Finite Group Databasebeta

← C2×#13079007 #15623060

Subgroups — C2×#13079007 #15623060

Order 2816.

2398 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C22×#66941C211yesmaximal, characteristic, complemented
3#13079007C2116yesmaximal, direct product factor
4C2×#10622408C212yesmaximal, complemented
5C2×#10622378C212yesmaximal, complemented
6C2×#10622405C212yesmaximal, complemented
7C2×#10622373C212yesmaximal, complemented
8C2×#10622746C211yesmaximal, characteristic, complemented
9C2×#10622845C211yesmaximal, characteristic, complemented
10C2×#10622579C211yesmaximal, characteristic, complemented
11C2×M16×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#417C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×Dic22—21no—
16C22×C11×M16C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18#10623363—24no—
19#10623363C2218yes—
20C2×#67000C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22C2×#66993C2211yescharacteristic
23C2×#66992—21no—
24C2×#66992—21no—
25C2×#66989C2211yescharacteristic
26C2×C4×C22⋊D11—21no—
27C2×C4×C22⋊D11—21no—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4—21no—
30C22×C4×Dic11C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C2×#66941—24no—
33C2×#66941—21no—
34C2×#66941—21no—
35C2×#66941C2212yes—
36C2×#66941C2212yes—
37C2×#66941C2218yescomplemented
38C11×#417C2218yescomplemented
39C2×C11×#103C2212yes—
40C2×C11×#102C2212yes—
41#10622845C2218yescomplemented
42C2×#66899C2212yes—
43C2×#66896C2212yes—
44#10622746C2218yescomplemented
45M16×Dic11C2218yescomplemented
46C2×#66885C2212yes—
47C2×#66880C2212yes—
48C2×#66879C2212yes—
49C2×C8×Dic11C2212yes—
50C2×#66874C2212yes—
51#10622579C2218yescomplemented
52C2×#66873C2212yes—
53#10622408C22116yescomplemented
54#10622405C22116yescomplemented
55#10622378C22116yescomplemented
56#10622373C22116yescomplemented
57C2×C11×#41—22no—
58C2×C11×#41—24no—
59C2×C11×#41—24no—
60C2×C11×#41C2314yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C23×Dic11—21no—
71C23×Dic11D411yescharacteristic
72C23×Dic11D411yescharacteristic
73C2×#4339—22no—
74C2×#4339—24no—
75C2×#4339—24no—
76C2×#4339C2314yes—
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C22×Dic22—22no—
80C22×Dic22—22no—
81C22×Dic22—28no—
82C22×Dic22—48no—
83C22×Dic22C2311yescharacteristic
84C2×C11×M16—24no—
85C2×C11×M16C2314yes—
86C22×C8×C11C2312yes—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93#67000—22no—
94#67000C2314yes—
95#66997—22no—
96#66997C2314yes—
97#66993—22no—
98#66993C2314yes—
99#66992—28no—
100#66992—28no—
101#66989—22no—
102#66989C2314yes—
103C4×C22⋊D11—28no—
104C4×C22⋊D11—28no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2314yes—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—28no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×C4×Dic11D411yescharacteristic
117C2×C4×Dic11D411yescharacteristic
118C2×C4×Dic11D414yes—
119C2×C4×Dic11C2314yes—
120C2×C4×Dic11C2311yescharacteristic
121C2×C4×Dic11C2311yescharacteristic
122C2×#4318—24no—
123C2×#4318C2314yes—
124C22×C11⋊C8C2312yes—
125#66941—24no—
126#66941—24no—
127#66941—28no—
128#66941—28no—
129#66941C2318yes—
130#66941C2318yes—
131C11×#103C2318yes—
132C11×#102C2318yes—
133#66899C2318yes—
134#66896C2318yes—
135#66885C2318yes—
136#66880C2318yes—
137#66879C2318yes—
138C8×Dic11C2318yes—
139#66874C2318yes—
140#66873C2318yes—
141C2×#3141—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C11×#41—28no—
146C11×#41—28no—
147C11×#41—48no—
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
151C2×Q8×C11C2412yes—
152C2×D4×C11—24no—
153C2×D4×C11—21no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—44no—
157C2×D4×C11C2412yes—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—22no—
161C22×C4×C11—24no—
162C22×C4×C11—44no—
163C22×C4×C11—44no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11#4114yes—
167C22×C4×C11#4114yes—
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2412yes—
170C2×C22⋊D11—24no—
171C2×C22⋊D11—24no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—44no—
174C2×C22⋊D11—44no—
175C2×C22⋊D11—44no—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11—24no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11—44no—
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D414yes—
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D414yes—
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188#4339—28no—
189#4339—28no—
190#4339—48no—
191C2×D44—21no—
192C2×D44—22no—
193C2×D44—22no—
194C2×D44C2412yes—
195C2×C4×D11—24no—
196C2×C4×D11—44no—
197C2×Dic22—28no—
198C2×Dic22—28no—
199C2×Dic22—21no—
200C2×Dic22—22no—
201C2×Dic22—22no—
202C2×Dic22—432no—
203C2×Dic22—48no—
204C2×Dic22—48no—
205C2×Dic22C2412yes—
206C11×M16—28no—
207C2×C8×C11—24no—
208C2×C8×C11C2414yes—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4C2414yes—
212C22⋊Dic11—24no—
213C22⋊Dic11—24no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—24no—
216C4⋊Dic11—22no—
217C4⋊Dic11—24no—
218C4⋊Dic11C2414yes—
219Dic11⋊C4—28no—
220Dic11⋊C4—28no—
221Dic11⋊C4—24no—
222Dic11⋊C4—24no—
223C4×Dic11C2×D414yes—
224C4×Dic11C2×D414yes—
225C4×Dic11C2×D412yes—
226C4×Dic11C2×D412yes—
227C4×Dic11C2412yes—
228C4×Dic11C2412yes—
229#4318—28no—
230C2×C11⋊C8—24no—
231C2×C11⋊C8C2414yes—
232C2×#532—111no—
233C22×C4⋊Q8—111no—
234#3141—1116no—
235C2×#489—112no—
236C2×#489—112no—
237C2×#487—112no—
238C2×#486—112no—
239C2×#417—111no—
240C2×#417—111no—
241C2×#417—111no—
242C2×#417D1111yescharacteristic, complemented
243C2×C4×M16—111no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11#12414yes—
251C23×C11C22×D412yes—
252C23×C11C22×D411yescharacteristic
253C22×D11—22no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—42no—
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11—42no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—48no—
263D4×C11—42no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—48no—
267C2×C4×C11—42no—
268C2×C4×C11—44no—
269C2×C4×C11—48no—
270C2×C4×C11#12414yes—
271C2×C4×C11#12418yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D412yes—
274C2×C4×C11C2×#4112yes—
275C2×C4×C11C2×#4114yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11C2×#4114yes—
278C2×C4×C11C2511yescharacteristic
279C22⋊D11—48no—
280C22⋊D11—48no—
281C22⋊D11—48no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—28no—
285C2×Dic11—28no—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—48no—
289C2×Dic11—42no—
290C2×Dic11—44no—
291C2×Dic11AGL(1,ℤ/8)14yes—
292C2×Dic11#13714yes—
293C2×Dic11C22×D412yes—
294C2×Dic11C22×D412yes—
295C2×Dic11C22×D412yes—
296C2×Dic11C22×D412yes—
297D44—22no—
298D44—22no—
299D44—42no—
300C4×D11—48no—
301Dic22—22no—
302Dic22—22no—
303Dic22—416no—
304Dic22—42no—
305Dic22—416no—
306C8×C11—24no—
307C11⋊C8—24no—
308C22×#41—111no—
309C22×#41C2×D1111yescharacteristic
310C23×Q8—221no—
311C22×M16—111no—
312C22×M16C2×D1111yescharacteristic
313#532—118no—
314#532—224no—
315C2×C4⋊Q8—112no—
316C2×C4⋊Q8—112no—
317C2×C4⋊Q8—118no—
318C2×C4⋊Q8—111no—
319C2×C4⋊Q8—221no—
320C2×C4⋊Q8—221no—
321C2×C4⋊Q8—224no—
322C2×#127—111no—
323C2×#124—111no—
324C2×#124—111no—
325C2×#121—221no—
326C2×#121—221no—
327C2×C4×D4—221no—
328C2×C4×D4—221no—
329C22×C4⋊C4—111no—
330C22×C4⋊C4—221no—
331C22×C4⋊C4C2×D1111yescharacteristic
332C22×C42—111no—
333#489—1116no—
334#489—1116no—
335#487—1116no—
336#486—1116no—
337#417—118no—
338#417—118no—
339#417—118no—
340#417C2×D1118yescomplemented
341C2×#103—112no—
342C2×#103—112no—
343C2×#103—112no—
344C2×#103C2×D1112yes—
345C2×#102—112no—
346C2×#102—112no—
347C2×#102—112no—
348C2×#102C2×D1112yes—
349C4×M16—118no—
350C2×#97—112no—
351C2×C4×C8—112no—
352C22×C11—28no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—84no—
359C22×C11C2×#12414yes—
360C22×C11C2×#12412yes—
361C22×C11C2×AGL(1,ℤ/8)12yes—
362C22×C11C2×#13712yes—
363C22×C11C23×D411yescharacteristic
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—84no—
368C4×C11—42no—
369C4×C11—44no—
370C4×C11C2×#12414yes—
371C4×C11C2×#12412yes—
372C4×C11C22×#4111yescharacteristic
373C4×C11C22×#4111yescharacteristic
374Dic11—22no—
375Dic11—22no—
376Dic11—42no—
377Dic11—44no—
378Dic11C2×AGL(1,ℤ/8)14yes—
379Dic11C2×#13714yes—
380C2×#41—22no—
381C2×#41—24no—
382C2×#41—24no—
383C2×#41—114no—
384C2×#41—222no—
385C2×#41—224no—
386C2×#41—224no—
387C2×#41C22×D1114yes—
388C22×Q8—111no—
389C22×Q8—228no—
390C22×Q8—222no—
391C22×Q8—222no—
392C22×Q8—448no—
393C22×Q8C22×D1111yescharacteristic
394C22×D4—21no—
395C22×D4—111no—
396C22×D4—221no—
397C22×D4—221no—
398C22×D4—221no—
399C22×D4C22×D1111yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C23×C4—111no—
403C23×C4—111no—
404C23×C4—221no—
405C23×C4—221no—
406C23×C4C22×D1111yescharacteristic
407C2×M16—24no—
408C2×M16—114no—
409C2×M16—224no—
410C2×M16C22×D1114yes—
411C22×C8—112no—
412C22×C8C22×D1112yes—
413C4⋊Q8—118no—
414C4⋊Q8—118no—
415C4⋊Q8—114no—
416C4⋊Q8—228no—
417C4⋊Q8—228no—
418C4⋊Q8—224no—
419C4⋊Q8—224no—
420C4⋊Q8—222no—
421#127—114no—
422#127—222no—
423#124—114no—
424#124—114no—
425#124—222no—
426#124—222no—
427#121—228no—
428#121—228no—
429C4×D4—228no—
430C4×D4—228no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4—228no—
436C2×C4⋊C4—222no—
437C2×C4⋊C4—222no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4C22×D1112yes—
443C2×C4⋊C4C22×D1114yes—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—114no—
451C2×C42—111no—
452C2×C42—111no—
453C2×C42—114no—
454#103—118no—
455#103—118no—
456#103—118no—
457#103C22×D1118yes—
458#102—118no—
459#102—118no—
460#102—118no—
461#102C22×D1118yes—
462#97—118no—
463C4×C8—118no—
464C2×C11—24no—
465C2×C11—82no—
466C2×C11#314114yescomplemented
467C2×C11C22×#12411yescharacteristic
468C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
469C2×C11C22×#13711yescharacteristic
470D11—82no—
471C24—21no—
472C24—221no—
473C24D4×D1111yescharacteristic
474#41—28no—
475#41—28no—
476#41—48no—
477#41—228no—
478#41—228no—
479#41—448no—
480C2×Q8—21no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—112no—
484C2×Q8—228no—
485C2×Q8—228no—
486C2×Q8—221no—
487C2×Q8—222no—
488C2×Q8—222no—
489C2×Q8—448no—
490C2×Q8—4432no—
491C2×Q8—448no—
492C2×Q8C23×D1112yes—
493C2×D4—24no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—22no—
497C2×D4—44no—
498C2×D4—112no—
499C2×D4—224no—
500C2×D4—224no—
501C2×D4—224no—
502C2×D4—222no—
503C2×D4—221no—
504C2×D4—222no—
505C2×D4—444no—
506C2×D4—444no—
507C2×D4—444no—
508C2×D4C23×D1112yes—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—114no—
518C22×C4—114no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—224no—
522C22×C4—224no—
523C22×C4—224no—
524C22×C4—221no—
525C22×C4—222no—
526C22×C4—224no—
527C22×C4—444no—
528C22×C4—444no—
529C22×C4#433914yes—
530C22×C4D4×D1112yes—
531C22×C4D4×D1111yescharacteristic
532C22×C4#434114yes—
533C22×C4C23×D1112yes—
534C22×C4C23×D1111yescharacteristic
535M16—28no—
536M16—228no—
537C2×C8—24no—
538C2×C8—114no—
539C2×C8—224no—
540C2×C8C23×D1114yes—
541C4⋊C4—24no—
542C4⋊C4—22no—
543C4⋊C4—114no—
544C4⋊C4—228no—
545C4⋊C4—228no—
546C4⋊C4—224no—
547C4⋊C4—224no—
548C4⋊C4—224no—
549C4⋊C4—222no—
550C4⋊C4C23×D1114yes—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C22⋊C4—224no—
554C22⋊C4—224no—
555C42—114no—
556C42—114no—
557C42—112no—
558C42—112no—
559C42—112no—
560C42—112no—
561C11C2×#314111yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—22no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—222no—
569C23—442no—
570C23—442no—
571C23—442no—
572C23#6693814yes—
573C23C2×D4×D1112yes—
574C23C2×D4×D1111yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—42no—
578Q8—222no—
579Q8—222no—
580Q8—4416no—
581Q8—4416no—
582Q8—442no—
583D4—22no—
584D4—22no—
585D4—48no—
586D4—42no—
587D4—222no—
588D4—222no—
589D4—448no—
590D4—448no—
591D4—448no—
592D4—442no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—48no—
596C2×C4—42no—
597C2×C4—44no—
598C2×C4—48no—
599C2×C4—114no—
600C2×C4—114no—
601C2×C4—112no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—228no—
606C2×C4—228no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—448no—
612C2×C4—442no—
613C2×C4—444no—
614C2×C4—448no—
615C2×C4#6693814yes—
616C2×C4#6693818yes—
617C2×C4C2×#433912yes—
618C2×C4C2×#433914yes—
619C2×C4C2×D4×D1112yes—
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4C2×#434112yes—
622C2×C4C2×#434114yes—
623C2×C4C24×D1111yescharacteristic
624C8—24no—
625C8—224no—
626C22—22no—
627C22—22no—
628C22—28no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—84no—
633C22—442no—
634C22—442no—
635C22—442no—
636C22—884no—
637C22C2×#6693814yes—
638C22C2×#6693812yes—
639C22D11×AGL(1,ℤ/8)12yes—
640C22D11×#13712yes—
641C22C22×D4×D1111yescharacteristic
642C4—42no—
643C4—44no—
644C4—114no—
645C4—114no—
646C4—222no—
647C4—222no—
648C4—442no—
649C4—444no—
650C4C2×#6693814yes—
651C4C2×#6693812yes—
652C4C22×#433911yescharacteristic
653C4C22×#434111yescharacteristic
654C2—24no—
655C2—82no—
656C2—882no—
657C2#1307900714yesdirect product factor
658C2C22×#6693811yescharacteristic
659C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
660C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623363C2
hypercenterC2×#417D11
hypocenterC11C2×#3141
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C22×#66941C2semidirect
3. #13079007C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622378C2semidirect
6. C2×#10622405C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622746C2semidirect
9. C2×#10622845C2semidirect
10. C2×#10622579C2semidirect
11. C2×M16×Dic11C2semidirect
12. C2×C11×#417C2semidirect
37. C2×#66941C22semidirect
38. C11×#417C22semidirect
41. #10622845C22semidirect
44. #10622746C22semidirect
45. M16×Dic11C22semidirect
51. #10622579C22semidirect
53. #10622408C22semidirect
54. #10622405C22semidirect
55. #10622378C22semidirect
56. #10622373C22semidirect
242. C2×#417D11semidirect
340. #417C2×D11semidirect
466. C2×C11#3141semidirect
561. C11C2×#3141semidirect
657. C2#13079007direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233632
C22×#669412
#130790072
C2×#106224082
C2×#106223782
C2×#106224052
C2×#106223732
C2×#106227462
C2×#106228452
C2×#106225792
C2×M16×Dic112
C2×C11×#4172
C2×#314111