Finite Group Databasebeta

← C2×#13071998 #14922389

Subgroups — C2×#13071998 #14922389

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×#66936C211yesmaximal, characteristic, complemented
2C22×#66990C211yesmaximal, characteristic
3C22×#66925C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13071998C2116yesmaximal, direct product factor
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622835C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622558C211yesmaximal, characteristic, complemented
12C2×#10622553C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic, complemented
27C22×C11×C22⋊C4C2211yescharacteristic, complemented
28C22×C42×C11C2211yescharacteristic, complemented
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic, complemented
33C22×C22⋊Dic11C2211yescharacteristic, complemented
34C2×#66990—28no—
35C2×#66990C2218yes—
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×C4⋊Dic11C2211yescharacteristic, complemented
45C22×Dic11⋊C4C2211yescharacteristic, complemented
46C22×Dic11⋊C4C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C22×Dic11⋊C4C2211yescharacteristic, complemented
49C22×C4×Dic11C2211yescharacteristic, complemented
50C2×#66936—28no—
51C2×#66936C2218yescomplemented
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54C2×#66925—28no—
55C2×#66925C2218yescomplemented
56C11×#390C2218yescomplemented
57#10622835C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62#10622607C2218yescomplemented
63#10622602C2218yescomplemented
64#10622572C2218yescomplemented
65#10622570C2218yescomplemented
66#10622569C2218yescomplemented
67#10622568C2218yescomplemented
68#10622561C2218yescomplemented
69#10622558C2218yescomplemented
70#10622553C2218yescomplemented
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—42no—
110C22×C4×D11—42no—
111C22×C4×D11D418yescomplemented
112C22×C4×D11C2314yes—
113C22×C4×D11C2314yes—
114C2×C11×C4⋊C4—42no—
115C2×C11×C4⋊C4C2314yescomplemented
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—42no—
119C2×C11×C22⋊C4—42no—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yescomplemented
123C2×C11×C22⋊C4C2314yescomplemented
124C2×C42×C11—24no—
125C2×C42×C11C2314yescomplemented
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—42no—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yescomplemented
135C2×C22⋊Dic11C2314yescomplemented
136#66990—232no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—42no—
144C2×(C2×D11)⋊C4D418yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×C4⋊Dic11—24no—
154C2×C4⋊Dic11C2314yescomplemented
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4—42no—
159C2×Dic11⋊C4C2314yescomplemented
160C2×Dic11⋊C4C2314yescomplemented
161C2×Dic11⋊C4C2314yescomplemented
162C2×Dic11⋊C4C2314yescomplemented
163C2×C4×Dic11—24no—
164C2×C4×Dic11C2314yescomplemented
165#66936—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—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11#4114yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—232no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—28no—
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×D11C2×D414yes—
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×C11C2×D414yes—
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×Dic11—22no—
268C22×Dic11C2×D414yes—
269C22×Dic11C2×D414yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
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—44no—
285C11×C22⋊C4—28no—
286C11×C22⋊C4—28no—
287C11×C22⋊C4—44no—
288C11×C22⋊C4—44no—
289C42×C11—28no—
290C22⋊Dic11—28no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—44no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—28no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4C2×D4116yes—
303C4⋊Dic11—28no—
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×#390D1111yescharacteristic, complemented
320C2×#388—111no—
321C2×#388—111no—
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—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—44no—
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×C11C22×D412yes—
353C23×C11C22×D412yes—
354C23×C11C2×#4114yes—
355C23×C11C2×#4112yes—
356C23×C11C2×#4112yes—
357C23×C11C2×#4112yes—
358C23×C11H(5,𝔽2)12yes—
359C23×C11H(5,𝔽2)12yes—
360C23×C11C2511yescharacteristic
361C22×D11—28no—
362C22×D11—28no—
363C22×D11—28no—
364C22×D11—28no—
365C22×D11—28no—
366C22×D11—28no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—232no—
372C22×D11—28no—
373C22×D11—28no—
374C22×D11—28no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—416no—
382C22×D11—416no—
383C22×D11—416no—
384C22×D11—416no—
385C22×D11—4128no—
386C22×D11—416no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—416no—
392C22×D11#121116yes—
393C22×D11C22×D414yes—
394C22×D11C22×D414yes—
395C22×D11C2×#4114yes—
396C22×D11C2×#4114yes—
397D4×C11—416no—
398C2×C4×C11—28no—
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—44no—
414C2×C4×C11—44no—
415C2×C4×C11—44no—
416C2×C4×C11C22×D414yes—
417C2×C4×C11C22×D414yes—
418C22⋊D11—416no—
419C22⋊D11—416no—
420C2×Dic11—28no—
421C2×Dic11—28no—
422C2×Dic11—22no—
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—44no—
439C2×Dic11—44no—
440C2×Dic11—44no—
441C2×Dic11—44no—
442C2×Dic11C22×D414yes—
443C2×Dic11C22×D414yes—
444C4×D11—232no—
445C4×D11—416no—
446C26—111no—
447C23×D4—111no—
448C23×D4—111no—
449C23×D4C2×D1111yescharacteristic
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—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#396—118no—
486#396—118no—
487#394—118no—
488#394—118no—
489#390—118no—
490#390C2×D1118yescomplemented
491#388—118no—
492#388—118no—
493#386—118no—
494#385—118no—
495#379—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
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×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—88no—
516C22×C11C2×#12114yes—
517C22×C11#52514yes—
518C22×C11#53514yes—
519C22×C11#54614yes—
520C22×C11#54614yes—
521C22×C11#55114yes—
522C22×C11#55114yes—
523C22×C11C23×D411yescharacteristic
524C22×C11C23×D411yescharacteristic
525C22×C11C22×#4111yescharacteristic
526C22×C11C22×#4111yescharacteristic
527C22×C11C22×#4111yescharacteristic
528C22×C11C2×H(5,𝔽2)11yescharacteristic
529C22×C11C2×H(5,𝔽2)11yescharacteristic
530C2×D11—232no—
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—416no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11C2×#12118yes—
547C4×C11—24no—
548C4×C11—24no—
549C4×C11—42no—
550C4×C11—42no—
551C4×C11—42no—
552Dic11—24no—
553Dic11—24no—
554Dic11—42no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558C25—111no—
559C25—111no—
560C25—114no—
561C25—224no—
562C25—224no—
563C25—224no—
564C25—224no—
565C25—224no—
566C25—442no—
567C25—442no—
568C25C22×D1111yescharacteristic
569C25C22×D1111yescharacteristic
570C22×D4—24no—
571C22×D4—24no—
572C22×D4—42no—
573C22×D4—114no—
574C22×D4—114no—
575C22×D4—224no—
576C22×D4—224no—
577C22×D4—224no—
578C22×D4—224no—
579C22×D4—224no—
580C22×D4—442no—
581C22×D4C22×D1114yes—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—118no—
585C23×C4—114no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—114no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—224no—
594C23×C4—442no—
595C23×C4—442no—
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—42no—
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—224no—
614C2×C4⋊C4—442no—
615C2×C4⋊C4C22×D1114yescomplemented
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—42no—
620C2×C22⋊C4—118no—
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—224no—
645C2×C22⋊C4—442no—
646C2×C22⋊C4—442no—
647C2×C22⋊C4C22×D1114yes—
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1114yescomplemented
650C2×C22⋊C4C22×D1114yescomplemented
651C2×C42—24no—
652C2×C42—114no—
653C2×C42—224no—
654C2×C42C22×D1114yescomplemented
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659C2×C11—44no—
660C2×C11—82no—
661C2×C11#241118yescomplemented
662C2×C11C22×#12111yescharacteristic
663C2×C11C2×#52511yescharacteristic
664C2×C11C2×#53511yescharacteristic
665C2×C11C2×#54611yescharacteristic
666C2×C11C2×#54611yescharacteristic
667C2×C11C2×#55111yescharacteristic
668C2×C11C2×#55111yescharacteristic
669D11—28no—
670D11—44no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—114no—
685C24—114no—
686C24—114no—
687C24—112no—
688C24—114no—
689C24—112no—
690C24—228no—
691C24—228no—
692C24—228no—
693C24—228no—
694C24—2232no—
695C24—222no—
696C24—222no—
697C24—222no—
698C24—222no—
699C24—228no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—444no—
707C24—444no—
708C24—4416no—
709C24—4416no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24#433914yes—
715C24C23×D1112yes—
716C24C23×D1112yes—
717C24C23×D1111yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—44no—
721C2×D4—416no—
722C2×D4—228no—
723C2×D4—228no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—444no—
728C2×D4—4416no—
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—114no—
744C22×C4—114no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—1116no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—228no—
753C22×C4—2232no—
754C22×C4—228no—
755C22×C4—228no—
756C22×C4—222no—
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—444no—
773C22×C4—444no—
774C22×C4—4416no—
775C22×C4D4×D1114yes—
776C22×C4D4×D1114yes—
777C22×C4C23×D1112yes—
778C22×C4C23×D1112yes—
779C22×C4C23×D1112yes—
780C22×C4C23×D1112yes—
781C22×C4C23×D1112yes—
782C4⋊C4—44no—
783C4⋊C4—228no—
784C4⋊C4—228no—
785C4⋊C4—228no—
786C4⋊C4—228no—
787C4⋊C4—444no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—1116no—
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—228no—
802C22⋊C4—228no—
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—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—1116no—
836C23—114no—
837C23—114no—
838C23—114no—
839C23—114no—
840C23—2232no—
841C23—228no—
842C23—228no—
843C23—228no—
844C23—228no—
845C23—228no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—228no—
851C23—228no—
852C23—228no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—228no—
860C23—4416no—
861C23—4416no—
862C23—4416no—
863C23—4416no—
864C23—4416no—
865C23—4416no—
866C23—44128no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23—444no—
871C23C2×#433914yes—
872C23C2×#433912yes—
873C23C2×D4×D1112yes—
874C23C2×D4×D1112yes—
875C23#6703712yes—
876C23#6703712yes—
877C23#41×D1112yes—
878C23#41×D1112yes—
879C23C24×D1111yescharacteristic
880D4—416no—
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—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—114no—
902C2×C4—114no—
903C2×C4—2232no—
904C2×C4—228no—
905C2×C4—228no—
906C2×C4—222no—
907C2×C4—222no—
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—4416no—
923C2×C4—444no—
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—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—88no—
945C22—118no—
946C22—224no—
947C22—224no—
948C22—224no—
949C22—224no—
950C22—2232no—
951C22—224no—
952C22—224no—
953C22—224no—
954C22—224no—
955C22—224no—
956C22—4464no—
957C22—442no—
958C22—442no—
959C22—4416no—
960C22—442no—
961C22—442no—
962C22#1062302114yes—
963C22#1062307814yes—
964C22#1062308714yes—
965C22D11×#12114yes—
966C22#1062314314yes—
967C22#1062321014yes—
968C22#1062324614yes—
969C22C22×#433911yescharacteristic
970C22C22×D4×D1111yescharacteristic
971C22C22×D4×D1111yescharacteristic
972C22C2×#6703711yescharacteristic
973C22C2×#6703711yescharacteristic
974C22C2×#41×D1111yescharacteristic
975C22C2×#41×D1111yescharacteristic
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—224no—
982C4—224no—
983C4—442no—
984C4—442no—
985C4—442no—
986C4—442no—
987C2—44no—
988C2—82no—
989C2—228no—
990C2—444no—
991C2#1307199818yesdirect product factor
992C2C2×D11×#12111yescharacteristic
993C2C2×#1062307811yescharacteristic
994C2C2×#1062324611yescharacteristic
995C2C2×#1062302111yescharacteristic
996C2C2×#1062314311yescharacteristic
997C2C2×#1062308711yescharacteristic
998C2C2×#1062321011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC22×#66990C2
hypercenterC2×#390D11
hypocenterC11C2×#2411
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
3. C22×#66925C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13071998C2direct (N × H)
6. C2×#10622561C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622835C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622558C2semidirect
12. C2×#10622553C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#390C2semidirect
23. C22×C11×C4⋊C4C22semidirect
26. C22×C11×C22⋊C4C22semidirect
27. C22×C11×C22⋊C4C22semidirect
28. C22×C42×C11C22semidirect
32. C22×C22⋊Dic11C22semidirect
33. C22×C22⋊Dic11C22semidirect
44. C22×C4⋊Dic11C22semidirect
45. C22×Dic11⋊C4C22semidirect
46. C22×Dic11⋊C4C22semidirect
47. C22×Dic11⋊C4C22semidirect
48. C22×Dic11⋊C4C22semidirect
49. C22×C4×Dic11C22semidirect
51. C2×#66936C22semidirect
53. C2×C22⋊C4×D11C22semidirect
55. C2×#66925C22semidirect
56. C11×#390C22semidirect
57. #10622835C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. #10622607C22semidirect
63. #10622602C22semidirect
64. #10622572C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
67. #10622568C22semidirect
68. #10622561C22semidirect
69. #10622558C22semidirect
70. #10622553C22semidirect
111. C22×C4×D11D4semidirect
115. C2×C11×C4⋊C4C23semidirect
122. C2×C11×C22⋊C4C23semidirect
123. C2×C11×C22⋊C4C23semidirect
125. C2×C42×C11C23semidirect
134. C2×C22⋊Dic11C23semidirect
135. C2×C22⋊Dic11C23semidirect
154. C2×C4⋊Dic11C23semidirect
159. C2×Dic11⋊C4C23semidirect
160. C2×Dic11⋊C4C23semidirect
161. C2×Dic11⋊C4C23semidirect
162. C2×Dic11⋊C4C23semidirect
164. C2×C4×Dic11C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
283. C2×C4×D11C2×D4semidirect
319. C2×#390D11semidirect
463. C22×C4⋊C4C2×D11semidirect
481. C22×C22⋊C4C2×D11semidirect
482. C22×C22⋊C4C2×D11semidirect
484. C22×C42C2×D11semidirect
490. #390C2×D11semidirect
615. C2×C4⋊C4C22×D11semidirect
649. C2×C22⋊C4C22×D11semidirect
650. C2×C22⋊C4C22×D11semidirect
654. C2×C42C22×D11semidirect
661. C2×C11#2411semidirect
807. C11C2×#2411semidirect
991. C2#13071998direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669902
C22×#669252
C22×C22⋊C4×D112
#130719982
C2×#106225612
C2×#106226072
C2×#106225722
C2×#106228352
C2×#106225702
C2×#106225582
C2×#106225532
C2×#106225692
C2×#106226022
C2×#106225682
C2×C11×#3902
C2×#241111