550C4—44no—
551C4—82no—
552C4—82no—
553C4C13×#39414yes—
554C4C2×C13×#12111yescharacteristic
555C4C2×C13×#12111yescharacteristic
556C4C2×C13×#12311yescharacteristic
557C4C2×C13×#12411yescharacteristic
558C2—44no—
559C2C13×#203618yesdirect product factor
560C2C2×C13×#39411yescharacteristic
561C2C2×C13×#45111yescharacteristic
562C2C2×C13×#44911yescharacteristic
563C2C2×C13×#46711yescharacteristic
564C2C2×C13×#46811yescharacteristic
565C2C2×C13×#48511yescharacteristic
566C2C2×C13×#48411yescharacteristic
subgroupG/H
center, socleC24×C13C2×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC25×C13D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C13 ◁ C24×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C13×#107C2semidirect
3. C22×C13×#103C2semidirect
4. C22×C13×#103C2semidirect
7. C13×#2036C2direct (N × H)
8. C2×C13×#340C2semidirect
24. C2×C13×#107C22semidirect
27. C2×C13×#103C22semidirect
28. C2×C13×#103C22semidirect
34. C13×#340C22semidirect
92. C2×#2036C13direct (N × H)
177. C22×#107C2×C13semidirect
178. C22×#103C2×C13semidirect
179. C22×#103C2×C13semidirect
182. #2036C2×C13direct (N × H)
183. C2×#340C2×C13semidirect
266. C2×#107C22×C13semidirect
269. C2×#103C22×C13semidirect
270. C2×#103C22×C13semidirect
276. #340C22×C13semidirect
367. C2×C13#2036direct (N × H)
458. C13C2×#2036direct (N × H)
559. C2C13×#2036direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×C22⋊Q82
C22×C13×#1072
C22×C13×#1032
C22×C13×C22⋊C82
C2×C13×#3802
C13×#20362
C2×C13×#3402
C2×#203613