Finite Group Databasebeta

← C4×#10622562 #14675602

Subgroups — C4×#10622562 #14675602

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622562C211yesmaximal, characteristic
2C2×C4×Dic11⋊C4C212yesmaximal, complemented
3C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C212yesmaximal
5#13066885C211yesmaximal, characteristic, complemented
6#13066882C212yesmaximal, complemented
7#13066880C211yesmaximal, characteristic, complemented
8#13066861C211yesmaximal, characteristic
9#13066859C212yesmaximal
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C22×C4×Dic11C2212yes—
25C4×C11×C22⋊C4—24no—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C4×C22⋊Dic11—28no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622562C418yesdirect product factor
38C4×C4⋊Dic11—24no—
39C4×Dic11⋊C4—28no—
40C25×C11C2311yescharacteristic
41C23×C4×C11—24no—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—24no—
45C23×C4×C11Q814yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4C2×C414yes—
62C2×C42×C11—24no—
63C2×C42×C11—24no—
64C2×C42×C11—22no—
65C2×C42×C11D414yes—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11C2×C418yes—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11C2×C414yescomplemented
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—24no—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4C2×C418yescomplemented
83C2×C4×Dic11—24no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—24no—
86C2×C4×Dic11—24no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11D418yes—
89C11×#95—22no—
90C11×#95—22no—
91C11⋊#95—24no—
92C11⋊#95—22no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95C2×C414yescomplemented
99C4×#399—111nomaximal, Sylow
100C24×C11—22no—
101C24×C11—21no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—21no—
107C24×C11—22no—
108C24×C11C22×C412yes—
109C24×C11C2×Q812yes—
110C24×C11#4112yes—
111C24×C11C2411yescharacteristic
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—216no—
131C22×C4×C11—28no—
132C22×C4×C11—48no—
133C22×C4×C11—44no—
134C22×C4×C11—44no—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×Q812yes—
142C22×C4×C11C2×Q812yes—
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×C4×C11#4112yes—
146C22×C4×C11#4114yes—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11C22×C414yes—
170C22×Dic11C22×C414yes—
171C22×Dic11C2×D414yes—
172C22×Dic11C2×D414yes—
173C22×Dic11#4114yes—
174C22×Dic11#4114yes—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—28no—
177C42×C11—28no—
178C42×C11—44no—
179C22⋊Dic11—216no—
180C22⋊Dic11—216no—
181C4⋊Dic11—28no—
182C4⋊Dic11—28no—
183Dic11⋊C4—216no—
184Dic11⋊C4—216no—
185C4×Dic11—216no—
186C4×Dic11—48no—
187C2×#399—111no—
188C2×C4×C4⋊C4—111no—
189C2×C4×C4⋊C4—112no—
190C2×C4×C22⋊C4—112no—
191C2×C4×C22⋊C4D1111yescharacteristic
192#1445—112no—
193#1445—111no—
194#1444—111no—
195#1439—112no—
196#1439—111no—
197C4×#95—111no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—42no—
211C23×C11—41no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—41no—
218C23×C11—42no—
219C23×C11—41no—
220C23×C11C4×Q814yes—
221C23×C11C23×C411yescharacteristic
222C23×C11C22×D412yes—
223C23×C11C22×D411yescharacteristic
224C23×C11C22×Q811yescharacteristic
225C23×C11C2×#4111yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4112yes—
230C23×C11C2×#4112yes—
231C23×C11C2×#4112yes—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—416no—
257C2×C4×C11C4×D414yes—
258C2×C4×C11C22⋊Q818yes—
259C2×C4×C11C22⋊Q814yes—
260C2×C4×C11#12318yes—
261C2×C4×C11#12314yes—
262C2×C4×C11#12714yes—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11C4×D418yes—
291C24×C4C2×D1111yescharacteristic
292C22×C4⋊C4—112no—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—112no—
295C22×C4⋊C4—111no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C22⋊C4C2×D1111yescharacteristic
300C22×C42—112no—
301C22×C42—112no—
302C22×C42C2×D1111yescharacteristic
303C22×C42C2×D1111yescharacteristic
304#399—118no—
305C4×C4⋊C4—228no—
306C4×C4⋊C4—224no—
307C4×C22⋊C4—24no—
308C4×C22⋊C4—228no—
309C2×#95—111no—
310C2×#95—112no—
311C2×#95—111no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95C2×D1111yescharacteristic
318C2×#95C2×D1111yescharacteristic
319C22×C11—28no—
320C22×C11—24no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11—42no—
326C22×C11—44no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—44no—
330C22×C11C2×C4×D411yescharacteristic
331C22×C11C2×C4×D412yes—
332C22×C11C2×C4×Q811yescharacteristic
333C22×C11C4×#4111yescharacteristic
334C22×C11C4×#4112yes—
335C22×C11C2×C22⋊Q812yes—
336C22×C11C2×C22⋊Q811yescharacteristic
337C22×C11C2×#12312yes—
338C22×C11C2×#12311yescharacteristic
339C22×C11#52511yescharacteristic
340C22×C11#52512yes—
341C22×C11#52512yes—
342C22×C11#52511yescharacteristic
343C22×C11#52911yescharacteristic
344C22×C11#52912yes—
345C22×C11#52912yes—
346C22×C11#52912yes—
347C22×C11#52912yes—
348C22×C11C2×#12711yescharacteristic
349C22×C11#53212yes—
350C22×C11#53211yescharacteristic
351C22×C11#53311yescharacteristic
352C22×C11#53312yes—
353C4×C11—24no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11#39918yescomplemented
359Dic11—28no—
360Dic11—44no—
361Dic11—44no—
362Dic11—44no—
363C25C22×D1111yescharacteristic
364C23×C4—22no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4—112no—
372C23×C4Dic2214yes—
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1111yescharacteristic
379C2×C4⋊C4—118no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—224no—
382C2×C4⋊C4—224no—
383C2×C4⋊C4—224no—
384C2×C4⋊C4—224no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—222no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4C4×D1114yes—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—118no—
406C2×C42—224no—
407C2×C42—224no—
408C2×C42—224no—
409C2×C42—224no—
410C2×C42—224no—
411C2×C42C22⋊D1114yes—
412#95—22no—
413#95—22no—
414#95—114no—
415#95—224no—
416#95—224no—
417#95—224no—
418#95—224no—
419#95—224no—
420#95—222no—
421#95—224no—
422C2×C11—44no—
423C2×C11C4×#12311yescharacteristic
424C2×C11C4×#12312yes—
425C2×C11C4×C22⋊Q812yes—
426C2×C11C4×C22⋊Q811yescharacteristic
427C2×C11C4×#12711yescharacteristic
428C2×C11C2×#39911yescharacteristic
429C2×C11#239511yescharacteristic
430C2×C11#239512yes—
431C2×C11#239611yescharacteristic
432C2×C11#239612yes—
433C2×C11#239711yescharacteristic
434C24—21no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24C2×Dic2212yes—
443C24C2×C4×D1112yes—
444C24#433912yes—
445C24C23×D1111yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—216no—
465C22×C4—28no—
466C22×C4—48no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4C2×Dic2212yes—
498C22×C4C2×Dic2212yes—
499C22×C4C2×C4×D1112yes—
500C22×C4C2×C4×D1112yes—
501C22×C4#433912yes—
502C22×C4#433912yes—
503C22×C4#433912yes—
504C22×C4D4×D1114yes—
505C22×C4#434114yes—
506C22×C4C2×C22⋊D1112yes—
507C22×C4C2×C22⋊D1112yes—
508C22×C4C2×C22⋊D1112yes—
509C4⋊C4—2216no—
510C4⋊C4—2216no—
511C4⋊C4—228no—
512C4⋊C4—228no—
513C22⋊C4—28no—
514C22⋊C4—28no—
515C22⋊C4—2216no—
516C22⋊C4—2216no—
517C42—28no—
518C42—44no—
519C42—2216no—
520C42—448no—
521C11C4×#39911yescharacteristic, complemented, Sylow
522C23—22no—
523C23—22no—
524C23—22no—
525C23—24no—
526C23—24no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—42no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—41no—
543C23—41no—
544C23C4×Dic2214yes—
545C23C22×Dic2211yescharacteristic
546C23C22×C4×D1111yescharacteristic
547C23C2×#433911yescharacteristic
548C23C2×#433911yescharacteristic
549C23C2×#433911yescharacteristic
550C23C2×#433911yescharacteristic
551C23C2×D4×D1112yes—
552C23C2×#434112yes—
553C23#41×D1112yes—
554C23#41×D1112yes—
555C23C22×C22⋊D1111yescharacteristic
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—416no—
581C2×C4—118no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4#6693118yes—
610C2×C4#6693618yes—
611C2×C4#6697714yes—
612C2×C4C4×C22⋊D1114yes—
613C2×C4#6698814yes—
614C2×C4#6699314yes—
615C22—28no—
616C22—24no—
617C22—42no—
618C22—44no—
619C22—42no—
620C22—44no—
621C22—42no—
622C22—42no—
623C22—44no—
624C22—42no—
625C22—42no—
626C22C2×C4×Dic2211yescharacteristic
627C22#1062300111yescharacteristic
628C22C4×#433911yescharacteristic
629C22#1062301011yescharacteristic
630C22C2×#6693112yes—
631C22C2×#6693612yes—
632C22#1062304812yes—
633C22#1062305912yes—
634C22C4×#434112yes—
635C22#1062306912yes—
636C22#1062306912yes—
637C22C4×D4×D1112yes—
638C22#1062307812yes—
639C22#1062307812yes—
640C22#1062307912yes—
641C22#1062308812yes—
642C22C2×#6697711yescharacteristic
643C22C2×C4×C22⋊D1111yescharacteristic
644C22#1062332211yescharacteristic
645C22C2×#6698811yescharacteristic
646C22C2×#6699311yescharacteristic
647C22#1062335911yescharacteristic
648C22#1062336311yescharacteristic
649C4—24no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—42no—
654C4—228no—
655C4—444no—
656C4—444no—
657C4—444no—
658C4#1062256218yesdirect product factor
659C2—44no—
660C2C4×#6698811yescharacteristic
661C2C4×#6693612yes—
662C2C4×#6693112yes—
663C2C4×#6697711yescharacteristic
664C2C4×#6699311yescharacteristic
665C2C2×#1062256211yescharacteristic
666C2#1307187511yescharacteristic
667C2#1307187712yes—
668C2#1307188411yescharacteristic
669C2#1307189012yes—
670C2#1307189511yescharacteristic
subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C4×#399
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic11⋊C4C2semidirect
3. C2×C4×C4⋊Dic11C2semidirect
5. #13066885C2semidirect
6. #13066882C2semidirect
7. #13066880C2semidirect
10. C4×C11⋊#95C2semidirect
37. #10622562C4direct (N × H)
76. C2×C4⋊Dic11C2×C4semidirect
82. C2×Dic11⋊C4C2×C4semidirect
98. C11⋊#95C2×C4semidirect
358. C4×C11#399semidirect
521. C11C4×#399semidirect
658. C4#10622562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225622
C2×C4×Dic11⋊C42
C2×C4×C4⋊Dic112
C2×C4×C22⋊Dic112
#130668852
#130668822
#130668802
#130668612
#130668592
C4×C11⋊#952
C2×C4×C11×C22⋊C42
C4×#39911