Finite Group Databasebeta

← C2×C11×#2651 #14611773

Subgroups — C2×C11×#2651 #14611773

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2651C2116yesmaximal, direct product factor
2C2×C11×#399C211yesmaximal, characteristic, complemented
3C2×C11×#398C211yesmaximal, characteristic, complemented
4C2×C11×#398C211yesmaximal, characteristic, complemented
5C2×C11×#397C211yesmaximal, characteristic, complemented
6C2×C11×#397C211yesmaximal, characteristic, complemented
7C2×C11×#396C211yesmaximal, characteristic, complemented
8C2×C11×#394C211yesmaximal, characteristic
9C2×C11×#394C211yesmaximal, characteristic
10C2×C11×#390C211yesmaximal, characteristic
11C2×C11×#388C211yesmaximal, characteristic, complemented
12C2×C11×#388C211yesmaximal, characteristic, complemented
13C2×C11×#388C211yesmaximal, characteristic, complemented
14C2×C11×#388C211yesmaximal, characteristic, complemented
15C2×C11×#387C211yesmaximal, characteristic, complemented
16C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
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×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊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×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C22×C42×C11C2211yescharacteristic
40C22×C42×C11C2211yescharacteristic
41C22×C42×C11C2211yescharacteristic
42C11×#399C2218yescomplemented
43C11×#398C2218yescomplemented
44C11×#398C2218yescomplemented
45C11×#397C2218yescomplemented
46C11×#397C2218yescomplemented
47C11×#396C2218yescomplemented
48C11×#394C2218yes—
49C11×#394C2218yes—
50C11×#390C2218yes—
51C11×#388C2218yescomplemented
52C11×#388C2218yescomplemented
53C11×#388C2218yescomplemented
54C11×#388C2218yescomplemented
55C11×#387C2218yescomplemented
56C4×C11×C4⋊C4C2218yescomplemented
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—42no—
71C22×D4×C11—42no—
72C22×D4×C11C2314yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
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×C11C2311yescharacteristic
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4—42no—
90C2×C11×C4⋊C4—42no—
91C2×C11×C4⋊C4—42no—
92C2×C11×C4⋊C4—42no—
93C2×C11×C4⋊C4—42no—
94C2×C11×C4⋊C4—42no—
95C2×C11×C4⋊C4C2314yes—
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×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—42no—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4—42no—
114C2×C11×C22⋊C4—42no—
115C2×C11×C22⋊C4—42no—
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×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C42×C11—24no—
129C2×C42×C11—42no—
130C2×C42×C11—42no—
131C2×C42×C11C2314yes—
132C2×C42×C11C2314yes—
133C2×C42×C11C2314yes—
134C11×#95C2314yes—
135C11×#95C2314yes—
136C11×#95C2314yes—
137C11×#95C2314yes—
138C11×#95C2314yes—
139C11×#95C2314yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C2×#2651C1111yesmaximal, 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—22no—
159C24×C11C2412yes—
160C24×C11C2412yes—
161C24×C11C2411yescharacteristic
162C2×D4×C11—28no—
163C2×D4×C11—44no—
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—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#4114yes—
203C22×C4×C11#4114yes—
204C22×C4×C11#4114yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
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—
218C11×C4⋊C4—28no—
219C11×C4⋊C4—28no—
220C11×C4⋊C4—28no—
221C11×C4⋊C4—44no—
222C11×C4⋊C4—44no—
223C11×C4⋊C4—44no—
224C11×C4⋊C4—44no—
225C11×C4⋊C4—44no—
226C11×C4⋊C4—44no—
227C11×C22⋊C4—28no—
228C11×C22⋊C4—28no—
229C11×C22⋊C4—28no—
230C11×C22⋊C4—28no—
231C11×C22⋊C4—44no—
232C11×C22⋊C4—44no—
233C11×C22⋊C4—44no—
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—
242#2651C2×C11116yesdirect product factor
243C2×#399C2×C1111yescharacteristic, complemented
244C2×#398C2×C1111yescharacteristic, complemented
245C2×#398C2×C1111yescharacteristic, complemented
246C2×#397C2×C1111yescharacteristic, complemented
247C2×#397C2×C1111yescharacteristic, complemented
248C2×#396C2×C1111yescharacteristic, complemented
249C2×#394C2×C1111yescharacteristic
250C2×#394C2×C1111yescharacteristic
251C2×#390C2×C1111yescharacteristic
252C2×#388C2×C1111yescharacteristic, complemented
253C2×#388C2×C1111yescharacteristic, complemented
254C2×#388C2×C1111yescharacteristic, complemented
255C2×#388C2×C1111yescharacteristic, complemented
256C2×#387C2×C1111yescharacteristic, complemented
257C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
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—44no—
273C23×C11—44no—
274C23×C11—44no—
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×#4112yes—
287C23×C11C2×#4112yes—
288C23×C11C2×#4112yes—
289C23×C11H(5,𝔽2)12yes—
290C23×C11H(5,𝔽2)12yes—
291C23×C11H(5,𝔽2)12yes—
292C23×C112−1+412yes—
293C23×C11C2511yescharacteristic
294D4×C11—416no—
295C2×C4×C11—28no—
296C2×C4×C11—28no—
297C2×C4×C11—28no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
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—44no—
335C2×C4×C11—44no—
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×C11C2×#4114yes—
345C2×C4×C11C2×#4114yes—
346C2×C4×C11C2×#4114yes—
347C23×D4C22×C1111yescharacteristic
348C22×C4⋊C4C22×C1111yescharacteristic
349C22×C4⋊C4C22×C1111yescharacteristic
350C22×C4⋊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×C22⋊C4C22×C1111yescharacteristic
369C22×C42C22×C1111yescharacteristic
370C22×C42C22×C1111yescharacteristic
371C22×C42C22×C1111yescharacteristic
372#399C22×C1118yescomplemented
373#398C22×C1118yescomplemented
374#398C22×C1118yescomplemented
375#397C22×C1118yescomplemented
376#397C22×C1118yescomplemented
377#396C22×C1118yescomplemented
378#394C22×C1118yes—
379#394C22×C1118yes—
380#390C22×C1118yes—
381#388C22×C1118yescomplemented
382#388C22×C1118yescomplemented
383#388C22×C1118yescomplemented
384#388C22×C1118yescomplemented
385#387C22×C1118yescomplemented
386C4×C4⋊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
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—88no—
412C22×C11—88no—
413C22×C11#52914yes—
414C22×C11#53814yes—
415C22×C11#53914yes—
416C22×C11#54014yes—
417C22×C11#54014yes—
418C22×C11#54214yes—
419C22×C11#54214yes—
420C22×C11C22×#4111yescharacteristic
421C22×C11C22×#4111yescharacteristic
422C22×C11C22×#4111yescharacteristic
423C22×C11C2×H(5,𝔽2)11yescharacteristic
424C22×C11C2×H(5,𝔽2)11yescharacteristic
425C22×C11C2×H(5,𝔽2)11yescharacteristic
426C22×C11C2×2−1+411yescharacteristic
427C4×C11—24no—
428C4×C11—24no—
429C4×C11—24no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440C25C23×C1111yescharacteristic
441C25C23×C1111yescharacteristic
442C22×D4—24no—
443C22×D4—42no—
444C22×D4—42no—
445C22×D4C23×C1114yes—
446C23×C4C23×C1111yescharacteristic
447C23×C4C23×C1111yescharacteristic
448C23×C4C23×C1111yescharacteristic
449C23×C4C23×C1111yescharacteristic
450C23×C4C23×C1111yescharacteristic
451C23×C4C23×C1111yescharacteristic
452C23×C4C23×C1111yescharacteristic
453C23×C4C23×C1111yescharacteristic
454C23×C4C23×C1111yescharacteristic
455C23×C4C23×C1111yescharacteristic
456C23×C4C23×C1111yescharacteristic
457C23×C4C23×C1111yescharacteristic
458C23×C4C23×C1111yescharacteristic
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4C23×C1114yes—
469C2×C4⋊C4C23×C1114yes—
470C2×C4⋊C4C23×C1114yes—
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—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
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×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—
517C2×C11—82no—
518C2×C11—82no—
519C2×C11#265118yesdirect product factor
520C2×C11C2×#52911yescharacteristic
521C2×C11C2×#53811yescharacteristic
522C2×C11C2×#53911yescharacteristic
523C2×C11C2×#54011yescharacteristic
524C2×C11C2×#54011yescharacteristic
525C2×C11C2×#54211yescharacteristic
526C2×C11C2×#54211yescharacteristic
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24C24×C1112yes—
542C24C24×C1112yes—
543C24C24×C1111yescharacteristic
544C2×D4—28no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—416no—
548C22×C4—22no—
549C22×C4—22no—
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—22no—
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×C4C11×#4114yes—
585C22×C4C11×#4114yes—
586C22×C4C11×#4114yes—
587C22×C4C24×C1112yes—
588C22×C4C24×C1112yes—
589C22×C4C24×C1112yes—
590C22×C4C24×C1112yes—
591C22×C4C24×C1112yes—
592C22×C4C24×C1112yes—
593C22×C4C24×C1112yes—
594C22×C4C24×C1112yes—
595C22×C4C24×C1112yes—
596C22×C4C24×C1112yes—
597C22×C4C24×C1112yes—
598C22×C4C24×C1112yes—
599C22×C4C24×C1112yes—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C42—28no—
622C42—44no—
623C42—44no—
624C11C2×#265111yescharacteristic, direct product factor, Sylow
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23C2×C11×#4112yes—
654C23C2×C11×#4112yes—
655C23C2×C11×#4112yes—
656C23C11×H(5,𝔽2)12yes—
657C23C11×H(5,𝔽2)12yes—
658C23C11×H(5,𝔽2)12yes—
659C23C11×2−1+412yes—
660C23C25×C1111yescharacteristic
661D4—416no—
662C2×C4—28no—
663C2×C4—28no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
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—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4C2×C11×#4114yes—
712C2×C4C2×C11×#4114yes—
713C2×C4C2×C11×#4114yes—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—88no—
729C22—88no—
730C22C11×#52914yes—
731C22C11×#53814yes—
732C22C11×#53914yes—
733C22C11×#54014yes—
734C22C11×#54014yes—
735C22C11×#54214yes—
736C22C11×#54214yes—
737C22C22×C11×#4111yescharacteristic
738C22C22×C11×#4111yescharacteristic
739C22C22×C11×#4111yescharacteristic
740C22C2×C11×H(5,𝔽2)11yescharacteristic
741C22C2×C11×H(5,𝔽2)11yescharacteristic
742C22C2×C11×H(5,𝔽2)11yescharacteristic
743C22C2×C11×2−1+411yescharacteristic
744C4—24no—
745C4—24no—
746C4—24no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C2—82no—
758C2—82no—
759C2C11×#265118yesdirect product factor
760C2C2×C11×#52911yescharacteristic
761C2C2×C11×#53811yescharacteristic
762C2C2×C11×#53911yescharacteristic
763C2C2×C11×#54011yescharacteristic
764C2C2×C11×#54011yescharacteristic
765C2C2×C11×#54211yescharacteristic
766C2C2×C11×#54211yescharacteristic
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×#2651C2direct (N × H)
2. C2×C11×#399C2semidirect
3. C2×C11×#398C2semidirect
4. C2×C11×#398C2semidirect
5. C2×C11×#397C2semidirect
6. C2×C11×#397C2semidirect
7. C2×C11×#396C2semidirect
11. C2×C11×#388C2semidirect
12. C2×C11×#388C2semidirect
13. C2×C11×#388C2semidirect
14. C2×C11×#388C2semidirect
15. C2×C11×#387C2semidirect
16. C2×C4×C11×C4⋊C4C2semidirect
42. C11×#399C22semidirect
43. C11×#398C22semidirect
44. C11×#398C22semidirect
45. C11×#397C22semidirect
46. C11×#397C22semidirect
47. C11×#396C22semidirect
51. C11×#388C22semidirect
52. C11×#388C22semidirect
53. C11×#388C22semidirect
54. C11×#388C22semidirect
55. C11×#387C22semidirect
56. C4×C11×C4⋊C4C22semidirect
144. C2×#2651C11direct (N × H)
242. #2651C2×C11direct (N × H)
243. C2×#399C2×C11semidirect
244. C2×#398C2×C11semidirect
245. C2×#398C2×C11semidirect
246. C2×#397C2×C11semidirect
247. C2×#397C2×C11semidirect
248. C2×#396C2×C11semidirect
252. C2×#388C2×C11semidirect
253. C2×#388C2×C11semidirect
254. C2×#388C2×C11semidirect
255. C2×#388C2×C11semidirect
256. C2×#387C2×C11semidirect
257. C2×C4×C4⋊C4C2×C11semidirect
372. #399C22×C11semidirect
373. #398C22×C11semidirect
374. #398C22×C11semidirect
375. #397C22×C11semidirect
376. #397C22×C11semidirect
377. #396C22×C11semidirect
381. #388C22×C11semidirect
382. #388C22×C11semidirect
383. #388C22×C11semidirect
384. #388C22×C11semidirect
385. #387C22×C11semidirect
386. C4×C4⋊C4C22×C11semidirect
519. C2×C11#2651direct (N × H)
624. C11C2×#2651direct (N × H)
759. C2C11×#2651direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26512
C2×C11×#3992
C2×C11×#3982
C2×C11×#3972
C2×C11×#3962
C2×C11×#3942
C2×C11×#3902
C2×C11×#3882
C2×C11×#3872
C2×C4×C11×C4⋊C42
C2×#265111