Finite Group Databasebeta

← C11×#16289 #14593482

Subgroups — C11×#16289 #14593482

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#396C211yesmaximal, characteristic, complemented
2C2×C11×#394C211yesmaximal, characteristic, complemented
3C2×C11×#394C211yesmaximal, characteristic, complemented
4C2×C11×#392C211yesmaximal, characteristic
5C2×C11×#390C211yesmaximal, characteristic, complemented
6C2×C11×#387C211yesmaximal, characteristic, complemented
7C11×#1442C211yesmaximal, characteristic, complemented
8C11×#1440C211yesmaximal, characteristic, complemented
9C11×#1439C211yesmaximal, characteristic, complemented
10C11×#1439C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C11×#1438C211yesmaximal, characteristic, complemented
13C11×#1438C211yesmaximal, characteristic, complemented
14C11×#1438C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊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×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C42×C11C2211yescharacteristic
39C11×#396—24no—
40C11×#394—24no—
41C11×#394—24no—
42C11×#392—24no—
43C11×#390—24no—
44C11×#387—24no—
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
54C2×C11×#95C2211yescharacteristic
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C25×C11C2311yescharacteristic
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—22no—
70C22×D4×C11—22no—
71C22×D4×C11—41no—
72C22×D4×C11—41no—
73C22×D4×C11—41no—
74C22×D4×C11—41no—
75C22×D4×C11—41no—
76C22×D4×C11—41no—
77C22×D4×C11—41no—
78C22×D4×C11—41no—
79C22×D4×C11—41no—
80C22×D4×C11—41no—
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×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—41no—
101C2×C11×C4⋊C4—41no—
102C2×C11×C4⋊C4—41no—
103C2×C11×C4⋊C4—41no—
104C2×C11×C4⋊C4D414yescomplemented
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—22no—
123C2×C11×C22⋊C4—22no—
124C2×C11×C22⋊C4—22no—
125C2×C11×C22⋊C4—22no—
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4—41no—
128C2×C11×C22⋊C4—41no—
129C2×C11×C22⋊C4—41no—
130C2×C11×C22⋊C4—41no—
131C2×C11×C22⋊C4—41no—
132C2×C11×C22⋊C4—41no—
133C2×C11×C22⋊C4—41no—
134C2×C11×C22⋊C4—41no—
135C2×C11×C22⋊C4—41no—
136C2×C11×C22⋊C4—41no—
137C2×C11×C22⋊C4—41no—
138C2×C11×C22⋊C4—41no—
139C2×C11×C22⋊C4—41no—
140C2×C11×C22⋊C4—41no—
141C2×C11×C22⋊C4—41no—
142C2×C11×C22⋊C4—41no—
143C2×C11×C22⋊C4—41no—
144C2×C11×C22⋊C4—41no—
145C2×C11×C22⋊C4—41no—
146C2×C11×C22⋊C4—41no—
147C2×C11×C22⋊C4—41no—
148C2×C11×C22⋊C4—41no—
149C2×C11×C22⋊C4D414yescomplemented
150C2×C42×C11—22no—
151C2×C42×C11—22no—
152C2×C42×C11—41no—
153C11×#95—22no—
154C11×#95—22no—
155C11×#95—22no—
156C11×#95—22no—
157C11×#95—22no—
158C11×#95—22no—
159C11×#95—41no—
160C11×#95—41no—
161C11×#95—41no—
162C11×#95—41no—
163C11×#95—41no—
164C11×#95D414yes—
165#16289C1111yesmaximal, characteristic, direct product factor, Sylow
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×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11—21no—
198C24×C11—21no—
199C24×C11—21no—
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—21no—
204C24×C11—21no—
205C24×C11—21no—
206C24×C11—21no—
207C24×C11—21no—
208C24×C11C2×D412yes—
209C24×C11#4112yes—
210C24×C11#4112yes—
211C24×C11C2411yescharacteristic
212C2×D4×C11—28no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—44no—
217C2×D4×C11—44no—
218C2×D4×C11—44no—
219C2×D4×C11—44no—
220C2×D4×C11—44no—
221C2×D4×C11—44no—
222C2×D4×C11—44no—
223C2×D4×C11—44no—
224C2×D4×C11—44no—
225C2×D4×C11—44no—
226C2×D4×C11—44no—
227C2×D4×C11—44no—
228C2×D4×C11—44no—
229C2×D4×C11—44no—
230C2×D4×C11—44no—
231C2×D4×C11—44no—
232C2×D4×C11—44no—
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×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—21no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—21no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—21no—
285C22×C4×C11—21no—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—21no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11—21no—
296C22×C4×C11—21no—
297C22×C4×C11—21no—
298C22×C4×C11—21no—
299C22×C4×C11—21no—
300C22×C4×C11—21no—
301C22×C4×C11—21no—
302C22×C4×C11—21no—
303C22×C4×C11—21no—
304C22×C4×C11—21no—
305C22×C4×C11—21no—
306C22×C4×C11—21no—
307C22×C4×C11C2×D412yes—
308C22×C4×C11C2×D412yes—
309C22×C4×C11C2×D412yes—
310C22×C4×C11C2×D412yes—
311C22×C4×C11C2×D412yes—
312C22×C4×C11C2×D412yes—
313C22×C4×C11C2×D412yes—
314C22×C4×C11C2×D412yes—
315C22×C4×C11#4112yes—
316C22×C4×C11#4112yes—
317C11×C4⋊C4—28no—
318C11×C4⋊C4—44no—
319C11×C4⋊C4—44no—
320C11×C4⋊C4—44no—
321C11×C22⋊C4—44no—
322C11×C22⋊C4—44no—
323C11×C22⋊C4—44no—
324C11×C22⋊C4—44no—
325C11×C22⋊C4—44no—
326C11×C22⋊C4—44no—
327C11×C22⋊C4—44no—
328C11×C22⋊C4—44no—
329C11×C22⋊C4—44no—
330C11×C22⋊C4—44no—
331C11×C22⋊C4—44no—
332C11×C22⋊C4—44no—
333C11×C22⋊C4—44no—
334C11×C22⋊C4—44no—
335C11×C22⋊C4—44no—
336C42×C11—44no—
337C2×#396C2×C1111yescharacteristic, complemented
338C2×#394C2×C1111yescharacteristic, complemented
339C2×#394C2×C1111yescharacteristic, complemented
340C2×#392C2×C1111yescharacteristic
341C2×#390C2×C1111yescharacteristic, complemented
342C2×#387C2×C1111yescharacteristic, complemented
343#1442C2×C1111yescharacteristic, complemented
344#1440C2×C1111yescharacteristic, complemented
345#1439C2×C1111yescharacteristic, complemented
346#1439C2×C1111yescharacteristic, complemented
347#1439C2×C1111yescharacteristic, complemented
348#1438C2×C1111yescharacteristic, complemented
349#1438C2×C1111yescharacteristic, complemented
350#1438C2×C1111yescharacteristic, complemented
351#1437C2×C1111yescharacteristic, complemented
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11—41no—
437C23×C11—41no—
438C23×C11—41no—
439C23×C11—41no—
440C23×C11—41no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11—41no—
450C23×C11—41no—
451C23×C11—41no—
452C23×C11—41no—
453C23×C11—41no—
454C23×C11—41no—
455C23×C11—41no—
456C23×C11—41no—
457C23×C11C22×D411yescharacteristic
458C23×C11C22×D411yescharacteristic
459C23×C11C22×D411yescharacteristic
460C23×C11C2×#4111yescharacteristic
461C23×C11C2×#4111yescharacteristic
462C23×C11C2×#4111yescharacteristic
463C23×C11C2×#4111yescharacteristic
464C23×C11H(5,𝔽2)11yescharacteristic
465C23×C11H(5,𝔽2)11yescharacteristic
466C23×C11H(5,𝔽2)11yescharacteristic
467C23×C11H(5,𝔽2)11yescharacteristic
468C23×C11H(5,𝔽2)11yescharacteristic
469C23×C11H(5,𝔽2)11yescharacteristic
470C23×C11H(5,𝔽2)11yescharacteristic
471C23×C112−1+411yescharacteristic
472D4×C11—416no—
473D4×C11—416no—
474D4×C11—416no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11—41no—
535C2×C4×C11—41no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11—41no—
541C2×C4×C11—41no—
542C2×C4×C11—41no—
543C2×C4×C11—41no—
544C2×C4×C11—41no—
545C2×C4×C11—41no—
546C2×C4×C11—41no—
547C2×C4×C11—41no—
548C2×C4×C11—41no—
549C2×C4×C11—41no—
550C2×C4×C11—41no—
551C2×C4×C11—41no—
552C2×C4×C11—41no—
553C2×C4×C11—41no—
554C2×C4×C11—41no—
555C2×C4×C11—41no—
556C2×C4×C11—41no—
557C2×C4×C11—41no—
558C2×C4×C11#12114yes—
559C23×D4C22×C1111yescharacteristic
560C23×D4C22×C1111yescharacteristic
561C23×D4C22×C1111yescharacteristic
562C22×C4⋊C4C22×C1111yescharacteristic
563C22×C4⋊C4C22×C1111yescharacteristic
564C22×C4⋊C4C22×C1111yescharacteristic
565C22×C4⋊C4C22×C1111yescharacteristic
566C22×C22⋊C4C22×C1111yescharacteristic
567C22×C22⋊C4C22×C1111yescharacteristic
568C22×C22⋊C4C22×C1111yescharacteristic
569C22×C22⋊C4C22×C1111yescharacteristic
570C22×C22⋊C4C22×C1111yescharacteristic
571C22×C22⋊C4C22×C1111yescharacteristic
572C22×C22⋊C4C22×C1111yescharacteristic
573C22×C22⋊C4C22×C1111yescharacteristic
574C22×C22⋊C4C22×C1111yescharacteristic
575C22×C22⋊C4C22×C1111yescharacteristic
576C22×C22⋊C4C22×C1111yescharacteristic
577C22×C22⋊C4C22×C1111yescharacteristic
578C22×C22⋊C4C22×C1111yescharacteristic
579C22×C22⋊C4C22×C1111yescharacteristic
580C22×C22⋊C4C22×C1111yescharacteristic
581C22×C42C22×C1111yescharacteristic
582#396—24no—
583#394—24no—
584#394—24no—
585#392—24no—
586#390—24no—
587#387—24no—
588C2×#95C22×C1111yescharacteristic
589C2×#95C22×C1111yescharacteristic
590C2×#95C22×C1111yescharacteristic
591C2×#95C22×C1111yescharacteristic
592C2×#95C22×C1111yescharacteristic
593C2×#95C22×C1111yescharacteristic
594C2×#95C22×C1111yescharacteristic
595C2×#95C22×C1111yescharacteristic
596C2×#95C22×C1111yescharacteristic
597C2×#95C22×C1111yescharacteristic
598C2×#95C22×C1111yescharacteristic
599C2×#95C22×C1111yescharacteristic
600C22×C11—42no—
601C22×C11—42no—
602C22×C11—42no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—42no—
606C22×C11—42no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—42no—
612C22×C11—42no—
613C22×C11—42no—
614C22×C11—42no—
615C22×C11—42no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—42no—
621C22×C11—81no—
622C22×C11—81no—
623C22×C11—81no—
624C22×C11—81no—
625C22×C11—81no—
626C22×C11—81no—
627C22×C11—81no—
628C22×C11—81no—
629C22×C11—81no—
630C22×C11—81no—
631C22×C11—81no—
632C22×C11—81no—
633C22×C11—81no—
634C22×C11—81no—
635C22×C11—81no—
636C22×C11—81no—
637C22×C11—81no—
638C22×C11—81no—
639C22×C11—81no—
640C22×C11—81no—
641C22×C11—81no—
642C22×C11—81no—
643C22×C11—81no—
644C22×C11—81no—
645C22×C11C2×#12111yescharacteristic
646C22×C11#52511yescharacteristic
647C22×C11#52911yescharacteristic
648C22×C11#53411yescharacteristic
649C22×C11#53511yescharacteristic
650C22×C11#53511yescharacteristic
651C22×C11#53511yescharacteristic
652C22×C11#53511yescharacteristic
653C22×C11#53711yescharacteristic
654C22×C11#53811yescharacteristic
655C22×C11#53811yescharacteristic
656C22×C11#53811yescharacteristic
657C22×C11#53811yescharacteristic
658C22×C11#53811yescharacteristic
659C22×C11#53911yescharacteristic
660C22×C11#54011yescharacteristic
661C22×C11#54011yescharacteristic
662C22×C11#54011yescharacteristic
663C22×C11#54211yescharacteristic
664C22×C11D4211yescharacteristic
665C22×C11D4211yescharacteristic
666C22×C11#54611yescharacteristic
667C22×C11#54611yescharacteristic
668C22×C11#54611yescharacteristic
669C22×C11#54611yescharacteristic
670C22×C11#54611yescharacteristic
671C22×C11#54811yescharacteristic
672C22×C11#54811yescharacteristic
673C22×C11#55011yescharacteristic
674C22×C11#55111yescharacteristic
675C22×C11#55311yescharacteristic
676C22×C11#56011yescharacteristic
677C22×C11#56011yescharacteristic
678C22×C11#56211yescharacteristic
679C22×C11#56211yescharacteristic
680C4×C11—24no—
681C4×C11—42no—
682C4×C11—42no—
683C4×C11—42no—
684C4×C11—42no—
685C4×C11—42no—
686C4×C11—42no—
687C4×C11—42no—
688C4×C11—81no—
689C4×C11—81no—
690C4×C11—81no—
691C4×C11—81no—
692C25C23×C1111yescharacteristic
693C25C23×C1111yescharacteristic
694C25C23×C1111yescharacteristic
695C22×D4—22no—
696C22×D4—22no—
697C22×D4—22no—
698C22×D4—22no—
699C22×D4—22no—
700C22×D4—22no—
701C22×D4—22no—
702C22×D4—22no—
703C22×D4—22no—
704C22×D4—22no—
705C22×D4—22no—
706C22×D4—41no—
707C22×D4—41no—
708C22×D4—41no—
709C22×D4—41no—
710C22×D4—41no—
711C22×D4—41no—
712C22×D4—41no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C23×C4C23×C1111yescharacteristic
717C23×C4C23×C1111yescharacteristic
718C23×C4C23×C1111yescharacteristic
719C23×C4C23×C1111yescharacteristic
720C23×C4C23×C1111yescharacteristic
721C23×C4C23×C1111yescharacteristic
722C23×C4C23×C1111yescharacteristic
723C23×C4C23×C1111yescharacteristic
724C23×C4C23×C1111yescharacteristic
725C23×C4C23×C1111yescharacteristic
726C23×C4C23×C1111yescharacteristic
727C23×C4C23×C1111yescharacteristic
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—22no—
733C2×C4⋊C4—22no—
734C2×C4⋊C4—22no—
735C2×C4⋊C4—41no—
736C2×C4⋊C4—41no—
737C2×C4⋊C4—41no—
738C2×C4⋊C4—41no—
739C2×C4⋊C4D4×C1114yescomplemented
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4D4×C1114yescomplemented
785C2×C42—22no—
786C2×C42—22no—
787C2×C42—41no—
788#95—22no—
789#95—22no—
790#95—22no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—41no—
795#95—41no—
796#95—41no—
797#95—41no—
798#95—41no—
799#95D4×C1114yes—
800C2×C11—82no—
801C2×C11—82no—
802C2×C11—82no—
803C2×C11#242411yescharacteristic
804C2×C11#242611yescharacteristic
805C2×C11#245711yescharacteristic
806C2×C11#261911yescharacteristic
807C2×C11#263011yescharacteristic
808C2×C11#264811yescharacteristic
809C2×C11#267311yescharacteristic
810C2×C11#267611yescharacteristic
811C2×C11#267611yescharacteristic
812C2×C11#267811yescharacteristic
813C2×C11#268511yescharacteristic
814C2×C11#269611yescharacteristic
815C2×C11#271111yescharacteristic
816C2×C11#271411yescharacteristic
817C2×C11#282911yescharacteristic
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24C2×D4×C1112yes—
861C24C11×#4112yes—
862C24C11×#4112yes—
863C24C24×C1111yescharacteristic
864C2×D4—28no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4C2×D4×C1112yes—
960C22×C4C2×D4×C1112yes—
961C22×C4C2×D4×C1112yes—
962C22×C4C2×D4×C1112yes—
963C22×C4C2×D4×C1112yes—
964C22×C4C2×D4×C1112yes—
965C22×C4C2×D4×C1112yes—
966C22×C4C2×D4×C1112yes—
967C22×C4C11×#4112yes—
968C22×C4C11×#4112yes—
969C4⋊C4—28no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C42—44no—
989C11#1628911yescharacteristic, direct product factor, Sylow
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C22×D4×C1111yescharacteristic
1096C23C22×D4×C1111yescharacteristic
1097C23C22×D4×C1111yescharacteristic
1098C23C2×C11×#4111yescharacteristic
1099C23C2×C11×#4111yescharacteristic
1100C23C2×C11×#4111yescharacteristic
1101C23C2×C11×#4111yescharacteristic
1102C23C11×H(5,𝔽2)11yescharacteristic
1103C23C11×H(5,𝔽2)11yescharacteristic
1104C23C11×H(5,𝔽2)11yescharacteristic
1105C23C11×H(5,𝔽2)11yescharacteristic
1106C23C11×H(5,𝔽2)11yescharacteristic
1107C23C11×H(5,𝔽2)11yescharacteristic
1108C23C11×H(5,𝔽2)11yescharacteristic
1109C23C11×2−1+411yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4C11×#12114yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×C11×#12111yescharacteristic
1243C22C11×#52511yescharacteristic
1244C22C11×#52911yescharacteristic
1245C22C11×#53411yescharacteristic
1246C22C11×#53511yescharacteristic
1247C22C11×#53511yescharacteristic
1248C22C11×#53511yescharacteristic
1249C22C11×#53511yescharacteristic
1250C22C11×#53711yescharacteristic
1251C22C11×#53811yescharacteristic
1252C22C11×#53811yescharacteristic
1253C22C11×#53811yescharacteristic
1254C22C11×#53811yescharacteristic
1255C22C11×#53811yescharacteristic
1256C22C11×#53911yescharacteristic
1257C22C11×#54011yescharacteristic
1258C22C11×#54011yescharacteristic
1259C22C11×#54011yescharacteristic
1260C22C11×#54211yescharacteristic
1261C22D42×C1111yescharacteristic
1262C22D42×C1111yescharacteristic
1263C22C11×#54611yescharacteristic
1264C22C11×#54611yescharacteristic
1265C22C11×#54611yescharacteristic
1266C22C11×#54611yescharacteristic
1267C22C11×#54611yescharacteristic
1268C22C11×#54811yescharacteristic
1269C22C11×#54811yescharacteristic
1270C22C11×#55011yescharacteristic
1271C22C11×#55111yescharacteristic
1272C22C11×#55311yescharacteristic
1273C22C11×#56011yescharacteristic
1274C22C11×#56011yescharacteristic
1275C22C11×#56211yescharacteristic
1276C22C11×#56211yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C11×#242411yescharacteristic
1293C2C11×#242611yescharacteristic
1294C2C11×#245711yescharacteristic
1295C2C11×#261911yescharacteristic
1296C2C11×#263011yescharacteristic
1297C2C11×#264811yescharacteristic
1298C2C11×#267311yescharacteristic
1299C2C11×#267611yescharacteristic
1300C2C11×#267611yescharacteristic
1301C2C11×#267811yescharacteristic
1302C2C11×#268511yescharacteristic
1303C2C11×#269611yescharacteristic
1304C2C11×#271111yescharacteristic
1305C2C11×#271411yescharacteristic
1306C2C11×#282911yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC2×C11×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#396C2semidirect
2. C2×C11×#394C2semidirect
3. C2×C11×#394C2semidirect
5. C2×C11×#390C2semidirect
6. C2×C11×#387C2semidirect
7. C11×#1442C2semidirect
8. C11×#1440C2semidirect
9. C11×#1439C2semidirect
10. C11×#1439C2semidirect
11. C11×#1439C2semidirect
12. C11×#1438C2semidirect
13. C11×#1438C2semidirect
14. C11×#1438C2semidirect
15. C11×#1437C2semidirect
104. C2×C11×C4⋊C4D4semidirect
149. C2×C11×C22⋊C4D4semidirect
165. #16289C11direct (N × H)
337. C2×#396C2×C11semidirect
338. C2×#394C2×C11semidirect
339. C2×#394C2×C11semidirect
341. C2×#390C2×C11semidirect
342. C2×#387C2×C11semidirect
343. #1442C2×C11semidirect
344. #1440C2×C11semidirect
345. #1439C2×C11semidirect
346. #1439C2×C11semidirect
347. #1439C2×C11semidirect
348. #1438C2×C11semidirect
349. #1438C2×C11semidirect
350. #1438C2×C11semidirect
351. #1437C2×C11semidirect
739. C2×C4⋊C4D4×C11semidirect
784. C2×C22⋊C4D4×C11semidirect
989. C11#16289direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3962
C2×C11×#3942
C2×C11×#3922
C2×C11×#3902
C2×C11×#3872
C11×#14422
C11×#14402
C11×#14392
C11×#14382
C11×#14372
#1628911