Finite Group Databasebeta

← C2×#13072000 #14922393

Subgroups — C2×#13072000 #14922393

Order 2816.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2C22×#66935C211yesmaximal, characteristic
3C22×#66925C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13072000C2116yesmaximal, direct product factor
6C2×#10622289C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622285C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622552C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622603C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic, complemented
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C22×C4⋊Dic11C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C22×Dic11⋊C4C2211yescharacteristic, complemented
45C22×Dic11⋊C4C2211yescharacteristic, complemented
46C22×Dic11⋊C4C2211yescharacteristic, complemented
47C22×C4×Dic11C2211yescharacteristic, complemented
48C2×#66947—28no—
49C2×#66947C2218yescomplemented
50C2×#66935—28no—
51C2×#66935C2218yes—
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54C2×#66925—28no—
55C2×#66925C2218yescomplemented
56C11×#388C2218yescomplemented
57C2×C11×#95C2211yescharacteristic, complemented
58C2×C11×#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61#10622603C2218yescomplemented
62#10622572C2218yescomplemented
63#10622570C2218yescomplemented
64#10622568C2218yescomplemented
65#10622561C2218yescomplemented
66#10622552C2218yescomplemented
67#10622289C2218yescomplemented
68#10622285C2218yescomplemented
69#10622281C2218yescomplemented
70#10622278C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—42no—
78C24×D11—42no—
79C24×D11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C24×D11C2314yes—
82C24×D11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×D44—24no—
99C22×D44—24no—
100C22×D44—24no—
101C22×D44—24no—
102C22×D44—24no—
103C22×D44—42no—
104C22×D44C2314yes—
105C22×D44C2314yes—
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—42no—
110C22×C4×D11—42no—
111C22×C4×D11D418yescomplemented
112C22×C4×D11C2314yes—
113C22×C4×D11C2314yes—
114C2×C11×C4⋊C4—24no—
115C2×C11×C4⋊C4C2314yescomplemented
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C42×C11—24no—
123C2×C42×C11C2314yescomplemented
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—42no—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—42no—
137C2×(C2×D11)⋊C4—42no—
138C2×(C2×D11)⋊C4—42no—
139C2×(C2×D11)⋊C4D418yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yescomplemented
149C2×(C2×D11)⋊C4C2314yescomplemented
150C2×(C2×D11)⋊C4C2314yescomplemented
151C2×(C2×D11)⋊C4C2314yescomplemented
152C2×C4⋊Dic11—42no—
153C2×C4⋊Dic11C2314yescomplemented
154C2×Dic11⋊C4—24no—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—42no—
158C2×Dic11⋊C4C2314yescomplemented
159C2×Dic11⋊C4C2314yescomplemented
160C2×Dic11⋊C4C2314yescomplemented
161C2×Dic11⋊C4C2314yescomplemented
162C2×C4×Dic11—24no—
163C2×C4×Dic11C2314yescomplemented
164#66947—232no—
165#66935—232no—
166C22⋊C4×D11—232no—
167#66925—232no—
168C11×#95C2314yescomplemented
169C11×#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2411—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—232no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—28no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—28no—
195C23×D11—28no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—28no—
204C23×D11—28no—
205C23×D11—44no—
206C23×D11—44no—
207C23×D11—416no—
208C23×D11—416no—
209C23×D11—416no—
210C23×D11—416no—
211C23×D11—416no—
212C23×D11—416no—
213C23×D11C2×D414yes—
214C23×D11C2×D414yes—
215C23×D11#4114yes—
216C23×D11#4114yes—
217C23×D11C2412yes—
218C23×D11C2412yes—
219C23×D11C2412yes—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
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×C11C2×D414yes—
237C22×C4×C11C2×D414yes—
238C22×C4×C11C2412yes—
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—44no—
247C2×C22⋊D11—416no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
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×Dic11C2×D414yes—
262C22×Dic11C2×D414yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
268C2×D44—28no—
269C2×D44—28no—
270C2×D44—28no—
271C2×D44—28no—
272C2×D44—28no—
273C2×D44—44no—
274C2×D44—416no—
275C2×D44—416no—
276C2×C4×D11—232no—
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×D11C2×D4116yescomplemented
284C11×C4⋊C4—28no—
285C11×C22⋊C4—28no—
286C11×C22⋊C4—28no—
287C11×C22⋊C4—28no—
288C42×C11—28no—
289C22⋊Dic11—28no—
290C22⋊Dic11—44no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4C2×D4116yes—
303C4⋊Dic11—44no—
304Dic11⋊C4—28no—
305Dic11⋊C4—28no—
306Dic11⋊C4—28no—
307Dic11⋊C4—44no—
308C4×Dic11—28no—
309C22×#123—111no—
310C22×#120—111no—
311C22×#117—111no—
312C23×C22⋊C4—111no—
313#2411—1116no—
314C2×#396—111no—
315C2×#396—111no—
316C2×#394—111no—
317C2×#394—111no—
318C2×#390—111no—
319C2×#390—111no—
320C2×#388—111no—
321C2×#388D1111yescharacteristic, complemented
322C2×#386—111no—
323C2×#385—111no—
324C2×#379—111no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11C22×D412yes—
339C23×C11C22×D412yes—
340C23×C11C2×#4114yes—
341C23×C11C2×#4112yes—
342C23×C11C2×#4112yes—
343C23×C11C2×#4112yes—
344C23×C11H(5,𝔽2)12yes—
345C23×C11H(5,𝔽2)12yes—
346C23×C11C2511yescharacteristic
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—232no—
358C22×D11—28no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—416no—
375C22×D11—416no—
376C22×D11—416no—
377C22×D11—416no—
378C22×D11—4128no—
379C22×D11—416no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—416no—
385C22×D11—44no—
386C22×D11—44no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11#121116yes—
393C22×D11C22×D414yes—
394C22×D11C22×D414yes—
395C22×D11C2×#4114yes—
396C22×D11C2×#4114yes—
397C2×C4×C11—28no—
398C2×C4×C11—28no—
399C2×C4×C11—22no—
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—22no—
415C2×C4×C11—44no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11—44no—
419C2×C4×C11C22×D414yes—
420C2×C4×C11C22×D414yes—
421C22⋊D11—416no—
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—44no—
438C2×Dic11—44no—
439C2×Dic11—44no—
440C2×Dic11C22×D414yes—
441C2×Dic11C22×D414yes—
442D44—416no—
443D44—416no—
444C4×D11—232no—
445C4×D11—416no—
446C26—111no—
447C23×D4—111no—
448C23×D4—111no—
449C23×D4—111no—
450C24×C4—111no—
451C24×C4—111no—
452C2×#123—118no—
453C2×#123—228no—
454C2×#120—118no—
455C2×#120—228no—
456C2×#117—118no—
457C2×#117—228no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
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—111no—
478C22×C22⋊C4—118no—
479C22×C22⋊C4—228no—
480C22×C22⋊C4C2×D1111yescharacteristic
481C22×C22⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4C2×D1111yescharacteristic
483C22×C42—111no—
484C22×C42C2×D1111yescharacteristic, complemented
485#396—118no—
486#396—118no—
487#394—118no—
488#394—118no—
489#390—118no—
490#390—118no—
491#388—118no—
492#388C2×D1118yescomplemented
493#386—118no—
494#385—118no—
495#379—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95C2×D1111yescharacteristic, complemented
499C2×#95C2×D1111yescharacteristic, complemented
500C22×C11—24no—
501C22×C11—24no—
502C22×C11—24no—
503C22×C11—42no—
504C22×C11—416no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11C2×#12114yes—
509C22×C11#52514yes—
510C22×C11#53514yes—
511C22×C11#54614yes—
512C22×C11#54614yes—
513C22×C11#55114yes—
514C22×C11#55114yes—
515C22×C11C23×D411yescharacteristic
516C22×C11C23×D411yescharacteristic
517C22×C11C22×#4111yescharacteristic
518C22×C11C22×#4111yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C2×H(5,𝔽2)11yescharacteristic
521C22×C11C2×H(5,𝔽2)11yescharacteristic
522C2×D11—232no—
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—24no—
531C2×D11—24no—
532C2×D11—464no—
533C2×D11—42no—
534C2×D11—416no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—88no—
546C2×D11C2×#12118yes—
547C4×C11—24no—
548C4×C11—24no—
549C4×C11—42no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11—42no—
553Dic11—24no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558C25—111no—
559C25—111no—
560C25—111no—
561C25—114no—
562C25—224no—
563C25—224no—
564C25—224no—
565C25—224no—
566C25—224no—
567C25—442no—
568C25—442no—
569C25C22×D1111yescharacteristic
570C22×D4—114no—
571C22×D4—114no—
572C22×D4—114no—
573C22×D4—224no—
574C22×D4—224no—
575C22×D4—224no—
576C22×D4—224no—
577C22×D4—224no—
578C22×D4—224no—
579C22×D4—224no—
580C22×D4—442no—
581C22×D4—442no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—118no—
585C23×C4—114no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—114no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4C22×D1111yescharacteristic
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—2232no—
602#120—2232no—
603#117—2232no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—224no—
611C2×C4⋊C4—224no—
612C2×C4⋊C4—224no—
613C2×C4⋊C4—442no—
614C2×C4⋊C4—442no—
615C2×C4⋊C4C22×D1114yescomplemented
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—118no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
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—2232no—
635C2×C22⋊C4—224no—
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—442no—
645C2×C22⋊C4—442no—
646C2×C22⋊C4—442no—
647C2×C22⋊C4—442no—
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1114yes—
650C2×C22⋊C4C22×D1114yes—
651C2×C42—24no—
652C2×C42—114no—
653C2×C42—224no—
654C2×C42C22×D1114yescomplemented
655#95—114no—
656#95—114no—
657#95C22×D1114yescomplemented
658#95C22×D1114yescomplemented
659C2×C11—44no—
660C2×C11#241118yescomplemented
661C2×C11C22×#12111yescharacteristic
662C2×C11C2×#52511yescharacteristic
663C2×C11C2×#53511yescharacteristic
664C2×C11C2×#54611yescharacteristic
665C2×C11C2×#54611yescharacteristic
666C2×C11C2×#55111yescharacteristic
667C2×C11C2×#55111yescharacteristic
668D11—28no—
669D11—44no—
670D11—82no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—114no—
678C24—114no—
679C24—114no—
680C24—112no—
681C24—114no—
682C24—112no—
683C24—112no—
684C24—228no—
685C24—228no—
686C24—228no—
687C24—228no—
688C24—2232no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24—222no—
693C24—228no—
694C24—222no—
695C24—222no—
696C24—222no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—444no—
708C24—444no—
709C24—4416no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24—4416no—
715C24#433914yes—
716C24C23×D1112yes—
717C24C23×D1111yescharacteristic
718C2×D4—228no—
719C2×D4—228no—
720C2×D4—228no—
721C2×D4—228no—
722C2×D4—228no—
723C2×D4—228no—
724C2×D4—228no—
725C2×D4—444no—
726C2×D4—4416no—
727C2×D4—4416no—
728C2×D4—444no—
729C2×D4—4416no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
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—114no—
747C22×C4—114no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—1116no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—228no—
755C22×C4—2232no—
756C22×C4—228no—
757C22×C4—228no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
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—444no—
772C22×C4—444no—
773C22×C4—4416no—
774C22×C4D4×D1114yes—
775C22×C4D4×D1114yes—
776C22×C4C23×D1112yes—
777C22×C4C23×D1112yes—
778C22×C4C23×D1112yes—
779C22×C4C23×D1112yes—
780C22×C4C23×D1112yes—
781C22×C4C23×D1112yes—
782C4⋊C4—28no—
783C4⋊C4—228no—
784C4⋊C4—228no—
785C4⋊C4—228no—
786C4⋊C4—444no—
787C4⋊C4—444no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—1116no—
792C22⋊C4—228no—
793C22⋊C4—228no—
794C22⋊C4—228no—
795C22⋊C4—228no—
796C22⋊C4—228no—
797C22⋊C4—228no—
798C22⋊C4—228no—
799C22⋊C4—228no—
800C22⋊C4—228no—
801C22⋊C4—444no—
802C22⋊C4—444no—
803C22⋊C4—444no—
804C22⋊C4—444no—
805C42—28no—
806C42—228no—
807C11C2×#241111yescharacteristic, complemented, Sylow
808C23—28no—
809C23—28no—
810C23—28no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—1116no—
822C23—114no—
823C23—114no—
824C23—114no—
825C23—114no—
826C23—2232no—
827C23—228no—
828C23—228no—
829C23—228no—
830C23—228no—
831C23—228no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—228no—
837C23—228no—
838C23—228no—
839C23—228no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—4416no—
854C23—4416no—
855C23—4416no—
856C23—4416no—
857C23—4416no—
858C23—4416no—
859C23—44128no—
860C23—444no—
861C23—444no—
862C23—444no—
863C23—444no—
864C23—444no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23—444no—
871C23C2×#433914yes—
872C23C2×#433912yes—
873C23C2×D4×D1112yes—
874C23C2×D4×D1112yes—
875C23#41×D1112yes—
876C23#41×D1112yes—
877C23#6704212yes—
878C23#6704212yes—
879C23C24×D1111yescharacteristic
880D4—4416no—
881D4—4416no—
882D4—4416no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
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—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—114no—
906C2×C4—114no—
907C2×C4—2232no—
908C2×C4—228no—
909C2×C4—228no—
910C2×C4—222no—
911C2×C4—222no—
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—4416no—
924C2×C4—444no—
925C2×C4—444no—
926C2×C4—444no—
927C2×C4C2×D4×D1114yes—
928C2×C4C2×D4×D1114yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—416no—
935C22—42no—
936C22—42no—
937C22—118no—
938C22—224no—
939C22—224no—
940C22—224no—
941C22—2232no—
942C22—224no—
943C22—224no—
944C22—224no—
945C22—224no—
946C22—224no—
947C22—224no—
948C22—4464no—
949C22—442no—
950C22—4416no—
951C22—442no—
952C22—442no—
953C22—442no—
954C22—442no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—888no—
962C22#1062305814yes—
963C22#1062307814yes—
964C22#1062308114yes—
965C22D11×#12114yes—
966C22#1062318514yes—
967C22#1062320514yes—
968C22#1062323614yes—
969C22C22×#433911yescharacteristic
970C22C22×D4×D1111yescharacteristic
971C22C22×D4×D1111yescharacteristic
972C22C2×#41×D1111yescharacteristic
973C22C2×#41×D1111yescharacteristic
974C22C2×#6704211yescharacteristic
975C22C2×#6704211yescharacteristic
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—224no—
983C4—224no—
984C4—442no—
985C4—442no—
986C4—442no—
987C2—44no—
988C2—228no—
989C2—444no—
990C2—882no—
991C2#1307200018yesdirect product factor
992C2C2×D11×#12111yescharacteristic
993C2C2×#1062307811yescharacteristic
994C2C2×#1062320511yescharacteristic
995C2C2×#1062318511yescharacteristic
996C2C2×#1062308111yescharacteristic
997C2C2×#1062305811yescharacteristic
998C2C2×#1062323611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC22×#66935C2
hypercenterC2×#388D11
hypocenterC11C2×#2411
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
3. C22×#66925C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13072000C2direct (N × H)
6. C2×#10622289C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622285C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622552C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622603C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622281C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#388C2semidirect
23. C22×C11×C4⋊C4C22semidirect
27. C22×C42×C11C22semidirect
38. C22×(C2×D11)⋊C4C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C22×(C2×D11)⋊C4C22semidirect
42. C22×C4⋊Dic11C22semidirect
43. C22×Dic11⋊C4C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. C22×Dic11⋊C4C22semidirect
46. C22×Dic11⋊C4C22semidirect
47. C22×C4×Dic11C22semidirect
49. C2×#66947C22semidirect
53. C2×C22⋊C4×D11C22semidirect
55. C2×#66925C22semidirect
56. C11×#388C22semidirect
57. C2×C11×#95C22semidirect
58. C2×C11×#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. #10622603C22semidirect
62. #10622572C22semidirect
63. #10622570C22semidirect
64. #10622568C22semidirect
65. #10622561C22semidirect
66. #10622552C22semidirect
67. #10622289C22semidirect
68. #10622285C22semidirect
69. #10622281C22semidirect
70. #10622278C22semidirect
111. C22×C4×D11D4semidirect
115. C2×C11×C4⋊C4C23semidirect
123. C2×C42×C11C23semidirect
148. C2×(C2×D11)⋊C4C23semidirect
149. C2×(C2×D11)⋊C4C23semidirect
150. C2×(C2×D11)⋊C4C23semidirect
151. C2×(C2×D11)⋊C4C23semidirect
153. C2×C4⋊Dic11C23semidirect
158. C2×Dic11⋊C4C23semidirect
159. C2×Dic11⋊C4C23semidirect
160. C2×Dic11⋊C4C23semidirect
161. C2×Dic11⋊C4C23semidirect
163. C2×C4×Dic11C23semidirect
168. C11×#95C23semidirect
169. C11×#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
283. C2×C4×D11C2×D4semidirect
321. C2×#388D11semidirect
463. C22×C4⋊C4C2×D11semidirect
484. C22×C42C2×D11semidirect
492. #388C2×D11semidirect
498. C2×#95C2×D11semidirect
499. C2×#95C2×D11semidirect
615. C2×C4⋊C4C22×D11semidirect
654. C2×C42C22×D11semidirect
657. #95C22×D11semidirect
658. #95C22×D11semidirect
660. C2×C11#2411semidirect
807. C11C2×#2411semidirect
991. C2#13072000direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669352
C22×#669252
C22×C22⋊C4×D112
#130720002
C2×#106222892
C2×#106225612
C2×#106222852
C2×#106225722
C2×#106225522
C2×#106225702
C2×#106226032
C2×#106222782
C2×#106222812
C2×#106225682
C2×C11×#3882
C2×#241111