Finite Group Databasebeta

← C2×#13072071 #14921204

Subgroups — C2×#13072071 #14921204

Order 2816.

5054 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×#66988C211yesmaximal, characteristic, complemented
2C22×#66990C211yesmaximal, characteristic
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13072071C2116yesmaximal, direct product factor
6C2×#10622605C211yesmaximal, characteristic, complemented
7C2×#10622565C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622558C211yesmaximal, characteristic, complemented
10C2×#10622282C211yesmaximal, characteristic, complemented
11C2×#10622571C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622602C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic, complemented
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic, complemented
28C22×C11×C22⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic, complemented
33C2×#66990—28no—
34C2×#66990C2218yes—
35C2×#66988—28no—
36C2×#66988C2218yescomplemented
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×(C2×D11)⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic, complemented
46C22×Dic11⋊C4C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C22×Dic11⋊C4C2211yescharacteristic, complemented
49C22×C4×Dic11C2211yescharacteristic, complemented
50C2×(C22⋊D11)⋊C4—28no—
51C2×(C22⋊D11)⋊C4C2218yescomplemented
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54C11×#394C2218yescomplemented
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#10622605C2218yescomplemented
62#10622602C2218yescomplemented
63#10622572C2218yescomplemented
64#10622571C2218yescomplemented
65#10622569C2218yescomplemented
66#10622568C2218yescomplemented
67#10622565C2218yescomplemented
68#10622558C2218yescomplemented
69#10622282C2218yescomplemented
70#10622280C2218yescomplemented
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—42no—
97C22×C22⋊D11D418yes—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11—24no—
101C23×Dic11—24no—
102C23×Dic11—42no—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2314yescomplemented
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—
118C2×C11×C4⋊C4—42no—
119C2×C11×C4⋊C4C2314yescomplemented
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—42no—
123C2×C11×C22⋊C4—42no—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yescomplemented
127C2×C11×C22⋊C4C2314yescomplemented
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11D418yescomplemented
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yescomplemented
136#66990—232no—
137#66988—232no—
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—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
154C2×Dic11⋊C4—24no—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—42no—
158C2×Dic11⋊C4C2314yescomplemented
159C2×Dic11⋊C4C2314yescomplemented
160C2×Dic11⋊C4C2314yescomplemented
161C2×Dic11⋊C4C2314yescomplemented
162C2×C4×Dic11—24no—
163C2×C4×Dic11C2314yescomplemented
164(C22⋊D11)⋊C4—232no—
165C22⋊C4×D11—232no—
166C11×#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2418—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×C11C2×D414yes—
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×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×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—232no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—416no—
251C2×C22⋊D11C2×D4116yes—
252C22×Dic11—28no—
253C22×Dic11—22no—
254C22×Dic11—28no—
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×Dic11—22no—
269C22×Dic11—44no—
270C22×Dic11—416no—
271C22×Dic11C2×D414yes—
272C22×Dic11C2×D414yes—
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×C4⋊C4—44no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—28no—
291C11×C22⋊C4—44no—
292C11×C22⋊C4—44no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—28no—
296C22⋊Dic11C2×D4116yescomplemented
297(C2×D11)⋊C4—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—44no—
305Dic11⋊C4—28no—
306Dic11⋊C4—28no—
307Dic11⋊C4—28no—
308Dic11⋊C4—44no—
309C4×Dic11—28no—
310C22×#123—111no—
311C22×#120—111no—
312C22×C4×D4—111no—
313C23×C22⋊C4—111no—
314#2418—1116no—
315C2×#399—111no—
316C2×#397—111no—
317C2×#394—111no—
318C2×#394D1111yescharacteristic, complemented
319C2×#388—111no—
320C2×#388—111no—
321C2×#386—111no—
322C2×#386—111no—
323C2×#385—111no—
324C2×#380—111no—
325C2×#379—111no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—28no—
330C23×C11—28no—
331C23×C11—28no—
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—22no—
343C23×C11—22no—
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×D414yes—
353C23×C11C22×D414yes—
354C23×C11C22×D412yes—
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—4128no—
387C22×D11—416no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—416no—
393C22×D11#123116yescomplemented
394C22×D11C22×D414yes—
395C22×D11C2×#4114yes—
396C22×D11C2×#4114yes—
397C22×D11C2×#4114yes—
398D4×C11—416no—
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×C11—44no—
418C2×C4×C11—44no—
419C22⋊D11—232no—
420C22⋊D11—416no—
421C2×Dic11—28no—
422C2×Dic11—28no—
423C2×Dic11—28no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—416no—
440C2×Dic11—44no—
441C2×Dic11—44no—
442C2×Dic11—44no—
443C2×Dic11C22×D414yes—
444C2×Dic11C22×D414yes—
445C2×Dic11C22×D414yes—
446C4×D11—416no—
447C4×D11—416no—
448C26—111no—
449C23×D4—111no—
450C23×D4—111no—
451C23×D4C2×D1111yescharacteristic
452C24×C4—111no—
453C24×C4—111no—
454C24×C4—111no—
455C2×#123—118no—
456C2×#123—228no—
457C2×#120—118no—
458C2×#120—228no—
459C2×C4×D4—118no—
460C2×C4×D4—228no—
461C22×C4⋊C4—111no—
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—228no—
480C22×C22⋊C4C2×D1111yescharacteristic
481C22×C22⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4C2×D1111yescharacteristic, complemented
483C22×C22⋊C4C2×D1111yescharacteristic, complemented
484C22×C42—111no—
485#399—118no—
486#397—118no—
487#394—118no—
488#394C2×D1118yescomplemented
489#388—118no—
490#388—118no—
491#386—118no—
492#386—118no—
493#385—118no—
494#380—118no—
495#379—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95C2×D1111yescharacteristic, complemented
502C22×C11—24no—
503C22×C11—24no—
504C22×C11—24no—
505C22×C11—24no—
506C22×C11—24no—
507C22×C11—24no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—416no—
511C22×C11—416no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11C2×#12314yes—
519C22×C11#52514yes—
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—232no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—24no—
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—24no—
540C2×D11—24no—
541C2×D11—24no—
542C2×D11—464no—
543C2×D11—42no—
544C2×D11—416no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11C2×#12318yescomplemented
549C4×C11—42no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11—42no—
553C4×C11—42no—
554Dic11—24no—
555Dic11—24no—
556Dic11—24no—
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×D4—24no—
573C22×D4—24no—
574C22×D4—42no—
575C22×D4—118no—
576C22×D4—114no—
577C22×D4—114no—
578C22×D4—224no—
579C22×D4—224no—
580C22×D4—224no—
581C22×D4—224no—
582C22×D4—442no—
583C22×D4C22×D1114yes—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—114no—
591C23×C4—114no—
592C23×C4—114no—
593C23×C4—224no—
594C23×C4—224no—
595C23×C4—224no—
596C23×C4—224no—
597C23×C4—224no—
598C23×C4—224no—
599C23×C4—442no—
600C23×C4—442no—
601C23×C4—442no—
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#123—2232no—
608#120—2232no—
609C4×D4—2232no—
610C2×C4⋊C4—42no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—224no—
616C2×C4⋊C4—224no—
617C2×C4⋊C4—224no—
618C2×C4⋊C4—442no—
619C2×C4⋊C4C22×D1114yescomplemented
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—42no—
623C2×C22⋊C4—42no—
624C2×C22⋊C4—118no—
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—114no—
635C2×C22⋊C4—114no—
636C2×C22⋊C4—114no—
637C2×C22⋊C4—2232no—
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—224no—
646C2×C22⋊C4—224no—
647C2×C22⋊C4—224no—
648C2×C22⋊C4—442no—
649C2×C22⋊C4C22×D1114yes—
650C2×C22⋊C4C22×D1114yes—
651C2×C22⋊C4C22×D1114yescomplemented
652C2×C22⋊C4C22×D1114yescomplemented
653C2×C42—114no—
654C2×C42—224no—
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95—114no—
660#95C22×D1114yescomplemented
661C2×C11—44no—
662C2×C11—44no—
663C2×C11#241818yescomplemented
664C2×C11C22×#12311yescharacteristic
665C2×C11C2×#52511yescharacteristic
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—114no—
686C24—114no—
687C24—114no—
688C24—112no—
689C24—114no—
690C24—112no—
691C24—228no—
692C24—228no—
693C24—228no—
694C24—228no—
695C24—2232no—
696C24—222no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—228no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—444no—
708C24—444no—
709C24—4416no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24—4416no—
715C24D4×D1114yes—
716C24D4×D1114yes—
717C24C23×D1112yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—44no—
723C2×D4—416no—
724C2×D4—1116no—
725C2×D4—2232no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—444no—
731C2×D4—4416no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—114no—
748C22×C4—114no—
749C22×C4—114no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—228no—
757C22×C4—228no—
758C22×C4—228no—
759C22×C4—228no—
760C22×C4—228no—
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—228no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4—4416no—
780C22×C4—4416no—
781C22×C4—444no—
782C22×C4—4416no—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C4⋊C4—44no—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C4⋊C4—228no—
792C4⋊C4—444no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—1116no—
798C22⋊C4—228no—
799C22⋊C4—228no—
800C22⋊C4—228no—
801C22⋊C4—228no—
802C22⋊C4—228no—
803C22⋊C4—228no—
804C22⋊C4—228no—
805C22⋊C4—228no—
806C22⋊C4—228no—
807C22⋊C4—228no—
808C22⋊C4—444no—
809C42—228no—
810C11C2×#241811yescharacteristic, complemented, Sylow
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—1116no—
838C23—114no—
839C23—114no—
840C23—114no—
841C23—114no—
842C23—2232no—
843C23—228no—
844C23—228no—
845C23—228no—
846C23—228no—
847C23—228no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—228no—
853C23—228no—
854C23—228no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—228no—
862C23—4416no—
863C23—4416no—
864C23—4416no—
865C23—4416no—
866C23—4416no—
867C23—4416no—
868C23—44128no—
869C23—444no—
870C23—444no—
871C23—444no—
872C23—444no—
873C23C2×D4×D1114yes—
874C23C2×D4×D1114yes—
875C23C2×D4×D1112yes—
876C23C2×D4×D1112yes—
877C23#6703712yes—
878C23#6703712yes—
879C23#41×D1112yes—
880C23#41×D1112yes—
881C23#41×D1112yes—
882C23C24×D1111yescharacteristic
883D4—416no—
884D4—2232no—
885D4—4416no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—114no—
907C2×C4—114no—
908C2×C4—114no—
909C2×C4—228no—
910C2×C4—228no—
911C2×C4—228no—
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—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—4416no—
928C2×C4—4416no—
929C2×C4—4416no—
930C2×C4—444no—
931C2×C4—444no—
932C2×C4—444no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—416no—
944C22—416no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—118no—
950C22—224no—
951C22—224no—
952C22—224no—
953C22—2232no—
954C22—224no—
955C22—224no—
956C22—224no—
957C22—224no—
958C22—224no—
959C22—224no—
960C22—4464no—
961C22—442no—
962C22—442no—
963C22—4416no—
964C22—442no—
965C22—442no—
966C22#1062312114yes—
967C22#1062314114yes—
968C22#1062314114yes—
969C22#1062314414yes—
970C22D11×#12314yes—
971C22#1062318714yes—
972C22#1062321014yes—
973C22C22×D4×D1111yescharacteristic
974C22C22×D4×D1111yescharacteristic
975C22C2×#6703711yescharacteristic
976C22C2×#6703711yescharacteristic
977C22C2×#41×D1111yescharacteristic
978C22C2×#41×D1111yescharacteristic
979C22C2×#41×D1111yescharacteristic
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—224no—
986C4—224no—
987C4—224no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—44no—
992C2—44no—
993C2—228no—
994C2—444no—
995C2#1307207118yesdirect product factor
996C2C2×D11×#12311yescharacteristic
997C2C2×#1062318711yescharacteristic
998C2C2×#1062314411yescharacteristic
999C2C2×#1062312111yescharacteristic
1000C2C2×#1062314111yescharacteristic
1001C2C2×#1062314111yescharacteristic
1002C2C2×#1062321011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66990C2
hypercenterC2×#394D11
hypocenterC11C2×#2418
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66988C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13072071C2direct (N × H)
6. C2×#10622605C2semidirect
7. C2×#10622565C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622558C2semidirect
10. C2×#10622282C2semidirect
11. C2×#10622571C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622602C2semidirect
14. C2×#10622280C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#394C2semidirect
21. C24×Dic11C22semidirect
24. C22×C11×C4⋊C4C22semidirect
27. C22×C11×C22⋊C4C22semidirect
28. C22×C11×C22⋊C4C22semidirect
32. C22×C22⋊Dic11C22semidirect
36. C2×#66988C22semidirect
45. C22×Dic11⋊C4C22semidirect
46. C22×Dic11⋊C4C22semidirect
47. C22×Dic11⋊C4C22semidirect
48. C22×Dic11⋊C4C22semidirect
49. C22×C4×Dic11C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. C11×#394C22semidirect
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. #10622605C22semidirect
62. #10622602C22semidirect
63. #10622572C22semidirect
64. #10622571C22semidirect
65. #10622569C22semidirect
66. #10622568C22semidirect
67. #10622565C22semidirect
68. #10622558C22semidirect
69. #10622282C22semidirect
70. #10622280C22semidirect
109. C23×Dic11C23semidirect
119. C2×C11×C4⋊C4C23semidirect
126. C2×C11×C22⋊C4C23semidirect
127. C2×C11×C22⋊C4C23semidirect
131. C2×C22⋊Dic11D4semidirect
135. C2×C22⋊Dic11C23semidirect
158. C2×Dic11⋊C4C23semidirect
159. C2×Dic11⋊C4C23semidirect
160. C2×Dic11⋊C4C23semidirect
161. C2×Dic11⋊C4C23semidirect
163. C2×C4×Dic11C23semidirect
166. C11×#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
296. C22⋊Dic11C2×D4semidirect
318. C2×#394D11semidirect
393. C22×D11#123semidirect
465. C22×C4⋊C4C2×D11semidirect
482. C22×C22⋊C4C2×D11semidirect
483. C22×C22⋊C4C2×D11semidirect
488. #394C2×D11semidirect
501. C2×#95C2×D11semidirect
548. C2×D11C2×#123semidirect
619. C2×C4⋊C4C22×D11semidirect
651. C2×C22⋊C4C22×D11semidirect
652. C2×C22⋊C4C22×D11semidirect
660. #95C22×D11semidirect
663. C2×C11#2418semidirect
810. C11C2×#2418semidirect
995. C2#13072071direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
C22×#669902
C22×(C22⋊D11)⋊C42
C22×C22⋊C4×D112
#130720712
C2×#106226052
C2×#106225652
C2×#106225722
C2×#106225582
C2×#106222822
C2×#106225712
C2×#106225692
C2×#106226022
C2×#106222802
C2×#106225682
C2×C11×#3942
C2×#241811