Finite Group Databasebeta

← C2×#13073504 #14923780

Subgroups — C2×#13073504 #14923780

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×#66936C211yesmaximal, characteristic, complemented
2C22×#66990C211yesmaximal, characteristic
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13073504C2116yesmaximal, direct product factor
6C2×#10622289C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622835C211yesmaximal, characteristic, complemented
10C2×#10622283C211yesmaximal, characteristic, complemented
11C2×#10622557C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622277C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic, complemented
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic, complemented
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic, complemented
31C22×C22⋊Dic11C2211yescharacteristic, complemented
32C2×#66990—28no—
33C2×#66990C2218yes—
34C2×C4×C22⋊D11—28no—
35C2×C4×C22⋊D11C2218yescomplemented
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
54C11×#386C2218yescomplemented
55C2×C11×#95C2211yescharacteristic, complemented
56C2×C11×#95C2211yescharacteristic, complemented
57#10622835C2218yescomplemented
58#10622826C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62C2×C11⋊#95C2211yescharacteristic, complemented
63#10622572C2218yescomplemented
64#10622568C2218yescomplemented
65#10622561C2218yescomplemented
66#10622557C2218yescomplemented
67#10622289C2218yescomplemented
68#10622283C2218yescomplemented
69#10622280C2218yescomplemented
70#10622277C2218yescomplemented
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×C11—24no—
88C23×C4×C11—42no—
89C23×C4×C11—42no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2314yescomplemented
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11D418yes—
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—42no—
114C22×C4×D11—42no—
115C22×C4×D11D418yescomplemented
116C22×C4×D11C2314yes—
117C22×C4×D11C2314yes—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—42no—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yescomplemented
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yescomplemented
133C2×C22⋊Dic11C2314yescomplemented
134#66990—232no—
135C4×C22⋊D11—232no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—42no—
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)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×C4⋊Dic11—24no—
153C2×C4⋊Dic11C2314yescomplemented
154C2×Dic11⋊C4—24no—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4—42no—
157C2×Dic11⋊C4—42no—
158C2×Dic11⋊C4C2314yescomplemented
159C2×Dic11⋊C4C2314yescomplemented
160C2×Dic11⋊C4C2314yescomplemented
161C2×Dic11⋊C4C2314yescomplemented
162C2×C4×Dic11—24no—
163C2×C4×Dic11C2314yescomplemented
164#66936—232no—
165C22⋊C4×D11—232no—
166C11×#95C2314yescomplemented
167C11×#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2534—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×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×C11—22no—
238C22×C4×C11—28no—
239C22×C4×C11—44no—
240C22×C4×C11—44no—
241C22×C4×C11—416no—
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—232no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—416no—
255C2×C22⋊D11C2×D4116yes—
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×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—416no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—416no—
287C2×C4×D11C2×D4116yescomplemented
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—44no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—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—28no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—44no—
304C4⋊Dic11—28no—
305Dic11⋊C4—28no—
306Dic11⋊C4—28no—
307Dic11⋊C4—44no—
308Dic11⋊C4—44no—
309C4×Dic11—28no—
310C22×#123—111no—
311C22×#120—111no—
312C22×C4×D4—111no—
313C23×C22⋊C4—111no—
314#2534—1116no—
315C2×#396—111no—
316C2×#396—111no—
317C2×#394—111no—
318C2×#394—111no—
319C2×#388—111no—
320C2×#388—111no—
321C2×#386—111no—
322C2×#386D1111yescharacteristic, complemented
323C2×#381—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×D412yes—
354C23×C11C22×D412yes—
355C23×C11C2×#4114yes—
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#121116yes—
394C22×D11C22×D414yes—
395C22×D11C22×D414yes—
396C22×D11C2×#4114yes—
397C22×D11C2×#4114yes—
398D4×C11—416no—
399C2×C4×C11—28no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—416no—
415C2×C4×C11—44no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11—44no—
419C2×C4×C11C22×D414yes—
420C22⋊D11—232no—
421C22⋊D11—416no—
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—22no—
440C2×Dic11—44no—
441C2×Dic11—44no—
442C2×Dic11—44no—
443C2×Dic11—44no—
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×C4C2×D1111yescharacteristic, complemented
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⋊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—111no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—118no—
480C22×C22⋊C4—228no—
481C22×C22⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4C2×D1111yescharacteristic
483C22×C22⋊C4C2×D1111yescharacteristic, complemented
484C22×C42—111no—
485#396—118no—
486#396—118no—
487#394—118no—
488#394—118no—
489#388—118no—
490#388—118no—
491#386—118no—
492#386C2×D1118yescomplemented
493#381—118no—
494#380—118no—
495#379—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95C2×D1111yescharacteristic, complemented
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—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—416no—
517C22×C11—416no—
518C22×C11C2×#12114yes—
519C22×C11#52514yes—
520C22×C11#53414yes—
521C22×C11#54614yes—
522C22×C11#54614yes—
523C22×C11#55114yes—
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×#12118yes—
549C4×C11—24no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11—42no—
553C4×C11—42no—
554Dic11—24no—
555Dic11—24no—
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×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—24no—
585C23×C4—42no—
586C23×C4—42no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—118no—
590C23×C4—114no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—111no—
595C23×C4—114no—
596C23×C4—224no—
597C23×C4—224no—
598C23×C4—224no—
599C23×C4—442no—
600C23×C4—442no—
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1114yescomplemented
607#123—2232no—
608#120—2232no—
609C4×D4—2232no—
610C2×C4⋊C4—114no—
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⋊C4—442no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—42no—
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—114no—
635C2×C22⋊C4—114no—
636C2×C22⋊C4—2232no—
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—224no—
646C2×C22⋊C4—224no—
647C2×C22⋊C4—224no—
648C2×C22⋊C4—224no—
649C2×C22⋊C4—442no—
650C2×C22⋊C4C22×D1114yes—
651C2×C22⋊C4C22×D1114yes—
652C2×C22⋊C4C22×D1114yescomplemented
653C2×C42—114no—
654C2×C42—224no—
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95C22×D1114yescomplemented
660#95C22×D1114yescomplemented
661C2×C11—44no—
662C2×C11—44no—
663C2×C11#253418yescomplemented
664C2×C11C22×#12111yescharacteristic
665C2×C11C2×#52511yescharacteristic
666C2×C11C2×#53411yescharacteristic
667C2×C11C2×#54611yescharacteristic
668C2×C11C2×#54611yescharacteristic
669C2×C11C2×#55111yescharacteristic
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—
715C24#433914yes—
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—228no—
726C2×D4—2232no—
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—28no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—416no—
750C22×C4—114no—
751C22×C4—114no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—1116no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—228no—
760C22×C4—228no—
761C22×C4—228no—
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—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—4416no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4—4416no—
782C22×C4D4×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—
791C4⋊C4—444no—
792C4⋊C4—444no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—44no—
796C22⋊C4—228no—
797C22⋊C4—228no—
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×#253411yescharacteristic, 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—228no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—228no—
854C23—228no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—228no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—4416no—
863C23—4416no—
864C23—4416no—
865C23—4416no—
866C23—4416no—
867C23—4416no—
868C23—44128no—
869C23—444no—
870C23—444no—
871C23—444no—
872C23—444no—
873C23C2×#433914yes—
874C23C2×#433912yes—
875C23C2×D4×D1114yes—
876C23C2×D4×D1112yes—
877C23C2×D4×D1112yes—
878C23#6703712yes—
879C23#6703712yes—
880C23#41×D1112yes—
881C23#41×D1112yes—
882C23C24×D1111yescharacteristic
883D4—416no—
884D4—2232no—
885D4—4416no—
886C2×C4—28no—
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—416no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—114no—
907C2×C4—114no—
908C2×C4—228no—
909C2×C4—228no—
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—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—4416no—
927C2×C4—4416no—
928C2×C4—444no—
929C2×C4—444no—
930C2×C4—444no—
931C2×C4—444no—
932C2×C4C2×D4×D1114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—416no—
946C22—416no—
947C22—42no—
948C22—42no—
949C22—118no—
950C22—224no—
951C22—224no—
952C22—224no—
953C22—224no—
954C22—2232no—
955C22—224no—
956C22—224no—
957C22—224no—
958C22—224no—
959C22—224no—
960C22—4464no—
961C22—442no—
962C22—442no—
963C22—4416no—
964C22—442no—
965C22—442no—
966C22#1062302114yes—
967C22#1062307814yes—
968C22#1062308714yes—
969C22#1062312014yes—
970C22D11×#12114yes—
971C22#1062314114yes—
972C22#1062319014yes—
973C22C22×#433911yescharacteristic
974C22C22×D4×D1111yescharacteristic
975C22C22×D4×D1111yescharacteristic
976C22C2×#6703711yescharacteristic
977C22C2×#6703711yescharacteristic
978C22C2×#41×D1111yescharacteristic
979C22C2×#41×D1111yescharacteristic
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—224no—
986C4—224no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—44no—
992C2—44no—
993C2—228no—
994C2—444no—
995C2#1307350418yesdirect product factor
996C2C2×D11×#12111yescharacteristic
997C2C2×#1062307811yescharacteristic
998C2C2×#1062312011yescharacteristic
999C2C2×#1062314111yescharacteristic
1000C2C2×#1062302111yescharacteristic
1001C2C2×#1062319011yescharacteristic
1002C2C2×#1062308711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66990C2
hypercenterC2×#386D11
hypocenterC11C2×#2534
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13073504C2direct (N × H)
6. C2×#10622289C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622835C2semidirect
10. C2×#10622283C2semidirect
11. C2×#10622557C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622277C2semidirect
14. C2×#10622280C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#386C2semidirect
19. C24×C4×C11C22semidirect
26. C22×C11×C22⋊C4C22semidirect
30. C22×C22⋊Dic11C22semidirect
31. C22×C22⋊Dic11C22semidirect
35. C2×C4×C22⋊D11C22semidirect
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
54. C11×#386C22semidirect
55. C2×C11×#95C22semidirect
56. C2×C11×#95C22semidirect
57. #10622835C22semidirect
58. #10622826C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. C2×C11⋊#95C22semidirect
63. #10622572C22semidirect
64. #10622568C22semidirect
65. #10622561C22semidirect
66. #10622557C22semidirect
67. #10622289C22semidirect
68. #10622283C22semidirect
69. #10622280C22semidirect
70. #10622277C22semidirect
95. C23×C4×C11C23semidirect
115. C22×C4×D11D4semidirect
123. C2×C11×C22⋊C4C23semidirect
132. C2×C22⋊Dic11C23semidirect
133. C2×C22⋊Dic11C23semidirect
153. C2×C4⋊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
287. C2×C4×D11C2×D4semidirect
322. C2×#386D11semidirect
454. C24×C4C2×D11semidirect
483. C22×C22⋊C4C2×D11semidirect
492. #386C2×D11semidirect
500. C2×#95C2×D11semidirect
501. C2×#95C2×D11semidirect
606. C23×C4C22×D11semidirect
652. C2×C22⋊C4C22×D11semidirect
659. #95C22×D11semidirect
660. #95C22×D11semidirect
663. C2×C11#2534semidirect
810. C11C2×#2534semidirect
995. C2#13073504direct (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×C4×C22⋊D112
C22×C22⋊C4×D112
#130735042
C2×#106222892
C2×#106225612
C2×#106225722
C2×#106228352
C2×#106222832
C2×#106225572
C2×#106228262
C2×#106222772
C2×#106222802
C2×#106225682
C2×C11×#3862
C2×#253411