Finite Group Databasebeta

← C11×#14566 #14591759

Subgroups — C11×#14566 #14591759

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#394C211yesmaximal, characteristic
2C2×C11×#388C211yesmaximal, characteristic, complemented
3C2×C11×#388C211yesmaximal, characteristic, complemented
4C11×#1443C211yesmaximal, characteristic, complemented
5C11×#1439C211yesmaximal, characteristic, complemented
6C11×#1439C211yesmaximal, characteristic, complemented
7C11×#1438C211yesmaximal, characteristic
8C11×#1438C211yesmaximal, characteristic
9C11×#1437C211yesmaximal, characteristic, complemented
10C11×#1437C211yesmaximal, characteristic, complemented
11C11×#1437C211yesmaximal, characteristic, complemented
12C11×#1437C211yesmaximal, characteristic, complemented
13C11×#1436C211yesmaximal, characteristic, complemented
14C11×#1436C211yesmaximal, characteristic, complemented
15C11×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊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×C42×C11C2211yescharacteristic
33C22×C42×C11C2211yescharacteristic
34C22×C42×C11C2211yescharacteristic
35C11×#394C418yescomplemented
36C11×#388—24no—
37C11×#388—24no—
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C25×C11C2311yescharacteristic
55C25×C11C2311yescharacteristic
56C22×D4×C11—41no—
57C22×D4×C11—41no—
58C22×D4×C11—41no—
59C22×D4×C11—41no—
60C22×D4×C11—41no—
61C22×D4×C11—41no—
62C22×D4×C11C2×C414yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C4⋊C4—41no—
84C2×C11×C4⋊C4C2×C414yes—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4—41no—
103C2×C11×C22⋊C4—41no—
104C2×C11×C22⋊C4—41no—
105C2×C11×C22⋊C4—41no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4—41no—
108C2×C11×C22⋊C4—41no—
109C2×C11×C22⋊C4—41no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4—41no—
113C2×C11×C22⋊C4—41no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4—41no—
116C2×C11×C22⋊C4—41no—
117C2×C11×C22⋊C4C2×C414yes—
118C2×C11×C22⋊C4C2×C414yes—
119C2×C11×C22⋊C4C2×C414yes—
120C2×C11×C22⋊C4C2×C414yes—
121C2×C42×C11—22no—
122C2×C42×C11—22no—
123C2×C42×C11—22no—
124C2×C42×C11—41no—
125C2×C42×C11—41no—
126C2×C42×C11—41no—
127C2×C42×C11—41no—
128C2×C42×C11—41no—
129C2×C42×C11—41no—
130C11×#95—22no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—22no—
134C11×#95—41no—
135C11×#95—41no—
136C11×#95—41no—
137C11×#95—41no—
138C11×#95—41no—
139C11×#95—41no—
140C11×#95—41no—
141C11×#95—41no—
142C11×#95—41no—
143C11×#95—41no—
144C11×#95C2×C414yes—
145C11×#95D414yescomplemented
146#14566C1111yesmaximal, characteristic, direct product factor, Sylow
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11C22×C412yes—
176C24×C11C22×C412yes—
177C24×C11C2411yescharacteristic
178C2×D4×C11—44no—
179C2×D4×C11—44no—
180C2×D4×C11—44no—
181C2×D4×C11—44no—
182C2×D4×C11—44no—
183C2×D4×C11—44no—
184C2×D4×C11—44no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11C22×C412yes—
264C22×C4×C11C22×C412yes—
265C22×C4×C11C22×C412yes—
266C22×C4×C11C22×C412yes—
267C22×C4×C11C22×C412yes—
268C22×C4×C11C2×D412yes—
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2×D412yes—
271C22×C4×C11#4112yes—
272C22×C4×C11#4112yes—
273C22×C4×C11#4112yes—
274C22×C4×C11#4112yes—
275C22×C4×C11#4112yes—
276C11×C4⋊C4—44no—
277C11×C4⋊C4—44no—
278C11×C4⋊C4—44no—
279C11×C22⋊C4—28no—
280C11×C22⋊C4—28no—
281C11×C22⋊C4—44no—
282C11×C22⋊C4—44no—
283C11×C22⋊C4—44no—
284C11×C22⋊C4—44no—
285C11×C22⋊C4—44no—
286C11×C22⋊C4—44no—
287C11×C22⋊C4—44no—
288C11×C22⋊C4—44no—
289C11×C22⋊C4—44no—
290C11×C22⋊C4—44no—
291C42×C11—44no—
292C42×C11—44no—
293C42×C11—44no—
294C2×#394C2×C1111yescharacteristic
295C2×#388C2×C1111yescharacteristic, complemented
296C2×#388C2×C1111yescharacteristic, complemented
297#1443C2×C1111yescharacteristic, complemented
298#1439C2×C1111yescharacteristic, complemented
299#1439C2×C1111yescharacteristic, complemented
300#1438C2×C1111yescharacteristic
301#1438C2×C1111yescharacteristic
302#1437C2×C1111yescharacteristic, complemented
303#1437C2×C1111yescharacteristic, complemented
304#1437C2×C1111yescharacteristic, complemented
305#1437C2×C1111yescharacteristic, complemented
306#1436C2×C1111yescharacteristic, complemented
307#1436C2×C1111yescharacteristic, complemented
308C4⋊#95C2×C1111yescharacteristic, complemented
309C23×C11—22no—
310C23×C11—22no—
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—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11C23×C411yescharacteristic
380C23×C11C22×D411yescharacteristic
381C23×C11C2×#4111yescharacteristic
382C23×C11C2×#4111yescharacteristic
383C23×C11C2×#4111yescharacteristic
384C23×C11C2×#4111yescharacteristic
385C23×C11C2×#4111yescharacteristic
386C23×C11H(5,𝔽2)11yescharacteristic
387C23×C11H(5,𝔽2)11yescharacteristic
388C23×C11H(5,𝔽2)11yescharacteristic
389C23×C11H(5,𝔽2)11yescharacteristic
390C23×C11H(5,𝔽2)11yescharacteristic
391C23×C11H(5,𝔽2)11yescharacteristic
392C23×C11H(5,𝔽2)11yescharacteristic
393C23×C112−1+411yescharacteristic
394D4×C11—416no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
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—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11C4×D414yes—
486C23×D4C22×C1111yescharacteristic
487C22×C4⋊C4C22×C1111yescharacteristic
488C22×C4⋊C4C22×C1111yescharacteristic
489C22×C4⋊C4C22×C1111yescharacteristic
490C22×C22⋊C4C22×C1111yescharacteristic
491C22×C22⋊C4C22×C1111yescharacteristic
492C22×C22⋊C4C22×C1111yescharacteristic
493C22×C22⋊C4C22×C1111yescharacteristic
494C22×C22⋊C4C22×C1111yescharacteristic
495C22×C22⋊C4C22×C1111yescharacteristic
496C22×C22⋊C4C22×C1111yescharacteristic
497C22×C22⋊C4C22×C1111yescharacteristic
498C22×C22⋊C4C22×C1111yescharacteristic
499C22×C22⋊C4C22×C1111yescharacteristic
500C22×C22⋊C4C22×C1111yescharacteristic
501C22×C22⋊C4C22×C1111yescharacteristic
502C22×C42C22×C1111yescharacteristic
503C22×C42C22×C1111yescharacteristic
504C22×C42C22×C1111yescharacteristic
505#394C4×C1118yescomplemented
506#388—24no—
507#388—24no—
508C2×#95C22×C1111yescharacteristic
509C2×#95C22×C1111yescharacteristic
510C2×#95C22×C1111yescharacteristic
511C2×#95C22×C1111yescharacteristic
512C2×#95C22×C1111yescharacteristic
513C2×#95C22×C1111yescharacteristic
514C2×#95C22×C1111yescharacteristic
515C2×#95C22×C1111yescharacteristic
516C2×#95C22×C1111yescharacteristic
517C2×#95C22×C1111yescharacteristic
518C2×#95C22×C1111yescharacteristic
519C2×#95C22×C1111yescharacteristic
520C2×#95C22×C1111yescharacteristic
521C2×#95C22×C1111yescharacteristic
522C2×#95C22×C1111yescharacteristic
523C2×#95C22×C1111yescharacteristic
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—42no—
531C22×C11—42no—
532C22×C11—42no—
533C22×C11—42no—
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—42no—
537C22×C11—42no—
538C22×C11—81no—
539C22×C11—81no—
540C22×C11—81no—
541C22×C11—81no—
542C22×C11—81no—
543C22×C11—81no—
544C22×C11—81no—
545C22×C11—81no—
546C22×C11—81no—
547C22×C11—81no—
548C22×C11—81no—
549C22×C11—81no—
550C22×C11—81no—
551C22×C11—81no—
552C22×C11—81no—
553C22×C11—81no—
554C22×C11C2×C4×D411yescharacteristic
555C22×C11C4×#4111yescharacteristic
556C22×C11C4×#4111yescharacteristic
557C22×C11#51811yescharacteristic
558C22×C11#51811yescharacteristic
559C22×C11#51811yescharacteristic
560C22×C11#52011yescharacteristic
561C22×C11#53511yescharacteristic
562C22×C11#53711yescharacteristic
563C22×C11#53811yescharacteristic
564C22×C11#53811yescharacteristic
565C22×C11#53811yescharacteristic
566C22×C11#53911yescharacteristic
567C22×C11#54011yescharacteristic
568C22×C11#54011yescharacteristic
569C22×C11#54211yescharacteristic
570C22×C11#54211yescharacteristic
571C22×C11#54211yescharacteristic
572C22×C11#54211yescharacteristic
573C22×C11#54611yescharacteristic
574C22×C11#54611yescharacteristic
575C22×C11#54611yescharacteristic
576C22×C11#55011yescharacteristic
577C22×C11#55111yescharacteristic
578C22×C11#55311yescharacteristic
579C22×C11#55311yescharacteristic
580C22×C11#55311yescharacteristic
581C22×C11#55311yescharacteristic
582C22×C11#55311yescharacteristic
583C22×C11#55511yescharacteristic
584C22×C11#55911yescharacteristic
585C22×C11#56011yescharacteristic
586C22×C11#56011yescharacteristic
587C22×C11#56011yescharacteristic
588C22×C11H(3,𝔽4)11yescharacteristic
589C4×C11—24no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11—42no—
594C4×C11—42no—
595C4×C11—42no—
596C4×C11—42no—
597C4×C11—42no—
598C4×C11—42no—
599C4×C11—42no—
600C4×C11—81no—
601C4×C11—81no—
602C25C23×C1111yescharacteristic
603C25C23×C1111yescharacteristic
604C22×D4—41no—
605C22×D4—41no—
606C22×D4—41no—
607C22×D4—41no—
608C22×D4—41no—
609C22×D4—41no—
610C22×D4C2×C4×C1114yes—
611C23×C4C23×C1111yescharacteristic
612C23×C4C23×C1111yescharacteristic
613C23×C4C23×C1111yescharacteristic
614C23×C4C23×C1111yescharacteristic
615C23×C4C23×C1111yescharacteristic
616C23×C4C23×C1111yescharacteristic
617C23×C4C23×C1111yescharacteristic
618C23×C4C23×C1111yescharacteristic
619C23×C4C23×C1111yescharacteristic
620C23×C4C23×C1111yescharacteristic
621C23×C4C23×C1111yescharacteristic
622C23×C4C23×C1111yescharacteristic
623C23×C4C23×C1111yescharacteristic
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4C2×C4×C1114yes—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4C2×C4×C1114yes—
666C2×C22⋊C4C2×C4×C1114yes—
667C2×C22⋊C4C2×C4×C1114yes—
668C2×C22⋊C4C2×C4×C1114yes—
669C2×C42—22no—
670C2×C42—22no—
671C2×C42—22no—
672C2×C42—41no—
673C2×C42—41no—
674C2×C42—41no—
675C2×C42—41no—
676C2×C42—41no—
677C2×C42—41no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95C2×C4×C1114yes—
693#95D4×C1114yescomplemented
694C2×C11—82no—
695C2×C11—82no—
696C2×C11#232411yescharacteristic
697C2×C11#233511yescharacteristic
698C2×C11#233711yescharacteristic
699C2×C11#236311yescharacteristic
700C2×C11#236411yescharacteristic
701C2×C11#237411yescharacteristic
702C2×C11#237511yescharacteristic
703C2×C11#270311yescharacteristic
704C2×C11#270511yescharacteristic
705C2×C11#271211yescharacteristic
706C2×C11#271411yescharacteristic
707C2×C11#275311yescharacteristic
708C2×C11#279511yescharacteristic
709C2×C11#280111yescharacteristic
710C2×C11#280311yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24C22×C4×C1112yes—
740C24C22×C4×C1112yes—
741C24C24×C1111yescharacteristic
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4C22×C4×C1112yes—
828C22×C4C22×C4×C1112yes—
829C22×C4C22×C4×C1112yes—
830C22×C4C22×C4×C1112yes—
831C22×C4C22×C4×C1112yes—
832C22×C4C2×D4×C1112yes—
833C22×C4C2×D4×C1112yes—
834C22×C4C2×D4×C1112yes—
835C22×C4C11×#4112yes—
836C22×C4C11×#4112yes—
837C22×C4C11×#4112yes—
838C22×C4C11×#4112yes—
839C22×C4C11×#4112yes—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C42—44no—
856C42—44no—
857C42—44no—
858C11#1456611yescharacteristic, direct product factor, Sylow
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23C23×C4×C1111yescharacteristic
930C23C22×D4×C1111yescharacteristic
931C23C2×C11×#4111yescharacteristic
932C23C2×C11×#4111yescharacteristic
933C23C2×C11×#4111yescharacteristic
934C23C2×C11×#4111yescharacteristic
935C23C2×C11×#4111yescharacteristic
936C23C11×H(5,𝔽2)11yescharacteristic
937C23C11×H(5,𝔽2)11yescharacteristic
938C23C11×H(5,𝔽2)11yescharacteristic
939C23C11×H(5,𝔽2)11yescharacteristic
940C23C11×H(5,𝔽2)11yescharacteristic
941C23C11×H(5,𝔽2)11yescharacteristic
942C23C11×H(5,𝔽2)11yescharacteristic
943C23C11×2−1+411yescharacteristic
944D4—416no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4C4×D4×C1114yes—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22C2×C4×D4×C1111yescharacteristic
1067C22C4×C11×#4111yescharacteristic
1068C22C4×C11×#4111yescharacteristic
1069C22C11×#51811yescharacteristic
1070C22C11×#51811yescharacteristic
1071C22C11×#51811yescharacteristic
1072C22C11×#52011yescharacteristic
1073C22C11×#53511yescharacteristic
1074C22C11×#53711yescharacteristic
1075C22C11×#53811yescharacteristic
1076C22C11×#53811yescharacteristic
1077C22C11×#53811yescharacteristic
1078C22C11×#53911yescharacteristic
1079C22C11×#54011yescharacteristic
1080C22C11×#54011yescharacteristic
1081C22C11×#54211yescharacteristic
1082C22C11×#54211yescharacteristic
1083C22C11×#54211yescharacteristic
1084C22C11×#54211yescharacteristic
1085C22C11×#54611yescharacteristic
1086C22C11×#54611yescharacteristic
1087C22C11×#54611yescharacteristic
1088C22C11×#55011yescharacteristic
1089C22C11×#55111yescharacteristic
1090C22C11×#55311yescharacteristic
1091C22C11×#55311yescharacteristic
1092C22C11×#55311yescharacteristic
1093C22C11×#55311yescharacteristic
1094C22C11×#55311yescharacteristic
1095C22C11×#55511yescharacteristic
1096C22C11×#55911yescharacteristic
1097C22C11×#56011yescharacteristic
1098C22C11×#56011yescharacteristic
1099C22C11×#56011yescharacteristic
1100C22C11×H(3,𝔽4)11yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—81no—
1113C4—81no—
1114C2—82no—
1115C2—82no—
1116C2C11×#232411yescharacteristic
1117C2C11×#233511yescharacteristic
1118C2C11×#233711yescharacteristic
1119C2C11×#236311yescharacteristic
1120C2C11×#236411yescharacteristic
1121C2C11×#237411yescharacteristic
1122C2C11×#237511yescharacteristic
1123C2C11×#270311yescharacteristic
1124C2C11×#270511yescharacteristic
1125C2C11×#271211yescharacteristic
1126C2C11×#271411yescharacteristic
1127C2C11×#275311yescharacteristic
1128C2C11×#279511yescharacteristic
1129C2C11×#280111yescharacteristic
1130C2C11×#280311yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×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
2. C2×C11×#388C2semidirect
3. C2×C11×#388C2semidirect
4. C11×#1443C2semidirect
5. C11×#1439C2semidirect
6. C11×#1439C2semidirect
9. C11×#1437C2semidirect
10. C11×#1437C2semidirect
11. C11×#1437C2semidirect
12. C11×#1437C2semidirect
13. C11×#1436C2semidirect
14. C11×#1436C2semidirect
15. C11×C4⋊#95C2semidirect
35. C11×#394C4semidirect
145. C11×#95D4semidirect
146. #14566C11direct (N × H)
295. C2×#388C2×C11semidirect
296. C2×#388C2×C11semidirect
297. #1443C2×C11semidirect
298. #1439C2×C11semidirect
299. #1439C2×C11semidirect
302. #1437C2×C11semidirect
303. #1437C2×C11semidirect
304. #1437C2×C11semidirect
305. #1437C2×C11semidirect
306. #1436C2×C11semidirect
307. #1436C2×C11semidirect
308. C4⋊#95C2×C11semidirect
505. #394C4×C11semidirect
693. #95D4×C11semidirect
858. C11#14566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3942
C2×C11×#3882
C11×#14432
C11×#14392
C11×#14382
C11×#14372
C11×#14362
C11×C4⋊#952
#1456611