Finite Group Databasebeta

← C2×#13078162 #15620706

Subgroups — C2×#13078162 #15620706

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic, complemented
2C22×#67003C211yesmaximal, characteristic
3C2×#10623054C211yesmaximal, characteristic, complemented
4#13078162C2116yesmaximal, direct product factor
5C2×#10622667C212yesmaximal, complemented
6C2×#10622703C212yesmaximal, complemented
7C2×#10622670C212yesmaximal, complemented
8C2×#10622696C212yesmaximal, complemented
9C2×#10622612C211yesmaximal, characteristic, complemented
10C2×#10622845C211yesmaximal, characteristic, complemented
11C22×#66899C211yesmaximal, characteristic, complemented
12C2×C11×#536C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C11×#536—24no—
17C11×#536C2218yescomplemented
18C2×C11×C4⋊Q8C2212yes—
19C2×C11×#124C2212yes—
20C2×C11×#123—22no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×#117C2211yescharacteristic
24C2×#67003—28no—
25C2×#67003C2218yes—
26C22×#4326C2211yescharacteristic
27C22×#4326C2212yes—
28C2×#66995—28no—
29C2×#66995C2218yescomplemented
30C22×#4325C2211yescharacteristic
31C22×#4325C2212yes—
32C22×#4324C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×#4318C2211yescharacteristic
36C23×C11⋊C8C2211yescharacteristic
37#10623054—24no—
38#10623054C2218yescomplemented
39C2×#66945—21no—
40C2×C4⋊C4×D11—21no—
41C2×(C22⋊D11)⋊C4—22no—
42C2×C4×D44C2212yes—
43C2×C4×Dic22C2212yes—
44#10622845C2218yescomplemented
45C2×#66899C2212yes—
46C2×#66899C2212yes—
47C2×#66899C2212yes—
48C2×#66899C2218yescomplemented
49C2×#66896C2212yes—
50#10622703C22116yescomplemented
51#10622696C22116yescomplemented
52#10622670C22116yescomplemented
53#10622667C22116yescomplemented
54#10622612C2218yescomplemented
55C2×C4⋊(C11⋊C8)C2212yes—
56C2×C4⋊(C11⋊C8)C2212yes—
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×#4339D418yes—
78C2×#4339C2314yes—
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C22×C4×D11—22no—
82C22×Dic22C2311yescharacteristic
83C11×C4⋊Q8—24no—
84C11×C4⋊Q8C2318yes—
85C11×#124—24no—
86C11×#124C2318yes—
87C11×#123—216no—
88C11×C22⋊Q8—28no—
89C11×C22⋊Q8—28no—
90C11×#117D414yes—
91C11×#117C2314yes—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4D412yes—
99C2×C42×C11C2312yes—
100#67003—232no—
101C2×#4326—28no—
102C2×#4326—24no—
103C2×#4326C2318yes—
104C2×#4326C2314yes—
105#66995—232no—
106C2×#4325—28no—
107C2×#4325—24no—
108C2×#4325C2318yes—
109C2×#4325C2314yes—
110C2×#4324—24no—
111C2×#4324C2314yes—
112C2×#4323—24no—
113C2×#4323C2314yes—
114C2×(C2×D11)⋊C4—22no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2314yes—
119C2×Dic11⋊C4—22no—
120C2×C4×Dic11—22no—
121C2×#4318—24no—
122C2×#4318C2314yes—
123C22×C11⋊C8—24no—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2312yes—
127C22×C11⋊C8C2314yes—
128#66945—28no—
129C4⋊C4×D11—28no—
130(C22⋊D11)⋊C4—216no—
131C4×D44—24no—
132C4×D44C2318yes—
133C4×Dic22—24no—
134C4×Dic22C2318yes—
135#66899C2318yes—
136#66899C2318yes—
137#66899C2318yes—
138#66896C2318yes—
139C4⋊(C11⋊C8)C2318yes—
140C4⋊(C11⋊C8)C2318yes—
141C2×#3046—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C11×#41—28no—
146C11×#41—28no—
147C11×#41—48no—
148C2×Q8×C11—24no—
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—24no—
152C2×Q8×C11—22no—
153C2×Q8×C11—28no—
154C2×Q8×C11—24no—
155C2×Q8×C11—28no—
156C2×Q8×C11—22no—
157C2×Q8×C11—44no—
158C2×Q8×C11—48no—
159C2×Q8×C11C2414yes—
160C2×Q8×C11C2412yes—
161C2×D4×C11—24no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—22no—
165C2×D4×C11—44no—
166C2×D4×C11C2412yes—
167C22×C4×C11—22no—
168C22×C4×C11—21no—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—44no—
172C22×C4×C11—44no—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D414yes—
178C22×C4×C11#4114yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2412yes—
181C2×C22⋊D11—28no—
182C2×C22⋊D11—24no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—24no—
186C22×Dic11—82no—
187#4339—216no—
188#4339—28no—
189#4339C2×D4116yes—
190C2×D44—21no—
191C2×D44—22no—
192C2×D44C2×D414yes—
193C2×D44C2412yes—
194C2×C4×D11—28no—
195C2×C4×D11—24no—
196C2×C4×D11—28no—
197C2×C4×D11—84no—
198C2×Dic22—21no—
199C2×Dic22—22no—
200C2×Dic22C2×D414yes—
201C2×Dic22C2412yes—
202C11×C4⋊C4—28no—
203C11×C4⋊C4—28no—
204C11×C4⋊C4C2×D414yes—
205C11×C4⋊C4C2×D414yes—
206C11×C22⋊C4—28no—
207C11×C22⋊C4—28no—
208C11×C22⋊C4C2×D418yes—
209C42×C11C2×D414yes—
210C42×C11C2414yes—
211#4326—216no—
212#4326—28no—
213#4325—216no—
214#4325—28no—
215#4324—28no—
216#4323—28no—
217(C2×D11)⋊C4—28no—
218C4⋊Dic11—22no—
219C4⋊Dic11—24no—
220C4⋊Dic11C2414yes—
221Dic11⋊C4—28no—
222C4×Dic11—28no—
223#4318—28no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—28no—
227C2×C11⋊C8—24no—
228C2×C11⋊C8C2414yes—
229C2×C11⋊C8C2412yes—
230C2×C11⋊C8C2412yes—
231C22×#137—111no—
232C22×#135—111no—
233C2×#536D1111yescharacteristic, complemented
234C2×#520—111no—
235#3046—1116no—
236C2×#464—112no—
237C2×#462—112no—
238C2×#463—112no—
239C2×#461—112no—
240C2×#424—111no—
241C2×#417—111no—
242C22×#103—111no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11#12114yes—
250C23×C11C22×D412yes—
251C23×C11C22×D411yescharacteristic
252C22×D11—24no—
253C22×D11—22no—
254C22×D11—42no—
255C22×D11—42no—
256Q8×C11—24no—
257Q8×C11—22no—
258Q8×C11—24no—
259Q8×C11—22no—
260Q8×C11—48no—
261Q8×C11—44no—
262Q8×C11—42no—
263D4×C11—22no—
264D4×C11—22no—
265D4×C11—48no—
266D4×C11—42no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
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#12114yes—
276C2×C4×C11#12118yes—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D414yes—
279C2×C4×C11C22×D414yes—
280C2×C4×C11C22×D414yes—
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D412yes—
283C2×C4×C11C2×#4112yes—
284C2×C4×C11C2×#4114yes—
285C2×C4×C11C2511yescharacteristic
286C22⋊D11—216no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—44no—
291C2×Dic11—84no—
292D44—24no—
293D44—22no—
294D44C22×D414yes—
295C4×D11—216no—
296C4×D11—88no—
297Dic22—24no—
298Dic22—22no—
299Dic22C22×D414yes—
300C11⋊C8—22no—
301C11⋊C8—22no—
302C11⋊C8—24no—
303C22×#41—111no—
304C22×#41C2×D1111yescharacteristic
305C23×Q8C2×D1111yescharacteristic
306C2×#137—118no—
307C2×#137—228no—
308C2×#135—118no—
309C2×#135—228no—
310C22×Q16—111no—
311C22×Q16—112no—
312C22×SD16—111no—
313C22×SD16—112no—
314C22×SD16—111no—
315C22×D8—111no—
316C22×M16—111no—
317C23×C8—111no—
318#536—24no—
319#536C2×D1118yescomplemented
320C2×C4⋊Q8C2×D1112yes—
321C2×#124C2×D1112yes—
322C2×#123—22no—
323C2×C22⋊Q8—21no—
324C2×C22⋊Q8—21no—
325#520—118no—
326#520—224no—
327C2×C4×Q8—112no—
328C2×C4×D4—112no—
329C2×C4×D4—222no—
330C2×#117—221no—
331C2×#117C2×D1111yescharacteristic
332C22×C4⋊C4—111no—
333C22×C4⋊C4—221no—
334#464—1116no—
335#463—1116no—
336#462—1116no—
337#461—1116no—
338#424—118no—
339C2×C4⋊C8—112no—
340C2×C4⋊C8—112no—
341#417—118no—
342C2×#103—112no—
343C2×#103—112no—
344C2×#103—118no—
345C2×#103—112no—
346C2×#102—112no—
347C22×C11—28no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—84no—
354C22×C11C2×#12114yes—
355C22×C11C2×#12112yes—
356C22×C11#57712yes—
357C22×C11#57812yes—
358C22×C11C23×D411yescharacteristic
359C2×D11—24no—
360C2×D11—48no—
361C2×D11—42no—
362C2×D11—42no—
363C4×C11—24no—
364C4×C11—24no—
365C4×C11—42no—
366C4×C11—44no—
367C4×C11C2×#12114yes—
368C4×C11C2×#12112yes—
369C4×C11C23×D411yescharacteristic
370C4×C11C22×#4111yescharacteristic
371Dic11—24no—
372Dic11—44no—
373C2×#41—22no—
374C2×#41—24no—
375C2×#41—24no—
376C2×#41—118no—
377C2×#41—114no—
378C2×#41—224no—
379C2×#41—222no—
380C2×#41C22×D1114yes—
381C22×Q8—21no—
382C22×Q8—22no—
383C22×Q8—24no—
384C22×Q8—24no—
385C22×Q8—111no—
386C22×Q8C22×D1112yes—
387C22×Q8C22×D1111yescharacteristic
388C22×Q8C22×D1114yes—
389C22×D4—21no—
390C22×D4—111no—
391C22×D4—221no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—222no—
398C23×C4C22×D1111yescharacteristic
399#137—2232no—
400#135—2232no—
401C2×Q16—114no—
402C2×Q16—118no—
403C2×Q16—224no—
404C2×Q16—228no—
405C2×SD16—114no—
406C2×SD16—118no—
407C2×SD16—114no—
408C2×SD16—224no—
409C2×SD16—224no—
410C2×SD16—228no—
411C2×D8—114no—
412C2×D8—224no—
413C2×M16—114no—
414C2×M16—224no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8—114no—
418C22×C8—112no—
419C22×C8—224no—
420C4⋊Q8—24no—
421C4⋊Q8C22×D1118yes—
422#124—24no—
423#124C22×D1118yes—
424#123—216no—
425C22⋊Q8—28no—
426C22⋊Q8—28no—
427C4×Q8—118no—
428C4×Q8—224no—
429C4×D4—118no—
430C4×D4—2216no—
431C4×D4—224no—
432#117—228no—
433#117C22⋊D1114yes—
434#117C22×D1114yes—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—228no—
443C2×C4⋊C4C22⋊D1111yescharacteristic
444C2×C4⋊C4C22⋊D1111yescharacteristic
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—222no—
448C2×C22⋊C4C22⋊D1112yes—
449C2×C42—222no—
450C2×C42C22×D1112yes—
451C4⋊C8—118no—
452C4⋊C8—118no—
453#103—118no—
454#103—118no—
455#103—118no—
456#102—118no—
457C2×C11—24no—
458C2×C11—82no—
459C2×C11#304614yescomplemented
460C2×C11C22×#12111yescharacteristic
461C2×C11C2×#57711yescharacteristic
462C2×C11C2×#57811yescharacteristic
463D11—44no—
464C24—21no—
465C24—221no—
466C24C2×C22⋊D1111yescharacteristic
467#41—28no—
468#41—28no—
469#41—48no—
470#41—1116no—
471#41—2216no—
472#41—228no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—21no—
476C2×Q8—24no—
477C2×Q8—22no—
478C2×Q8—28no—
479C2×Q8—24no—
480C2×Q8—28no—
481C2×Q8—22no—
482C2×Q8—44no—
483C2×Q8—48no—
484C2×Q8—114no—
485C2×Q8—112no—
486C2×Q8—222no—
487C2×Q8—221no—
488C2×Q8C23×D1114yes—
489C2×Q8C23×D1112yes—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—44no—
495C2×D4—114no—
496C2×D4—112no—
497C2×D4—228no—
498C2×D4—224no—
499C2×D4—222no—
500C2×D4—221no—
501C2×D4C23×D1112yes—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—221no—
509C22×C4—228no—
510C22×C4—224no—
511C22×C4—222no—
512C22×C4—224no—
513C22×C4—228no—
514C22×C4—884no—
515C22×C4—882no—
516C22×C4D4×D1114yes—
517C22×C4#434114yes—
518C22×C4C2×C22⋊D1112yes—
519C22×C4C2×C22⋊D1112yes—
520C22×C4C2×C22⋊D1112yes—
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C23×D1112yes—
523C22×C4C23×D1111yescharacteristic
524Q16—228no—
525Q16—2216no—
526SD16—228no—
527SD16—228no—
528SD16—2216no—
529D8—228no—
530M16—228no—
531C2×C8—114no—
532C2×C8—112no—
533C2×C8—112no—
534C2×C8—222no—
535C2×C8—222no—
536C2×C8—228no—
537C2×C8—224no—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—114no—
541C4⋊C4—224no—
542C4⋊C4—222no—
543C4⋊C4—228no—
544C4⋊C4C2×C22⋊D1114yes—
545C4⋊C4C2×C22⋊D1114yes—
546C22⋊C4—28no—
547C22⋊C4—28no—
548C22⋊C4—228no—
549C22⋊C4C2×C22⋊D1118yes—
550C42—228no—
551C42C2×C22⋊D1114yes—
552C42C23×D1114yes—
553C11C2×#304611yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—22no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—224no—
561C23—222no—
562C23—442no—
563C23—442no—
564C23#6699114yes—
565C23C22×C22⋊D1112yes—
566C23C22×C22⋊D1111yescharacteristic
567Q8—24no—
568Q8—22no—
569Q8—24no—
570Q8—22no—
571Q8—48no—
572Q8—44no—
573Q8—42no—
574Q8—114no—
575Q8—224no—
576Q8—222no—
577D4—22no—
578D4—22no—
579D4—48no—
580D4—42no—
581D4—114no—
582D4—2216no—
583D4—224no—
584D4—222no—
585C2×C4—24no—
586C2×C4—24no—
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—2216no—
596C2×C4—224no—
597C2×C4—444no—
598C2×C4—888no—
599C2×C4—884no—
600C2×C4#6699114yes—
601C2×C4#6699118yes—
602C2×C4C2×D4×D1112yes—
603C2×C4C2×D4×D1114yes—
604C2×C4C2×#434112yes—
605C2×C4C2×#434114yes—
606C2×C4C22×C22⋊D1114yes—
607C2×C4C22×C22⋊D1114yes—
608C2×C4C22×C22⋊D1111yescharacteristic
609C2×C4C22×C22⋊D1112yes—
610C2×C4C24×D1111yescharacteristic
611C8—222no—
612C8—222no—
613C8—224no—
614C22—28no—
615C22—22no—
616C22—22no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—84no—
621C22—224no—
622C22—448no—
623C22—442no—
624C22—442no—
625C22C2×#6699114yes—
626C22C2×#6699112yes—
627C22#1062336812yes—
628C22#1062336912yes—
629C22C23×C22⋊D1111yescharacteristic
630C4—24no—
631C4—24no—
632C4—42no—
633C4—44no—
634C4—224no—
635C4—444no—
636C4C2×#6699114yes—
637C4C2×#6699112yes—
638C4C22×D4×D1111yescharacteristic
639C4C22×#434111yescharacteristic
640C2—24no—
641C2—82no—
642C2—444no—
643C2#1307816214yesdirect product factor
644C2C22×#6699111yescharacteristic
645C2C2×#1062336811yescharacteristic
646C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×#67003C2
hypercenterC2×#536D11
hypocenterC11C2×#3046
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
3. C2×#10623054C2semidirect
4. #13078162C2direct (N × H)
5. C2×#10622667C2semidirect
6. C2×#10622703C2semidirect
7. C2×#10622670C2semidirect
8. C2×#10622696C2semidirect
9. C2×#10622612C2semidirect
10. C2×#10622845C2semidirect
11. C22×#66899C2semidirect
12. C2×C11×#536C2semidirect
17. C11×#536C22semidirect
29. C2×#66995C22semidirect
38. #10623054C22semidirect
44. #10622845C22semidirect
48. C2×#66899C22semidirect
50. #10622703C22semidirect
51. #10622696C22semidirect
52. #10622670C22semidirect
53. #10622667C22semidirect
54. #10622612C22semidirect
233. C2×#536D11semidirect
319. #536C2×D11semidirect
459. C2×C11#3046semidirect
553. C11C2×#3046semidirect
643. C2#13078162direct (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×#670032
C2×#106230542
#130781622
C2×#106226672
C2×#106227032
C2×#106226702
C2×#106226962
C2×#106226122
C2×#106228452
C22×#668992
C2×C11×#5362
C2×#304611