Finite Group Databasebeta

← C2×#13114554 #15860321

Subgroups — C2×#13114554 #15860321

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6094C211yesmaximal, characteristic
2C22×#88146C211yesmaximal, characteristic
3C22×C4⋊C4×D13C211yesmaximal, characteristic
4#13114554C218yesmaximal, direct product factor
5C2×#11718143C211yesmaximal, characteristic, complemented
6C2×#11718121C211yesmaximal, characteristic, complemented
7C2×#11718121C211yesmaximal, characteristic, complemented
8C2×C13×#340C211yesmaximal, characteristic, complemented
9C23×C4×D13—21no—
10C23×C4×D13C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×#6103—21no—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101—21no—
18C22×C4×Dic13—21no—
19C23×#1055C2211yescharacteristic
20C22×#6094—24no—
21C22×#6094—24no—
22C22×#6094C418yescomplemented
23C22×#6094C2214yes—
24C2×#88146—22no—
25C2×#88146—24no—
26C2×#88146C418yescomplemented
27C2×#88146C2214yes—
28C2×C4⋊C4×D13—22no—
29C2×C4⋊C4×D13—24no—
30C2×C4⋊C4×D13C418yescomplemented
31C2×C4⋊C4×D13C2214yes—
32C13×#340C2214yescomplemented
33#11718143C2214yescomplemented
34#11718121C2214yescomplemented
35#11718121C2214yescomplemented
36C24×D13D411yescharacteristic
37C23×C4×C13—21no—
38C23×C4×C13—21no—
39C23×C4×C13C2311yescharacteristic
40C23×Dic13—21no—
41C23×Dic13—21no—
42C23×Dic13D411yescharacteristic
43C22×C4×D13—28no—
44C22×C4×D13—24no—
45C22×C4×D13—44no—
46C22×C4×D13—44no—
47C22×C4×D13C2×C414yes—
48C22×C4×D13C2×C414yes—
49C22×C4×D13C2×C414yes—
50C22×C4×D13D412yes—
51C22×C4×D13D414yes—
52C22×C4×D13D414yes—
53C22×C4×D13Q814yes—
54C22×C4×D13C2312yes—
55C22×C8×C13—22no—
56C22×C8×C13—22no—
57C22×C8×C13C2×C414yescomplemented
58C22×C8×C13C2312yes—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4C2×C414yes—
64C2×C13×C4⋊C4C2×C414yescomplemented
65C2×C13×C4⋊C4C2312yes—
66C2×C13×C4⋊C4C2312yes—
67C2×#6103—28no—
68C2×#6103—24no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13C2×C414yes—
74C2×C4⋊Dic13C2×C414yescomplemented
75C2×C4⋊Dic13C2312yes—
76C2×C4⋊Dic13C2312yes—
77C2×#6101—28no—
78C2×#6101—24no—
79C2×C4×Dic13—28no—
80C2×C4×Dic13—24no—
81C22×#1055—22no—
82C22×#1055—22no—
83C22×#1055C2×C414yescomplemented
84C22×#1055C2312yes—
85C2×#6094—232no—
86C2×#6094—28no—
87C2×#6094—28no—
88C2×#6094C2×C4116yescomplemented
89#88146—216no—
90#88146—28no—
91#88146C2×C4116yescomplemented
92C4⋊C4×D13—216no—
93C4⋊C4×D13—28no—
94C4⋊C4×D13C2×C4116yescomplemented
95C2×#1736—131nomaximal, Sylow
96C24×C13C2×D411yescharacteristic
97C23×D13—22no—
98C23×D13—22no—
99C23×D13—22no—
100C23×D13—22no—
101C23×D13C22⋊C414yes—
102C23×D13C22⋊C414yes—
103C23×D13C4⋊C414yes—
104C23×D13C2×D412yes—
105C22×C4×C13—24no—
106C22×C4×C13—24no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—42no—
110C22×C4×C13—42no—
111C22×C4×C13—42no—
112C22×C4×C13—42no—
113C22×C4×C13C22×C412yes—
114C22×C4×C13C22×C412yes—
115C22×C4×C13C22×C412yes—
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D412yes—
118C22×C4×C13C2×D412yes—
119C22×C4×C13C2×Q812yes—
120C22×C4×C13C2411yescharacteristic
121C22×Dic13—24no—
122C22×Dic13—24no—
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—42no—
126C22×Dic13—42no—
127C22×Dic13—42no—
128C22×Dic13—42no—
129C22×Dic13C22⋊C414yes—
130C22×Dic13C22⋊C414yes—
131C22×Dic13C4⋊C414yes—
132C22×Dic13C2×D412yes—
133C2×C4×D13—216no—
134C2×C4×D13—48no—
135C2×C4×D13—48no—
136C2×C4×D13—432no—
137C2×C4×D13C42116yes—
138C2×C4×D13C22⋊C418yes—
139C2×C4×D13C22⋊C418yes—
140C2×C4×D13C22⋊C4116yes—
141C2×C4×D13C4⋊C418yes—
142C2×C4×D13C4⋊C4116yes—
143C2×C4×D13C4⋊C4116yes—
144C2×C4×D13C22×C414yes—
145C2×C4×D13C22×C414yes—
146C2×C4×D13C22×C414yes—
147C2×C4×D13C2×D414yes—
148C2×C4×D13C2×D414yes—
149C2×C4×D13C2×Q814yes—
150C2×C8×C13—28no—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C2×C8×C13C22×C414yescomplemented
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4C22×C414yes—
159C13×C4⋊C4C22×C414yescomplemented
160#6103—216no—
161C4⋊Dic13—24no—
162C4⋊Dic13—24no—
163C4⋊Dic13—22no—
164C4⋊Dic13—22no—
165C4⋊Dic13C22×C414yes—
166C4⋊Dic13C22×C414yescomplemented
167#6101—216no—
168C4×Dic13—216no—
169C2×#1055—28no—
170C2×#1055—22no—
171C2×#1055—22no—
172C2×#1055C22×C414yescomplemented
173#6094—232no—
174C23×M16—131no—
175C22×#117—131no—
176C23×C4⋊C4—131no—
177#1736—138no—
178C2×#340—131no—
179C2×#340—131no—
180C2×#340—131no—
181C2×#340D1311yescharacteristic, complemented
182C23×C13C2×C22⋊C412yes—
183C23×C13C2×C22⋊C412yes—
184C23×C13C2×C4⋊C412yes—
185C23×C13AGL(1,ℤ/8)12yes—
186C23×C13AGL(1,ℤ/8)12yes—
187C23×C13#13712yes—
188C23×C13#13712yes—
189C23×C13C22×D411yescharacteristic
190C22×D13—22no—
191C22×D13—22no—
192C22×D13—22no—
193C22×D13—22no—
194C22×D13—28no—
195C22×D13—28no—
196C22×D13—28no—
197C22×D13—28no—
198C22×D13—28no—
199C22×D13—28no—
200C22×D13#95116yes—
201C22×D13C2×C22⋊C414yes—
202C22×D13C2×C22⋊C414yes—
203C22×D13C2×C4⋊C414yes—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—48no—
211C2×C4×C13—48no—
212C2×C4×C13C2×C4214yes—
213C2×C4×C13C2×C22⋊C414yes—
214C2×C4×C13C2×C22⋊C412yes—
215C2×C4×C13C2×C22⋊C412yes—
216C2×C4×C13C2×C4⋊C414yes—
217C2×C4×C13C2×C4⋊C414yes—
218C2×C4×C13C2×C4⋊C412yes—
219C2×C4×C13C23×C411yescharacteristic
220C2×C4×C13C23×C411yescharacteristic
221C2×C4×C13C23×C411yescharacteristic
222C2×C4×C13C22×D411yescharacteristic
223C2×C4×C13C22×D411yescharacteristic
224C2×C4×C13C22×Q811yescharacteristic
225C2×Dic13—24no—
226C2×Dic13—24no—
227C2×Dic13—42no—
228C2×Dic13—42no—
229C2×Dic13—42no—
230C2×Dic13—42no—
231C2×Dic13—48no—
232C2×Dic13—48no—
233C2×Dic13#95116yes—
234C2×Dic13C2×C22⋊C414yes—
235C2×Dic13C2×C22⋊C414yes—
236C2×Dic13C2×C4⋊C414yes—
237C4×D13—432no—
238C4×D13#95132yes—
239C4×D13C2×C4218yes—
240C4×D13C2×C22⋊C418yes—
241C4×D13C2×C4⋊C418yes—
242C4×D13C2×C4⋊C418yes—
243C8×C13—24no—
244#1055—24no—
245C24×C4—131no—
246C24×C4—261no—
247C22×M16—138no—
248C22×M16—134no—
249C22×M16—264no—
250C22×M16—264no—
251C23×C8—131no—
252C23×C8C2×D1311yescharacteristic
253C2×#117—138no—
254C2×#117—134no—
255C2×#117—262no—
256C2×#117—264no—
257C22×C4⋊C4—131no—
258C22×C4⋊C4—131no—
259C22×C4⋊C4—138no—
260C22×C4⋊C4—134no—
261C22×C4⋊C4—262no—
262C22×C4⋊C4—264no—
263C22×C4⋊C4—261no—
264C22×C4⋊C4C2×D1311yescharacteristic
265C22×C4⋊C4C2×D1311yescharacteristic
266C22×C22⋊C4—261no—
267C22×C42—261no—
268#340—134no—
269#340—134no—
270#340—134no—
271#340C2×D1314yescomplemented
272C22×C13C2×#9514yes—
273C22×C13#41714yes—
274C22×C13#41714yes—
275C22×C13#41814yes—
276C22×C13#41914yes—
277C22×C13#42814yes—
278C22×C13#42814yes—
279C22×C13C22×C22⋊C411yescharacteristic
280C22×C13C22×C22⋊C411yescharacteristic
281C22×C13C22×C4⋊C411yescharacteristic
282C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C13C2×#13711yescharacteristic
285C22×C13C2×#13711yescharacteristic
286C2×D13—24no—
287C2×D13—24no—
288C2×D13—24no—
289C2×D13—24no—
290C2×D13—24no—
291C2×D13—24no—
292C2×D13—232no—
293C2×D13C2×#9518yes—
294C4×C13—44no—
295C4×C13—44no—
296C4×C13C2×#9514yes—
297C4×C13C22×C4211yescharacteristic
298C4×C13C22×C22⋊C411yescharacteristic
299C4×C13C22×C4⋊C411yescharacteristic
300C4×C13C22×C4⋊C411yescharacteristic
301Dic13—44no—
302Dic13—44no—
303Dic13C2×#9518yes—
304C25—131no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—131no—
308C23×C4—134no—
309C23×C4—134no—
310C23×C4—134no—
311C23×C4—132no—
312C23×C4—134no—
313C23×C4—134no—
314C23×C4—134no—
315C23×C4—132no—
316C23×C4—268no—
317C23×C4—264no—
318C23×C4—261no—
319C23×C4—261no—
320C23×C4—524no—
321C23×C4—524no—
322C23×C4C22×D1311yescharacteristic
323C2×M16—1316no—
324C2×M16—2632no—
325C2×M16—268no—
326C2×M16—268no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—134no—
330C22×C8—132no—
331C22×C8—262no—
332C22×C8—262no—
333C22×C8C4×D1314yescomplemented
334C22×C8C22×D1312yes—
335#117—1316no—
336#117—2616no—
337#117—268no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—134no—
343C2×C4⋊C4—134no—
344C2×C4⋊C4—132no—
345C2×C4⋊C4—132no—
346C2×C4⋊C4—1316no—
347C2×C4⋊C4—2616no—
348C2×C4⋊C4—268no—
349C2×C4⋊C4—268no—
350C2×C4⋊C4—264no—
351C2×C4⋊C4—261no—
352C2×C4⋊C4—262no—
353C2×C4⋊C4—261no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4C4×D1314yes—
356C2×C4⋊C4C4×D1314yescomplemented
357C2×C4⋊C4C22×D1312yes—
358C2×C4⋊C4C22×D1312yes—
359C2×C22⋊C4—268no—
360C2×C22⋊C4—264no—
361C2×C42—268no—
362C2×C42—264no—
363C2×C13#173618yescomplemented
364C2×C13C22×#9511yescharacteristic
365C2×C13C2×#41811yescharacteristic
366C2×C13C2×#41911yescharacteristic
367C2×C13C2×#41711yescharacteristic
368C2×C13C2×#41711yescharacteristic
369C2×C13C2×#42811yescharacteristic
370C2×C13C2×#42811yescharacteristic
371D13—28no—
372C24—134no—
373C24—134no—
374C24—134no—
375C24—132no—
376C24—262no—
377C24—262no—
378C24—262no—
379C24—262no—
380C24D4×D1311yescharacteristic
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—134no—
390C22×C4—134no—
391C22×C4—134no—
392C22×C4—132no—
393C22×C4—1316no—
394C22×C4—138no—
395C22×C4—138no—
396C22×C4—1316no—
397C22×C4—138no—
398C22×C4—1316no—
399C22×C4—1316no—
400C22×C4—134no—
401C22×C4—134no—
402C22×C4—134no—
403C22×C4—134no—
404C22×C4—134no—
405C22×C4—134no—
406C22×C4—2616no—
407C22×C4—264no—
408C22×C4—264no—
409C22×C4—262no—
410C22×C4—262no—
411C22×C4—5232no—
412C22×C4—528no—
413C22×C4—528no—
414C22×C4—522no—
415C22×C4—522no—
416C22×C4—522no—
417C22×C4—522no—
418C22×C4C2×C4×D1312yes—
419C22×C4C2×C4×D1312yes—
420C22×C4C2×C4×D1312yes—
421C22×C4D4×D1311yescharacteristic
422C22×C4D4×D1312yes—
423C22×C4D4×D1312yes—
424C22×C4Q8×D1312yes—
425C22×C4C23×D1311yescharacteristic
426M16—2632no—
427C2×C8—28no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—134no—
431C2×C8—268no—
432C2×C8—262no—
433C2×C8—262no—
434C2×C8C2×C4×D1314yescomplemented
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—134no—
440C4⋊C4—134no—
441C4⋊C4—2616no—
442C4⋊C4—264no—
443C4⋊C4—264no—
444C4⋊C4—262no—
445C4⋊C4—262no—
446C4⋊C4C2×C4×D1314yes—
447C4⋊C4C2×C4×D1314yescomplemented
448C22⋊C4—2616no—
449C42—2616no—
450C13C2×#173611yescharacteristic, complemented, Sylow
451C23—134no—
452C23—134no—
453C23—134no—
454C23—1316no—
455C23—268no—
456C23—268no—
457C23—262no—
458C23—262no—
459C23—262no—
460C23—262no—
461C23—268no—
462C23—268no—
463C23—268no—
464C23—268no—
465C23C22⋊C4×D1312yes—
466C23C22⋊C4×D1312yes—
467C23C4⋊C4×D1312yes—
468C23#8816512yes—
469C23#8816812yes—
470C23#8816912yes—
471C23#8817212yes—
472C23C2×D4×D1311yescharacteristic
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—48no—
476C2×C4—48no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—134no—
482C2×C4—134no—
483C2×C4—134no—
484C2×C4—1316no—
485C2×C4—138no—
486C2×C4—138no—
487C2×C4—138no—
488C2×C4—138no—
489C2×C4—1332no—
490C2×C4—264no—
491C2×C4—264no—
492C2×C4—5232no—
493C2×C4—528no—
494C2×C4—522no—
495C2×C4—522no—
496C2×C4—522no—
497C2×C4—522no—
498C2×C4—528no—
499C2×C4C42×D1314yes—
500C2×C4C22⋊C4×D1314yes—
501C2×C4C22⋊C4×D1312yes—
502C2×C4C22⋊C4×D1312yes—
503C2×C4C4⋊C4×D1314yes—
504C2×C4C4⋊C4×D1314yes—
505C2×C4C4⋊C4×D1312yes—
506C2×C4C22×C4×D1311yescharacteristic
507C2×C4C22×C4×D1311yescharacteristic
508C2×C4C22×C4×D1311yescharacteristic
509C2×C4C2×D4×D1311yescharacteristic
510C2×C4C2×D4×D1311yescharacteristic
511C2×C4C2×Q8×D1311yescharacteristic
512C8—24no—
513C8—264no—
514C22—138no—
515C22—264no—
516C22—264no—
517C22—264no—
518C22—264no—
519C22—264no—
520C22—264no—
521C22—2632no—
522C22D13×#9514yes—
523C22#1171843114yes—
524C22#1171843214yes—
525C22#1171846314yes—
526C22#1171846414yes—
527C22#1171852214yes—
528C22#1171854214yes—
529C22C2×C22⋊C4×D1311yescharacteristic
530C22C2×C22⋊C4×D1311yescharacteristic
531C22C2×C4⋊C4×D1311yescharacteristic
532C22C2×#8816511yescharacteristic
533C22C2×#8816811yescharacteristic
534C22C2×#8816911yescharacteristic
535C22C2×#8817211yescharacteristic
536C4—44no—
537C4—44no—
538C4—138no—
539C4—524no—
540C4—524no—
541C4D13×#9514yes—
542C4C2×C42×D1311yescharacteristic
543C4C2×C22⋊C4×D1311yescharacteristic
544C4C2×C4⋊C4×D1311yescharacteristic
545C4C2×C4⋊C4×D1311yescharacteristic
546C2—268no—
547C2#1311455418yesdirect product factor
548C2C2×D13×#9511yescharacteristic
549C2C2×#1171843111yescharacteristic
550C2C2×#1171846311yescharacteristic
551C2C2×#1171843211yescharacteristic
552C2C2×#1171846411yescharacteristic
553C2C2×#1171852211yescharacteristic
554C2C2×#1171854211yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenterC2×#340D13
hypocenterC13C2×#1736
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #13114554C2direct (N × H)
5. C2×#11718143C2semidirect
6. C2×#11718121C2semidirect
7. C2×#11718121C2semidirect
8. C2×C13×#340C2semidirect
22. C22×#6094C4semidirect
26. C2×#88146C4semidirect
30. C2×C4⋊C4×D13C4semidirect
32. C13×#340C22semidirect
33. #11718143C22semidirect
34. #11718121C22semidirect
35. #11718121C22semidirect
57. C22×C8×C13C2×C4semidirect
64. C2×C13×C4⋊C4C2×C4semidirect
74. C2×C4⋊Dic13C2×C4semidirect
83. C22×#1055C2×C4semidirect
88. C2×#6094C2×C4semidirect
91. #88146C2×C4semidirect
94. C4⋊C4×D13C2×C4semidirect
153. C2×C8×C13C22×C4semidirect
159. C13×C4⋊C4C22×C4semidirect
166. C4⋊Dic13C22×C4semidirect
172. C2×#1055C22×C4semidirect
181. C2×#340D13semidirect
271. #340C2×D13semidirect
333. C22×C8C4×D13semidirect
356. C2×C4⋊C4C4×D13semidirect
363. C2×C13#1736semidirect
434. C2×C8C2×C4×D13semidirect
447. C4⋊C4C2×C4×D13semidirect
450. C13C2×#1736semidirect
547. C2#13114554direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#60942
C22×#881462
C22×C4⋊C4×D132
#131145542
C2×#117181432
C2×#117181212
C2×C13×#3402
C2×#173613