Finite Group Databasebeta

← C2×#13078164 #15620708

Subgroups — C2×#13078164 #15620708

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×#67004C211yesmaximal, characteristic, complemented
2C2×#10623356C211yesmaximal, characteristic, complemented
3C2×#10623358C211yesmaximal, characteristic, complemented
4#13078164C2116yesmaximal, direct product factor
5C2×#10622779C212yesmaximal, complemented
6C2×#10622795C212yesmaximal, complemented
7C2×#10622766C212yesmaximal, complemented
8C2×#10622775C212yesmaximal, complemented
9C2×#10622715C211yesmaximal, characteristic, complemented
10C2×#10622845C211yesmaximal, characteristic, complemented
11C22×#66880C211yesmaximal, characteristic, complemented
12C22×C11×#135C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C22×C11×#41C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C2×C11×#135—28no—
17C2×C11×#135C2218yes—
18C22×C11×Q16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic
23#10623358—24no—
24#10623358C2218yescomplemented
25#10623356—24no—
26#10623356C2218yescomplemented
27C2×#67004—28no—
28C2×#67004C2218yescomplemented
29C2×Q8×Dic11C2212yes—
30C2×#66997C2212yes—
31C22×#4326C2212yes—
32C2×#66989C2212yes—
33C2×#66988—22no—
34C2×D4×Dic11—22no—
35C2×D4×Dic11C2212yes—
36C22×#4324C2212yes—
37C2×#66979—21no—
38C2×#66979C2211yescharacteristic
39C22×C4⋊Dic11—21no—
40C22×C4⋊Dic11C2211yescharacteristic
41C2×#66977—21no—
42C2×#66977—21no—
43C22×#4318C2211yescharacteristic
44#10622845C2218yescomplemented
45C2×#66899C2212yes—
46C2×#66896C2212yes—
47#10622795C22116yescomplemented
48#10622779C22116yescomplemented
49#10622775C22116yescomplemented
50#10622766C22116yescomplemented
51C2×#66880C2212yes—
52C2×#66880C2212yes—
53C2×#66880C2218yescomplemented
54#10622715C2218yescomplemented
55C2×Dic11⋊C8C2212yes—
56C2×Dic11⋊C8C2212yes—
57C2×C11×#41—22no—
58C2×C11×#41—22no—
59C2×C11×#41—24no—
60C2×C11×#41—24no—
61C2×C11×#41—24no—
62C2×C11×#41D418yes—
63C2×C11×#41C2314yes—
64C2×C11×#41C2314yes—
65C22×Q8×C11C2311yescharacteristic
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C23×Dic11—21no—
75C23×Dic11—21no—
76C23×Dic11—22no—
77C22×Dic22—24no—
78C22×Dic22—24no—
79C22×Dic22—21no—
80C22×Dic22—22no—
81C22×Dic22C2312yes—
82C22×Dic22C2314yes—
83C11×#135—232no—
84C2×C11×Q16—24no—
85C2×C11×Q16C2314yes—
86C2×C11×SD16—24no—
87C2×C11×SD16—24no—
88C2×C11×SD16C2314yes—
89C2×C11×SD16C2314yes—
90C2×C11×D8—24no—
91C2×C11×D8C2314yes—
92C22×C8×C11—24no—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2314yes—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11D412yes—
100#67004—232no—
101Q8×Dic11—24no—
102Q8×Dic11C2318yes—
103#66997—24no—
104#66997C2318yes—
105C2×#4326—28no—
106C2×#4326C2318yes—
107#66989—24no—
108#66989C2318yes—
109#66988—216no—
110D4×Dic11—216no—
111D4×Dic11—24no—
112D4×Dic11C2318yes—
113C2×#4324—28no—
114C2×#4324C2318yes—
115#66979—28no—
116#66979D414yes—
117#66979C2314yes—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—28no—
122C2×C4⋊Dic11D411yescharacteristic
123C2×C4⋊Dic11D411yescharacteristic
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2314yes—
126#66977—28no—
127#66977—28no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11C2312yes—
132C2×#4318—24no—
133C2×#4318C2314yes—
134C22×C11⋊C8C2312yes—
135#66899C2318yes—
136#66896C2318yes—
137#66880C2318yes—
138#66880C2318yes—
139Dic11⋊C8C2318yes—
140Dic11⋊C8C2318yes—
141C2×#3046—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11—21no—
144C24×C11C2×D411yescharacteristic
145C11×#41—216no—
146C11×#41—28no—
147C11×#41—28no—
148C11×#41—28no—
149C11×#41—48no—
150C11×#41C2×D4116yes—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—22no—
154C2×Q8×C11—22no—
155C2×Q8×C11—22no—
156C2×Q8×C11C2×D414yes—
157C2×Q8×C11C2412yes—
158C2×Q8×C11C2412yes—
159C2×D4×C11—28no—
160C2×D4×C11—24no—
161C2×D4×C11—24no—
162C2×D4×C11—21no—
163C2×D4×C11—22no—
164C2×D4×C11—21no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—44no—
168C2×D4×C11C2×D414yes—
169C2×D4×C11C2412yes—
170C2×D4×C11C2412yes—
171C22×C4×C11—21no—
172C22×C4×C11—28no—
173C22×C4×C11—24no—
174C22×C4×C11—21no—
175C22×C4×C11—24no—
176C22×C4×C11—44no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D414yes—
180C22×C4×C11#4114yes—
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2412yes—
183C22×Dic11—28no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—24no—
187C22×Dic11—24no—
188C22×Dic11—44no—
189C22×Dic11—82no—
190C22×Dic11—84no—
191C22×Dic11C2×D412yes—
192C22×Dic11C2×D412yes—
193C2×Dic22—24no—
194C2×Dic22—28no—
195C2×Dic22—24no—
196C2×Dic22—22no—
197C2×Dic22—24no—
198C2×Dic22—28no—
199C2×Dic22—44no—
200C2×Dic22—48no—
201C2×Dic22C2414yes—
202C11×Q16—28no—
203C11×SD16—28no—
204C11×SD16—28no—
205C11×D8—28no—
206C2×C8×C11—22no—
207C2×C8×C11—22no—
208C2×C8×C11—28no—
209C2×C8×C11C2412yes—
210C2×C8×C11C2412yes—
211C22⋊Dic11—28no—
212C22⋊Dic11—28no—
213C22⋊Dic11—28no—
214C22⋊Dic11C2×D418yes—
215#4326—216no—
216#4324—216no—
217C4⋊Dic11—28no—
218C4⋊Dic11—24no—
219C4⋊Dic11—22no—
220C4⋊Dic11C2×D414yes—
221C4⋊Dic11C2×D414yes—
222C4⋊Dic11C2414yes—
223Dic11⋊C4—28no—
224Dic11⋊C4—28no—
225C4×Dic11—28no—
226C4×Dic11C2×D414yes—
227C4×Dic11C2414yes—
228#4318—28no—
229C2×C11⋊C8—24no—
230C2×C11⋊C8C2414yes—
231C22×#137—111no—
232C22×#135D1111yescharacteristic
233C2×#536—111no—
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—24no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11#12114yes—
254C23×C11C22×D412yes—
255C23×C11C22×D411yescharacteristic
256Q8×C11—24no—
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11—22no—
260Q8×C11—42no—
261Q8×C11C22×D414yes—
262D4×C11—216no—
263D4×C11—24no—
264D4×C11—22no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—48no—
268D4×C11—42no—
269D4×C11C22×D414yes—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—216no—
273C2×C4×C11—22no—
274C2×C4×C11—42no—
275C2×C4×C11—48no—
276C2×C4×C11#12114yes—
277C2×C4×C11#12118yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D412yes—
280C2×C4×C11C22×D412yes—
281C2×C4×C11C22×D414yes—
282C2×C4×C11C2×#4112yes—
283C2×C4×C11C2×#4114yes—
284C2×C4×C11C2511yescharacteristic
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—48no—
290C2×Dic11—44no—
291C2×Dic11—44no—
292C2×Dic11—88no—
293C2×Dic11—84no—
294C2×Dic11C22×D414yes—
295C2×Dic11C22×D414yes—
296Dic22—24no—
297Dic22—24no—
298Dic22—48no—
299Dic22—44no—
300C8×C11—22no—
301C8×C11—22no—
302C11⋊C8—24no—
303C22×#41C2×D1111yescharacteristic
304C22×#41C2×D1111yescharacteristic
305C23×Q8—111no—
306C2×#137—118no—
307C2×#137—228no—
308C2×#135—28no—
309C2×#135C2×D1118yes—
310C22×Q16—112no—
311C22×Q16C2×D1111yescharacteristic
312C22×SD16—112no—
313C22×SD16C2×D1111yescharacteristic
314C22×SD16C2×D1111yescharacteristic
315C22×D8C2×D1111yescharacteristic
316C22×M16—111no—
317C23×C8C2×D1111yescharacteristic
318#536—118no—
319#536—224no—
320C2×C4⋊Q8—112no—
321C2×#124—112no—
322C2×#123—222no—
323C2×C22⋊Q8—221no—
324C2×C22⋊Q8—221no—
325#520—118no—
326#520—224no—
327C2×C4×Q8—112no—
328C2×C4×D4—112no—
329C2×C4×D4—222no—
330C2×#117—111no—
331C2×#117—221no—
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—112no—
345C2×#103—118no—
346C2×#102—112no—
347C22×C11—28no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—24no—
351C22×C11—48no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—84no—
358C22×C11C2×#12114yes—
359C22×C11C2×#12112yes—
360C22×C11#57712yes—
361C22×C11#57812yes—
362C22×C11C23×D411yescharacteristic
363C4×C11—24no—
364C4×C11—42no—
365C4×C11C2×#12114yes—
366C4×C11C2×#12112yes—
367C4×C11C23×D411yescharacteristic
368C4×C11C22×#4111yescharacteristic
369Dic11—24no—
370Dic11—24no—
371Dic11—44no—
372Dic11—44no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—24no—
376C2×#41—24no—
377C2×#41—24no—
378C2×#41C22⋊D1118yes—
379C2×#41C22×D1114yes—
380C2×#41C22×D1114yes—
381C22×Q8—112no—
382C22×Q8—114no—
383C22×Q8—221no—
384C22×Q8—222no—
385C22×Q8—224no—
386C22×Q8—224no—
387C22×Q8C22×D1111yescharacteristic
388C22×Q8C22×D1111yescharacteristic
389C22×D4—21no—
390C22×D4—21no—
391C22×D4C22×D1111yescharacteristic
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—222no—
396C23×C4—221no—
397C23×C4—221no—
398C23×C4C22×D1111yescharacteristic
399#137—2232no—
400#135—232no—
401C2×Q16—24no—
402C2×Q16—118no—
403C2×Q16—228no—
404C2×Q16C22×D1114yes—
405C2×SD16—24no—
406C2×SD16—24no—
407C2×SD16—118no—
408C2×SD16—228no—
409C2×SD16C22×D1114yes—
410C2×SD16C22×D1114yes—
411C2×D8—24no—
412C2×D8C22×D1114yes—
413C2×M16—114no—
414C2×M16—224no—
415C22×C8—24no—
416C22×C8—112no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C22×C8C22×D1114yes—
420C4⋊Q8—118no—
421C4⋊Q8—224no—
422#124—118no—
423#124—224no—
424#123—2216no—
425C22⋊Q8—228no—
426C22⋊Q8—228no—
427C4×Q8—118no—
428C4×Q8—224no—
429C4×D4—118no—
430C4×D4—224no—
431C4×D4—2216no—
432#117—114no—
433#117—114no—
434#117—228no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—228no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—222no—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—222no—
447C2×C22⋊C4—222no—
448C2×C22⋊C4—222no—
449C2×C42—112no—
450C2×C42—222no—
451C4⋊C8—118no—
452C4⋊C8—118no—
453#103—118no—
454#103—118no—
455#103—118no—
456#102—118no—
457C2×C11—24no—
458C2×C11—44no—
459C2×C11—82no—
460C2×C11#304614yescomplemented
461C2×C11C22×#12111yescharacteristic
462C2×C11C2×#57711yescharacteristic
463C2×C11C2×#57811yescharacteristic
464C24—21no—
465C24—21no—
466C24D4×D1111yescharacteristic
467#41—216no—
468#41—28no—
469#41—28no—
470#41—28no—
471#41—48no—
472#41C2×C22⋊D11116yes—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—114no—
479C2×Q8—224no—
480C2×Q8—222no—
481C2×Q8—224no—
482C2×Q8—228no—
483C2×Q8—224no—
484C2×Q8—228no—
485C2×Q8—444no—
486C2×Q8—448no—
487C2×Q8C2×C22⋊D1114yes—
488C2×Q8C23×D1112yes—
489C2×Q8C23×D1112yes—
490C2×D4—28no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—44no—
499C2×D4C2×C22⋊D1114yes—
500C2×D4C23×D1112yes—
501C2×D4C23×D1112yes—
502C22×C4—21no—
503C22×C4—28no—
504C22×C4—24no—
505C22×C4—21no—
506C22×C4—24no—
507C22×C4—44no—
508C22×C4—112no—
509C22×C4—112no—
510C22×C4—228no—
511C22×C4—224no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—224no—
515C22×C4—444no—
516C22×C4—884no—
517C22×C4—882no—
518C22×C4D4×D1112yes—
519C22×C4D4×D1111yescharacteristic
520C22×C4#434114yes—
521C22×C4C2×C22⋊D1114yes—
522C22×C4C23×D1112yes—
523C22×C4C23×D1111yescharacteristic
524Q16—28no—
525Q16—2216no—
526SD16—28no—
527SD16—28no—
528SD16—2216no—
529D8—28no—
530M16—228no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—28no—
534C2×C8—114no—
535C2×C8—224no—
536C2×C8C23×D1112yes—
537C2×C8C23×D1112yes—
538C4⋊C4—114no—
539C4⋊C4—114no—
540C4⋊C4—114no—
541C4⋊C4—228no—
542C4⋊C4—228no—
543C4⋊C4—228no—
544C4⋊C4—224no—
545C4⋊C4—222no—
546C22⋊C4—118no—
547C22⋊C4—228no—
548C22⋊C4—228no—
549C22⋊C4—228no—
550C42—114no—
551C42—114no—
552C42—228no—
553C11C2×#304611yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—24no—
557C23—22no—
558C23—22no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23#6699214yes—
565C23C2×D4×D1112yes—
566C23C2×D4×D1111yescharacteristic
567Q8—24no—
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—42no—
572Q8—224no—
573Q8—224no—
574Q8—448no—
575Q8—444no—
576Q8C22×C22⋊D1114yes—
577D4—216no—
578D4—24no—
579D4—22no—
580D4—22no—
581D4—22no—
582D4—48no—
583D4—42no—
584D4C22×C22⋊D1114yes—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—216no—
588C2×C4—22no—
589C2×C4—42no—
590C2×C4—48no—
591C2×C4—114no—
592C2×C4—114no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—444no—
598C2×C4—448no—
599C2×C4—444no—
600C2×C4—888no—
601C2×C4—884no—
602C2×C4#6699214yes—
603C2×C4#6699218yes—
604C2×C4C2×D4×D1111yescharacteristic
605C2×C4C2×D4×D1112yes—
606C2×C4C2×#434112yes—
607C2×C4C2×#434114yes—
608C2×C4C22×C22⋊D1112yes—
609C2×C4C22×C22⋊D1114yes—
610C2×C4C24×D1111yescharacteristic
611C8—22no—
612C8—22no—
613C8—224no—
614C22—28no—
615C22—22no—
616C22—22no—
617C22—24no—
618C22—48no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—84no—
625C22#1062330112yes—
626C22#1062330212yes—
627C22C2×#6699214yes—
628C22C2×#6699212yes—
629C22C22×D4×D1111yescharacteristic
630C4—24no—
631C4—42no—
632C4—224no—
633C4—224no—
634C4—444no—
635C4—444no—
636C4C2×#6699214yes—
637C4C2×#6699212yes—
638C4C22×#434111yescharacteristic
639C4C23×C22⋊D1111yescharacteristic
640C2—24no—
641C2—44no—
642C2—82no—
643C2#1307816414yesdirect product factor
644C2C22×#6699211yescharacteristic
645C2C2×#1062330111yescharacteristic
646C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC22×C11×#135C2
socleC23×C11C22×D4
hypercenterC22×#135D11
hypocenterC11C2×#3046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C2×#10623356C2semidirect
3. C2×#10623358C2semidirect
4. #13078164C2direct (N × H)
5. C2×#10622779C2semidirect
6. C2×#10622795C2semidirect
7. C2×#10622766C2semidirect
8. C2×#10622775C2semidirect
9. C2×#10622715C2semidirect
10. C2×#10622845C2semidirect
11. C22×#66880C2semidirect
24. #10623358C22semidirect
26. #10623356C22semidirect
28. C2×#67004C22semidirect
44. #10622845C22semidirect
47. #10622795C22semidirect
48. #10622779C22semidirect
49. #10622775C22semidirect
50. #10622766C22semidirect
53. C2×#66880C22semidirect
54. #10622715C22semidirect
460. C2×C11#3046semidirect
553. C11C2×#3046semidirect
643. C2#13078164direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106233562
C2×#106233582
#130781642
C2×#106227792
C2×#106227952
C2×#106227662
C2×#106227752
C2×#106227152
C2×#106228452
C22×#668802
C22×C11×#1352
C2×#304611