Finite Group Databasebeta

← C2×C11×#2576 #14612040

Subgroups — C2×C11×#2576 #14612040

Order 2816.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2576C2116yesmaximal, direct product factor
2C2×C11×#401C211yesmaximal, characteristic, complemented
3C2×C11×#397C211yesmaximal, characteristic, complemented
4C2×C11×#396C211yesmaximal, characteristic, complemented
5C2×C11×#394C211yesmaximal, characteristic
6C2×C11×#388C211yesmaximal, characteristic, complemented
7C2×C11×#388C211yesmaximal, characteristic, complemented
8C2×C11×#387C211yesmaximal, characteristic, complemented
9C2×C11×#387C211yesmaximal, characteristic, complemented
10C2×C11×#386C211yesmaximal, characteristic
11C2×C11×#386C211yesmaximal, characteristic
12C2×C11×#385C211yesmaximal, characteristic, complemented
13C2×C11×#382C211yesmaximal, characteristic, complemented
14C2×C11×#381C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
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×C42×C11C2211yescharacteristic
36C22×C42×C11C2211yescharacteristic
37C22×C42×C11C2211yescharacteristic
38C11×#401C2218yescomplemented
39C11×#397C2218yescomplemented
40C11×#396C2218yescomplemented
41C11×#394C2218yes—
42C11×#388C2218yescomplemented
43C11×#388C2218yescomplemented
44C11×#387C2218yescomplemented
45C11×#387C2218yescomplemented
46C11×#386C2218yes—
47C11×#386C2218yes—
48C11×#385C2218yescomplemented
49C11×#382C2218yescomplemented
50C11×#381C2218yescomplemented
51C4×C11×C22⋊C4C2218yescomplemented
52C4×C11×C22⋊C4C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
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—24no—
76C23×C4×C11—42no—
77C23×C4×C11—42no—
78C23×C4×C11—42no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2314yes—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2314yes—
94C2×C11×C4⋊C4—24no—
95C2×C11×C4⋊C4—24no—
96C2×C11×C4⋊C4—42no—
97C2×C11×C4⋊C4—42no—
98C2×C11×C4⋊C4—42no—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4—42no—
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×C11C2314yes—
128C2×C42×C11C2314yes—
129C2×C42×C11C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
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×#2576C1111yesmaximal, 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#4114yes—
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—28no—
188C22×C4×C11—22no—
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—22no—
203C22×C4×C11—28no—
204C22×C4×C11—28no—
205C22×C4×C11—44no—
206C22×C4×C11—44no—
207C22×C4×C11—44no—
208C22×C4×C11—416no—
209C22×C4×C11—416no—
210C22×C4×C11#4114yes—
211C22×C4×C11#4114yes—
212C22×C4×C11#4114yes—
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—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C11×C4⋊C4—28no—
227C11×C4⋊C4—28no—
228C11×C4⋊C4—44no—
229C11×C4⋊C4—44no—
230C11×C4⋊C4—44no—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—28no—
233C11×C22⋊C4—28no—
234C11×C22⋊C4—28no—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—28no—
237C11×C22⋊C4—28no—
238C11×C22⋊C4—44no—
239C11×C22⋊C4—44no—
240C11×C22⋊C4—44no—
241C42×C11—28no—
242C42×C11—44no—
243C42×C11—44no—
244#2576C2×C11116yesdirect product factor
245C2×#401C2×C1111yescharacteristic, complemented
246C2×#397C2×C1111yescharacteristic, complemented
247C2×#396C2×C1111yescharacteristic, complemented
248C2×#394C2×C1111yescharacteristic
249C2×#388C2×C1111yescharacteristic, complemented
250C2×#388C2×C1111yescharacteristic, complemented
251C2×#387C2×C1111yescharacteristic, complemented
252C2×#387C2×C1111yescharacteristic, complemented
253C2×#386C2×C1111yescharacteristic
254C2×#386C2×C1111yescharacteristic
255C2×#385C2×C1111yescharacteristic, complemented
256C2×#382C2×C1111yescharacteristic, complemented
257C2×#381C2×C1111yescharacteristic, complemented
258C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
259C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
260C23×C11—28no—
261C23×C11—28no—
262C23×C11—28no—
263C23×C11—28no—
264C23×C11—28no—
265C23×C11—28no—
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—22no—
276C23×C11—22no—
277C23×C11—22no—
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×#4114yes—
288C23×C11C2×#4112yes—
289C23×C11C2×#4112yes—
290C23×C11C2×#4112yes—
291C23×C11C2×#4112yes—
292C23×C11C2×#4112yes—
293C23×C11H(5,𝔽2)12yes—
294C23×C11H(5,𝔽2)12yes—
295C23×C11C2511yescharacteristic
296D4×C11—416no—
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—22no—
336C2×C4×C11—416no—
337C2×C4×C11—416no—
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×C11—44no—
346C2×C4×C11—44no—
347C2×C4×C11—44no—
348C2×C4×C11C2×#4114yes—
349C2×C4×C11C2×#4114yes—
350C2×C4×C11C2×#4114yes—
351C23×D4C22×C1111yescharacteristic
352C24×C4C22×C1111yescharacteristic
353C24×C4C22×C1111yescharacteristic
354C22×C4⋊C4C22×C1111yescharacteristic
355C22×C4⋊C4C22×C1111yescharacteristic
356C22×C4⋊C4C22×C1111yescharacteristic
357C22×C4⋊C4C22×C1111yescharacteristic
358C22×C4⋊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×C22⋊C4C22×C1111yescharacteristic
369C22×C42C22×C1111yescharacteristic
370C22×C42C22×C1111yescharacteristic
371C22×C42C22×C1111yescharacteristic
372#401C22×C1118yescomplemented
373#397C22×C1118yescomplemented
374#396C22×C1118yescomplemented
375#394C22×C1118yes—
376#388C22×C1118yescomplemented
377#388C22×C1118yescomplemented
378#387C22×C1118yescomplemented
379#387C22×C1118yescomplemented
380#386C22×C1118yes—
381#386C22×C1118yes—
382#385C22×C1118yescomplemented
383#382C22×C1118yescomplemented
384#381C22×C1118yescomplemented
385C4×C22⋊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
399C2×#95C22×C1111yescharacteristic
400C2×#95C22×C1111yescharacteristic
401C22×C11—24no—
402C22×C11—24no—
403C22×C11—24no—
404C22×C11—24no—
405C22×C11—24no—
406C22×C11—24no—
407C22×C11—416no—
408C22×C11—416no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11#52914yes—
418C22×C11#52914yes—
419C22×C11#53814yes—
420C22×C11#55114yes—
421C22×C11#55114yes—
422C22×C11#55314yes—
423C22×C11#55314yes—
424C22×C11C22×#4111yescharacteristic
425C22×C11C22×#4111yescharacteristic
426C22×C11C22×#4111yescharacteristic
427C22×C11C22×#4111yescharacteristic
428C22×C11C22×#4111yescharacteristic
429C22×C11C2×H(5,𝔽2)11yescharacteristic
430C22×C11C2×H(5,𝔽2)11yescharacteristic
431C4×C11—24no—
432C4×C11—24no—
433C4×C11—24no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11—42no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11—42no—
444C25C23×C1111yescharacteristic
445C25C23×C1111yescharacteristic
446C22×D4—24no—
447C22×D4—24no—
448C22×D4—42no—
449C22×D4C23×C1114yes—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—42no—
454C23×C4—42no—
455C23×C4—42no—
456C23×C4C23×C1111yescharacteristic
457C23×C4C23×C1111yescharacteristic
458C23×C4C23×C1111yescharacteristic
459C23×C4C23×C1111yescharacteristic
460C23×C4C23×C1111yescharacteristic
461C23×C4C23×C1111yescharacteristic
462C23×C4C23×C1111yescharacteristic
463C23×C4C23×C1111yescharacteristic
464C23×C4C23×C1111yescharacteristic
465C23×C4C23×C1111yescharacteristic
466C23×C4C23×C1114yes—
467C23×C4C23×C1111yescharacteristic
468C23×C4C23×C1111yescharacteristic
469C23×C4C23×C1111yescharacteristic
470C23×C4C23×C1114yes—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4C23×C1114yes—
477C2×C4⋊C4C23×C1114yes—
478C2×C4⋊C4C23×C1114yes—
479C2×C4⋊C4C23×C1114yes—
480C2×C4⋊C4C23×C1114yes—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
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×C22⋊C4C23×C1114yes—
500C2×C22⋊C4C23×C1114yes—
501C2×C42—24no—
502C2×C42—42no—
503C2×C42—42no—
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—
519#95C23×C1114yes—
520#95C23×C1114yes—
521C2×C11—44no—
522C2×C11—44no—
523C2×C11#257618yesdirect product factor
524C2×C11C2×#52911yescharacteristic
525C2×C11C2×#52911yescharacteristic
526C2×C11C2×#53811yescharacteristic
527C2×C11C2×#55111yescharacteristic
528C2×C11C2×#55111yescharacteristic
529C2×C11C2×#55311yescharacteristic
530C2×C11C2×#55311yescharacteristic
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24C11×#4114yes—
544C24C11×#4114yes—
545C24C24×C1112yes—
546C24C24×C1112yes—
547C24C24×C1111yescharacteristic
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—44no—
551C2×D4—416no—
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—22no—
573C22×C4—28no—
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—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—416no—
595C22×C4—416no—
596C22×C4C11×#4114yes—
597C22×C4C11×#4114yes—
598C22×C4C11×#4114yes—
599C22×C4C24×C1112yes—
600C22×C4C24×C1112yes—
601C22×C4C24×C1112yes—
602C22×C4C24×C1112yes—
603C22×C4C24×C1112yes—
604C22×C4C24×C1112yes—
605C22×C4C24×C1112yes—
606C22×C4C24×C1112yes—
607C22×C4C24×C1112yes—
608C22×C4C24×C1112yes—
609C22×C4C24×C1112yes—
610C22×C4C24×C1112yes—
611C22×C4C24×C1112yes—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C22⋊C4—28no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—28no—
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C42—28no—
628C42—44no—
629C42—44no—
630C11C2×#257611yescharacteristic, direct product factor, Sylow
631C23—28no—
632C23—28no—
633C23—28no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23C2×C11×#4114yes—
658C23C2×C11×#4114yes—
659C23C2×C11×#4112yes—
660C23C2×C11×#4112yes—
661C23C2×C11×#4112yes—
662C23C2×C11×#4112yes—
663C23C2×C11×#4112yes—
664C23C11×H(5,𝔽2)12yes—
665C23C11×H(5,𝔽2)12yes—
666C23C25×C1111yescharacteristic
667D4—416no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
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—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—416no—
708C2×C4—416no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4C2×C11×#4114yes—
720C2×C4C2×C11×#4114yes—
721C2×C4C2×C11×#4114yes—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—416no—
737C22—416no—
738C22C11×#52914yes—
739C22C11×#52914yes—
740C22C11×#53814yes—
741C22C11×#55114yes—
742C22C11×#55114yes—
743C22C11×#55314yes—
744C22C11×#55314yes—
745C22C22×C11×#4111yescharacteristic
746C22C22×C11×#4111yescharacteristic
747C22C22×C11×#4111yescharacteristic
748C22C22×C11×#4111yescharacteristic
749C22C22×C11×#4111yescharacteristic
750C22C2×C11×H(5,𝔽2)11yescharacteristic
751C22C2×C11×H(5,𝔽2)11yescharacteristic
752C4—24no—
753C4—24no—
754C4—24no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—42no—
765C2—44no—
766C2—44no—
767C2C11×#257618yesdirect product factor
768C2C2×C11×#52911yescharacteristic
769C2C2×C11×#52911yescharacteristic
770C2C2×C11×#53811yescharacteristic
771C2C2×C11×#55111yescharacteristic
772C2C2×C11×#55111yescharacteristic
773C2C2×C11×#55311yescharacteristic
774C2C2×C11×#55311yescharacteristic
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×#2576C2direct (N × H)
2. C2×C11×#401C2semidirect
3. C2×C11×#397C2semidirect
4. C2×C11×#396C2semidirect
6. C2×C11×#388C2semidirect
7. C2×C11×#388C2semidirect
8. C2×C11×#387C2semidirect
9. C2×C11×#387C2semidirect
12. C2×C11×#385C2semidirect
13. C2×C11×#382C2semidirect
14. C2×C11×#381C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
38. C11×#401C22semidirect
39. C11×#397C22semidirect
40. C11×#396C22semidirect
42. C11×#388C22semidirect
43. C11×#388C22semidirect
44. C11×#387C22semidirect
45. C11×#387C22semidirect
48. C11×#385C22semidirect
49. C11×#382C22semidirect
50. C11×#381C22semidirect
51. C4×C11×C22⋊C4C22semidirect
52. C4×C11×C22⋊C4C22semidirect
144. C2×#2576C11direct (N × H)
244. #2576C2×C11direct (N × H)
245. C2×#401C2×C11semidirect
246. C2×#397C2×C11semidirect
247. C2×#396C2×C11semidirect
249. C2×#388C2×C11semidirect
250. C2×#388C2×C11semidirect
251. C2×#387C2×C11semidirect
252. C2×#387C2×C11semidirect
255. C2×#385C2×C11semidirect
256. C2×#382C2×C11semidirect
257. C2×#381C2×C11semidirect
258. C2×C4×C22⋊C4C2×C11semidirect
259. C2×C4×C22⋊C4C2×C11semidirect
372. #401C22×C11semidirect
373. #397C22×C11semidirect
374. #396C22×C11semidirect
376. #388C22×C11semidirect
377. #388C22×C11semidirect
378. #387C22×C11semidirect
379. #387C22×C11semidirect
382. #385C22×C11semidirect
383. #382C22×C11semidirect
384. #381C22×C11semidirect
385. C4×C22⋊C4C22×C11semidirect
386. C4×C22⋊C4C22×C11semidirect
523. C2×C11#2576direct (N × H)
630. C11C2×#2576direct (N × H)
767. C2C11×#2576direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25762
C2×C11×#4012
C2×C11×#3972
C2×C11×#3962
C2×C11×#3942
C2×C11×#3882
C2×C11×#3872
C2×C11×#3862
C2×C11×#3852
C2×C11×#3822
C2×C11×#3812
C2×C4×C11×C22⋊C42
C2×#257611