Finite Group Databasebeta

← C2×#13072005 #14921332

Subgroups — C2×#13072005 #14921332

Order 2816.

5162 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2C22×#66935C211yesmaximal, characteristic
3C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13072005C2116yesmaximal, direct product factor
6C2×#10622565C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622278C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622277C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×#10622600C211yesmaximal, characteristic, complemented
16C2×C11×#397C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic, complemented
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
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, complemented
38C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C22×C4⋊Dic11C2211yescharacteristic, complemented
42C22×Dic11⋊C4C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C2×#66947—28no—
45C2×#66947C2218yescomplemented
46C2×#66935—28no—
47C2×#66935C2218yes—
48C2×C22⋊C4×D11—28no—
49C2×C22⋊C4×D11—28no—
50C2×C22⋊C4×D11C2218yescomplemented
51C2×C22⋊C4×D11C2218yescomplemented
52C11×#397C2218yescomplemented
53C2×C11×#95C2211yescharacteristic, complemented
54C2×C11×#95C2211yescharacteristic, complemented
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#10622600C2218yescomplemented
62#10622574C2218yescomplemented
63#10622572C2218yescomplemented
64#10622565C2218yescomplemented
65#10622281C2218yescomplemented
66#10622280C2218yescomplemented
67#10622278C2218yescomplemented
68#10622278C2218yescomplemented
69#10622278C2218yescomplemented
70#10622277C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—42no—
77C24×D11—42no—
78C24×D11D418yes—
79C24×D11C2311yescharacteristic
80C24×D11C2314yes—
81C24×D11C2311yescharacteristic
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—42no—
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—24no—
104C22×D44C2314yes—
105C22×D44C2314yes—
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—24no—
113C22×C4×D11—24no—
114C22×C4×D11—42no—
115C22×C4×D11—42no—
116C22×C4×D11—42no—
117C22×C4×D11—42no—
118C22×C4×D11C2314yes—
119C22×C4×D11C2314yes—
120C22×C4×D11C2314yes—
121C22×C4×D11C2314yes—
122C2×C11×C4⋊C4—24no—
123C2×C11×C4⋊C4C2314yescomplemented
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4—24no—
126C2×C11×C22⋊C4—24no—
127C2×C11×C22⋊C4C2314yes—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2314yes—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4—42no—
143C2×(C2×D11)⋊C4D418yescomplemented
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yescomplemented
151C2×(C2×D11)⋊C4C2314yescomplemented
152C2×(C2×D11)⋊C4C2314yescomplemented
153C2×(C2×D11)⋊C4C2314yescomplemented
154C2×C4⋊Dic11—42no—
155C2×C4⋊Dic11C2314yescomplemented
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—42no—
158C2×Dic11⋊C4C2314yescomplemented
159C2×Dic11⋊C4C2314yescomplemented
160#66947—232no—
161#66935—232no—
162C22⋊C4×D11—232no—
163C22⋊C4×D11—232no—
164C11×#95C2314yescomplemented
165C11×#95C2314yescomplemented
166C11×#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2412—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11C2×D414yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—232no—
191C23×D11—232no—
192C23×D11—28no—
193C23×D11—28no—
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—416no—
204C23×D11—44no—
205C23×D11—44no—
206C23×D11—416no—
207C23×D11—416no—
208C23×D11—416no—
209C23×D11—416no—
210C23×D11C2×D4116yes—
211C23×D11C2×D414yes—
212C23×D11C2×D414yes—
213C23×D11C2×D414yes—
214C23×D11#4114yes—
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×C11—22no—
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—44no—
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×Dic11—22no—
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—28no—
274C2×D44—416no—
275C2×D44—416no—
276C2×C4×D11—28no—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—416no—
289C2×C4×D11—416no—
290C2×C4×D11—416no—
291C2×C4×D11—416no—
292C11×C4⋊C4—28no—
293C11×C22⋊C4—28no—
294C11×C22⋊C4—28no—
295C11×C22⋊C4—28no—
296C22⋊Dic11—28no—
297C22⋊Dic11—28no—
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—28no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4C2×D4116yescomplemented
308C4⋊Dic11—44no—
309Dic11⋊C4—28no—
310Dic11⋊C4—44no—
311C22×#123—111no—
312C22×#120—111no—
313C23×C22⋊C4—111no—
314C23×C22⋊C4—111no—
315#2412—1116no—
316C2×#397—111no—
317C2×#397D1111yescharacteristic, complemented
318C2×#394—111no—
319C2×#394—111no—
320C2×#386—111no—
321C2×#386—111no—
322C2×#386—111no—
323C2×#385—111no—
324C2×#381—111no—
325C2×#380—111no—
326C2×#380—111no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—28no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11C22×D414yes—
341C23×C11C22×D412yes—
342C23×C11C22×D412yes—
343C23×C11C2×#4112yes—
344C23×C11C2×#4112yes—
345C23×C11C2×#4112yes—
346C23×C11H(5,𝔽2)12yes—
347C23×C11H(5,𝔽2)12yes—
348C23×C11C2511yescharacteristic
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—28no—
355C22×D11—28no—
356C22×D11—28no—
357C22×D11—28no—
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—232no—
370C22×D11—232no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—416no—
379C22×D11—4128no—
380C22×D11—416no—
381C22×D11—416no—
382C22×D11—416no—
383C22×D11—416no—
384C22×D11—44no—
385C22×D11—44no—
386C22×D11—44no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11#121116yes—
392C22×D11#123116yescomplemented
393C22×D11C22×D414yes—
394C22×D11C22×D414yes—
395C22×D11C22×D414yes—
396C22×D11C2×#4114yes—
397C22×D11C2×#4114yes—
398C22×D11C2×#4114yes—
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—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—44no—
418C2×C4×C11—44no—
419C2×C4×C11—44no—
420C2×C4×C11—44no—
421C2×C4×C11—44no—
422C2×C4×C11C22×D414yes—
423C22⋊D11—416no—
424C2×Dic11—28no—
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×Dic11—44no—
443C2×Dic11C22×D414yes—
444D44—416no—
445D44—416no—
446C4×D11—416no—
447C4×D11—416no—
448C4×D11—416no—
449C4×D11—416no—
450C26—111no—
451C23×D4—111no—
452C23×D4—111no—
453C23×D4—111no—
454C24×C4—111no—
455C24×C4—111no—
456C24×C4—111no—
457C24×C4—111no—
458C2×#123—118no—
459C2×#123—228no—
460C2×#120—118no—
461C2×#120—228no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4—111no—
464C22×C4⋊C4—111no—
465C22×C4⋊C4C2×D1111yescharacteristic, complemented
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—118no—
480C22×C22⋊C4—228no—
481C22×C22⋊C4—228no—
482C22×C22⋊C4C2×D1111yescharacteristic
483C22×C22⋊C4C2×D1111yescharacteristic
484C22×C22⋊C4C2×D1111yescharacteristic
485#397—118no—
486#397C2×D1118yescomplemented
487#394—118no—
488#394—118no—
489#386—118no—
490#386—118no—
491#386—118no—
492#385—118no—
493#381—118no—
494#380—118no—
495#380—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95C2×D1111yescharacteristic, complemented
502C2×#95C2×D1111yescharacteristic, complemented
503C2×#95C2×D1111yescharacteristic, complemented
504C22×C11—24no—
505C22×C11—24no—
506C22×C11—24no—
507C22×C11—416no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11C2×#12114yes—
513C22×C11C2×#12314yes—
514C22×C11#53414yes—
515C22×C11#54614yes—
516C22×C11#54614yes—
517C22×C11#55114yes—
518C22×C11#55114yes—
519C22×C11C23×D411yescharacteristic
520C22×C11C23×D411yescharacteristic
521C22×C11C22×#4111yescharacteristic
522C22×C11C22×#4111yescharacteristic
523C22×C11C22×#4111yescharacteristic
524C22×C11C2×H(5,𝔽2)11yescharacteristic
525C22×C11C2×H(5,𝔽2)11yescharacteristic
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—232no—
529C2×D11—232no—
530C2×D11—24no—
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—24no—
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—24no—
540C2×D11—464no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—88no—
549C2×D11C2×#12118yes—
550C2×D11C2×#12318yescomplemented
551C4×C11—24no—
552C4×C11—42no—
553C4×C11—42no—
554C4×C11—42no—
555C4×C11—42no—
556C4×C11—42no—
557Dic11—24no—
558Dic11—42no—
559Dic11—42no—
560Dic11—42no—
561Dic11—42no—
562C25—111no—
563C25—111no—
564C25—118no—
565C25—114no—
566C25—111no—
567C25—224no—
568C25—224no—
569C25—224no—
570C25—224no—
571C25—442no—
572C25—442no—
573C25C22×D1111yescharacteristic
574C22×D4—114no—
575C22×D4—114no—
576C22×D4—114no—
577C22×D4—224no—
578C22×D4—224no—
579C22×D4—224no—
580C22×D4—224no—
581C22×D4—224no—
582C22×D4—224no—
583C22×D4—224no—
584C22×D4—442no—
585C22×D4—442no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—114no—
592C23×C4—114no—
593C23×C4—114no—
594C23×C4—114no—
595C23×C4—224no—
596C23×C4—224no—
597C23×C4—224no—
598C23×C4—224no—
599C23×C4—224no—
600C23×C4—224no—
601C23×C4—224no—
602C23×C4—224no—
603C23×C4—442no—
604C23×C4—442no—
605C23×C4—442no—
606C23×C4—442no—
607C23×C4C22×D1111yescharacteristic
608C23×C4C22×D1111yescharacteristic
609C23×C4C22×D1111yescharacteristic
610C23×C4C22×D1111yescharacteristic
611C23×C4C22×D1111yescharacteristic
612C23×C4C22×D1111yescharacteristic
613#123—2232no—
614#120—2232no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—114no—
618C2×C4⋊C4—114no—
619C2×C4⋊C4—224no—
620C2×C4⋊C4—442no—
621C2×C4⋊C4—442no—
622C2×C4⋊C4C22×D1114yescomplemented
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—118no—
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—114no—
636C2×C22⋊C4—114no—
637C2×C22⋊C4—114no—
638C2×C22⋊C4—114no—
639C2×C22⋊C4—2232no—
640C2×C22⋊C4—2232no—
641C2×C22⋊C4—224no—
642C2×C22⋊C4—224no—
643C2×C22⋊C4—224no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4—224no—
646C2×C22⋊C4—224no—
647C2×C22⋊C4—224no—
648C2×C22⋊C4—224no—
649C2×C22⋊C4—224no—
650C2×C22⋊C4—442no—
651C2×C22⋊C4—442no—
652C2×C22⋊C4C22×D1114yes—
653C2×C22⋊C4C22×D1114yes—
654C2×C22⋊C4C22×D1114yes—
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95—114no—
660#95C22×D1114yescomplemented
661#95C22×D1114yescomplemented
662#95C22×D1114yescomplemented
663C2×C11—44no—
664C2×C11#241218yescomplemented
665C2×C11C22×#12111yescharacteristic
666C2×C11C22×#12311yescharacteristic
667C2×C11C2×#53411yescharacteristic
668C2×C11C2×#54611yescharacteristic
669C2×C11C2×#54611yescharacteristic
670C2×C11C2×#55111yescharacteristic
671C2×C11C2×#55111yescharacteristic
672D11—28no—
673D11—28no—
674D11—82no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—114no—
682C24—114no—
683C24—114no—
684C24—114no—
685C24—114no—
686C24—114no—
687C24—112no—
688C24—112no—
689C24—1116no—
690C24—112no—
691C24—228no—
692C24—2232no—
693C24—2232no—
694C24—228no—
695C24—228no—
696C24—228no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—222no—
708C24—222no—
709C24—222no—
710C24—222no—
711C24—222no—
712C24—4416no—
713C24—444no—
714C24—444no—
715C24—4416no—
716C24—4416no—
717C24—4416no—
718C24—4416no—
719C24D4×D1114yes—
720C24C23×D1112yes—
721C24C23×D1111yescharacteristic
722C2×D4—228no—
723C2×D4—228no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—4416no—
730C2×D4—4416no—
731C2×D4—444no—
732C2×D4—444no—
733C2×D4—4416no—
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—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—114no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—228no—
758C22×C4—228no—
759C22×C4—228no—
760C22×C4—228no—
761C22×C4—228no—
762C22×C4—228no—
763C22×C4—228no—
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—228no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4—444no—
782C22×C4—444no—
783C22×C4—4416no—
784C22×C4—4416no—
785C22×C4—4416no—
786C22×C4—4416no—
787C22×C4D4×D1114yes—
788C22×C4C23×D1112yes—
789C22×C4C23×D1112yes—
790C22×C4C23×D1112yes—
791C22×C4C23×D1112yes—
792C22×C4C23×D1112yes—
793C22×C4C23×D1112yes—
794C4⋊C4—28no—
795C4⋊C4—228no—
796C4⋊C4—444no—
797C4⋊C4—444no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—1116no—
802C22⋊C4—228no—
803C22⋊C4—228no—
804C22⋊C4—228no—
805C22⋊C4—228no—
806C22⋊C4—228no—
807C22⋊C4—228no—
808C22⋊C4—228no—
809C22⋊C4—228no—
810C22⋊C4—228no—
811C22⋊C4—444no—
812C22⋊C4—444no—
813C11C2×#241211yescharacteristic, complemented, Sylow
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—1116no—
828C23—1116no—
829C23—114no—
830C23—114no—
831C23—114no—
832C23—114no—
833C23—114no—
834C23—114no—
835C23—2232no—
836C23—2232no—
837C23—228no—
838C23—228no—
839C23—228no—
840C23—228no—
841C23—228no—
842C23—228no—
843C23—228no—
844C23—228no—
845C23—228no—
846C23—228no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—228no—
856C23—228no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—4416no—
865C23—4416no—
866C23—4416no—
867C23—44128no—
868C23—4416no—
869C23—4416no—
870C23—444no—
871C23—444no—
872C23—444no—
873C23—444no—
874C23—444no—
875C23—444no—
876C23—444no—
877C23C2×D4×D1114yes—
878C23C2×D4×D1112yes—
879C23C2×D4×D1112yes—
880C23#41×D1112yes—
881C23#41×D1112yes—
882C23#41×D1112yes—
883C23#6704212yes—
884C23#6704212yes—
885C23C24×D1111yescharacteristic
886D4—4416no—
887D4—4416no—
888D4—4416no—
889C2×C4—28no—
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—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—44no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—114no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—228no—
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—222no—
928C2×C4—4416no—
929C2×C4—4416no—
930C2×C4—4416no—
931C2×C4—4416no—
932C2×C4—444no—
933C2×C4—444no—
934C2×C4—444no—
935C2×C4—444no—
936C2×C4C2×D4×D1114yes—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—42no—
941C22—42no—
942C22—416no—
943C22—42no—
944C22—42no—
945C22—118no—
946C22—118no—
947C22—224no—
948C22—224no—
949C22—224no—
950C22—224no—
951C22—224no—
952C22—224no—
953C22—2232no—
954C22—2232no—
955C22—224no—
956C22—224no—
957C22—224no—
958C22—224no—
959C22—224no—
960C22—224no—
961C22—4464no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—888no—
970C22D11×#12114yes—
971C22D11×#12314yes—
972C22#1062318414yes—
973C22#1062318514yes—
974C22#1062320714yes—
975C22#1062323614yes—
976C22#1062323614yes—
977C22C22×D4×D1111yescharacteristic
978C22C22×D4×D1111yescharacteristic
979C22C2×#41×D1111yescharacteristic
980C22C2×#41×D1111yescharacteristic
981C22C2×#41×D1111yescharacteristic
982C22C2×#6704211yescharacteristic
983C22C2×#6704211yescharacteristic
984C4—24no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—224no—
991C4—442no—
992C4—442no—
993C4—442no—
994C4—442no—
995C2—44no—
996C2—228no—
997C2—228no—
998C2—882no—
999C2#1307200518yesdirect product factor
1000C2C2×D11×#12111yescharacteristic
1001C2C2×D11×#12311yescharacteristic
1002C2C2×#1062318411yescharacteristic
1003C2C2×#1062318511yescharacteristic
1004C2C2×#1062320711yescharacteristic
1005C2C2×#1062323611yescharacteristic
1006C2C2×#1062323611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC22×#66935C2
hypercenterC2×#397D11
hypocenterC11C2×#2412
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
3. C22×C22⋊C4×D11C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13072005C2direct (N × H)
6. C2×#10622565C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622277C2semidirect
14. C2×#10622280C2semidirect
15. C2×#10622600C2semidirect
16. C2×C11×#397C2semidirect
25. C22×C11×C4⋊C4C22semidirect
37. C22×(C2×D11)⋊C4C22semidirect
38. C22×(C2×D11)⋊C4C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C22×C4⋊Dic11C22semidirect
42. C22×Dic11⋊C4C22semidirect
43. C22×Dic11⋊C4C22semidirect
45. C2×#66947C22semidirect
50. C2×C22⋊C4×D11C22semidirect
51. C2×C22⋊C4×D11C22semidirect
52. C11×#397C22semidirect
53. C2×C11×#95C22semidirect
54. C2×C11×#95C22semidirect
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. #10622600C22semidirect
62. #10622574C22semidirect
63. #10622572C22semidirect
64. #10622565C22semidirect
65. #10622281C22semidirect
66. #10622280C22semidirect
67. #10622278C22semidirect
68. #10622278C22semidirect
69. #10622278C22semidirect
70. #10622277C22semidirect
123. C2×C11×C4⋊C4C23semidirect
143. C2×(C2×D11)⋊C4D4semidirect
150. C2×(C2×D11)⋊C4C23semidirect
151. C2×(C2×D11)⋊C4C23semidirect
152. C2×(C2×D11)⋊C4C23semidirect
153. C2×(C2×D11)⋊C4C23semidirect
155. C2×C4⋊Dic11C23semidirect
158. C2×Dic11⋊C4C23semidirect
159. C2×Dic11⋊C4C23semidirect
164. C11×#95C23semidirect
165. C11×#95C23semidirect
166. C11×#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
307. (C2×D11)⋊C4C2×D4semidirect
317. C2×#397D11semidirect
392. C22×D11#123semidirect
465. C22×C4⋊C4C2×D11semidirect
486. #397C2×D11semidirect
501. C2×#95C2×D11semidirect
502. C2×#95C2×D11semidirect
503. C2×#95C2×D11semidirect
550. C2×D11C2×#123semidirect
622. C2×C4⋊C4C22×D11semidirect
660. #95C22×D11semidirect
661. #95C22×D11semidirect
662. #95C22×D11semidirect
664. C2×C11#2412semidirect
813. C11C2×#2412semidirect
999. C2#13072005direct (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×C22⋊C4×D112
#130720052
C2×#106225652
C2×#106225742
C2×#106225722
C2×#106222782
C2×#106222812
C2×#106222772
C2×#106222802
C2×#106226002
C2×C11×#3972
C2×#241211