Finite Group Databasebeta

← C2×#13071596 #14913263

Subgroups — C2×#13071596 #14913263

Order 2816.

5942 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66990C211yesmaximal, characteristic
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
6#13071596C2116yesmaximal, direct product factor
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622283C211yesmaximal, characteristic, complemented
9C2×#10622282C211yesmaximal, characteristic, complemented
10C2×#10622571C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622559C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic, complemented
24C23×C4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic, complemented
28C22×C11×C22⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic, complemented
32C2×#66990C4116yescomplemented
33C2×#66990C2218yes—
34C2×D4×Dic11—28no—
35C2×D4×Dic11C2218yescomplemented
36C22×(C2×D11)⋊C4—28no—
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2218yescomplemented
46C22×C4⋊Dic11C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C22×Dic11⋊C4C2211yescharacteristic, complemented
49C22×C4×Dic11C2211yescharacteristic, complemented
50C22×C4×Dic11C2211yescharacteristic, complemented
51C22×C4×Dic11C2211yescharacteristic, complemented
52C2×(C22⋊D11)⋊C4—28no—
53C2×(C22⋊D11)⋊C4C2218yescomplemented
54C2×C22⋊C4×D11—28no—
55C2×C22⋊C4×D11C2218yescomplemented
56C11×#386C2218yescomplemented
57C2×C11×#95C2211yescharacteristic, complemented
58C2×C11×#95C2211yescharacteristic, complemented
59C4×C22⋊Dic11C2218yescomplemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62C2×C11⋊#95C2211yescharacteristic, complemented
63C2×C11⋊#95C2211yescharacteristic, complemented
64#10622571C2218yescomplemented
65#10622570C2218yescomplemented
66#10622569C2218yescomplemented
67#10622559C2218yescomplemented
68#10622283C2218yescomplemented
69#10622282C2218yescomplemented
70#10622281C2218yescomplemented
71#10622279C2218yescomplemented
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—24no—
78C24×D11—42no—
79C24×D11—42no—
80C24×D11C2×C418yescomplemented
81C24×D11C2311yescharacteristic
82C24×D11C2314yes—
83C24×D11C2311yescharacteristic
84C22×D4×C11—24no—
85C22×D4×C11—24no—
86C22×D4×C11C2×C418yescomplemented
87C22×D4×C11C2314yes—
88C23×C4×C11—24no—
89C23×C4×C11—24no—
90C23×C4×C11—42no—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2314yes—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—42no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11C2×C418yescomplemented
102C22×C22⋊D11C2×C418yescomplemented
103C22×C22⋊D11C2314yes—
104C22×C22⋊D11C2314yes—
105C23×Dic11—24no—
106C23×Dic11—24no—
107C23×Dic11—24no—
108C23×Dic11—24no—
109C23×Dic11—42no—
110C23×Dic11—42no—
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2314yes—
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2311yescharacteristic
118C23×Dic11C2314yescomplemented
119C22×C4×D11—24no—
120C22×C4×D11—24no—
121C22×C4×D11—24no—
122C22×C4×D11—24no—
123C22×C4×D11—42no—
124C22×C4×D11—42no—
125C22×C4×D11C2314yes—
126C22×C4×D11C2314yes—
127C2×C11×C22⋊C4—24no—
128C2×C11×C22⋊C4—24no—
129C2×C11×C22⋊C4—42no—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yescomplemented
132C2×C11×C22⋊C4C2314yescomplemented
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11C2×C418yescomplemented
135C2×C22⋊Dic11D418yescomplemented
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yescomplemented
139#66990C2×C4164yescomplemented
140D4×Dic11—232no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—24no—
146C2×(C2×D11)⋊C4—232no—
147C2×(C2×D11)⋊C4C2×C418yescomplemented
148C2×(C2×D11)⋊C4C2×C418yescomplemented
149C2×(C2×D11)⋊C4D418yescomplemented
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×(C2×D11)⋊C4C2314yes—
157C2×(C2×D11)⋊C4C2314yes—
158C2×C4⋊Dic11—24no—
159C2×C4⋊Dic11C2314yescomplemented
160C2×Dic11⋊C4—24no—
161C2×Dic11⋊C4—42no—
162C2×Dic11⋊C4C2314yescomplemented
163C2×Dic11⋊C4C2314yescomplemented
164C2×C4×Dic11—24no—
165C2×C4×Dic11—24no—
166C2×C4×Dic11—42no—
167C2×C4×Dic11C2314yescomplemented
168C2×C4×Dic11C2314yescomplemented
169C2×C4×Dic11C2314yescomplemented
170(C22⋊D11)⋊C4—232no—
171C22⋊C4×D11—232no—
172C11×#95C2314yescomplemented
173C11×#95C2314yescomplemented
174C11⋊#95C2314yescomplemented
175C11⋊#95C2314yescomplemented
176C11⋊#95C2314yescomplemented
177C11⋊#95C2314yescomplemented
178C2×#2358—111nomaximal, Sylow
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11C22×C414yes—
190C24×C11C22×C414yes—
191C24×C11C2×D414yes—
192C24×C11#4114yes—
193C24×C11C2412yes—
194C24×C11C2412yes—
195C24×C11C2411yescharacteristic
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—232no—
201C23×D11—28no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—28no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11—22no—
209C23×D11—232no—
210C23×D11—28no—
211C23×D11—28no—
212C23×D11—416no—
213C23×D11—44no—
214C23×D11—44no—
215C23×D11—416no—
216C23×D11—416no—
217C23×D11—416no—
218C23×D11—416no—
219C23×D11C22×C414yes—
220C23×D11C22×C414yes—
221C23×D11C22×C4116yescomplemented
222C23×D11C2×D414yes—
223C23×D11#4114yes—
224C23×D11C2412yes—
225C23×D11C2412yes—
226C2×D4×C11—232no—
227C2×D4×C11—28no—
228C2×D4×C11—28no—
229C2×D4×C11C22×C4116yescomplemented
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—28no—
240C22×C4×C11—22no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—28no—
245C22×C4×C11—44no—
246C22×C4×C11—416no—
247C22×C4×C11C22×C414yes—
248C22×C4×C11C2×D414yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C2×C22⋊D11—232no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11—28no—
257C2×C22⋊D11—416no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11C22×C4116yescomplemented
261C2×C22⋊D11C22×C4116yescomplemented
262C22×Dic11—28no—
263C22×Dic11—28no—
264C22×Dic11—28no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—28no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11—22no—
274C22×Dic11—22no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—22no—
278C22×Dic11—22no—
279C22×Dic11—44no—
280C22×Dic11—44no—
281C22×Dic11—416no—
282C22×Dic11—416no—
283C22×Dic11C22×C414yes—
284C22×Dic11C22×C414yes—
285C22×Dic11C2×D414yes—
286C22×Dic11C2×D414yes—
287C22×Dic11C2×D414yes—
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C22×Dic11C2412yes—
291C22×Dic11C2412yes—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C2×C4×D11—28no—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—416no—
301C2×C4×D11—416no—
302C11×C22⋊C4—28no—
303C11×C22⋊C4—28no—
304C11×C22⋊C4—44no—
305C22⋊Dic11—28no—
306C22⋊Dic11C22×C4116yescomplemented
307C22⋊Dic11C2×D4116yescomplemented
308(C2×D11)⋊C4—28no—
309(C2×D11)⋊C4—28no—
310(C2×D11)⋊C4—28no—
311(C2×D11)⋊C4—28no—
312(C2×D11)⋊C4—28no—
313(C2×D11)⋊C4C22×C4116yescomplemented
314(C2×D11)⋊C4C22×C4116yescomplemented
315(C2×D11)⋊C4C2×D4116yescomplemented
316C4⋊Dic11—28no—
317Dic11⋊C4—28no—
318Dic11⋊C4—44no—
319C4×Dic11—28no—
320C4×Dic11—28no—
321C4×Dic11—44no—
322C22×#120—111no—
323C22×C4×D4—111no—
324C22×C4×D4—111no—
325C23×C22⋊C4—111no—
326C23×C22⋊C4—111no—
327#2358—1116no—
328C2×#390—111no—
329C2×#388—111no—
330C2×#388—111no—
331C2×#386—111no—
332C2×#386—111no—
333C2×#386D1111yescharacteristic, complemented
334C2×#385—111no—
335C2×#385—111no—
336C2×C4×C22⋊C4—111no—
337C2×C4×C22⋊C4—111no—
338C23×C11—28no—
339C23×C11—28no—
340C23×C11—28no—
341C23×C11—28no—
342C23×C11—28no—
343C23×C11—28no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—28no—
349C23×C11—28no—
350C23×C11—28no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11—44no—
361C23×C11C4×D4116yescomplemented
362C23×C11C23×C414yes—
363C23×C11C23×C414yes—
364C23×C11C23×C412yes—
365C23×C11C22×D414yes—
366C23×C11C22×D412yes—
367C23×C11C22×D412yes—
368C23×C11C2×#4114yes—
369C23×C11C2×#4112yes—
370C23×C11C2×#4112yes—
371C23×C11H(5,𝔽2)12yes—
372C23×C11H(5,𝔽2)12yes—
373C23×C11C2511yescharacteristic
374C22×D11—28no—
375C22×D11—28no—
376C22×D11—28no—
377C22×D11—28no—
378C22×D11—28no—
379C22×D11—28no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—28no—
385C22×D11—28no—
386C22×D11—232no—
387C22×D11—28no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—232no—
395C22×D11—416no—
396C22×D11—4128no—
397C22×D11—416no—
398C22×D11—416no—
399C22×D11—416no—
400C22×D11—416no—
401C22×D11—44no—
402C22×D11—44no—
403C22×D11—44no—
404C22×D11—44no—
405C22×D11C4×D4116yescomplemented
406C22×D11C23×C414yes—
407C22×D11C23×C414yes—
408C22×D11C22×D414yes—
409C22×D11C2×#4114yes—
410D4×C11—232no—
411C2×C4×C11—28no—
412C2×C4×C11—28no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—416no—
427C2×C4×C11—44no—
428C2×C4×C11—44no—
429C2×C4×C11—44no—
430C2×C4×C11C23×C414yes—
431C2×C4×C11C22×D414yes—
432C22⋊D11—232no—
433C22⋊D11—416no—
434C2×Dic11—28no—
435C2×Dic11—28no—
436C2×Dic11—28no—
437C2×Dic11—28no—
438C2×Dic11—28no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—416no—
453C2×Dic11—416no—
454C2×Dic11—44no—
455C2×Dic11C23×C414yes—
456C2×Dic11C23×C414yes—
457C2×Dic11C22×D414yes—
458C2×Dic11C22×D414yes—
459C2×Dic11C22×D414yes—
460C4×D11—416no—
461C4×D11—416no—
462C26—111no—
463C23×D4—111no—
464C23×D4—111no—
465C23×D4C2×D1111yescharacteristic
466C24×C4—111no—
467C24×C4—111no—
468C24×C4—111no—
469C24×C4—111no—
470C24×C4C2×D1111yescharacteristic
471C2×#120—118no—
472C2×#120—1116no—
473C2×C4×D4—118no—
474C2×C4×D4—118no—
475C2×C4×D4—228no—
476C2×C4×D4—228no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C22⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—118no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C22⋊C4—118no—
493C22×C22⋊C4—228no—
494C22×C22⋊C4—228no—
495C22×C22⋊C4C2×D1111yescharacteristic
496C22×C22⋊C4C2×D1111yescharacteristic, complemented
497C22×C22⋊C4C2×D1111yescharacteristic, complemented
498C22×C42—111no—
499C22×C42—111no—
500C22×C42—111no—
501#390—118no—
502#388—118no—
503#388—118no—
504#386—118no—
505#386—118no—
506#386C2×D1118yescomplemented
507#385—118no—
508#385—118no—
509C4×C22⋊C4—118no—
510C4×C22⋊C4—118no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95C2×D1111yescharacteristic, complemented
516C2×#95C2×D1111yescharacteristic, complemented
517C22×C11—232no—
518C22×C11—24no—
519C22×C11—24no—
520C22×C11—24no—
521C22×C11—24no—
522C22×C11—24no—
523C22×C11—24no—
524C22×C11—24no—
525C22×C11—24no—
526C22×C11—24no—
527C22×C11—416no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—42no—
531C22×C11—42no—
532C22×C11C2×C4×D414yes—
533C22×C11C2×C4×D414yes—
534C22×C11C2×C4×D418yescomplemented
535C22×C11#51814yes—
536C22×C11D4214yes—
537C22×C11#54614yes—
538C22×C11#54614yes—
539C22×C11#55114yes—
540C22×C11C24×C411yescharacteristic
541C22×C11C23×D411yescharacteristic
542C22×C11C23×D411yescharacteristic
543C22×C11C22×#4111yescharacteristic
544C22×C11C22×#4111yescharacteristic
545C22×C11C2×H(5,𝔽2)11yescharacteristic
546C22×C11C2×H(5,𝔽2)11yescharacteristic
547C2×D11—232no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—24no—
552C2×D11—24no—
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—24no—
556C2×D11—24no—
557C2×D11—464no—
558C2×D11—416no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—42no—
563C2×D11C2×C4×D418yescomplemented
564C4×C11—24no—
565C4×C11—24no—
566C4×C11—42no—
567C4×C11—42no—
568C4×C11—42no—
569Dic11—24no—
570Dic11—24no—
571Dic11—24no—
572Dic11—24no—
573Dic11—24no—
574Dic11—42no—
575C25—111no—
576C25—111no—
577C25—118no—
578C25—114no—
579C25—224no—
580C25—224no—
581C25—224no—
582C25—224no—
583C25—442no—
584C25—442no—
585C25C22×D1111yescharacteristic
586C25C22×D1111yescharacteristic
587C22×D4—24no—
588C22×D4—24no—
589C22×D4—118no—
590C22×D4—114no—
591C22×D4—118no—
592C22×D4—114no—
593C22×D4—224no—
594C22×D4—224no—
595C22×D4—442no—
596C22×D4—442no—
597C22×D4C4×D1118yescomplemented
598C22×D4C22×D1114yes—
599C23×C4—24no—
600C23×C4—24no—
601C23×C4—42no—
602C23×C4—111no—
603C23×C4—111no—
604C23×C4—111no—
605C23×C4—111no—
606C23×C4—111no—
607C23×C4—111no—
608C23×C4—114no—
609C23×C4—114no—
610C23×C4—114no—
611C23×C4—114no—
612C23×C4—224no—
613C23×C4—224no—
614C23×C4—224no—
615C23×C4—224no—
616C23×C4—224no—
617C23×C4—224no—
618C23×C4—224no—
619C23×C4—224no—
620C23×C4—442no—
621C23×C4—442no—
622C23×C4—442no—
623C23×C4—442no—
624C23×C4C22×D1111yescharacteristic
625C23×C4C22×D1111yescharacteristic
626C23×C4C22×D1111yescharacteristic
627C23×C4C22×D1114yes—
628C23×C4C22×D1111yescharacteristic
629C23×C4C22×D1111yescharacteristic
630#120—1164no—
631C4×D4—2232no—
632C4×D4—2232no—
633C2×C4⋊C4—114no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—224no—
637C2×C4⋊C4—224no—
638C2×C4⋊C4—442no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—118no—
643C2×C22⋊C4—118no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—118no—
647C2×C22⋊C4—118no—
648C2×C22⋊C4—118no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—2232no—
659C2×C22⋊C4—2232no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—224no—
663C2×C22⋊C4—224no—
664C2×C22⋊C4—224no—
665C2×C22⋊C4—224no—
666C2×C22⋊C4C22×D1114yes—
667C2×C22⋊C4C22×D1114yescomplemented
668C2×C22⋊C4C22×D1114yescomplemented
669C2×C42—114no—
670C2×C42—114no—
671C2×C42—114no—
672C2×C42—224no—
673C2×C42—224no—
674C2×C42—442no—
675#95—114no—
676#95—114no—
677#95—114no—
678#95—114no—
679#95C22×D1114yescomplemented
680#95C22×D1114yescomplemented
681C2×C11—28no—
682C2×C11—44no—
683C2×C11#235818yescomplemented
684C2×C11C22×C4×D411yescharacteristic
685C2×C11C22×C4×D411yescharacteristic
686C2×C11C2×#51811yescharacteristic
687C2×C11C2×D4211yescharacteristic
688C2×C11C2×#54611yescharacteristic
689C2×C11C2×#54611yescharacteristic
690C2×C11C2×#55111yescharacteristic
691D11—28no—
692D11—44no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—22no—
703C24—114no—
704C24—114no—
705C24—114no—
706C24—112no—
707C24—114no—
708C24—112no—
709C24—1116no—
710C24—228no—
711C24—2232no—
712C24—228no—
713C24—222no—
714C24—222no—
715C24—222no—
716C24—222no—
717C24—2232no—
718C24—228no—
719C24—222no—
720C24—222no—
721C24—228no—
722C24—222no—
723C24—222no—
724C24—222no—
725C24—222no—
726C24—4416no—
727C24—444no—
728C24—444no—
729C24—4416no—
730C24—4416no—
731C24—4416no—
732C24—4416no—
733C24C2×C4×D1114yes—
734C24C2×C4×D1114yes—
735C24D4×D1114yes—
736C24#434114yes—
737C24C23×D1112yes—
738C24C23×D1112yes—
739C24C23×D1111yescharacteristic
740C2×D4—232no—
741C2×D4—28no—
742C2×D4—28no—
743C2×D4—1116no—
744C2×D4—1116no—
745C2×D4—228no—
746C2×D4—2232no—
747C2×D4—228no—
748C2×D4—4416no—
749C2×D4—444no—
750C2×D4—444no—
751C2×D4C2×C4×D11116yescomplemented
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—28no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—28no—
767C22×C4—44no—
768C22×C4—416no—
769C22×C4—114no—
770C22×C4—114no—
771C22×C4—114no—
772C22×C4—114no—
773C22×C4—114no—
774C22×C4—112no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—112no—
779C22×C4—112no—
780C22×C4—228no—
781C22×C4—228no—
782C22×C4—228no—
783C22×C4—228no—
784C22×C4—228no—
785C22×C4—228no—
786C22×C4—228no—
787C22×C4—222no—
788C22×C4—222no—
789C22×C4—222no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—222no—
798C22×C4—222no—
799C22×C4—228no—
800C22×C4—222no—
801C22×C4—444no—
802C22×C4—444no—
803C22×C4—4416no—
804C22×C4—4416no—
805C22×C4—444no—
806C22×C4—444no—
807C22×C4—4416no—
808C22×C4—4416no—
809C22×C4C2×C4×D1114yes—
810C22×C4D4×D1114yes—
811C22×C4C23×D1112yes—
812C22×C4C23×D1112yes—
813C22×C4C23×D1112yes—
814C22×C4C23×D1112yes—
815C22×C4C23×D1112yes—
816C4⋊C4—228no—
817C4⋊C4—228no—
818C4⋊C4—444no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—44no—
822C22⋊C4—1116no—
823C22⋊C4—1116no—
824C22⋊C4—1116no—
825C22⋊C4—1116no—
826C22⋊C4—1116no—
827C22⋊C4—228no—
828C22⋊C4—228no—
829C22⋊C4—228no—
830C22⋊C4—228no—
831C22⋊C4—228no—
832C22⋊C4—228no—
833C42—228no—
834C42—228no—
835C42—444no—
836C11C2×#235811yescharacteristic, complemented, Sylow
837C23—28no—
838C23—28no—
839C23—28no—
840C23—28no—
841C23—28no—
842C23—22no—
843C23—28no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—28no—
848C23—28no—
849C23—28no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—44no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—1116no—
861C23—114no—
862C23—114no—
863C23—114no—
864C23—114no—
865C23—2232no—
866C23—228no—
867C23—228no—
868C23—228no—
869C23—228no—
870C23—228no—
871C23—222no—
872C23—228no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—228no—
877C23—2232no—
878C23—228no—
879C23—228no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—222no—
885C23—222no—
886C23—4416no—
887C23—4416no—
888C23—4416no—
889C23—4416no—
890C23—44128no—
891C23—4416no—
892C23—444no—
893C23—444no—
894C23—444no—
895C23—444no—
896C23(C22⋊D11)⋊C4116yescomplemented
897C23C22×C4×D1114yes—
898C23C22×C4×D1114yes—
899C23C22×C4×D1112yes—
900C23C2×D4×D1114yes—
901C23C2×D4×D1112yes—
902C23C2×D4×D1112yes—
903C23C2×#434114yes—
904C23C2×#434112yes—
905C23#6703712yes—
906C23#41×D1112yes—
907C23#6704212yes—
908C23C24×D1111yescharacteristic
909D4—232no—
910D4—2232no—
911D4—4416no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—416no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—114no—
932C2×C4—114no—
933C2×C4—114no—
934C2×C4—114no—
935C2×C4—114no—
936C2×C4—228no—
937C2×C4—228no—
938C2×C4—228no—
939C2×C4—228no—
940C2×C4—228no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—4416no—
955C2×C4—4416no—
956C2×C4—4416no—
957C2×C4—4416no—
958C2×C4—444no—
959C2×C4C22×C4×D1114yes—
960C2×C4C2×D4×D1114yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—232no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—416no—
975C22—42no—
976C22—118no—
977C22—224no—
978C22—224no—
979C22—224no—
980C22—224no—
981C22—224no—
982C22—2232no—
983C22—224no—
984C22—224no—
985C22—224no—
986C22—224no—
987C22—4464no—
988C22—442no—
989C22—442no—
990C22—442no—
991C22—4416no—
992C22—442no—
993C22C2×(C22⋊D11)⋊C414yes—
994C22C2×(C22⋊D11)⋊C418yescomplemented
995C22C4×D4×D1114yes—
996C22#1062307614yes—
997C22#1062312214yes—
998C22#1062314014yes—
999C22#1062314114yes—
1000C22#1062318914yes—
1001C22C23×C4×D1111yescharacteristic
1002C22C22×D4×D1111yescharacteristic
1003C22C22×D4×D1111yescharacteristic
1004C22C22×#434111yescharacteristic
1005C22C2×#6703711yescharacteristic
1006C22C2×#41×D1111yescharacteristic
1007C22C2×#6704211yescharacteristic
1008C4—24no—
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—224no—
1014C4—224no—
1015C4—224no—
1016C4—224no—
1017C4—224no—
1018C4—442no—
1019C2—28no—
1020C2—44no—
1021C2—228no—
1022C2—444no—
1023C2#1307159618yesdirect product factor
1024C2C2×C4×D4×D1111yescharacteristic
1025C2C22×(C22⋊D11)⋊C411yescharacteristic
1026C2C2×#1062307611yescharacteristic
1027C2C2×#1062314011yescharacteristic
1028C2C2×#1062312211yescharacteristic
1029C2C2×#1062314111yescharacteristic
1030C2C2×#1062318911yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66990C2
cosocleC23×C11C25
hypercenterC2×#386D11
hypocenterC11C2×#2358
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic11C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. C23×(C2×D11)⋊C4C2semidirect
5. C22×C22⋊C4×D11C2semidirect
6. #13071596C2direct (N × H)
7. C2×#10622570C2semidirect
8. C2×#10622283C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622571C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622559C2semidirect
14. C2×C4×C22⋊Dic11C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#386C2semidirect
23. C24×Dic11C22semidirect
27. C22×C11×C22⋊C4C22semidirect
28. C22×C11×C22⋊C4C22semidirect
31. C22×C22⋊Dic11C22semidirect
32. C2×#66990C4semidirect
35. C2×D4×Dic11C22semidirect
45. C22×(C2×D11)⋊C4C22semidirect
46. C22×C4⋊Dic11C22semidirect
47. C22×Dic11⋊C4C22semidirect
48. C22×Dic11⋊C4C22semidirect
49. C22×C4×Dic11C22semidirect
50. C22×C4×Dic11C22semidirect
51. C22×C4×Dic11C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
55. C2×C22⋊C4×D11C22semidirect
56. C11×#386C22semidirect
57. C2×C11×#95C22semidirect
58. C2×C11×#95C22semidirect
59. C4×C22⋊Dic11C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. C2×C11⋊#95C22semidirect
63. C2×C11⋊#95C22semidirect
64. #10622571C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
67. #10622559C22semidirect
68. #10622283C22semidirect
69. #10622282C22semidirect
70. #10622281C22semidirect
71. #10622279C22semidirect
80. C24×D11C2×C4semidirect
86. C22×D4×C11C2×C4semidirect
101. C22×C22⋊D11C2×C4semidirect
102. C22×C22⋊D11C2×C4semidirect
118. C23×Dic11C23semidirect
131. C2×C11×C22⋊C4C23semidirect
132. C2×C11×C22⋊C4C23semidirect
134. C2×C22⋊Dic11C2×C4semidirect
135. C2×C22⋊Dic11D4semidirect
138. C2×C22⋊Dic11C23semidirect
139. #66990C2×C4semidirect
147. C2×(C2×D11)⋊C4C2×C4semidirect
148. C2×(C2×D11)⋊C4C2×C4semidirect
149. C2×(C2×D11)⋊C4D4semidirect
159. C2×C4⋊Dic11C23semidirect
162. C2×Dic11⋊C4C23semidirect
163. C2×Dic11⋊C4C23semidirect
167. C2×C4×Dic11C23semidirect
168. C2×C4×Dic11C23semidirect
169. C2×C4×Dic11C23semidirect
172. C11×#95C23semidirect
173. C11×#95C23semidirect
174. C11⋊#95C23semidirect
175. C11⋊#95C23semidirect
176. C11⋊#95C23semidirect
177. C11⋊#95C23semidirect
221. C23×D11C22×C4semidirect
229. C2×D4×C11C22×C4semidirect
260. C2×C22⋊D11C22×C4semidirect
261. C2×C22⋊D11C22×C4semidirect
306. C22⋊Dic11C22×C4semidirect
307. C22⋊Dic11C2×D4semidirect
313. (C2×D11)⋊C4C22×C4semidirect
314. (C2×D11)⋊C4C22×C4semidirect
315. (C2×D11)⋊C4C2×D4semidirect
333. C2×#386D11semidirect
361. C23×C11C4×D4semidirect
405. C22×D11C4×D4semidirect
496. C22×C22⋊C4C2×D11semidirect
497. C22×C22⋊C4C2×D11semidirect
506. #386C2×D11semidirect
515. C2×#95C2×D11semidirect
516. C2×#95C2×D11semidirect
534. C22×C11C2×C4×D4semidirect
563. C2×D11C2×C4×D4semidirect
597. C22×D4C4×D11semidirect
667. C2×C22⋊C4C22×D11semidirect
668. C2×C22⋊C4C22×D11semidirect
679. #95C22×D11semidirect
680. #95C22×D11semidirect
683. C2×C11#2358semidirect
751. C2×D4C2×C4×D11semidirect
836. C11C2×#2358semidirect
896. C23(C22⋊D11)⋊C4semidirect
994. C22C2×(C22⋊D11)⋊C4semidirect
1023. C2#13071596direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669902
C22×D4×Dic112
C22×(C22⋊D11)⋊C42
C23×(C2×D11)⋊C42
C22×C22⋊C4×D112
#130715962
C2×#106225702
C2×#106222832
C2×#106222822
C2×#106225712
C2×#106225692
C2×#106222812
C2×#106225592
C2×C4×C22⋊Dic112
C2×#106222792
C2×C11×#3862
C2×#235811