Finite Group Databasebeta

← C11×#34319 #14611512

Subgroups — C11×#34319 #14611512

Order 2816.

2344 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C11×#2374C212yesmaximal, complemented
3C11×#2373C212yesmaximal, complemented
4C11×#2370C211yesmaximal, characteristic, complemented
5C11×#2363C211yesmaximal, characteristic, complemented
6C11×#2363C212yesmaximal, complemented
7C11×#2361C211yesmaximal, characteristic, complemented
8C11×#2357C212yesmaximal, complemented
9C11×#2357C211yesmaximal, characteristic, complemented
10C11×#2352C211yesmaximal, characteristic, complemented
11C11×#2346C211yesmaximal, characteristic, complemented
12C11×#2344C211yesmaximal, characteristic, complemented
13C11×#2334C212yesmaximal, complemented
14C11×#2333C212yesmaximal, complemented
15C11×#2324C211yesmaximal, characteristic, complemented
16C11×#2324C211yesmaximal, characteristic, complemented
17C4×C11×#125C211yesmaximal, characteristic, complemented
18C4×C11×#123C212yesmaximal, complemented
19C11×#2293C211yesmaximal, characteristic, complemented
20C11×#2290C212yesmaximal, complemented
21C11×#2274C211yesmaximal, characteristic, complemented
22C11×#2274C211yesmaximal, characteristic, complemented
23C42×D4×C11C211yesmaximal, 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×C11C2211yescharacteristic
33C2×C4×D4×C11C2212yes—
34C2×C4×D4×C11C2211yescharacteristic
35C2×C4×D4×C11C2212yes—
36C2×C4×D4×C11C2211yescharacteristic
37C2×C11×#117C2211yescharacteristic
38C2×C11×#117C2211yescharacteristic
39C2×C11×#117C2211yescharacteristic
40C2×C11×#117C2212yes—
41C2×C11×#117C2211yescharacteristic
42C22×C11×C4⋊C4C2211yescharacteristic
43C22×C11×C4⋊C4C2211yescharacteristic
44C22×C42×C11C2212yes—
45C11×#390C2211yescharacteristic
46C11×#390C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#390C2212yes—
50C11×#390C2212yes—
51C11×#390C2212yes—
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#389C2211yescharacteristic
55C11×#389C2211yescharacteristic
56C11×#389C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#389C2212yes—
59C11×#388C2211yescharacteristic
60C11×#388C2212yes—
61C11×#388C2211yescharacteristic
62C11×#388C2211yescharacteristic
63C11×#388C2211yescharacteristic
64C11×#388C2212yes—
65C11×#388C2212yes—
66C11×#388C2212yes—
67C11×#388C2212yes—
68C11×#388C2212yes—
69C11×#388C2212yes—
70C11×#388C2212yes—
71C11×#388C2212yes—
72C11×#387C2212yes—
73C11×#387C2212yes—
74C11×#387C2212yes—
75C11×#387C2212yes—
76C11×#387C2212yes—
77C11×#387C2212yes—
78C11×#387C2212yes—
79C11×#386C2212yes—
80C11×#386C2212yes—
81C11×#386C2212yes—
82C11×#386C2212yes—
83C11×#386C2212yes—
84C11×#385C2212yes—
85C11×#385C2212yes—
86C11×#385C2212yes—
87C11×#382C2211yescharacteristic
88C11×#382C2212yes—
89C11×#381C2212yes—
90C11×#381C2212yes—
91C11×#380C2211yescharacteristic
92C11×#380C2211yescharacteristic
93C4×C11×C4⋊C4C2211yescharacteristic
94C4×C11×C4⋊C4C2211yescharacteristic
95C4×C11×C4⋊C4C2211yescharacteristic
96C4×C11×C4⋊C4C2212yes—
97C4×C11×C4⋊C4C2212yes—
98C4×C11×C4⋊C4C2211yescharacteristic
99C4×C11×C4⋊C4C2211yescharacteristic
100C4×C11×C4⋊C4C2211yescharacteristic
101C4×C11×C4⋊C4C2211yescharacteristic
102C4×C11×C4⋊C4C2212yes—
103C4×C11×C4⋊C4C2211yescharacteristic
104C4×C11×C4⋊C4C2211yescharacteristic
105C4×C11×C4⋊C4C2212yes—
106C4×C11×C4⋊C4C2211yescharacteristic
107C4×C11×C4⋊C4C2212yes—
108C4×C11×C4⋊C4C2212yes—
109C4×C11×C4⋊C4C2212yes—
110C4×C11×C22⋊C4C2212yes—
111C4×C11×C22⋊C4C2212yes—
112C4×C11×C22⋊C4C2212yes—
113C4×C11×C22⋊C4C2212yes—
114C4×C11×C22⋊C4C2212yes—
115C4×C11×C22⋊C4C2212yes—
116C4×C11×C22⋊C4C2212yes—
117C4×C11×C22⋊C4C2212yes—
118C4×C11×C22⋊C4C2211yescharacteristic
119C4×C11×C22⋊C4C2211yescharacteristic
120C4×C11×C22⋊C4C2212yes—
121C4×C11×C22⋊C4C2212yes—
122C11×#376C2212yes—
123C43×C11C2211yescharacteristic
124C22×D4×C11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C22×D4×C11C2312yes—
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2312yes—
132C23×C4×C11C2312yes—
133C23×C4×C11C2312yes—
134C23×C4×C11C2312yes—
135C11×#126C2×C4116yescomplemented
136C11×#125C2×C418yescomplemented
137C11×#123C2×C4116yescomplemented
138C11×#121C2×C418yes—
139C11×#121C2×C4116yescomplemented
140C11×#121C2×C418yescomplemented
141C4×D4×C11—24no—
142C4×D4×C11—24no—
143C4×D4×C11—44no—
144C4×D4×C11C2×C4116yescomplemented
145C4×D4×C11C2×C418yescomplemented
146C4×D4×C11C2×C418yescomplemented
147C11×#117—24no—
148C11×#117—24no—
149C11×#117—24no—
150C11×#117—44no—
151C11×#117C2×C418yescomplemented
152C2×C11×C4⋊C4—24no—
153C2×C11×C4⋊C4C2×C418yescomplemented
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2312yes—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2312yes—
180C2×C11×C22⋊C4C2311yescharacteristic
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2311yescharacteristic
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2311yescharacteristic
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2311yescharacteristic
192C2×C11×C22⋊C4C2312yes—
193C2×C11×C22⋊C4C2312yes—
194C2×C11×C22⋊C4C2312yes—
195C2×C11×C22⋊C4C2311yescharacteristic
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2311yescharacteristic
198C2×C11×C22⋊C4C2312yes—
199C2×C42×C11—44no—
200C2×C42×C11C2311yescharacteristic
201C2×C42×C11C2312yes—
202C2×C42×C11C2311yescharacteristic
203C2×C42×C11C2312yes—
204C2×C42×C11C2311yescharacteristic
205C2×C42×C11C2311yescharacteristic
206C2×C42×C11C2312yes—
207C2×C42×C11C2312yes—
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2312yes—
212C2×C42×C11C2312yes—
213C2×C42×C11C2312yes—
214C2×C42×C11C2312yes—
215C2×C42×C11C2312yes—
216C2×C42×C11C2312yes—
217C2×C42×C11C2311yescharacteristic
218C2×C42×C11C2312yes—
219C2×C42×C11C2311yescharacteristic
220C11×#95C2311yescharacteristic
221C11×#95C2312yes—
222C11×#95C2312yes—
223C11×#95C2312yes—
224C11×#95C2312yes—
225C11×#95C2311yescharacteristic
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2311yescharacteristic
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2311yescharacteristic
238C11×#95C2311yescharacteristic
239C11×#95C2311yescharacteristic
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243#34319C1111yesmaximal, characteristic, direct product factor, Sylow
244C24×C11C2411yescharacteristic
245C24×C11C2411yescharacteristic
246C24×C11C2412yes—
247C2×D4×C11—22no—
248C2×D4×C11—22no—
249C2×D4×C11—42no—
250C2×D4×C11—42no—
251C2×D4×C11—41no—
252C2×D4×C11—41no—
253C2×D4×C11—42no—
254C2×D4×C11—42no—
255C2×D4×C11C22×C414yes—
256C2×D4×C11C22×C418yes—
257C2×D4×C11C22×C414yes—
258C2×D4×C11C22×C418yes—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—24no—
264C22×C4×C11—24no—
265C22×C4×C11—24no—
266C22×C4×C11—24no—
267C22×C4×C11—42no—
268C22×C4×C11—42no—
269C22×C4×C11—42no—
270C22×C4×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C22×C414yes—
278C22×C4×C11C22×C418yes—
279C22×C4×C11C22×C418yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2412yes—
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C11×C4⋊C4—24no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—22no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—22no—
307C11×C4⋊C4—22no—
308C11×C4⋊C4—24no—
309C11×C4⋊C4—41no—
310C11×C4⋊C4—41no—
311C11×C4⋊C4—42no—
312C11×C4⋊C4—42no—
313C11×C4⋊C4—42no—
314C11×C4⋊C4C22×C414yes—
315C11×C4⋊C4C22×C414yes—
316C11×C4⋊C4C22×C418yes—
317C11×C4⋊C4C22×C414yes—
318C11×C4⋊C4C22×C418yes—
319C11×C4⋊C4C22×C414yes—
320C11×C4⋊C4C22×C418yes—
321C11×C4⋊C4#4114yes—
322C11×C22⋊C4—24no—
323C11×C22⋊C4—22no—
324C11×C22⋊C4—22no—
325C11×C22⋊C4—22no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—24no—
328C11×C22⋊C4—24no—
329C11×C22⋊C4—22no—
330C11×C22⋊C4—22no—
331C11×C22⋊C4—41no—
332C11×C22⋊C4—42no—
333C11×C22⋊C4—41no—
334C11×C22⋊C4—42no—
335C11×C22⋊C4—42no—
336C11×C22⋊C4—42no—
337C11×C22⋊C4—42no—
338C11×C22⋊C4—42no—
339C11×C22⋊C4C22×C418yes—
340C11×C22⋊C4C22×C414yes—
341C11×C22⋊C4C22×C418yes—
342C11×C22⋊C4C22×C418yes—
343C11×C22⋊C4C22×C414yes—
344C11×C22⋊C4C22×C418yes—
345C42×C11—24no—
346C42×C11—22no—
347C42×C11—22no—
348C42×C11—22no—
349C42×C11—22no—
350C42×C11—24no—
351C42×C11—42no—
352C42×C11—42no—
353C42×C11—42no—
354C42×C11—41no—
355C42×C11—41no—
356C42×C11—42no—
357C42×C11—42no—
358C42×C11—41no—
359C42×C11—42no—
360C42×C11—42no—
361C42×C11—42no—
362C42×C11C22×C418yes—
363C42×C11C22×C414yes—
364C42×C11#4114yes—
365C2×#553C2×C1111yescharacteristic
366#2374C2×C1112yescomplemented
367#2373C2×C1112yescomplemented
368#2370C2×C1111yescharacteristic, complemented
369#2363C2×C1111yescharacteristic, complemented
370#2363C2×C1112yescomplemented
371#2361C2×C1111yescharacteristic, complemented
372#2357C2×C1111yescharacteristic, complemented
373#2357C2×C1112yescomplemented
374#2352C2×C1111yescharacteristic, complemented
375#2346C2×C1111yescharacteristic, complemented
376#2344C2×C1111yescharacteristic, complemented
377#2334C2×C1112yescomplemented
378#2333C2×C1112yescomplemented
379#2324C2×C1111yescharacteristic, complemented
380#2324C2×C1111yescharacteristic, complemented
381C4×#125C2×C1111yescharacteristic, complemented
382C4×#123C2×C1112yescomplemented
383#2293C2×C1111yescharacteristic, complemented
384#2290C2×C1112yescomplemented
385#2274C2×C1111yescharacteristic, complemented
386#2274C2×C1111yescharacteristic, complemented
387C42×D4C2×C1111yescharacteristic, complemented
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—21no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—21no—
394C23×C11—21no—
395C23×C11—21no—
396C23×C11—22no—
397C23×C11—21no—
398C23×C11—21no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—21no—
403C23×C11—21no—
404C23×C11—21no—
405C23×C11—21no—
406C23×C11C23×C412yes—
407C23×C11C23×C414yes—
408C23×C11C23×C412yes—
409C23×C11C2511yescharacteristic
410D4×C11—28no—
411D4×C11—48no—
412D4×C11—44no—
413D4×C11—48no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11—21no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—22no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—22no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—28no—
437C2×C4×C11—28no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—22no—
450C2×C4×C11—21no—
451C2×C4×C11—22no—
452C2×C4×C11—21no—
453C2×C4×C11—21no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—48no—
463C2×C4×C11—48no—
464C2×C4×C11—48no—
465C2×C4×C11—48no—
466C2×C4×C11—84no—
467C2×C4×C11C23×C412yes—
468C2×C4×C11C23×C414yes—
469C2×C4×C11C23×C412yes—
470C2×C4×C11C23×C414yes—
471C2×C4×C11C23×C412yes—
472C2×C4×C11C23×C412yes—
473C2×C4×C11C23×C414yes—
474C2×C4×C11C23×C412yes—
475C2×C4×C11C2×#4114yes—
476C2×C4×C11C2×#4112yes—
477C2×C4×C11C2×#4112yes—
478C2×C4×C11C2×#4112yes—
479C2×C4×C11C2×#4112yes—
480C2×C4×C11H(5,𝔽2)12yes—
481#553C4×C11116yescomplemented
482C2×#126C22×C1112yes—
483C2×#125C22×C1111yescharacteristic
484C2×#123C22×C1112yes—
485C2×#121C22×C1111yescharacteristic
486C2×#121C22×C1111yescharacteristic
487C2×#121C22×C1112yes—
488C2×C4×D4C22×C1111yescharacteristic
489C2×C4×D4C22×C1111yescharacteristic
490C2×C4×D4C22×C1112yes—
491C2×C4×D4C22×C1111yescharacteristic
492C2×C4×D4C22×C1111yescharacteristic
493C2×C4×D4C22×C1112yes—
494C2×#117C22×C1111yescharacteristic
495C2×#117C22×C1111yescharacteristic
496C2×#117C22×C1111yescharacteristic
497C2×#117C22×C1112yes—
498C2×#117C22×C1111yescharacteristic
499C22×C4⋊C4C22×C1111yescharacteristic
500C22×C4⋊C4C22×C1111yescharacteristic
501C22×C42C22×C1112yes—
502#390C22×C1111yescharacteristic
503#390C22×C1111yescharacteristic
504#390C22×C1112yes—
505#390C22×C1112yes—
506#390C22×C1111yescharacteristic
507#390C22×C1112yes—
508#390C22×C1111yescharacteristic
509#389C22×C1111yescharacteristic
510#389C22×C1111yescharacteristic
511#389C22×C1111yescharacteristic
512#389C22×C1111yescharacteristic
513#389C22×C1111yescharacteristic
514#389C22×C1112yes—
515#389C22×C1111yescharacteristic
516#388C22×C1112yes—
517#388C22×C1112yes—
518#388C22×C1112yes—
519#388C22×C1112yes—
520#388C22×C1112yes—
521#388C22×C1112yes—
522#388C22×C1112yes—
523#388C22×C1112yes—
524#388C22×C1112yes—
525#388C22×C1111yescharacteristic
526#388C22×C1111yescharacteristic
527#388C22×C1111yescharacteristic
528#388C22×C1111yescharacteristic
529#387C22×C1112yes—
530#387C22×C1112yes—
531#387C22×C1112yes—
532#387C22×C1112yes—
533#387C22×C1112yes—
534#387C22×C1112yes—
535#387C22×C1112yes—
536#386C22×C1112yes—
537#386C22×C1112yes—
538#386C22×C1112yes—
539#386C22×C1112yes—
540#386C22×C1112yes—
541#385C22×C1112yes—
542#385C22×C1112yes—
543#385C22×C1112yes—
544#382C22×C1111yescharacteristic
545#382C22×C1112yes—
546#381C22×C1112yes—
547#381C22×C1112yes—
548#380C22×C1111yescharacteristic
549#380C22×C1111yescharacteristic
550C4×C4⋊C4C22×C1111yescharacteristic
551C4×C4⋊C4C22×C1111yescharacteristic
552C4×C4⋊C4C22×C1112yes—
553C4×C4⋊C4C22×C1112yes—
554C4×C4⋊C4C22×C1112yes—
555C4×C4⋊C4C22×C1112yes—
556C4×C4⋊C4C22×C1111yescharacteristic
557C4×C4⋊C4C22×C1111yescharacteristic
558C4×C4⋊C4C22×C1111yescharacteristic
559C4×C4⋊C4C22×C1111yescharacteristic
560C4×C4⋊C4C22×C1111yescharacteristic
561C4×C4⋊C4C22×C1112yes—
562C4×C4⋊C4C22×C1112yes—
563C4×C4⋊C4C22×C1111yescharacteristic
564C4×C4⋊C4C22×C1111yescharacteristic
565C4×C4⋊C4C22×C1112yes—
566C4×C4⋊C4C22×C1111yescharacteristic
567C4×C22⋊C4C22×C1112yes—
568C4×C22⋊C4C22×C1112yes—
569C4×C22⋊C4C22×C1112yes—
570C4×C22⋊C4C22×C1111yescharacteristic
571C4×C22⋊C4C22×C1111yescharacteristic
572C4×C22⋊C4C22×C1112yes—
573C4×C22⋊C4C22×C1112yes—
574C4×C22⋊C4C22×C1112yes—
575C4×C22⋊C4C22×C1112yes—
576C4×C22⋊C4C22×C1112yes—
577C4×C22⋊C4C22×C1112yes—
578C4×C22⋊C4C22×C1112yes—
579#376C22×C1112yes—
580C43C22×C1111yescharacteristic
581C22×C11—22no—
582C22×C11—22no—
583C22×C11—24no—
584C22×C11—22no—
585C22×C11—22no—
586C22×C11—24no—
587C22×C11—22no—
588C22×C11—24no—
589C22×C11—22no—
590C22×C11—42no—
591C22×C11—41no—
592C22×C11—41no—
593C22×C11—41no—
594C22×C11—41no—
595C22×C11—42no—
596C22×C11—42no—
597C22×C11—41no—
598C22×C11—41no—
599C22×C11—41no—
600C22×C11—42no—
601C22×C11—41no—
602C22×C11C24×C411yescharacteristic
603C22×C11C22×#4111yescharacteristic
604C22×C11C22×#4111yescharacteristic
605C22×C11C2×H(5,𝔽2)11yescharacteristic
606C22×C11#58511yescharacteristic
607C22×C11#58511yescharacteristic
608C22×C11#58511yescharacteristic
609C4×C11—22no—
610C4×C11—22no—
611C4×C11—24no—
612C4×C11—22no—
613C4×C11—22no—
614C4×C11—24no—
615C4×C11—24no—
616C4×C11—22no—
617C4×C11—22no—
618C4×C11—22no—
619C4×C11—24no—
620C4×C11—41no—
621C4×C11—41no—
622C4×C11—42no—
623C4×C11—41no—
624C4×C11—41no—
625C4×C11—42no—
626C4×C11—41no—
627C4×C11—42no—
628C4×C11C4×#4114yes—
629C22×D4C23×C1111yescharacteristic
630C22×D4C23×C1112yes—
631C22×D4C23×C1111yescharacteristic
632C22×D4C23×C1112yes—
633C23×C4C23×C1112yes—
634C23×C4C23×C1111yescharacteristic
635C23×C4C23×C1111yescharacteristic
636C23×C4C23×C1112yes—
637C23×C4C23×C1112yes—
638C23×C4C23×C1112yes—
639C23×C4C23×C1112yes—
640#126C2×C4×C11116yescomplemented
641#125C2×C4×C1118yescomplemented
642#123C2×C4×C11116yescomplemented
643#121C2×C4×C1118yes—
644#121C2×C4×C11116yescomplemented
645#121C2×C4×C1118yescomplemented
646C4×D4—24no—
647C4×D4—24no—
648C4×D4—44no—
649C4×D4C2×C4×C11116yescomplemented
650C4×D4C2×C4×C1118yescomplemented
651C4×D4C2×C4×C1118yescomplemented
652#117—24no—
653#117—24no—
654#117—24no—
655#117—44no—
656#117C2×C4×C1118yescomplemented
657C2×C4⋊C4—24no—
658C2×C4⋊C4C2×C4×C1118yescomplemented
659C2×C4⋊C4C23×C1111yescharacteristic
660C2×C4⋊C4C23×C1112yes—
661C2×C4⋊C4C23×C1112yes—
662C2×C4⋊C4C23×C1111yescharacteristic
663C2×C4⋊C4C23×C1111yescharacteristic
664C2×C4⋊C4C23×C1111yescharacteristic
665C2×C4⋊C4C23×C1111yescharacteristic
666C2×C4⋊C4C23×C1111yescharacteristic
667C2×C4⋊C4C23×C1111yescharacteristic
668C2×C4⋊C4C23×C1112yes—
669C2×C4⋊C4C23×C1112yes—
670C2×C4⋊C4C23×C1112yes—
671C2×C4⋊C4C23×C1111yescharacteristic
672C2×C4⋊C4C23×C1111yescharacteristic
673C2×C4⋊C4C23×C1111yescharacteristic
674C2×C4⋊C4C23×C1111yescharacteristic
675C2×C4⋊C4C23×C1112yes—
676C2×C4⋊C4C23×C1111yescharacteristic
677C2×C4⋊C4C23×C1112yes—
678C2×C4⋊C4C23×C1111yescharacteristic
679C2×C4⋊C4C23×C1112yes—
680C2×C4⋊C4C23×C1111yescharacteristic
681C2×C22⋊C4C23×C1111yescharacteristic
682C2×C22⋊C4C23×C1111yescharacteristic
683C2×C22⋊C4C23×C1111yescharacteristic
684C2×C22⋊C4C23×C1112yes—
685C2×C22⋊C4C23×C1111yescharacteristic
686C2×C22⋊C4C23×C1111yescharacteristic
687C2×C22⋊C4C23×C1111yescharacteristic
688C2×C22⋊C4C23×C1112yes—
689C2×C22⋊C4C23×C1112yes—
690C2×C22⋊C4C23×C1112yes—
691C2×C22⋊C4C23×C1112yes—
692C2×C22⋊C4C23×C1112yes—
693C2×C22⋊C4C23×C1111yescharacteristic
694C2×C22⋊C4C23×C1112yes—
695C2×C22⋊C4C23×C1112yes—
696C2×C22⋊C4C23×C1112yes—
697C2×C22⋊C4C23×C1111yescharacteristic
698C2×C22⋊C4C23×C1112yes—
699C2×C22⋊C4C23×C1111yescharacteristic
700C2×C22⋊C4C23×C1112yes—
701C2×C22⋊C4C23×C1112yes—
702C2×C22⋊C4C23×C1111yescharacteristic
703C2×C22⋊C4C23×C1112yes—
704C2×C42—44no—
705C2×C42C23×C1112yes—
706C2×C42C23×C1112yes—
707C2×C42C23×C1111yescharacteristic
708C2×C42C23×C1111yescharacteristic
709C2×C42C23×C1111yescharacteristic
710C2×C42C23×C1111yescharacteristic
711C2×C42C23×C1112yes—
712C2×C42C23×C1112yes—
713C2×C42C23×C1111yescharacteristic
714C2×C42C23×C1111yescharacteristic
715C2×C42C23×C1111yescharacteristic
716C2×C42C23×C1112yes—
717C2×C42C23×C1112yes—
718C2×C42C23×C1112yes—
719C2×C42C23×C1112yes—
720C2×C42C23×C1112yes—
721C2×C42C23×C1112yes—
722C2×C42C23×C1112yes—
723C2×C42C23×C1111yescharacteristic
724C2×C42C23×C1111yescharacteristic
725#95C23×C1111yescharacteristic
726#95C23×C1112yes—
727#95C23×C1112yes—
728#95C23×C1112yes—
729#95C23×C1112yes—
730#95C23×C1111yescharacteristic
731#95C23×C1112yes—
732#95C23×C1112yes—
733#95C23×C1112yes—
734#95C23×C1111yescharacteristic
735#95C23×C1112yes—
736#95C23×C1112yes—
737#95C23×C1112yes—
738#95C23×C1112yes—
739#95C23×C1112yes—
740#95C23×C1112yes—
741#95C23×C1112yes—
742#95C23×C1111yescharacteristic
743#95C23×C1111yescharacteristic
744#95C23×C1111yescharacteristic
745#95C23×C1112yes—
746#95C23×C1112yes—
747#95C23×C1112yes—
748C2×C11—42no—
749C2×C11—42no—
750C2×C11—44no—
751C2×C11C2×C4×#4111yescharacteristic
752C2×C11#342811yescharacteristic
753C2×C11C4×H(5,𝔽2)11yescharacteristic
754C2×C11#350611yescharacteristic
755C2×C11#351211yescharacteristic
756C2×C11#351311yescharacteristic
757C2×C11#352411yescharacteristic
758C24C24×C1111yescharacteristic
759C24C24×C1111yescharacteristic
760C24C24×C1112yes—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4C22×C4×C1114yes—
770C2×D4C22×C4×C1118yes—
771C2×D4C22×C4×C1114yes—
772C2×D4C22×C4×C1118yes—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4C22×C4×C1114yes—
791C22×C4C22×C4×C1114yes—
792C22×C4C22×C4×C1118yes—
793C22×C4C22×C4×C1118yes—
794C22×C4C24×C1111yescharacteristic
795C22×C4C24×C1111yescharacteristic
796C22×C4C24×C1112yes—
797C22×C4C24×C1111yescharacteristic
798C22×C4C24×C1112yes—
799C22×C4C24×C1112yes—
800C22×C4C24×C1111yescharacteristic
801C22×C4C24×C1111yescharacteristic
802C22×C4C24×C1112yes—
803C22×C4C24×C1111yescharacteristic
804C22×C4C24×C1112yes—
805C22×C4C24×C1111yescharacteristic
806C22×C4C24×C1111yescharacteristic
807C22×C4C24×C1111yescharacteristic
808C22×C4C24×C1112yes—
809C22×C4C24×C1111yescharacteristic
810C22×C4C24×C1112yes—
811C22×C4C24×C1111yescharacteristic
812C22×C4C24×C1111yescharacteristic
813C22×C4C24×C1111yescharacteristic
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—24no—
823C4⋊C4—42no—
824C4⋊C4—41no—
825C4⋊C4—41no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C4⋊C4C22×C4×C1114yes—
829C4⋊C4C22×C4×C1114yes—
830C4⋊C4C22×C4×C1118yes—
831C4⋊C4C22×C4×C1114yes—
832C4⋊C4C22×C4×C1118yes—
833C4⋊C4C22×C4×C1114yes—
834C4⋊C4C22×C4×C1118yes—
835C4⋊C4C11×#4114yes—
836C22⋊C4—24no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—22no—
840C22⋊C4—22no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—22no—
844C22⋊C4—22no—
845C22⋊C4—42no—
846C22⋊C4—42no—
847C22⋊C4—41no—
848C22⋊C4—42no—
849C22⋊C4—41no—
850C22⋊C4—42no—
851C22⋊C4—42no—
852C22⋊C4—42no—
853C22⋊C4C22×C4×C1118yes—
854C22⋊C4C22×C4×C1114yes—
855C22⋊C4C22×C4×C1118yes—
856C22⋊C4C22×C4×C1118yes—
857C22⋊C4C22×C4×C1114yes—
858C22⋊C4C22×C4×C1118yes—
859C42—24no—
860C42—22no—
861C42—22no—
862C42—22no—
863C42—22no—
864C42—24no—
865C42—42no—
866C42—42no—
867C42—42no—
868C42—42no—
869C42—42no—
870C42—41no—
871C42—41no—
872C42—42no—
873C42—42no—
874C42—41no—
875C42—42no—
876C42C22×C4×C1118yes—
877C42C22×C4×C1114yes—
878C42C11×#4114yes—
879C11#3431911yescharacteristic, direct product factor, Sylow
880C23—21no—
881C23—21no—
882C23—21no—
883C23—22no—
884C23—22no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23C23×C4×C1112yes—
899C23C23×C4×C1114yes—
900C23C23×C4×C1112yes—
901C23C25×C1111yescharacteristic
902D4—28no—
903D4—48no—
904D4—44no—
905D4—48no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—28no—
929C2×C4—28no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—21no—
954C2×C4—48no—
955C2×C4—48no—
956C2×C4—48no—
957C2×C4—48no—
958C2×C4—84no—
959C2×C4C23×C4×C1112yes—
960C2×C4C23×C4×C1114yes—
961C2×C4C23×C4×C1112yes—
962C2×C4C23×C4×C1114yes—
963C2×C4C23×C4×C1112yes—
964C2×C4C23×C4×C1112yes—
965C2×C4C23×C4×C1114yes—
966C2×C4C23×C4×C1112yes—
967C2×C4C2×C11×#4114yes—
968C2×C4C2×C11×#4112yes—
969C2×C4C2×C11×#4112yes—
970C2×C4C2×C11×#4112yes—
971C2×C4C2×C11×#4112yes—
972C2×C4C11×H(5,𝔽2)12yes—
973C22—22no—
974C22—22no—
975C22—24no—
976C22—22no—
977C22—22no—
978C22—24no—
979C22—22no—
980C22—24no—
981C22—22no—
982C22—42no—
983C22—41no—
984C22—41no—
985C22—41no—
986C22—41no—
987C22—42no—
988C22—42no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—42no—
993C22—41no—
994C22C24×C4×C1111yescharacteristic
995C22C22×C11×#4111yescharacteristic
996C22C22×C11×#4111yescharacteristic
997C22C2×C11×H(5,𝔽2)11yescharacteristic
998C22C11×#58511yescharacteristic
999C22C11×#58511yescharacteristic
1000C22C11×#58511yescharacteristic
1001C4—22no—
1002C4—22no—
1003C4—24no—
1004C4—22no—
1005C4—22no—
1006C4—24no—
1007C4—24no—
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—24no—
1012C4—42no—
1013C4—41no—
1014C4—41no—
1015C4—41no—
1016C4—41no—
1017C4—42no—
1018C4—41no—
1019C4—42no—
1020C4C4×C11×#4114yes—
1021C2—42no—
1022C2—42no—
1023C2—44no—
1024C2C2×C4×C11×#4111yescharacteristic
1025C2C11×#342811yescharacteristic
1026C2C4×C11×H(5,𝔽2)11yescharacteristic
1027C2C11×#350611yescharacteristic
1028C2C11×#351211yescharacteristic
1029C2C11×#351311yescharacteristic
1030C2C11×#352411yescharacteristic
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×#2374C2semidirect
3. C11×#2373C2semidirect
4. C11×#2370C2semidirect
5. C11×#2363C2semidirect
6. C11×#2363C2semidirect
7. C11×#2361C2semidirect
8. C11×#2357C2semidirect
9. C11×#2357C2semidirect
10. C11×#2352C2semidirect
11. C11×#2346C2semidirect
12. C11×#2344C2semidirect
13. C11×#2334C2semidirect
14. C11×#2333C2semidirect
15. C11×#2324C2semidirect
16. C11×#2324C2semidirect
17. C4×C11×#125C2semidirect
18. C4×C11×#123C2semidirect
19. C11×#2293C2semidirect
20. C11×#2290C2semidirect
21. C11×#2274C2semidirect
22. C11×#2274C2semidirect
23. C42×D4×C11C2semidirect
24. C11×#553C4semidirect
135. C11×#126C2×C4semidirect
136. C11×#125C2×C4semidirect
137. C11×#123C2×C4semidirect
139. C11×#121C2×C4semidirect
140. C11×#121C2×C4semidirect
144. C4×D4×C11C2×C4semidirect
145. C4×D4×C11C2×C4semidirect
146. C4×D4×C11C2×C4semidirect
151. C11×#117C2×C4semidirect
153. C2×C11×C4⋊C4C2×C4semidirect
243. #34319C11direct (N × H)
366. #2374C2×C11semidirect
367. #2373C2×C11semidirect
368. #2370C2×C11semidirect
369. #2363C2×C11semidirect
370. #2363C2×C11semidirect
371. #2361C2×C11semidirect
372. #2357C2×C11semidirect
373. #2357C2×C11semidirect
374. #2352C2×C11semidirect
375. #2346C2×C11semidirect
376. #2344C2×C11semidirect
377. #2334C2×C11semidirect
378. #2333C2×C11semidirect
379. #2324C2×C11semidirect
380. #2324C2×C11semidirect
381. C4×#125C2×C11semidirect
382. C4×#123C2×C11semidirect
383. #2293C2×C11semidirect
384. #2290C2×C11semidirect
385. #2274C2×C11semidirect
386. #2274C2×C11semidirect
387. C42×D4C2×C11semidirect
481. #553C4×C11semidirect
640. #126C2×C4×C11semidirect
641. #125C2×C4×C11semidirect
642. #123C2×C4×C11semidirect
644. #121C2×C4×C11semidirect
645. #121C2×C4×C11semidirect
649. C4×D4C2×C4×C11semidirect
650. C4×D4C2×C4×C11semidirect
651. C4×D4C2×C4×C11semidirect
656. #117C2×C4×C11semidirect
658. C2×C4⋊C4C2×C4×C11semidirect
879. C11#34319direct (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×#23742
C11×#23732
C11×#23702
C11×#23632
C11×#23612
C11×#23572
C11×#23522
C11×#23462
C11×#23442
C11×#23342
C11×#23332
C11×#23242
C4×C11×#1252
C4×C11×#1232
C11×#22932
C11×#22902
C11×#22742
C42×D4×C112
#3431911