Finite Group Databasebeta

← C2×#13071691 #14913384

Subgroups — C2×#13071691 #14913384

Order 2816.

3678 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic
3#13071691C2116yesmaximal, direct product factor
4C2×#10622843C211yesmaximal, characteristic, complemented
5C2×#10622834C211yesmaximal, characteristic
6C2×#10622564C212yesmaximal, complemented
7C2×#10622564C212yesmaximal, complemented
8C2×#10622563C212yesmaximal, complemented
9C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
10C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic11C212yesmaximal, complemented
12C22×C11×#124C211yesmaximal, characteristic
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C24×Dic11C2212yes—
16C2×C11×#124C4116yescomplemented
17C2×C11×#124C2218yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×Q8×Dic11—28no—
25C2×Q8×Dic11C2218yescomplemented
26C2×D4×Dic11—28no—
27C2×D4×Dic11C2218yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2212yes—
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4×Dic11C2212yes—
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2212yes—
37#10622843C2218yescomplemented
38#10622834C2218yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2212yes—
44#10622564C22116yescomplemented
45#10622564C22116yescomplemented
46#10622563C22116yescomplemented
47C22⋊C4×Dic11C22116yescomplemented
48C4×C4⋊Dic11C2218yescomplemented
49C4×C4⋊Dic11C2218yescomplemented
50C25×C11C2312yes—
51C22×Q8×C11—24no—
52C22×Q8×C11—24no—
53C22×Q8×C11C2×C418yescomplemented
54C22×Q8×C11C2314yes—
55C22×D4×C11—24no—
56C22×D4×C11—24no—
57C22×D4×C11C2×C418yes—
58C22×D4×C11C2314yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—28no—
64C23×Dic11—28no—
65C23×Dic11—44no—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2318yes—
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C11×#124C2×C4164yescomplemented
74C2×C11×C22⋊C4C2×C4116yescomplemented
75C2×C11×C22⋊C4C2×C4116yescomplemented
76C2×C11×C22⋊C4C2318yes—
77C2×C11×C22⋊C4C2318yes—
78C2×C42×C11C2×C418yescomplemented
79C2×C42×C11C2314yes—
80C2×C22⋊Dic11—28no—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—44no—
83C2×C22⋊Dic11C2318yes—
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2318yes—
86Q8×Dic11—232no—
87D4×Dic11—232no—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—28no—
90C2×C4⋊Dic11—24no—
91C2×C4⋊Dic11—24no—
92C2×C4⋊Dic11D418yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2318yes—
97C2×C4⋊Dic11C2314yes—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—28no—
101C2×C4×Dic11—44no—
102C2×C4×Dic11C2314yes—
103C2×C4×Dic11C2314yes—
104C2×C4×Dic11C2318yes—
105C2×C4×Dic11C2318yes—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C11⋊#95C2314yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2367—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11C22×C418yes—
119C24×C11C2414yes—
120C24×C11C2411yescharacteristic
121C2×Q8×C11—232no—
122C2×Q8×C11—28no—
123C2×Q8×C11—28no—
124C2×Q8×C11C22×C4116yescomplemented
125C2×D4×C11—232no—
126C2×D4×C11—28no—
127C2×D4×C11—28no—
128C2×D4×C11C22×C4116yes—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C22×C418yes—
138C22×C4×C11C22×C414yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11#4114yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×Dic11—216no—
146C22×Dic11—216no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—48no—
163C22×Dic11—432no—
164C22×Dic11C2×D418yes—
165C22×Dic11#4114yes—
166C22×Dic11#4114yes—
167C22×Dic11C2412yes—
168C22×Dic11C2414yes—
169C22×Dic11C2412yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C11×C22⋊C4C22×C4132yescomplemented
174C11×C22⋊C4C22×C4132yescomplemented
175C42×C11C22×C4116yescomplemented
176C22⋊Dic11—216no—
177C22⋊Dic11—216no—
178C22⋊Dic11—48no—
179C4⋊Dic11—216no—
180C4⋊Dic11—28no—
181C4⋊Dic11—28no—
182C4⋊Dic11—28no—
183C4⋊Dic11C2×D4116yes—
184C4×Dic11—216no—
185C4×Dic11—28no—
186C4×Dic11—28no—
187C4×Dic11—48no—
188C22×#124D1111yescharacteristic
189C22×C4×Q8—111no—
190C22×C4×D4—111no—
191#2367—1116no—
192C2×#391—111no—
193C2×#390—111no—
194C2×#388—112no—
195C2×#388—112no—
196C2×#385—112no—
197C2×C4×C4⋊C4—111no—
198C2×C4×C4⋊C4—111no—
199C2×C4×C22⋊C4—112no—
200C23×C11—216no—
201C23×C11—216no—
202C23×C11—216no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11C23×C418yes—
214C23×C11C23×C412yes—
215C23×C11C22×D412yes—
216C23×C11C2×#4112yes—
217C23×C11C2×#4112yes—
218C23×C11C2×#4112yes—
219C23×C11H(5,𝔽2)12yes—
220C23×C112−1+412yes—
221C23×C11C2511yescharacteristic
222Q8×C11—232no—
223D4×C11—232no—
224C2×C4×C11—216no—
225C2×C4×C11—28no—
226C2×C4×C11—28no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11C4×D4116yes—
234C2×C4×C11C23×C414yes—
235C2×C4×C11C23×C414yes—
236C2×C4×C11C23×C418yes—
237C2×C4×C11C23×C414yes—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C2×#4114yes—
240C2×Dic11—28no—
241C2×Dic11—216no—
242C2×Dic11—28no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—432no—
259C2×Dic11—44no—
260C2×Dic11—44no—
261C2×Dic11—48no—
262C2×Dic11C22×D418yes—
263C2×Dic11C2×#4114yes—
264C2×Dic11C2×#4114yes—
265C23×Q8C2×D1111yescharacteristic
266C23×D4C2×D1111yescharacteristic
267C24×C4—112no—
268C2×#124Dic11116yescomplemented
269C2×#124C2×D1118yes—
270C2×C4×Q8—118no—
271C2×C4×Q8—228no—
272C2×C4×D4—118no—
273C2×C4×D4—228no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—112no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4C2×D1112yes—
283C22×C22⋊C4C2×D1112yes—
284C22×C42—111no—
285C22×C42—112no—
286C22×C42—111no—
287C22×C42—112no—
288C22×C42C2×D1111yescharacteristic
289#391—118no—
290#390—118no—
291#388—1116no—
292#388—1116no—
293#385—1116no—
294C4×C4⋊C4—118no—
295C4×C4⋊C4—118no—
296C4×C22⋊C4—1116no—
297C2×#95—111no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—111no—
301C2×#95—112no—
302C22×C11—28no—
303C22×C11—28no—
304C22×C11—28no—
305C22×C11—432no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11C2×C4×D414yes—
311C22×C11C4×#4114yes—
312C22×C11#52014yes—
313C22×C11#54614yes—
314C22×C11#54814yes—
315C22×C11#55614yes—
316C22×C11#55914yes—
317C22×C11C24×C411yescharacteristic
318C22×C11C23×D411yescharacteristic
319C22×C11C22×#4111yescharacteristic
320C22×C11C22×#4111yescharacteristic
321C22×C11C22×#4111yescharacteristic
322C22×C11C2×H(5,𝔽2)11yescharacteristic
323C22×C11C2×2−1+411yescharacteristic
324C4×C11—28no—
325C4×C11—24no—
326C4×C11—24no—
327C4×C11C2×C4×D418yes—
328Dic11—24no—
329Dic11—28no—
330Dic11—24no—
331Dic11—42no—
332Dic11—42no—
333Dic11—44no—
334C25C22×D1112yes—
335C22×Q8—24no—
336C22×Q8—24no—
337C22×Q8C2×Dic1118yescomplemented
338C22×Q8C22×D1114yes—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4C2×Dic1118yes—
342C22×D4C22×D1114yes—
343C23×C4—111no—
344C23×C4—112no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—112no—
349C23×C4—118no—
350C23×C4—228no—
351C23×C4—228no—
352C23×C4—444no—
353C23×C4C22×D1111yescharacteristic
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357#124C2×Dic11164yescomplemented
358C4×Q8—2232no—
359C4×D4—2232no—
360C2×C4⋊C4—118no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—228no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—224no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4—444no—
376C2×C22⋊C4C2×Dic11116yescomplemented
377C2×C22⋊C4C2×Dic11116yescomplemented
378C2×C22⋊C4C22×D1118yes—
379C2×C22⋊C4C22×D1118yes—
380C2×C42—114no—
381C2×C42—118no—
382C2×C42—114no—
383C2×C42—118no—
384C2×C42—228no—
385C2×C42—224no—
386C2×C42—224no—
387C2×C42—444no—
388C2×C42C2×Dic1118yescomplemented
389C2×C42C22×D1114yes—
390#95—114no—
391#95—118no—
392#95—118no—
393#95—114no—
394#95—118no—
395C2×C11—48no—
396C2×C11#236718yescomplemented
397C2×C11C22×C4×D411yescharacteristic
398C2×C11C2×C4×#4111yescharacteristic
399C2×C11C2×#52011yescharacteristic
400C2×C11C2×#54611yescharacteristic
401C2×C11C2×#54811yescharacteristic
402C2×C11C2×#55611yescharacteristic
403C2×C11C2×#55911yescharacteristic
404C24—24no—
405C24—24no—
406C24—24no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24C22×Dic1118yes—
411C24C23×D1114yes—
412C24C23×D1111yescharacteristic
413C2×Q8—232no—
414C2×Q8—28no—
415C2×Q8—28no—
416C2×Q8C22×Dic11116yescomplemented
417C2×D4—232no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4C22×Dic11116yes—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—118no—
428C22×C4—114no—
429C22×C4—114no—
430C22×C4—112no—
431C22×C4—112no—
432C22×C4—114no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—112no—
436C22×C4—2216no—
437C22×C4—2216no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—224no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—448no—
454C22×C4—4432no—
455C22×C4D4×D1114yes—
456C22×C4#434114yes—
457C22×C4C22×Dic1114yes—
458C22×C4C22×Dic1114yes—
459C22×C4C22×Dic1118yes—
460C22×C4C22×Dic1114yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1114yes—
463C22×C4C23×D1112yes—
464C22×C4C23×D1112yes—
465C4⋊C4—1116no—
466C4⋊C4—2216no—
467C4⋊C4—228no—
468C4⋊C4—228no—
469C4⋊C4—228no—
470C22⋊C4—2216no—
471C22⋊C4—2216no—
472C22⋊C4—448no—
473C22⋊C4C22×Dic11132yescomplemented
474C22⋊C4C22×Dic11132yescomplemented
475C42—2216no—
476C42—228no—
477C42—228no—
478C42—448no—
479C42C22×Dic11116yescomplemented
480C11C2×#236711yescharacteristic, complemented, Sylow
481C23—216no—
482C23—216no—
483C23—216no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—48no—
491C23—48no—
492C23—48no—
493C23—48no—
494C23C2×D4×D1112yes—
495C23C2×#434112yes—
496C23#41×D1112yes—
497C23#41×D1112yes—
498C23#6704212yes—
499C23#6704312yes—
500C23C23×Dic1118yes—
501C23C23×Dic1112yes—
502C23C24×D1111yescharacteristic
503Q8—232no—
504D4—232no—
505C2×C4—216no—
506C2×C4—28no—
507C2×C4—28no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—118no—
515C2×C4—114no—
516C2×C4—114no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—228no—
524C2×C4—2216no—
525C2×C4—228no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—4432no—
536C2×C4—444no—
537C2×C4—444no—
538C2×C4—448no—
539C2×C4D4×Dic11116yes—
540C2×C4C2×D4×D1114yes—
541C2×C4C2×#434114yes—
542C2×C4C23×Dic1114yes—
543C2×C4C23×Dic1114yes—
544C2×C4C23×Dic1118yes—
545C2×C4C23×Dic1114yes—
546C22—28no—
547C22—28no—
548C22—28no—
549C22—44no—
550C22—432no—
551C22—44no—
552C22—44no—
553C22—44no—
554C22#1062320214yes—
555C22#1062320714yes—
556C22#1062320814yes—
557C22#1062321214yes—
558C22C2×D4×Dic1114yes—
559C22#41×Dic1114yes—
560C22#1062335814yes—
561C22C22×D4×D1111yescharacteristic
562C22C22×#434111yescharacteristic
563C22C2×#41×D1111yescharacteristic
564C22C2×#41×D1111yescharacteristic
565C22C2×#6704211yescharacteristic
566C22C2×#6704311yescharacteristic
567C22C24×Dic1111yescharacteristic
568C4—28no—
569C4—24no—
570C4—24no—
571C4—224no—
572C4—228no—
573C4—224no—
574C4—444no—
575C4—442no—
576C4—442no—
577C4C2×D4×Dic1118yes—
578C2—48no—
579C2#1307169118yesdirect product factor
580C2C22×D4×Dic1111yescharacteristic
581C2C2×#41×Dic1111yescharacteristic
582C2C2×#1062335811yescharacteristic
583C2C2×#1062320711yescharacteristic
584C2C2×#1062320811yescharacteristic
585C2C2×#1062320211yescharacteristic
586C2C2×#1062321211yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C11×#124C2
socleC24×C11C24
prime radicalC23×D4×C11C22
cosocleC23×C11C25
hypercenterC22×#124D11
hypocenterC11C2×#2367
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic11C2semidirect
3. #13071691C2direct (N × H)
4. C2×#10622843C2semidirect
6. C2×#10622564C2semidirect
7. C2×#10622564C2semidirect
8. C2×#10622563C2semidirect
9. C2×C4×C4⋊Dic11C2semidirect
10. C2×C4×C4⋊Dic11C2semidirect
11. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#124C4semidirect
25. C2×Q8×Dic11C22semidirect
37. #10622843C22semidirect
44. #10622564C22semidirect
45. #10622564C22semidirect
46. #10622563C22semidirect
47. C22⋊C4×Dic11C22semidirect
48. C4×C4⋊Dic11C22semidirect
49. C4×C4⋊Dic11C22semidirect
53. C22×Q8×C11C2×C4semidirect
73. C11×#124C2×C4semidirect
74. C2×C11×C22⋊C4C2×C4semidirect
75. C2×C11×C22⋊C4C2×C4semidirect
78. C2×C42×C11C2×C4semidirect
124. C2×Q8×C11C22×C4semidirect
173. C11×C22⋊C4C22×C4semidirect
174. C11×C22⋊C4C22×C4semidirect
175. C42×C11C22×C4semidirect
268. C2×#124Dic11semidirect
337. C22×Q8C2×Dic11semidirect
357. #124C2×Dic11semidirect
376. C2×C22⋊C4C2×Dic11semidirect
377. C2×C22⋊C4C2×Dic11semidirect
388. C2×C42C2×Dic11semidirect
396. C2×C11#2367semidirect
416. C2×Q8C22×Dic11semidirect
473. C22⋊C4C22×Dic11semidirect
474. C22⋊C4C22×Dic11semidirect
479. C42C22×Dic11semidirect
480. C11C2×#2367semidirect
579. C2#13071691direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C22×D4×Dic112
#130716912
C2×#106228432
C2×#106228342
C2×#106225642
C2×#106225632
C2×C4×C4⋊Dic112
C2×C22⋊C4×Dic112
C22×C11×#1242
C2×#236711