Finite Group Databasebeta

← C2×#13071689 #14913382

Subgroups — C2×#13071689 #14913382

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×#66989C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3#13071689C2116yesmaximal, direct product factor
4C2×#10622542C211yesmaximal, characteristic, complemented
5C2×#10622834C211yesmaximal, characteristic
6C2×#10622558C212yesmaximal, complemented
7C2×#10622557C212yesmaximal, complemented
8C2×#10622823C212yesmaximal, complemented
9C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic11C212yesmaximal, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2212yes—
15C23×Dic22C2211yescharacteristic
16C2×C4×D4×C11—28no—
17C2×C4×D4×C11C2218yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66989C4116yescomplemented
26C2×#66989C2218yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2212yes—
34C22×C4×Dic11C2211yescharacteristic
35C2×#66940—28no—
36C2×#66940C2218yescomplemented
37#10622834C2218yes—
38#10622823C22116yescomplemented
39C4×C22⋊Dic11C22116yescomplemented
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45C4⋊C4×Dic11C2218yescomplemented
46#10622558C22116yescomplemented
47#10622557C22116yescomplemented
48C4×Dic11⋊C4C2218yescomplemented
49#10622542C2218yescomplemented
50C25×C11C2312yes—
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11C2×C418yes—
54C22×D4×C11C2314yes—
55C23×C4×C11—28no—
56C23×C4×C11—28no—
57C23×C4×C11—44no—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2318yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C22×Dic22—24no—
70C22×Dic22—24no—
71C22×Dic22C2×C418yescomplemented
72C22×Dic22C2314yes—
73C4×D4×C11—232no—
74C2×C11×C4⋊C4D418yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C22⋊C4—28no—
77C2×C11×C22⋊C4C2318yes—
78C2×C42×C11—24no—
79C2×C42×C11C2314yes—
80C2×C22⋊Dic11—28no—
81C2×C22⋊Dic11—44no—
82C2×C22⋊Dic11C2×C4116yescomplemented
83C2×C22⋊Dic11C2×C4116yescomplemented
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2318yes—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88#66989C2×C4164yescomplemented
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11C2314yes—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×C4×Dic11—28no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—44no—
100C2×C4×Dic11C2×C418yescomplemented
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2318yes—
103C2×C4×Dic11C2318yes—
104C2×C4×Dic11C2314yes—
105#66940—232no—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
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×D4×C11—232no—
122C2×D4×C11—28no—
123C2×D4×C11—28no—
124C2×D4×C11C22×C4116yes—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—216no—
133C22×C4×C11—216no—
134C22×C4×C11—48no—
135C22×C4×C11—432no—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C2×D418yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11#4114yes—
140C22×C4×C11#4114yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11C22×C414yes—
160C22×Dic11C22×C414yes—
161C22×Dic11C22×C418yes—
162C22×Dic11#4114yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C2×Dic22—232no—
170C2×Dic22—28no—
171C2×Dic22—28no—
172C2×Dic22C22×C4116yescomplemented
173C11×C4⋊C4C2×D4116yes—
174C11×C22⋊C4—216no—
175C42×C11—28no—
176C22⋊Dic11—216no—
177C22⋊Dic11—48no—
178C22⋊Dic11C22×C4132yescomplemented
179C22⋊Dic11C22×C4132yescomplemented
180C4⋊Dic11—28no—
181Dic11⋊C4—28no—
182Dic11⋊C4—216no—
183Dic11⋊C4—28no—
184C4×Dic11—216no—
185C4×Dic11—28no—
186C4×Dic11—48no—
187C4×Dic11C22×C4116yescomplemented
188C22×#124—111no—
189C22×C4×Q8—111no—
190C22×C4×D4D1111yescharacteristic
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
222D4×C11—232no—
223C2×C4×C11—28no—
224C2×C4×C11—216no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—432no—
233C2×C4×C11—44no—
234C2×C4×C11C4×D4116yes—
235C2×C4×C11C23×C414yes—
236C2×C4×C11C22×D418yes—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C2×#4114yes—
239C2×C4×C11C2×#4114yes—
240C2×Dic11—216no—
241C2×Dic11—28no—
242C2×Dic11—28no—
243C2×Dic11—28no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—44no—
259C2×Dic11—48no—
260C2×Dic11C23×C414yes—
261C2×Dic11C23×C414yes—
262C2×Dic11C23×C418yes—
263C2×Dic11C2×#4114yes—
264Dic22—232no—
265C23×Q8—111no—
266C23×D4C2×D1111yescharacteristic
267C24×C4C2×D1112yes—
268C2×#124—118no—
269C2×#124—1116no—
270C2×C4×Q8—118no—
271C2×C4×Q8—228no—
272C2×C4×D4—28no—
273C2×C4×D4C2×D1118yes—
274C22×C4⋊C4—112no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
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—24no—
325C4×C11—28no—
326C4×C11—42no—
327C4×C11C2×C4×D418yes—
328Dic11—28no—
329Dic11—24no—
330Dic11—24no—
331Dic11—24no—
332Dic11—42no—
333Dic11—44no—
334C25C22×D1112yes—
335C22×Q8—118no—
336C22×Q8—114no—
337C22×Q8—224no—
338C22×Q8—224no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4C4×D1118yes—
342C22×D4C22×D1114yes—
343C23×C4—28no—
344C23×C4—28no—
345C23×C4—44no—
346C23×C4—111no—
347C23×C4—112no—
348C23×C4—111no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—112no—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1118yes—
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1112yes—
356C23×C4C22×D1111yescharacteristic
357#124—1164no—
358C4×Q8—2232no—
359C4×D4—232no—
360C2×C4⋊C4—118no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—228no—
368C2×C4⋊C4C22⋊D1118yes—
369C2×C4⋊C4C22×D1114yes—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—1116no—
372C2×C22⋊C4—1116no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—228no—
378C2×C22⋊C4—444no—
379C2×C22⋊C4C22×D1118yes—
380C2×C42—24no—
381C2×C42—118no—
382C2×C42—114no—
383C2×C42—118no—
384C2×C42—114no—
385C2×C42—118no—
386C2×C42—228no—
387C2×C42—224no—
388C2×C42—444no—
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—
410C24C2×C4×D1118yes—
411C24C23×D1114yes—
412C24C23×D1111yescharacteristic
413C2×Q8—1116no—
414C2×Q8—2232no—
415C2×Q8—228no—
416C2×Q8—228no—
417C2×D4—232no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4C2×C4×D11116yes—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—216no—
429C22×C4—216no—
430C22×C4—48no—
431C22×C4—432no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—118no—
435C22×C4—114no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—114no—
441C22×C4—112no—
442C22×C4—224no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—222no—
452C22×C4—224no—
453C22×C4—222no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4C2×C4×D1114yes—
457C22×C4#433914yes—
458C22×C4#434114yes—
459C22×C4C2×C22⋊D1118yes—
460C22×C4C2×C22⋊D1114yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C22×C4C23×D1114yes—
464C22×C4C23×D1112yes—
465C4⋊C4—228no—
466C4⋊C4—228no—
467C4⋊C4—228no—
468C4⋊C4—2216no—
469C4⋊C4C2×C22⋊D11116yes—
470C22⋊C4—216no—
471C22⋊C4—1132no—
472C22⋊C4—1132no—
473C22⋊C4—2216no—
474C22⋊C4—448no—
475C42—28no—
476C42—1116no—
477C42—2216no—
478C42—228no—
479C42—448no—
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—
494C23C22×C4×D1118yes—
495C23C22×C4×D1112yes—
496C23C2×#433912yes—
497C23C2×#434112yes—
498C23#6703712yes—
499C23#41×D1112yes—
500C23#6704312yes—
501C23C22×C22⋊D1112yes—
502C23C24×D1111yescharacteristic
503Q8—2232no—
504D4—232no—
505C2×C4—28no—
506C2×C4—216no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—432no—
515C2×C4—44no—
516C2×C4—114no—
517C2×C4—114no—
518C2×C4—118no—
519C2×C4—114no—
520C2×C4—2216no—
521C2×C4—228no—
522C2×C4—228no—
523C2×C4—228no—
524C2×C4—224no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—224no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—444no—
539C2×C4—448no—
540C2×C4C4×C22⋊D11116yes—
541C2×C4C22×C4×D1114yes—
542C2×C4C2×#433914yes—
543C2×C4C2×#434114yes—
544C2×C4C22×C22⋊D1118yes—
545C2×C4C22×C22⋊D1114yes—
546C22—28no—
547C22—28no—
548C22—28no—
549C22—44no—
550C22—432no—
551C22—44no—
552C22—44no—
553C22—44no—
554C22C4×#434114yes—
555C22#1062307314yes—
556C22#1062307714yes—
557C22#1062309014yes—
558C22C2×C4×C22⋊D1114yes—
559C22#1062333714yes—
560C22#1062336214yes—
561C22C23×C4×D1111yescharacteristic
562C22C22×#433911yescharacteristic
563C22C22×#434111yescharacteristic
564C22C2×#6703711yescharacteristic
565C22C2×#41×D1111yescharacteristic
566C22C2×#6704311yescharacteristic
567C22C23×C22⋊D1111yescharacteristic
568C4—24no—
569C4—28no—
570C4—42no—
571C4—228no—
572C4—224no—
573C4—224no—
574C4—224no—
575C4—444no—
576C4—442no—
577C4C2×C4×C22⋊D1118yes—
578C2—48no—
579C2#1307168918yesdirect product factor
580C2C22×C4×C22⋊D1111yescharacteristic
581C2C2×C4×#434111yescharacteristic
582C2C2×#1062307711yescharacteristic
583C2C2×#1062333711yescharacteristic
584C2C2×#1062336211yescharacteristic
585C2C2×#1062307311yescharacteristic
586C2C2×#1062309011yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC23×D4×C11C22
cosocleC23×C11C25
hypercenterC22×C4×D4D11
hypocenterC11C2×#2367
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. #13071689C2direct (N × H)
4. C2×#10622542C2semidirect
6. C2×#10622558C2semidirect
7. C2×#10622557C2semidirect
8. C2×#10622823C2semidirect
9. C2×C4⋊C4×Dic11C2semidirect
10. C2×C4×Dic11⋊C4C2semidirect
11. C2×C4×C22⋊Dic11C2semidirect
25. C2×#66989C4semidirect
36. C2×#66940C22semidirect
38. #10622823C22semidirect
39. C4×C22⋊Dic11C22semidirect
45. C4⋊C4×Dic11C22semidirect
46. #10622558C22semidirect
47. #10622557C22semidirect
48. C4×Dic11⋊C4C22semidirect
49. #10622542C22semidirect
71. C22×Dic22C2×C4semidirect
82. C2×C22⋊Dic11C2×C4semidirect
83. C2×C22⋊Dic11C2×C4semidirect
88. #66989C2×C4semidirect
100. C2×C4×Dic11C2×C4semidirect
172. C2×Dic22C22×C4semidirect
178. C22⋊Dic11C22×C4semidirect
179. C22⋊Dic11C22×C4semidirect
187. C4×Dic11C22×C4semidirect
396. C2×C11#2367semidirect
480. C11C2×#2367semidirect
579. C2#13071689direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669892
C22×#669402
#130716892
C2×#106225422
C2×#106228342
C2×#106225582
C2×#106225572
C2×#106228232
C2×C4⋊C4×Dic112
C2×C4×Dic11⋊C42
C2×C4×C22⋊Dic112
C22×C4×D4×C112
C2×#236711