Finite Group Databasebeta

← C4×#10622336 #14760943

Subgroups — C4×#10622336 #14760943

Order 2816.

888 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622336C211yesmaximal, characteristic
2C4×#66977C211yesmaximal, characteristic
3C4×#66979C211yesmaximal, characteristic
4#13069258C211yesmaximal, characteristic, complemented
5#13069251C211yesmaximal, characteristic, complemented
6#13069195C211yesmaximal, characteristic, complemented
7#13069188C211yesmaximal, characteristic, complemented
8#13068926C211yesmaximal, characteristic
9#13068817C211yesmaximal, characteristic
10#13068712C211yesmaximal, characteristic
11C4×#66882C211yesmaximal, characteristic, complemented
12C4×#66881C211yesmaximal, characteristic, complemented
13C4×#66880C211yesmaximal, characteristic, complemented
14C4×#66880C211yesmaximal, characteristic, complemented
15C4×C11×C22⋊C8C211yesmaximal, characteristic
16C22×C42×C11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25#10622825C2211yescharacteristic
26#10622823—21no—
27C4×C22⋊Dic11—21no—
28C4×C22⋊Dic11—21no—
29C4×C22⋊Dic11—21no—
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622546—21no—
44#10622545—21no—
45C4×Dic11⋊C4—21no—
46C42×Dic11—21no—
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622336C418yesdirect product factor
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11D411yescharacteristic
71C2×C42×C11D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78#66979—22no—
79#66979—22no—
80#66979—22no—
81#66979C2×C414yes—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89#66977—22no—
90#66977C2×C414yes—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C4×Dic22—22no—
103C4×Dic22—22no—
104C11×C22⋊C8—22no—
105C11×C22⋊C8C2×C414yes—
106C4×C8×C11—22no—
107C4×C8×C11—22no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66882—22no—
118#66882C2×C414yescomplemented
119#66881—22no—
120#66881C2×C414yescomplemented
121#66880—22no—
122#66880—22no—
123#66880C2×C414yescomplemented
124#66880C2×C414yescomplemented
125C4×#485—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—41no—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22C22×C412yes—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C22×C412yes—
170C2×C8×C11C22×C412yes—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11#4112yes—
176C42×C11#4112yes—
177C22⋊Dic11—24no—
178C22⋊Dic11—24no—
179C22⋊Dic11—24no—
180C22⋊Dic11—42no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C412yes—
191C4⋊Dic11C22×C412yes—
192C4⋊Dic11C22×C412yes—
193C4⋊Dic11#4112yes—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—24no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198C4×Dic11—24no—
199C4×Dic11—24no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C2×#485—111no—
207C4×C22⋊Q8—111no—
208C4×#117—111no—
209#1928—111no—
210#1927—111no—
211#1919—111no—
212#1918—111no—
213#1873—111no—
214#1854—111no—
215#1825—111no—
216C4×#107—111no—
217C4×#106—111no—
218C4×#103—111no—
219C4×#103—111no—
220C4×C22⋊C8D1111yescharacteristic
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11C4×D412yes—
228C23×C11C22×D411yescharacteristic
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11C4×D412yes—
245C2×C4×C11#12312yes—
246C2×C4×C11#12312yes—
247C2×C4×C11#13512yes—
248C2×C4×C11#13512yes—
249C2×C4×C11#13712yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280Dic22—22no—
281Dic22—22no—
282Dic22—41no—
283Dic22—41no—
284C8×C11—22no—
285C8×C11—22no—
286C8×C11—41no—
287C8×C11—41no—
288C2×C22⋊Q8—111no—
289C2×C4×Q8—111no—
290C2×#117—111no—
291C2×#117—111no—
292C22×C42C2×D1111yescharacteristic
293#485—118no—
294C2×#107—111no—
295C2×#107—111no—
296C2×#106—111no—
297C2×#106—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×C22⋊C8C2×D1111yescharacteristic
303C2×C22⋊C8C2×D1111yescharacteristic
304C2×C4×C8C2×D1111yescharacteristic
305C2×C4×C8C2×D1111yescharacteristic
306#391—111no—
307#389—111no—
308#387—221no—
309#385—221no—
310#380—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—221no—
317C4×C22⋊C4—221no—
318C4×C22⋊C4—221no—
319C4×C22⋊C4—221no—
320#376—221no—
321C43—221no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#336C2×D1111yescharacteristic
331#336C2×D1111yescharacteristic
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×C4×D411yescharacteristic
340C22×C11C2×#12311yescharacteristic
341C22×C11#52511yescharacteristic
342C22×C11C2×#13511yescharacteristic
343C22×C11C2×#13511yescharacteristic
344C22×C11C2×#13711yescharacteristic
345C22×C11#57511yescharacteristic
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—41no—
350C4×C11#48514yescomplemented
351C4×C11C4×#4111yescharacteristic
352C4×C11C4×#4111yescharacteristic
353C4×C11#52911yescharacteristic
354C4×C11#52911yescharacteristic
355Dic11—42no—
356Dic11—42no—
357Dic11—42no—
358Dic11—42no—
359Dic11—42no—
360Dic11—42no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—111no—
364C23×C4D4411yescharacteristic
365C23×C4D4411yescharacteristic
366C23×C4C22×D1111yescharacteristic
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22⋊Q8—114no—
372C22⋊Q8—222no—
373C4×Q8—222no—
374C4×Q8—222no—
375#117—114no—
376#117—222no—
377#117—222no—
378#117—222no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42D4411yescharacteristic
404C2×C42D4411yescharacteristic
405C2×C42C22×D1111yescharacteristic
406C2×C42C22×D1111yescharacteristic
407#107—114no—
408#107—222no—
409#106—114no—
410#106—222no—
411#103—114no—
412#103—114no—
413#103—222no—
414#103—222no—
415C22⋊C8—22no—
416C22⋊C8C4×D1114yes—
417C4×C8—22no—
418C4×C8—22no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428C2×C11—42no—
429C2×C11C4×#12311yescharacteristic
430C2×C11C4×#13511yescharacteristic
431C2×C11C4×#13711yescharacteristic
432C2×C11C2×#48511yescharacteristic
433C2×C11#309111yescharacteristic
434C2×C11#310211yescharacteristic
435C2×C11#310711yescharacteristic
436C24C2×D4411yescharacteristic
437C2×Q8—112no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—41no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4C2×C4×D1112yes—
462C22×C4C2×D4411yescharacteristic
463C22×C4C2×D4411yescharacteristic
464C22×C4C2×D4411yescharacteristic
465C22×C4C2×D4411yescharacteristic
466C22×C4C2×D4411yescharacteristic
467C22×C4#433912yes—
468C22×C4C23×D1111yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8C2×C4×D1112yes—
480C2×C8C2×C4×D1112yes—
481C4⋊C4—112no—
482C4⋊C4—112no—
483C4⋊C4—112no—
484C4⋊C4—112no—
485C4⋊C4—112no—
486C4⋊C4—224no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C22⋊C4—224no—
499C22⋊C4—224no—
500C22⋊C4—224no—
501C22⋊C4—442no—
502C42—22no—
503C42—22no—
504C42—21no—
505C42—21no—
506C42—224no—
507C42—224no—
508C42—442no—
509C42—442no—
510C42—442no—
511C42—442no—
512C42—442no—
513C42—442no—
514C42#434112yes—
515C42#434112yes—
516C11C4×#48511yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23C4×D4412yes—
524C23C22×D4411yescharacteristic
525Q8—222no—
526Q8—222no—
527Q8—441no—
528Q8—441no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4C4×D4412yes—
569C2×C4#6693912yes—
570C2×C4#6693912yes—
571C2×C4#6695712yes—
572C2×C4#6695712yes—
573C2×C4#6696212yes—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C2×#433911yescharacteristic
576C2×C4C2×#434111yescharacteristic
577C2×C4C2×#434111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C8—22no—
581C8—22no—
582C8—41no—
583C8—41no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C2×C4×D4411yescharacteristic
592C22C2×#6693911yescharacteristic
593C22#1062305511yescharacteristic
594C22C2×#6695711yescharacteristic
595C22C2×#6695711yescharacteristic
596C22C2×#6696211yescharacteristic
597C22#1062327911yescharacteristic
598C4—22no—
599C4—22no—
600C4—22no—
601C4—41no—
602C4—442no—
603C4—442no—
604C4—442no—
605C4—442no—
606C4—442no—
607C4—442no—
608C4—881no—
609C4—881no—
610C4#1062233614yesdirect product factor
611C4C4×#434111yescharacteristic
612C4C4×#434111yescharacteristic
613C4#1062306911yescharacteristic
614C4#1062306911yescharacteristic
615C2—42no—
616C2C4×#6693911yescharacteristic
617C2C4×#6695711yescharacteristic
618C2C4×#6696211yescharacteristic
619C2C2×#1062233611yescharacteristic
620C2#1307853111yescharacteristic
621C2#1307863611yescharacteristic
622C2#1307868811yescharacteristic
subgroupG/H
centerC22×C4C2×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊C8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11C4×#485
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #13069258C2semidirect
5. #13069251C2semidirect
6. #13069195C2semidirect
7. #13069188C2semidirect
11. C4×#66882C2semidirect
12. C4×#66881C2semidirect
13. C4×#66880C2semidirect
14. C4×#66880C2semidirect
49. #10622336C4direct (N × H)
118. #66882C2×C4semidirect
120. #66881C2×C4semidirect
123. #66880C2×C4semidirect
124. #66880C2×C4semidirect
350. C4×C11#485semidirect
516. C11C4×#485semidirect
610. C4#10622336direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106223362
C4×#669772
C4×#669792
#130692582
#130692512
#130691952
#130691882
#130689262
#130688172
#130687122
C4×#668822
C4×#668812
C4×#668802
C4×C11×C22⋊C82
C4×#48511