Finite Group Databasebeta

← C11×#34511 #14611704

Subgroups — C11×#34511 #14611704

Order 2816.

2544 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#560C211yesmaximal, characteristic
2C11×#2375C211yesmaximal, characteristic, complemented
3C11×#2375C212yesmaximal, complemented
4C11×#2374C211yesmaximal, characteristic, complemented
5C11×#2373C212yesmaximal, complemented
6C11×#2366C211yesmaximal, characteristic, complemented
7C11×#2364C212yesmaximal, complemented
8C11×#2363C212yesmaximal, complemented
9C11×#2361C212yesmaximal, complemented
10C11×#2359C212yesmaximal, complemented
11C11×#2335C212yesmaximal, complemented
12C11×#2334C212yesmaximal, complemented
13C11×#2333C212yesmaximal, complemented
14C11×#2328C211yesmaximal, characteristic, complemented
15C11×#2325C212yesmaximal, complemented
16C11×#2324C212yesmaximal, complemented
17C11×#2322C211yesmaximal, characteristic, complemented
18C4×C11×#120C212yesmaximal, complemented
19C4×C11×#120C211yesmaximal, characteristic, complemented
20C24×C4×C11C2211yescharacteristic
21C11×#560C4116yescomplemented
22C2×C11×#127C2211yescharacteristic
23C2×C11×#126C2212yes—
24C2×C11×#123C2211yescharacteristic
25C2×C11×#123C2212yes—
26C2×C11×#121C2212yes—
27C2×C11×#121C2212yes—
28C2×C11×#121C2212yes—
29C2×C11×#120C2212yes—
30C2×C11×#120C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2212yes—
33C2×C4×D4×C11C2212yes—
34C2×C4×D4×C11C2212yes—
35C2×C4×D4×C11C2212yes—
36C2×C4×D4×C11C2212yescomplemented
37C2×C4×D4×C11C2211yescharacteristic, complemented
38C2×C11×#117C2212yescomplemented
39C22×C11×C4⋊C4C2211yescharacteristic, complemented
40C11×#390C2212yes—
41C11×#390C2212yes—
42C11×#390C2211yescharacteristic
43C11×#390C2212yes—
44C11×#390C2212yes—
45C11×#390C2211yescharacteristic, complemented
46C11×#390C2212yescomplemented
47C11×#389C2212yescomplemented
48C11×#389C2212yescomplemented
49C11×#389C2212yescomplemented
50C11×#388C2212yes—
51C11×#388C2212yes—
52C11×#388C2212yes—
53C11×#388C2212yes—
54C11×#388C2212yes—
55C11×#388C2212yes—
56C11×#388C2212yes—
57C11×#388C2212yes—
58C11×#388C2212yes—
59C11×#388C2212yescomplemented
60C11×#388C2212yescomplemented
61C11×#388C2212yescomplemented
62C11×#387C2212yescomplemented
63C11×#387C2212yescomplemented
64C11×#387C2212yescomplemented
65C11×#387C2212yescomplemented
66C11×#387C2212yescomplemented
67C11×#387C2212yescomplemented
68C11×#386C2212yes—
69C11×#386C2212yes—
70C11×#386C2212yes—
71C11×#386C2212yes—
72C11×#386C2211yescharacteristic
73C11×#386C2211yescharacteristic
74C11×#386C2212yes—
75C11×#386C2212yes—
76C11×#386C2212yes—
77C11×#386C2212yes—
78C11×#386C2212yescomplemented
79C11×#386C2212yescomplemented
80C11×#386C2212yescomplemented
81C11×#385C2212yes—
82C11×#385C2212yes—
83C11×#385C2212yes—
84C11×#385C2211yescharacteristic
85C11×#385C2212yes—
86C11×#385C2211yescharacteristic, complemented
87C11×#385C2212yescomplemented
88C11×#382C2211yescharacteristic, complemented
89C11×#381C2211yescharacteristic, complemented
90C11×#380C2212yescomplemented
91C11×#379C2211yescharacteristic
92C11×#379C2212yes—
93C4×C11×C4⋊C4C2212yescomplemented
94C4×C11×C4⋊C4C2212yescomplemented
95C4×C11×C4⋊C4C2212yescomplemented
96C4×C11×C4⋊C4C2212yescomplemented
97C4×C11×C22⋊C4C2212yes—
98C4×C11×C22⋊C4C2211yescharacteristic
99C4×C11×C22⋊C4C2212yes—
100C4×C11×C22⋊C4C2212yes—
101C4×C11×C22⋊C4C2212yes—
102C4×C11×C22⋊C4C2211yescharacteristic, complemented
103C4×C11×C22⋊C4C2212yescomplemented
104C4×C11×C22⋊C4C2212yescomplemented
105C4×C11×C22⋊C4C2212yescomplemented
106C11×#376C2211yescharacteristic, complemented
107C2×C11×#95C2212yescomplemented
108C25×C11C2311yescharacteristic
109C22×D4×C11C2312yes—
110C22×D4×C11C2312yes—
111C22×D4×C11C2312yes—
112C22×D4×C11C2311yescharacteristic
113C22×D4×C11C2312yes—
114C22×D4×C11C2312yes—
115C22×D4×C11C2311yescharacteristic
116C23×C4×C11—44no—
117C23×C4×C11—42no—
118C23×C4×C11C2311yescharacteristic
119C23×C4×C11C2312yes—
120C23×C4×C11C2312yes—
121C23×C4×C11C2311yescharacteristic
122C23×C4×C11C2312yes—
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2312yes—
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C11×#127C2×C418yescomplemented
129C11×#126C2×C4116yescomplemented
130C11×#123C2×C418yescomplemented
131C11×#123C2×C4116yescomplemented
132C11×#121C2×C4116yescomplemented
133C11×#121C2×C4116yescomplemented
134C11×#121C2×C4116yescomplemented
135C11×#120C2×C4116yescomplemented
136C11×#120C2×C418yescomplemented
137C4×D4×C11—42no—
138C4×D4×C11—44no—
139C4×D4×C11—42no—
140C4×D4×C11—44no—
141C4×D4×C11—44no—
142C4×D4×C11—44no—
143C4×D4×C11—44no—
144C11×#117—44no—
145C2×C11×C4⋊C4—42no—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C4⋊C4C2312yes—
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C4⋊C4C2312yes—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2312yes—
179C2×C11×C22⋊C4C2312yes—
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2311yescharacteristic
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2311yescharacteristic
185C2×C11×C22⋊C4C2312yes—
186C2×C42×C11C2311yescharacteristic
187C2×C42×C11C2312yes—
188C2×C42×C11C2311yescharacteristic
189C2×C42×C11C2312yes—
190C2×C42×C11C2312yes—
191C2×C42×C11C2312yes—
192C2×C42×C11C2312yes—
193C2×C42×C11C2312yes—
194C2×C42×C11C2312yes—
195C2×C42×C11C2312yes—
196C2×C42×C11C2311yescharacteristic
197C11×#95C2312yes—
198C11×#95C2312yes—
199C11×#95C2312yes—
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—
215#34511C1111yesmaximal, characteristic, direct product factor, Sylow
216C24×C11—42no—
217C24×C11—41no—
218C24×C11—41no—
219C24×C11—42no—
220C24×C11C22×C414yes—
221C24×C11C2412yes—
222C24×C11C2411yescharacteristic
223C24×C11C2412yes—
224C24×C11C2411yescharacteristic
225C2×D4×C11—42no—
226C2×D4×C11—41no—
227C2×D4×C11—41no—
228C2×D4×C11—42no—
229C2×D4×C11—42no—
230C2×D4×C11—42no—
231C2×D4×C11—42no—
232C2×D4×C11—42no—
233C2×D4×C11—42no—
234C2×D4×C11—41no—
235C2×D4×C11—41no—
236C2×D4×C11—42no—
237C2×D4×C11—42no—
238C2×D4×C11—42no—
239C2×D4×C11C22×C418yes—
240C2×D4×C11C22×C418yes—
241C2×D4×C11C22×C418yes—
242C2×D4×C11C22×C414yes—
243C2×D4×C11C22×C418yes—
244C2×D4×C11C22×C414yescomplemented
245C2×D4×C11C22×C418yescomplemented
246C22×C4×C11—24no—
247C22×C4×C11—24no—
248C22×C4×C11—24no—
249C22×C4×C11—24no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—24no—
253C22×C4×C11—41no—
254C22×C4×C11—42no—
255C22×C4×C11—42no—
256C22×C4×C11—41no—
257C22×C4×C11—42no—
258C22×C4×C11—42no—
259C22×C4×C11—42no—
260C22×C4×C11—41no—
261C22×C4×C11—42no—
262C22×C4×C11—41no—
263C22×C4×C11—42no—
264C22×C4×C11—42no—
265C22×C4×C11—42no—
266C22×C4×C11—42no—
267C22×C4×C11—42no—
268C22×C4×C11—42no—
269C22×C4×C11—42no—
270C22×C4×C11—416no—
271C22×C4×C11C22×C418yescomplemented
272C22×C4×C11C22×C414yescomplemented
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2412yes—
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C11×C4⋊C4—24no—
289C11×C4⋊C4—24no—
290C11×C4⋊C4—24no—
291C11×C4⋊C4—42no—
292C11×C4⋊C4—42no—
293C11×C4⋊C4—42no—
294C11×C4⋊C4—42no—
295C11×C4⋊C4—42no—
296C11×C4⋊C4—41no—
297C11×C4⋊C4—41no—
298C11×C4⋊C4C22×C418yescomplemented
299C11×C4⋊C4C22×C418yescomplemented
300C11×C4⋊C4C22×C418yescomplemented
301C11×C22⋊C4—24no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—24no—
304C11×C22⋊C4—42no—
305C11×C22⋊C4—41no—
306C11×C22⋊C4—42no—
307C11×C22⋊C4—42no—
308C11×C22⋊C4—42no—
309C11×C22⋊C4—41no—
310C11×C22⋊C4—42no—
311C11×C22⋊C4—42no—
312C11×C22⋊C4—42no—
313C11×C22⋊C4—42no—
314C11×C22⋊C4—42no—
315C11×C22⋊C4—41no—
316C11×C22⋊C4—41no—
317C11×C22⋊C4—42no—
318C11×C22⋊C4—42no—
319C11×C22⋊C4—42no—
320C11×C22⋊C4—42no—
321C11×C22⋊C4C22×C418yes—
322C11×C22⋊C4C22×C418yes—
323C11×C22⋊C4C22×C418yes—
324C11×C22⋊C4C22×C414yes—
325C11×C22⋊C4C22×C418yes—
326C11×C22⋊C4C22×C414yescomplemented
327C11×C22⋊C4C22×C418yescomplemented
328C42×C11—24no—
329C42×C11—22no—
330C42×C11—42no—
331C42×C11—42no—
332C42×C11—41no—
333C42×C11—42no—
334C42×C11—42no—
335C42×C11—42no—
336C42×C11—42no—
337C42×C11—42no—
338C42×C11C22×C414yescomplemented
339C2×#560C2×C1111yescharacteristic
340#2375C2×C1111yescharacteristic, complemented
341#2375C2×C1112yescomplemented
342#2374C2×C1111yescharacteristic, complemented
343#2373C2×C1112yescomplemented
344#2366C2×C1111yescharacteristic, complemented
345#2364C2×C1112yescomplemented
346#2363C2×C1112yescomplemented
347#2361C2×C1112yescomplemented
348#2359C2×C1112yescomplemented
349#2335C2×C1112yescomplemented
350#2334C2×C1112yescomplemented
351#2333C2×C1112yescomplemented
352#2328C2×C1111yescharacteristic, complemented
353#2325C2×C1112yescomplemented
354#2324C2×C1112yescomplemented
355#2322C2×C1111yescharacteristic, complemented
356C4×#120C2×C1111yescharacteristic, complemented
357C4×#120C2×C1112yescomplemented
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—21no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—21no—
367C23×C11—22no—
368C23×C11—21no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—21no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—48no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11—48no—
382C23×C11—44no—
383C23×C11C23×C414yes—
384C23×C11C23×C412yes—
385C23×C11C23×C414yes—
386C23×C11C23×C412yes—
387C23×C11C2511yescharacteristic
388D4×C11—48no—
389D4×C11—48no—
390D4×C11—48no—
391D4×C11—44no—
392D4×C11—48no—
393D4×C11—44no—
394D4×C11—48no—
395C2×C4×C11—22no—
396C2×C4×C11—21no—
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—21no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—21no—
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—21no—
418C2×C4×C11—22no—
419C2×C4×C11—21no—
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—44no—
430C2×C4×C11—48no—
431C2×C4×C11—48no—
432C2×C4×C11—44no—
433C2×C4×C11—44no—
434C2×C4×C11—48no—
435C2×C4×C11—82no—
436C2×C4×C11—84no—
437C2×C4×C11—82no—
438C2×C4×C11—84no—
439C2×C4×C11C23×C412yes—
440C2×C4×C11C23×C414yes—
441C2×C4×C11C23×C414yes—
442C2×C4×C11C23×C414yes—
443C2×C4×C11C23×C414yes—
444C2×C4×C11H(5,𝔽2)14yes—
445C2×C4×C11H(5,𝔽2)12yes—
446C24×C4C22×C1111yescharacteristic
447#560C4×C11116yescomplemented
448C2×#127C22×C1111yescharacteristic
449C2×#126C22×C1112yes—
450C2×#123C22×C1111yescharacteristic
451C2×#123C22×C1112yes—
452C2×#121C22×C1112yes—
453C2×#121C22×C1112yes—
454C2×#121C22×C1112yes—
455C2×#120C22×C1111yescharacteristic
456C2×#120C22×C1112yes—
457C2×C4×D4C22×C1111yescharacteristic
458C2×C4×D4C22×C1112yes—
459C2×C4×D4C22×C1112yes—
460C2×C4×D4C22×C1112yes—
461C2×C4×D4C22×C1112yes—
462C2×C4×D4C22×C1112yescomplemented
463C2×C4×D4C22×C1111yescharacteristic, complemented
464C2×#117C22×C1112yescomplemented
465C22×C4⋊C4C22×C1111yescharacteristic, complemented
466#390C22×C1112yes—
467#390C22×C1112yes—
468#390C22×C1111yescharacteristic
469#390C22×C1112yes—
470#390C22×C1112yes—
471#390C22×C1111yescharacteristic, complemented
472#390C22×C1112yescomplemented
473#389C22×C1112yescomplemented
474#389C22×C1112yescomplemented
475#389C22×C1112yescomplemented
476#388C22×C1112yes—
477#388C22×C1112yes—
478#388C22×C1112yes—
479#388C22×C1112yes—
480#388C22×C1112yes—
481#388C22×C1112yes—
482#388C22×C1112yes—
483#388C22×C1112yes—
484#388C22×C1112yes—
485#388C22×C1112yescomplemented
486#388C22×C1112yescomplemented
487#388C22×C1112yescomplemented
488#387C22×C1112yescomplemented
489#387C22×C1112yescomplemented
490#387C22×C1112yescomplemented
491#387C22×C1112yescomplemented
492#387C22×C1112yescomplemented
493#387C22×C1112yescomplemented
494#386C22×C1111yescharacteristic
495#386C22×C1112yes—
496#386C22×C1112yes—
497#386C22×C1112yes—
498#386C22×C1112yes—
499#386C22×C1112yes—
500#386C22×C1112yes—
501#386C22×C1112yes—
502#386C22×C1112yes—
503#386C22×C1111yescharacteristic
504#386C22×C1112yescomplemented
505#386C22×C1112yescomplemented
506#386C22×C1112yescomplemented
507#385C22×C1112yes—
508#385C22×C1112yes—
509#385C22×C1112yes—
510#385C22×C1111yescharacteristic
511#385C22×C1112yes—
512#385C22×C1111yescharacteristic, complemented
513#385C22×C1112yescomplemented
514#382C22×C1111yescharacteristic, complemented
515#381C22×C1111yescharacteristic, complemented
516#380C22×C1112yescomplemented
517#379C22×C1112yes—
518#379C22×C1111yescharacteristic
519C4×C4⋊C4C22×C1112yescomplemented
520C4×C4⋊C4C22×C1112yescomplemented
521C4×C4⋊C4C22×C1112yescomplemented
522C4×C4⋊C4C22×C1112yescomplemented
523C4×C22⋊C4C22×C1112yes—
524C4×C22⋊C4C22×C1111yescharacteristic
525C4×C22⋊C4C22×C1112yes—
526C4×C22⋊C4C22×C1112yes—
527C4×C22⋊C4C22×C1112yes—
528C4×C22⋊C4C22×C1111yescharacteristic, complemented
529C4×C22⋊C4C22×C1112yescomplemented
530C4×C22⋊C4C22×C1112yescomplemented
531C4×C22⋊C4C22×C1112yescomplemented
532#376C22×C1111yescharacteristic, complemented
533C2×#95C22×C1112yescomplemented
534C22×C11—24no—
535C22×C11—22no—
536C22×C11—24no—
537C22×C11—24no—
538C22×C11—24no—
539C22×C11—24no—
540C22×C11—24no—
541C22×C11—24no—
542C22×C11—24no—
543C22×C11—22no—
544C22×C11—416no—
545C22×C11—42no—
546C22×C11—41no—
547C22×C11—41no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—41no—
557C22×C11—41no—
558C22×C11—42no—
559C22×C11C24×C411yescharacteristic
560C22×C11C2×H(5,𝔽2)12yes—
561C22×C11C2×H(5,𝔽2)11yescharacteristic
562C22×C11#58511yescharacteristic
563C22×C11#58512yes—
564C4×C11—24no—
565C4×C11—24no—
566C4×C11—24no—
567C4×C11—22no—
568C4×C11—24no—
569C4×C11—22no—
570C4×C11—24no—
571C4×C11—41no—
572C4×C11—41no—
573C4×C11—42no—
574C4×C11—42no—
575C4×C11—42no—
576C4×C11—42no—
577C4×C11—42no—
578C4×C11—41no—
579C25C23×C1111yescharacteristic
580C22×D4C23×C1112yes—
581C22×D4C23×C1112yes—
582C22×D4C23×C1112yes—
583C22×D4C23×C1111yescharacteristic
584C22×D4C23×C1112yes—
585C22×D4C23×C1112yes—
586C22×D4C23×C1111yescharacteristic
587C23×C4—44no—
588C23×C4—42no—
589C23×C4C23×C1111yescharacteristic
590C23×C4C23×C1112yes—
591C23×C4C23×C1111yescharacteristic
592C23×C4C23×C1112yes—
593C23×C4C23×C1111yescharacteristic
594C23×C4C23×C1112yes—
595C23×C4C23×C1111yescharacteristic
596C23×C4C23×C1112yes—
597C23×C4C23×C1111yescharacteristic
598C23×C4C23×C1112yes—
599#127C2×C4×C1118yescomplemented
600#126C2×C4×C11116yescomplemented
601#123C2×C4×C1118yescomplemented
602#123C2×C4×C11116yescomplemented
603#121C2×C4×C11116yescomplemented
604#121C2×C4×C11116yescomplemented
605#121C2×C4×C11116yescomplemented
606#120C2×C4×C1118yescomplemented
607#120C2×C4×C11116yescomplemented
608C4×D4—42no—
609C4×D4—44no—
610C4×D4—42no—
611C4×D4—44no—
612C4×D4—44no—
613C4×D4—44no—
614C4×D4—44no—
615#117—44no—
616C2×C4⋊C4—42no—
617C2×C4⋊C4C23×C1112yes—
618C2×C4⋊C4C23×C1112yes—
619C2×C4⋊C4C23×C1112yes—
620C2×C4⋊C4C23×C1112yes—
621C2×C4⋊C4C23×C1112yes—
622C2×C4⋊C4C23×C1112yes—
623C2×C4⋊C4C23×C1111yescharacteristic
624C2×C4⋊C4C23×C1111yescharacteristic
625C2×C4⋊C4C23×C1112yes—
626C2×C4⋊C4C23×C1112yes—
627C2×C4⋊C4C23×C1112yes—
628C2×C4⋊C4C23×C1112yes—
629C2×C4⋊C4C23×C1112yes—
630C2×C22⋊C4C23×C1112yes—
631C2×C22⋊C4C23×C1112yes—
632C2×C22⋊C4C23×C1112yes—
633C2×C22⋊C4C23×C1112yes—
634C2×C22⋊C4C23×C1111yescharacteristic
635C2×C22⋊C4C23×C1112yes—
636C2×C22⋊C4C23×C1112yes—
637C2×C22⋊C4C23×C1112yes—
638C2×C22⋊C4C23×C1112yes—
639C2×C22⋊C4C23×C1112yes—
640C2×C22⋊C4C23×C1111yescharacteristic
641C2×C22⋊C4C23×C1112yes—
642C2×C22⋊C4C23×C1112yes—
643C2×C22⋊C4C23×C1112yes—
644C2×C22⋊C4C23×C1112yes—
645C2×C22⋊C4C23×C1111yescharacteristic
646C2×C22⋊C4C23×C1112yes—
647C2×C22⋊C4C23×C1111yescharacteristic
648C2×C22⋊C4C23×C1112yes—
649C2×C22⋊C4C23×C1112yes—
650C2×C22⋊C4C23×C1112yes—
651C2×C22⋊C4C23×C1112yes—
652C2×C22⋊C4C23×C1112yes—
653C2×C22⋊C4C23×C1112yes—
654C2×C22⋊C4C23×C1111yescharacteristic
655C2×C22⋊C4C23×C1112yes—
656C2×C22⋊C4C23×C1111yescharacteristic
657C2×C42C23×C1112yes—
658C2×C42C23×C1111yescharacteristic
659C2×C42C23×C1112yes—
660C2×C42C23×C1112yes—
661C2×C42C23×C1112yes—
662C2×C42C23×C1112yes—
663C2×C42C23×C1112yes—
664C2×C42C23×C1111yescharacteristic
665C2×C42C23×C1112yes—
666C2×C42C23×C1112yes—
667C2×C42C23×C1111yescharacteristic
668#95C23×C1112yes—
669#95C23×C1112yes—
670#95C23×C1112yes—
671#95C23×C1112yes—
672#95C23×C1112yes—
673#95C23×C1112yes—
674#95C23×C1112yes—
675#95C23×C1112yes—
676#95C23×C1112yes—
677#95C23×C1112yes—
678#95C23×C1112yes—
679#95C23×C1112yes—
680#95C23×C1112yes—
681#95C23×C1112yes—
682#95C23×C1112yes—
683#95C23×C1112yes—
684#95C23×C1112yes—
685#95C23×C1112yes—
686C2×C11—42no—
687C2×C11—44no—
688C2×C11—44no—
689C2×C11—42no—
690C2×C11C4×H(5,𝔽2)12yes—
691C2×C11C4×H(5,𝔽2)11yescharacteristic
692C2×C11#353211yescharacteristic
693C2×C11#353912yes—
694C2×C11#354011yescharacteristic
695C24—42no—
696C24—41no—
697C24—41no—
698C24—42no—
699C24C22×C4×C1114yes—
700C24C24×C1111yescharacteristic
701C24C24×C1112yes—
702C24C24×C1112yes—
703C24C24×C1111yescharacteristic
704C2×D4—42no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C22×C4×C1118yes—
719C2×D4C22×C4×C1118yes—
720C2×D4C22×C4×C1118yes—
721C2×D4C22×C4×C1114yes—
722C2×D4C22×C4×C1118yes—
723C2×D4C22×C4×C1114yescomplemented
724C2×D4C22×C4×C1118yescomplemented
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—24no—
732C22×C4—41no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—41no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—41no—
740C22×C4—42no—
741C22×C4—41no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—416no—
750C22×C4C22×C4×C1114yescomplemented
751C22×C4C22×C4×C1118yescomplemented
752C22×C4C24×C1111yescharacteristic
753C22×C4C24×C1112yes—
754C22×C4C24×C1111yescharacteristic
755C22×C4C24×C1112yes—
756C22×C4C24×C1112yes—
757C22×C4C24×C1112yes—
758C22×C4C24×C1112yes—
759C22×C4C24×C1111yescharacteristic
760C22×C4C24×C1111yescharacteristic
761C22×C4C24×C1112yes—
762C22×C4C24×C1112yes—
763C22×C4C24×C1112yes—
764C22×C4C24×C1112yes—
765C22×C4C24×C1112yes—
766C22×C4C24×C1111yescharacteristic
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—42no—
771C4⋊C4—42no—
772C4⋊C4—42no—
773C4⋊C4—41no—
774C4⋊C4—41no—
775C4⋊C4—42no—
776C4⋊C4—42no—
777C4⋊C4C22×C4×C1118yescomplemented
778C4⋊C4C22×C4×C1118yescomplemented
779C4⋊C4C22×C4×C1118yescomplemented
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—24no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—41no—
787C22⋊C4—41no—
788C22⋊C4—42no—
789C22⋊C4—42no—
790C22⋊C4—42no—
791C22⋊C4—42no—
792C22⋊C4—42no—
793C22⋊C4—41no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—42no—
799C22⋊C4—42no—
800C22⋊C4C22×C4×C1118yes—
801C22⋊C4C22×C4×C1118yes—
802C22⋊C4C22×C4×C1118yes—
803C22⋊C4C22×C4×C1118yes—
804C22⋊C4C22×C4×C1114yes—
805C22⋊C4C22×C4×C1118yescomplemented
806C22⋊C4C22×C4×C1114yescomplemented
807C42—24no—
808C42—22no—
809C42—42no—
810C42—42no—
811C42—42no—
812C42—42no—
813C42—42no—
814C42—42no—
815C42—42no—
816C42—41no—
817C42C22×C4×C1114yescomplemented
818C11#3451111yescharacteristic, direct product factor, Sylow
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—21no—
828C23—22no—
829C23—21no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—21no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—48no—
840C23—44no—
841C23—44no—
842C23—48no—
843C23—44no—
844C23C23×C4×C1114yes—
845C23C23×C4×C1112yes—
846C23C23×C4×C1114yes—
847C23C23×C4×C1112yes—
848C23C25×C1111yescharacteristic
849D4—48no—
850D4—48no—
851D4—48no—
852D4—44no—
853D4—48no—
854D4—44no—
855D4—48no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—44no—
891C2×C4—48no—
892C2×C4—48no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—48no—
896C2×C4—84no—
897C2×C4—82no—
898C2×C4—82no—
899C2×C4—84no—
900C2×C4C23×C4×C1112yes—
901C2×C4C23×C4×C1114yes—
902C2×C4C23×C4×C1114yes—
903C2×C4C23×C4×C1114yes—
904C2×C4C23×C4×C1114yes—
905C2×C4C11×H(5,𝔽2)14yes—
906C2×C4C11×H(5,𝔽2)12yes—
907C22—24no—
908C22—22no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—22no—
917C22—416no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—41no—
930C22—42no—
931C22—41no—
932C22C24×C4×C1111yescharacteristic
933C22C2×C11×H(5,𝔽2)12yes—
934C22C2×C11×H(5,𝔽2)11yescharacteristic
935C22C11×#58511yescharacteristic
936C22C11×#58512yes—
937C4—24no—
938C4—24no—
939C4—24no—
940C4—22no—
941C4—24no—
942C4—22no—
943C4—24no—
944C4—41no—
945C4—42no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—42no—
950C4—41no—
951C4—42no—
952C2—44no—
953C2—42no—
954C2—42no—
955C2—44no—
956C2C4×C11×H(5,𝔽2)12yes—
957C2C4×C11×H(5,𝔽2)11yescharacteristic
958C2C11×#353211yescharacteristic
959C2C11×#353912yes—
960C2C11×#354011yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#560C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2375C2semidirect
3. C11×#2375C2semidirect
4. C11×#2374C2semidirect
5. C11×#2373C2semidirect
6. C11×#2366C2semidirect
7. C11×#2364C2semidirect
8. C11×#2363C2semidirect
9. C11×#2361C2semidirect
10. C11×#2359C2semidirect
11. C11×#2335C2semidirect
12. C11×#2334C2semidirect
13. C11×#2333C2semidirect
14. C11×#2328C2semidirect
15. C11×#2325C2semidirect
16. C11×#2324C2semidirect
17. C11×#2322C2semidirect
18. C4×C11×#120C2semidirect
19. C4×C11×#120C2semidirect
21. C11×#560C4semidirect
36. C2×C4×D4×C11C22semidirect
37. C2×C4×D4×C11C22semidirect
38. C2×C11×#117C22semidirect
39. C22×C11×C4⋊C4C22semidirect
45. C11×#390C22semidirect
46. C11×#390C22semidirect
47. C11×#389C22semidirect
48. C11×#389C22semidirect
49. C11×#389C22semidirect
59. C11×#388C22semidirect
60. C11×#388C22semidirect
61. C11×#388C22semidirect
62. C11×#387C22semidirect
63. C11×#387C22semidirect
64. C11×#387C22semidirect
65. C11×#387C22semidirect
66. C11×#387C22semidirect
67. C11×#387C22semidirect
78. C11×#386C22semidirect
79. C11×#386C22semidirect
80. C11×#386C22semidirect
86. C11×#385C22semidirect
87. C11×#385C22semidirect
88. C11×#382C22semidirect
89. C11×#381C22semidirect
90. C11×#380C22semidirect
93. C4×C11×C4⋊C4C22semidirect
94. C4×C11×C4⋊C4C22semidirect
95. C4×C11×C4⋊C4C22semidirect
96. 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
107. C2×C11×#95C22semidirect
128. C11×#127C2×C4semidirect
129. C11×#126C2×C4semidirect
130. C11×#123C2×C4semidirect
131. C11×#123C2×C4semidirect
132. C11×#121C2×C4semidirect
133. C11×#121C2×C4semidirect
134. C11×#121C2×C4semidirect
135. C11×#120C2×C4semidirect
136. C11×#120C2×C4semidirect
215. #34511C11direct (N × H)
244. C2×D4×C11C22×C4semidirect
245. C2×D4×C11C22×C4semidirect
271. C22×C4×C11C22×C4semidirect
272. C22×C4×C11C22×C4semidirect
298. C11×C4⋊C4C22×C4semidirect
299. C11×C4⋊C4C22×C4semidirect
300. C11×C4⋊C4C22×C4semidirect
326. C11×C22⋊C4C22×C4semidirect
327. C11×C22⋊C4C22×C4semidirect
338. C42×C11C22×C4semidirect
340. #2375C2×C11semidirect
341. #2375C2×C11semidirect
342. #2374C2×C11semidirect
343. #2373C2×C11semidirect
344. #2366C2×C11semidirect
345. #2364C2×C11semidirect
346. #2363C2×C11semidirect
347. #2361C2×C11semidirect
348. #2359C2×C11semidirect
349. #2335C2×C11semidirect
350. #2334C2×C11semidirect
351. #2333C2×C11semidirect
352. #2328C2×C11semidirect
353. #2325C2×C11semidirect
354. #2324C2×C11semidirect
355. #2322C2×C11semidirect
356. C4×#120C2×C11semidirect
357. C4×#120C2×C11semidirect
447. #560C4×C11semidirect
462. C2×C4×D4C22×C11semidirect
463. C2×C4×D4C22×C11semidirect
464. C2×#117C22×C11semidirect
465. C22×C4⋊C4C22×C11semidirect
471. #390C22×C11semidirect
472. #390C22×C11semidirect
473. #389C22×C11semidirect
474. #389C22×C11semidirect
475. #389C22×C11semidirect
485. #388C22×C11semidirect
486. #388C22×C11semidirect
487. #388C22×C11semidirect
488. #387C22×C11semidirect
489. #387C22×C11semidirect
490. #387C22×C11semidirect
491. #387C22×C11semidirect
492. #387C22×C11semidirect
493. #387C22×C11semidirect
504. #386C22×C11semidirect
505. #386C22×C11semidirect
506. #386C22×C11semidirect
512. #385C22×C11semidirect
513. #385C22×C11semidirect
514. #382C22×C11semidirect
515. #381C22×C11semidirect
516. #380C22×C11semidirect
519. C4×C4⋊C4C22×C11semidirect
520. C4×C4⋊C4C22×C11semidirect
521. C4×C4⋊C4C22×C11semidirect
522. C4×C4⋊C4C22×C11semidirect
528. C4×C22⋊C4C22×C11semidirect
529. C4×C22⋊C4C22×C11semidirect
530. C4×C22⋊C4C22×C11semidirect
531. C4×C22⋊C4C22×C11semidirect
532. #376C22×C11semidirect
533. C2×#95C22×C11semidirect
599. #127C2×C4×C11semidirect
600. #126C2×C4×C11semidirect
601. #123C2×C4×C11semidirect
602. #123C2×C4×C11semidirect
603. #121C2×C4×C11semidirect
604. #121C2×C4×C11semidirect
605. #121C2×C4×C11semidirect
606. #120C2×C4×C11semidirect
607. #120C2×C4×C11semidirect
723. C2×D4C22×C4×C11semidirect
724. C2×D4C22×C4×C11semidirect
750. C22×C4C22×C4×C11semidirect
751. C22×C4C22×C4×C11semidirect
777. C4⋊C4C22×C4×C11semidirect
778. C4⋊C4C22×C4×C11semidirect
779. C4⋊C4C22×C4×C11semidirect
805. C22⋊C4C22×C4×C11semidirect
806. C22⋊C4C22×C4×C11semidirect
817. C42C22×C4×C11semidirect
818. C11#34511direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5602
C11×#23752
C11×#23742
C11×#23732
C11×#23662
C11×#23642
C11×#23632
C11×#23612
C11×#23592
C11×#23352
C11×#23342
C11×#23332
C11×#23282
C11×#23252
C11×#23242
C11×#23222
C4×C11×#1202
#3451111