Finite Group Databasebeta

← C4×#10622658 #14760935

Subgroups — C4×#10622658 #14760935

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×#10622658C211yesmaximal, characteristic
2C4×#66979C211yesmaximal, characteristic
3#13069254C211yesmaximal, characteristic, complemented
4#13069247C211yesmaximal, characteristic, complemented
5#13069191C211yesmaximal, characteristic, complemented
6#13069184C211yesmaximal, characteristic, complemented
7#13068929C211yesmaximal, characteristic
8#13068813C211yesmaximal, characteristic
9#13068708C211yesmaximal, characteristic
10C4×#66871C211yesmaximal, characteristic, complemented
11C4×#66872C211yesmaximal, characteristic, complemented
12C4×#66899C211yesmaximal, characteristic, complemented
13C4×#66899C211yesmaximal, characteristic, complemented
14C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
15C4×C11×C22⋊Q8C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#387—21no—
24C11×#385—21no—
25C11×#380C2211yescharacteristic
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C4×C22⋊Dic11—21no—
34C4×C22⋊Dic11—21no—
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622658C418yesdirect product factor
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622545—21no—
47C42×Dic11—21no—
48C2×C4×C11⋊C8C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8C2×C414yes—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86#66979—22no—
87#66979—22no—
88#66979—22no—
89#66979C2×C414yes—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109#66899—22no—
110#66899—22no—
111#66899C2×C414yescomplemented
112#66899C2×C414yescomplemented
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118C22⋊(C11⋊C8)C2×C414yes—
119#66872—22no—
120#66872C2×C414yescomplemented
121#66871—22no—
122#66871C2×C414yescomplemented
123C4×C11⋊C8—22no—
124C4×C11⋊C8—22no—
125C4×#485—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—41no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4C22×C412yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—42no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—42no—
175C42×C11—42no—
176C42×C11#4112yes—
177C42×C11#4112yes—
178C22⋊Dic11—24no—
179C22⋊Dic11—24no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C22×C412yes—
185C4⋊Dic11C22×C412yes—
186C4⋊Dic11#4112yes—
187C4⋊Dic11#4112yes—
188C4×Dic11—24no—
189C4×Dic11—24no—
190C4×Dic11—42no—
191C4×Dic11—42no—
192C4×Dic11—42no—
193C4×Dic11—42no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C412yes—
205C2×C11⋊C8C22×C412yes—
206C2×#485—111no—
207C4×C22⋊Q8D1111yescharacteristic
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⋊C8—111no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11C4×D412yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—41no—
232Q8×C11—41no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—44no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—44no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11C4×D412yes—
261C2×C4×C11#12312yes—
262C2×C4×C11#12312yes—
263C2×C4×C11#13512yes—
264C2×C4×C11#13512yes—
265C2×C4×C11#13712yes—
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C11⋊C8—22no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C2×C22⋊Q8C2×D1111yescharacteristic
289C2×C4×Q8C2×D1111yescharacteristic
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⋊C8—111no—
303C2×C22⋊C8—111no—
304C2×C4×C8—111no—
305C2×C4×C8—111no—
306#391C2×D1111yescharacteristic
307#389C2×D1111yescharacteristic
308#387—21no—
309#385—21no—
310#380C2×D1111yescharacteristic
311C4×C4⋊C4—21no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4C2×D1111yescharacteristic
317C4×C22⋊C4—21no—
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#336—111no—
331#336—111no—
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—42no—
351C4×C11—42no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11#48514yescomplemented
355C4×C11C4×#4111yescharacteristic
356C4×C11C4×#4111yescharacteristic
357C4×C11#52911yescharacteristic
358C4×C11#52911yescharacteristic
359Dic11—42no—
360Dic11—42no—
361Dic11—42no—
362Dic11—42no—
363C22×Q8C22×D1111yescharacteristic
364C23×C4C22⋊D1111yescharacteristic
365C23×C4C22⋊D1111yescharacteristic
366C23×C4C22×D1111yescharacteristic
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—111no—
371C22⋊Q8—22no—
372C22⋊Q8C4×D1114yes—
373C4×Q8—22no—
374C4×Q8—22no—
375#117—114no—
376#117—222no—
377#117—222no—
378#117—222no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42C22⋊D1111yescharacteristic
404C2×C42C22⋊D1111yescharacteristic
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—114no—
416C22⋊C8—222no—
417C4×C8—222no—
418C4×C8—222no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
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×C22⋊D1111yescharacteristic
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×C4×D1112yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4C2×C4×D1112yes—
462C22×C4#433912yes—
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C4⋊C4—24no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—112no—
490C4⋊C4—112no—
491C4⋊C4—112no—
492C4⋊C4—112no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4C2×C4×D1112yes—
498C22⋊C4—24no—
499C22⋊C4—42no—
500C22⋊C4—224no—
501C22⋊C4—224no—
502C42—22no—
503C42—22no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—42no—
508C42—224no—
509C42—224no—
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×C22⋊D1112yes—
524C23C22×C22⋊D1111yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—41no—
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—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—44no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—44no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
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×C22⋊D1112yes—
569C2×C4#6698812yes—
570C2×C4#6698812yes—
571C2×C4#6699512yes—
572C2×C4#6700312yes—
573C2×C4#6700312yes—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C2×#433911yescharacteristic
576C2×C4C2×#434111yescharacteristic
577C2×C4C2×#434111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C8—222no—
581C8—222no—
582C8—441no—
583C8—441no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C2×C4×C22⋊D1111yescharacteristic
592C22C2×#6698811yescharacteristic
593C22C2×#6699511yescharacteristic
594C22C2×#6700311yescharacteristic
595C22C2×#6700311yescharacteristic
596C22#1062335311yescharacteristic
597C22#1062335911yescharacteristic
598C4—22no—
599C4—22no—
600C4—22no—
601C4—42no—
602C4—42no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—442no—
607C4—442no—
608C4—442no—
609C4—442no—
610C4#1062265814yesdirect product factor
611C4C4×#434111yescharacteristic
612C4C4×#434111yescharacteristic
613C4#1062306911yescharacteristic
614C4#1062306911yescharacteristic
615C2—42no—
616C2C4×#6698811yescharacteristic
617C2C4×#6700311yescharacteristic
618C2C4×#6699511yescharacteristic
619C2C2×#1062265811yescharacteristic
620C2#1307852511yescharacteristic
621C2#1307862811yescharacteristic
622C2#1307868111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊Q8D11
hypocenterC11C4×#485
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13069254C2semidirect
4. #13069247C2semidirect
5. #13069191C2semidirect
6. #13069184C2semidirect
10. C4×#66871C2semidirect
11. C4×#66872C2semidirect
12. C4×#66899C2semidirect
13. C4×#66899C2semidirect
37. #10622658C4direct (N × H)
111. #66899C2×C4semidirect
112. #66899C2×C4semidirect
120. #66872C2×C4semidirect
122. #66871C2×C4semidirect
354. C4×C11#485semidirect
516. C11C4×#485semidirect
610. C4#10622658direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226582
C4×#669792
#130692542
#130692472
#130691912
#130691842
#130689292
#130688132
#130687082
C4×#668712
C4×#668722
C4×#668992
C4×C22⋊(C11⋊C8)2
C4×C11×C22⋊Q82
C4×#48511