Finite Group Databasebeta

← C2×#13079014 #15623068

Subgroups — C2×#13079014 #15623068

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C22×#66943C211yesmaximal, characteristic, complemented
3#13079014C2116yesmaximal, direct product factor
4C2×#10622410C212yesmaximal, complemented
5C2×#10622377C212yesmaximal, complemented
6C2×#10622413C212yesmaximal, complemented
7C2×#10622381C212yesmaximal, 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
15C22×C11×M16C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17#10623363—24no—
18#10623363C2218yes—
19C2×#67000C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C2×#66992—21no—
23C2×#66992—21no—
24C2×#66989C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C2×C4×C22⋊D11—21no—
27C22×C4⋊Dic11—21no—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4—21no—
30C22×C4×Dic11C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C2×#66943—24no—
33C2×#66943—21no—
34C2×#66943—21no—
35C2×#66943C2212yes—
36C2×#66943C2212yes—
37C2×#66943C2218yescomplemented
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#10622413C22116yescomplemented
54#10622410C22116yescomplemented
55#10622381C22116yescomplemented
56#10622377C22116yescomplemented
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×Dic22C2311yescharacteristic
80C2×C11×M16—24no—
81C2×C11×M16C2314yes—
82C22×C8×C11C2312yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89#67000—22no—
90#67000C2314yes—
91#66997—22no—
92#66997C2314yes—
93#66993—22no—
94#66993C2314yes—
95#66992—28no—
96#66992—28no—
97#66989—22no—
98#66989C2314yes—
99C4×C22⋊D11—28no—
100C4×C22⋊D11—28no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—28no—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2314yes—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—28no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×C4×Dic11D411yescharacteristic
116C2×C4×Dic11D411yescharacteristic
117C2×C4×Dic11D414yes—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2311yescharacteristic
121C2×#4318—24no—
122C2×#4318C2314yes—
123C22×C11⋊C8C2312yes—
124#66943—24no—
125#66943—24no—
126#66943—28no—
127#66943—28no—
128#66943C2318yes—
129#66943C2318yes—
130C11×#103C2318yes—
131C11×#102C2318yes—
132#66899C2318yes—
133#66896C2318yes—
134#66885C2318yes—
135#66880C2318yes—
136#66879C2318yes—
137C8×Dic11C2318yes—
138#66874C2318yes—
139#66873C2318yes—
140C2×#3142—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11C2×D411yescharacteristic
143C23×D11—21no—
144C11×#41—28no—
145C11×#41—28no—
146C11×#41—48no—
147C2×Q8×C11—21no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11C2412yes—
151C2×D4×C11—24no—
152C2×D4×C11—21no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—44no—
156C2×D4×C11C2412yes—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—44no—
162C22×C4×C11—44no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4114yes—
166C22×C4×C11#4114yes—
167C22×C4×C11C2411yescharacteristic
168C22×C4×C11C2412yes—
169C2×C22⋊D11—24no—
170C2×C22⋊D11—24no—
171C2×C22⋊D11—24no—
172C2×C22⋊D11—44no—
173C2×C22⋊D11—44no—
174C2×C22⋊D11—44no—
175C22×Dic11—24no—
176C22×Dic11—22no—
177C22×Dic11—21no—
178C22×Dic11—42no—
179C22×Dic11—42no—
180C22×Dic11—44no—
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D414yes—
186C22×Dic11C2×D414yes—
187#4339—28no—
188#4339—28no—
189#4339—48no—
190C2×D44—21no—
191C2×D44—22no—
192C2×D44—22no—
193C2×D44C2412yes—
194C2×C4×D11—24no—
195C2×C4×D11—44no—
196C2×Dic22—21no—
197C2×Dic22—22no—
198C2×Dic22—22no—
199C2×Dic22C2412yes—
200C11×M16—28no—
201C2×C8×C11—24no—
202C2×C8×C11C2414yes—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4C2414yes—
206C22⋊Dic11—24no—
207C22⋊Dic11—24no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210C4⋊Dic11—28no—
211C4⋊Dic11—28no—
212C4⋊Dic11—22no—
213C4⋊Dic11—24no—
214C4⋊Dic11C2414yes—
215Dic11⋊C4—28no—
216Dic11⋊C4—28no—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
219C4×Dic11C2×D414yes—
220C4×Dic11C2×D414yes—
221C4×Dic11C2×D412yes—
222C4×Dic11C2×D412yes—
223C4×Dic11C2412yes—
224C4×Dic11C2412yes—
225#4318—28no—
226C2×C11⋊C8—24no—
227C2×C11⋊C8C2414yes—
228C2×#532—111no—
229C22×#125—111no—
230#3142—1116no—
231C2×#491—112no—
232C2×#490—112no—
233C2×#488—112no—
234C2×#488—112no—
235C2×#417—111no—
236C2×#417—111no—
237C2×#417—111no—
238C2×#417D1111yescharacteristic, complemented
239C2×C4×M16—111no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11#12414yes—
247C23×C11C22×D412yes—
248C23×C11C22×D411yescharacteristic
249C22×D11—22no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—42no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—48no—
259D4×C11—42no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—48no—
263C2×C4×C11—42no—
264C2×C4×C11—44no—
265C2×C4×C11—48no—
266C2×C4×C11#12414yes—
267C2×C4×C11#12418yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D412yes—
270C2×C4×C11C2×#4112yes—
271C2×C4×C11C2×#4114yes—
272C2×C4×C11C2×#4112yes—
273C2×C4×C11C2×#4114yes—
274C2×C4×C11C2511yescharacteristic
275C22⋊D11—48no—
276C22⋊D11—48no—
277C22⋊D11—48no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—22no—
284C2×Dic11—44no—
285C2×Dic11—44no—
286C2×Dic11—48no—
287C2×Dic11—42no—
288C2×Dic11—44no—
289C2×Dic11C22×D412yes—
290C2×Dic11C22×D412yes—
291C2×Dic11C22×D412yes—
292C2×Dic11C22×D412yes—
293D44—22no—
294D44—22no—
295D44—42no—
296C4×D11—48no—
297Dic22—22no—
298Dic22—22no—
299Dic22—42no—
300C8×C11—24no—
301C11⋊C8—24no—
302C22×#41—111no—
303C22×#41C2×D1111yescharacteristic
304C22×M16—111no—
305C22×M16C2×D1111yescharacteristic
306#532—118no—
307#532—224no—
308C2×C4⋊Q8—111no—
309C2×#127—111no—
310C2×#125—112no—
311C2×#125—112no—
312C2×#125—118no—
313C2×#125—221no—
314C2×#125—221no—
315C2×#125—224no—
316C2×#124—111no—
317C2×#124—111no—
318C2×#121—221no—
319C2×#121—221no—
320C2×C4×D4—221no—
321C2×C4×D4—221no—
322C22×C4⋊C4—111no—
323C22×C4⋊C4—221no—
324C22×C4⋊C4—221no—
325C22×C4⋊C4C2×D1111yescharacteristic
326C22×C42—111no—
327#491—1116no—
328#490—1116no—
329#488—1116no—
330#488—1116no—
331#417—118no—
332#417—118no—
333#417—118no—
334#417C2×D1118yescomplemented
335C2×#103—112no—
336C2×#103—112no—
337C2×#103—112no—
338C2×#103C2×D1112yes—
339C2×#102—112no—
340C2×#102—112no—
341C2×#102—112no—
342C2×#102C2×D1112yes—
343C4×M16—118no—
344C2×#97—112no—
345C2×C4×C8—112no—
346C22×C11—28no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—84no—
353C22×C11C2×#12414yes—
354C22×C11C2×#12412yes—
355C22×C11#57512yes—
356C22×C11#57512yes—
357C22×C11C23×D411yescharacteristic
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—84no—
362C4×C11—42no—
363C4×C11—44no—
364C4×C11C2×#12414yes—
365C4×C11C2×#12412yes—
366C4×C11C22×#4111yescharacteristic
367C4×C11C22×#4111yescharacteristic
368Dic11—22no—
369Dic11—22no—
370Dic11—22no—
371Dic11—22no—
372Dic11—42no—
373Dic11—44no—
374C2×#41—22no—
375C2×#41—24no—
376C2×#41—24no—
377C2×#41—114no—
378C2×#41—222no—
379C2×#41—224no—
380C2×#41—224no—
381C2×#41C22×D1114yes—
382C22×Q8—111no—
383C22×Q8C22×D1111yescharacteristic
384C22×D4—21no—
385C22×D4—111no—
386C22×D4—221no—
387C22×D4—221no—
388C22×D4—221no—
389C22×D4C22×D1111yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—221no—
395C23×C4—221no—
396C23×C4C22×D1111yescharacteristic
397C2×M16—24no—
398C2×M16—114no—
399C2×M16—224no—
400C2×M16C22×D1114yes—
401C22×C8—112no—
402C22×C8C22×D1112yes—
403C4⋊Q8—114no—
404C4⋊Q8—222no—
405#127—114no—
406#127—222no—
407#125—118no—
408#125—118no—
409#125—228no—
410#125—228no—
411#125—224no—
412#125—224no—
413#124—114no—
414#124—114no—
415#124—222no—
416#124—222no—
417#121—228no—
418#121—228no—
419C4×D4—228no—
420C4×D4—228no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—114no—
425C2×C4⋊C4—228no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—228no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—222no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4C22×D1112yes—
436C2×C4⋊C4C22×D1114yes—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—114no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—114no—
447#103—118no—
448#103—118no—
449#103—118no—
450#103C22×D1118yes—
451#102—118no—
452#102—118no—
453#102—118no—
454#102C22×D1118yes—
455#97—118no—
456C4×C8—118no—
457C2×C11—24no—
458C2×C11—82no—
459C2×C11#314214yescomplemented
460C2×C11C22×#12411yescharacteristic
461C2×C11C2×#57511yescharacteristic
462C2×C11C2×#57511yescharacteristic
463D11—82no—
464C24—21no—
465C24—221no—
466C24D4×D1111yescharacteristic
467#41—28no—
468#41—28no—
469#41—48no—
470#41—228no—
471#41—228no—
472#41—448no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—112no—
477C2×Q8—221no—
478C2×Q8—222no—
479C2×Q8—222no—
480C2×Q8C23×D1112yes—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—22no—
485C2×D4—44no—
486C2×D4—112no—
487C2×D4—224no—
488C2×D4—224no—
489C2×D4—224no—
490C2×D4—222no—
491C2×D4—221no—
492C2×D4—222no—
493C2×D4—444no—
494C2×D4—444no—
495C2×D4—444no—
496C2×D4C23×D1112yes—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—114no—
508C22×C4—114no—
509C22×C4—224no—
510C22×C4—221no—
511C22×C4—222no—
512C22×C4—224no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—444no—
516C22×C4—444no—
517C22×C4#433914yes—
518C22×C4D4×D1112yes—
519C22×C4D4×D1111yescharacteristic
520C22×C4#434114yes—
521C22×C4C23×D1112yes—
522C22×C4C23×D1111yescharacteristic
523M16—28no—
524M16—228no—
525C2×C8—24no—
526C2×C8—114no—
527C2×C8—224no—
528C2×C8C23×D1114yes—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—114no—
532C4⋊C4—228no—
533C4⋊C4—228no—
534C4⋊C4—228no—
535C4⋊C4—228no—
536C4⋊C4—224no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—222no—
540C4⋊C4C23×D1114yes—
541C22⋊C4—224no—
542C22⋊C4—224no—
543C22⋊C4—224no—
544C22⋊C4—224no—
545C42—114no—
546C42—114no—
547C42—112no—
548C42—112no—
549C42—112no—
550C42—112no—
551C11C2×#314211yescharacteristic, complemented, Sylow
552C23—22no—
553C23—22no—
554C23—22no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—222no—
559C23—442no—
560C23—442no—
561C23—442no—
562C23#6693814yes—
563C23C2×D4×D1112yes—
564C23C2×D4×D1111yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—42no—
568Q8—222no—
569Q8—222no—
570Q8—442no—
571D4—22no—
572D4—22no—
573D4—48no—
574D4—42no—
575D4—222no—
576D4—222no—
577D4—448no—
578D4—448no—
579D4—448no—
580D4—442no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—48no—
584C2×C4—42no—
585C2×C4—44no—
586C2×C4—48no—
587C2×C4—112no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—444no—
598C2×C4—444no—
599C2×C4—448no—
600C2×C4—442no—
601C2×C4—444no—
602C2×C4—448no—
603C2×C4#6693814yes—
604C2×C4#6693818yes—
605C2×C4C2×#433912yes—
606C2×C4C2×#433914yes—
607C2×C4C2×D4×D1112yes—
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4C2×#434112yes—
610C2×C4C2×#434114yes—
611C2×C4C24×D1111yescharacteristic
612C8—24no—
613C8—224no—
614C22—22no—
615C22—22no—
616C22—28no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—84no—
621C22—442no—
622C22—442no—
623C22—442no—
624C22—884no—
625C22C2×#6693814yes—
626C22C2×#6693812yes—
627C22#1062330412yes—
628C22#1062330812yes—
629C22C22×D4×D1111yescharacteristic
630C4—42no—
631C4—44no—
632C4—222no—
633C4—222no—
634C4—222no—
635C4—222no—
636C4—442no—
637C4—444no—
638C4C2×#6693814yes—
639C4C2×#6693812yes—
640C4C22×#433911yescharacteristic
641C4C22×#434111yescharacteristic
642C2—24no—
643C2—82no—
644C2—882no—
645C2#1307901414yesdirect product factor
646C2C22×#6693811yescharacteristic
647C2C2×#1062330411yescharacteristic
648C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623363C2
hypercenterC2×#417D11
hypocenterC11C2×#3142
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×#66943C2semidirect
3. #13079014C2direct (N × H)
4. C2×#10622410C2semidirect
5. C2×#10622377C2semidirect
6. C2×#10622413C2semidirect
7. C2×#10622381C2semidirect
8. C2×#10622746C2semidirect
9. C2×#10622845C2semidirect
10. C2×#10622579C2semidirect
11. C2×M16×Dic11C2semidirect
12. C2×C11×#417C2semidirect
37. C2×#66943C22semidirect
38. C11×#417C22semidirect
41. #10622845C22semidirect
44. #10622746C22semidirect
45. M16×Dic11C22semidirect
51. #10622579C22semidirect
53. #10622413C22semidirect
54. #10622410C22semidirect
55. #10622381C22semidirect
56. #10622377C22semidirect
238. C2×#417D11semidirect
334. #417C2×D11semidirect
459. C2×C11#3142semidirect
551. C11C2×#3142semidirect
645. C2#13079014direct (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×#669432
#130790142
C2×#106224102
C2×#106223772
C2×#106224132
C2×#106223812
C2×#106227462
C2×#106228452
C2×#106225792
C2×M16×Dic112
C2×C11×#4172
C2×#314211