Finite Group Databasebeta

← C11×#59940 #14637133

Subgroups — C11×#59940 #14637133

Order 2816.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2797C212yesmaximal, complemented
2C11×#2748C211yesmaximal, characteristic, complemented
3C11×#2697C211yesmaximal, characteristic, complemented
4C11×#2603C212yesmaximal, complemented
5C11×#2579C212yesmaximal, complemented
6C11×#2554C212yesmaximal, complemented
7C11×#2531C212yesmaximal, complemented
8C11×#2480C212yesmaximal, complemented
9C11×#2471C212yesmaximal, complemented
10C11×#2418C212yesmaximal, complemented
11C11×#2411C212yesmaximal, complemented
12C11×#2405C211yesmaximal, characteristic, complemented
13C11×#2403C211yesmaximal, characteristic
14C11×#2374C211yesmaximal, characteristic, complemented
15C11×#2358C212yesmaximal, complemented
16C11×#2358C211yesmaximal, characteristic, complemented
17D4×C11×C22⋊C4C212yesmaximal, complemented
18C2×C11×#390C211yesmaximal, characteristic, complemented
19C11×#2290C212yesmaximal, complemented
20C23×D4×C11C2211yescharacteristic
21C23×D4×C11C2211yescharacteristic
22C2×C11×#126C2212yescomplemented
23C2×C11×#123C2211yescharacteristic
24C2×C11×#123C2211yescharacteristic, complemented
25C2×C11×#123C2212yescomplemented
26C2×C11×#120C2212yes—
27C2×C11×#120C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C2×C4×D4×C11C2212yes—
30C2×C4×D4×C11C2212yes—
31C2×C4×D4×C11C2212yescomplemented
32C2×C11×#117C2212yescomplemented
33C22×C11×C4⋊C4C2211yescharacteristic, complemented
34C22×C11×C22⋊C4C2212yes—
35C22×C11×C22⋊C4C2211yescharacteristic, complemented
36C22×C11×C22⋊C4C2212yescomplemented
37C22×C11×C22⋊C4C2212yescomplemented
38C22×C42×C11C2211yescharacteristic, complemented
39C11×#399C2212yescomplemented
40C11×#398C2212yescomplemented
41C11×#398C2212yescomplemented
42C11×#397C2212yescomplemented
43C11×#397C2212yescomplemented
44C11×#397C2212yescomplemented
45C11×#397C2212yescomplemented
46C11×#396C2212yescomplemented
47C11×#396C2212yescomplemented
48C11×#396C2212yescomplemented
49C11×#394C2212yes—
50C11×#394C2212yescomplemented
51C11×#394C2212yescomplemented
52C11×#394C2212yescomplemented
53C11×#392C2212yes—
54C11×#392C2212yes—
55C11×#390C2212yes—
56C11×#390C2211yescharacteristic
57C11×#390C2211yescharacteristic
58C11×#390C2212yescomplemented
59C11×#390C2212yescomplemented
60C11×#390C2212yescomplemented
61C11×#390C2211yescharacteristic, complemented
62C11×#390C2211yescharacteristic, complemented
63C11×#390C2212yescomplemented
64C11×#388C2212yescomplemented
65C11×#388C2212yescomplemented
66C11×#388C2212yescomplemented
67C11×#388C2212yescomplemented
68C11×#388C2212yescomplemented
69C11×#388C2212yescomplemented
70C11×#388C2212yescomplemented
71C11×#388C2212yescomplemented
72C11×#388C2212yescomplemented
73C11×#387C2212yescomplemented
74C11×#387C2212yescomplemented
75C11×#387C2212yescomplemented
76C11×#387C2212yescomplemented
77C11×#386C2211yescharacteristic
78C11×#386C2211yescharacteristic
79C11×#386C2212yes—
80C11×#386C2211yescharacteristic
81C11×#386C2212yes—
82C11×#386C2212yes—
83C11×#386C2211yescharacteristic, complemented
84C11×#386C2212yescomplemented
85C11×#386C2212yescomplemented
86C11×#386C2212yescomplemented
87C11×#386C2212yescomplemented
88C11×#386C2212yescomplemented
89C11×#385C2212yescomplemented
90C11×#385C2212yescomplemented
91C11×#385C2212yescomplemented
92C11×#385C2212yescomplemented
93C11×#385C2212yescomplemented
94C11×#385C2212yescomplemented
95C11×#380C2212yescomplemented
96C11×#380C2212yescomplemented
97C11×#379C2211yescharacteristic
98C11×#379C2212yes—
99C11×#379C2211yescharacteristic, complemented
100C11×#379C2212yescomplemented
101C4×C11×C4⋊C4C2212yescomplemented
102C4×C11×C22⋊C4C2212yescomplemented
103C4×C11×C22⋊C4C2212yescomplemented
104C4×C11×C22⋊C4C2212yescomplemented
105C4×C11×C22⋊C4C2212yescomplemented
106C11×#376C2212yescomplemented
107C25×C11C2311yescharacteristic
108C25×C11C2311yescharacteristic
109C25×C11C2311yescharacteristic
110C22×D4×C11—24no—
111C22×D4×C11—28no—
112C22×D4×C11—42no—
113C22×D4×C11—42no—
114C22×D4×C11—42no—
115C22×D4×C11C2312yes—
116C22×D4×C11C2311yescharacteristic
117C22×D4×C11C2312yes—
118C22×D4×C11C2311yescharacteristic
119C22×D4×C11C2312yes—
120C22×D4×C11C2312yes—
121C22×D4×C11C2311yescharacteristic
122C22×D4×C11C2311yescharacteristic
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2312yes—
125C23×C4×C11C2312yes—
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C11×#126—44no—
132C11×#123—24no—
133C11×#123—44no—
134C11×#123—42no—
135C11×#120—24no—
136C11×#120—28no—
137C11×#120—42no—
138C4×D4×C11—28no—
139C4×D4×C11—44no—
140C4×D4×C11—44no—
141C11×#117—44no—
142C2×C11×C4⋊C4—42no—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C4⋊C4C2312yes—
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C22⋊C4—44no—
157C2×C11×C22⋊C4—44no—
158C2×C11×C22⋊C4—44no—
159C2×C11×C22⋊C4—42no—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179C2×C11×C22⋊C4C2312yes—
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2311yescharacteristic
191C2×C11×C22⋊C4C2312yes—
192C2×C42×C11—42no—
193C2×C42×C11C2312yes—
194C2×C42×C11C2312yes—
195C2×C42×C11C2312yes—
196C2×C42×C11C2311yescharacteristic
197C2×C42×C11C2311yescharacteristic
198C2×C42×C11C2312yes—
199C2×C42×C11C2312yes—
200C11×#95C2312yes—
201C11×#95C2312yes—
202C11×#95C2312yes—
203C11×#95C2312yes—
204C11×#95C2312yes—
205C11×#95C2312yes—
206C11×#95C2312yes—
207C11×#95C2312yes—
208C11×#95C2312yes—
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2312yes—
216#59940C1111yesmaximal, characteristic, direct product factor, Sylow
217C24×C11—22no—
218C24×C11—22no—
219C24×C11—22no—
220C24×C11—24no—
221C24×C11—24no—
222C24×C11—24no—
223C24×C11—22no—
224C24×C11—22no—
225C24×C11—42no—
226C24×C11—42no—
227C24×C11—42no—
228C24×C11—41no—
229C24×C11—41no—
230C24×C11—41no—
231C24×C11—41no—
232C24×C11C2411yescharacteristic
233C24×C11C2411yescharacteristic
234C24×C11C2411yescharacteristic
235C24×C11C2411yescharacteristic
236C24×C11C2412yes—
237C24×C11C2411yescharacteristic
238C2×D4×C11—24no—
239C2×D4×C11—24no—
240C2×D4×C11—24no—
241C2×D4×C11—24no—
242C2×D4×C11—22no—
243C2×D4×C11—24no—
244C2×D4×C11—22no—
245C2×D4×C11—24no—
246C2×D4×C11—24no—
247C2×D4×C11—22no—
248C2×D4×C11—22no—
249C2×D4×C11—22no—
250C2×D4×C11—42no—
251C2×D4×C11—41no—
252C2×D4×C11—41no—
253C2×D4×C11—42no—
254C2×D4×C11—41no—
255C2×D4×C11—41no—
256C2×D4×C11—41no—
257C2×D4×C11—41no—
258C2×D4×C11—416no—
259C2×D4×C11—42no—
260C2×D4×C11—42no—
261C2×D4×C11—416no—
262C2×D4×C11#4118yes—
263C2×D4×C11#4114yes—
264C22×C4×C11—22no—
265C22×C4×C11—22no—
266C22×C4×C11—22no—
267C22×C4×C11—24no—
268C22×C4×C11—24no—
269C22×C4×C11—22no—
270C22×C4×C11—24no—
271C22×C4×C11—24no—
272C22×C4×C11—24no—
273C22×C4×C11—24no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—41no—
277C22×C4×C11—41no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—41no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—41no—
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2412yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2412yes—
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2412yes—
299C11×C4⋊C4—24no—
300C11×C4⋊C4—24no—
301C11×C4⋊C4—24no—
302C11×C4⋊C4—24no—
303C11×C4⋊C4—41no—
304C11×C4⋊C4—42no—
305C11×C4⋊C4—41no—
306C11×C4⋊C4—42no—
307C11×C4⋊C4—42no—
308C11×C4⋊C4—42no—
309C11×C4⋊C4—42no—
310C11×C4⋊C4—42no—
311C11×C4⋊C4—42no—
312C11×C22⋊C4—24no—
313C11×C22⋊C4—24no—
314C11×C22⋊C4—22no—
315C11×C22⋊C4—24no—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—24no—
318C11×C22⋊C4—24no—
319C11×C22⋊C4—24no—
320C11×C22⋊C4—24no—
321C11×C22⋊C4—24no—
322C11×C22⋊C4—24no—
323C11×C22⋊C4—24no—
324C11×C22⋊C4—24no—
325C11×C22⋊C4—24no—
326C11×C22⋊C4—24no—
327C11×C22⋊C4—24no—
328C11×C22⋊C4—42no—
329C11×C22⋊C4—42no—
330C11×C22⋊C4—42no—
331C11×C22⋊C4—42no—
332C11×C22⋊C4—42no—
333C11×C22⋊C4—42no—
334C11×C22⋊C4—42no—
335C11×C22⋊C4—42no—
336C11×C22⋊C4—42no—
337C11×C22⋊C4—41no—
338C11×C22⋊C4—42no—
339C11×C22⋊C4—42no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—41no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4—42no—
344C42×C11—24no—
345C42×C11—24no—
346C42×C11—24no—
347C42×C11—41no—
348C42×C11—41no—
349C42×C11—42no—
350C42×C11—42no—
351#2797C2×C1112yescomplemented
352#2748C2×C1111yescharacteristic, complemented
353#2697C2×C1111yescharacteristic, complemented
354#2603C2×C1112yescomplemented
355#2579C2×C1112yescomplemented
356#2554C2×C1112yescomplemented
357#2531C2×C1112yescomplemented
358#2480C2×C1112yescomplemented
359#2471C2×C1112yescomplemented
360#2418C2×C1112yescomplemented
361#2411C2×C1112yescomplemented
362#2405C2×C1111yescharacteristic, complemented
363#2403C2×C1111yescharacteristic
364#2374C2×C1111yescharacteristic, complemented
365#2358C2×C1112yescomplemented
366#2358C2×C1111yescharacteristic, complemented
367D4×C22⋊C4C2×C1112yescomplemented
368C2×#390C2×C1111yescharacteristic, complemented
369#2290C2×C1112yescomplemented
370C23×C11—21no—
371C23×C11—22no—
372C23×C11—21no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—21no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—21no—
390C23×C11—21no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—21no—
394C23×C11—21no—
395C23×C11—21no—
396C23×C11—21no—
397C23×C11—44no—
398C23×C11—44no—
399C23×C11—44no—
400C23×C11—48no—
401C23×C11—48no—
402C23×C11—48no—
403C23×C11—44no—
404C23×C11—44no—
405C23×C11—84no—
406C23×C11—84no—
407C23×C11—82no—
408C23×C11—82no—
409C23×C11—82no—
410C23×C11—84no—
411C23×C11—82no—
412C23×C11C2×#4112yes—
413C23×C11C2×#4114yes—
414C23×C11C2×#4112yes—
415C23×C11C2×#4114yes—
416C23×C11H(5,𝔽2)12yes—
417C23×C11C2511yescharacteristic
418D4×C11—216no—
419D4×C11—44no—
420D4×C11—48no—
421D4×C11—44no—
422D4×C11—44no—
423D4×C11—44no—
424D4×C11—48no—
425D4×C11—84no—
426C2×C4×C11—28no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—21no—
430C2×C4×C11—22no—
431C2×C4×C11—21no—
432C2×C4×C11—22no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—44no—
463C2×C4×C11—48no—
464C2×C4×C11—48no—
465C2×C4×C11—82no—
466C2×C4×C11—84no—
467C2×C4×C11—82no—
468C2×C4×C11—84no—
469C2×C4×C11C2×#4114yes—
470C2×C4×C11C2×#4112yes—
471C2×C4×C11H(5,𝔽2)12yes—
472C2×C4×C11H(5,𝔽2)14yes—
473C23×D4C22×C1111yescharacteristic
474C23×D4C22×C1111yescharacteristic
475C2×#126C22×C1112yescomplemented
476C2×#123C22×C1111yescharacteristic
477C2×#123C22×C1111yescharacteristic, complemented
478C2×#123C22×C1112yescomplemented
479C2×#120C22×C1112yes—
480C2×#120C22×C1111yescharacteristic
481C2×#120C22×C1111yescharacteristic
482C2×C4×D4C22×C1112yes—
483C2×C4×D4C22×C1112yes—
484C2×C4×D4C22×C1112yescomplemented
485C2×#117C22×C1112yescomplemented
486C22×C4⋊C4C22×C1111yescharacteristic, complemented
487C22×C22⋊C4C22×C1112yes—
488C22×C22⋊C4C22×C1112yescomplemented
489C22×C22⋊C4C22×C1111yescharacteristic, complemented
490C22×C22⋊C4C22×C1112yescomplemented
491C22×C42C22×C1111yescharacteristic, complemented
492#399C22×C1112yescomplemented
493#398C22×C1112yescomplemented
494#398C22×C1112yescomplemented
495#397C22×C1112yescomplemented
496#397C22×C1112yescomplemented
497#397C22×C1112yescomplemented
498#397C22×C1112yescomplemented
499#396C22×C1112yescomplemented
500#396C22×C1112yescomplemented
501#396C22×C1112yescomplemented
502#394C22×C1112yes—
503#394C22×C1112yescomplemented
504#394C22×C1112yescomplemented
505#394C22×C1112yescomplemented
506#392C22×C1112yes—
507#392C22×C1112yes—
508#390C22×C1111yescharacteristic
509#390C22×C1112yes—
510#390C22×C1111yescharacteristic
511#390C22×C1112yescomplemented
512#390C22×C1112yescomplemented
513#390C22×C1112yescomplemented
514#390C22×C1112yescomplemented
515#390C22×C1111yescharacteristic, complemented
516#390C22×C1111yescharacteristic, complemented
517#388C22×C1112yescomplemented
518#388C22×C1112yescomplemented
519#388C22×C1112yescomplemented
520#388C22×C1112yescomplemented
521#388C22×C1112yescomplemented
522#388C22×C1112yescomplemented
523#388C22×C1112yescomplemented
524#388C22×C1112yescomplemented
525#388C22×C1112yescomplemented
526#387C22×C1112yescomplemented
527#387C22×C1112yescomplemented
528#387C22×C1112yescomplemented
529#387C22×C1112yescomplemented
530#386C22×C1112yes—
531#386C22×C1112yes—
532#386C22×C1112yes—
533#386C22×C1111yescharacteristic
534#386C22×C1111yescharacteristic
535#386C22×C1111yescharacteristic
536#386C22×C1112yescomplemented
537#386C22×C1112yescomplemented
538#386C22×C1111yescharacteristic, complemented
539#386C22×C1112yescomplemented
540#386C22×C1112yescomplemented
541#386C22×C1112yescomplemented
542#385C22×C1112yescomplemented
543#385C22×C1112yescomplemented
544#385C22×C1112yescomplemented
545#385C22×C1112yescomplemented
546#385C22×C1112yescomplemented
547#385C22×C1112yescomplemented
548#380C22×C1112yescomplemented
549#380C22×C1112yescomplemented
550#379C22×C1112yes—
551#379C22×C1111yescharacteristic
552#379C22×C1112yescomplemented
553#379C22×C1111yescharacteristic, complemented
554C4×C4⋊C4C22×C1112yescomplemented
555C4×C22⋊C4C22×C1112yescomplemented
556C4×C22⋊C4C22×C1112yescomplemented
557C4×C22⋊C4C22×C1112yescomplemented
558C4×C22⋊C4C22×C1112yescomplemented
559#376C22×C1112yescomplemented
560C22×C11—24no—
561C22×C11—22no—
562C22×C11—24no—
563C22×C11—22no—
564C22×C11—24no—
565C22×C11—24no—
566C22×C11—24no—
567C22×C11—24no—
568C22×C11—22no—
569C22×C11—22no—
570C22×C11—24no—
571C22×C11—41no—
572C22×C11—41no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—41no—
579C22×C11—42no—
580C22×C11—41no—
581C22×C11—41no—
582C22×C11—41no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11—41no—
586C22×C11—41no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—41no—
590C22×C11—41no—
591C22×C11—88no—
592C22×C11—88no—
593C22×C11—88no—
594C22×C11#55114yes—
595C22×C11C22×#4112yes—
596C22×C11C22×#4111yescharacteristic
597C22×C11C2×H(5,𝔽2)11yescharacteristic
598C22×C11C2×H(5,𝔽2)12yes—
599C22×C11C2×H(5,𝔽2)11yescharacteristic
600C4×C11—24no—
601C4×C11—22no—
602C4×C11—22no—
603C4×C11—24no—
604C4×C11—42no—
605C4×C11—42no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—42no—
612C4×C11—42no—
613C25C23×C1111yescharacteristic
614C25C23×C1111yescharacteristic
615C25C23×C1111yescharacteristic
616C22×D4—24no—
617C22×D4—28no—
618C22×D4—42no—
619C22×D4—42no—
620C22×D4—42no—
621C22×D4C23×C1112yes—
622C22×D4C23×C1111yescharacteristic
623C22×D4C23×C1111yescharacteristic
624C22×D4C23×C1112yes—
625C22×D4C23×C1112yes—
626C22×D4C23×C1112yes—
627C22×D4C23×C1111yescharacteristic
628C22×D4C23×C1111yescharacteristic
629C23×C4C23×C1111yescharacteristic
630C23×C4C23×C1112yes—
631C23×C4C23×C1112yes—
632C23×C4C23×C1111yescharacteristic
633C23×C4C23×C1112yes—
634C23×C4C23×C1111yescharacteristic
635C23×C4C23×C1112yes—
636C23×C4C23×C1111yescharacteristic
637#126—44no—
638#123—24no—
639#123—44no—
640#123—42no—
641#120—24no—
642#120—28no—
643#120—42no—
644C4×D4—28no—
645C4×D4—44no—
646C4×D4—44no—
647#117—44no—
648C2×C4⋊C4—42no—
649C2×C4⋊C4C23×C1112yes—
650C2×C4⋊C4C23×C1112yes—
651C2×C4⋊C4C23×C1112yes—
652C2×C4⋊C4C23×C1112yes—
653C2×C4⋊C4C23×C1111yescharacteristic
654C2×C4⋊C4C23×C1112yes—
655C2×C4⋊C4C23×C1111yescharacteristic
656C2×C4⋊C4C23×C1112yes—
657C2×C4⋊C4C23×C1112yes—
658C2×C4⋊C4C23×C1112yes—
659C2×C4⋊C4C23×C1112yes—
660C2×C4⋊C4C23×C1112yes—
661C2×C4⋊C4C23×C1112yes—
662C2×C22⋊C4—44no—
663C2×C22⋊C4—44no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4—42no—
666C2×C22⋊C4C23×C1112yes—
667C2×C22⋊C4C23×C1112yes—
668C2×C22⋊C4C23×C1112yes—
669C2×C22⋊C4C23×C1112yes—
670C2×C22⋊C4C23×C1112yes—
671C2×C22⋊C4C23×C1112yes—
672C2×C22⋊C4C23×C1112yes—
673C2×C22⋊C4C23×C1112yes—
674C2×C22⋊C4C23×C1112yes—
675C2×C22⋊C4C23×C1112yes—
676C2×C22⋊C4C23×C1112yes—
677C2×C22⋊C4C23×C1112yes—
678C2×C22⋊C4C23×C1111yescharacteristic
679C2×C22⋊C4C23×C1112yes—
680C2×C22⋊C4C23×C1112yes—
681C2×C22⋊C4C23×C1111yescharacteristic
682C2×C22⋊C4C23×C1112yes—
683C2×C22⋊C4C23×C1112yes—
684C2×C22⋊C4C23×C1112yes—
685C2×C22⋊C4C23×C1112yes—
686C2×C22⋊C4C23×C1112yes—
687C2×C22⋊C4C23×C1112yes—
688C2×C22⋊C4C23×C1112yes—
689C2×C22⋊C4C23×C1112yes—
690C2×C22⋊C4C23×C1112yes—
691C2×C22⋊C4C23×C1111yescharacteristic
692C2×C22⋊C4C23×C1112yes—
693C2×C22⋊C4C23×C1112yes—
694C2×C22⋊C4C23×C1111yescharacteristic
695C2×C22⋊C4C23×C1112yes—
696C2×C22⋊C4C23×C1112yes—
697C2×C22⋊C4C23×C1112yes—
698C2×C42—42no—
699C2×C42C23×C1112yes—
700C2×C42C23×C1112yes—
701C2×C42C23×C1112yes—
702C2×C42C23×C1112yes—
703C2×C42C23×C1112yes—
704C2×C42C23×C1111yescharacteristic
705C2×C42C23×C1111yescharacteristic
706#95C23×C1112yes—
707#95C23×C1112yes—
708#95C23×C1112yes—
709#95C23×C1112yes—
710#95C23×C1112yes—
711#95C23×C1112yes—
712#95C23×C1112yes—
713#95C23×C1112yes—
714#95C23×C1112yes—
715#95C23×C1112yes—
716#95C23×C1112yes—
717#95C23×C1112yes—
718#95C23×C1112yes—
719#95C23×C1112yes—
720#95C23×C1112yes—
721#95C23×C1112yes—
722C2×C11—24no—
723C2×C11—44no—
724C2×C11—42no—
725C2×C11—42no—
726C2×C11—81no—
727C2×C11—81no—
728C2×C11C2×#55111yescharacteristic
729C2×C11#348112yes—
730C2×C11#349011yescharacteristic
731C2×C11#351912yes—
732C2×C11#354311yescharacteristic
733C24—22no—
734C24—22no—
735C24—22no—
736C24—24no—
737C24—24no—
738C24—24no—
739C24—22no—
740C24—22no—
741C24—42no—
742C24—42no—
743C24—42no—
744C24—41no—
745C24—41no—
746C24—41no—
747C24—41no—
748C24C24×C1111yescharacteristic
749C24C24×C1111yescharacteristic
750C24C24×C1111yescharacteristic
751C24C24×C1111yescharacteristic
752C24C24×C1112yes—
753C24C24×C1111yescharacteristic
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—22no—
759C2×D4—22no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—22no—
766C2×D4—42no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—416no—
775C2×D4—42no—
776C2×D4—42no—
777C2×D4—416no—
778C2×D4C11×#4118yes—
779C2×D4C11×#4114yes—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—22no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—41no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—41no—
802C22×C4C24×C1112yes—
803C22×C4C24×C1112yes—
804C22×C4C24×C1112yes—
805C22×C4C24×C1112yes—
806C22×C4C24×C1112yes—
807C22×C4C24×C1112yes—
808C22×C4C24×C1112yes—
809C22×C4C24×C1112yes—
810C22×C4C24×C1112yes—
811C22×C4C24×C1112yes—
812C22×C4C24×C1111yescharacteristic
813C22×C4C24×C1111yescharacteristic
814C22×C4C24×C1112yes—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—41no—
820C4⋊C4—42no—
821C4⋊C4—41no—
822C4⋊C4—42no—
823C4⋊C4—42no—
824C4⋊C4—42no—
825C4⋊C4—42no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C22⋊C4—24no—
829C22⋊C4—24no—
830C22⋊C4—22no—
831C22⋊C4—24no—
832C22⋊C4—22no—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—24no—
844C22⋊C4—42no—
845C22⋊C4—42no—
846C22⋊C4—42no—
847C22⋊C4—42no—
848C22⋊C4—42no—
849C22⋊C4—42no—
850C22⋊C4—42no—
851C22⋊C4—42no—
852C22⋊C4—42no—
853C22⋊C4—41no—
854C22⋊C4—42no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—41no—
858C22⋊C4—42no—
859C22⋊C4—42no—
860C42—24no—
861C42—24no—
862C42—24no—
863C42—41no—
864C42—41no—
865C42—42no—
866C42—42no—
867C11#5994011yescharacteristic, direct product factor, Sylow
868C23—21no—
869C23—22no—
870C23—21no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—22no—
886C23—22no—
887C23—21no—
888C23—21no—
889C23—22no—
890C23—22no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—44no—
896C23—44no—
897C23—44no—
898C23—48no—
899C23—48no—
900C23—48no—
901C23—44no—
902C23—44no—
903C23—84no—
904C23—84no—
905C23—82no—
906C23—82no—
907C23—82no—
908C23—84no—
909C23—82no—
910C23C2×C11×#4112yes—
911C23C2×C11×#4114yes—
912C23C2×C11×#4112yes—
913C23C2×C11×#4114yes—
914C23C11×H(5,𝔽2)12yes—
915C23C25×C1111yescharacteristic
916D4—216no—
917D4—44no—
918D4—48no—
919D4—44no—
920D4—44no—
921D4—44no—
922D4—48no—
923D4—84no—
924C2×C4—28no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
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—44no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—82no—
964C2×C4—84no—
965C2×C4—82no—
966C2×C4—84no—
967C2×C4C2×C11×#4114yes—
968C2×C4C2×C11×#4112yes—
969C2×C4C11×H(5,𝔽2)12yes—
970C2×C4C11×H(5,𝔽2)14yes—
971C22—24no—
972C22—22no—
973C22—24no—
974C22—22no—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—22no—
980C22—22no—
981C22—24no—
982C22—41no—
983C22—41no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—41no—
990C22—42no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—42no—
995C22—42no—
996C22—41no—
997C22—41no—
998C22—42no—
999C22—42no—
1000C22—41no—
1001C22—41no—
1002C22—88no—
1003C22—88no—
1004C22—88no—
1005C22C11×#55114yes—
1006C22C22×C11×#4112yes—
1007C22C22×C11×#4111yescharacteristic
1008C22C2×C11×H(5,𝔽2)11yescharacteristic
1009C22C2×C11×H(5,𝔽2)12yes—
1010C22C2×C11×H(5,𝔽2)11yescharacteristic
1011C4—24no—
1012C4—22no—
1013C4—22no—
1014C4—24no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C2—24no—
1025C2—42no—
1026C2—44no—
1027C2—42no—
1028C2—81no—
1029C2—81no—
1030C2C2×C11×#55111yescharacteristic
1031C2C11×#348112yes—
1032C2C11×#349011yescharacteristic
1033C2C11×#351912yes—
1034C2C11×#354311yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC11×#2403C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2797C2semidirect
2. C11×#2748C2semidirect
3. C11×#2697C2semidirect
4. C11×#2603C2semidirect
5. C11×#2579C2semidirect
6. C11×#2554C2semidirect
7. C11×#2531C2semidirect
8. C11×#2480C2semidirect
9. C11×#2471C2semidirect
10. C11×#2418C2semidirect
11. C11×#2411C2semidirect
12. C11×#2405C2semidirect
14. C11×#2374C2semidirect
15. C11×#2358C2semidirect
16. C11×#2358C2semidirect
17. D4×C11×C22⋊C4C2semidirect
18. C2×C11×#390C2semidirect
19. C11×#2290C2semidirect
22. C2×C11×#126C22semidirect
24. C2×C11×#123C22semidirect
25. C2×C11×#123C22semidirect
31. C2×C4×D4×C11C22semidirect
32. C2×C11×#117C22semidirect
33. C22×C11×C4⋊C4C22semidirect
35. C22×C11×C22⋊C4C22semidirect
36. C22×C11×C22⋊C4C22semidirect
37. C22×C11×C22⋊C4C22semidirect
38. C22×C42×C11C22semidirect
39. C11×#399C22semidirect
40. C11×#398C22semidirect
41. C11×#398C22semidirect
42. C11×#397C22semidirect
43. C11×#397C22semidirect
44. C11×#397C22semidirect
45. C11×#397C22semidirect
46. C11×#396C22semidirect
47. C11×#396C22semidirect
48. C11×#396C22semidirect
50. C11×#394C22semidirect
51. C11×#394C22semidirect
52. C11×#394C22semidirect
58. C11×#390C22semidirect
59. C11×#390C22semidirect
60. C11×#390C22semidirect
61. C11×#390C22semidirect
62. C11×#390C22semidirect
63. C11×#390C22semidirect
64. C11×#388C22semidirect
65. C11×#388C22semidirect
66. C11×#388C22semidirect
67. C11×#388C22semidirect
68. C11×#388C22semidirect
69. C11×#388C22semidirect
70. C11×#388C22semidirect
71. C11×#388C22semidirect
72. C11×#388C22semidirect
73. C11×#387C22semidirect
74. C11×#387C22semidirect
75. C11×#387C22semidirect
76. C11×#387C22semidirect
83. C11×#386C22semidirect
84. C11×#386C22semidirect
85. C11×#386C22semidirect
86. C11×#386C22semidirect
87. C11×#386C22semidirect
88. C11×#386C22semidirect
89. C11×#385C22semidirect
90. C11×#385C22semidirect
91. C11×#385C22semidirect
92. C11×#385C22semidirect
93. C11×#385C22semidirect
94. C11×#385C22semidirect
95. C11×#380C22semidirect
96. C11×#380C22semidirect
99. C11×#379C22semidirect
100. C11×#379C22semidirect
101. C4×C11×C4⋊C4C22semidirect
102. C4×C11×C22⋊C4C22semidirect
103. C4×C11×C22⋊C4C22semidirect
104. C4×C11×C22⋊C4C22semidirect
105. C4×C11×C22⋊C4C22semidirect
106. C11×#376C22semidirect
216. #59940C11direct (N × H)
351. #2797C2×C11semidirect
352. #2748C2×C11semidirect
353. #2697C2×C11semidirect
354. #2603C2×C11semidirect
355. #2579C2×C11semidirect
356. #2554C2×C11semidirect
357. #2531C2×C11semidirect
358. #2480C2×C11semidirect
359. #2471C2×C11semidirect
360. #2418C2×C11semidirect
361. #2411C2×C11semidirect
362. #2405C2×C11semidirect
364. #2374C2×C11semidirect
365. #2358C2×C11semidirect
366. #2358C2×C11semidirect
367. D4×C22⋊C4C2×C11semidirect
368. C2×#390C2×C11semidirect
369. #2290C2×C11semidirect
475. C2×#126C22×C11semidirect
477. C2×#123C22×C11semidirect
478. C2×#123C22×C11semidirect
484. C2×C4×D4C22×C11semidirect
485. C2×#117C22×C11semidirect
486. C22×C4⋊C4C22×C11semidirect
488. C22×C22⋊C4C22×C11semidirect
489. C22×C22⋊C4C22×C11semidirect
490. C22×C22⋊C4C22×C11semidirect
491. C22×C42C22×C11semidirect
492. #399C22×C11semidirect
493. #398C22×C11semidirect
494. #398C22×C11semidirect
495. #397C22×C11semidirect
496. #397C22×C11semidirect
497. #397C22×C11semidirect
498. #397C22×C11semidirect
499. #396C22×C11semidirect
500. #396C22×C11semidirect
501. #396C22×C11semidirect
503. #394C22×C11semidirect
504. #394C22×C11semidirect
505. #394C22×C11semidirect
511. #390C22×C11semidirect
512. #390C22×C11semidirect
513. #390C22×C11semidirect
514. #390C22×C11semidirect
515. #390C22×C11semidirect
516. #390C22×C11semidirect
517. #388C22×C11semidirect
518. #388C22×C11semidirect
519. #388C22×C11semidirect
520. #388C22×C11semidirect
521. #388C22×C11semidirect
522. #388C22×C11semidirect
523. #388C22×C11semidirect
524. #388C22×C11semidirect
525. #388C22×C11semidirect
526. #387C22×C11semidirect
527. #387C22×C11semidirect
528. #387C22×C11semidirect
529. #387C22×C11semidirect
536. #386C22×C11semidirect
537. #386C22×C11semidirect
538. #386C22×C11semidirect
539. #386C22×C11semidirect
540. #386C22×C11semidirect
541. #386C22×C11semidirect
542. #385C22×C11semidirect
543. #385C22×C11semidirect
544. #385C22×C11semidirect
545. #385C22×C11semidirect
546. #385C22×C11semidirect
547. #385C22×C11semidirect
548. #380C22×C11semidirect
549. #380C22×C11semidirect
552. #379C22×C11semidirect
553. #379C22×C11semidirect
554. C4×C4⋊C4C22×C11semidirect
555. C4×C22⋊C4C22×C11semidirect
556. C4×C22⋊C4C22×C11semidirect
557. C4×C22⋊C4C22×C11semidirect
558. C4×C22⋊C4C22×C11semidirect
559. #376C22×C11semidirect
867. C11#59940direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#27972
C11×#27482
C11×#26972
C11×#26032
C11×#25792
C11×#25542
C11×#25312
C11×#24802
C11×#24712
C11×#24182
C11×#24112
C11×#24052
C11×#24032
C11×#23742
C11×#23582
D4×C11×C22⋊C42
C2×C11×#3902
C11×#22902
#5994011