Finite Group Databasebeta

← C2×#13071269 #14912484

Subgroups — C2×#13071269 #14912484

Order 2816.

5094 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×#66935C211yesmaximal, characteristic
2C22×#66946C211yesmaximal, characteristic, complemented
3C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4#13071269C2116yesmaximal, direct product factor
5C2×#10622552C211yesmaximal, characteristic, complemented
6C2×#10622570C211yesmaximal, characteristic, complemented
7C2×#10622564C211yesmaximal, characteristic, complemented
8C2×#10622603C211yesmaximal, characteristic, complemented
9C2×#10622282C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic, complemented
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic, complemented
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
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C22×C4⋊Dic11C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C22×C4×Dic11C2211yescharacteristic, complemented
45C22×C4×Dic11C2211yescharacteristic, complemented
46C2×#66946—28no—
47C2×#66946C2218yescomplemented
48C2×#66935C4116yescomplemented
49C2×#66935C2218yes—
50C2×C22⋊C4×D11—28no—
51C2×C22⋊C4×D11C2218yescomplemented
52C11×#388C2218yescomplemented
53C2×C11×#95C2211yescharacteristic, complemented
54C2×C11×#95C2211yescharacteristic, complemented
55C2×C11⋊#95C2211yescharacteristic, complemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59#10622603C2218yescomplemented
60#10622570C2218yescomplemented
61#10622569C2218yescomplemented
62#10622568C2218yescomplemented
63#10622564C2218yescomplemented
64#10622552C2218yescomplemented
65C4×(C2×D11)⋊C4C2218yescomplemented
66#10622282C2218yescomplemented
67#10622281C2218yescomplemented
68#10622278C2218yescomplemented
69#10622278C2218yescomplemented
70C25×C11C2311yescharacteristic
71C24×D11—24no—
72C24×D11—24no—
73C24×D11—42no—
74C24×D11—42no—
75C24×D11—42no—
76C24×D11—42no—
77C24×D11C2×C418yescomplemented
78C24×D11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C24×D11C2314yes—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11C2×C418yescomplemented
91C22×C22⋊D11C2314yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C22×D44—24no—
98C22×D44—24no—
99C22×D44—42no—
100C22×D44—42no—
101C22×D44C2×C418yes—
102C22×D44C2×C418yescomplemented
103C22×D44C2314yes—
104C22×D44C2314yes—
105C22×C4×D11—24no—
106C22×C4×D11—24no—
107C22×C4×D11—42no—
108C22×C4×D11—42no—
109C22×C4×D11—42no—
110C22×C4×D11—42no—
111C22×C4×D11—42no—
112C22×C4×D11—42no—
113C22×C4×D11D418yescomplemented
114C22×C4×D11C2314yes—
115C22×C4×D11C2314yes—
116C22×C4×D11C2314yescomplemented
117C2×C11×C4⋊C4—24no—
118C2×C11×C4⋊C4C2314yescomplemented
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—42no—
121C2×C11×C22⋊C4C2×C418yescomplemented
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C42×C11—42no—
126C2×C42×C11C2314yescomplemented
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—42no—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
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)⋊C4—42no—
140C2×(C2×D11)⋊C4C2×C418yescomplemented
141C2×(C2×D11)⋊C4C2×C418yescomplemented
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)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yescomplemented
151C2×(C2×D11)⋊C4C2314yescomplemented
152C2×(C2×D11)⋊C4C2314yescomplemented
153C2×C4⋊Dic11—42no—
154C2×C4⋊Dic11C2314yescomplemented
155C2×Dic11⋊C4—42no—
156C2×Dic11⋊C4C2314yescomplemented
157C2×C4×Dic11—24no—
158C2×C4×Dic11—42no—
159C2×C4×Dic11C2314yescomplemented
160C2×C4×Dic11C2314yescomplemented
161#66946—232no—
162#66935C2×C4164yescomplemented
163C22⋊C4×D11—232no—
164C11×#95C2314yescomplemented
165C11×#95C2314yescomplemented
166C11⋊#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C2×#2321—111nomaximal, Sylow
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11C22×C414yes—
178C24×C11C2412yes—
179C24×C11C2411yescharacteristic
180C23×D11—22no—
181C23×D11—22no—
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—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—232no—
197C23×D11—28no—
198C23×D11—28no—
199C23×D11—416no—
200C23×D11—416no—
201C23×D11—44no—
202C23×D11—44no—
203C23×D11—44no—
204C23×D11—44no—
205C23×D11—416no—
206C23×D11—416no—
207C23×D11—416no—
208C23×D11—416no—
209C23×D11C22×C414yes—
210C23×D11C22×C414yes—
211C23×D11C22×C414yes—
212C23×D11C22×C4116yescomplemented
213C23×D11C2×D414yes—
214C23×D11#4114yes—
215C23×D11C2412yes—
216C23×D11C2412yes—
217C23×D11C2412yes—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
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×C11C22×C414yes—
234C22×C4×C11C22×C414yes—
235C22×C4×C11C2×D414yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C22×C4×C11C2412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C2×C22⋊D11—416no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11C22×C4116yescomplemented
246C22×Dic11—22no—
247C22×Dic11—22no—
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×Dic11C22×C414yes—
260C22×Dic11C2×D414yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C2×D44—232no—
267C2×D44—28no—
268C2×D44—28no—
269C2×D44—416no—
270C2×D44—44no—
271C2×D44—44no—
272C2×D44C22×C4116yes—
273C2×D44C22×C4116yescomplemented
274C2×C4×D11—28no—
275C2×C4×D11—28no—
276C2×C4×D11—416no—
277C2×C4×D11—44no—
278C2×C4×D11—44no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—44no—
283C2×C4×D11—416no—
284C2×C4×D11—416no—
285C2×C4×D11C2×D4116yescomplemented
286C11×C4⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—44no—
289C11×C22⋊C4C22×C4116yescomplemented
290C42×C11—44no—
291C22⋊Dic11—28no—
292C22⋊Dic11—44no—
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—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4C22×C4116yescomplemented
303(C2×D11)⋊C4C22×C4116yescomplemented
304C4⋊Dic11—44no—
305Dic11⋊C4—44no—
306C4×Dic11—28no—
307C4×Dic11—44no—
308C22×#120—111no—
309C22×C4×D4—111no—
310C23×C22⋊C4—111no—
311#2321—1116no—
312C2×#390—111no—
313C2×#390—111no—
314C2×#388—111no—
315C2×#388—111no—
316C2×#388—111no—
317C2×#388D1111yescharacteristic, complemented
318C2×#386—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×#385—111no—
322C2×#379—111no—
323C2×C4×C22⋊C4—111no—
324C23×C11—28no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11C23×C414yes—
338C23×C11C23×C412yes—
339C23×C11C22×D412yes—
340C23×C11C2×#4112yes—
341C23×C11H(5,𝔽2)12yes—
342C23×C11H(5,𝔽2)12yes—
343C23×C11H(5,𝔽2)12yes—
344C23×C11H(5,𝔽2)12yes—
345C23×C11C2511yescharacteristic
346C22×D11—28no—
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—28no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—28no—
357C22×D11—28no—
358C22×D11—28no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—28no—
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—232no—
375C22×D11—416no—
376C22×D11—416no—
377C22×D11—4128no—
378C22×D11—416no—
379C22×D11—416no—
380C22×D11—416no—
381C22×D11—416no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11—44no—
386C22×D11—44no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11C4×D4116yes—
391C22×D11C23×C414yes—
392C22×D11C23×C414yes—
393C22×D11C23×C414yes—
394C22×D11C22×D414yes—
395C22×D11C2×#4114yes—
396C2×C4×C11—28no—
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—44no—
415C2×C4×C11—44no—
416C2×C4×C11—44no—
417C2×C4×C11C23×C414yes—
418C2×C4×C11C23×C414yes—
419C2×C4×C11C22×D414yes—
420C22⋊D11—416no—
421C2×Dic11—28no—
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—44no—
437C2×Dic11—44no—
438C2×Dic11—44no—
439C2×Dic11C23×C414yes—
440C2×Dic11C22×D414yes—
441D44—232no—
442D44—416no—
443C4×D11—416no—
444C4×D11—416no—
445C4×D11—416no—
446C26—111no—
447C23×D4—111no—
448C23×D4—111no—
449C23×D4—111no—
450C24×C4—111no—
451C24×C4—111no—
452C24×C4—111no—
453C2×#120—118no—
454C2×#120—1116no—
455C2×C4×D4—118no—
456C2×C4×D4—228no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4C2×D1111yescharacteristic, complemented
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊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—118no—
474C22×C22⋊C4—228no—
475C22×C22⋊C4C2×D1111yescharacteristic
476C22×C22⋊C4C2×D1111yescharacteristic
477C22×C22⋊C4C2×D1111yescharacteristic
478C22×C42—111no—
479C22×C42—111no—
480C22×C42C2×D1111yescharacteristic, complemented
481#390—118no—
482#390—118no—
483#388—118no—
484#388—118no—
485#388—118no—
486#388C2×D1118yescomplemented
487#386—118no—
488#386—118no—
489#386—118no—
490#385—118no—
491#379—118no—
492C4×C22⋊C4—118no—
493C2×#95—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—111no—
497C2×#95C2×D1111yescharacteristic, complemented
498C2×#95C2×D1111yescharacteristic, complemented
499C22×C11—24no—
500C22×C11—24no—
501C22×C11—24no—
502C22×C11—416no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11C2×C4×D414yes—
508C22×C11#51814yes—
509C22×C11#51814yes—
510C22×C11#53414yes—
511C22×C11#53514yes—
512C22×C11#53814yes—
513C22×C11#53814yes—
514C22×C11C24×C411yescharacteristic
515C22×C11C23×D411yescharacteristic
516C22×C11C22×#4111yescharacteristic
517C22×C11C2×H(5,𝔽2)11yescharacteristic
518C22×C11C2×H(5,𝔽2)11yescharacteristic
519C22×C11C2×H(5,𝔽2)11yescharacteristic
520C22×C11C2×H(5,𝔽2)11yescharacteristic
521C2×D11—232no—
522C2×D11—24no—
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—24no—
533C2×D11—24no—
534C2×D11—464no—
535C2×D11—416no—
536C2×D11—416no—
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×D11C2×C4×D418yes—
546C4×C11—24no—
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—
557C25—111no—
558C25—111no—
559C25—111no—
560C25—118no—
561C25—114no—
562C25—224no—
563C25—224no—
564C25—442no—
565C25—442no—
566C25—442no—
567C25—442no—
568C25C22×D1111yescharacteristic
569C22×D4—118no—
570C22×D4—114no—
571C22×D4—118no—
572C22×D4—118no—
573C22×D4—114no—
574C22×D4—114no—
575C22×D4—224no—
576C22×D4—224no—
577C22×D4—442no—
578C22×D4—442no—
579C22×D4—442no—
580C22×D4—442no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—118no—
584C23×C4—114no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—114no—
589C23×C4—114no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—442no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4—442no—
596C23×C4—442no—
597C23×C4—442no—
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604#120—1164no—
605C4×D4—2232no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—442no—
610C2×C4⋊C4—442no—
611C2×C4⋊C4C22×D1114yescomplemented
612C2×C22⋊C4—24no—
613C2×C22⋊C4—42no—
614C2×C22⋊C4—118no—
615C2×C22⋊C4—118no—
616C2×C22⋊C4—114no—
617C2×C22⋊C4—114no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
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—2232no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—224no—
636C2×C22⋊C4—442no—
637C2×C22⋊C4—442no—
638C2×C22⋊C4—442no—
639C2×C22⋊C4—442no—
640C2×C22⋊C4—442no—
641C2×C22⋊C4C4×D1118yescomplemented
642C2×C22⋊C4C22×D1114yes—
643C2×C22⋊C4C22×D1114yes—
644C2×C22⋊C4C22×D1114yes—
645C2×C42—42no—
646C2×C42—114no—
647C2×C42—114no—
648C2×C42—224no—
649C2×C42—442no—
650C2×C42C22×D1114yescomplemented
651#95—114no—
652#95—114no—
653#95—114no—
654#95—114no—
655#95C22×D1114yescomplemented
656#95C22×D1114yescomplemented
657C2×C11—44no—
658C2×C11#232118yescomplemented
659C2×C11C22×C4×D411yescharacteristic
660C2×C11C2×#51811yescharacteristic
661C2×C11C2×#51811yescharacteristic
662C2×C11C2×#53411yescharacteristic
663C2×C11C2×#53511yescharacteristic
664C2×C11C2×#53811yescharacteristic
665C2×C11C2×#53811yescharacteristic
666D11—28no—
667D11—44no—
668D11—44no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—114no—
676C24—114no—
677C24—114no—
678C24—112no—
679C24—114no—
680C24—114no—
681C24—112no—
682C24—112no—
683C24—1116no—
684C24—228no—
685C24—2232no—
686C24—228no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24—222no—
693C24—222no—
694C24—222no—
695C24—222no—
696C24—222no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—4416no—
704C24—4416no—
705C24—444no—
706C24—444no—
707C24—444no—
708C24—444no—
709C24—4416no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24C2×C4×D1114yes—
714C24C23×D1112yes—
715C24C23×D1111yescharacteristic
716C2×D4—1116no—
717C2×D4—1116no—
718C2×D4—1116no—
719C2×D4—228no—
720C2×D4—2232no—
721C2×D4—228no—
722C2×D4—4416no—
723C2×D4—444no—
724C2×D4—444no—
725C2×D4—4416no—
726C2×D4—444no—
727C2×D4—444no—
728C22×C4—22no—
729C22×C4—22no—
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—228no—
752C22×C4—228no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
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—4416no—
767C22×C4—444no—
768C22×C4—444no—
769C22×C4—444no—
770C22×C4—444no—
771C22×C4—444no—
772C22×C4—444no—
773C22×C4—4416no—
774C22×C4—4416no—
775C22×C4C2×C4×D1114yes—
776C22×C4C2×C4×D1114yes—
777C22×C4D4×D1114yes—
778C22×C4C23×D1112yes—
779C22×C4C23×D1112yes—
780C22×C4C23×D1112yes—
781C22×C4C23×D1112yes—
782C22×C4C23×D1112yes—
783C22×C4C23×D1112yes—
784C4⋊C4—28no—
785C4⋊C4—444no—
786C4⋊C4—444no—
787C22⋊C4—28no—
788C22⋊C4—44no—
789C22⋊C4—1116no—
790C22⋊C4—1116no—
791C22⋊C4—228no—
792C22⋊C4—228no—
793C22⋊C4—228no—
794C22⋊C4—228no—
795C22⋊C4—228no—
796C22⋊C4—228no—
797C22⋊C4—444no—
798C22⋊C4—444no—
799C22⋊C4—444no—
800C22⋊C4—444no—
801C22⋊C4—444no—
802C22⋊C4C2×C4×D11116yescomplemented
803C42—44no—
804C42—228no—
805C42—444no—
806C11C2×#232111yescharacteristic, complemented, Sylow
807C23—28no—
808C23—28no—
809C23—28no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—1116no—
821C23—114no—
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—228no—
841C23—228no—
842C23—228no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—4416no—
856C23—4416no—
857C23—4416no—
858C23—4416no—
859C23—4416no—
860C23—4416no—
861C23—44128no—
862C23—444no—
863C23—444no—
864C23—444no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23C22×C4×D1114yes—
871C23C22×C4×D1112yes—
872C23C2×D4×D1112yes—
873C23#6703712yes—
874C23#41×D1112yes—
875C23#6704212yes—
876C23#6704212yes—
877C23#6704212yes—
878C23C24×D1111yescharacteristic
879D4—2232no—
880D4—4416no—
881D4—4416no—
882C2×C4—28no—
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—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—114no—
904C2×C4—114no—
905C2×C4—228no—
906C2×C4—228no—
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—4416no—
921C2×C4—4416no—
922C2×C4—4416no—
923C2×C4—444no—
924C2×C4—444no—
925C2×C4—444no—
926C2×C4C22×C4×D1114yes—
927C2×C4C22×C4×D1114yes—
928C2×C4C2×D4×D1114yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—416no—
937C22—118no—
938C22—224no—
939C22—224no—
940C22—224no—
941C22—224no—
942C22—2232no—
943C22—224no—
944C22—224no—
945C22—224no—
946C22—224no—
947C22—224no—
948C22—224no—
949C22—224no—
950C22—224no—
951C22—4464no—
952C22—442no—
953C22—442no—
954C22—442no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—4416no—
961C22—4416no—
962C22#1062305214yes—
963C22C4×D4×D1114yes—
964C22#1062307614yes—
965C22#1062313614yes—
966C22#1062318814yes—
967C22#1062320514yes—
968C22#1062323514yes—
969C22C23×C4×D1111yescharacteristic
970C22C22×D4×D1111yescharacteristic
971C22C2×#6703711yescharacteristic
972C22C2×#41×D1111yescharacteristic
973C22C2×#6704211yescharacteristic
974C22C2×#6704211yescharacteristic
975C22C2×#6704211yescharacteristic
976C4—24no—
977C4—24no—
978C4—24no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—224no—
983C4—224no—
984C4—442no—
985C4—442no—
986C4—442no—
987C2—44no—
988C2—228no—
989C2—444no—
990C2—444no—
991C2#1307126918yesdirect product factor
992C2C2×C4×D4×D1111yescharacteristic
993C2C2×#1062307611yescharacteristic
994C2C2×#1062305211yescharacteristic
995C2C2×#1062313611yescharacteristic
996C2C2×#1062320511yescharacteristic
997C2C2×#1062318811yescharacteristic
998C2C2×#1062323511yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC22×#66935C2
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2321
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#66946C2semidirect
3. C22×C22⋊C4×D11C2semidirect
4. #13071269C2direct (N × H)
5. C2×#10622552C2semidirect
6. C2×#10622570C2semidirect
7. C2×#10622564C2semidirect
8. C2×#10622603C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622568C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#388C2semidirect
23. C23×C4×D11C22semidirect
24. C22×C11×C4⋊C4C22semidirect
28. C22×C42×C11C22semidirect
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×C4×Dic11C22semidirect
45. C22×C4×Dic11C22semidirect
47. C2×#66946C22semidirect
48. C2×#66935C4semidirect
51. C2×C22⋊C4×D11C22semidirect
52. C11×#388C22semidirect
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. #10622603C22semidirect
60. #10622570C22semidirect
61. #10622569C22semidirect
62. #10622568C22semidirect
63. #10622564C22semidirect
64. #10622552C22semidirect
65. C4×(C2×D11)⋊C4C22semidirect
66. #10622282C22semidirect
67. #10622281C22semidirect
68. #10622278C22semidirect
69. #10622278C22semidirect
77. C24×D11C2×C4semidirect
90. C22×C22⋊D11C2×C4semidirect
102. C22×D44C2×C4semidirect
113. C22×C4×D11D4semidirect
116. C22×C4×D11C23semidirect
118. C2×C11×C4⋊C4C23semidirect
121. C2×C11×C22⋊C4C2×C4semidirect
126. C2×C42×C11C23semidirect
140. C2×(C2×D11)⋊C4C2×C4semidirect
141. C2×(C2×D11)⋊C4C2×C4semidirect
150. C2×(C2×D11)⋊C4C23semidirect
151. C2×(C2×D11)⋊C4C23semidirect
152. C2×(C2×D11)⋊C4C23semidirect
154. C2×C4⋊Dic11C23semidirect
156. C2×Dic11⋊C4C23semidirect
159. C2×C4×Dic11C23semidirect
160. C2×C4×Dic11C23semidirect
162. #66935C2×C4semidirect
164. C11×#95C23semidirect
165. C11×#95C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
212. C23×D11C22×C4semidirect
245. C2×C22⋊D11C22×C4semidirect
273. C2×D44C22×C4semidirect
285. C2×C4×D11C2×D4semidirect
289. C11×C22⋊C4C22×C4semidirect
302. (C2×D11)⋊C4C22×C4semidirect
303. (C2×D11)⋊C4C22×C4semidirect
317. C2×#388D11semidirect
459. C22×C4⋊C4C2×D11semidirect
480. C22×C42C2×D11semidirect
486. #388C2×D11semidirect
497. C2×#95C2×D11semidirect
498. C2×#95C2×D11semidirect
611. C2×C4⋊C4C22×D11semidirect
641. C2×C22⋊C4C4×D11semidirect
650. C2×C42C22×D11semidirect
655. #95C22×D11semidirect
656. #95C22×D11semidirect
658. C2×C11#2321semidirect
802. C22⋊C4C2×C4×D11semidirect
806. C11C2×#2321semidirect
991. C2#13071269direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669352
C22×#669462
C22×C22⋊C4×D112
#130712692
C2×#106225522
C2×#106225702
C2×#106225642
C2×#106226032
C2×#106222822
C2×#106222782
C2×#106225692
C2×#106222812
C2×#106225682
C2×C4×(C2×D11)⋊C42
C2×C11×#3882
C2×#232111