Finite Group Databasebeta

← C2×#13072738 #14921346

Subgroups — C2×#13072738 #14921346

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×#66999C211yesmaximal, characteristic, complemented
2C22×#66990C211yesmaximal, characteristic
3C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4#13072738C2116yesmaximal, direct product factor
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622844C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622564C211yesmaximal, characteristic, complemented
11C2×#10622553C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C22×C11×#124C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic, complemented
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C2×C11×#124—28no—
25C2×C11×#124C2218yescomplemented
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic, complemented
29C22×C11×C22⋊C4C2211yescharacteristic, complemented
30C22×C42×C11C2211yescharacteristic, complemented
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic, complemented
35C22×C22⋊Dic11C2211yescharacteristic, complemented
36C2×#66999—28no—
37C2×#66999C2218yescomplemented
38C2×#66990—28no—
39C2×#66990C2218yes—
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×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×C4⋊Dic11C2211yescharacteristic, complemented
49C22×Dic11⋊C4C2211yescharacteristic, complemented
50C22×Dic11⋊C4C2211yescharacteristic, complemented
51C22×C4×Dic11C2211yescharacteristic, complemented
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54#10622844C2218yescomplemented
55#10622835C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62#10622574C2218yescomplemented
63#10622570C2218yescomplemented
64#10622569C2218yescomplemented
65#10622569C2218yescomplemented
66#10622568C2218yescomplemented
67#10622565C2218yescomplemented
68#10622564C2218yescomplemented
69#10622553C2218yescomplemented
70C4×(C2×D11)⋊C4C2218yescomplemented
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×Q8×C11—24no—
84C22×Q8×C11—24no—
85C22×Q8×C11—42no—
86C22×Q8×C11C2314yescomplemented
87C22×D4×C11—24no—
88C22×D4×C11—24no—
89C22×D4×C11—42no—
90C22×D4×C11C2314yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11—42no—
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
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×D11C2314yes—
117C22×C4×D11C2314yes—
118C11×#124—232no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4D418yescomplemented
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yescomplemented
126C2×C11×C22⋊C4C2314yescomplemented
127C2×C42×C11—24no—
128C2×C42×C11C2314yescomplemented
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—42no—
132C2×C22⋊Dic11—42no—
133C2×C22⋊Dic11—42no—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yescomplemented
138C2×C22⋊Dic11C2314yescomplemented
139#66999—232no—
140#66990—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—24no—
147C2×(C2×D11)⋊C4—42no—
148C2×(C2×D11)⋊C4D418yes—
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×(C2×D11)⋊C4C2314yes—
157C2×C4⋊Dic11—24no—
158C2×C4⋊Dic11C2314yescomplemented
159C2×Dic11⋊C4—24no—
160C2×Dic11⋊C4—24no—
161C2×Dic11⋊C4C2314yescomplemented
162C2×Dic11⋊C4C2314yescomplemented
163C2×C4×Dic11—42no—
164C2×C4×Dic11C2314yescomplemented
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×Q8×C11—28no—
221C2×Q8×C11—28no—
222C2×Q8×C11—44no—
223C2×Q8×C11—416no—
224C2×D4×C11—28no—
225C2×D4×C11—28no—
226C2×D4×C11—44no—
227C2×D4×C11—416no—
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×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11C2×D414yes—
241C22×C4×C11C2×D414yes—
242C22×C4×C11C2×D414yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—416no—
255C2×C22⋊D11—416no—
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×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11C2×D414yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
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—416no—
287C2×C4×D11—416no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—28no—
291C11×C22⋊C4C2×D4116yescomplemented
292C42×C11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—44no—
296C22⋊Dic11—44no—
297C22⋊Dic11—44no—
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—
306C4⋊Dic11—28no—
307Dic11⋊C4—28no—
308Dic11⋊C4—28no—
309C4×Dic11—44no—
310C22×#124D1111yescharacteristic, complemented
311C22×C22⋊Q8—111no—
312C22×#120—111no—
313C23×C22⋊C4—111no—
314#2472—1116no—
315C2×#397—111no—
316C2×#394—111no—
317C2×#394—111no—
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×D412yes—
354C23×C11C22×D414yes—
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—
398Q8×C11—416no—
399D4×C11—416no—
400C2×C4×C11—28no—
401C2×C4×C11—28no—
402C2×C4×C11—28no—
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×C11C22×D414yes—
418C2×C4×C11C22×D414yes—
419C2×C4×C11C22×D414yes—
420C22⋊D11—416no—
421C22⋊D11—416no—
422C2×Dic11—28no—
423C2×Dic11—22no—
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—22no—
440C2×Dic11—44no—
441C2×Dic11—44no—
442C2×Dic11—44no—
443C2×Dic11—44no—
444C2×Dic11—44no—
445C2×Dic11C22×D414yes—
446C4×D11—416no—
447C4×D11—416no—
448C26—111no—
449C23×Q8C2×D1111yescharacteristic, complemented
450C23×D4—111no—
451C23×D4—111no—
452C23×D4C2×D1111yescharacteristic
453C24×C4—111no—
454C24×C4—111no—
455C2×#124—28no—
456C2×#124C2×D1118yescomplemented
457C2×C22⋊Q8—118no—
458C2×C22⋊Q8—228no—
459C2×#120—118no—
460C2×#120—228no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4—111no—
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×C42C2×D1111yescharacteristic, complemented
485#397—118no—
486#394—118no—
487#394—118no—
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×#95—111no—
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—24no—
551C4×C11—24no—
552C4×C11—42no—
553C4×C11—42no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
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—24no—
573C22×Q8—24no—
574C22×Q8—42no—
575C22×Q8C22×D1114yescomplemented
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—232no—
608C22⋊Q8—2232no—
609#120—2232no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4—224no—
615C2×C4⋊C4—224no—
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—224no—
634C2×C22⋊C4—224no—
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—2232no—
642C2×C22⋊C4—442no—
643C2×C22⋊C4—442no—
644C2×C22⋊C4—442no—
645C2×C22⋊C4—442no—
646C2×C22⋊C4C22⋊D1118yescomplemented
647C2×C22⋊C4C22×D1114yes—
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1114yescomplemented
650C2×C22⋊C4C22×D1114yescomplemented
651C2×C42—24no—
652C2×C42—114no—
653C2×C42—442no—
654C2×C42C22×D1114yescomplemented
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95—114no—
660#95—114no—
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—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—228no—
707C24—222no—
708C24—444no—
709C24—444no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24—4416no—
715C24—4416no—
716C24C2×C22⋊D1114yes—
717C24C23×D1112yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—44no—
723C2×Q8—416no—
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—114no—
749C22×C4—112no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—228no—
756C22×C4—228no—
757C22×C4—222no—
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—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—228no—
775C22×C4—228no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—4416no—
779C22×C4—4416no—
780C22×C4D4×D1114yes—
781C22×C4C2×C22⋊D1114yes—
782C22×C4C2×C22⋊D1114yes—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C4⋊C4—228no—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—1116no—
795C22⋊C4—228no—
796C22⋊C4—228no—
797C22⋊C4—228no—
798C22⋊C4—228no—
799C22⋊C4—228no—
800C22⋊C4—228no—
801C22⋊C4—228no—
802C22⋊C4—228no—
803C22⋊C4—444no—
804C22⋊C4—444no—
805C22⋊C4—444no—
806C22⋊C4—444no—
807C22⋊C4C2×C22⋊D11116yescomplemented
808C42—28no—
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—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—228no—
852C23—228no—
853C23—228no—
854C23—228no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—228no—
862C23—228no—
863C23—4416no—
864C23—4416no—
865C23—4416no—
866C23—4416no—
867C23—4416no—
868C23—4416no—
869C23—44128no—
870C23—444no—
871C23—444no—
872C23—444no—
873C23—444no—
874C23C2×D4×D1112yes—
875C23#6703712yes—
876C23#41×D1112yes—
877C23#41×D1112yes—
878C23#41×D1112yes—
879C23#6704212yes—
880C23C22×C22⋊D1114yes—
881C23C22×C22⋊D1112yes—
882C23C24×D1111yescharacteristic
883Q8—416no—
884D4—416no—
885D4—4416no—
886D4—4416no—
887C2×C4—28no—
888C2×C4—28no—
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—44no—
903C2×C4—44no—
904C2×C4—114no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—228no—
908C2×C4—222no—
909C2×C4—222no—
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—4416no—
925C2×C4—444no—
926C2×C4—444no—
927C2×C4—444no—
928C2×C4—444no—
929C2×C4—444no—
930C2×C4C2×D4×D1114yes—
931C2×C4C22×C22⋊D1114yes—
932C2×C4C22×C22⋊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—
966C22D11×#12414yes—
967C22#1062320714yes—
968C22#1062320914yes—
969C22#1062321014yes—
970C22D4×C22⋊D1114yes—
971C22#1062335914yes—
972C22#1062336014yes—
973C22C22×D4×D1111yescharacteristic
974C22C2×#6703711yescharacteristic
975C22C2×#41×D1111yescharacteristic
976C22C2×#41×D1111yescharacteristic
977C22C2×#41×D1111yescharacteristic
978C22C2×#6704211yescharacteristic
979C22C23×C22⋊D1111yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—224no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—44no—
992C2—82no—
993C2—228no—
994C2—444no—
995C2#1307273818yesdirect product factor
996C2C2×#1062335911yescharacteristic
997C2C2×D11×#12411yescharacteristic
998C2C2×#1062320911yescharacteristic
999C2C2×D4×C22⋊D1111yescharacteristic
1000C2C2×#1062336011yescharacteristic
1001C2C2×#1062320711yescharacteristic
1002C2C2×#1062321011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#124C2
socleC24×C11C24
prime radicalC22×#66990C2
hypercenterC22×#124D11
hypocenterC11C2×#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×#66999C2semidirect
3. C22×C22⋊C4×D11C2semidirect
4. #13072738C2direct (N × H)
5. C2×#10622565C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622844C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622553C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622568C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C22×C11×#124C2semidirect
18. C23×Q8×C11C22semidirect
25. C2×C11×#124C22semidirect
28. C22×C11×C22⋊C4C22semidirect
29. C22×C11×C22⋊C4C22semidirect
30. C22×C42×C11C22semidirect
34. C22×C22⋊Dic11C22semidirect
35. C22×C22⋊Dic11C22semidirect
37. C2×#66999C22semidirect
48. C22×C4⋊Dic11C22semidirect
49. C22×Dic11⋊C4C22semidirect
50. C22×Dic11⋊C4C22semidirect
51. C22×C4×Dic11C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. #10622844C22semidirect
55. #10622835C22semidirect
56. C2×C11⋊#95C22semidirect
57. C2×C11⋊#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. #10622574C22semidirect
63. #10622570C22semidirect
64. #10622569C22semidirect
65. #10622569C22semidirect
66. #10622568C22semidirect
67. #10622565C22semidirect
68. #10622564C22semidirect
69. #10622553C22semidirect
70. C4×(C2×D11)⋊C4C22semidirect
86. C22×Q8×C11C23semidirect
122. C2×C11×C22⋊C4D4semidirect
125. C2×C11×C22⋊C4C23semidirect
126. C2×C11×C22⋊C4C23semidirect
128. C2×C42×C11C23semidirect
137. C2×C22⋊Dic11C23semidirect
138. C2×C22⋊Dic11C23semidirect
158. C2×C4⋊Dic11C23semidirect
161. C2×Dic11⋊C4C23semidirect
162. C2×Dic11⋊C4C23semidirect
164. C2×C4×Dic11C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
291. C11×C22⋊C4C2×D4semidirect
310. C22×#124D11semidirect
393. C22×D11#124semidirect
449. C23×Q8C2×D11semidirect
456. C2×#124C2×D11semidirect
481. C22×C22⋊C4C2×D11semidirect
482. C22×C22⋊C4C2×D11semidirect
484. C22×C42C2×D11semidirect
548. C2×D11C2×#124semidirect
575. C22×Q8C22×D11semidirect
646. C2×C22⋊C4C22⋊D11semidirect
649. C2×C22⋊C4C22×D11semidirect
650. C2×C22⋊C4C22×D11semidirect
654. C2×C42C22×D11semidirect
663. C2×C11#2472semidirect
807. C22⋊C4C2×C22⋊D11semidirect
810. C11C2×#2472semidirect
995. C2#13072738direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×#669902
C22×C22⋊C4×D112
#130727382
C2×#106225652
C2×#106225742
C2×#106228352
C2×#106228442
C2×#106225702
C2×#106225642
C2×#106225532
C2×#106225692
C2×#106225682
C2×C4×(C2×D11)⋊C42
C22×C11×#1242
C2×#247211