Finite Group Databasebeta

← C2×#13072737 #14921348

Subgroups — C2×#13072737 #14921348

Order 2816.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66989C211yesmaximal, characteristic, complemented
2C22×#66949C211yesmaximal, characteristic, complemented
3C22×#66990C211yesmaximal, characteristic
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13072737C2116yesmaximal, direct product factor
6C2×#10622565C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622286C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622603C211yesmaximal, characteristic, complemented
11C2×#10622557C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×Dic22C2211yescharacteristic, complemented
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic, complemented
28C22×C11×C22⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic, complemented
33C22×C22⋊Dic11C2211yescharacteristic, complemented
34C2×#66990—28no—
35C2×#66990C2218yes—
36C2×#66989—28no—
37C2×#66989C2218yescomplemented
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)⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C22×C4×Dic11C2211yescharacteristic, complemented
49C22×C4×Dic11C2211yescharacteristic, complemented
50C2×#66949—28no—
51C2×#66949C2218yescomplemented
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54C11×#394C2218yescomplemented
55C2×C11×#95C2211yescharacteristic, complemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61#10622603C2218yescomplemented
62#10622572C2218yescomplemented
63#10622570C2218yescomplemented
64#10622569C2218yescomplemented
65#10622569C2218yescomplemented
66#10622568C2218yescomplemented
67#10622565C2218yescomplemented
68#10622557C2218yescomplemented
69#10622286C2218yescomplemented
70#10622279C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—24no—
78C24×D11—42no—
79C24×D11—42no—
80C24×D11C2311yescharacteristic
81C24×D11C2314yes—
82C24×D11C2311yescharacteristic
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11—42no—
86C22×D4×C11C2314yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—42no—
111C22×C4×D11—42no—
112C22×C4×D11C2314yes—
113C22×C4×D11C2314yes—
114C22×Dic22—24no—
115C22×Dic22—24no—
116C22×Dic22—42no—
117C22×Dic22C2314yescomplemented
118C2×C11×C4⋊C4—24no—
119C2×C11×C4⋊C4C2314yescomplemented
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—42no—
122C2×C11×C22⋊C4—42no—
123C2×C11×C22⋊C4—42no—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yescomplemented
127C2×C11×C22⋊C4C2314yescomplemented
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11D418yescomplemented
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yescomplemented
137C2×C22⋊Dic11C2314yescomplemented
138#66990—232no—
139#66989—232no—
140C2×(C2×D11)⋊C4—24no—
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—42no—
147C2×(C2×D11)⋊C4D418yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
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×Dic11⋊C4—24no—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4C2314yescomplemented
159C2×Dic11⋊C4C2314yescomplemented
160C2×C4×Dic11—24no—
161C2×C4×Dic11—42no—
162C2×C4×Dic11C2314yescomplemented
163C2×C4×Dic11C2314yescomplemented
164#66949—232no—
165C22⋊C4×D11—232no—
166C11×#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2472—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11C2×D414yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—232no—
195C23×D11—28no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—28no—
203C23×D11—28no—
204C23×D11—28no—
205C23×D11—28no—
206C23×D11—44no—
207C23×D11—44no—
208C23×D11—416no—
209C23×D11—416no—
210C23×D11—416no—
211C23×D11—416no—
212C23×D11—416no—
213C23×D11—416no—
214C23×D11C2×D414yes—
215C23×D11#4114yes—
216C23×D11#4114yes—
217C23×D11#4114yes—
218C23×D11C2412yes—
219C23×D11C2412yes—
220C2×D4×C11—28no—
221C2×D4×C11—28no—
222C2×D4×C11—44no—
223C2×D4×C11—416no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
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×C11C2×D414yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—416no—
251C2×C22⋊D11—416no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11C2×D414yes—
268C22×Dic11C2×D414yes—
269C22×Dic11C2×D414yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C2×C4×D11—28no—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—416no—
283C2×C4×D11—416no—
284C2×Dic22—28no—
285C2×Dic22—28no—
286C2×Dic22—44no—
287C2×Dic22—416no—
288C11×C4⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—44no—
291C11×C22⋊C4—44no—
292C11×C22⋊C4—44no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—28no—
296C22⋊Dic11—28no—
297C22⋊Dic11C2×D4116yescomplemented
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—28no—
301(C2×D11)⋊C4—28no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4C2×D4116yes—
306Dic11⋊C4—28no—
307Dic11⋊C4—28no—
308C4×Dic11—28no—
309C4×Dic11—44no—
310C22×#124—111no—
311C22×C22⋊Q8—111no—
312C22×#120—111no—
313C23×C22⋊C4—111no—
314#2472—1116no—
315C2×#397—111no—
316C2×#394—111no—
317C2×#394D1111yescharacteristic, complemented
318C2×#393—111no—
319C2×#390—111no—
320C2×#388—111no—
321C2×#388—111no—
322C2×#386—111no—
323C2×#386—111no—
324C2×#379—111no—
325C2×C4×C22⋊C4—111no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11—44no—
351C23×C11—44no—
352C23×C11—44no—
353C23×C11C22×D414yes—
354C23×C11C22×D412yes—
355C23×C11C22×D412yes—
356C23×C11C2×#4112yes—
357C23×C11C2×#4112yes—
358C23×C11C2×#4112yes—
359C23×C11H(5,𝔽2)12yes—
360C23×C11H(5,𝔽2)12yes—
361C23×C11C2511yescharacteristic
362C22×D11—28no—
363C22×D11—28no—
364C22×D11—28no—
365C22×D11—28no—
366C22×D11—28no—
367C22×D11—28no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—232no—
373C22×D11—28no—
374C22×D11—28no—
375C22×D11—28no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—416no—
383C22×D11—416no—
384C22×D11—416no—
385C22×D11—416no—
386C22×D11—416no—
387C22×D11—4128no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—416no—
393C22×D11#124116yescomplemented
394C22×D11C22×D414yes—
395C22×D11C2×#4114yes—
396C22×D11C2×#4114yes—
397C22×D11C2×#4114yes—
398D4×C11—416no—
399C2×C4×C11—28no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—44no—
415C2×C4×C11—44no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11C22×D414yes—
419C22⋊D11—416no—
420C22⋊D11—416no—
421C2×Dic11—28no—
422C2×Dic11—28no—
423C2×Dic11—28no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—44no—
440C2×Dic11—44no—
441C2×Dic11—44no—
442C2×Dic11C22×D414yes—
443C2×Dic11C22×D414yes—
444C2×Dic11C22×D414yes—
445C4×D11—416no—
446C4×D11—416no—
447Dic22—416no—
448C26—111no—
449C23×Q8—111no—
450C23×D4—111no—
451C23×D4—111no—
452C23×D4C2×D1111yescharacteristic
453C24×C4—111no—
454C24×C4—111no—
455C2×#124—118no—
456C2×#124—228no—
457C2×C22⋊Q8—118no—
458C2×C22⋊Q8—228no—
459C2×#120—118no—
460C2×#120—228no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4C2×D1111yescharacteristic, complemented
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C22⋊C4—111no—
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4—111no—
477C22×C22⋊C4—118no—
478C22×C22⋊C4—228no—
479C22×C22⋊C4C2×D1111yescharacteristic
480C22×C22⋊C4C2×D1111yescharacteristic
481C22×C22⋊C4C2×D1111yescharacteristic, complemented
482C22×C22⋊C4C2×D1111yescharacteristic, complemented
483C22×C42—111no—
484C22×C42—111no—
485#397—118no—
486#394—118no—
487#394C2×D1118yescomplemented
488#393—118no—
489#390—118no—
490#388—118no—
491#388—118no—
492#386—118no—
493#386—118no—
494#379—118no—
495C4×C22⋊C4—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95C2×D1111yescharacteristic, complemented
502C22×C11—24no—
503C22×C11—24no—
504C22×C11—24no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—416no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—88no—
518C22×C11#52514yes—
519C22×C11C2×#12414yes—
520C22×C11#53814yes—
521C22×C11D4214yes—
522C22×C11#54614yes—
523C22×C11#54614yes—
524C22×C11#55114yes—
525C22×C11C23×D411yescharacteristic
526C22×C11C23×D411yescharacteristic
527C22×C11C22×#4111yescharacteristic
528C22×C11C22×#4111yescharacteristic
529C22×C11C22×#4111yescharacteristic
530C22×C11C2×H(5,𝔽2)11yescharacteristic
531C22×C11C2×H(5,𝔽2)11yescharacteristic
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—24no—
537C2×D11—24no—
538C2×D11—232no—
539C2×D11—24no—
540C2×D11—24no—
541C2×D11—24no—
542C2×D11—464no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—416no—
548C2×D11C2×#12418yescomplemented
549C4×C11—24no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11—42no—
553C4×C11—42no—
554Dic11—24no—
555Dic11—24no—
556Dic11—24no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25—111no—
561C25—111no—
562C25—114no—
563C25—224no—
564C25—224no—
565C25—224no—
566C25—224no—
567C25—224no—
568C25—442no—
569C25—442no—
570C25C22×D1111yescharacteristic
571C25C22×D1111yescharacteristic
572C22×Q8—114no—
573C22×Q8—224no—
574C22×Q8—224no—
575C22×Q8—442no—
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—42no—
579C22×D4—114no—
580C22×D4—114no—
581C22×D4—224no—
582C22×D4—224no—
583C22×D4—224no—
584C22×D4—224no—
585C22×D4—224no—
586C22×D4—442no—
587C22×D4C22×D1114yes—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—114no—
595C23×C4—114no—
596C23×C4—224no—
597C23×C4—224no—
598C23×C4—224no—
599C23×C4—224no—
600C23×C4—442no—
601C23×C4—442no—
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#124—2232no—
608C22⋊Q8—2232no—
609#120—2232no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4—224no—
615C2×C4⋊C4C22×D1114yescomplemented
616C2×C22⋊C4—24no—
617C2×C22⋊C4—42no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—42no—
620C2×C22⋊C4—118no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—118no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4—114no—
633C2×C22⋊C4—114no—
634C2×C22⋊C4—114no—
635C2×C22⋊C4—2232no—
636C2×C22⋊C4—224no—
637C2×C22⋊C4—224no—
638C2×C22⋊C4—224no—
639C2×C22⋊C4—224no—
640C2×C22⋊C4—224no—
641C2×C22⋊C4—224no—
642C2×C22⋊C4—224no—
643C2×C22⋊C4—224no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4—224no—
646C2×C22⋊C4—442no—
647C2×C22⋊C4C22×D1114yes—
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1114yescomplemented
650C2×C22⋊C4C22×D1114yescomplemented
651C2×C42—114no—
652C2×C42—114no—
653C2×C42—224no—
654C2×C42—442no—
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95—114no—
660#95C22×D1114yescomplemented
661C2×C11—44no—
662C2×C11—82no—
663C2×C11#247218yescomplemented
664C2×C11C2×#52511yescharacteristic
665C2×C11C22×#12411yescharacteristic
666C2×C11C2×#53811yescharacteristic
667C2×C11C2×D4211yescharacteristic
668C2×C11C2×#54611yescharacteristic
669C2×C11C2×#54611yescharacteristic
670C2×C11C2×#55111yescharacteristic
671D11—28no—
672D11—44no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—114no—
687C24—114no—
688C24—114no—
689C24—112no—
690C24—114no—
691C24—112no—
692C24—228no—
693C24—228no—
694C24—228no—
695C24—228no—
696C24—2232no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—228no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—222no—
708C24—444no—
709C24—444no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24—4416no—
715C24—4416no—
716C24D4×D1114yes—
717C24C23×D1112yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×Q8—228no—
721C2×Q8—228no—
722C2×Q8—444no—
723C2×Q8—4416no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—44no—
727C2×D4—416no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—228no—
731C2×D4—228no—
732C2×D4—228no—
733C2×D4—444no—
734C2×D4—4416no—
735C2×D4—4416no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—114no—
751C22×C4—114no—
752C22×C4—114no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—228no—
760C22×C4—228no—
761C22×C4—228no—
762C22×C4—228no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—222no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4—4416no—
781C22×C4—4416no—
782C22×C4D4×D1114yes—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C4⋊C4—28no—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C22⋊C4—28no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—1116no—
796C22⋊C4—1116no—
797C22⋊C4—228no—
798C22⋊C4—228no—
799C22⋊C4—228no—
800C22⋊C4—228no—
801C22⋊C4—228no—
802C22⋊C4—228no—
803C22⋊C4—228no—
804C22⋊C4—228no—
805C22⋊C4—228no—
806C22⋊C4—228no—
807C22⋊C4—444no—
808C42—228no—
809C42—444no—
810C11C2×#247211yescharacteristic, complemented, Sylow
811C23—28no—
812C23—28no—
813C23—28no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—114no—
839C23—114no—
840C23—114no—
841C23—1116no—
842C23—114no—
843C23—2232no—
844C23—228no—
845C23—228no—
846C23—228no—
847C23—228no—
848C23—228no—
849C23—222no—
850C23—228no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—228no—
855C23—228no—
856C23—222no—
857C23—222no—
858C23—228no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—4416no—
864C23—4416no—
865C23—4416no—
866C23—4416no—
867C23—4416no—
868C23—4416no—
869C23—44128no—
870C23—444no—
871C23—444no—
872C23—444no—
873C23—444no—
874C23C2×D4×D1114yes—
875C23C2×D4×D1112yes—
876C23C2×D4×D1112yes—
877C23#6703712yes—
878C23#6703712yes—
879C23#41×D1112yes—
880C23#41×D1112yes—
881C23#41×D1112yes—
882C23C24×D1111yescharacteristic
883Q8—4416no—
884D4—416no—
885D4—4416no—
886D4—4416no—
887C2×C4—28no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—114no—
907C2×C4—114no—
908C2×C4—114no—
909C2×C4—228no—
910C2×C4—228no—
911C2×C4—228no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—4416no—
928C2×C4—4416no—
929C2×C4—444no—
930C2×C4—444no—
931C2×C4—444no—
932C2×C4C2×D4×D1114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—416no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—88no—
949C22—118no—
950C22—224no—
951C22—224no—
952C22—2232no—
953C22—224no—
954C22—224no—
955C22—224no—
956C22—224no—
957C22—224no—
958C22—224no—
959C22—224no—
960C22—4464no—
961C22—442no—
962C22—442no—
963C22—4416no—
964C22—442no—
965C22—442no—
966C22#1062312114yes—
967C22#1062314114yes—
968C22#1062314314yes—
969C22#1062314414yes—
970C22#1062318714yes—
971C22#1062319014yes—
972C22D11×#12414yes—
973C22C22×D4×D1111yescharacteristic
974C22C22×D4×D1111yescharacteristic
975C22C2×#6703711yescharacteristic
976C22C2×#6703711yescharacteristic
977C22C2×#41×D1111yescharacteristic
978C22C2×#41×D1111yescharacteristic
979C22C2×#41×D1111yescharacteristic
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—224no—
986C4—224no—
987C4—224no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—44no—
992C2—82no—
993C2—228no—
994C2—444no—
995C2#1307273718yesdirect product factor
996C2C2×#1062318711yescharacteristic
997C2C2×D11×#12411yescharacteristic
998C2C2×#1062314411yescharacteristic
999C2C2×#1062312111yescharacteristic
1000C2C2×#1062314111yescharacteristic
1001C2C2×#1062314311yescharacteristic
1002C2C2×#1062319011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66990C2
hypercenterC2×#394D11
hypocenterC11C2×#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66989C2semidirect
2. C22×#66949C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13072737C2direct (N × H)
6. C2×#10622565C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622286C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622603C2semidirect
11. C2×#10622557C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622568C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#394C2semidirect
23. C23×Dic22C22semidirect
24. C22×C11×C4⋊C4C22semidirect
27. C22×C11×C22⋊C4C22semidirect
28. C22×C11×C22⋊C4C22semidirect
32. C22×C22⋊Dic11C22semidirect
33. C22×C22⋊Dic11C22semidirect
37. C2×#66989C22semidirect
46. C22×Dic11⋊C4C22semidirect
47. C22×Dic11⋊C4C22semidirect
48. C22×C4×Dic11C22semidirect
49. C22×C4×Dic11C22semidirect
51. C2×#66949C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. C11×#394C22semidirect
55. C2×C11×#95C22semidirect
56. C2×C11⋊#95C22semidirect
57. C2×C11⋊#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. #10622603C22semidirect
62. #10622572C22semidirect
63. #10622570C22semidirect
64. #10622569C22semidirect
65. #10622569C22semidirect
66. #10622568C22semidirect
67. #10622565C22semidirect
68. #10622557C22semidirect
69. #10622286C22semidirect
70. #10622279C22semidirect
117. C22×Dic22C23semidirect
119. C2×C11×C4⋊C4C23semidirect
126. C2×C11×C22⋊C4C23semidirect
127. C2×C11×C22⋊C4C23semidirect
132. C2×C22⋊Dic11D4semidirect
136. C2×C22⋊Dic11C23semidirect
137. C2×C22⋊Dic11C23semidirect
158. C2×Dic11⋊C4C23semidirect
159. C2×Dic11⋊C4C23semidirect
162. C2×C4×Dic11C23semidirect
163. C2×C4×Dic11C23semidirect
166. C11×#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
297. C22⋊Dic11C2×D4semidirect
317. C2×#394D11semidirect
393. C22×D11#124semidirect
463. C22×C4⋊C4C2×D11semidirect
481. C22×C22⋊C4C2×D11semidirect
482. C22×C22⋊C4C2×D11semidirect
487. #394C2×D11semidirect
501. C2×#95C2×D11semidirect
548. C2×D11C2×#124semidirect
615. C2×C4⋊C4C22×D11semidirect
649. C2×C22⋊C4C22×D11semidirect
650. C2×C22⋊C4C22×D11semidirect
660. #95C22×D11semidirect
663. C2×C11#2472semidirect
810. C11C2×#2472semidirect
995. C2#13072737direct (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×#669492
C22×#669902
C22×C22⋊C4×D112
#130727372
C2×#106225652
C2×#106225722
C2×#106222862
C2×#106225702
C2×#106226032
C2×#106225572
C2×#106225692
C2×#106225682
C2×#106222792
C2×C11×#3942
C2×#247211