Finite Group Databasebeta

← C11×#34277 #14611470

Subgroups — C11×#34277 #14611470

Order 2816.

2634 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#538C211yesmaximal, characteristic
2C11×#2374C212yesmaximal, complemented
3C11×#2373C212yesmaximal, complemented
4C11×#2373C212yesmaximal, complemented
5C11×#2372C212yesmaximal, complemented
6C11×#2367C212yesmaximal, complemented
7C11×#2364C212yesmaximal, complemented
8C11×#2363C212yesmaximal, complemented
9C11×#2359C212yesmaximal, complemented
10C11×#2329C211yesmaximal, characteristic, complemented
11C11×#2325C211yesmaximal, characteristic, complemented
12C11×#2321C212yesmaximal, complemented
13C11×#2312C211yesmaximal, characteristic, complemented
14C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
15C4×C11×#121C211yesmaximal, characteristic, complemented
16C4×C11×#120C212yesmaximal, complemented
17C11×#2290C212yesmaximal, complemented
18C11×#2275C212yesmaximal, complemented
19C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
20C24×C4×C11C2211yescharacteristic
21C11×#538C4116yescomplemented
22C2×C11×#126C2212yes—
23C2×C11×#124C2212yes—
24C2×C11×#123C2212yes—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2212yes—
28C2×C11×#120C2212yes—
29C2×C4×Q8×C11C2211yescharacteristic, complemented
30C2×C4×D4×C11C2212yes—
31C2×C4×D4×C11C2212yes—
32C2×C4×D4×C11C2212yes—
33C2×C4×D4×C11C2212yes—
34C2×C4×D4×C11C2212yes—
35C2×C4×D4×C11C2211yescharacteristic, complemented
36C2×C11×#117C2212yescomplemented
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C22×C42×C11C2211yescharacteristic
40C22×C42×C11C2211yescharacteristic
41C11×#391C2211yescharacteristic, complemented
42C11×#391C2212yescomplemented
43C11×#390C2212yes—
44C11×#390C2212yes—
45C11×#390C2211yescharacteristic, complemented
46C11×#389C2211yescharacteristic, complemented
47C11×#389C2211yescharacteristic, complemented
48C11×#389C2212yescomplemented
49C11×#388C2212yes—
50C11×#388C2212yes—
51C11×#388C2212yes—
52C11×#388C2212yes—
53C11×#388C2212yes—
54C11×#388C2212yes—
55C11×#388C2212yes—
56C11×#388C2212yes—
57C11×#388C2212yescomplemented
58C11×#388C2212yescomplemented
59C11×#388C2212yescomplemented
60C11×#388C2212yescomplemented
61C11×#387C2212yescomplemented
62C11×#387C2212yescomplemented
63C11×#387C2212yescomplemented
64C11×#387C2212yescomplemented
65C11×#387C2212yescomplemented
66C11×#387C2212yescomplemented
67C11×#386C2212yes—
68C11×#386C2212yes—
69C11×#386C2212yes—
70C11×#386C2212yes—
71C11×#386C2212yes—
72C11×#386C2212yes—
73C11×#386C2212yescomplemented
74C11×#385C2212yes—
75C11×#385C2212yes—
76C11×#385C2212yes—
77C11×#385C2212yes—
78C11×#385C2212yescomplemented
79C11×#380C2211yescharacteristic
80C11×#380C2211yescharacteristic
81C11×#379C2212yes—
82C4×C11×C4⋊C4C2212yescomplemented
83C4×C11×C4⋊C4C2212yescomplemented
84C4×C11×C4⋊C4C2212yescomplemented
85C4×C11×C4⋊C4C2212yescomplemented
86C4×C11×C4⋊C4C2211yescharacteristic, complemented
87C4×C11×C4⋊C4C2212yescomplemented
88C4×C11×C4⋊C4C2211yescharacteristic, complemented
89C4×C11×C22⋊C4C2212yes—
90C4×C11×C22⋊C4C2212yes—
91C4×C11×C22⋊C4C2212yes—
92C4×C11×C22⋊C4C2212yes—
93C4×C11×C22⋊C4C2212yes—
94C4×C11×C22⋊C4C2212yes—
95C4×C11×C22⋊C4C2212yes—
96C4×C11×C22⋊C4C2212yes—
97C4×C11×C22⋊C4C2212yes—
98C4×C11×C22⋊C4C2212yescomplemented
99C4×C11×C22⋊C4C2212yescomplemented
100C4×C11×C22⋊C4C2212yescomplemented
101C4×C11×C22⋊C4C2212yescomplemented
102C4×C11×C22⋊C4C2212yescomplemented
103C11×#376C2212yescomplemented
104C11×#376C2212yescomplemented
105C2×C11×#95C2211yescharacteristic
106C2×C11×#95C2211yescharacteristic
107C2×C11×#95C2212yescomplemented
108C25×C11C2311yescharacteristic
109C22×Q8×C11C2311yescharacteristic
110C22×D4×C11C2312yes—
111C22×D4×C11C2312yes—
112C22×D4×C11C2312yes—
113C22×D4×C11C2311yescharacteristic
114C23×C4×C11—24no—
115C23×C4×C11—42no—
116C23×C4×C11—42no—
117C23×C4×C11C2311yescharacteristic
118C23×C4×C11C2312yes—
119C23×C4×C11C2312yes—
120C23×C4×C11C2311yescharacteristic
121C23×C4×C11C2312yes—
122C23×C4×C11C2312yes—
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2312yes—
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C11×#126C2×C4116yescomplemented
129C11×#124C2×C4116yescomplemented
130C11×#123C2×C4116yescomplemented
131C11×C22⋊Q8C2×C418yescomplemented
132C11×#121C2×C4116yescomplemented
133C11×#121C2×C418yescomplemented
134C11×#120C2×C4116yescomplemented
135C4×Q8×C11—42no—
136C4×D4×C11—28no—
137C4×D4×C11—28no—
138C4×D4×C11—42no—
139C4×D4×C11—44no—
140C4×D4×C11—44no—
141C4×D4×C11C2×C4116yescomplemented
142C11×#117—44no—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C4⋊C4C2311yescharacteristic
151C2×C11×C4⋊C4C2312yes—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—24no—
158C2×C11×C22⋊C4C2×C418yescomplemented
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⋊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⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179C2×C11×C22⋊C4C2312yes—
180C2×C42×C11—42no—
181C2×C42×C11—42no—
182C2×C42×C11C2312yes—
183C2×C42×C11C2311yescharacteristic
184C2×C42×C11C2311yescharacteristic
185C2×C42×C11C2312yes—
186C2×C42×C11C2312yes—
187C2×C42×C11C2311yescharacteristic
188C2×C42×C11C2312yes—
189C2×C42×C11C2311yescharacteristic
190C2×C42×C11C2312yes—
191C2×C42×C11C2312yes—
192C2×C42×C11C2312yes—
193C2×C42×C11C2312yes—
194C2×C42×C11C2312yes—
195C2×C42×C11C2312yes—
196C2×C42×C11C2312yes—
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—
215C11×#95C2312yes—
216C11×#95C2312yes—
217#34277C1111yesmaximal, characteristic, direct product factor, Sylow
218C24×C11—22no—
219C24×C11—22no—
220C24×C11—41no—
221C24×C11—41no—
222C24×C11—41no—
223C24×C11—41no—
224C24×C11C22×C414yes—
225C24×C11C2412yes—
226C24×C11C2412yes—
227C24×C11C2411yescharacteristic
228C2×Q8×C11—41no—
229C2×Q8×C11—41no—
230C2×Q8×C11C22×C414yescomplemented
231C2×D4×C11—24no—
232C2×D4×C11—24no—
233C2×D4×C11—41no—
234C2×D4×C11—42no—
235C2×D4×C11—42no—
236C2×D4×C11—42no—
237C2×D4×C11—41no—
238C2×D4×C11—42no—
239C2×D4×C11C22×C418yes—
240C2×D4×C11C22×C418yes—
241C2×D4×C11C22×C418yes—
242C2×D4×C11C22×C414yescomplemented
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—24no—
248C22×C4×C11—24no—
249C22×C4×C11—24no—
250C22×C4×C11—24no—
251C22×C4×C11—24no—
252C22×C4×C11—24no—
253C22×C4×C11—41no—
254C22×C4×C11—41no—
255C22×C4×C11—41no—
256C22×C4×C11—41no—
257C22×C4×C11—42no—
258C22×C4×C11—42no—
259C22×C4×C11—42no—
260C22×C4×C11—41no—
261C22×C4×C11—41no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11—42no—
265C22×C4×C11—41no—
266C22×C4×C11—41no—
267C22×C4×C11—42no—
268C22×C4×C11—42no—
269C22×C4×C11—42no—
270C22×C4×C11—42no—
271C22×C4×C11—416no—
272C22×C4×C11C22×C414yes—
273C22×C4×C11C22×C414yes—
274C22×C4×C11C22×C418yescomplemented
275C22×C4×C11#4114yes—
276C22×C4×C11#4114yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2412yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C11×C4⋊C4—24no—
294C11×C4⋊C4—24no—
295C11×C4⋊C4—24no—
296C11×C4⋊C4—24no—
297C11×C4⋊C4—41no—
298C11×C4⋊C4—41no—
299C11×C4⋊C4—42no—
300C11×C4⋊C4—42no—
301C11×C4⋊C4—41no—
302C11×C4⋊C4—41no—
303C11×C4⋊C4C22×C418yescomplemented
304C11×C4⋊C4C22×C418yescomplemented
305C11×C4⋊C4C22×C414yescomplemented
306C11×C4⋊C4C22×C414yescomplemented
307C11×C22⋊C4—24no—
308C11×C22⋊C4—24no—
309C11×C22⋊C4—24no—
310C11×C22⋊C4—24no—
311C11×C22⋊C4—24no—
312C11×C22⋊C4—24no—
313C11×C22⋊C4—24no—
314C11×C22⋊C4—24no—
315C11×C22⋊C4—42no—
316C11×C22⋊C4—42no—
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×C418yes—
325C11×C22⋊C4C22×C418yes—
326C11×C22⋊C4C22×C418yescomplemented
327C11×C22⋊C4C22×C418yescomplemented
328C42×C11—24no—
329C42×C11—24no—
330C42×C11—24no—
331C42×C11—22no—
332C42×C11—22no—
333C42×C11—41no—
334C42×C11—42no—
335C42×C11—41no—
336C42×C11—42no—
337C42×C11—42no—
338C42×C11—42no—
339C42×C11—42no—
340C42×C11—42no—
341C42×C11—42no—
342C42×C11C22×C418yescomplemented
343C2×#538C2×C1111yescharacteristic
344#2374C2×C1112yescomplemented
345#2373C2×C1112yescomplemented
346#2373C2×C1112yescomplemented
347#2372C2×C1112yescomplemented
348#2367C2×C1112yescomplemented
349#2364C2×C1112yescomplemented
350#2363C2×C1112yescomplemented
351#2359C2×C1112yescomplemented
352#2329C2×C1111yescharacteristic, complemented
353#2325C2×C1111yescharacteristic, complemented
354#2321C2×C1112yescomplemented
355#2312C2×C1111yescharacteristic, complemented
356C4×C22⋊Q8C2×C1111yescharacteristic, complemented
357C4×#121C2×C1111yescharacteristic, complemented
358C4×#120C2×C1112yescomplemented
359#2290C2×C1112yescomplemented
360#2275C2×C1112yescomplemented
361C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
362C23×C11—21no—
363C23×C11—21no—
364C23×C11—21no—
365C23×C11—21no—
366C23×C11—28no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11—44no—
382C23×C11—44no—
383C23×C11—44no—
384C23×C11—44no—
385C23×C11C23×C414yes—
386C23×C11C23×C414yes—
387C23×C11C23×C412yes—
388C23×C11C2×#4112yes—
389C23×C11C2×#4112yes—
390C23×C11C2511yescharacteristic
391Q8×C11—44no—
392D4×C11—216no—
393D4×C11—48no—
394D4×C11—48no—
395D4×C11—44no—
396C2×C4×C11—28no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—22no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—22no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—21no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—22no—
418C2×C4×C11—21no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—44no—
435C2×C4×C11—44no—
436C2×C4×C11—44no—
437C2×C4×C11—48no—
438C2×C4×C11—44no—
439C2×C4×C11—48no—
440C2×C4×C11—48no—
441C2×C4×C11—44no—
442C2×C4×C11—84no—
443C2×C4×C11—84no—
444C2×C4×C11C23×C414yes—
445C2×C4×C11C23×C414yes—
446C2×C4×C11C23×C414yes—
447C2×C4×C11C23×C412yes—
448C2×C4×C11C23×C412yes—
449C2×C4×C11C23×C414yes—
450C2×C4×C11C2×#4112yes—
451C2×C4×C11C2×#4114yes—
452C2×C4×C11C2×#4112yes—
453C2×C4×C11H(5,𝔽2)12yes—
454C2×C4×C11H(5,𝔽2)12yes—
455C24×C4C22×C1111yescharacteristic
456#538C4×C11116yescomplemented
457C2×#126C22×C1112yes—
458C2×#124C22×C1112yes—
459C2×#123C22×C1112yes—
460C2×C22⋊Q8C22×C1111yescharacteristic
461C2×#121C22×C1111yescharacteristic
462C2×#121C22×C1112yes—
463C2×#120C22×C1112yes—
464C2×C4×Q8C22×C1111yescharacteristic, complemented
465C2×C4×D4C22×C1112yes—
466C2×C4×D4C22×C1112yes—
467C2×C4×D4C22×C1112yes—
468C2×C4×D4C22×C1112yes—
469C2×C4×D4C22×C1112yes—
470C2×C4×D4C22×C1111yescharacteristic, complemented
471C2×#117C22×C1112yescomplemented
472C22×C22⋊C4C22×C1111yescharacteristic
473C22×C22⋊C4C22×C1111yescharacteristic
474C22×C42C22×C1111yescharacteristic
475C22×C42C22×C1111yescharacteristic
476#391C22×C1112yescomplemented
477#391C22×C1111yescharacteristic, complemented
478#390C22×C1112yes—
479#390C22×C1112yes—
480#390C22×C1111yescharacteristic, complemented
481#389C22×C1112yescomplemented
482#389C22×C1111yescharacteristic, complemented
483#389C22×C1111yescharacteristic, complemented
484#388C22×C1112yes—
485#388C22×C1112yes—
486#388C22×C1112yes—
487#388C22×C1112yes—
488#388C22×C1112yes—
489#388C22×C1112yes—
490#388C22×C1112yes—
491#388C22×C1112yes—
492#388C22×C1112yescomplemented
493#388C22×C1112yescomplemented
494#388C22×C1112yescomplemented
495#388C22×C1112yescomplemented
496#387C22×C1112yescomplemented
497#387C22×C1112yescomplemented
498#387C22×C1112yescomplemented
499#387C22×C1112yescomplemented
500#387C22×C1112yescomplemented
501#387C22×C1112yescomplemented
502#386C22×C1112yes—
503#386C22×C1112yes—
504#386C22×C1112yes—
505#386C22×C1112yes—
506#386C22×C1112yes—
507#386C22×C1112yes—
508#386C22×C1112yescomplemented
509#385C22×C1112yes—
510#385C22×C1112yes—
511#385C22×C1112yes—
512#385C22×C1112yes—
513#385C22×C1112yescomplemented
514#380C22×C1111yescharacteristic
515#380C22×C1111yescharacteristic
516#379C22×C1112yes—
517C4×C4⋊C4C22×C1112yescomplemented
518C4×C4⋊C4C22×C1112yescomplemented
519C4×C4⋊C4C22×C1112yescomplemented
520C4×C4⋊C4C22×C1112yescomplemented
521C4×C4⋊C4C22×C1111yescharacteristic, complemented
522C4×C4⋊C4C22×C1112yescomplemented
523C4×C4⋊C4C22×C1111yescharacteristic, complemented
524C4×C22⋊C4C22×C1112yes—
525C4×C22⋊C4C22×C1112yes—
526C4×C22⋊C4C22×C1112yes—
527C4×C22⋊C4C22×C1112yes—
528C4×C22⋊C4C22×C1112yes—
529C4×C22⋊C4C22×C1112yes—
530C4×C22⋊C4C22×C1112yes—
531C4×C22⋊C4C22×C1112yes—
532C4×C22⋊C4C22×C1112yes—
533C4×C22⋊C4C22×C1112yescomplemented
534C4×C22⋊C4C22×C1112yescomplemented
535C4×C22⋊C4C22×C1112yescomplemented
536C4×C22⋊C4C22×C1112yescomplemented
537C4×C22⋊C4C22×C1112yescomplemented
538#376C22×C1112yescomplemented
539#376C22×C1112yescomplemented
540C2×#95C22×C1111yescharacteristic
541C2×#95C22×C1111yescharacteristic
542C2×#95C22×C1112yescomplemented
543C22×C11—22no—
544C22×C11—22no—
545C22×C11—22no—
546C22×C11—22no—
547C22×C11—22no—
548C22×C11—22no—
549C22×C11—24no—
550C22×C11—24no—
551C22×C11—24no—
552C22×C11—24no—
553C22×C11—24no—
554C22×C11—24no—
555C22×C11—416no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11C4×#4114yes—
565C22×C11C24×C411yescharacteristic
566C22×C11C22×#4111yescharacteristic
567C22×C11C22×#4111yescharacteristic
568C22×C11C2×H(5,𝔽2)11yescharacteristic
569C22×C11C2×H(5,𝔽2)11yescharacteristic
570C22×C11#58511yescharacteristic
571C22×C11#58511yescharacteristic
572C4×C11—24no—
573C4×C11—24no—
574C4×C11—22no—
575C4×C11—24no—
576C4×C11—22no—
577C4×C11—24no—
578C4×C11—22no—
579C4×C11—22no—
580C4×C11—24no—
581C4×C11—22no—
582C4×C11—22no—
583C4×C11—42no—
584C4×C11—42no—
585C4×C11—42no—
586C4×C11—42no—
587C4×C11—42no—
588C25C23×C1111yescharacteristic
589C22×Q8C23×C1111yescharacteristic
590C22×D4C23×C1112yes—
591C22×D4C23×C1112yes—
592C22×D4C23×C1112yes—
593C22×D4C23×C1111yescharacteristic
594C23×C4—24no—
595C23×C4—42no—
596C23×C4—42no—
597C23×C4C23×C1111yescharacteristic
598C23×C4C23×C1112yes—
599C23×C4C23×C1112yes—
600C23×C4C23×C1111yescharacteristic
601C23×C4C23×C1112yes—
602C23×C4C23×C1112yes—
603C23×C4C23×C1111yescharacteristic
604C23×C4C23×C1111yescharacteristic
605C23×C4C23×C1112yes—
606C23×C4C23×C1111yescharacteristic
607C23×C4C23×C1111yescharacteristic
608#126C2×C4×C11116yescomplemented
609#124C2×C4×C11116yescomplemented
610#123C2×C4×C11116yescomplemented
611C22⋊Q8C2×C4×C1118yescomplemented
612#121C2×C4×C11116yescomplemented
613#121C2×C4×C1118yescomplemented
614#120C2×C4×C11116yescomplemented
615C4×Q8—42no—
616C4×D4—28no—
617C4×D4—28no—
618C4×D4—42no—
619C4×D4—44no—
620C4×D4—44no—
621C4×D4C2×C4×C11116yescomplemented
622#117—44no—
623C2×C4⋊C4C23×C1112yes—
624C2×C4⋊C4C23×C1112yes—
625C2×C4⋊C4C23×C1112yes—
626C2×C4⋊C4C23×C1112yes—
627C2×C4⋊C4C23×C1112yes—
628C2×C4⋊C4C23×C1111yescharacteristic
629C2×C4⋊C4C23×C1111yescharacteristic
630C2×C4⋊C4C23×C1111yescharacteristic
631C2×C4⋊C4C23×C1111yescharacteristic
632C2×C4⋊C4C23×C1112yes—
633C2×C4⋊C4C23×C1112yes—
634C2×C4⋊C4C23×C1112yes—
635C2×C4⋊C4C23×C1111yescharacteristic
636C2×C4⋊C4C23×C1111yescharacteristic
637C2×C22⋊C4—24no—
638C2×C22⋊C4C2×C4×C1118yescomplemented
639C2×C22⋊C4C23×C1112yes—
640C2×C22⋊C4C23×C1112yes—
641C2×C22⋊C4C23×C1112yes—
642C2×C22⋊C4C23×C1112yes—
643C2×C22⋊C4C23×C1112yes—
644C2×C22⋊C4C23×C1112yes—
645C2×C22⋊C4C23×C1112yes—
646C2×C22⋊C4C23×C1112yes—
647C2×C22⋊C4C23×C1112yes—
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×C1112yes—
655C2×C22⋊C4C23×C1112yes—
656C2×C22⋊C4C23×C1112yes—
657C2×C22⋊C4C23×C1112yes—
658C2×C22⋊C4C23×C1112yes—
659C2×C22⋊C4C23×C1112yes—
660C2×C42—42no—
661C2×C42—42no—
662C2×C42C23×C1112yes—
663C2×C42C23×C1112yes—
664C2×C42C23×C1112yes—
665C2×C42C23×C1111yescharacteristic
666C2×C42C23×C1111yescharacteristic
667C2×C42C23×C1112yes—
668C2×C42C23×C1112yes—
669C2×C42C23×C1112yes—
670C2×C42C23×C1112yes—
671C2×C42C23×C1112yes—
672C2×C42C23×C1111yescharacteristic
673C2×C42C23×C1112yes—
674C2×C42C23×C1111yescharacteristic
675C2×C42C23×C1112yes—
676C2×C42C23×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—
686#95C23×C1112yes—
687#95C23×C1112yes—
688#95C23×C1112yes—
689#95C23×C1112yes—
690#95C23×C1112yes—
691#95C23×C1112yes—
692#95C23×C1112yes—
693#95C23×C1112yes—
694#95C23×C1112yes—
695#95C23×C1112yes—
696#95C23×C1112yes—
697C2×C11—24no—
698C2×C11—44no—
699C2×C11—44no—
700C2×C11C2×C4×#4111yescharacteristic
701C2×C11C4×H(5,𝔽2)11yescharacteristic
702C2×C11C4×H(5,𝔽2)11yescharacteristic
703C2×C11#349011yescharacteristic
704C2×C11#349311yescharacteristic
705C2×C11#350511yescharacteristic
706C2×C11#350611yescharacteristic
707C24—22no—
708C24—22no—
709C24—41no—
710C24—41no—
711C24—41no—
712C24—41no—
713C24C22×C4×C1114yes—
714C24C24×C1112yes—
715C24C24×C1112yes—
716C24C24×C1111yescharacteristic
717C2×Q8—41no—
718C2×Q8—41no—
719C2×Q8C22×C4×C1114yescomplemented
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—41no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—41no—
727C2×D4—42no—
728C2×D4C22×C4×C1118yes—
729C2×D4C22×C4×C1118yes—
730C2×D4C22×C4×C1118yes—
731C2×D4C22×C4×C1114yescomplemented
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—41no—
752C22×C4—41no—
753C22×C4—42no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—416no—
761C22×C4C22×C4×C1114yes—
762C22×C4C22×C4×C1114yes—
763C22×C4C22×C4×C1118yescomplemented
764C22×C4C11×#4114yes—
765C22×C4C11×#4114yes—
766C22×C4C24×C1112yes—
767C22×C4C24×C1112yes—
768C22×C4C24×C1112yes—
769C22×C4C24×C1112yes—
770C22×C4C24×C1112yes—
771C22×C4C24×C1112yes—
772C22×C4C24×C1112yes—
773C22×C4C24×C1112yes—
774C22×C4C24×C1111yescharacteristic
775C22×C4C24×C1111yescharacteristic
776C22×C4C24×C1112yes—
777C22×C4C24×C1111yescharacteristic
778C22×C4C24×C1112yes—
779C22×C4C24×C1111yescharacteristic
780C22×C4C24×C1111yescharacteristic
781C22×C4C24×C1111yescharacteristic
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—42no—
787C4⋊C4—41no—
788C4⋊C4—41no—
789C4⋊C4—41no—
790C4⋊C4—41no—
791C4⋊C4—42no—
792C4⋊C4C22×C4×C1118yescomplemented
793C4⋊C4C22×C4×C1118yescomplemented
794C4⋊C4C22×C4×C1114yescomplemented
795C4⋊C4C22×C4×C1114yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—24no—
802C22⋊C4—24no—
803C22⋊C4—24no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4—42no—
808C22⋊C4—42no—
809C22⋊C4—42no—
810C22⋊C4C22×C4×C1118yes—
811C22⋊C4C22×C4×C1118yes—
812C22⋊C4C22×C4×C1118yes—
813C22⋊C4C22×C4×C1118yes—
814C22⋊C4C22×C4×C1118yes—
815C22⋊C4C22×C4×C1118yescomplemented
816C22⋊C4C22×C4×C1118yescomplemented
817C42—24no—
818C42—24no—
819C42—24no—
820C42—22no—
821C42—22no—
822C42—41no—
823C42—42no—
824C42—41no—
825C42—42no—
826C42—42no—
827C42—42no—
828C42—42no—
829C42—42no—
830C42—42no—
831C42C22×C4×C1118yescomplemented
832C11#3427711yescharacteristic, direct product factor, Sylow
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—28no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—44no—
855C23—44no—
856C23C23×C4×C1114yes—
857C23C23×C4×C1114yes—
858C23C23×C4×C1112yes—
859C23C2×C11×#4112yes—
860C23C2×C11×#4112yes—
861C23C25×C1111yescharacteristic
862Q8—44no—
863D4—216no—
864D4—48no—
865D4—48no—
866D4—44no—
867C2×C4—28no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—21no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—48no—
909C2×C4—44no—
910C2×C4—48no—
911C2×C4—48no—
912C2×C4—44no—
913C2×C4—84no—
914C2×C4—84no—
915C2×C4C23×C4×C1114yes—
916C2×C4C23×C4×C1114yes—
917C2×C4C23×C4×C1114yes—
918C2×C4C23×C4×C1112yes—
919C2×C4C23×C4×C1112yes—
920C2×C4C23×C4×C1114yes—
921C2×C4C2×C11×#4112yes—
922C2×C4C2×C11×#4114yes—
923C2×C4C2×C11×#4112yes—
924C2×C4C11×H(5,𝔽2)12yes—
925C2×C4C11×H(5,𝔽2)12yes—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—24no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—416no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22C4×C11×#4114yes—
948C22C24×C4×C1111yescharacteristic
949C22C22×C11×#4111yescharacteristic
950C22C22×C11×#4111yescharacteristic
951C22C2×C11×H(5,𝔽2)11yescharacteristic
952C22C2×C11×H(5,𝔽2)11yescharacteristic
953C22C11×#58511yescharacteristic
954C22C11×#58511yescharacteristic
955C4—24no—
956C4—24no—
957C4—22no—
958C4—24no—
959C4—22no—
960C4—24no—
961C4—22no—
962C4—22no—
963C4—24no—
964C4—22no—
965C4—22no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C2—24no—
972C2—44no—
973C2—44no—
974C2C2×C4×C11×#4111yescharacteristic
975C2C4×C11×H(5,𝔽2)11yescharacteristic
976C2C4×C11×H(5,𝔽2)11yescharacteristic
977C2C11×#349011yescharacteristic
978C2C11×#349311yescharacteristic
979C2C11×#350511yescharacteristic
980C2C11×#350611yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#538C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2374C2semidirect
3. C11×#2373C2semidirect
4. C11×#2373C2semidirect
5. C11×#2372C2semidirect
6. C11×#2367C2semidirect
7. C11×#2364C2semidirect
8. C11×#2363C2semidirect
9. C11×#2359C2semidirect
10. C11×#2329C2semidirect
11. C11×#2325C2semidirect
12. C11×#2321C2semidirect
13. C11×#2312C2semidirect
14. C4×C11×C22⋊Q8C2semidirect
15. C4×C11×#121C2semidirect
16. C4×C11×#120C2semidirect
17. C11×#2290C2semidirect
18. C11×#2275C2semidirect
19. C2×C4×C11×C22⋊C4C2semidirect
21. C11×#538C4semidirect
29. C2×C4×Q8×C11C22semidirect
35. C2×C4×D4×C11C22semidirect
36. C2×C11×#117C22semidirect
41. C11×#391C22semidirect
42. C11×#391C22semidirect
45. C11×#390C22semidirect
46. C11×#389C22semidirect
47. C11×#389C22semidirect
48. C11×#389C22semidirect
57. C11×#388C22semidirect
58. C11×#388C22semidirect
59. C11×#388C22semidirect
60. C11×#388C22semidirect
61. C11×#387C22semidirect
62. C11×#387C22semidirect
63. C11×#387C22semidirect
64. C11×#387C22semidirect
65. C11×#387C22semidirect
66. C11×#387C22semidirect
73. C11×#386C22semidirect
78. C11×#385C22semidirect
82. C4×C11×C4⋊C4C22semidirect
83. C4×C11×C4⋊C4C22semidirect
84. C4×C11×C4⋊C4C22semidirect
85. C4×C11×C4⋊C4C22semidirect
86. C4×C11×C4⋊C4C22semidirect
87. C4×C11×C4⋊C4C22semidirect
88. C4×C11×C4⋊C4C22semidirect
98. C4×C11×C22⋊C4C22semidirect
99. C4×C11×C22⋊C4C22semidirect
100. C4×C11×C22⋊C4C22semidirect
101. C4×C11×C22⋊C4C22semidirect
102. C4×C11×C22⋊C4C22semidirect
103. C11×#376C22semidirect
104. C11×#376C22semidirect
107. C2×C11×#95C22semidirect
128. C11×#126C2×C4semidirect
129. C11×#124C2×C4semidirect
130. C11×#123C2×C4semidirect
131. C11×C22⋊Q8C2×C4semidirect
132. C11×#121C2×C4semidirect
133. C11×#121C2×C4semidirect
134. C11×#120C2×C4semidirect
141. C4×D4×C11C2×C4semidirect
158. C2×C11×C22⋊C4C2×C4semidirect
217. #34277C11direct (N × H)
230. C2×Q8×C11C22×C4semidirect
242. C2×D4×C11C22×C4semidirect
274. C22×C4×C11C22×C4semidirect
303. C11×C4⋊C4C22×C4semidirect
304. C11×C4⋊C4C22×C4semidirect
305. C11×C4⋊C4C22×C4semidirect
306. C11×C4⋊C4C22×C4semidirect
326. C11×C22⋊C4C22×C4semidirect
327. C11×C22⋊C4C22×C4semidirect
342. C42×C11C22×C4semidirect
344. #2374C2×C11semidirect
345. #2373C2×C11semidirect
346. #2373C2×C11semidirect
347. #2372C2×C11semidirect
348. #2367C2×C11semidirect
349. #2364C2×C11semidirect
350. #2363C2×C11semidirect
351. #2359C2×C11semidirect
352. #2329C2×C11semidirect
353. #2325C2×C11semidirect
354. #2321C2×C11semidirect
355. #2312C2×C11semidirect
356. C4×C22⋊Q8C2×C11semidirect
357. C4×#121C2×C11semidirect
358. C4×#120C2×C11semidirect
359. #2290C2×C11semidirect
360. #2275C2×C11semidirect
361. C2×C4×C22⋊C4C2×C11semidirect
456. #538C4×C11semidirect
464. C2×C4×Q8C22×C11semidirect
470. C2×C4×D4C22×C11semidirect
471. C2×#117C22×C11semidirect
476. #391C22×C11semidirect
477. #391C22×C11semidirect
480. #390C22×C11semidirect
481. #389C22×C11semidirect
482. #389C22×C11semidirect
483. #389C22×C11semidirect
492. #388C22×C11semidirect
493. #388C22×C11semidirect
494. #388C22×C11semidirect
495. #388C22×C11semidirect
496. #387C22×C11semidirect
497. #387C22×C11semidirect
498. #387C22×C11semidirect
499. #387C22×C11semidirect
500. #387C22×C11semidirect
501. #387C22×C11semidirect
508. #386C22×C11semidirect
513. #385C22×C11semidirect
517. C4×C4⋊C4C22×C11semidirect
518. C4×C4⋊C4C22×C11semidirect
519. C4×C4⋊C4C22×C11semidirect
520. C4×C4⋊C4C22×C11semidirect
521. C4×C4⋊C4C22×C11semidirect
522. C4×C4⋊C4C22×C11semidirect
523. C4×C4⋊C4C22×C11semidirect
533. C4×C22⋊C4C22×C11semidirect
534. C4×C22⋊C4C22×C11semidirect
535. C4×C22⋊C4C22×C11semidirect
536. C4×C22⋊C4C22×C11semidirect
537. C4×C22⋊C4C22×C11semidirect
538. #376C22×C11semidirect
539. #376C22×C11semidirect
542. C2×#95C22×C11semidirect
608. #126C2×C4×C11semidirect
609. #124C2×C4×C11semidirect
610. #123C2×C4×C11semidirect
611. C22⋊Q8C2×C4×C11semidirect
612. #121C2×C4×C11semidirect
613. #121C2×C4×C11semidirect
614. #120C2×C4×C11semidirect
621. C4×D4C2×C4×C11semidirect
638. C2×C22⋊C4C2×C4×C11semidirect
719. C2×Q8C22×C4×C11semidirect
731. C2×D4C22×C4×C11semidirect
763. C22×C4C22×C4×C11semidirect
792. C4⋊C4C22×C4×C11semidirect
793. C4⋊C4C22×C4×C11semidirect
794. C4⋊C4C22×C4×C11semidirect
795. C4⋊C4C22×C4×C11semidirect
815. C22⋊C4C22×C4×C11semidirect
816. C22⋊C4C22×C4×C11semidirect
831. C42C22×C4×C11semidirect
832. C11#34277direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5382
C11×#23742
C11×#23732
C11×#23722
C11×#23672
C11×#23642
C11×#23632
C11×#23592
C11×#23292
C11×#23252
C11×#23212
C11×#23122
C4×C11×C22⋊Q82
C4×C11×#1212
C4×C11×#1202
C11×#22902
C11×#22752
C2×C4×C11×C22⋊C42
#3427711