Finite Group Databasebeta

← C2×#13079107 #15623271

Subgroups — C2×#13079107 #15623271

Order 2816.

3150 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic, complemented
2C22×#67004C211yesmaximal, characteristic, complemented
3C22×#67003C211yesmaximal, characteristic
4C23×#4326C211yesmaximal, characteristic, complemented
5C2×#10623057C211yesmaximal, characteristic, complemented
6#13079107C2116yesmaximal, direct product factor
7C2×#10622673C212yesmaximal, complemented
8C2×#10622699C212yesmaximal, complemented
9C2×#10622672C212yesmaximal, complemented
10C2×#10622705C212yesmaximal, complemented
11C2×#10622610C211yesmaximal, characteristic, complemented
12C2×C11×#536C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C11×#536—24no—
18C11×#536C2218yescomplemented
19C2×C11×C4⋊Q8C2212yes—
20C2×C11×#124C2212yes—
21C2×C11×#123—22no—
22C2×C11×C22⋊Q8—22no—
23C2×C11×#117C2211yescharacteristic
24C2×#67004—28no—
25C2×#67004C2218yescomplemented
26C2×#67003—28no—
27C2×#67003C2218yes—
28C22×#4326—28no—
29C22×#4326C2212yes—
30C22×#4326C2212yes—
31C22×#4326C2212yes—
32C22×#4326C2212yes—
33C22×#4326C2211yescharacteristic
34C22×#4326C2218yescomplemented
35C2×#66995—28no—
36C2×#66995C2218yescomplemented
37C22×#4325C2211yescharacteristic
38C22×#4325C2212yes—
39C22×#4324C2211yescharacteristic
40C22×#4324C2212yes—
41C22×#4323C2211yescharacteristic
42C22×#4318C2211yescharacteristic
43C23×C11⋊C8C2211yescharacteristic
44#10623057—24no—
45#10623057C2218yescomplemented
46C2×#66950—22no—
47C2×#66939—22no—
48C2×#66928C2212yes—
49C2×#66922C2212yes—
50#10622705C22116yescomplemented
51#10622699C22116yescomplemented
52#10622673C22116yescomplemented
53#10622672C22116yescomplemented
54#10622610C2218yescomplemented
55C2×#66867C2212yes—
56C2×C4×C11⋊C8C2212yes—
57C2×C11×#41—22no—
58C2×C11×#41—24no—
59C2×C11×#41—24no—
60C2×C11×#41C2314yes—
61C22×Q8×C11—21no—
62C22×Q8×C11—22no—
63C22×Q8×C11—24no—
64C22×Q8×C11—24no—
65C22×Q8×C11C2312yes—
66C22×Q8×C11C2311yescharacteristic
67C22×Q8×C11C2314yes—
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—21no—
74C23×Dic11—21no—
75C2×#4339—22no—
76C2×#4339—24no—
77C2×#4339—24no—
78C2×#4339C2314yes—
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C22×Dic22—24no—
82C22×Dic22—24no—
83C22×Dic22—21no—
84C22×Dic22—22no—
85C22×Dic22C2311yescharacteristic
86C22×Dic22C2312yes—
87C22×Dic22C2314yes—
88C11×C4⋊Q8—24no—
89C11×C4⋊Q8C2318yes—
90C11×#124—24no—
91C11×#124C2318yes—
92C11×#123—216no—
93C11×C22⋊Q8—216no—
94C11×#117D414yes—
95C11×#117C2314yes—
96C2×C11×C4⋊C4—24no—
97C2×C11×C4⋊C4D412yes—
98C2×C11×C22⋊C4—24no—
99C2×C11×C22⋊C4D412yes—
100C2×C42×C11C2312yes—
101#67004—232no—
102#67003—232no—
103C2×#4326—28no—
104C2×#4326—28no—
105C2×#4326—28no—
106C2×#4326—232no—
107C2×#4326—24no—
108C2×#4326—28no—
109C2×#4326C2318yes—
110C2×#4326C2318yes—
111C2×#4326C2318yes—
112C2×#4326C2314yes—
113C2×#4326C2318yes—
114#66995—232no—
115C2×#4325—28no—
116C2×#4325—24no—
117C2×#4325C2318yes—
118C2×#4325C2314yes—
119C2×#4324—24no—
120C2×#4324—28no—
121C2×#4324C2314yes—
122C2×#4324C2318yes—
123C2×#4323—24no—
124C2×#4323C2314yes—
125C2×(C2×D11)⋊C4—24no—
126C2×C4⋊Dic11—24no—
127C2×#4318D418yes—
128C2×#4318C2314yes—
129C22×C11⋊C8D418yes—
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2312yes—
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2314yes—
134#66950—216no—
135#66939—216no—
136#66928—24no—
137#66928C2318yes—
138#66922—24no—
139#66922C2318yes—
140#66867C2318yes—
141C4×C11⋊C8C2318yes—
142C2×#3156—111nomaximal, Sylow
143C24×C11—21no—
144C24×C11C2×D411yescharacteristic
145C23×D11—21no—
146C11×#41—28no—
147C11×#41—28no—
148C11×#41—48no—
149C2×Q8×C11—24no—
150C2×Q8×C11—22no—
151C2×Q8×C11—21no—
152C2×Q8×C11—24no—
153C2×Q8×C11—22no—
154C2×Q8×C11—28no—
155C2×Q8×C11—24no—
156C2×Q8×C11—28no—
157C2×Q8×C11—22no—
158C2×Q8×C11—44no—
159C2×Q8×C11—48no—
160C2×Q8×C11C2414yes—
161C2×Q8×C11C2412yes—
162C2×D4×C11—24no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—44no—
167C2×D4×C11C2412yes—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—24no—
171C22×C4×C11—24no—
172C22×C4×C11—44no—
173C22×C4×C11—44no—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D414yes—
178C22×C4×C11C2×D414yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2412yes—
181C2×C22⋊D11—24no—
182C2×C22⋊D11—44no—
183C22×Dic11—24no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11—44no—
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—24no—
197C2×Dic22—22no—
198C2×Dic22—24no—
199C2×Dic22—28no—
200C2×Dic22—22no—
201C2×Dic22—28no—
202C2×Dic22—21no—
203C2×Dic22—22no—
204C2×Dic22—24no—
205C2×Dic22—44no—
206C2×Dic22—48no—
207C2×Dic22C2412yes—
208C2×Dic22C2414yes—
209C11×C4⋊C4—216no—
210C11×C4⋊C4C2×D418yes—
211C11×C22⋊C4—216no—
212C11×C22⋊C4C2×D418yes—
213C42×C11C2×D414yes—
214C42×C11C2414yes—
215#4326—216no—
216#4326—216no—
217#4326—216no—
218#4326—28no—
219#4326—216no—
220#4325—216no—
221#4325—28no—
222#4324—28no—
223#4324—216no—
224#4323—28no—
225(C2×D11)⋊C4—216no—
226C4⋊Dic11—216no—
227#4318C2×D4116yes—
228C2×C11⋊C8C2×D414yes—
229C2×C11⋊C8C2×D414yes—
230C2×C11⋊C8C2×D4116yes—
231C2×C11⋊C8C2×D418yes—
232C2×C11⋊C8C2412yes—
233C2×C11⋊C8C2414yes—
234C2×C11⋊C8C2412yes—
235C22×#137—111no—
236C22×#137—111no—
237C22×#135—111no—
238C23×Q16—111no—
239C2×#536—111no—
240C2×#536D1111yescharacteristic, complemented
241#3156—1116no—
242C2×#497—112no—
243C2×#497—112no—
244C2×#495—112no—
245C2×#494—112no—
246C2×#405—111no—
247C23×C11—24no—
248C23×C11—22no—
249C23×C11—42no—
250C23×C11—44no—
251C23×C11#12714yes—
252C23×C11C22×D412yes—
253C23×C11C22×D411yescharacteristic
254C22×D11—22no—
255C22×D11—42no—
256C22×D11—44no—
257Q8×C11—24no—
258Q8×C11—22no—
259Q8×C11—24no—
260Q8×C11—22no—
261Q8×C11—48no—
262Q8×C11—44no—
263Q8×C11—42no—
264D4×C11—22no—
265D4×C11—22no—
266D4×C11—48no—
267D4×C11—42no—
268C2×C4×C11—28no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—42no—
272C2×C4×C11—48no—
273C2×C4×C11—44no—
274C2×C4×C11—48no—
275C2×C4×C11#12714yes—
276C2×C4×C11#12718yes—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D412yes—
279C2×C4×C11C22×D414yes—
280C2×C4×C11C22×D414yes—
281C2×C4×C11C22×D418yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D412yes—
284C2×C4×C11C2511yescharacteristic
285C22⋊D11—48no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—48no—
289C2×Dic11—44no—
290C2×Dic11—42no—
291D44—22no—
292D44—22no—
293D44—42no—
294C4×D11—48no—
295Dic22—24no—
296Dic22—22no—
297Dic22—24no—
298Dic22—22no—
299Dic22—48no—
300Dic22—44no—
301Dic22—42no—
302C11⋊C8C22×D414yes—
303C11⋊C8C22×D414yes—
304C11⋊C8C22×D418yes—
305C22×#41—111no—
306C22×#41C2×D1111yescharacteristic
307C23×Q8—111no—
308C23×Q8C2×D1111yescharacteristic
309C2×#137—118no—
310C2×#137—118no—
311C2×#137—228no—
312C2×#137—228no—
313C2×#135—118no—
314C2×#135—228no—
315C22×Q16—111no—
316C22×Q16—112no—
317C22×Q16—112no—
318C22×Q16—112no—
319C22×Q16—112no—
320C22×Q16—118no—
321C22×Q16—228no—
322C22×SD16—112no—
323C22×SD16—111no—
324C22×SD16—112no—
325C22×SD16—111no—
326C22×D8—111no—
327C22×M16—111no—
328C23×C8—111no—
329#536—24no—
330#536—118no—
331#536—224no—
332#536C2×D1118yescomplemented
333C2×C4⋊Q8—112no—
334C2×C4⋊Q8C2×D1112yes—
335C2×#124—112no—
336C2×#124C2×D1112yes—
337C2×#123—22no—
338C2×#123—222no—
339C2×C22⋊Q8—22no—
340C2×C22⋊Q8—222no—
341C2×#117C2×D1111yescharacteristic
342#497—1116no—
343#497—1116no—
344#495—1116no—
345#494—1116no—
346#405—118no—
347C2×#97—112no—
348C2×C4×C8—112no—
349C22×C11—28no—
350C22×C11—24no—
351C22×C11—42no—
352C22×C11—44no—
353C22×C11—84no—
354C22×C11C2×#12714yes—
355C22×C11C2×#12712yes—
356C22×C11#57814yes—
357C22×C11C23×D411yescharacteristic
358C2×D11—42no—
359C2×D11—44no—
360C2×D11—84no—
361C4×C11—28no—
362C4×C11—42no—
363C4×C11—44no—
364C4×C11C2×#12714yes—
365C4×C11C2×#12712yes—
366C4×C11C23×D411yescharacteristic
367C4×C11C23×D411yescharacteristic
368Dic11—44no—
369Dic11—42no—
370C2×#41—22no—
371C2×#41—24no—
372C2×#41—24no—
373C2×#41—114no—
374C2×#41—222no—
375C2×#41—224no—
376C2×#41—224no—
377C2×#41C22×D1114yes—
378C22×Q8—21no—
379C22×Q8—22no—
380C22×Q8—24no—
381C22×Q8—24no—
382C22×Q8—112no—
383C22×Q8—111no—
384C22×Q8—114no—
385C22×Q8—221no—
386C22×Q8—222no—
387C22×Q8—224no—
388C22×Q8—224no—
389C22×Q8C22×D1112yes—
390C22×Q8C22×D1111yescharacteristic
391C22×Q8C22×D1114yes—
392C22×D4—21no—
393C22×D4—111no—
394C22×D4—221no—
395C22×D4C22×D1111yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—221no—
399C23×C4—221no—
400C23×C4C22×D1111yescharacteristic
401#137—2232no—
402#137—2232no—
403#135—2232no—
404C2×Q16—118no—
405C2×Q16—118no—
406C2×Q16—114no—
407C2×Q16—118no—
408C2×Q16—118no—
409C2×Q16—228no—
410C2×Q16—228no—
411C2×Q16—2232no—
412C2×Q16—224no—
413C2×Q16—228no—
414C2×Q16—228no—
415C2×SD16—114no—
416C2×SD16—118no—
417C2×SD16—114no—
418C2×SD16—118no—
419C2×SD16—224no—
420C2×SD16—228no—
421C2×SD16—224no—
422C2×SD16—228no—
423C2×D8—114no—
424C2×D8—224no—
425C2×M16—118no—
426C2×M16—114no—
427C22×C8—118no—
428C22×C8—111no—
429C22×C8—111no—
430C22×C8—114no—
431C22×C8—112no—
432C4⋊Q8—24no—
433C4⋊Q8—118no—
434C4⋊Q8—224no—
435C4⋊Q8C22×D1118yes—
436#124—24no—
437#124—118no—
438#124—224no—
439#124C22×D1118yes—
440#123—216no—
441#123—2216no—
442C22⋊Q8—216no—
443C22⋊Q8—2216no—
444#117C22⋊D1114yes—
445#117C22×D1114yes—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—224no—
448C2×C4⋊C4C22⋊D1112yes—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—224no—
451C2×C22⋊C4C22⋊D1112yes—
452C2×C42C22×D1112yes—
453#97—118no—
454C4×C8—118no—
455C2×C11—24no—
456C2×C11—82no—
457C2×C11#315614yescomplemented
458C2×C11C22×#12711yescharacteristic
459C2×C11C2×#57812yes—
460D11—82no—
461C24—21no—
462C24—221no—
463C24C2×C22⋊D1111yescharacteristic
464#41—28no—
465#41—28no—
466#41—48no—
467#41—228no—
468#41—228no—
469#41—448no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—21no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—28no—
477C2×Q8—22no—
478C2×Q8—28no—
479C2×Q8—44no—
480C2×Q8—48no—
481C2×Q8—114no—
482C2×Q8—112no—
483C2×Q8—224no—
484C2×Q8—222no—
485C2×Q8—221no—
486C2×Q8—224no—
487C2×Q8—222no—
488C2×Q8—224no—
489C2×Q8—228no—
490C2×Q8—222no—
491C2×Q8—228no—
492C2×Q8—444no—
493C2×Q8—448no—
494C2×Q8C23×D1114yes—
495C2×Q8C23×D1112yes—
496C2×D4—24no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—44no—
501C2×D4—112no—
502C2×D4—224no—
503C2×D4—222no—
504C2×D4—222no—
505C2×D4—221no—
506C2×D4—444no—
507C2×D4C23×D1112yes—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—224no—
515C22×C4—222no—
516C22×C4—221no—
517C22×C4—224no—
518C22×C4—444no—
519C22×C4—444no—
520C22×C4D4×D1114yes—
521C22×C4D4×D1114yes—
522C22×C4C2×C22⋊D1114yes—
523C22×C4C2×C22⋊D1112yes—
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C23×D1112yes—
526C22×C4C23×D1111yescharacteristic
527Q16—2216no—
528Q16—2216no—
529Q16—228no—
530Q16—2216no—
531Q16—2216no—
532SD16—228no—
533SD16—2216no—
534SD16—228no—
535SD16—2216no—
536D8—228no—
537M16—1116no—
538C2×C8—114no—
539C2×C8—114no—
540C2×C8—1116no—
541C2×C8—118no—
542C2×C8—112no—
543C2×C8—114no—
544C2×C8—112no—
545C4⋊C4—216no—
546C4⋊C4—2216no—
547C4⋊C4C2×C22⋊D1118yes—
548C22⋊C4—216no—
549C22⋊C4—2216no—
550C22⋊C4C2×C22⋊D1118yes—
551C42C2×C22⋊D1114yes—
552C42C23×D1114yes—
553C11C2×#315611yescharacteristic, complemented, Sylow
554C23—24no—
555C23—22no—
556C23—42no—
557C23—44no—
558C23—222no—
559C23—442no—
560C23—444no—
561C23#6699314yes—
562C23C22×C22⋊D1112yes—
563C23C22×C22⋊D1111yescharacteristic
564Q8—24no—
565Q8—22no—
566Q8—24no—
567Q8—22no—
568Q8—48no—
569Q8—44no—
570Q8—42no—
571Q8—224no—
572Q8—222no—
573Q8—224no—
574Q8—222no—
575Q8—448no—
576Q8—444no—
577Q8—442no—
578D4—22no—
579D4—22no—
580D4—48no—
581D4—42no—
582D4—222no—
583D4—222no—
584D4—448no—
585D4—442no—
586C2×C4—28no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—42no—
590C2×C4—48no—
591C2×C4—44no—
592C2×C4—48no—
593C2×C4—224no—
594C2×C4—222no—
595C2×C4—442no—
596C2×C4—448no—
597C2×C4—444no—
598C2×C4—448no—
599C2×C4#6699314yes—
600C2×C4#6699318yes—
601C2×C4C2×D4×D1112yes—
602C2×C4C2×D4×D1112yes—
603C2×C4C2×D4×D1114yes—
604C2×C4C2×D4×D1114yes—
605C2×C4C22×C22⋊D1118yes—
606C2×C4C22×C22⋊D1111yescharacteristic
607C2×C4C22×C22⋊D1112yes—
608C2×C4C24×D1111yescharacteristic
609C8—114no—
610C8—114no—
611C8—118no—
612C22—28no—
613C22—24no—
614C22—42no—
615C22—44no—
616C22—84no—
617C22—442no—
618C22—444no—
619C22—884no—
620C22C2×#6699314yes—
621C22C2×#6699312yes—
622C22#1062336914yes—
623C22C23×C22⋊D1111yescharacteristic
624C4—28no—
625C4—42no—
626C4—44no—
627C4—442no—
628C4—444no—
629C4C2×#6699314yes—
630C4C2×#6699312yes—
631C4C22×D4×D1111yescharacteristic
632C4C22×D4×D1111yescharacteristic
633C2—24no—
634C2—82no—
635C2—882no—
636C2#1307910714yesdirect product factor
637C2C22×#6699311yescharacteristic
638C2C2×#1062336912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×#67003C2
hypercenterC2×#536D11
hypocenterC11C2×#3156
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
2. C22×#67004C2semidirect
4. C23×#4326C2semidirect
5. C2×#10623057C2semidirect
6. #13079107C2direct (N × H)
7. C2×#10622673C2semidirect
8. C2×#10622699C2semidirect
9. C2×#10622672C2semidirect
10. C2×#10622705C2semidirect
11. C2×#10622610C2semidirect
12. C2×C11×#536C2semidirect
18. C11×#536C22semidirect
25. C2×#67004C22semidirect
34. C22×#4326C22semidirect
36. C2×#66995C22semidirect
45. #10623057C22semidirect
50. #10622705C22semidirect
51. #10622699C22semidirect
52. #10622673C22semidirect
53. #10622672C22semidirect
54. #10622610C22semidirect
240. C2×#536D11semidirect
332. #536C2×D11semidirect
457. C2×C11#3156semidirect
553. C11C2×#3156semidirect
636. C2#13079107direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669952
C22×#670042
C22×#670032
C23×#43262
C2×#106230572
#130791072
C2×#106226732
C2×#106226992
C2×#106226722
C2×#106227052
C2×#106226102
C2×C11×#5362
C2×#315611