Finite Group Databasebeta

← C4×#11719144 #16797353

Subgroups — C4×#11719144 #16797353

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719144C212yesmaximal
2C2×C4×#6122C211yesmaximal, characteristic, complemented
3C22×C4×#1057C211yesmaximal, characteristic, complemented
4#13130636C212yesmaximal, complemented
5C4×#88112C211yesmaximal, characteristic, complemented
6#13130578C212yesmaximal, complemented
7#13130573C212yesmaximal, complemented
8C4×C22⋊#1057C211yesmaximal, characteristic, complemented
9C4×C22⋊#1057C211yesmaximal, characteristic, complemented
10C4×#88110C211yesmaximal, characteristic, complemented
11C4×D4×Dic13C211yesmaximal, characteristic
12C22×#6122C2212yes—
13C23×#1057C2212yes—
14C2×C4×D4×C13C411yescharacteristic
15C2×D4×Dic13C411yescharacteristic
16C2×D4×Dic13C2211yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C2×C22⋊#1057C2212yes—
20C2×C22⋊#1057C2212yes—
21#11719144C4116yesdirect product factor
22C2×#88112C2212yes—
23C4×#6122—24no—
24C2×#88110C2212yes—
25C2×#88110C2212yes—
26C2×#88110C2212yes—
27C2×C4×#1057—24no—
28C2×C4×#1057C2211yescharacteristic
29C2×C4×#1057C2211yescharacteristic
30C2×C4×#1057C2211yescharacteristic
31C2×C4×#1057C2212yes—
32C2×C4×#1057C2211yescharacteristic
33C4×C22⋊Dic13C411yescharacteristic
34C4×C22⋊Dic13C411yescharacteristic
35C4⋊C4×Dic13C411yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37C22⋊C4×Dic13C411yescharacteristic
38C22⋊C4×Dic13C411yescharacteristic
39C22⋊C4×Dic13C2211yescharacteristic
40C22⋊C4×Dic13C2211yescharacteristic
41C4×C4⋊Dic13C411yescharacteristic
42C42×Dic13C2211yescharacteristic
43#11718290C2212yes—
44#11718290C2212yes—
45#11718290C2212yes—
46C22×D4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×C4×C13C2×C411yescharacteristic
49C23×Dic13C2×C411yescharacteristic
50C23×Dic13C2×C411yescharacteristic
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C2×#6122—24no—
54C2×#6122—24no—
55C2×#6122C2×C418yescomplemented
56C22×#1057—24no—
57C22×#1057—24no—
58C22×#1057C2×C418yescomplemented
59C22×#1057C2312yes—
60C22×#1057C2312yes—
61C22×#1057C2312yes—
62C22×#1057C2312yes—
63C4×D4×C13—24no—
64C2×C13×C4⋊C4C2×C411yescharacteristic
65C2×C13×C22⋊C4C2×C411yescharacteristic
66C2×C13×C22⋊C4C2×C411yescharacteristic
67C2×C42×C13C2×C411yescharacteristic
68C2×C22⋊Dic13C2×C411yescharacteristic
69C2×C22⋊Dic13C2×C411yescharacteristic
70C2×C22⋊Dic13C2×C411yescharacteristic
71C2×C22⋊Dic13C2×C411yescharacteristic
72D4×Dic13—24no—
73D4×Dic13C2×C418yes—
74C2×C4⋊Dic13C2×C411yescharacteristic
75C2×C4⋊Dic13C2×C411yescharacteristic
76C2×C4×Dic13—22no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—22no—
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C411yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C22⋊#1057C2×C418yescomplemented
93C22⋊#1057C2×C418yescomplemented
94#88112C2×C418yescomplemented
95#88110—24no—
96#88110—24no—
97#88110C2×C418yescomplemented
98C4×#1057—24no—
99C4×#1057—22no—
100C4×#1057—22no—
101C4×#1057—22no—
102C4×#1057D414yescomplemented
103#88071C2×C411yescharacteristic
104#88071C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109C4×#435—131nomaximal, Sylow
110C24×C13C22×C411yescharacteristic
111C24×C13C22×C411yescharacteristic
112C2×D4×C13—22no—
113C2×D4×C13—22no—
114C2×D4×C13C4214yes—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13M1614yescomplemented
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C411yescharacteristic
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13M1614yescomplemented
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C414yes—
144C22×Dic13C22×C414yes—
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C2411yescharacteristic
148#6122—216no—
149C2×#1057—22no—
150C2×#1057—22no—
151C2×#1057—22no—
152C2×#1057—22no—
153C2×#1057—22no—
154C2×#1057—22no—
155C2×#1057—216no—
156C2×#1057C22×C414yes—
157C2×#1057C22×C414yes—
158C2×#1057C22×C414yes—
159C2×#1057C22×C414yes—
160C2×#1057C2×D414yes—
161C2×#1057#4114yes—
162C13×C4⋊C4—22no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—22no—
165C42×C13—22no—
166C22⋊Dic13—22no—
167C22⋊Dic13—22no—
168C22⋊Dic13C4214yes—
169C22⋊Dic13C4214yes—
170C4⋊Dic13—22no—
171C4⋊Dic13C4214yes—
172C4×Dic13—22no—
173C4×Dic13—22no—
174C4×Dic13—22no—
175C4×Dic13—22no—
176C4×Dic13—22no—
177C4×Dic13—22no—
178C4×Dic13—22no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—22no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13C22×C414yes—
185C4×Dic13C2×D412yes—
186C4×Dic13#4112yes—
187C2×#435—132no—
188C2×C4×M16—131no—
189C22×C4×C8—131no—
190C42×D4—131no—
191#1771—132no—
192C4×C4⋊C8—131no—
193#1753—132no—
194#1752—132no—
195C4×C22⋊C8—131no—
196C4×C22⋊C8—131no—
197C4×#97—131no—
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—21no—
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13C2×C4212yes—
209C23×C13C2×C4212yes—
210C23×C13C2×M1612yes—
211C23×C13C2×M1612yes—
212C23×C13C23×C411yescharacteristic
213D4×C13—28no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—28no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—44no—
226C2×C4×C13C2×C4212yes—
227C2×C4×C13C4×D412yes—
228C2×C4×C13C2×M1612yes—
229C2×C4×C13C2×M1612yes—
230C2×C4×C13#13112yes—
231C2×Dic13—21no—
232C2×Dic13—21no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—24no—
240C2×Dic13—24no—
241C2×Dic13—24no—
242C2×Dic13—24no—
243C2×Dic13—28no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—44no—
251C2×Dic13C2×C4212yes—
252C2×Dic13C2×C4212yes—
253C2×Dic13C2×C4212yes—
254C2×Dic13C4×D412yes—
255C2×Dic13C2×M1612yes—
256C2×Dic13C2×M1612yes—
257C2×Dic13#13112yes—
258C2×Dic13C23×C412yes—
259C2×Dic13C22×D411yescharacteristic
260C2×Dic13C2×#4112yes—
261C2×Dic13C2×#4111yescharacteristic
262#1057—24no—
263#1057—24no—
264#1057—24no—
265#1057C4×D418yescomplemented
266C22×M16—132no—
267C23×C8—132no—
268C2×C4×D4—131no—
269C2×C4×D4—131no—
270C2×C4×D4#26111yescharacteristic
271C22×C42—131no—
272C22×C42—131no—
273#435—1316no—
274C2×C4⋊C8—132no—
275C2×C22⋊C8—132no—
276C2×C22⋊C8—132no—
277C4×M16—264no—
278C2×#97—132no—
279C2×#97—132no—
280C2×#97—132no—
281C2×C4×C8—131no—
282C2×C4×C8—131no—
283C2×C4×C8—132no—
284C2×C4×C8—131no—
285C2×C4×C8—131no—
286C2×C4×C8—264no—
287C4×C4⋊C4—131no—
288C4×C4⋊C4—131no—
289C4×C4⋊C4—131no—
290C4×C22⋊C4—131no—
291C4×C22⋊C4—131no—
292C4×C22⋊C4—131no—
293C4×C22⋊C4—131no—
294C4×C22⋊C4—131no—
295C4×C22⋊C4—131no—
296C43—131no—
297#336—132no—
298#336—132no—
299#336—132no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13—41no—
310C22×C13—41no—
311C22×C13—41no—
312C22×C13—41no—
313C22×C13C4×M1614yescomplemented
314C22×C13C22×C4211yescharacteristic
315C22×C13C2×C4×D411yescharacteristic
316C22×C13C4×#4111yescharacteristic
317C22×C13C22×M1611yescharacteristic
318C22×C13C22×M1611yescharacteristic
319C22×C13C2×#13111yescharacteristic
320C22×C13C2×#13111yescharacteristic
321C4×C13—22no—
322C4×C13—22no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13#43514yescomplemented
326Dic13—22no—
327Dic13—22no—
328Dic13—22no—
329Dic13—22no—
330Dic13—41no—
331Dic13—41no—
332Dic13#43514yescomplemented
333Dic13C2×C4×D412yes—
334Dic13C4×#4112yes—
335C22×D4C2×#26111yescharacteristic
336C23×C4—131no—
337C23×C4—131no—
338C23×C4—131no—
339C23×C4—131no—
340C23×C4C2×#26111yescharacteristic
341C23×C4C2×#26111yescharacteristic
342C2×M16—138no—
343C2×M16—264no—
344C2×M16—264no—
345C22×C8—132no—
346C22×C8—132no—
347C22×C8—138no—
348C22×C8—132no—
349C22×C8—132no—
350C22×C8—264no—
351C22×C8—264no—
352C4×D4—24no—
353C4×D4—138no—
354C4×D4—264no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—131no—
357C2×C4⋊C4C2×#26111yescharacteristic
358C2×C22⋊C4—131no—
359C2×C22⋊C4—131no—
360C2×C22⋊C4—131no—
361C2×C22⋊C4—131no—
362C2×C22⋊C4C2×#26111yescharacteristic
363C2×C22⋊C4C2×#26111yescharacteristic
364C2×C42—131no—
365C2×C42—131no—
366C2×C42—131no—
367C2×C42—131no—
368C2×C42—131no—
369C2×C42—131no—
370C2×C42—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—262no—
377C2×C42—262no—
378C2×C42—262no—
379C2×C42—262no—
380C2×C42C2×#26111yescharacteristic
381C4⋊C8—138no—
382C22⋊C8—138no—
383C22⋊C8—138no—
384#97—138no—
385#97—264no—
386#97—264no—
387C4×C8—134no—
388C4×C8—262no—
389C4×C8—262no—
390C4×C8—262no—
391C4×C8—264no—
392#95—131no—
393#95—131no—
394#95—131no—
395#95—131no—
396#95—131no—
397#95—131no—
398C2×C13—24no—
399C2×C13—42no—
400C2×C13C42×D411yescharacteristic
401C2×C13C2×C4×M1611yescharacteristic
402C2×C13C4×#13111yescharacteristic
403C2×C13C2×#43511yescharacteristic
404C2×C13C2×#43511yescharacteristic
405C2×C13#296511yescharacteristic
406C2×C13#296511yescharacteristic
407C24C22×#26111yescharacteristic
408C24C22×#26111yescharacteristic
409C2×D4—22no—
410C2×D4—22no—
411C2×D4C4×#26114yes—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—131no—
418C22×C4—131no—
419C22×C4—134no—
420C22×C4—134no—
421C22×C4—134no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4#612214yescomplemented
440C22×C4C22×#26111yescharacteristic
441C22×C4C22×#26111yescharacteristic
442C22×C4C22×#26111yescharacteristic
443C22×C4C22×#26111yescharacteristic
444C22×C4C22×#26111yescharacteristic
445M16—2616no—
446C2×C8—134no—
447C2×C8—134no—
448C2×C8—134no—
449C2×C8—134no—
450C2×C8—134no—
451C2×C8—134no—
452C2×C8—2616no—
453C2×C8—262no—
454C2×C8—262no—
455C2×C8—262no—
456C2×C8—262no—
457C2×C8—262no—
458C2×C8—262no—
459C4⋊C4—22no—
460C4⋊C4—134no—
461C4⋊C4—262no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—134no—
465C22⋊C4—134no—
466C22⋊C4—262no—
467C22⋊C4—262no—
468C42—22no—
469C42—134no—
470C42—132no—
471C42—132no—
472C42—261no—
473C42—261no—
474C42—262no—
475C42—261no—
476C42—262no—
477C42—261no—
478C42—262no—
479C42—262no—
480C42—262no—
481C42—262no—
482C42—262no—
483C42—262no—
484C13C4×#43511yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23D13⋊M1612yes—
496C23C2×C4×#26112yes—
497C23C2×C4×#26112yes—
498C23C2×#612212yes—
499C23C23×#26111yescharacteristic
500D4—28no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—28no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—44no—
513C2×C4—132no—
514C2×C4—132no—
515C2×C4—131no—
516C2×C4—131no—
517C2×C4—132no—
518C2×C4—132no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—132no—
522C2×C4—132no—
523C2×C4—132no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—264no—
527C2×C4—264no—
528C2×C4—268no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—524no—
544C2×C4C2×C4×#26112yes—
545C2×C4#8823812yes—
546C2×C4D4×#26112yes—
547C2×C4C2×#612212yes—
548C2×C4C2×#612212yes—
549C8—138no—
550C8—264no—
551C8—264no—
552C8—264no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C4×#612214yescomplemented
567C22C2×D13⋊M1611yescharacteristic
568C22C22×C4×#26111yescharacteristic
569C22C2×#8823811yescharacteristic
570C22C2×D4×#26111yescharacteristic
571C22D13⋊#13111yescharacteristic
572C22#41×#26111yescharacteristic
573C22C22×#612211yescharacteristic
574C4—22no—
575C4—22no—
576C4—41no—
577C4—41no—
578C4—132no—
579C4—132no—
580C4—134no—
581C4—262no—
582C4—262no—
583C4—262no—
584C4—262no—
585C4—521no—
586C4—521no—
587C4#1171914414yesdirect product factor
588C2—24no—
589C2—42no—
590C2C4×D4×#26111yescharacteristic
591C2C2×C4×#612211yescharacteristic
592C2C4×#8823811yescharacteristic
593C2C2×#1171914411yescharacteristic
594C2D13⋊#43511yescharacteristic
595C2#1313164511yescharacteristic
596C2#1313164611yescharacteristic
subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×D4×C13C2×C4
cosocleC22×Dic13C24
hypercenterC2×C4×D4#261
hypocenterC13C4×#435
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6122C2semidirect
3. C22×C4×#1057C2semidirect
4. #13130636C2semidirect
5. C4×#88112C2semidirect
6. #13130578C2semidirect
7. #13130573C2semidirect
8. C4×C22⋊#1057C2semidirect
9. C4×C22⋊#1057C2semidirect
10. C4×#88110C2semidirect
21. #11719144C4direct (N × H)
55. C2×#6122C2×C4semidirect
58. C22×#1057C2×C4semidirect
92. C22⋊#1057C2×C4semidirect
93. C22⋊#1057C2×C4semidirect
94. #88112C2×C4semidirect
97. #88110C2×C4semidirect
102. C4×#1057D4semidirect
120. C22×C4×C13M16semidirect
137. C22×Dic13M16semidirect
265. #1057C4×D4semidirect
313. C22×C13C4×M16semidirect
325. C4×C13#435semidirect
332. Dic13#435semidirect
439. C22×C4#6122semidirect
484. C13C4×#435semidirect
566. C22C4×#6122semidirect
587. C4#11719144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191442
C2×C4×#61222
C22×C4×#10572
#131306362
C4×#881122
#131305782
#131305732
C4×C22⋊#10572
C4×#881102
C4×D4×Dic132
C4×#43513