Finite Group Databasebeta

← C2×#13071440 #14912950

Subgroups — C2×#13071440 #14912950

Order 2816.

6150 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C212yesmaximal, complemented
3#13071440C2116yesmaximal, direct product factor
4C2×#10622259C212yesmaximal, complemented
5C2×#10622278C212yesmaximal, complemented
6C2×#10622571C212yesmaximal, complemented
7C2×#10622277C211yesmaximal, characteristic, complemented
8C2×#10622280C211yesmaximal, characteristic, complemented
9C2×#10622279C211yesmaximal, characteristic, complemented
10C22×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#381C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C24×Dic11C2212yes—
17C22×#4339—216no—
18C22×#4339C4116yescomplemented
19C22×#4339C2218yes—
20C23×D44C2211yescharacteristic
21C23×C4×D11C2212yes—
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×Dic22C2211yescharacteristic
25C22×C11×C22⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2212yes—
31C2×(C22⋊D11)⋊C4—216no—
32C2×(C22⋊D11)⋊C4C22116yescomplemented
33C11×#381C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2218yescomplemented
43#10622571C22116yescomplemented
44#10622280C2218yescomplemented
45#10622279C2218yescomplemented
46#10622278C22116yescomplemented
47#10622277C2218yescomplemented
48D11×#95C2218yescomplemented
49#10622259C22116yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C23×C4×C11—28no—
54C23×C4×C11C2×C418yescomplemented
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2314yes—
60C22×C22⋊D11—28no—
61C22×C22⋊D11C2×C418yes—
62C22×C22⋊D11C2×C418yescomplemented
63C22×C22⋊D11D4116yes—
64C22×C22⋊D11C2314yes—
65C22×C22⋊D11C2314yes—
66C23×Dic11—28no—
67C23×Dic11—28no—
68C23×Dic11—44no—
69C23×Dic11C2312yes—
70C23×Dic11C2318yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C2×#4339—2128no—
75C2×#4339—264no—
76C2×#4339C2×C4164yescomplemented
77C22×D44—28no—
78C22×D44C2×C418yescomplemented
79C22×D44C2314yes—
80C22×C4×D11—28no—
81C22×C4×D11—28no—
82C22×C4×D11—28no—
83C22×C4×D11—28no—
84C22×C4×D11—44no—
85C22×C4×D11C2×C418yescomplemented
86C22×C4×D11C2×C418yescomplemented
87C22×C4×D11C2318yes—
88C22×C4×D11C2314yes—
89C22×C4×D11C2314yes—
90C22×Dic22—28no—
91C22×Dic22C2×C418yescomplemented
92C22×Dic22C2314yes—
93C2×C11×C22⋊C4—28no—
94C2×C11×C22⋊C4C2318yes—
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4—28no—
97C2×(C2×D11)⋊C4—44no—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×Dic11⋊C4—28no—
102C2×Dic11⋊C4C2318yes—
103C2×C4×Dic11—28no—
104C2×C4×Dic11C2318yes—
105(C22⋊D11)⋊C4—264no—
106C11×#95C2318yes—
107C11×#95C2314yes—
108C11×#95C2314yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C11⋊#95C2314yes—
113C11⋊#95C2314yes—
114C2×#2339—111nomaximal, Sylow
115C24×C11—24no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11C22×C414yes—
119C24×C11C2×D418yes—
120C24×C11C2412yes—
121C24×C11C2411yescharacteristic
122C23×D11—24no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11C22×C414yes—
130C23×D11C22×C414yes—
131C23×D11C2×D418yes—
132C23×D11C2412yes—
133C23×D11C2412yes—
134C22×C4×C11—232no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—216no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C22×C4116yescomplemented
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C2×C22⋊D11—232no—
152C2×C22⋊D11—216no—
153C2×C22⋊D11C22⋊C4164yescomplemented
154C2×C22⋊D11C22×C4116yes—
155C2×C22⋊D11C22×C4116yescomplemented
156C2×C22⋊D11C2×D4132yes—
157C22×Dic11—216no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—216no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—48no—
166C22×Dic11—432no—
167C22×Dic11C22×C414yes—
168C22×Dic11C22×C414yes—
169C22×Dic11C2×D418yes—
170C22×Dic11#4118yescomplemented
171C22×Dic11C2414yes—
172C22×Dic11C2412yes—
173C22×Dic11C2414yes—
174C22×Dic11C2412yes—
175#4339—2256no—
176C2×D44—232no—
177C2×D44—216no—
178C2×D44C22×C4116yescomplemented
179C2×C4×D11—232no—
180C2×C4×D11—216no—
181C2×C4×D11—216no—
182C2×C4×D11—232no—
183C2×C4×D11—216no—
184C2×C4×D11—216no—
185C2×C4×D11—48no—
186C2×C4×D11—432no—
187C2×C4×D11C22×C4116yescomplemented
188C2×C4×D11C22×C4116yescomplemented
189C2×Dic22—232no—
190C2×Dic22—216no—
191C2×Dic22C22×C4116yescomplemented
192C11×C22⋊C4—216no—
193(C2×D11)⋊C4—216no—
194(C2×D11)⋊C4—216no—
195(C2×D11)⋊C4—48no—
196Dic11⋊C4—216no—
197C4×Dic11—216no—
198C23×#41—111no—
199C22×C4×D4—112no—
200#2339—1116no—
201C2×#391—112no—
202C2×#386—112no—
203C2×#386—112no—
204C2×#381—111no—
205C2×#381D1111yescharacteristic, complemented
206C2×#380—111no—
207C2×C4×C22⋊C4—111no—
208C22×#95—111no—
209C22×#95—111no—
210C23×C11—28no—
211C23×C11—28no—
212C23×C11—216no—
213C23×C11—216no—
214C23×C11—24no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11C2×C22⋊C4116yes—
218C23×C11C23×C414yes—
219C23×C11C23×C412yes—
220C23×C11C22×D418yes—
221C23×C11C22×D414yes—
222C23×C11C2×#4114yes—
223C23×C11H(5,𝔽2)12yes—
224C23×C112−1+412yes—
225C23×C11C2511yescharacteristic
226C22×D11—28no—
227C22×D11—28no—
228C22×D11—216no—
229C22×D11—216no—
230C22×D11—24no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—28no—
234C22×D11—28no—
235C22×D11—28no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11C2×C22⋊C4116yes—
243C22×D11C23×C414yes—
244C22×D11C23×C414yes—
245C22×D11C22×D418yes—
246C2×C4×C11—28no—
247C2×C4×C11—28no—
248C2×C4×C11—232no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—48no—
258C2×C4×C11—48no—
259C2×C4×C11C23×C414yes—
260C2×C4×C11C23×C414yes—
261C22⋊D11—232no—
262C22⋊D11C2×C22⋊C4164yescomplemented
263C2×Dic11—28no—
264C2×Dic11—216no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—432no—
272C2×Dic11—48no—
273C2×Dic11C2×C22⋊C4116yes—
274C2×Dic11C23×C414yes—
275C2×Dic11C23×C414yes—
276C2×Dic11C22×D418yes—
277C2×Dic11C2×#4118yescomplemented
278D44—232no—
279C4×D11—232no—
280C4×D11—232no—
281C4×D11—432no—
282Dic22—232no—
283C22×#41—118no—
284C22×#41—1116no—
285C22×#41—2216no—
286C23×Q8—111no—
287C23×D4—111no—
288C23×D4—111no—
289C23×D4—111no—
290C24×C4—111no—
291C24×C4—111no—
292C24×C4—112no—
293C24×C4—112no—
294C24×C4C2×D1111yescharacteristic
295C2×C4×D4—1116no—
296C2×C4×D4—2216no—
297C22×C4⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4C2×D1112yes—
302C22×C42—112no—
303#391—1116no—
304#386—1116no—
305#386—1116no—
306#381—118no—
307#381C2×D1118yescomplemented
308#380—118no—
309C4×C22⋊C4—118no—
310C2×#95—118no—
311C2×#95—111no—
312C2×#95—111no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—118no—
317C2×#95C2×D1111yescharacteristic
318C2×#95C2×D1111yescharacteristic
319C2×#95C2×D1112yes—
320C22×C11—232no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—28no—
324C22×C11—28no—
325C22×C11C22×C22⋊C418yes—
326C22×C11C22×C22⋊C414yes—
327C22×C11C4×#4114yes—
328C22×C11#52014yes—
329C22×C11#54618yes—
330C22×C11#54718yes—
331C22×C11C24×C411yescharacteristic
332C22×C11C23×D412yes—
333C22×C11C22×#4112yes—
334C22×C11C2×H(5,𝔽2)11yescharacteristic
335C22×C11C2×2−1+411yescharacteristic
336C2×D11—232no—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—28no—
340C2×D11—28no—
341C2×D11—24no—
342C2×D11—24no—
343C2×D11—24no—
344C2×D11—416no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11C22×C22⋊C418yes—
348C4×C11—24no—
349C4×C11—24no—
350C4×C11—44no—
351C4×C11—44no—
352Dic11—24no—
353Dic11—28no—
354Dic11—44no—
355Dic11C22×C22⋊C418yes—
356C25—111no—
357C25—111no—
358C25C22×D1111yescharacteristic
359C2×#41—1164no—
360C2×#41—22128no—
361C2×#41—2264no—
362C22×Q8—118no—
363C22×Q8—114no—
364C22×Q8—228no—
365C22×D4—118no—
366C22×D4—1116no—
367C22×D4—114no—
368C22×D4—118no—
369C22×D4—114no—
370C22×D4—118no—
371C22×D4—114no—
372C22×D4—228no—
373C22×D4—228no—
374C23×C4—28no—
375C23×C4—111no—
376C23×C4—112no—
377C23×C4—111no—
378C23×C4—118no—
379C23×C4—118no—
380C23×C4—114no—
381C23×C4—114no—
382C23×C4—112no—
383C23×C4—118no—
384C23×C4—118no—
385C23×C4—228no—
386C23×C4—228no—
387C23×C4—228no—
388C23×C4—228no—
389C23×C4—228no—
390C23×C4—228no—
391C23×C4—444no—
392C23×C4—444no—
393C23×C4C4×D1118yescomplemented
394C23×C4C22×D1112yes—
395C23×C4C22×D1112yes—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1114yes—
399C4×D4—2264no—
400C2×C4⋊C4—118no—
401C2×C4⋊C4—228no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—118no—
404C2×C22⋊C4—118no—
405C2×C22⋊C4—118no—
406C2×C22⋊C4—228no—
407C2×C22⋊C4—228no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4C22×D1118yes—
410C2×C42—118no—
411C2×C42—228no—
412#95—114no—
413#95—114no—
414#95—118no—
415#95—118no—
416#95—118no—
417#95C22×D1114yes—
418#95C22×D1114yes—
419#95C22×D1118yes—
420C2×C11—28no—
421C2×C11#233918yescomplemented
422C2×C11C23×C22⋊C411yescharacteristic
423C2×C11C2×C4×#4111yescharacteristic
424C2×C11C2×#52011yescharacteristic
425C2×C11C2×#54612yes—
426C2×C11C2×#54712yes—
427D11—28no—
428D11—44no—
429C24—24no—
430C24—22no—
431C24—22no—
432C24—114no—
433C24—118no—
434C24—112no—
435C24—114no—
436C24—112no—
437C24—224no—
438C24—222no—
439C24—222no—
440C24—224no—
441C24—224no—
442C24—222no—
443C24—222no—
444C24C2×C4×D1114yes—
445C24D4×D1118yes—
446C24C23×D1112yes—
447C24C23×D1111yescharacteristic
448#41—22256no—
449C2×Q8—1116no—
450C2×Q8—2232no—
451C2×Q8—2216no—
452C2×D4—1164no—
453C2×D4—1116no—
454C2×D4—1132no—
455C2×D4—1116no—
456C2×D4—1116no—
457C2×D4—2232no—
458C2×D4—2216no—
459C2×D4—2232no—
460C2×D4—2216no—
461C22×C4—232no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—216no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—114no—
472C22×C4—118no—
473C22×C4—112no—
474C22×C4—114no—
475C22×C4—118no—
476C22×C4—112no—
477C22×C4—114no—
478C22×C4—1116no—
479C22×C4—1116no—
480C22×C4—114no—
481C22×C4—2232no—
482C22×C4—2216no—
483C22×C4—2216no—
484C22×C4—2232no—
485C22×C4—2216no—
486C22×C4—2216no—
487C22×C4—2216no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—224no—
492C22×C4—2216no—
493C22×C4—224no—
494C22×C4—224no—
495C22×C4—448no—
496C22×C4—4432no—
497C22×C4—448no—
498C22×C4—4432no—
499C22×C4C2×C4×D1114yes—
500C22×C4C2×C4×D1114yes—
501C22×C4C2×C4×D11116yescomplemented
502C22×C4C23×D1114yes—
503C22×C4C23×D1114yes—
504C22×C4C23×D1112yes—
505C22×C4C23×D1112yes—
506C4⋊C4—2216no—
507C22⋊C4—216no—
508C22⋊C4—2216no—
509C22⋊C4—2216no—
510C22⋊C4—448no—
511C42—2216no—
512C11C2×#233911yescharacteristic, complemented, Sylow
513C23—28no—
514C23—28no—
515C23—216no—
516C23—216no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—1116no—
521C23—114no—
522C23—118no—
523C23—114no—
524C23—228no—
525C23—228no—
526C23—2216no—
527C23—2216no—
528C23—224no—
529C23—222no—
530C23—222no—
531C23—228no—
532C23—228no—
533C23—228no—
534C23—224no—
535C23—224no—
536C23—222no—
537C23—222no—
538C23—448no—
539C23—448no—
540C23C22⋊C4×D11116yes—
541C23C22×C4×D1114yes—
542C23C22×C4×D1112yes—
543C23C2×D4×D1118yes—
544C23C2×D4×D1114yes—
545C23#41×D1114yes—
546C23#6704212yes—
547C23#6704312yes—
548C23C24×D1111yescharacteristic
549Q8—2232no—
550D4—1164no—
551D4—2232no—
552D4—2232no—
553C2×C4—28no—
554C2×C4—28no—
555C2×C4—232no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—48no—
565C2×C4—48no—
566C2×C4—1116no—
567C2×C4—114no—
568C2×C4—118no—
569C2×C4—114no—
570C2×C4—118no—
571C2×C4—2232no—
572C2×C4—2232no—
573C2×C4—228no—
574C2×C4—2216no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—4432no—
582C2×C4—4432no—
583C2×C4—448no—
584C2×C4C22×C4×D1114yes—
585C2×C4C22×C4×D1114yes—
586C22—232no—
587C22—24no—
588C22—28no—
589C22—24no—
590C22—28no—
591C22—118no—
592C22—2232no—
593C22—224no—
594C22—228no—
595C22—224no—
596C22—228no—
597C22—224no—
598C22—224no—
599C22—224no—
600C22—4416no—
601C22—444no—
602C22—444no—
603C22C2×C22⋊C4×D1118yes—
604C22C2×C22⋊C4×D1114yes—
605C22#1062305314yes—
606C22#1062305414yes—
607C22#1062318518yes—
608C22#1062318618yes—
609C22C23×C4×D1111yescharacteristic
610C22C22×D4×D1112yes—
611C22C2×#41×D1112yes—
612C22C2×#6704211yescharacteristic
613C22C2×#6704311yescharacteristic
614C4—24no—
615C4—24no—
616C4—44no—
617C4—44no—
618C4—118no—
619C4—224no—
620C4—228no—
621C4—444no—
622C2—28no—
623C2—228no—
624C2—444no—
625C2#1307144018yesdirect product factor
626C2C22×C22⋊C4×D1111yescharacteristic
627C2C2×#1062305311yescharacteristic
628C2C2×#1062305411yescharacteristic
629C2C2×#1062318512yes—
630C2C2×#1062318612yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#381C2
socleC24×C11C24
prime radicalC23×#4339C2
cosocleC23×C11C25
hypercenterC2×#381D11
hypocenterC11C2×#2339
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13071440C2direct (N × H)
4. C2×#10622259C2semidirect
5. C2×#10622278C2semidirect
6. C2×#10622571C2semidirect
7. C2×#10622277C2semidirect
8. C2×#10622280C2semidirect
9. C2×#10622279C2semidirect
10. C22×C11⋊#95C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#381C2semidirect
18. C22×#4339C4semidirect
32. C2×(C22⋊D11)⋊C4C22semidirect
33. C11×#381C22semidirect
42. C2×C11⋊#95C22semidirect
43. #10622571C22semidirect
44. #10622280C22semidirect
45. #10622279C22semidirect
46. #10622278C22semidirect
47. #10622277C22semidirect
48. D11×#95C22semidirect
49. #10622259C22semidirect
54. C23×C4×C11C2×C4semidirect
62. C22×C22⋊D11C2×C4semidirect
76. C2×#4339C2×C4semidirect
78. C22×D44C2×C4semidirect
85. C22×C4×D11C2×C4semidirect
86. C22×C4×D11C2×C4semidirect
91. C22×Dic22C2×C4semidirect
146. C22×C4×C11C22×C4semidirect
153. C2×C22⋊D11C22⋊C4semidirect
155. C2×C22⋊D11C22×C4semidirect
170. C22×Dic11#41semidirect
178. C2×D44C22×C4semidirect
187. C2×C4×D11C22×C4semidirect
188. C2×C4×D11C22×C4semidirect
191. C2×Dic22C22×C4semidirect
205. C2×#381D11semidirect
262. C22⋊D11C2×C22⋊C4semidirect
277. C2×Dic11C2×#41semidirect
307. #381C2×D11semidirect
393. C23×C4C4×D11semidirect
421. C2×C11#2339semidirect
501. C22×C4C2×C4×D11semidirect
512. C11C2×#2339semidirect
625. C2#13071440direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×(C22⋊D11)⋊C42
#130714402
C2×#106222592
C2×#106222782
C2×#106225712
C2×#106222772
C2×#106222802
C2×#106222792
C22×C11⋊#952
C2×D11×#952
C2×C11×#3812
C2×#233911