Finite Group Databasebeta

← C2×C11×#2464 #14611868

Subgroups — C2×C11×#2464 #14611868

Order 2816.

4218 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#123C211yesmaximal, characteristic, complemented
2C22×C11×#121C211yesmaximal, characteristic, complemented
3C22×C11×#121C211yesmaximal, characteristic, complemented
4C22×C4×D4×C11C211yesmaximal, characteristic, complemented
5C11×#2464C2116yesmaximal, direct product factor
6C2×C11×#398C211yesmaximal, characteristic, complemented
7C2×C11×#394C211yesmaximal, characteristic, complemented
8C2×C11×#392C211yesmaximal, characteristic, complemented
9C2×C11×#392C211yesmaximal, characteristic, complemented
10C2×C11×#390C211yesmaximal, characteristic, complemented
11C2×C11×#388C211yesmaximal, characteristic, complemented
12C2×C11×#388C211yesmaximal, characteristic, complemented
13C2×C11×#386C211yesmaximal, characteristic, complemented
14C2×C11×#386C211yesmaximal, characteristic, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic
21C23×D4×C11C2211yescharacteristic
22C23×D4×C11C2211yescharacteristic
23C24×C4×C11C2211yescharacteristic
24C24×C4×C11C2211yescharacteristic
25C24×C4×C11C2211yescharacteristic
26C2×C11×#123—28no—
27C2×C11×#123C2218yescomplemented
28C2×C11×#121—28no—
29C2×C11×#121—28no—
30C2×C11×#121C2218yescomplemented
31C2×C11×#121C2218yescomplemented
32C2×C4×D4×C11—28no—
33C2×C4×D4×C11C2218yescomplemented
34C22×C11×C4⋊C4C2211yescharacteristic
35C22×C11×C4⋊C4C2211yescharacteristic
36C22×C11×C4⋊C4C2211yescharacteristic
37C22×C11×C4⋊C4C2211yescharacteristic
38C22×C11×C4⋊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×C11×C22⋊C4C2211yescharacteristic
47C22×C11×C22⋊C4C2211yescharacteristic
48C22×C11×C22⋊C4C2211yescharacteristic
49C22×C11×C22⋊C4C2211yescharacteristic
50C22×C11×C22⋊C4C2211yescharacteristic
51C22×C11×C22⋊C4C2211yescharacteristic
52C22×C42×C11C2211yescharacteristic
53C22×C42×C11C2211yescharacteristic
54C11×#398C2218yescomplemented
55C11×#394C2218yescomplemented
56C11×#392C2218yescomplemented
57C11×#392C2218yescomplemented
58C11×#390C2218yescomplemented
59C11×#388C2218yescomplemented
60C11×#388C2218yescomplemented
61C11×#386C2218yescomplemented
62C11×#386C2218yescomplemented
63C11×#385C2218yescomplemented
64C4×C11×C22⋊C4C2218yescomplemented
65C2×C11×#95C2211yescharacteristic
66C2×C11×#95C2211yescharacteristic
67C2×C11×#95C2211yescharacteristic
68C2×C11×#95C2211yescharacteristic
69C2×C11×#95C2211yescharacteristic
70C2×C11×#95C2211yescharacteristic
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11—24no—
86C22×D4×C11—24no—
87C22×D4×C11—24no—
88C22×D4×C11—42no—
89C22×D4×C11—42no—
90C22×D4×C11—42no—
91C22×D4×C11—42no—
92C22×D4×C11—42no—
93C22×D4×C11C2314yes—
94C22×D4×C11C2314yes—
95C22×D4×C11C2314yes—
96C22×D4×C11C2314yes—
97C22×D4×C11C2314yes—
98C22×D4×C11C2314yes—
99C23×C4×C11—24no—
100C23×C4×C11—24no—
101C23×C4×C11—24no—
102C23×C4×C11—24no—
103C23×C4×C11—24no—
104C23×C4×C11—24no—
105C23×C4×C11—42no—
106C23×C4×C11—42no—
107C23×C4×C11—42no—
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2314yes—
114C23×C4×C11C2314yes—
115C23×C4×C11C2314yes—
116C23×C4×C11C2311yescharacteristic
117C23×C4×C11C2311yescharacteristic
118C23×C4×C11C2311yescharacteristic
119C23×C4×C11C2311yescharacteristic
120C23×C4×C11C2311yescharacteristic
121C23×C4×C11C2311yescharacteristic
122C11×#123—232no—
123C11×#121—232no—
124C11×#121—232no—
125C4×D4×C11—232no—
126C2×C11×C4⋊C4—24no—
127C2×C11×C4⋊C4—24no—
128C2×C11×C4⋊C4—24no—
129C2×C11×C4⋊C4—24no—
130C2×C11×C4⋊C4—24no—
131C2×C11×C4⋊C4C2314yes—
132C2×C11×C4⋊C4C2314yes—
133C2×C11×C4⋊C4C2314yes—
134C2×C11×C4⋊C4C2314yes—
135C2×C11×C4⋊C4C2314yes—
136C2×C11×C22⋊C4—24no—
137C2×C11×C22⋊C4—24no—
138C2×C11×C22⋊C4—24no—
139C2×C11×C22⋊C4—24no—
140C2×C11×C22⋊C4—24no—
141C2×C11×C22⋊C4—24no—
142C2×C11×C22⋊C4—24no—
143C2×C11×C22⋊C4—24no—
144C2×C11×C22⋊C4—42no—
145C2×C11×C22⋊C4—42no—
146C2×C11×C22⋊C4—42no—
147C2×C11×C22⋊C4D418yescomplemented
148C2×C11×C22⋊C4D418yescomplemented
149C2×C11×C22⋊C4C2314yes—
150C2×C11×C22⋊C4C2314yes—
151C2×C11×C22⋊C4C2314yes—
152C2×C11×C22⋊C4C2314yes—
153C2×C11×C22⋊C4C2314yes—
154C2×C11×C22⋊C4C2314yes—
155C2×C11×C22⋊C4C2314yes—
156C2×C11×C22⋊C4C2314yes—
157C2×C11×C22⋊C4C2314yes—
158C2×C11×C22⋊C4C2314yes—
159C2×C11×C22⋊C4C2314yes—
160C2×C11×C22⋊C4C2314yes—
161C2×C11×C22⋊C4C2314yes—
162C2×C42×C11—24no—
163C2×C42×C11—42no—
164C2×C42×C11C2314yes—
165C2×C42×C11C2314yes—
166C11×#95C2314yes—
167C11×#95C2314yes—
168C11×#95C2314yes—
169C11×#95C2314yes—
170C11×#95C2314yes—
171C11×#95C2314yes—
172C2×#2464C1111yesmaximal, characteristic, direct product factor, 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×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11—22no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11C2×D414yes—
199C24×C11C2×D414yes—
200C24×C11#4114yes—
201C24×C11C2412yes—
202C24×C11C2412yes—
203C24×C11C2412yes—
204C24×C11C2412yes—
205C24×C11C2411yescharacteristic
206C2×D4×C11—232no—
207C2×D4×C11—28no—
208C2×D4×C11—28no—
209C2×D4×C11—28no—
210C2×D4×C11—28no—
211C2×D4×C11—28no—
212C2×D4×C11—28no—
213C2×D4×C11—28no—
214C2×D4×C11—28no—
215C2×D4×C11—28no—
216C2×D4×C11—28no—
217C2×D4×C11—28no—
218C2×D4×C11—28no—
219C2×D4×C11—28no—
220C2×D4×C11—44no—
221C2×D4×C11—44no—
222C2×D4×C11—44no—
223C2×D4×C11—44no—
224C2×D4×C11—44no—
225C2×D4×C11—416no—
226C2×D4×C11—416no—
227C2×D4×C11—416no—
228C2×D4×C11—416no—
229C2×D4×C11—416no—
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—22no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—28no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—28no—
259C22×C4×C11—28no—
260C22×C4×C11—28no—
261C22×C4×C11—28no—
262C22×C4×C11—28no—
263C22×C4×C11—44no—
264C22×C4×C11—44no—
265C22×C4×C11—44no—
266C22×C4×C11—416no—
267C22×C4×C11—416no—
268C22×C4×C11—416no—
269C22×C4×C11C2×D414yes—
270C22×C4×C11C2×D414yes—
271C22×C4×C11C2×D414yes—
272C22×C4×C11C2×D414yes—
273C22×C4×C11#4114yes—
274C22×C4×C11#4114yes—
275C22×C4×C11C2412yes—
276C22×C4×C11C2412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2412yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2412yes—
286C11×C4⋊C4—28no—
287C11×C4⋊C4—28no—
288C11×C4⋊C4—28no—
289C11×C4⋊C4—28no—
290C11×C4⋊C4—28no—
291C11×C22⋊C4—28no—
292C11×C22⋊C4—28no—
293C11×C22⋊C4—28no—
294C11×C22⋊C4—28no—
295C11×C22⋊C4—28no—
296C11×C22⋊C4—28no—
297C11×C22⋊C4—28no—
298C11×C22⋊C4—28no—
299C11×C22⋊C4—44no—
300C11×C22⋊C4—44no—
301C11×C22⋊C4—44no—
302C11×C22⋊C4C2×D4116yescomplemented
303C11×C22⋊C4C2×D4116yescomplemented
304C42×C11—28no—
305C42×C11—44no—
306C22×#123C2×C1111yescharacteristic, complemented
307C22×#121C2×C1111yescharacteristic, complemented
308C22×#121C2×C1111yescharacteristic, complemented
309C22×C4×D4C2×C1111yescharacteristic, complemented
310#2464C2×C11116yesdirect product factor
311C2×#398C2×C1111yescharacteristic, complemented
312C2×#394C2×C1111yescharacteristic, complemented
313C2×#392C2×C1111yescharacteristic, complemented
314C2×#392C2×C1111yescharacteristic, complemented
315C2×#390C2×C1111yescharacteristic, complemented
316C2×#388C2×C1111yescharacteristic, complemented
317C2×#388C2×C1111yescharacteristic, complemented
318C2×#386C2×C1111yescharacteristic, complemented
319C2×#386C2×C1111yescharacteristic, complemented
320C2×#385C2×C1111yescharacteristic, complemented
321C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—28no—
330C23×C11—28no—
331C23×C11—22no—
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—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11—44no—
361C23×C11—44no—
362C23×C11—44no—
363C23×C11—44no—
364C23×C11—44no—
365C23×C11—44no—
366C23×C11—44no—
367C23×C11—44no—
368C23×C11—44no—
369C23×C11—44no—
370C23×C11—44no—
371C23×C11—44no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11—44no—
375C23×C11C22×D414yes—
376C23×C11C22×D414yes—
377C23×C11C22×D412yes—
378C23×C11C22×D412yes—
379C23×C11C2×#4114yes—
380C23×C11C2×#4112yes—
381C23×C11C2×#4112yes—
382C23×C11C2×#4112yes—
383C23×C11H(5,𝔽2)12yes—
384C23×C11H(5,𝔽2)12yes—
385C23×C11C2511yescharacteristic
386D4×C11—232no—
387D4×C11—416no—
388D4×C11—416no—
389D4×C11—416no—
390D4×C11—416no—
391D4×C11—416no—
392C2×C4×C11—28no—
393C2×C4×C11—28no—
394C2×C4×C11—28no—
395C2×C4×C11—28no—
396C2×C4×C11—28no—
397C2×C4×C11—28no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
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—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—416no—
426C2×C4×C11—416no—
427C2×C4×C11—416no—
428C2×C4×C11—44no—
429C2×C4×C11—44no—
430C2×C4×C11—44no—
431C2×C4×C11—44no—
432C2×C4×C11—44no—
433C2×C4×C11C22×D414yes—
434C2×C4×C11C22×D414yes—
435C2×C4×C11C22×D414yes—
436C2×C4×C11C22×D414yes—
437C2×C4×C11C2×#4114yes—
438C2×C4×C11C2×#4114yes—
439C23×D4C22×C1111yescharacteristic
440C23×D4C22×C1111yescharacteristic
441C23×D4C22×C1111yescharacteristic
442C23×D4C22×C1111yescharacteristic
443C23×D4C22×C1111yescharacteristic
444C23×D4C22×C1111yescharacteristic
445C24×C4C22×C1111yescharacteristic
446C24×C4C22×C1111yescharacteristic
447C24×C4C22×C1111yescharacteristic
448C2×#123—28no—
449C2×#123C22×C1118yescomplemented
450C2×#121—28no—
451C2×#121—28no—
452C2×#121C22×C1118yescomplemented
453C2×#121C22×C1118yescomplemented
454C2×C4×D4—28no—
455C2×C4×D4C22×C1118yescomplemented
456C22×C4⋊C4C22×C1111yescharacteristic
457C22×C4⋊C4C22×C1111yescharacteristic
458C22×C4⋊C4C22×C1111yescharacteristic
459C22×C4⋊C4C22×C1111yescharacteristic
460C22×C4⋊C4C22×C1111yescharacteristic
461C22×C22⋊C4C22×C1111yescharacteristic
462C22×C22⋊C4C22×C1111yescharacteristic
463C22×C22⋊C4C22×C1111yescharacteristic
464C22×C22⋊C4C22×C1111yescharacteristic
465C22×C22⋊C4C22×C1111yescharacteristic
466C22×C22⋊C4C22×C1111yescharacteristic
467C22×C22⋊C4C22×C1111yescharacteristic
468C22×C22⋊C4C22×C1111yescharacteristic
469C22×C22⋊C4C22×C1111yescharacteristic
470C22×C22⋊C4C22×C1111yescharacteristic
471C22×C22⋊C4C22×C1111yescharacteristic
472C22×C22⋊C4C22×C1111yescharacteristic
473C22×C22⋊C4C22×C1111yescharacteristic
474C22×C42C22×C1111yescharacteristic
475C22×C42C22×C1111yescharacteristic
476#398C22×C1118yescomplemented
477#394C22×C1118yescomplemented
478#392C22×C1118yescomplemented
479#392C22×C1118yescomplemented
480#390C22×C1118yescomplemented
481#388C22×C1118yescomplemented
482#388C22×C1118yescomplemented
483#386C22×C1118yescomplemented
484#386C22×C1118yescomplemented
485#385C22×C1118yescomplemented
486C4×C22⋊C4C22×C1118yescomplemented
487C2×#95C22×C1111yescharacteristic
488C2×#95C22×C1111yescharacteristic
489C2×#95C22×C1111yescharacteristic
490C2×#95C22×C1111yescharacteristic
491C2×#95C22×C1111yescharacteristic
492C2×#95C22×C1111yescharacteristic
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—24no—
500C22×C11—24no—
501C22×C11—24no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—416no—
515C22×C11—416no—
516C22×C11—416no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—88no—
525C22×C11#52514yes—
526C22×C11#53214yes—
527C22×C11#54014yes—
528C22×C11D4214yes—
529C22×C11#54614yes—
530C22×C11#54614yes—
531C22×C11#55314yes—
532C22×C11C23×D411yescharacteristic
533C22×C11C23×D411yescharacteristic
534C22×C11C22×#4111yescharacteristic
535C22×C11C22×#4111yescharacteristic
536C22×C11C22×#4111yescharacteristic
537C22×C11C2×H(5,𝔽2)11yescharacteristic
538C22×C11C2×H(5,𝔽2)11yescharacteristic
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—24no—
542C4×C11—24no—
543C4×C11—24no—
544C4×C11—24no—
545C4×C11—42no—
546C4×C11—42no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11—42no—
550C25C23×C1111yescharacteristic
551C25C23×C1111yescharacteristic
552C25C23×C1111yescharacteristic
553C25C23×C1111yescharacteristic
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—24no—
561C22×D4—24no—
562C22×D4—24no—
563C22×D4—24no—
564C22×D4—24no—
565C22×D4—24no—
566C22×D4—24no—
567C22×D4—42no—
568C22×D4—42no—
569C22×D4—42no—
570C22×D4—42no—
571C22×D4—42no—
572C22×D4C23×C1114yes—
573C22×D4C23×C1114yes—
574C22×D4C23×C1114yes—
575C22×D4C23×C1114yes—
576C22×D4C23×C1114yes—
577C22×D4C23×C1114yes—
578C23×C4—24no—
579C23×C4—24no—
580C23×C4—24no—
581C23×C4—24no—
582C23×C4—24no—
583C23×C4—24no—
584C23×C4—42no—
585C23×C4—42no—
586C23×C4—42no—
587C23×C4C23×C1111yescharacteristic
588C23×C4C23×C1111yescharacteristic
589C23×C4C23×C1111yescharacteristic
590C23×C4C23×C1111yescharacteristic
591C23×C4C23×C1111yescharacteristic
592C23×C4C23×C1114yes—
593C23×C4C23×C1114yes—
594C23×C4C23×C1114yes—
595C23×C4C23×C1111yescharacteristic
596C23×C4C23×C1111yescharacteristic
597C23×C4C23×C1111yescharacteristic
598C23×C4C23×C1111yescharacteristic
599C23×C4C23×C1111yescharacteristic
600C23×C4C23×C1111yescharacteristic
601#123—232no—
602#121—232no—
603#121—232no—
604C4×D4—232no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4C23×C1114yes—
611C2×C4⋊C4C23×C1114yes—
612C2×C4⋊C4C23×C1114yes—
613C2×C4⋊C4C23×C1114yes—
614C2×C4⋊C4C23×C1114yes—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—42no—
624C2×C22⋊C4—42no—
625C2×C22⋊C4—42no—
626C2×C22⋊C4D4×C1118yescomplemented
627C2×C22⋊C4D4×C1118yescomplemented
628C2×C22⋊C4C23×C1114yes—
629C2×C22⋊C4C23×C1114yes—
630C2×C22⋊C4C23×C1114yes—
631C2×C22⋊C4C23×C1114yes—
632C2×C22⋊C4C23×C1114yes—
633C2×C22⋊C4C23×C1114yes—
634C2×C22⋊C4C23×C1114yes—
635C2×C22⋊C4C23×C1114yes—
636C2×C22⋊C4C23×C1114yes—
637C2×C22⋊C4C23×C1114yes—
638C2×C22⋊C4C23×C1114yes—
639C2×C22⋊C4C23×C1114yes—
640C2×C22⋊C4C23×C1114yes—
641C2×C42—24no—
642C2×C42—42no—
643C2×C42C23×C1114yes—
644C2×C42C23×C1114yes—
645#95C23×C1114yes—
646#95C23×C1114yes—
647#95C23×C1114yes—
648#95C23×C1114yes—
649#95C23×C1114yes—
650#95C23×C1114yes—
651C2×C11—44no—
652C2×C11—44no—
653C2×C11—44no—
654C2×C11—82no—
655C2×C11#246418yesdirect product factor
656C2×C11C2×#52511yescharacteristic
657C2×C11C2×#53211yescharacteristic
658C2×C11C2×#54011yescharacteristic
659C2×C11C2×D4211yescharacteristic
660C2×C11C2×#54611yescharacteristic
661C2×C11C2×#54611yescharacteristic
662C2×C11C2×#55311yescharacteristic
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
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—22no—
686C24—22no—
687C24—22no—
688C24C2×D4×C1114yes—
689C24C2×D4×C1114yes—
690C24C11×#4114yes—
691C24C24×C1112yes—
692C24C24×C1112yes—
693C24C24×C1112yes—
694C24C24×C1112yes—
695C24C24×C1111yescharacteristic
696C2×D4—232no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—416no—
716C2×D4—416no—
717C2×D4—416no—
718C2×D4—416no—
719C2×D4—416no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—28no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—416no—
757C22×C4—416no—
758C22×C4—416no—
759C22×C4C2×D4×C1114yes—
760C22×C4C2×D4×C1114yes—
761C22×C4C2×D4×C1114yes—
762C22×C4C2×D4×C1114yes—
763C22×C4C11×#4114yes—
764C22×C4C11×#4114yes—
765C22×C4C24×C1112yes—
766C22×C4C24×C1112yes—
767C22×C4C24×C1112yes—
768C22×C4C24×C1112yes—
769C22×C4C24×C1112yes—
770C22×C4C24×C1112yes—
771C22×C4C24×C1112yes—
772C22×C4C24×C1112yes—
773C22×C4C24×C1112yes—
774C22×C4C24×C1112yes—
775C22×C4C24×C1112yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—28no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4C2×D4×C11116yescomplemented
793C22⋊C4C2×D4×C11116yescomplemented
794C42—28no—
795C42—44no—
796C11C2×#246411yescharacteristic, direct product factor, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—28no—
803C23—28no—
804C23—28no—
805C23—28no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
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—22no—
830C23—22no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—44no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23C22×D4×C1114yes—
851C23C22×D4×C1114yes—
852C23C22×D4×C1112yes—
853C23C22×D4×C1112yes—
854C23C2×C11×#4114yes—
855C23C2×C11×#4112yes—
856C23C2×C11×#4112yes—
857C23C2×C11×#4112yes—
858C23C11×H(5,𝔽2)12yes—
859C23C11×H(5,𝔽2)12yes—
860C23C25×C1111yescharacteristic
861D4—232no—
862D4—416no—
863D4—416no—
864D4—416no—
865D4—416no—
866D4—416no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
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—416no—
901C2×C4—416no—
902C2×C4—416no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4C22×D4×C1114yes—
909C2×C4C22×D4×C1114yes—
910C2×C4C22×D4×C1114yes—
911C2×C4C22×D4×C1114yes—
912C2×C4C2×C11×#4114yes—
913C2×C4C2×C11×#4114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—24no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—416no—
936C22—416no—
937C22—416no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—88no—
946C22C11×#52514yes—
947C22C11×#53214yes—
948C22C11×#54014yes—
949C22D42×C1114yes—
950C22C11×#54614yes—
951C22C11×#54614yes—
952C22C11×#55314yes—
953C22C23×D4×C1111yescharacteristic
954C22C23×D4×C1111yescharacteristic
955C22C22×C11×#4111yescharacteristic
956C22C22×C11×#4111yescharacteristic
957C22C22×C11×#4111yescharacteristic
958C22C2×C11×H(5,𝔽2)11yescharacteristic
959C22C2×C11×H(5,𝔽2)11yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C2—44no—
972C2—44no—
973C2—44no—
974C2—82no—
975C2C11×#246418yesdirect product factor
976C2C2×C11×#52511yescharacteristic
977C2C2×C11×#53211yescharacteristic
978C2C2×C11×#54011yescharacteristic
979C2C2×D42×C1111yescharacteristic
980C2C2×C11×#54611yescharacteristic
981C2C2×C11×#54611yescharacteristic
982C2C2×C11×#55311yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#123C2semidirect
2. C22×C11×#121C2semidirect
3. C22×C11×#121C2semidirect
4. C22×C4×D4×C11C2semidirect
5. C11×#2464C2direct (N × H)
6. C2×C11×#398C2semidirect
7. C2×C11×#394C2semidirect
8. C2×C11×#392C2semidirect
9. C2×C11×#392C2semidirect
10. C2×C11×#390C2semidirect
11. C2×C11×#388C2semidirect
12. C2×C11×#388C2semidirect
13. C2×C11×#386C2semidirect
14. C2×C11×#386C2semidirect
15. C2×C11×#385C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
27. C2×C11×#123C22semidirect
30. C2×C11×#121C22semidirect
31. C2×C11×#121C22semidirect
33. C2×C4×D4×C11C22semidirect
54. C11×#398C22semidirect
55. C11×#394C22semidirect
56. C11×#392C22semidirect
57. C11×#392C22semidirect
58. C11×#390C22semidirect
59. C11×#388C22semidirect
60. C11×#388C22semidirect
61. C11×#386C22semidirect
62. C11×#386C22semidirect
63. C11×#385C22semidirect
64. C4×C11×C22⋊C4C22semidirect
147. C2×C11×C22⋊C4D4semidirect
148. C2×C11×C22⋊C4D4semidirect
172. C2×#2464C11direct (N × H)
302. C11×C22⋊C4C2×D4semidirect
303. C11×C22⋊C4C2×D4semidirect
306. C22×#123C2×C11semidirect
307. C22×#121C2×C11semidirect
308. C22×#121C2×C11semidirect
309. C22×C4×D4C2×C11semidirect
310. #2464C2×C11direct (N × H)
311. C2×#398C2×C11semidirect
312. C2×#394C2×C11semidirect
313. C2×#392C2×C11semidirect
314. C2×#392C2×C11semidirect
315. C2×#390C2×C11semidirect
316. C2×#388C2×C11semidirect
317. C2×#388C2×C11semidirect
318. C2×#386C2×C11semidirect
319. C2×#386C2×C11semidirect
320. C2×#385C2×C11semidirect
321. C2×C4×C22⋊C4C2×C11semidirect
449. C2×#123C22×C11semidirect
452. C2×#121C22×C11semidirect
453. C2×#121C22×C11semidirect
455. C2×C4×D4C22×C11semidirect
476. #398C22×C11semidirect
477. #394C22×C11semidirect
478. #392C22×C11semidirect
479. #392C22×C11semidirect
480. #390C22×C11semidirect
481. #388C22×C11semidirect
482. #388C22×C11semidirect
483. #386C22×C11semidirect
484. #386C22×C11semidirect
485. #385C22×C11semidirect
486. C4×C22⋊C4C22×C11semidirect
626. C2×C22⋊C4D4×C11semidirect
627. C2×C22⋊C4D4×C11semidirect
655. C2×C11#2464direct (N × H)
792. C22⋊C4C2×D4×C11semidirect
793. C22⋊C4C2×D4×C11semidirect
796. C11C2×#2464direct (N × H)
975. C2C11×#2464direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C22×C11×#1212
C22×C4×D4×C112
C11×#24642
C2×C11×#3982
C2×C11×#3942
C2×C11×#3922
C2×C11×#3902
C2×C11×#3882
C2×C11×#3862
C2×C11×#3852
C2×C4×C11×C22⋊C42
C2×#246411