Finite Group Databasebeta

← C4×#10622593 #14675607

Subgroups — C4×#10622593 #14675607

Order 2816.

1574 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622593C211yesmaximal, characteristic
2C2×C4×Dic11⋊C4C211yesmaximal, characteristic
3C2×C4×Dic11⋊C4C212yesmaximal
4#13066884C211yesmaximal, characteristic
5#13066879C211yesmaximal, characteristic
6#13066871C212yesmaximal
7#13066867C212yesmaximal
8#13066866C211yesmaximal, characteristic
9C4×C11⋊#95C212yesmaximal
10C4×C11⋊#95C211yesmaximal, characteristic
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C4×C11×C4⋊C4—24no—
24C2×C11×#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36#10622593C418yesdirect product factor
37C4×Dic11⋊C4—24no—
38C4×Dic11⋊C4—28no—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C42×C11—24no—
56C2×C42×C11—24no—
57C2×C42×C11—24no—
58C2×C42×C11—24no—
59C2×C42×C11D414yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—24no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4C2×C418yes—
71C2×Dic11⋊C4C2×C414yes—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11D414yes—
79C2×C4×Dic11Q818yes—
80C11×#95—24no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—24no—
84C11⋊#95—22no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95C2×C418yes—
91C11⋊#95C2×C414yes—
92C4×#398—111nomaximal, Sylow
93C24×C11C2411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11C22×C414yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×Q814yes—
119C22×C4×C11#4114yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4114yes—
123C22×Dic11—22no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11C22×C412yes—
150C22×Dic11C22×C412yes—
151C22×Dic11C22×C414yes—
152C22×Dic11C2×D412yes—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×Q814yes—
155C22×Dic11C2×Q814yes—
156C22×Dic11#4112yes—
157C22×Dic11#4112yes—
158C22×Dic11#4114yes—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—28no—
161C42×C11—28no—
162C42×C11—48no—
163Dic11⋊C4—28no—
164Dic11⋊C4—216no—
165Dic11⋊C4—216no—
166Dic11⋊C4—28no—
167C4×Dic11—28no—
168C4×Dic11—216no—
169C4×Dic11—44no—
170C2×#398—111no—
171C2×C4×C4⋊C4—111no—
172C2×C4×C4⋊C4—112no—
173C2×C4×C4⋊C4D1111yescharacteristic
174#1445—111no—
175#1444—111no—
176#1442—112no—
177#1441—112no—
178#1441—111no—
179C4×#95—112no—
180C4×#95—111no—
181C23×C11C23×C411yescharacteristic
182C23×C11C22×D411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×Q812yes—
185C23×C11C2×#4111yescharacteristic
186C23×C11C2×#4112yes—
187C23×C11C2×#4112yes—
188C23×C11C2×#4111yescharacteristic
189C23×C11C2×#4111yescharacteristic
190C23×C11C2×#4112yes—
191C23×C11C2×#4111yescharacteristic
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11C4×D414yes—
216C2×C4×C11#12114yes—
217C2×C4×C11C22⋊Q818yes—
218C2×C4×C11#12314yes—
219C2×C4×C11#12518yes—
220C2×C4×C11C4⋊Q814yes—
221C2×Dic11—22no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—24no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11C4×D414yes—
256C2×Dic11C4×Q818yes—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—111no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C4⋊C4C2×D1111yescharacteristic
263C22×C42—112no—
264C22×C42—111no—
265C22×C42—111no—
266C22×C42C2×D1112yes—
267C22×C42C2×D1111yescharacteristic
268#398—118no—
269C4×C4⋊C4—24no—
270C4×C4⋊C4—228no—
271C4×C4⋊C4—224no—
272C2×#95—112no—
273C2×#95—111no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—111no—
279C2×#95—112no—
280C2×#95—111no—
281C2×#95—112no—
282C2×#95—111no—
283C2×#95C2×D1112yes—
284C22×C11C2×C4×D411yescharacteristic
285C22×C11C2×C4×D411yescharacteristic
286C22×C11C2×C4×Q812yes—
287C22×C11C4×#4112yes—
288C22×C11C4×#4111yescharacteristic
289C22×C11C2×#12111yescharacteristic
290C22×C11C2×C22⋊Q812yes—
291C22×C11C2×#12311yescharacteristic
292C22×C11#52511yescharacteristic
293C22×C11#52512yes—
294C22×C11#52511yescharacteristic
295C22×C11C2×#12512yes—
296C22×C11#52912yes—
297C22×C11#52912yes—
298C22×C11#52912yes—
299C22×C11#52912yes—
300C22×C11#52911yescharacteristic
301C22×C11C2×C4⋊Q811yescharacteristic
302C22×C11#53211yescharacteristic
303C22×C11#53211yescharacteristic
304C22×C11#53312yes—
305C22×C11#53312yes—
306C22×C11#53312yes—
307C4×C11—24no—
308C4×C11—44no—
309C4×C11—42no—
310C4×C11—44no—
311C4×C11#39818yescomplemented
312Dic11—24no—
313Dic11—28no—
314Dic11—42no—
315Dic11—42no—
316Dic11—44no—
317Dic11—42no—
318C23×C4—111no—
319C23×C4—112no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—111no—
323C23×C4—112no—
324C23×C4C22×D1112yes—
325C23×C4C22×D1112yes—
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1111yescharacteristic
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—118no—
334C2×C4⋊C4—114no—
335C2×C4⋊C4—224no—
336C2×C4⋊C4—224no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—224no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4C4×D1114yes—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—114no—
351C2×C42—118no—
352C2×C42—224no—
353C2×C42—224no—
354C2×C42—222no—
355C2×C42—222no—
356C2×C42—224no—
357C2×C42—222no—
358C2×C42C22⋊D1114yes—
359#95—24no—
360#95—114no—
361#95—118no—
362#95—224no—
363#95—224no—
364#95—224no—
365#95—224no—
366#95—224no—
367#95—224no—
368#95—222no—
369#95—222no—
370#95—222no—
371C2×C11C4×#12111yescharacteristic
372C2×C11C4×#12311yescharacteristic
373C2×C11C4×C22⋊Q812yes—
374C2×C11C4×#12512yes—
375C2×C11C4×C4⋊Q811yescharacteristic
376C2×C11C2×#39811yescharacteristic
377C2×C11#239211yescharacteristic
378C2×C11#239511yescharacteristic
379C2×C11#239612yes—
380C2×C11#239911yescharacteristic
381C2×C11#240212yes—
382C24C23×D1111yescharacteristic
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—114no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—114no—
405C22×C4—114no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—114no—
410C22×C4—112no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—221no—
414C22×C4—222no—
415C22×C4—221no—
416C22×C4—222no—
417C22×C4—221no—
418C22×C4—221no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—221no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—221no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4C2×C4×D1114yes—
438C22×C4C2×C4×D1112yes—
439C22×C4#433914yes—
440C22×C4#433912yes—
441C22×C4#433914yes—
442C22×C4D4×D1112yes—
443C22×C4#434112yes—
444C22×C4Q8×D1114yes—
445C22×C4C2×C22⋊D1112yes—
446C22×C4C2×C22⋊D1112yes—
447C22×C4C2×C22⋊D1112yes—
448C4⋊C4—28no—
449C4⋊C4—28no—
450C4⋊C4—2216no—
451C4⋊C4—2216no—
452C4⋊C4—228no—
453C4⋊C4—228no—
454C42—28no—
455C42—48no—
456C42—2216no—
457C42—228no—
458C42—444no—
459C11C4×#39811yescharacteristic, complemented, Sylow
460C23C22×C4×D1111yescharacteristic
461C23C2×#433912yes—
462C23C2×#433912yes—
463C23C2×#433911yescharacteristic
464C23C2×D4×D1111yescharacteristic
465C23C2×#434111yescharacteristic
466C23C2×Q8×D1112yes—
467C23#41×D1111yescharacteristic
468C23#41×D1112yes—
469C23#41×D1111yescharacteristic
470C23C22×C22⋊D1111yescharacteristic
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—114no—
495C2×C4—118no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—224no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—224no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4#6694218yes—
531C2×C4#6694918yes—
532C2×C4C4×C22⋊D1114yes—
533C2×C4#6698214yes—
534C2×C4#6699114yes—
535C2×C4#6699714yes—
536C22C4×#433912yes—
537C22#1062301012yes—
538C22C2×#6694212yes—
539C22C2×#6694912yes—
540C22#1062305912yes—
541C22#1062305912yes—
542C22C4×#434111yescharacteristic
543C22#1062306912yes—
544C22C4×D4×D1111yescharacteristic
545C22#1062307812yes—
546C22#1062307911yescharacteristic
547C22#1062308811yescharacteristic
548C22C4×Q8×D1112yes—
549C22#1062310912yes—
550C22#1062310912yes—
551C22#1062310912yes—
552C22C2×C4×C22⋊D1111yescharacteristic
553C22C2×#6698211yescharacteristic
554C22#1062332211yescharacteristic
555C22C2×#6699111yescharacteristic
556C22C2×#6699711yescharacteristic
557C22#1062335911yescharacteristic
558C22#1062336311yescharacteristic
559C4—24no—
560C4—42no—
561C4—44no—
562C4—44no—
563C4—224no—
564C4—228no—
565C4—442no—
566C4—444no—
567C4—442no—
568C4—442no—
569C4#1062259318yesdirect product factor
570C2C4×#6699111yescharacteristic
571C2C4×#6698211yescharacteristic
572C2C4×#6694912yes—
573C2C4×#6694212yes—
574C2C4×#6699711yescharacteristic
575C2C2×#1062259311yescharacteristic
576C2#1307185411yescharacteristic
577C2#1307187311yescharacteristic
578C2#1307189212yes—
579C2#1307190711yescharacteristic
580C2#1307192312yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C4×C11×C4⋊C4C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C4×#398
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. #10622593C4direct (N × H)
311. C4×C11#398semidirect
459. C11C4×#398semidirect
569. C4#10622593direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225932
C2×C4×Dic11⋊C42
#130668842
#130668792
#130668712
#130668672
#130668662
C4×C11⋊#952
C2×C4×C11×C4⋊C42
C4×#39811