Finite Group Databasebeta

← C11×#34461 #14611654

Subgroups — C11×#34461 #14611654

Order 2816.

2368 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C11×#2383C212yesmaximal, complemented
3C11×#2376C212yesmaximal, complemented
4C11×#2370C211yesmaximal, characteristic, complemented
5C11×#2361C211yesmaximal, characteristic, complemented
6C11×#2361C212yesmaximal, complemented
7C11×#2361C211yesmaximal, characteristic, complemented
8D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
9D4×C11×C4⋊C4C212yesmaximal, complemented
10D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C11×#2347C211yesmaximal, characteristic, complemented
12C11×#2345C211yesmaximal, characteristic, complemented
13C11×#2334C212yesmaximal, complemented
14C11×#2330C211yesmaximal, characteristic, complemented
15C11×#2325C212yesmaximal, complemented
16C11×#2324C211yesmaximal, characteristic, complemented
17C11×#2322C212yesmaximal, complemented
18C11×#2319C211yesmaximal, characteristic, complemented
19C11×#2318C212yesmaximal, complemented
20C11×#2317C211yesmaximal, characteristic, complemented
21C4×C11×#121C211yesmaximal, characteristic, complemented
22C2×C11×#389C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C11×#553C4116yescomplemented
25C2×C11×#126C2212yes—
26C2×C11×#125C2211yescharacteristic
27C2×C11×#123C2212yes—
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2212yes—
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2212yes—
33C2×C4×D4×C11C2212yes—
34C2×C4×D4×C11C2211yescharacteristic
35C2×C4×D4×C11C2212yes—
36C2×C4×D4×C11C2212yes—
37C2×C4×D4×C11C2211yescharacteristic
38C2×C4×D4×C11C2212yes—
39C2×C4×D4×C11C2211yescharacteristic
40C2×C11×#117C2211yescharacteristic
41C2×C11×#117C2211yescharacteristic
42C22×C11×C4⋊C4C2212yes—
43C22×C11×C4⋊C4C2211yescharacteristic
44C22×C11×C4⋊C4C2211yescharacteristic
45C22×C11×C4⋊C4C2212yes—
46C22×C11×C4⋊C4C2211yescharacteristic
47C22×C42×C11C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2212yes—
51C11×#389C2212yes—
52C11×#389C2212yes—
53C11×#389C2212yes—
54C11×#389C2211yescharacteristic
55C11×#389C2212yes—
56C11×#389C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#389C2211yescharacteristic
60C11×#389C2211yescharacteristic
61C11×#389C2211yescharacteristic
62C11×#389C2211yescharacteristic
63C11×#389C2212yes—
64C11×#389C2212yes—
65C11×#388C2212yes—
66C11×#388C2212yes—
67C11×#388C2212yes—
68C11×#388C2211yescharacteristic
69C11×#388C2211yescharacteristic
70C11×#388C2212yes—
71C11×#388C2212yes—
72C11×#388C2212yes—
73C11×#388C2212yes—
74C11×#388C2212yes—
75C11×#387C2211yescharacteristic
76C11×#387C2212yes—
77C11×#387C2212yes—
78C11×#387C2211yescharacteristic
79C11×#387C2212yes—
80C11×#387C2212yes—
81C11×#387C2212yes—
82C11×#387C2212yes—
83C11×#386C2211yescharacteristic
84C11×#386C2211yescharacteristic
85C11×#386C2212yes—
86C11×#386C2212yes—
87C11×#386C2212yes—
88C11×#386C2212yes—
89C11×#385C2212yes—
90C11×#385C2212yes—
91C11×#385C2212yes—
92C11×#385C2211yescharacteristic
93C11×#385C2211yescharacteristic
94C11×#385C2212yes—
95C11×#385C2212yes—
96C11×#385C2212yes—
97C11×#385C2212yes—
98C11×#385C2212yes—
99C11×#385C2212yes—
100C11×#384C2212yes—
101C11×#384C2211yescharacteristic
102C11×#383C2212yes—
103C11×#382C2212yes—
104C11×#381C2212yes—
105C11×#380C2211yescharacteristic
106C11×#380C2212yes—
107C11×#380C2212yes—
108C11×#380C2211yescharacteristic
109C11×#380C2212yes—
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2211yescharacteristic
112C4×C11×C4⋊C4C2211yescharacteristic
113C4×C11×C4⋊C4C2211yescharacteristic
114C4×C11×C4⋊C4C2211yescharacteristic
115C4×C11×C4⋊C4C2211yescharacteristic
116C4×C11×C4⋊C4C2212yes—
117C4×C11×C4⋊C4C2212yes—
118C4×C11×C22⋊C4C2211yescharacteristic
119C4×C11×C22⋊C4C2211yescharacteristic
120C4×C11×C22⋊C4C2212yes—
121C4×C11×C22⋊C4C2212yes—
122C11×#376C2211yescharacteristic
123C2×C11×#95C2212yes—
124C22×D4×C11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2312yes—
134C23×C4×C11C2312yes—
135C23×C4×C11C2312yes—
136C23×C4×C11C2312yes—
137C23×C4×C11C2312yes—
138C11×#126C2×C4116yescomplemented
139C11×#125C2×C418yescomplemented
140C11×#123C2×C4116yescomplemented
141C11×#121C2×C4116yescomplemented
142C11×#121C2×C418yescomplemented
143C11×#121C2×C418yescomplemented
144C4×D4×C11—42no—
145C4×D4×C11—42no—
146C4×D4×C11—44no—
147C4×D4×C11—44no—
148C4×D4×C11—44no—
149C4×D4×C11—44no—
150C4×D4×C11C2×C4116yescomplemented
151C4×D4×C11C2×C418yescomplemented
152C4×D4×C11C2×C418yescomplemented
153C11×#117—42no—
154C11×#117C2×C418yescomplemented
155C2×C11×C4⋊C4—44no—
156C2×C11×C4⋊C4—42no—
157C2×C11×C4⋊C4—42no—
158C2×C11×C4⋊C4—44no—
159C2×C11×C4⋊C4C2×C418yescomplemented
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2312yes—
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2311yescharacteristic
179C2×C11×C4⋊C4C2312yes—
180C2×C11×C4⋊C4C2311yescharacteristic
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C4⋊C4C2311yescharacteristic
184C2×C11×C4⋊C4C2312yes—
185C2×C11×C4⋊C4C2311yescharacteristic
186C2×C11×C4⋊C4C2312yes—
187C2×C11×C22⋊C4C2311yescharacteristic
188C2×C11×C22⋊C4C2311yescharacteristic
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2311yescharacteristic
191C2×C11×C22⋊C4C2311yescharacteristic
192C2×C11×C22⋊C4C2311yescharacteristic
193C2×C11×C22⋊C4C2312yes—
194C2×C11×C22⋊C4C2311yescharacteristic
195C2×C11×C22⋊C4C2312yes—
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2312yes—
198C2×C11×C22⋊C4C2312yes—
199C2×C11×C22⋊C4C2312yes—
200C2×C11×C22⋊C4C2312yes—
201C2×C11×C22⋊C4C2312yes—
202C2×C11×C22⋊C4C2312yes—
203C2×C11×C22⋊C4C2311yescharacteristic
204C2×C11×C22⋊C4C2312yes—
205C2×C11×C22⋊C4C2312yes—
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C42×C11—42no—
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2312yes—
215C2×C42×C11C2312yes—
216C2×C42×C11C2312yes—
217C2×C42×C11C2312yes—
218C2×C42×C11C2312yes—
219C2×C42×C11C2311yescharacteristic
220C2×C42×C11C2312yes—
221C11×#95C2312yes—
222C11×#95C2312yes—
223C11×#95C2312yes—
224C11×#95C2312yes—
225C11×#95C2311yescharacteristic
226C11×#95C2311yescharacteristic
227C11×#95C2311yescharacteristic
228C11×#95C2311yescharacteristic
229C11×#95C2311yescharacteristic
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2311yescharacteristic
235C11×#95C2311yescharacteristic
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246#34461C1111yesmaximal, characteristic, direct product factor, Sylow
247C24×C11C2411yescharacteristic
248C24×C11C2412yes—
249C24×C11C2411yescharacteristic
250C2×D4×C11—24no—
251C2×D4×C11—22no—
252C2×D4×C11—24no—
253C2×D4×C11—22no—
254C2×D4×C11—22no—
255C2×D4×C11—22no—
256C2×D4×C11—42no—
257C2×D4×C11—42no—
258C2×D4×C11C22×C418yes—
259C2×D4×C11C22×C414yes—
260C2×D4×C11C22×C414yes—
261C2×D4×C11C22×C418yes—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—22no—
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11—24no—
269C22×C4×C11—22no—
270C22×C4×C11—24no—
271C22×C4×C11—41no—
272C22×C4×C11—41no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—41no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11C22×C414yes—
289C22×C4×C11C22×C414yes—
290C22×C4×C11C22×C418yes—
291C22×C4×C11C22×C418yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2412yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2412yes—
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C11×C4⋊C4—22no—
313C11×C4⋊C4—24no—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—24no—
316C11×C4⋊C4—22no—
317C11×C4⋊C4—22no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—42no—
320C11×C4⋊C4—42no—
321C11×C4⋊C4—42no—
322C11×C4⋊C4—42no—
323C11×C4⋊C4—42no—
324C11×C4⋊C4—42no—
325C11×C4⋊C4—41no—
326C11×C4⋊C4—42no—
327C11×C4⋊C4—41no—
328C11×C4⋊C4—41no—
329C11×C4⋊C4—42no—
330C11×C4⋊C4—42no—
331C11×C4⋊C4—42no—
332C11×C4⋊C4C22×C414yes—
333C11×C4⋊C4C22×C414yes—
334C11×C4⋊C4C22×C418yes—
335C11×C4⋊C4C22×C414yes—
336C11×C4⋊C4C22×C418yes—
337C11×C4⋊C4C22×C414yes—
338C11×C4⋊C4C22×C418yes—
339C11×C22⋊C4—22no—
340C11×C22⋊C4—24no—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—41no—
345C11×C22⋊C4—41no—
346C11×C22⋊C4—41no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4—42no—
349C11×C22⋊C4—42no—
350C11×C22⋊C4—42no—
351C11×C22⋊C4—42no—
352C11×C22⋊C4—42no—
353C11×C22⋊C4C22×C418yes—
354C11×C22⋊C4C22×C414yes—
355C11×C22⋊C4C22×C418yes—
356C11×C22⋊C4C22×C418yes—
357C11×C22⋊C4C22×C414yes—
358C11×C22⋊C4C22×C418yes—
359C42×C11—22no—
360C42×C11—22no—
361C42×C11—22no—
362C42×C11—22no—
363C42×C11—41no—
364C42×C11—41no—
365C42×C11—42no—
366C42×C11—42no—
367C42×C11—42no—
368C42×C11—42no—
369C42×C11—42no—
370C42×C11C22×C418yes—
371C42×C11C22×C414yes—
372C2×#553C2×C1111yescharacteristic
373#2383C2×C1112yescomplemented
374#2376C2×C1112yescomplemented
375#2370C2×C1111yescharacteristic, complemented
376#2361C2×C1111yescharacteristic, complemented
377#2361C2×C1112yescomplemented
378#2361C2×C1111yescharacteristic, complemented
379D4×C4⋊C4C2×C1111yescharacteristic, complemented
380D4×C4⋊C4C2×C1111yescharacteristic, complemented
381D4×C4⋊C4C2×C1112yescomplemented
382#2347C2×C1111yescharacteristic, complemented
383#2345C2×C1111yescharacteristic, complemented
384#2334C2×C1112yescomplemented
385#2330C2×C1111yescharacteristic, complemented
386#2325C2×C1112yescomplemented
387#2324C2×C1111yescharacteristic, complemented
388#2322C2×C1112yescomplemented
389#2319C2×C1111yescharacteristic, complemented
390#2318C2×C1112yescomplemented
391#2317C2×C1111yescharacteristic, complemented
392C4×#121C2×C1111yescharacteristic, complemented
393C2×#389C2×C1111yescharacteristic, complemented
394#2290C2×C1111yescharacteristic, complemented
395C23×C11—21no—
396C23×C11—21no—
397C23×C11—21no—
398C23×C11—21no—
399C23×C11—21no—
400C23×C11—21no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—21no—
404C23×C11—22no—
405C23×C11—21no—
406C23×C11—21no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—21no—
411C23×C11C23×C412yes—
412C23×C11C23×C414yes—
413C23×C11C23×C412yes—
414C23×C11H(5,𝔽2)12yes—
415C23×C112−1+412yes—
416C23×C11C2511yescharacteristic
417D4×C11—216no—
418D4×C11—28no—
419D4×C11—28no—
420D4×C11—48no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—22no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—22no—
427C2×C4×C11—21no—
428C2×C4×C11—22no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—21no—
436C2×C4×C11—22no—
437C2×C4×C11—28no—
438C2×C4×C11—28no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—21no—
451C2×C4×C11—22no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—22no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—48no—
473C2×C4×C11—48no—
474C2×C4×C11—44no—
475C2×C4×C11—44no—
476C2×C4×C11—84no—
477C2×C4×C11—84no—
478C2×C4×C11—84no—
479C2×C4×C11—84no—
480C2×C4×C11C23×C412yes—
481C2×C4×C11C23×C414yes—
482C2×C4×C11C23×C412yes—
483C2×C4×C11C23×C414yes—
484C2×C4×C11C23×C412yes—
485C2×C4×C11C23×C412yes—
486C2×C4×C11C23×C414yes—
487C2×C4×C11C23×C412yes—
488C2×C4×C11H(5,𝔽2)12yes—
489C2×C4×C11H(5,𝔽2)12yes—
490C2×C4×C112−1+412yes—
491#553C4×C11116yescomplemented
492C2×#126C22×C1112yes—
493C2×#125C22×C1111yescharacteristic
494C2×#123C22×C1112yes—
495C2×#121C22×C1111yescharacteristic
496C2×#121C22×C1112yes—
497C2×#121C22×C1111yescharacteristic
498C2×C4×D4C22×C1112yes—
499C2×C4×D4C22×C1111yescharacteristic
500C2×C4×D4C22×C1112yes—
501C2×C4×D4C22×C1112yes—
502C2×C4×D4C22×C1111yescharacteristic
503C2×C4×D4C22×C1112yes—
504C2×C4×D4C22×C1112yes—
505C2×C4×D4C22×C1111yescharacteristic
506C2×C4×D4C22×C1111yescharacteristic
507C2×#117C22×C1111yescharacteristic
508C2×#117C22×C1111yescharacteristic
509C22×C4⋊C4C22×C1111yescharacteristic
510C22×C4⋊C4C22×C1112yes—
511C22×C4⋊C4C22×C1112yes—
512C22×C4⋊C4C22×C1111yescharacteristic
513C22×C4⋊C4C22×C1111yescharacteristic
514C22×C42C22×C1111yescharacteristic
515#390C22×C1111yescharacteristic
516#390C22×C1111yescharacteristic
517#390C22×C1112yes—
518#389C22×C1111yescharacteristic
519#389C22×C1111yescharacteristic
520#389C22×C1111yescharacteristic
521#389C22×C1111yescharacteristic
522#389C22×C1111yescharacteristic
523#389C22×C1112yes—
524#389C22×C1112yes—
525#389C22×C1111yescharacteristic
526#389C22×C1112yes—
527#389C22×C1112yes—
528#389C22×C1112yes—
529#389C22×C1111yescharacteristic
530#389C22×C1111yescharacteristic
531#389C22×C1112yes—
532#388C22×C1112yes—
533#388C22×C1112yes—
534#388C22×C1112yes—
535#388C22×C1112yes—
536#388C22×C1111yescharacteristic
537#388C22×C1112yes—
538#388C22×C1112yes—
539#388C22×C1112yes—
540#388C22×C1111yescharacteristic
541#388C22×C1112yes—
542#387C22×C1112yes—
543#387C22×C1112yes—
544#387C22×C1112yes—
545#387C22×C1112yes—
546#387C22×C1112yes—
547#387C22×C1111yescharacteristic
548#387C22×C1112yes—
549#387C22×C1111yescharacteristic
550#386C22×C1112yes—
551#386C22×C1112yes—
552#386C22×C1112yes—
553#386C22×C1111yescharacteristic
554#386C22×C1112yes—
555#386C22×C1111yescharacteristic
556#385C22×C1112yes—
557#385C22×C1112yes—
558#385C22×C1111yescharacteristic
559#385C22×C1112yes—
560#385C22×C1112yes—
561#385C22×C1112yes—
562#385C22×C1112yes—
563#385C22×C1112yes—
564#385C22×C1112yes—
565#385C22×C1112yes—
566#385C22×C1111yescharacteristic
567#384C22×C1112yes—
568#384C22×C1111yescharacteristic
569#383C22×C1112yes—
570#382C22×C1112yes—
571#381C22×C1112yes—
572#380C22×C1112yes—
573#380C22×C1112yes—
574#380C22×C1111yescharacteristic
575#380C22×C1112yes—
576#380C22×C1111yescharacteristic
577C4×C4⋊C4C22×C1111yescharacteristic
578C4×C4⋊C4C22×C1111yescharacteristic
579C4×C4⋊C4C22×C1111yescharacteristic
580C4×C4⋊C4C22×C1111yescharacteristic
581C4×C4⋊C4C22×C1112yes—
582C4×C4⋊C4C22×C1112yes—
583C4×C4⋊C4C22×C1111yescharacteristic
584C4×C4⋊C4C22×C1111yescharacteristic
585C4×C22⋊C4C22×C1112yes—
586C4×C22⋊C4C22×C1112yes—
587C4×C22⋊C4C22×C1111yescharacteristic
588C4×C22⋊C4C22×C1111yescharacteristic
589#376C22×C1111yescharacteristic
590C2×#95C22×C1112yes—
591C22×C11—22no—
592C22×C11—22no—
593C22×C11—22no—
594C22×C11—22no—
595C22×C11—22no—
596C22×C11—22no—
597C22×C11—22no—
598C22×C11—22no—
599C22×C11—24no—
600C22×C11—24no—
601C22×C11—24no—
602C22×C11—22no—
603C22×C11—42no—
604C22×C11—41no—
605C22×C11—41no—
606C22×C11—42no—
607C22×C11—41no—
608C22×C11—42no—
609C22×C11—41no—
610C22×C11—42no—
611C22×C11#52014yes—
612C22×C11C24×C411yescharacteristic
613C22×C11C2×H(5,𝔽2)11yescharacteristic
614C22×C11C2×H(5,𝔽2)11yescharacteristic
615C22×C11C2×H(5,𝔽2)11yescharacteristic
616C22×C11C2×2−1+411yescharacteristic
617C22×C11C2×2−1+411yescharacteristic
618C22×C11#58511yescharacteristic
619C4×C11—22no—
620C4×C11—22no—
621C4×C11—24no—
622C4×C11—22no—
623C4×C11—22no—
624C4×C11—24no—
625C4×C11—24no—
626C4×C11—22no—
627C4×C11—41no—
628C4×C11—41no—
629C4×C11—42no—
630C4×C11—42no—
631C4×C11—42no—
632C4×C11—41no—
633C4×C11—41no—
634C4×C11—41no—
635C4×C11—41no—
636C4×C11—41no—
637C4×C11—42no—
638C4×C11#52014yes—
639C22×D4C23×C1111yescharacteristic
640C22×D4C23×C1112yes—
641C22×D4C23×C1111yescharacteristic
642C22×D4C23×C1112yes—
643C23×C4C23×C1111yescharacteristic
644C23×C4C23×C1111yescharacteristic
645C23×C4C23×C1111yescharacteristic
646C23×C4C23×C1112yes—
647C23×C4C23×C1112yes—
648C23×C4C23×C1111yescharacteristic
649C23×C4C23×C1112yes—
650C23×C4C23×C1112yes—
651C23×C4C23×C1112yes—
652C23×C4C23×C1112yes—
653#126C2×C4×C11116yescomplemented
654#125C2×C4×C1118yescomplemented
655#123C2×C4×C11116yescomplemented
656#121C2×C4×C11116yescomplemented
657#121C2×C4×C1118yescomplemented
658#121C2×C4×C1118yescomplemented
659C4×D4—42no—
660C4×D4—42no—
661C4×D4—44no—
662C4×D4—44no—
663C4×D4—44no—
664C4×D4—44no—
665C4×D4C2×C4×C11116yescomplemented
666C4×D4C2×C4×C1118yescomplemented
667C4×D4C2×C4×C1118yescomplemented
668#117—42no—
669#117C2×C4×C1118yescomplemented
670C2×C4⋊C4—44no—
671C2×C4⋊C4—42no—
672C2×C4⋊C4—42no—
673C2×C4⋊C4—44no—
674C2×C4⋊C4C2×C4×C1118yescomplemented
675C2×C4⋊C4C23×C1111yescharacteristic
676C2×C4⋊C4C23×C1112yes—
677C2×C4⋊C4C23×C1111yescharacteristic
678C2×C4⋊C4C23×C1111yescharacteristic
679C2×C4⋊C4C23×C1111yescharacteristic
680C2×C4⋊C4C23×C1112yes—
681C2×C4⋊C4C23×C1111yescharacteristic
682C2×C4⋊C4C23×C1112yes—
683C2×C4⋊C4C23×C1112yes—
684C2×C4⋊C4C23×C1112yes—
685C2×C4⋊C4C23×C1112yes—
686C2×C4⋊C4C23×C1112yes—
687C2×C4⋊C4C23×C1112yes—
688C2×C4⋊C4C23×C1111yescharacteristic
689C2×C4⋊C4C23×C1111yescharacteristic
690C2×C4⋊C4C23×C1112yes—
691C2×C4⋊C4C23×C1112yes—
692C2×C4⋊C4C23×C1112yes—
693C2×C4⋊C4C23×C1111yescharacteristic
694C2×C4⋊C4C23×C1112yes—
695C2×C4⋊C4C23×C1111yescharacteristic
696C2×C4⋊C4C23×C1111yescharacteristic
697C2×C4⋊C4C23×C1112yes—
698C2×C4⋊C4C23×C1111yescharacteristic
699C2×C4⋊C4C23×C1112yes—
700C2×C4⋊C4C23×C1111yescharacteristic
701C2×C4⋊C4C23×C1112yes—
702C2×C22⋊C4C23×C1111yescharacteristic
703C2×C22⋊C4C23×C1112yes—
704C2×C22⋊C4C23×C1111yescharacteristic
705C2×C22⋊C4C23×C1111yescharacteristic
706C2×C22⋊C4C23×C1111yescharacteristic
707C2×C22⋊C4C23×C1111yescharacteristic
708C2×C22⋊C4C23×C1112yes—
709C2×C22⋊C4C23×C1112yes—
710C2×C22⋊C4C23×C1112yes—
711C2×C22⋊C4C23×C1112yes—
712C2×C22⋊C4C23×C1112yes—
713C2×C22⋊C4C23×C1112yes—
714C2×C22⋊C4C23×C1112yes—
715C2×C22⋊C4C23×C1111yescharacteristic
716C2×C22⋊C4C23×C1112yes—
717C2×C22⋊C4C23×C1111yescharacteristic
718C2×C22⋊C4C23×C1112yes—
719C2×C22⋊C4C23×C1112yes—
720C2×C22⋊C4C23×C1111yescharacteristic
721C2×C22⋊C4C23×C1112yes—
722C2×C42—42no—
723C2×C42C23×C1111yescharacteristic
724C2×C42C23×C1111yescharacteristic
725C2×C42C23×C1111yescharacteristic
726C2×C42C23×C1111yescharacteristic
727C2×C42C23×C1112yes—
728C2×C42C23×C1112yes—
729C2×C42C23×C1112yes—
730C2×C42C23×C1112yes—
731C2×C42C23×C1111yescharacteristic
732C2×C42C23×C1112yes—
733C2×C42C23×C1111yescharacteristic
734C2×C42C23×C1112yes—
735C2×C42C23×C1111yescharacteristic
736#95C23×C1112yes—
737#95C23×C1112yes—
738#95C23×C1112yes—
739#95C23×C1112yes—
740#95C23×C1111yescharacteristic
741#95C23×C1111yescharacteristic
742#95C23×C1111yescharacteristic
743#95C23×C1111yescharacteristic
744#95C23×C1111yescharacteristic
745#95C23×C1112yes—
746#95C23×C1112yes—
747#95C23×C1112yes—
748#95C23×C1112yes—
749#95C23×C1111yescharacteristic
750#95C23×C1111yescharacteristic
751#95C23×C1111yescharacteristic
752#95C23×C1111yescharacteristic
753#95C23×C1112yes—
754#95C23×C1112yes—
755#95C23×C1112yes—
756#95C23×C1112yes—
757#95C23×C1112yes—
758#95C23×C1112yes—
759#95C23×C1112yes—
760#95C23×C1111yescharacteristic
761C2×C11—24no—
762C2×C11—42no—
763C2×C11—44no—
764C2×C11C2×#52011yescharacteristic
765C2×C11C2×#52011yescharacteristic
766C2×C11C4×H(5,𝔽2)11yescharacteristic
767C2×C11#353711yescharacteristic
768C2×C11#354111yescharacteristic
769C2×C11#355211yescharacteristic
770C2×C11#355911yescharacteristic
771C24C24×C1111yescharacteristic
772C24C24×C1112yes—
773C24C24×C1111yescharacteristic
774C2×D4—24no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—24no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—42no—
781C2×D4—42no—
782C2×D4C22×C4×C1118yes—
783C2×D4C22×C4×C1114yes—
784C2×D4C22×C4×C1114yes—
785C2×D4C22×C4×C1118yes—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—22no—
794C22×C4—24no—
795C22×C4—41no—
796C22×C4—41no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—41no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4C22×C4×C1114yes—
813C22×C4C22×C4×C1114yes—
814C22×C4C22×C4×C1118yes—
815C22×C4C22×C4×C1118yes—
816C22×C4C24×C1111yescharacteristic
817C22×C4C24×C1111yescharacteristic
818C22×C4C24×C1111yescharacteristic
819C22×C4C24×C1111yescharacteristic
820C22×C4C24×C1111yescharacteristic
821C22×C4C24×C1112yes—
822C22×C4C24×C1111yescharacteristic
823C22×C4C24×C1112yes—
824C22×C4C24×C1112yes—
825C22×C4C24×C1112yes—
826C22×C4C24×C1111yescharacteristic
827C22×C4C24×C1111yescharacteristic
828C22×C4C24×C1112yes—
829C22×C4C24×C1111yescharacteristic
830C22×C4C24×C1111yescharacteristic
831C22×C4C24×C1112yes—
832C22×C4C24×C1112yes—
833C22×C4C24×C1111yescharacteristic
834C22×C4C24×C1111yescharacteristic
835C22×C4C24×C1111yescharacteristic
836C4⋊C4—22no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—41no—
855C4⋊C4—42no—
856C4⋊C4C22×C4×C1114yes—
857C4⋊C4C22×C4×C1114yes—
858C4⋊C4C22×C4×C1118yes—
859C4⋊C4C22×C4×C1114yes—
860C4⋊C4C22×C4×C1118yes—
861C4⋊C4C22×C4×C1114yes—
862C4⋊C4C22×C4×C1118yes—
863C22⋊C4—22no—
864C22⋊C4—24no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—41no—
868C22⋊C4—41no—
869C22⋊C4—42no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—41no—
877C22⋊C4C22×C4×C1118yes—
878C22⋊C4C22×C4×C1114yes—
879C22⋊C4C22×C4×C1118yes—
880C22⋊C4C22×C4×C1118yes—
881C22⋊C4C22×C4×C1114yes—
882C22⋊C4C22×C4×C1118yes—
883C42—22no—
884C42—22no—
885C42—22no—
886C42—22no—
887C42—41no—
888C42—41no—
889C42—42no—
890C42—42no—
891C42—42no—
892C42—42no—
893C42—42no—
894C42C22×C4×C1118yes—
895C42C22×C4×C1114yes—
896C11#3446111yescharacteristic, direct product factor, Sylow
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—22no—
905C23—21no—
906C23—22no—
907C23—21no—
908C23—21no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—21no—
913C23C23×C4×C1112yes—
914C23C23×C4×C1114yes—
915C23C23×C4×C1112yes—
916C23C11×H(5,𝔽2)12yes—
917C23C11×2−1+412yes—
918C23C25×C1111yescharacteristic
919D4—216no—
920D4—28no—
921D4—28no—
922D4—48no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—28no—
940C2×C4—28no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—48no—
975C2×C4—48no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—84no—
979C2×C4—84no—
980C2×C4—84no—
981C2×C4—84no—
982C2×C4C23×C4×C1112yes—
983C2×C4C23×C4×C1114yes—
984C2×C4C23×C4×C1112yes—
985C2×C4C23×C4×C1114yes—
986C2×C4C23×C4×C1112yes—
987C2×C4C23×C4×C1112yes—
988C2×C4C23×C4×C1114yes—
989C2×C4C23×C4×C1112yes—
990C2×C4C11×H(5,𝔽2)12yes—
991C2×C4C11×H(5,𝔽2)12yes—
992C2×C4C11×2−1+412yes—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—22no—
998C22—22no—
999C22—22no—
1000C22—22no—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—22no—
1005C22—42no—
1006C22—41no—
1007C22—41no—
1008C22—42no—
1009C22—41no—
1010C22—42no—
1011C22—41no—
1012C22—42no—
1013C22C11×#52014yes—
1014C22C24×C4×C1111yescharacteristic
1015C22C2×C11×H(5,𝔽2)11yescharacteristic
1016C22C2×C11×H(5,𝔽2)11yescharacteristic
1017C22C2×C11×H(5,𝔽2)11yescharacteristic
1018C22C2×C11×2−1+411yescharacteristic
1019C22C2×C11×2−1+411yescharacteristic
1020C22C11×#58511yescharacteristic
1021C4—22no—
1022C4—22no—
1023C4—24no—
1024C4—22no—
1025C4—22no—
1026C4—24no—
1027C4—24no—
1028C4—22no—
1029C4—41no—
1030C4—41no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—41no—
1038C4—41no—
1039C4—42no—
1040C4C11×#52014yes—
1041C2—24no—
1042C2—42no—
1043C2—44no—
1044C2C2×C11×#52011yescharacteristic
1045C2C2×C11×#52011yescharacteristic
1046C2C4×C11×H(5,𝔽2)11yescharacteristic
1047C2C11×#353711yescharacteristic
1048C2C11×#354111yescharacteristic
1049C2C11×#355211yescharacteristic
1050C2C11×#355911yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#553C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2383C2semidirect
3. C11×#2376C2semidirect
4. C11×#2370C2semidirect
5. C11×#2361C2semidirect
6. C11×#2361C2semidirect
7. C11×#2361C2semidirect
8. D4×C11×C4⋊C4C2semidirect
9. D4×C11×C4⋊C4C2semidirect
10. D4×C11×C4⋊C4C2semidirect
11. C11×#2347C2semidirect
12. C11×#2345C2semidirect
13. C11×#2334C2semidirect
14. C11×#2330C2semidirect
15. C11×#2325C2semidirect
16. C11×#2324C2semidirect
17. C11×#2322C2semidirect
18. C11×#2319C2semidirect
19. C11×#2318C2semidirect
20. C11×#2317C2semidirect
21. C4×C11×#121C2semidirect
22. C2×C11×#389C2semidirect
23. C11×#2290C2semidirect
24. C11×#553C4semidirect
138. C11×#126C2×C4semidirect
139. C11×#125C2×C4semidirect
140. C11×#123C2×C4semidirect
141. C11×#121C2×C4semidirect
142. C11×#121C2×C4semidirect
143. C11×#121C2×C4semidirect
150. C4×D4×C11C2×C4semidirect
151. C4×D4×C11C2×C4semidirect
152. C4×D4×C11C2×C4semidirect
154. C11×#117C2×C4semidirect
159. C2×C11×C4⋊C4C2×C4semidirect
246. #34461C11direct (N × H)
373. #2383C2×C11semidirect
374. #2376C2×C11semidirect
375. #2370C2×C11semidirect
376. #2361C2×C11semidirect
377. #2361C2×C11semidirect
378. #2361C2×C11semidirect
379. D4×C4⋊C4C2×C11semidirect
380. D4×C4⋊C4C2×C11semidirect
381. D4×C4⋊C4C2×C11semidirect
382. #2347C2×C11semidirect
383. #2345C2×C11semidirect
384. #2334C2×C11semidirect
385. #2330C2×C11semidirect
386. #2325C2×C11semidirect
387. #2324C2×C11semidirect
388. #2322C2×C11semidirect
389. #2319C2×C11semidirect
390. #2318C2×C11semidirect
391. #2317C2×C11semidirect
392. C4×#121C2×C11semidirect
393. C2×#389C2×C11semidirect
394. #2290C2×C11semidirect
491. #553C4×C11semidirect
653. #126C2×C4×C11semidirect
654. #125C2×C4×C11semidirect
655. #123C2×C4×C11semidirect
656. #121C2×C4×C11semidirect
657. #121C2×C4×C11semidirect
658. #121C2×C4×C11semidirect
665. C4×D4C2×C4×C11semidirect
666. C4×D4C2×C4×C11semidirect
667. C4×D4C2×C4×C11semidirect
669. #117C2×C4×C11semidirect
674. C2×C4⋊C4C2×C4×C11semidirect
896. C11#34461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C11×#23832
C11×#23762
C11×#23702
C11×#23612
D4×C11×C4⋊C42
C11×#23472
C11×#23452
C11×#23342
C11×#23302
C11×#23252
C11×#23242
C11×#23222
C11×#23192
C11×#23182
C11×#23172
C4×C11×#1212
C2×C11×#3892
C11×#22902
#3446111