Finite Group Databasebeta

← C2×#13124759 #16730697

Subgroups — C2×#13124759 #16730697

Order 3328.

2650 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2#13124759C2116yesmaximal, direct product factor
3C2×#11718631C212yesmaximal, complemented
4C2×#11718629C212yesmaximal, complemented
5C2×#11718632C212yesmaximal, complemented
6C2×#11718628C212yesmaximal, complemented
7C2×#11718625C212yesmaximal, complemented
8C2×#11718627C212yesmaximal, complemented
9C2×#11718868C211yesmaximal, characteristic, complemented
10C23×C13×C4⋊C4C211yesmaximal, characteristic, complemented
11C24×C4×C13—21no—
12C24×C4×C13C2211yescharacteristic
13C22×#6127C2211yescharacteristic
14C22×C13×C4⋊C4—24no—
15C22×C13×C4⋊C4—21no—
16C22×C13×C4⋊C4—21no—
17C22×C13×C4⋊C4—21no—
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2212yes—
21C22×C13×C4⋊C4C2218yescomplemented
22C2×#88207—21no—
23#11719496—24no—
24#11719496C2218yes—
25C2×#88184C2211yescharacteristic
26C2×#88184C2211yescharacteristic
27C2×#88183—21no—
28C2×C4×C22⋊D13—21no—
29C2×C4×C22⋊D13—21no—
30C2×#88180C2211yescharacteristic
31C2×#88178C2211yescharacteristic
32C2×#88178C2211yescharacteristic
33C22×#6099C2212yes—
34#11718868C2218yescomplemented
35C2×C22⋊#1055C2212yes—
36C2×C22⋊#1055C2212yes—
37#11718632C22116yescomplemented
38#11718631C22116yescomplemented
39C2×#88050C2214yescomplemented
40#11718629C22116yescomplemented
41#11718628C22116yescomplemented
42#11718627C22116yescomplemented
43C2×#88049C2214yescomplemented
44#11718625C22116yescomplemented
45C2×#88048C2214yescomplemented
46C2×#88047C2214yescomplemented
47C25×C13D411yescharacteristic
48C23×C4×C13—28no—
49C23×C4×C13—22no—
50C23×C4×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13—28no—
53C23×C4×C13—48no—
54C23×C4×C13D411yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13D411yescharacteristic
57C23×C4×C13D414yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2314yes—
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C22×C22⋊D13—21no—
64C22×C22⋊D13—21no—
65C2×#6127—22no—
66C2×#6127—28no—
67C2×#6127C2314yes—
68C22×D52C2311yescharacteristic
69C22×C4×D13—21no—
70C22×Dic26C2311yescharacteristic
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—24no—
77C2×C13×C4⋊C4—28no—
78C2×C13×C4⋊C4—28no—
79C2×C13×C4⋊C4—28no—
80C2×C13×C4⋊C4C2314yes—
81C2×C13×C4⋊C4C2318yes—
82C2×C13×C4⋊C4C2318yes—
83C2×C13×C4⋊C4C2318yes—
84#88207—28no—
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88#88184—22no—
89#88184—22no—
90#88184C2314yes—
91#88184C2314yes—
92#88183—28no—
93C4×C22⋊D13—28no—
94C4×C22⋊D13—28no—
95C2×#6103—21no—
96C2×#6103—21no—
97#88180—22no—
98#88180C2314yes—
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101#88178—22no—
102#88178—22no—
103#88178C2314yes—
104#88178C2314yes—
105C2×#6101—21no—
106C2×#6101—21no—
107C2×C4×Dic13—21no—
108C2×#6099—28no—
109C2×#6099C2318yes—
110C22×#1055C2314yes—
111C22⋊#1055C2318yes—
112C22⋊#1055C2318yes—
113#88050C23116yescomplemented
114#88049C23116yescomplemented
115#88048C23116yescomplemented
116#88047C23116yescomplemented
117C2×#3092—131nomaximal, Sylow
118C24×C13—24no—
119C24×C13—24no—
120C24×C13—24no—
121C24×C13C2×D414yes—
122C24×C13C2×D411yescharacteristic
123C24×C13C2×D411yescharacteristic
124C24×C13C2×D411yescharacteristic
125C23×D13—21no—
126C22×C4×C13—24no—
127C22×C4×C13—24no—
128C22×C4×C13—24no—
129C22×C4×C13—216no—
130C22×C4×C13—24no—
131C22×C4×C13—24no—
132C22×C4×C13—216no—
133C22×C4×C13—28no—
134C22×C4×C13—28no—
135C22×C4×C13—28no—
136C22×C4×C13—24no—
137C22×C4×C13—48no—
138C22×C4×C13—48no—
139C22×C4×C13—432no—
140C22×C4×C13—48no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D412yes—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D414yes—
146C22×C4×C13C2×D414yes—
147C22×C4×C13C2×D414yes—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D412yes—
150C22×C4×C13#4118yes—
151C22×C4×C13C2412yes—
152C22×C4×C13C2412yes—
153C22×C4×C13C2411yescharacteristic
154C22×C4×C13C2412yes—
155C2×C22⋊D13—24no—
156C2×C22⋊D13—24no—
157C2×C22⋊D13—24no—
158C2×C22⋊D13—44no—
159C2×C22⋊D13—44no—
160C2×C22⋊D13—44no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164#6127—216no—
165#6127—48no—
166C2×D52—24no—
167C2×D52—21no—
168C2×D52C2412yes—
169C2×C4×D13—24no—
170C2×C4×D13—44no—
171C2×Dic26—24no—
172C2×Dic26—21no—
173C2×Dic26C2412yes—
174C13×C4⋊C4—28no—
175C13×C4⋊C4—28no—
176C13×C4⋊C4—28no—
177C13×C4⋊C4—24no—
178C13×C4⋊C4C2418yes—
179C22⋊Dic13—24no—
180C22⋊Dic13—24no—
181C22⋊Dic13—24no—
182#6103—24no—
183#6103—24no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C2412yes—
187C4⋊Dic13C2412yes—
188#6101—24no—
189#6101—24no—
190C4×Dic13—24no—
191#6099—216no—
192C2×#1055—28no—
193C2×#1055C2418yes—
194C2×#525—131no—
195C23×C4⋊C4D1311yescharacteristic, complemented
196#3092—1316no—
197C2×#484—132no—
198C2×#481—132no—
199C2×#483—132no—
200C2×#480—132no—
201C2×#428—132no—
202C2×#417—132no—
203C2×#407—131no—
204C23×C13—232no—
205C23×C13—28no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13—28no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13—28no—
212C23×C13—22no—
213C23×C13—22no—
214C23×C13#12314yes—
215C23×C13AGL(1,ℤ/8)14yes—
216C23×C13#13714yes—
217C23×C13C22×D412yes—
218C23×C13C22×D412yes—
219C23×C13C22×D412yes—
220C23×C13C22×D411yescharacteristic
221C22×D13—22no—
222C22×D13—42no—
223C22×D13—42no—
224C22×D13—42no—
225C2×C4×C13—28no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—28no—
231C2×C4×C13—28no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—28no—
235C2×C4×C13—416no—
236C2×C4×C13—416no—
237C2×C4×C13—416no—
238C2×C4×C13—48no—
239C2×C4×C13#12314yes—
240C2×C4×C13#12318yes—
241C2×C4×C13C22×D412yes—
242C2×C4×C13C22×D412yes—
243C2×C4×C13C22×D412yes—
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4114yes—
246C2×C4×C13C2×#4118yes—
247C2×C4×C13C2511yescharacteristic
248C22⋊D13—48no—
249C22⋊D13—48no—
250C22⋊D13—48no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257D52—24no—
258D52—42no—
259C4×D13—48no—
260Dic26—24no—
261Dic26—42no—
262#1055—28no—
263C22×#41—131no—
264C24×C4—21no—
265C24×C4C2×D1311yescharacteristic
266C22×M16—132no—
267#525—138no—
268#525—264no—
269C2×#123—261no—
270C2×C22⋊Q8—131no—
271C2×C22⋊Q8—131no—
272C2×#121—131no—
273C2×#121—131no—
274C2×#120—261no—
275C2×C4×D4—261no—
276C2×C4×D4—261no—
277C2×#117—131no—
278C22×C4⋊C4—24no—
279C22×C4⋊C4—21no—
280C22×C4⋊C4—21no—
281C22×C4⋊C4—21no—
282C22×C4⋊C4C2×D1312yes—
283C22×C4⋊C4C2×D1312yes—
284C22×C4⋊C4C2×D1312yes—
285C22×C4⋊C4C2×D1318yescomplemented
286#484—1316no—
287#483—1316no—
288#481—1316no—
289#480—1316no—
290#428—1316no—
291C2×#107—134no—
292C2×#106—134no—
293#417—1316no—
294C2×#103—134no—
295C2×#102—134no—
296#407—138no—
297C2×C22⋊C8—132no—
298C2×C22⋊C8—132no—
299C22×C13—232no—
300C22×C13—28no—
301C22×C13—28no—
302C22×C13—28no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13C2×#12314yes—
310C22×C13C2×#12312yes—
311C22×C13C2×AGL(1,ℤ/8)14yes—
312C22×C13C2×AGL(1,ℤ/8)12yes—
313C22×C13C2×#13714yes—
314C22×C13C2×#13712yes—
315C22×C13C23×D411yescharacteristic
316C2×D13—42no—
317C2×D13—42no—
318C2×D13—42no—
319C2×D13—84no—
320C4×C13—22no—
321C4×C13—22no—
322C4×C13—48no—
323C4×C13C2×#12312yes—
324C4×C13C2×#12314yes—
325C4×C13C22×#4112yes—
326Dic13—42no—
327Dic13—42no—
328Dic13—42no—
329C25C22⋊D1311yescharacteristic
330C2×#41—134no—
331C2×#41—262no—
332C2×#41—268no—
333C22×Q8—131no—
334C22×D4—131no—
335C22×D4—261no—
336C22×D4—261no—
337C22×D4—261no—
338C23×C4—28no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—28no—
343C23×C4—48no—
344C23×C4—261no—
345C23×C4C22⋊D1311yescharacteristic
346C23×C4C22⋊D1311yescharacteristic
347C23×C4C22⋊D1311yescharacteristic
348C23×C4C22⋊D1314yes—
349C23×C4C22×D1311yescharacteristic
350C23×C4C22×D1311yescharacteristic
351C23×C4C22×D1314yes—
352C23×C4C22×D1311yescharacteristic
353C2×M16—138no—
354C2×M16—268no—
355C22×C8—134no—
356#123—268no—
357C22⋊Q8—134no—
358C22⋊Q8—134no—
359C22⋊Q8—262no—
360C22⋊Q8—262no—
361#121—134no—
362#121—134no—
363#121—262no—
364#121—262no—
365#120—268no—
366C4×D4—268no—
367C4×D4—268no—
368#117—134no—
369#117—262no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4C22×D1314yes—
384C2×C4⋊C4C22×D1318yes—
385C2×C4⋊C4C22×D1318yes—
386C2×C4⋊C4C22×D1318yes—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C42—261no—
393#107—1316no—
394#106—1316no—
395#103—1316no—
396#102—1316no—
397C22⋊C8—138no—
398C22⋊C8—138no—
399C2×C13—24no—
400C2×C13—24no—
401C2×C13—24no—
402C2×C13#309214yescomplemented
403C2×C13C22×#12311yescharacteristic
404C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
405C2×C13C22×#13711yescharacteristic
406D13—82no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—261no—
411C24C2×C22⋊D1314yes—
412C24C2×C22⋊D1311yescharacteristic
413C24C2×C22⋊D1311yescharacteristic
414C24C2×C22⋊D1311yescharacteristic
415#41—2616no—
416#41—528no—
417C2×Q8—132no—
418C2×Q8—261no—
419C2×Q8—264no—
420C2×D4—132no—
421C2×D4—264no—
422C2×D4—264no—
423C2×D4—264no—
424C2×D4—264no—
425C2×D4—261no—
426C2×D4—524no—
427C2×D4—524no—
428C2×D4—524no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—216no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—216no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—24no—
440C22×C4—48no—
441C22×C4—48no—
442C22×C4—432no—
443C22×C4—48no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—264no—
448C22×C4—524no—
449C22×C4#612718yes—
450C22×C4C2×C22⋊D1314yes—
451C22×C4C2×C22⋊D1314yes—
452C22×C4C2×C22⋊D1312yes—
453C22×C4C2×C22⋊D1312yes—
454C22×C4C2×C22⋊D1314yes—
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1312yes—
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C23×D1312yes—
460C22×C4C23×D1312yes—
461C22×C4C23×D1312yes—
462C22×C4C23×D1311yescharacteristic
463M16—2616no—
464C2×C8—138no—
465C2×C8—268no—
466C4⋊C4—28no—
467C4⋊C4—28no—
468C4⋊C4—28no—
469C4⋊C4—24no—
470C4⋊C4—132no—
471C4⋊C4—132no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—264no—
475C4⋊C4—264no—
476C4⋊C4C23×D1318yes—
477C22⋊C4—264no—
478C22⋊C4—264no—
479C22⋊C4—264no—
480C22⋊C4—264no—
481C22⋊C4—264no—
482C42—264no—
483C13C2×#309211yescharacteristic, complemented, Sylow
484C23—232no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—28no—
489C23—22no—
490C23—22no—
491C23—28no—
492C23—22no—
493C23—22no—
494C23—262no—
495C23—522no—
496C23—522no—
497C23—522no—
498C23#8818314yes—
499C23#8818614yes—
500C23#8819614yes—
501C23C22×C22⋊D1312yes—
502C23C22×C22⋊D1312yes—
503C23C22×C22⋊D1312yes—
504C23C22×C22⋊D1311yescharacteristic
505Q8—264no—
506Q8—522no—
507D4—264no—
508D4—528no—
509D4—528no—
510D4—528no—
511D4—522no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—28no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—28no—
522C2×C4—416no—
523C2×C4—416no—
524C2×C4—416no—
525C2×C4—48no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—528no—
533C2×C4#8818314yes—
534C2×C4#8818318yes—
535C2×C4C2×#612714yes—
536C2×C4C2×#612718yes—
537C2×C4C22×C22⋊D1312yes—
538C2×C4C22×C22⋊D1312yes—
539C2×C4C22×C22⋊D1312yes—
540C2×C4C22×C22⋊D1311yescharacteristic
541C2×C4C24×D1311yescharacteristic
542C8—268no—
543C22—232no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—28no—
551C22—28no—
552C22—28no—
553C22—522no—
554C22—522no—
555C22—522no—
556C22—1044no—
557C22C2×#8818314yes—
558C22C2×#8818312yes—
559C22C2×#8818614yes—
560C22C2×#8818612yes—
561C22C2×#8819614yes—
562C22C2×#8819612yes—
563C22C23×C22⋊D1311yescharacteristic
564C4—22no—
565C4—22no—
566C4—48no—
567C4—522no—
568C4—522no—
569C4—522no—
570C4C2×#8818314yes—
571C4C2×#8818312yes—
572C4C22×#612712yes—
573C2—24no—
574C2—24no—
575C2—24no—
576C2—1042no—
577C2#1312475914yesdirect product factor
578C2C22×#8818311yescharacteristic
579C2C22×#8818611yescharacteristic
580C2C22×#8819611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC23×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC2×#11719496C2
hypercenterC23×C4⋊C4D13
hypocenterC13C2×#3092
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13124759C2direct (N × H)
3. C2×#11718631C2semidirect
4. C2×#11718629C2semidirect
5. C2×#11718632C2semidirect
6. C2×#11718628C2semidirect
7. C2×#11718625C2semidirect
8. C2×#11718627C2semidirect
9. C2×#11718868C2semidirect
10. C23×C13×C4⋊C4C2semidirect
21. C22×C13×C4⋊C4C22semidirect
34. #11718868C22semidirect
37. #11718632C22semidirect
38. #11718631C22semidirect
39. C2×#88050C22semidirect
40. #11718629C22semidirect
41. #11718628C22semidirect
42. #11718627C22semidirect
43. C2×#88049C22semidirect
44. #11718625C22semidirect
45. C2×#88048C22semidirect
46. C2×#88047C22semidirect
113. #88050C23semidirect
114. #88049C23semidirect
115. #88048C23semidirect
116. #88047C23semidirect
195. C23×C4⋊C4D13semidirect
285. C22×C4⋊C4C2×D13semidirect
402. C2×C13#3092semidirect
483. C13C2×#3092semidirect
577. C2#13124759direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194962
#131247592
C2×#117186312
C2×#117186292
C2×#117186322
C2×#117186282
C2×#117186252
C2×#117186272
C2×#117188682
C23×C13×C4⋊C42
C2×#309213