Finite Group Databasebeta

← C2×C11×#2516 #14611976

Subgroups — C2×C11×#2516 #14611976

Order 2816.

2442 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2516C2116yesmaximal, direct product factor
2C2×C11×#400C211yesmaximal, characteristic, complemented
3C2×C11×#399C211yesmaximal, characteristic, complemented
4C2×C11×#397C211yesmaximal, characteristic, complemented
5C2×C11×#394C211yesmaximal, characteristic
6C2×C11×#390C211yesmaximal, characteristic
7C2×C11×#388C211yesmaximal, characteristic, complemented
8C2×C11×#388C211yesmaximal, characteristic, complemented
9C2×C11×#388C211yesmaximal, characteristic, complemented
10C2×C11×#388C211yesmaximal, characteristic, complemented
11C2×C11×#387C211yesmaximal, characteristic, complemented
12C2×C11×#387C211yesmaximal, characteristic, complemented
13C2×C11×#386C211yesmaximal, characteristic
14C2×C11×#381C211yesmaximal, characteristic, complemented
15C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
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⋊C4C2211yescharacteristic
36C22×C42×C11C2211yescharacteristic
37C22×C42×C11C2211yescharacteristic
38C22×C42×C11C2211yescharacteristic
39C22×C42×C11C2211yescharacteristic
40C11×#400C2218yescomplemented
41C11×#399C2218yescomplemented
42C11×#397C2218yescomplemented
43C11×#394C2218yes—
44C11×#390C2218yes—
45C11×#388C2218yescomplemented
46C11×#388C2218yescomplemented
47C11×#388C2218yescomplemented
48C11×#388C2218yescomplemented
49C11×#387C2218yescomplemented
50C11×#387C2218yescomplemented
51C11×#386C2218yes—
52C11×#381C2218yescomplemented
53C4×C11×C4⋊C4C2218yescomplemented
54C4×C11×C22⋊C4C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59C2×C11×#95C2211yescharacteristic
60C2×C11×#95C2211yescharacteristic
61C2×C11×#95C2211yescharacteristic
62C2×C11×#95C2211yescharacteristic
63C2×C11×#95C2211yescharacteristic
64C2×C11×#95C2211yescharacteristic
65C2×C11×#95C2211yescharacteristic
66C2×C11×#95C2211yescharacteristic
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C22×D4×C11—24no—
70C22×D4×C11—24no—
71C22×D4×C11—42no—
72C22×D4×C11C2314yes—
73C23×C4×C11—24no—
74C23×C4×C11—24no—
75C23×C4×C11—42no—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4—24no—
94C2×C11×C4⋊C4—42no—
95C2×C11×C4⋊C4—42no—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C42×C11—24no—
125C2×C42×C11—42no—
126C2×C42×C11—42no—
127C2×C42×C11—42no—
128C2×C42×C11C2314yes—
129C2×C42×C11C2314yes—
130C2×C42×C11C2314yes—
131C2×C42×C11C2314yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11×#95C2314yes—
136C11×#95C2314yes—
137C11×#95C2314yes—
138C11×#95C2314yes—
139C11×#95C2314yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C2×#2516C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11—22no—
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—22no—
150C24×C11—22no—
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11#4114yes—
159C24×C11C2412yes—
160C24×C11C2412yes—
161C24×C11C2411yescharacteristic
162C2×D4×C11—28no—
163C2×D4×C11—28no—
164C2×D4×C11—44no—
165C2×D4×C11—416no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—28no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—28no—
203C22×C4×C11—44no—
204C22×C4×C11—416no—
205C22×C4×C11#4114yes—
206C22×C4×C11#4114yes—
207C22×C4×C11#4114yes—
208C22×C4×C11#4114yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C11×C4⋊C4—28no—
223C11×C4⋊C4—28no—
224C11×C4⋊C4—28no—
225C11×C4⋊C4—28no—
226C11×C4⋊C4—44no—
227C11×C4⋊C4—44no—
228C11×C22⋊C4—28no—
229C11×C22⋊C4—28no—
230C11×C22⋊C4—28no—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—28no—
233C11×C22⋊C4—28no—
234C11×C22⋊C4—44no—
235C11×C22⋊C4—44no—
236C11×C22⋊C4—44no—
237C11×C22⋊C4—44no—
238C11×C22⋊C4—44no—
239C42×C11—28no—
240C42×C11—44no—
241C42×C11—44no—
242C42×C11—44no—
243#2516C2×C11116yesdirect product factor
244C2×#400C2×C1111yescharacteristic, complemented
245C2×#399C2×C1111yescharacteristic, complemented
246C2×#397C2×C1111yescharacteristic, complemented
247C2×#394C2×C1111yescharacteristic
248C2×#390C2×C1111yescharacteristic
249C2×#388C2×C1111yescharacteristic, complemented
250C2×#388C2×C1111yescharacteristic, complemented
251C2×#388C2×C1111yescharacteristic, complemented
252C2×#388C2×C1111yescharacteristic, complemented
253C2×#387C2×C1111yescharacteristic, complemented
254C2×#387C2×C1111yescharacteristic, complemented
255C2×#386C2×C1111yescharacteristic
256C2×#381C2×C1111yescharacteristic, complemented
257C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
258C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
259C23×C11—28no—
260C23×C11—28no—
261C23×C11—28no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11—44no—
284C23×C11—44no—
285C23×C11—44no—
286C23×C11C2×#4114yes—
287C23×C11C2×#4112yes—
288C23×C11C2×#4112yes—
289C23×C11C2×#4112yes—
290C23×C11C2×#4112yes—
291C23×C11C2×#4112yes—
292C23×C11H(5,𝔽2)12yes—
293C23×C11H(5,𝔽2)12yes—
294C23×C11C2511yescharacteristic
295D4×C11—416no—
296C2×C4×C11—28no—
297C2×C4×C11—28no—
298C2×C4×C11—28no—
299C2×C4×C11—28no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—416no—
336C2×C4×C11—44no—
337C2×C4×C11—44no—
338C2×C4×C11—44no—
339C2×C4×C11—44no—
340C2×C4×C11—44no—
341C2×C4×C11—44no—
342C2×C4×C11—44no—
343C2×C4×C11—44no—
344C2×C4×C11—44no—
345C2×C4×C11C2×#4114yes—
346C2×C4×C11C2×#4114yes—
347C2×C4×C11C2×#4114yes—
348C2×C4×C11C2×#4114yes—
349C23×D4C22×C1111yescharacteristic
350C24×C4C22×C1111yescharacteristic
351C22×C4⋊C4C22×C1111yescharacteristic
352C22×C4⋊C4C22×C1111yescharacteristic
353C22×C4⋊C4C22×C1111yescharacteristic
354C22×C4⋊C4C22×C1111yescharacteristic
355C22×C4⋊C4C22×C1111yescharacteristic
356C22×C4⋊C4C22×C1111yescharacteristic
357C22×C22⋊C4C22×C1111yescharacteristic
358C22×C22⋊C4C22×C1111yescharacteristic
359C22×C22⋊C4C22×C1111yescharacteristic
360C22×C22⋊C4C22×C1111yescharacteristic
361C22×C22⋊C4C22×C1111yescharacteristic
362C22×C22⋊C4C22×C1111yescharacteristic
363C22×C22⋊C4C22×C1111yescharacteristic
364C22×C22⋊C4C22×C1111yescharacteristic
365C22×C22⋊C4C22×C1111yescharacteristic
366C22×C22⋊C4C22×C1111yescharacteristic
367C22×C22⋊C4C22×C1111yescharacteristic
368C22×C42C22×C1111yescharacteristic
369C22×C42C22×C1111yescharacteristic
370C22×C42C22×C1111yescharacteristic
371C22×C42C22×C1111yescharacteristic
372#400C22×C1118yescomplemented
373#399C22×C1118yescomplemented
374#397C22×C1118yescomplemented
375#394C22×C1118yes—
376#390C22×C1118yes—
377#388C22×C1118yescomplemented
378#388C22×C1118yescomplemented
379#388C22×C1118yescomplemented
380#388C22×C1118yescomplemented
381#387C22×C1118yescomplemented
382#387C22×C1118yescomplemented
383#386C22×C1118yes—
384#381C22×C1118yescomplemented
385C4×C4⋊C4C22×C1118yescomplemented
386C4×C22⋊C4C22×C1118yescomplemented
387C2×#95C22×C1111yescharacteristic
388C2×#95C22×C1111yescharacteristic
389C2×#95C22×C1111yescharacteristic
390C2×#95C22×C1111yescharacteristic
391C2×#95C22×C1111yescharacteristic
392C2×#95C22×C1111yescharacteristic
393C2×#95C22×C1111yescharacteristic
394C2×#95C22×C1111yescharacteristic
395C2×#95C22×C1111yescharacteristic
396C2×#95C22×C1111yescharacteristic
397C2×#95C22×C1111yescharacteristic
398C2×#95C22×C1111yescharacteristic
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—24no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—416no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—88no—
415C22×C11#52914yes—
416C22×C11#52914yes—
417C22×C11#54014yes—
418C22×C11#55114yes—
419C22×C11#55114yes—
420C22×C11#55314yes—
421C22×C11#55914yes—
422C22×C11C22×#4111yescharacteristic
423C22×C11C22×#4111yescharacteristic
424C22×C11C22×#4111yescharacteristic
425C22×C11C22×#4111yescharacteristic
426C22×C11C22×#4111yescharacteristic
427C22×C11C2×H(5,𝔽2)11yescharacteristic
428C22×C11C2×H(5,𝔽2)11yescharacteristic
429C4×C11—24no—
430C4×C11—24no—
431C4×C11—24no—
432C4×C11—24no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11—42no—
441C4×C11—42no—
442C25C23×C1111yescharacteristic
443C25C23×C1111yescharacteristic
444C22×D4—24no—
445C22×D4—24no—
446C22×D4—42no—
447C22×D4C23×C1114yes—
448C23×C4—24no—
449C23×C4—24no—
450C23×C4—42no—
451C23×C4C23×C1111yescharacteristic
452C23×C4C23×C1111yescharacteristic
453C23×C4C23×C1111yescharacteristic
454C23×C4C23×C1111yescharacteristic
455C23×C4C23×C1111yescharacteristic
456C23×C4C23×C1111yescharacteristic
457C23×C4C23×C1111yescharacteristic
458C23×C4C23×C1111yescharacteristic
459C23×C4C23×C1111yescharacteristic
460C23×C4C23×C1114yes—
461C23×C4C23×C1111yescharacteristic
462C23×C4C23×C1111yescharacteristic
463C23×C4C23×C1111yescharacteristic
464C23×C4C23×C1111yescharacteristic
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4C23×C1114yes—
472C2×C4⋊C4C23×C1114yes—
473C2×C4⋊C4C23×C1114yes—
474C2×C4⋊C4C23×C1114yes—
475C2×C4⋊C4C23×C1114yes—
476C2×C4⋊C4C23×C1114yes—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4C23×C1114yes—
489C2×C22⋊C4C23×C1114yes—
490C2×C22⋊C4C23×C1114yes—
491C2×C22⋊C4C23×C1114yes—
492C2×C22⋊C4C23×C1114yes—
493C2×C22⋊C4C23×C1114yes—
494C2×C22⋊C4C23×C1114yes—
495C2×C22⋊C4C23×C1114yes—
496C2×C22⋊C4C23×C1114yes—
497C2×C22⋊C4C23×C1114yes—
498C2×C22⋊C4C23×C1114yes—
499C2×C42—24no—
500C2×C42—42no—
501C2×C42—42no—
502C2×C42—42no—
503C2×C42C23×C1114yes—
504C2×C42C23×C1114yes—
505C2×C42C23×C1114yes—
506C2×C42C23×C1114yes—
507#95C23×C1114yes—
508#95C23×C1114yes—
509#95C23×C1114yes—
510#95C23×C1114yes—
511#95C23×C1114yes—
512#95C23×C1114yes—
513#95C23×C1114yes—
514#95C23×C1114yes—
515#95C23×C1114yes—
516#95C23×C1114yes—
517#95C23×C1114yes—
518#95C23×C1114yes—
519C2×C11—44no—
520C2×C11—82no—
521C2×C11#251618yesdirect product factor
522C2×C11C2×#52911yescharacteristic
523C2×C11C2×#52911yescharacteristic
524C2×C11C2×#54011yescharacteristic
525C2×C11C2×#55111yescharacteristic
526C2×C11C2×#55111yescharacteristic
527C2×C11C2×#55311yescharacteristic
528C2×C11C2×#55911yescharacteristic
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24C11×#4114yes—
543C24C24×C1112yes—
544C24C24×C1112yes—
545C24C24×C1111yescharacteristic
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—44no—
549C2×D4—416no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—28no—
587C22×C4—44no—
588C22×C4—416no—
589C22×C4C11×#4114yes—
590C22×C4C11×#4114yes—
591C22×C4C11×#4114yes—
592C22×C4C11×#4114yes—
593C22×C4C24×C1112yes—
594C22×C4C24×C1112yes—
595C22×C4C24×C1112yes—
596C22×C4C24×C1112yes—
597C22×C4C24×C1112yes—
598C22×C4C24×C1112yes—
599C22×C4C24×C1112yes—
600C22×C4C24×C1112yes—
601C22×C4C24×C1112yes—
602C22×C4C24×C1112yes—
603C22×C4C24×C1112yes—
604C22×C4C24×C1112yes—
605C22×C4C24×C1112yes—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—28no—
616C22⋊C4—28no—
617C22⋊C4—28no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C42—28no—
624C42—44no—
625C42—44no—
626C42—44no—
627C11C2×#251611yescharacteristic, direct product factor, Sylow
628C23—28no—
629C23—28no—
630C23—28no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23C2×C11×#4114yes—
656C23C2×C11×#4112yes—
657C23C2×C11×#4112yes—
658C23C2×C11×#4112yes—
659C23C2×C11×#4112yes—
660C23C2×C11×#4112yes—
661C23C11×H(5,𝔽2)12yes—
662C23C11×H(5,𝔽2)12yes—
663C23C25×C1111yescharacteristic
664D4—416no—
665C2×C4—28no—
666C2×C4—28no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—416no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4C2×C11×#4114yes—
715C2×C4C2×C11×#4114yes—
716C2×C4C2×C11×#4114yes—
717C2×C4C2×C11×#4114yes—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—416no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—88no—
734C22C11×#52914yes—
735C22C11×#52914yes—
736C22C11×#54014yes—
737C22C11×#55114yes—
738C22C11×#55114yes—
739C22C11×#55314yes—
740C22C11×#55914yes—
741C22C22×C11×#4111yescharacteristic
742C22C22×C11×#4111yescharacteristic
743C22C22×C11×#4111yescharacteristic
744C22C22×C11×#4111yescharacteristic
745C22C22×C11×#4111yescharacteristic
746C22C2×C11×H(5,𝔽2)11yescharacteristic
747C22C2×C11×H(5,𝔽2)11yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C2—44no—
762C2—82no—
763C2C11×#251618yesdirect product factor
764C2C2×C11×#52911yescharacteristic
765C2C2×C11×#52911yescharacteristic
766C2C2×C11×#54011yescharacteristic
767C2C2×C11×#55111yescharacteristic
768C2C2×C11×#55111yescharacteristic
769C2C2×C11×#55311yescharacteristic
770C2C2×C11×#55911yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2516C2direct (N × H)
2. C2×C11×#400C2semidirect
3. C2×C11×#399C2semidirect
4. C2×C11×#397C2semidirect
7. C2×C11×#388C2semidirect
8. C2×C11×#388C2semidirect
9. C2×C11×#388C2semidirect
10. C2×C11×#388C2semidirect
11. C2×C11×#387C2semidirect
12. C2×C11×#387C2semidirect
14. C2×C11×#381C2semidirect
15. C2×C4×C11×C4⋊C4C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
40. C11×#400C22semidirect
41. C11×#399C22semidirect
42. C11×#397C22semidirect
45. C11×#388C22semidirect
46. C11×#388C22semidirect
47. C11×#388C22semidirect
48. C11×#388C22semidirect
49. C11×#387C22semidirect
50. C11×#387C22semidirect
52. C11×#381C22semidirect
53. C4×C11×C4⋊C4C22semidirect
54. C4×C11×C22⋊C4C22semidirect
144. C2×#2516C11direct (N × H)
243. #2516C2×C11direct (N × H)
244. C2×#400C2×C11semidirect
245. C2×#399C2×C11semidirect
246. C2×#397C2×C11semidirect
249. C2×#388C2×C11semidirect
250. C2×#388C2×C11semidirect
251. C2×#388C2×C11semidirect
252. C2×#388C2×C11semidirect
253. C2×#387C2×C11semidirect
254. C2×#387C2×C11semidirect
256. C2×#381C2×C11semidirect
257. C2×C4×C4⋊C4C2×C11semidirect
258. C2×C4×C22⋊C4C2×C11semidirect
372. #400C22×C11semidirect
373. #399C22×C11semidirect
374. #397C22×C11semidirect
377. #388C22×C11semidirect
378. #388C22×C11semidirect
379. #388C22×C11semidirect
380. #388C22×C11semidirect
381. #387C22×C11semidirect
382. #387C22×C11semidirect
384. #381C22×C11semidirect
385. C4×C4⋊C4C22×C11semidirect
386. C4×C22⋊C4C22×C11semidirect
521. C2×C11#2516direct (N × H)
627. C11C2×#2516direct (N × H)
763. C2C11×#2516direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25162
C2×C11×#4002
C2×C11×#3992
C2×C11×#3972
C2×C11×#3942
C2×C11×#3902
C2×C11×#3882
C2×C11×#3872
C2×C11×#3862
C2×C11×#3812
C2×C4×C11×C4⋊C42
C2×C4×C11×C22⋊C42
C2×#251611