Finite Group Databasebeta

← C2×C11×#2480 #14611853

Subgroups — C2×C11×#2480 #14611853

Order 2816.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#126C211yesmaximal, characteristic, complemented
2C23×C11×C22⋊C4C211yesmaximal, characteristic
3C11×#2480C2116yesmaximal, direct product factor
4C2×C11×#397C211yesmaximal, characteristic, complemented
5C2×C11×#397C211yesmaximal, characteristic, complemented
6C2×C11×#397C211yesmaximal, characteristic, complemented
7C2×C11×#396C211yesmaximal, characteristic, complemented
8C2×C11×#388C211yesmaximal, characteristic, complemented
9C2×C11×#388C211yesmaximal, characteristic, complemented
10C2×C11×#388C211yesmaximal, characteristic, complemented
11C2×C11×#385C211yesmaximal, characteristic, complemented
12C2×C11×#385C211yesmaximal, characteristic, complemented
13C2×C11×#380C211yesmaximal, characteristic, complemented
14C2×C11×#379C211yesmaximal, characteristic
15C2×C11×#379C211yesmaximal, characteristic
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C26×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C2×C11×#126—28no—
21C2×C11×#126C2218yescomplemented
22C22×C11×C4⋊C4C2211yescharacteristic, complemented
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C22×C11×C4⋊C4C2211yescharacteristic, complemented
26C22×C11×C4⋊C4C2211yescharacteristic, complemented
27C22×C11×C4⋊C4C2211yescharacteristic, complemented
28C22×C11×C22⋊C4—28no—
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2218yes—
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C22×C11×C22⋊C4C2211yescharacteristic
40C22×C11×C22⋊C4C2211yescharacteristic
41C22×C11×C22⋊C4C2211yescharacteristic
42C22×C11×C22⋊C4C2211yescharacteristic
43C22×C11×C22⋊C4C2211yescharacteristic
44C22×C11×C22⋊C4C2211yescharacteristic
45C22×C11×C22⋊C4C2211yescharacteristic
46C22×C42×C11C2211yescharacteristic, complemented
47C22×C42×C11C2211yescharacteristic, complemented
48C11×#397C2218yescomplemented
49C11×#397C2218yescomplemented
50C11×#397C2218yescomplemented
51C11×#396C2218yescomplemented
52C11×#388C2218yescomplemented
53C11×#388C2218yescomplemented
54C11×#388C2218yescomplemented
55C11×#385C2218yescomplemented
56C11×#385C2218yescomplemented
57C11×#380C2218yescomplemented
58C11×#379C2218yes—
59C11×#379C2218yes—
60C4×C11×C22⋊C4C2218yescomplemented
61C2×C11×#95C2211yescharacteristic, complemented
62C2×C11×#95C2211yescharacteristic, complemented
63C2×C11×#95C2211yescharacteristic, complemented
64C2×C11×#95C2211yescharacteristic, complemented
65C2×C11×#95C2211yescharacteristic, complemented
66C2×C11×#95C2211yescharacteristic, complemented
67C2×C11×#95C2211yescharacteristic, complemented
68C2×C11×#95C2211yescharacteristic, complemented
69C25×C11—24no—
70C25×C11—24no—
71C25×C11—24no—
72C25×C11—24no—
73C25×C11—24no—
74C25×C11—42no—
75C25×C11—42no—
76C25×C11C2311yescharacteristic
77C25×C11C2311yescharacteristic
78C25×C11C2314yes—
79C25×C11C2311yescharacteristic
80C23×C4×C11—24no—
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11—24no—
84C23×C4×C11—42no—
85C23×C4×C11—42no—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2314yes—
97C23×C4×C11C2314yes—
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C11×#126—232no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4—24no—
104C2×C11×C4⋊C4—42no—
105C2×C11×C4⋊C4—42no—
106C2×C11×C4⋊C4—42no—
107C2×C11×C4⋊C4C2314yescomplemented
108C2×C11×C4⋊C4C2314yescomplemented
109C2×C11×C4⋊C4C2314yescomplemented
110C2×C11×C4⋊C4C2314yescomplemented
111C2×C11×C4⋊C4C2314yescomplemented
112C2×C11×C4⋊C4C2314yescomplemented
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—232no—
125C2×C11×C22⋊C4—42no—
126C2×C11×C22⋊C4—42no—
127C2×C11×C22⋊C4—42no—
128C2×C11×C22⋊C4—42no—
129C2×C11×C22⋊C4D418yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C11×C22⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×C11×C22⋊C4C2314yes—
135C2×C11×C22⋊C4C2314yes—
136C2×C11×C22⋊C4C2314yes—
137C2×C11×C22⋊C4C2314yes—
138C2×C11×C22⋊C4C2314yes—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2314yes—
141C2×C11×C22⋊C4C2314yes—
142C2×C11×C22⋊C4C2314yes—
143C2×C11×C22⋊C4C2314yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C42×C11—24no—
147C2×C42×C11—42no—
148C2×C42×C11C2314yescomplemented
149C2×C42×C11C2314yescomplemented
150C11×#95C2314yescomplemented
151C11×#95C2314yescomplemented
152C11×#95C2314yescomplemented
153C11×#95C2314yescomplemented
154C11×#95C2314yescomplemented
155C11×#95C2314yescomplemented
156C11×#95C2314yescomplemented
157C11×#95C2314yescomplemented
158C2×#2480C1111yesmaximal, characteristic, direct product factor, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—232no—
164C24×C11—28no—
165C24×C11—22no—
166C24×C11—28no—
167C24×C11—28no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—28no—
180C24×C11—28no—
181C24×C11—44no—
182C24×C11—44no—
183C24×C11—416no—
184C24×C11—416no—
185C24×C11—416no—
186C24×C11—416no—
187C24×C11—416no—
188C24×C11—416no—
189C24×C11C2×D414yes—
190C24×C11#4114yes—
191C24×C11#4114yes—
192C24×C11#4114yes—
193C24×C11#4114yes—
194C24×C11C2412yes—
195C24×C11C2412yes—
196C24×C11C2412yes—
197C24×C11C2411yescharacteristic
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—28no—
221C22×C4×C11—28no—
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×C11—22no—
234C22×C4×C11—28no—
235C22×C4×C11—28no—
236C22×C4×C11—44no—
237C22×C4×C11—44no—
238C22×C4×C11—416no—
239C22×C4×C11—416no—
240C22×C4×C11C2×D414yes—
241C22×C4×C11C2×D414yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C11×C4⋊C4—28no—
255C11×C4⋊C4—28no—
256C11×C4⋊C4—28no—
257C11×C4⋊C4—44no—
258C11×C4⋊C4—44no—
259C11×C4⋊C4—44no—
260C11×C22⋊C4—28no—
261C11×C22⋊C4—28no—
262C11×C22⋊C4—28no—
263C11×C22⋊C4—28no—
264C11×C22⋊C4—28no—
265C11×C22⋊C4—28no—
266C11×C22⋊C4—28no—
267C11×C22⋊C4—28no—
268C11×C22⋊C4—28no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4—44no—
272C11×C22⋊C4—44no—
273C11×C22⋊C4—44no—
274C11×C22⋊C4—44no—
275C11×C22⋊C4C2×D4116yes—
276C42×C11—28no—
277C42×C11—44no—
278C22×#126C2×C1111yescharacteristic, complemented
279C23×C22⋊C4C2×C1111yescharacteristic
280#2480C2×C11116yesdirect product factor
281C2×#397C2×C1111yescharacteristic, complemented
282C2×#397C2×C1111yescharacteristic, complemented
283C2×#397C2×C1111yescharacteristic, complemented
284C2×#396C2×C1111yescharacteristic, complemented
285C2×#388C2×C1111yescharacteristic, complemented
286C2×#388C2×C1111yescharacteristic, complemented
287C2×#388C2×C1111yescharacteristic, complemented
288C2×#385C2×C1111yescharacteristic, complemented
289C2×#385C2×C1111yescharacteristic, complemented
290C2×#380C2×C1111yescharacteristic, complemented
291C2×#379C2×C1111yescharacteristic
292C2×#379C2×C1111yescharacteristic
293C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—28no—
298C23×C11—28no—
299C23×C11—28no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—232no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—28no—
310C23×C11—28no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—416no—
324C23×C11—416no—
325C23×C11—416no—
326C23×C11—416no—
327C23×C11—416no—
328C23×C11—4128no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—416no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11#126116yescomplemented
339C23×C11C22×D414yes—
340C23×C11C22×D412yes—
341C23×C11C2×#4114yes—
342C23×C11C2×#4114yes—
343C23×C11C2×#4114yes—
344C23×C11C2×#4114yes—
345C23×C11C2×#4112yes—
346C23×C11C2×#4112yes—
347C23×C11C2×#4112yes—
348C23×C11C2×#4112yes—
349C23×C11H(5,𝔽2)12yes—
350C23×C11H(5,𝔽2)12yes—
351C23×C11C2511yescharacteristic
352C2×C4×C11—28no—
353C2×C4×C11—28no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—416no—
389C2×C4×C11—416no—
390C2×C4×C11—44no—
391C2×C4×C11—44no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11—44no—
395C2×C4×C11—44no—
396C2×C4×C11—44no—
397C2×C4×C11—44no—
398C2×C4×C11—44no—
399C2×C4×C11—44no—
400C2×C4×C11C22×D414yes—
401C2×C4×C11C22×D414yes—
402C26C22×C1111yescharacteristic
403C24×C4C22×C1111yescharacteristic
404C24×C4C22×C1111yescharacteristic
405C2×#126—28no—
406C2×#126C22×C1118yescomplemented
407C22×C4⋊C4C22×C1111yescharacteristic, complemented
408C22×C4⋊C4C22×C1111yescharacteristic, complemented
409C22×C4⋊C4C22×C1111yescharacteristic, complemented
410C22×C4⋊C4C22×C1111yescharacteristic, complemented
411C22×C4⋊C4C22×C1111yescharacteristic, complemented
412C22×C4⋊C4C22×C1111yescharacteristic, complemented
413C22×C22⋊C4—28no—
414C22×C22⋊C4C22×C1111yescharacteristic
415C22×C22⋊C4C22×C1111yescharacteristic
416C22×C22⋊C4C22×C1111yescharacteristic
417C22×C22⋊C4C22×C1111yescharacteristic
418C22×C22⋊C4C22×C1111yescharacteristic
419C22×C22⋊C4C22×C1111yescharacteristic
420C22×C22⋊C4C22×C1118yes—
421C22×C22⋊C4C22×C1111yescharacteristic
422C22×C22⋊C4C22×C1111yescharacteristic
423C22×C22⋊C4C22×C1111yescharacteristic
424C22×C22⋊C4C22×C1111yescharacteristic
425C22×C22⋊C4C22×C1111yescharacteristic
426C22×C22⋊C4C22×C1111yescharacteristic
427C22×C22⋊C4C22×C1111yescharacteristic
428C22×C22⋊C4C22×C1111yescharacteristic
429C22×C22⋊C4C22×C1111yescharacteristic
430C22×C22⋊C4C22×C1111yescharacteristic
431C22×C42C22×C1111yescharacteristic, complemented
432C22×C42C22×C1111yescharacteristic, complemented
433#397C22×C1118yescomplemented
434#397C22×C1118yescomplemented
435#397C22×C1118yescomplemented
436#396C22×C1118yescomplemented
437#388C22×C1118yescomplemented
438#388C22×C1118yescomplemented
439#388C22×C1118yescomplemented
440#385C22×C1118yescomplemented
441#385C22×C1118yescomplemented
442#380C22×C1118yescomplemented
443#379C22×C1118yes—
444#379C22×C1118yes—
445C4×C22⋊C4C22×C1118yescomplemented
446C2×#95C22×C1111yescharacteristic, complemented
447C2×#95C22×C1111yescharacteristic, complemented
448C2×#95C22×C1111yescharacteristic, complemented
449C2×#95C22×C1111yescharacteristic, complemented
450C2×#95C22×C1111yescharacteristic, complemented
451C2×#95C22×C1111yescharacteristic, complemented
452C2×#95C22×C1111yescharacteristic, complemented
453C2×#95C22×C1111yescharacteristic, complemented
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—24no—
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—232no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—464no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—416no—
477C22×C11—416no—
478C22×C11#52514yes—
479C22×C11C2×#12614yes—
480C22×C11C2×#12618yescomplemented
481C22×C11#53814yes—
482C22×C11#54614yes—
483C22×C11#54614yes—
484C22×C11#55114yes—
485C22×C11#55114yes—
486C22×C11C23×D411yescharacteristic
487C22×C11C22×#4111yescharacteristic
488C22×C11C22×#4111yescharacteristic
489C22×C11C22×#4111yescharacteristic
490C22×C11C22×#4111yescharacteristic
491C22×C11C2×H(5,𝔽2)11yescharacteristic
492C22×C11C2×H(5,𝔽2)11yescharacteristic
493C4×C11—24no—
494C4×C11—24no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11—42no—
499C4×C11—42no—
500C4×C11—42no—
501C4×C11—42no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505C25—24no—
506C25—24no—
507C25—24no—
508C25—24no—
509C25—24no—
510C25—42no—
511C25—42no—
512C25C23×C1111yescharacteristic
513C25C23×C1111yescharacteristic
514C25C23×C1114yes—
515C25C23×C1111yescharacteristic
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—24no—
519C23×C4—24no—
520C23×C4—42no—
521C23×C4—42no—
522C23×C4C23×C1111yescharacteristic
523C23×C4C23×C1111yescharacteristic
524C23×C4C23×C1111yescharacteristic
525C23×C4C23×C1111yescharacteristic
526C23×C4C23×C1111yescharacteristic
527C23×C4C23×C1111yescharacteristic
528C23×C4C23×C1111yescharacteristic
529C23×C4C23×C1111yescharacteristic
530C23×C4C23×C1111yescharacteristic
531C23×C4C23×C1111yescharacteristic
532C23×C4C23×C1114yes—
533C23×C4C23×C1114yes—
534C23×C4C23×C1111yescharacteristic
535C23×C4C23×C1111yescharacteristic
536#126—232no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—42no—
541C2×C4⋊C4—42no—
542C2×C4⋊C4—42no—
543C2×C4⋊C4C23×C1114yescomplemented
544C2×C4⋊C4C23×C1114yescomplemented
545C2×C4⋊C4C23×C1114yescomplemented
546C2×C4⋊C4C23×C1114yescomplemented
547C2×C4⋊C4C23×C1114yescomplemented
548C2×C4⋊C4C23×C1114yescomplemented
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—232no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4D4×C1118yes—
566C2×C22⋊C4C23×C1114yes—
567C2×C22⋊C4C23×C1114yes—
568C2×C22⋊C4C23×C1114yes—
569C2×C22⋊C4C23×C1114yes—
570C2×C22⋊C4C23×C1114yes—
571C2×C22⋊C4C23×C1114yes—
572C2×C22⋊C4C23×C1114yes—
573C2×C22⋊C4C23×C1114yes—
574C2×C22⋊C4C23×C1114yes—
575C2×C22⋊C4C23×C1114yes—
576C2×C22⋊C4C23×C1114yes—
577C2×C22⋊C4C23×C1114yes—
578C2×C22⋊C4C23×C1114yes—
579C2×C22⋊C4C23×C1114yes—
580C2×C22⋊C4C23×C1114yes—
581C2×C22⋊C4C23×C1114yes—
582C2×C42—24no—
583C2×C42—42no—
584C2×C42C23×C1114yescomplemented
585C2×C42C23×C1114yescomplemented
586#95C23×C1114yescomplemented
587#95C23×C1114yescomplemented
588#95C23×C1114yescomplemented
589#95C23×C1114yescomplemented
590#95C23×C1114yescomplemented
591#95C23×C1114yescomplemented
592#95C23×C1114yescomplemented
593#95C23×C1114yescomplemented
594C2×C11—28no—
595C2×C11—44no—
596C2×C11—44no—
597C2×C11#248018yesdirect product factor
598C2×C11C2×#52511yescharacteristic
599C2×C11C22×#12611yescharacteristic
600C2×C11C2×#53811yescharacteristic
601C2×C11C2×#54611yescharacteristic
602C2×C11C2×#54611yescharacteristic
603C2×C11C2×#55111yescharacteristic
604C2×C11C2×#55111yescharacteristic
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—232no—
610C24—28no—
611C24—22no—
612C24—28no—
613C24—28no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—28no—
626C24—28no—
627C24—44no—
628C24—44no—
629C24—416no—
630C24—416no—
631C24—416no—
632C24—416no—
633C24—416no—
634C24—416no—
635C24C2×D4×C1114yes—
636C24C11×#4114yes—
637C24C11×#4114yes—
638C24C11×#4114yes—
639C24C11×#4114yes—
640C24C24×C1112yes—
641C24C24×C1112yes—
642C24C24×C1112yes—
643C24C24×C1111yescharacteristic
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—416no—
685C22×C4—416no—
686C22×C4C2×D4×C1114yes—
687C22×C4C2×D4×C1114yes—
688C22×C4C24×C1112yes—
689C22×C4C24×C1112yes—
690C22×C4C24×C1112yes—
691C22×C4C24×C1112yes—
692C22×C4C24×C1112yes—
693C22×C4C24×C1112yes—
694C22×C4C24×C1112yes—
695C22×C4C24×C1112yes—
696C22×C4C24×C1112yes—
697C22×C4C24×C1112yes—
698C22×C4C24×C1112yes—
699C22×C4C24×C1112yes—
700C4⋊C4—28no—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—28no—
713C22⋊C4—28no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—44no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—44no—
721C22⋊C4C2×D4×C11116yes—
722C42—28no—
723C42—44no—
724C11C2×#248011yescharacteristic, direct product factor, Sylow
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—232no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—416no—
755C23—416no—
756C23—416no—
757C23—416no—
758C23—416no—
759C23—4128no—
760C23—44no—
761C23—44no—
762C23—416no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23C11×#126116yescomplemented
770C23C22×D4×C1114yes—
771C23C22×D4×C1112yes—
772C23C2×C11×#4114yes—
773C23C2×C11×#4114yes—
774C23C2×C11×#4114yes—
775C23C2×C11×#4114yes—
776C23C2×C11×#4112yes—
777C23C2×C11×#4112yes—
778C23C2×C11×#4112yes—
779C23C2×C11×#4112yes—
780C23C11×H(5,𝔽2)12yes—
781C23C11×H(5,𝔽2)12yes—
782C23C25×C1111yescharacteristic
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—416no—
820C2×C4—416no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4C22×D4×C1114yes—
832C2×C4C22×D4×C1114yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—232no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—464no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—416no—
856C22—416no—
857C22C11×#52514yes—
858C22C2×C11×#12614yes—
859C22C2×C11×#12618yescomplemented
860C22C11×#53814yes—
861C22C11×#54614yes—
862C22C11×#54614yes—
863C22C11×#55114yes—
864C22C11×#55114yes—
865C22C23×D4×C1111yescharacteristic
866C22C22×C11×#4111yescharacteristic
867C22C22×C11×#4111yescharacteristic
868C22C22×C11×#4111yescharacteristic
869C22C22×C11×#4111yescharacteristic
870C22C2×C11×H(5,𝔽2)11yescharacteristic
871C22C2×C11×H(5,𝔽2)11yescharacteristic
872C4—24no—
873C4—24no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C2—28no—
885C2—44no—
886C2—44no—
887C2C11×#248018yesdirect product factor
888C2C2×C11×#52511yescharacteristic
889C2C22×C11×#12611yescharacteristic
890C2C2×C11×#53811yescharacteristic
891C2C2×C11×#54611yescharacteristic
892C2C2×C11×#54611yescharacteristic
893C2C2×C11×#55111yescharacteristic
894C2C2×C11×#55111yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC26×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#126C2semidirect
3. C11×#2480C2direct (N × H)
4. C2×C11×#397C2semidirect
5. C2×C11×#397C2semidirect
6. C2×C11×#397C2semidirect
7. C2×C11×#396C2semidirect
8. C2×C11×#388C2semidirect
9. C2×C11×#388C2semidirect
10. C2×C11×#388C2semidirect
11. C2×C11×#385C2semidirect
12. C2×C11×#385C2semidirect
13. C2×C11×#380C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
21. C2×C11×#126C22semidirect
22. C22×C11×C4⋊C4C22semidirect
23. C22×C11×C4⋊C4C22semidirect
24. C22×C11×C4⋊C4C22semidirect
25. C22×C11×C4⋊C4C22semidirect
26. C22×C11×C4⋊C4C22semidirect
27. C22×C11×C4⋊C4C22semidirect
46. C22×C42×C11C22semidirect
47. C22×C42×C11C22semidirect
48. C11×#397C22semidirect
49. C11×#397C22semidirect
50. C11×#397C22semidirect
51. C11×#396C22semidirect
52. C11×#388C22semidirect
53. C11×#388C22semidirect
54. C11×#388C22semidirect
55. C11×#385C22semidirect
56. C11×#385C22semidirect
57. C11×#380C22semidirect
60. C4×C11×C22⋊C4C22semidirect
61. C2×C11×#95C22semidirect
62. C2×C11×#95C22semidirect
63. C2×C11×#95C22semidirect
64. C2×C11×#95C22semidirect
65. C2×C11×#95C22semidirect
66. C2×C11×#95C22semidirect
67. C2×C11×#95C22semidirect
68. C2×C11×#95C22semidirect
107. C2×C11×C4⋊C4C23semidirect
108. C2×C11×C4⋊C4C23semidirect
109. C2×C11×C4⋊C4C23semidirect
110. C2×C11×C4⋊C4C23semidirect
111. C2×C11×C4⋊C4C23semidirect
112. C2×C11×C4⋊C4C23semidirect
148. C2×C42×C11C23semidirect
149. C2×C42×C11C23semidirect
150. C11×#95C23semidirect
151. C11×#95C23semidirect
152. C11×#95C23semidirect
153. C11×#95C23semidirect
154. C11×#95C23semidirect
155. C11×#95C23semidirect
156. C11×#95C23semidirect
157. C11×#95C23semidirect
158. C2×#2480C11direct (N × H)
278. C22×#126C2×C11semidirect
280. #2480C2×C11direct (N × H)
281. C2×#397C2×C11semidirect
282. C2×#397C2×C11semidirect
283. C2×#397C2×C11semidirect
284. C2×#396C2×C11semidirect
285. C2×#388C2×C11semidirect
286. C2×#388C2×C11semidirect
287. C2×#388C2×C11semidirect
288. C2×#385C2×C11semidirect
289. C2×#385C2×C11semidirect
290. C2×#380C2×C11semidirect
293. C2×C4×C22⋊C4C2×C11semidirect
338. C23×C11#126semidirect
406. C2×#126C22×C11semidirect
407. C22×C4⋊C4C22×C11semidirect
408. C22×C4⋊C4C22×C11semidirect
409. C22×C4⋊C4C22×C11semidirect
410. C22×C4⋊C4C22×C11semidirect
411. C22×C4⋊C4C22×C11semidirect
412. C22×C4⋊C4C22×C11semidirect
431. C22×C42C22×C11semidirect
432. C22×C42C22×C11semidirect
433. #397C22×C11semidirect
434. #397C22×C11semidirect
435. #397C22×C11semidirect
436. #396C22×C11semidirect
437. #388C22×C11semidirect
438. #388C22×C11semidirect
439. #388C22×C11semidirect
440. #385C22×C11semidirect
441. #385C22×C11semidirect
442. #380C22×C11semidirect
445. C4×C22⋊C4C22×C11semidirect
446. C2×#95C22×C11semidirect
447. C2×#95C22×C11semidirect
448. C2×#95C22×C11semidirect
449. C2×#95C22×C11semidirect
450. C2×#95C22×C11semidirect
451. C2×#95C22×C11semidirect
452. C2×#95C22×C11semidirect
453. C2×#95C22×C11semidirect
480. C22×C11C2×#126semidirect
543. C2×C4⋊C4C23×C11semidirect
544. C2×C4⋊C4C23×C11semidirect
545. C2×C4⋊C4C23×C11semidirect
546. C2×C4⋊C4C23×C11semidirect
547. C2×C4⋊C4C23×C11semidirect
548. C2×C4⋊C4C23×C11semidirect
584. C2×C42C23×C11semidirect
585. C2×C42C23×C11semidirect
586. #95C23×C11semidirect
587. #95C23×C11semidirect
588. #95C23×C11semidirect
589. #95C23×C11semidirect
590. #95C23×C11semidirect
591. #95C23×C11semidirect
592. #95C23×C11semidirect
593. #95C23×C11semidirect
597. C2×C11#2480direct (N × H)
724. C11C2×#2480direct (N × H)
769. C23C11×#126semidirect
859. C22C2×C11×#126semidirect
887. C2C11×#2480direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1262
C23×C11×C22⋊C42
C11×#24802
C2×C11×#3972
C2×C11×#3962
C2×C11×#3882
C2×C11×#3852
C2×C11×#3802
C2×C11×#3792
C2×C4×C11×C22⋊C42
C2×#248011