Finite Group Databasebeta

← C4×#11719146 #16796878

Subgroups — C4×#11719146 #16796878

Order 3328.

1662 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719146C212yesmaximal
2C2×C4×#6122C211yesmaximal, characteristic, complemented
3C22×C4×#1057C211yesmaximal, characteristic, complemented
4#13130566C212yesmaximal, complemented
5#13130565C212yesmaximal, complemented
6C4×#88111C212yesmaximal, complemented
7C4×C22⋊#1057C212yesmaximal, complemented
8#13130502C212yesmaximal, complemented
9C2×C4×#6129C211yesmaximal, characteristic
10C22×#6129C2211yescharacteristic
11C22×#6122C2212yes—
12C23×#1057C2212yes—
13C2×C4×D4×C13C411yescharacteristic
14C2×D4×Dic13C411yescharacteristic
15C2×C4×C22⋊D13C411yescharacteristic
16C2×C4×C22⋊D13C411yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C4×#6129—24no—
20C4×#6129—24no—
21C2×#88146C2211yescharacteristic
22C2×#88141C411yescharacteristic
23C2×#88135C411yescharacteristic
24C2×#88135C411yescharacteristic
25C2×#88131C2211yescharacteristic
26C2×#88131C2211yescharacteristic
27C2×C42×D13C2211yescharacteristic
28C2×C4×Dic26C411yescharacteristic
29C2×C22⋊#1057C2214yes—
30#11719146C4116yesdirect product factor
31C2×#88111C2214yes—
32C4×#6122—24no—
33C2×#88110C2212yes—
34C2×C4×#1057—24no—
35C2×C4×#1057C2212yes—
36C2×C4×#1057C2212yes—
37C2×C4×#1057C2212yes—
38#11718290C2214yes—
39#11718290C2214yes—
40C22×D4×C13C2×C411yescharacteristic
41C23×C4×C13C2×C411yescharacteristic
42C23×C4×C13C2×C411yescharacteristic
43C22×C22⋊D13C2×C411yescharacteristic
44C22×C22⋊D13C2×C411yescharacteristic
45C23×Dic13C2×C411yescharacteristic
46C23×Dic13C2×C411yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C2×#6129—22no—
50C2×#6129—22no—
51C2×#6129—24no—
52C2×#6129C2×C418yes—
53C22×C4×D13C2×C411yescharacteristic
54C22×C4×D13C2×C411yescharacteristic
55C22×C4×D13C2311yescharacteristic
56C22×Dic26C2×C411yescharacteristic
57C2×#6122—24no—
58C2×#6122—24no—
59C2×#6122C2×C418yescomplemented
60C22×#1057—24no—
61C22×#1057—24no—
62C22×#1057C2×C418yescomplemented
63C22×#1057C2314yes—
64C22×#1057C2314yes—
65C4×D4×C13—24no—
66C2×C13×C4⋊C4C2×C411yescharacteristic
67C2×C13×C22⋊C4C2×C411yescharacteristic
68C2×C13×C22⋊C4C2×C411yescharacteristic
69C2×C42×C13C2×C411yescharacteristic
70C2×C22⋊Dic13C2×C411yescharacteristic
71C2×C22⋊Dic13C2×C411yescharacteristic
72D4×Dic13—24no—
73C4×C22⋊D13—24no—
74C4×C22⋊D13—24no—
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2×C411yescharacteristic
77C2×C4⋊Dic13C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×C4×Dic13—22no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13C2×C411yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2×C411yescharacteristic
89C2×C4×Dic13D414yes—
90C2×C4×Dic13D414yes—
91C2×C4×Dic13C2311yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95#88146—22no—
96#88146—22no—
97#88141—24no—
98#88135—24no—
99#88135—24no—
100#88131—22no—
101#88131—22no—
102#88131—22no—
103#88131—22no—
104C42×D13—22no—
105C42×D13—22no—
106C4×Dic26—24no—
107C22⋊#1057C2×C4116yescomplemented
108#88111C2×C4116yescomplemented
109#88110—24no—
110C4×#1057—24no—
111C4×#1057—24no—
112C4×#1057—24no—
113C4×#408—131nomaximal, Sylow
114C24×C13C22×C411yescharacteristic
115C24×C13C22×C411yescharacteristic
116C23×D13C22×C411yescharacteristic
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13C4214yes—
120C22×C4×C13—24no—
121C22×C4×C13—22no—
122C22×C4×C13—24no—
123C22×C4×C13C22⋊C414yes—
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C2×C22⋊D13—22no—
130C2×C22⋊D13—22no—
131C2×C22⋊D13—22no—
132C2×C22⋊D13—22no—
133C2×C22⋊D13C4214yes—
134C2×C22⋊D13C4214yes—
135C22×Dic13—24no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—24no—
141C22×Dic13C22⋊C414yes—
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C414yes—
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C414yes—
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C2×D412yes—
151C22×Dic13C2×D412yes—
152C22×Dic13#4114yes—
153C22×Dic13C2411yescharacteristic
154#6129—216no—
155#6129—216no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—24no—
161C2×C4×D13—22no—
162C2×C4×D13—24no—
163C2×C4×D13C22×C414yes—
164C2×Dic26—22no—
165C2×Dic26—22no—
166C2×Dic26C4214yes—
167#6122—216no—
168C2×#1057—216no—
169C2×#1057—24no—
170C2×#1057—24no—
171C2×#1057—24no—
172C2×#1057—24no—
173C2×#1057C22×C418yes—
174C2×#1057C22×C418yes—
175C13×C4⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C42×C13—22no—
179C22⋊Dic13—22no—
180C22⋊Dic13—22no—
181#6103—22no—
182#6103—22no—
183C4⋊Dic13—22no—
184#6101—22no—
185#6101—22no—
186#6101—22no—
187#6101—22no—
188C4×Dic13—22no—
189C4×Dic13—22no—
190C4×Dic13—22no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13C22⋊C414yes—
196C4×Dic13C22⋊C414yes—
197C4×Dic13C2×D412yes—
198C4×Dic13C2×D412yes—
199C4×Dic13C2×D412yes—
200C4×Dic13C2×D412yes—
201C2×C4×#41—131no—
202C2×#408—132no—
203C2×C4×M16—131no—
204C22×C4×C8—131no—
205#1750—132no—
206#1750—132no—
207C4×C22⋊C8—132no—
208C4×C22⋊C8—132no—
209#1729—132no—
210C23×C13—22no—
211C23×C13—22no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—22no—
215C23×C13—22no—
216C23×C13C2×C4212yes—
217C23×C13C2×C4212yes—
218C23×C13C2×C22⋊C412yes—
219C23×C13#11712yes—
220C23×C13C23×C411yescharacteristic
221C22×D13—21no—
222C22×D13—21no—
223C22×D13—22no—
224C22×D13—22no—
225C22×D13C2×C4212yes—
226D4×C13—28no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—22no—
230C2×C4×C13—28no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—44no—
236C2×C4×C13C2×C4212yes—
237C2×C4×C13C2×C22⋊C412yes—
238C2×C4×C13C2×C22⋊C412yes—
239C2×C4×C13#13114yes—
240C22⋊D13—28no—
241C22⋊D13—28no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—22no—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—28no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—44no—
253C2×Dic13C2×C4212yes—
254C2×Dic13C2×C4212yes—
255C2×Dic13C2×C22⋊C412yes—
256C2×Dic13C2×C22⋊C412yes—
257C2×Dic13C2×C22⋊C412yes—
258C2×Dic13#11712yes—
259C2×Dic13C4×D418yes—
260C2×Dic13C4×D418yes—
261C2×Dic13#13114yes—
262C2×Dic13C23×C412yes—
263C2×Dic13C22×D411yescharacteristic
264C2×Dic13C22×D411yescharacteristic
265C2×Dic13C2×#4112yes—
266C4×D13—24no—
267C4×D13—24no—
268C4×D13—44no—
269C4×D13—44no—
270Dic26—28no—
271#1057—28no—
272#1057—28no—
273C22×#41—131no—
274C22×M16—132no—
275C23×C8—132no—
276C4×#41—264no—
277C4×#41—264no—
278C2×C4×Q8—131no—
279C2×C4×Q8—131no—
280C2×C4×D4—131no—
281C2×C4×D4—131no—
282C2×C4×D4—131no—
283C2×C4×D4—131no—
284C2×C4×D4—131no—
285C2×C4×D4#26111yescharacteristic
286C2×#117—131no—
287C2×#117—131no—
288C2×#117—131no—
289C22×C42—131no—
290C22×C42—131no—
291C22×C42—131no—
292#408—1316no—
293C2×C22⋊C8—134no—
294C2×C22⋊C8—134no—
295C4×M16—264no—
296C2×#97—132no—
297C2×C4×C8—132no—
298C2×C4×C8—132no—
299C2×C4×C8—132no—
300C2×C4×C8—264no—
301#336—134no—
302#336—134no—
303C22×C13—24no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—24no—
307C22×C13—24no—
308C22×C13—22no—
309C22×C13—41no—
310C22×C13—41no—
311C22×C13—42no—
312C22×C13C4×C22⋊C414yes—
313C22×C13C22×C4211yescharacteristic
314C22×C13C22×C22⋊C411yescharacteristic
315C22×C13C2×#11711yescharacteristic
316C22×C13C2×#13112yes—
317C22×C13C2×#13112yes—
318C2×D13—24no—
319C2×D13—22no—
320C2×D13—41no—
321C2×D13—41no—
322C2×D13—42no—
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13#40814yescomplemented
328Dic13—22no—
329Dic13—22no—
330Dic13—41no—
331Dic13—41no—
332Dic13C4×C22⋊C414yes—
333Dic13#40814yescomplemented
334Dic13C2×C4×D412yes—
335Dic13C2×C4×D412yes—
336C2×#41—138no—
337C2×#41—262no—
338C2×#41—262no—
339C2×#41—264no—
340C22×Q8—131no—
341C22×D4—131no—
342C22×D4—131no—
343C22×D4C2×#26111yescharacteristic
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—131no—
347C23×C4—131no—
348C23×C4—131no—
349C23×C4—131no—
350C23×C4—131no—
351C23×C4C2×#26111yescharacteristic
352C23×C4C2×#26111yescharacteristic
353C2×M16—138no—
354C2×M16—264no—
355C2×M16—264no—
356C22×C8—134no—
357C22×C8—138no—
358C22×C8—134no—
359C22×C8—264no—
360C22×C8—264no—
361C4×Q8—264no—
362C4×Q8—264no—
363C4×D4—24no—
364C4×D4—264no—
365C4×D4—264no—
366C4×D4—264no—
367C4×D4—264no—
368C4×D4—264no—
369#117—262no—
370#117—262no—
371#117—262no—
372#117—262no—
373#117—262no—
374#117—262no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4C2×#26111yescharacteristic
381C2×C22⋊C4—131no—
382C2×C22⋊C4—131no—
383C2×C22⋊C4—131no—
384C2×C22⋊C4—131no—
385C2×C22⋊C4C2×#26111yescharacteristic
386C2×C22⋊C4C2×#26111yescharacteristic
387C2×C42—134no—
388C2×C42—134no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—131no—
398C2×C42—262no—
399C2×C42—262no—
400C2×C42—262no—
401C2×C42—262no—
402C2×C42C2×#26111yescharacteristic
403C22⋊C8—1316no—
404C22⋊C8—1316no—
405#97—264no—
406C4×C8—264no—
407C4×C8—264no—
408C4×C8—264no—
409C2×C13—24no—
410C2×C13—42no—
411C2×C13C2×C4×C22⋊C411yescharacteristic
412C2×C13C4×#13112yes—
413C2×C13C2×#40811yescharacteristic
414C2×C13C2×#40811yescharacteristic
415C2×C13#292212yes—
416D13—42no—
417C24—131no—
418C24C22×#26111yescharacteristic
419C24C22×#26111yescharacteristic
420#41—2616no—
421#41—2616no—
422C2×Q8—134no—
423C2×Q8—262no—
424C2×Q8—262no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—134no—
428C2×D4—134no—
429C2×D4—262no—
430C2×D4—262no—
431C2×D4—262no—
432C2×D4—262no—
433C2×D4C4×#26114yes—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—134no—
438C22×C4—134no—
439C22×C4—132no—
440C22×C4—132no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—134no—
445C22×C4—134no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—134no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—264no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—262no—
459C22×C4—264no—
460C22×C4—262no—
461C22×C4—264no—
462C22×C4—264no—
463C22×C4—262no—
464C22×C4C22⋊#26114yes—
465C22×C4C22×#26111yescharacteristic
466C22×C4C22×#26111yescharacteristic
467C22×C4C22×#26111yescharacteristic
468C22×C4C22×#26111yescharacteristic
469C22×C4C22×#26111yescharacteristic
470M16—2616no—
471C2×C8—138no—
472C2×C8—138no—
473C2×C8—264no—
474C2×C8—264no—
475C2×C8—264no—
476C2×C8—2616no—
477C2×C8—264no—
478C4⋊C4—22no—
479C4⋊C4—262no—
480C4⋊C4—262no—
481C4⋊C4—262no—
482C4⋊C4—262no—
483C4⋊C4—262no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—262no—
487C22⋊C4—262no—
488C22⋊C4—262no—
489C22⋊C4—262no—
490C42—22no—
491C42—132no—
492C42—132no—
493C42—132no—
494C42—132no—
495C42—134no—
496C42—134no—
497C42—261no—
498C42—261no—
499C42—261no—
500C42—261no—
501C42—262no—
502C42—262no—
503C42—262no—
504C13C4×#40811yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—21no—
508C23—22no—
509C23—22no—
510C23—21no—
511C23—132no—
512C23—261no—
513C23—262no—
514C23—262no—
515C23—261no—
516C23C2×C4×#26112yes—
517C23C2×C4×#26112yes—
518C23#8823712yes—
519C23C2×C22⋊#26112yes—
520C23C23×#26111yescharacteristic
521Q8—268no—
522D4—28no—
523D4—268no—
524D4—268no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—28no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—44no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—134no—
539C2×C4—131no—
540C2×C4—131no—
541C2×C4—132no—
542C2×C4—132no—
543C2×C4—138no—
544C2×C4—138no—
545C2×C4—132no—
546C2×C4—132no—
547C2×C4—264no—
548C2×C4—264no—
549C2×C4—268no—
550C2×C4—264no—
551C2×C4—264no—
552C2×C4—261no—
553C2×C4—262no—
554C2×C4—261no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—524no—
560C2×C4—524no—
561C2×C4—524no—
562C2×C4C2×C4×#26112yes—
563C2×C4#8823814yes—
564C2×C4C2×C22⋊#26112yes—
565C2×C4C2×C22⋊#26112yes—
566C8—268no—
567C8—268no—
568C22—24no—
569C22—22no—
570C22—22no—
571C22—24no—
572C22—22no—
573C22—24no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—262no—
578C22—264no—
579C22—521no—
580C22—521no—
581C22—522no—
582C22C4×C22⋊#26114yes—
583C22C22×C4×#26111yescharacteristic
584C22C2×#8823711yescharacteristic
585C22C2×#8823812yes—
586C22D13⋊#13112yes—
587C22C22×C22⋊#26111yescharacteristic
588C4—22no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—132no—
593C4—132no—
594C4—134no—
595C4—134no—
596C4—262no—
597C4—262no—
598C4—521no—
599C4—521no—
600C4#1171914614yesdirect product factor
601C2—24no—
602C2—42no—
603C2—522no—
604C2C2×C4×C22⋊#26111yescharacteristic
605C2C4×#8823812yes—
606C2C2×#1171914611yescharacteristic
607C2D13⋊#40811yescharacteristic
608C2#1313151912yes—
subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×#6129C22
cosocleC22×Dic13C24
hypercenterC2×C4×D4#261
hypocenterC13C4×#408
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. #13130566C2semidirect
5. #13130565C2semidirect
6. C4×#88111C2semidirect
7. C4×C22⋊#1057C2semidirect
8. #13130502C2semidirect
30. #11719146C4direct (N × H)
59. C2×#6122C2×C4semidirect
62. C22×#1057C2×C4semidirect
107. C22⋊#1057C2×C4semidirect
108. #88111C2×C4semidirect
327. C4×C13#408semidirect
333. Dic13#408semidirect
504. C13C4×#408semidirect
600. C4#11719146direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191462
C2×C4×#61222
C22×C4×#10572
#131305662
#131305652
C4×#881112
C4×C22⋊#10572
#131305022
C2×C4×#61292
C4×#40813