Finite Group Databasebeta

← C11×#34437 #14611630

Subgroups — C11×#34437 #14611630

Order 2816.

2810 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#534C211yesmaximal, characteristic
2C11×#2376C212yesmaximal, complemented
3C11×#2375C212yesmaximal, complemented
4C11×#2374C212yesmaximal, complemented
5C11×#2364C212yesmaximal, complemented
6C11×#2361C212yesmaximal, complemented
7C11×#2358C212yesmaximal, complemented
8D4×C11×C22⋊C4C212yesmaximal, complemented
9D4×C11×C22⋊C4C212yesmaximal, complemented
10C11×#2335C212yesmaximal, complemented
11C11×#2335C212yesmaximal, complemented
12C11×#2325C211yesmaximal, characteristic, complemented
13C11×#2325C211yesmaximal, characteristic, complemented
14C11×#2321C212yesmaximal, complemented
15C11×#2321C212yesmaximal, complemented
16C11×#2312C211yesmaximal, characteristic, complemented
17C4×C11×#121C211yesmaximal, characteristic, complemented
18C4×C11×#121C211yesmaximal, characteristic, complemented
19C2×C11×#388C211yesmaximal, characteristic, complemented
20C23×D4×C11C2212yes—
21C11×#534C4116yescomplemented
22C2×C11×#123C2212yes—
23C2×C11×#123C2212yes—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2212yes—
27C2×C11×#120C2212yes—
28C2×C11×#120C2212yes—
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C2×C4×D4×C11C2212yescomplemented
31C2×C4×D4×C11C2212yescomplemented
32C2×C4×D4×C11C2211yescharacteristic, complemented
33C2×C4×D4×C11C2212yescomplemented
34C2×C4×D4×C11C2212yescomplemented
35C2×C4×D4×C11C2212yescomplemented
36C22×C11×C4⋊C4C2211yescharacteristic, complemented
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C22×C11×C22⋊C4C2211yescharacteristic
40C22×C11×C22⋊C4C2212yescomplemented
41C22×C11×C22⋊C4C2212yescomplemented
42C22×C42×C11C2211yescharacteristic, complemented
43C11×#390C2212yes—
44C11×#390C2212yes—
45C11×#390C2212yes—
46C11×#390C2212yes—
47C11×#390C2211yescharacteristic, complemented
48C11×#390C2211yescharacteristic, complemented
49C11×#390C2212yescomplemented
50C11×#389C2211yescharacteristic, complemented
51C11×#389C2211yescharacteristic, complemented
52C11×#389C2212yescomplemented
53C11×#388C2212yescomplemented
54C11×#388C2212yescomplemented
55C11×#388C2212yescomplemented
56C11×#388C2212yescomplemented
57C11×#388C2212yescomplemented
58C11×#388C2212yescomplemented
59C11×#388C2212yescomplemented
60C11×#388C2212yescomplemented
61C11×#388C2212yescomplemented
62C11×#388C2212yescomplemented
63C11×#388C2212yescomplemented
64C11×#388C2212yescomplemented
65C11×#388C2212yescomplemented
66C11×#388C2212yescomplemented
67C11×#388C2212yescomplemented
68C11×#388C2212yescomplemented
69C11×#387C2212yescomplemented
70C11×#387C2212yescomplemented
71C11×#387C2212yescomplemented
72C11×#387C2212yescomplemented
73C11×#386C2212yes—
74C11×#386C2212yes—
75C11×#386C2212yes—
76C11×#386C2212yes—
77C11×#386C2212yescomplemented
78C11×#386C2212yescomplemented
79C11×#386C2212yescomplemented
80C11×#386C2212yescomplemented
81C11×#386C2212yescomplemented
82C11×#386C2212yescomplemented
83C11×#386C2212yescomplemented
84C11×#386C2212yescomplemented
85C11×#385C2212yescomplemented
86C11×#385C2212yescomplemented
87C11×#385C2212yescomplemented
88C11×#385C2212yescomplemented
89C11×#380C2211yescharacteristic, complemented
90C11×#380C2211yescharacteristic, complemented
91C11×#380C2212yescomplemented
92C11×#380C2212yescomplemented
93C11×#379C2212yes—
94C11×#379C2212yescomplemented
95C11×#379C2212yescomplemented
96C4×C11×C4⋊C4C2211yescharacteristic, complemented
97C4×C11×C4⋊C4C2211yescharacteristic, complemented
98C4×C11×C4⋊C4C2212yescomplemented
99C4×C11×C22⋊C4C2212yescomplemented
100C4×C11×C22⋊C4C2212yescomplemented
101C4×C11×C22⋊C4C2212yescomplemented
102C4×C11×C22⋊C4C2212yescomplemented
103C4×C11×C22⋊C4C2212yescomplemented
104C4×C11×C22⋊C4C2212yescomplemented
105C4×C11×C22⋊C4C2212yescomplemented
106C2×C11×#95C2211yescharacteristic, complemented
107C2×C11×#95C2211yescharacteristic, complemented
108C25×C11C2311yescharacteristic
109C25×C11C2312yes—
110C22×D4×C11—44no—
111C22×D4×C11—44no—
112C22×D4×C11C2×C4116yescomplemented
113C22×D4×C11C2312yes—
114C22×D4×C11C2312yes—
115C22×D4×C11C2311yescharacteristic
116C22×D4×C11C2311yescharacteristic
117C22×D4×C11C2312yes—
118C22×D4×C11C2312yes—
119C22×D4×C11C2312yes—
120C23×C4×C11C2311yescharacteristic
121C23×C4×C11C2311yescharacteristic
122C23×C4×C11C2311yescharacteristic
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2312yes—
125C23×C4×C11C2312yes—
126C23×C4×C11C2312yes—
127C23×C4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C11×#123C2×C4116yescomplemented
132C11×#123C2×C4116yescomplemented
133C11×#121C2×C418yescomplemented
134C11×#121C2×C418yescomplemented
135C11×#121C2×C4116yescomplemented
136C11×#120C2×C4116yescomplemented
137C11×#120C2×C4116yescomplemented
138C4×D4×C11—42no—
139C4×D4×C11—42no—
140C4×D4×C11—44no—
141C4×D4×C11—44no—
142C4×D4×C11—44no—
143C4×D4×C11—44no—
144C4×D4×C11—44no—
145C2×C11×C4⋊C4—42no—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C4⋊C4C2312yes—
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C22⋊C4—42no—
160C2×C11×C22⋊C4—42no—
161C2×C11×C22⋊C4—44no—
162C2×C11×C22⋊C4—44no—
163C2×C11×C22⋊C4C2×C418yescomplemented
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×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C42×C11—42no—
193C2×C42×C11C2311yescharacteristic
194C2×C42×C11C2311yescharacteristic
195C2×C42×C11C2311yescharacteristic
196C2×C42×C11C2311yescharacteristic
197C2×C42×C11C2312yes—
198C2×C42×C11C2312yes—
199C2×C42×C11C2312yes—
200C2×C42×C11C2312yes—
201C2×C42×C11C2312yes—
202C2×C42×C11C2312yes—
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—
217C11×#95C2312yes—
218C11×#95C2312yes—
219#34437C1111yesmaximal, characteristic, direct product factor, Sylow
220C24×C11—22no—
221C24×C11—22no—
222C24×C11—41no—
223C24×C11—41no—
224C24×C11—42no—
225C24×C11—42no—
226C24×C11—42no—
227C24×C11—42no—
228C24×C11—41no—
229C24×C11—41no—
230C24×C11—42no—
231C24×C11—42no—
232C24×C11C22×C414yes—
233C24×C11C22×C418yes—
234C24×C11C2412yes—
235C24×C11C2412yes—
236C24×C11C2412yes—
237C24×C11C2411yescharacteristic
238C2×D4×C11—24no—
239C2×D4×C11—24no—
240C2×D4×C11—24no—
241C2×D4×C11—24no—
242C2×D4×C11—41no—
243C2×D4×C11—41no—
244C2×D4×C11—42no—
245C2×D4×C11—42no—
246C2×D4×C11—42no—
247C2×D4×C11—42no—
248C2×D4×C11—42no—
249C2×D4×C11—42no—
250C2×D4×C11—41no—
251C2×D4×C11—41no—
252C2×D4×C11—432no—
253C2×D4×C11C22×C418yes—
254C2×D4×C11C22×C418yes—
255C2×D4×C11C22×C414yes—
256C2×D4×C11C22×C418yes—
257C2×D4×C11C22×C414yes—
258C2×D4×C11C22×C418yes—
259C2×D4×C11C22×C418yes—
260C22×C4×C11—22no—
261C22×C4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—22no—
266C22×C4×C11—24no—
267C22×C4×C11—24no—
268C22×C4×C11—41no—
269C22×C4×C11—41no—
270C22×C4×C11—41no—
271C22×C4×C11—41no—
272C22×C4×C11—41no—
273C22×C4×C11—41no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—41no—
278C22×C4×C11—41no—
279C22×C4×C11—42no—
280C22×C4×C11—41no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11—41no—
290C22×C4×C11C22×C414yes—
291C22×C4×C11C22×C414yes—
292C22×C4×C11C22×C418yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2412yes—
304C22×C4×C11C2412yes—
305C22×C4×C11C2412yes—
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C11×C4⋊C4—24no—
309C11×C4⋊C4—42no—
310C11×C4⋊C4—41no—
311C11×C4⋊C4—41no—
312C11×C4⋊C4—41no—
313C11×C4⋊C4—41no—
314C11×C4⋊C4—42no—
315C11×C4⋊C4—42no—
316C11×C4⋊C4—42no—
317C11×C4⋊C4—42no—
318C11×C4⋊C4C22×C414yes—
319C11×C4⋊C4C22×C414yes—
320C11×C4⋊C4C22×C418yes—
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—42no—
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—42no—
338C11×C22⋊C4—42no—
339C11×C22⋊C4—42no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4C22×C418yes—
344C11×C22⋊C4C22×C418yes—
345C11×C22⋊C4C22×C418yes—
346C11×C22⋊C4C22×C418yes—
347C11×C22⋊C4C22×C418yes—
348C11×C22⋊C4C22×C418yes—
349C42×C11—22no—
350C42×C11—22no—
351C42×C11—41no—
352C42×C11—41no—
353C42×C11—42no—
354C42×C11—42no—
355C42×C11—42no—
356C42×C11—42no—
357C42×C11—42no—
358C42×C11—42no—
359C2×#534C2×C1111yescharacteristic
360#2376C2×C1112yescomplemented
361#2375C2×C1112yescomplemented
362#2374C2×C1112yescomplemented
363#2364C2×C1112yescomplemented
364#2361C2×C1112yescomplemented
365#2358C2×C1112yescomplemented
366D4×C22⋊C4C2×C1112yescomplemented
367D4×C22⋊C4C2×C1112yescomplemented
368#2335C2×C1112yescomplemented
369#2335C2×C1112yescomplemented
370#2325C2×C1111yescharacteristic, complemented
371#2325C2×C1111yescharacteristic, complemented
372#2321C2×C1112yescomplemented
373#2321C2×C1112yescomplemented
374#2312C2×C1111yescharacteristic, complemented
375C4×#121C2×C1111yescharacteristic, complemented
376C4×#121C2×C1111yescharacteristic, complemented
377C2×#388C2×C1111yescharacteristic, complemented
378C23×C11—21no—
379C23×C11—21no—
380C23×C11—21no—
381C23×C11—21no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—28no—
401C23×C11—48no—
402C23×C11—44no—
403C23×C11—44no—
404C23×C11—48no—
405C23×C11—48no—
406C23×C11—82no—
407C23×C11—82no—
408C23×C11—82no—
409C23×C11—82no—
410C23×C11—84no—
411C23×C11—84no—
412C23×C11—84no—
413C23×C11—84no—
414C23×C11C23×C414yes—
415C23×C11C23×C414yes—
416C23×C11C23×C414yes—
417C23×C11C23×C412yes—
418C23×C11H(5,𝔽2)12yes—
419C23×C11H(5,𝔽2)12yes—
420C23×C11C2511yescharacteristic
421D4×C11—216no—
422D4×C11—216no—
423D4×C11—48no—
424D4×C11—48no—
425D4×C11—44no—
426D4×C11—44no—
427D4×C11—48no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—22no—
444C2×C4×C11—21no—
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—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—21no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—44no—
467C2×C4×C11—44no—
468C2×C4×C11—48no—
469C2×C4×C11—44no—
470C2×C4×C11—44no—
471C2×C4×C11—84no—
472C2×C4×C11—84no—
473C2×C4×C11—82no—
474C2×C4×C11—82no—
475C2×C4×C11—84no—
476C2×C4×C11—84no—
477C2×C4×C11C23×C412yes—
478C2×C4×C11C23×C412yes—
479C2×C4×C11C23×C414yes—
480C2×C4×C11C23×C414yes—
481C2×C4×C11C23×C414yes—
482C2×C4×C11H(5,𝔽2)12yes—
483C2×C4×C11H(5,𝔽2)12yes—
484C23×D4C22×C1112yes—
485#534C4×C11116yescomplemented
486C2×#123C22×C1112yes—
487C2×#123C22×C1112yes—
488C2×#121C22×C1111yescharacteristic
489C2×#121C22×C1111yescharacteristic
490C2×#121C22×C1112yes—
491C2×#120C22×C1112yes—
492C2×#120C22×C1112yes—
493C2×C4×D4C22×C1111yescharacteristic, complemented
494C2×C4×D4C22×C1112yescomplemented
495C2×C4×D4C22×C1112yescomplemented
496C2×C4×D4C22×C1112yescomplemented
497C2×C4×D4C22×C1112yescomplemented
498C2×C4×D4C22×C1112yescomplemented
499C2×C4×D4C22×C1111yescharacteristic, complemented
500C22×C4⋊C4C22×C1111yescharacteristic, complemented
501C22×C22⋊C4C22×C1111yescharacteristic
502C22×C22⋊C4C22×C1111yescharacteristic
503C22×C22⋊C4C22×C1111yescharacteristic
504C22×C22⋊C4C22×C1112yescomplemented
505C22×C22⋊C4C22×C1112yescomplemented
506C22×C42C22×C1111yescharacteristic, complemented
507#390C22×C1112yes—
508#390C22×C1112yes—
509#390C22×C1112yes—
510#390C22×C1112yes—
511#390C22×C1111yescharacteristic, complemented
512#390C22×C1112yescomplemented
513#390C22×C1111yescharacteristic, complemented
514#389C22×C1111yescharacteristic, complemented
515#389C22×C1112yescomplemented
516#389C22×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#388C22×C1112yescomplemented
527#388C22×C1112yescomplemented
528#388C22×C1112yescomplemented
529#388C22×C1112yescomplemented
530#388C22×C1112yescomplemented
531#388C22×C1112yescomplemented
532#388C22×C1112yescomplemented
533#387C22×C1112yescomplemented
534#387C22×C1112yescomplemented
535#387C22×C1112yescomplemented
536#387C22×C1112yescomplemented
537#386C22×C1112yes—
538#386C22×C1112yes—
539#386C22×C1112yes—
540#386C22×C1112yes—
541#386C22×C1112yescomplemented
542#386C22×C1112yescomplemented
543#386C22×C1112yescomplemented
544#386C22×C1112yescomplemented
545#386C22×C1112yescomplemented
546#386C22×C1112yescomplemented
547#386C22×C1112yescomplemented
548#386C22×C1112yescomplemented
549#385C22×C1112yescomplemented
550#385C22×C1112yescomplemented
551#385C22×C1112yescomplemented
552#385C22×C1112yescomplemented
553#380C22×C1111yescharacteristic, complemented
554#380C22×C1111yescharacteristic, complemented
555#380C22×C1112yescomplemented
556#380C22×C1112yescomplemented
557#379C22×C1112yes—
558#379C22×C1112yescomplemented
559#379C22×C1112yescomplemented
560C4×C4⋊C4C22×C1111yescharacteristic, complemented
561C4×C4⋊C4C22×C1112yescomplemented
562C4×C4⋊C4C22×C1111yescharacteristic, complemented
563C4×C22⋊C4C22×C1112yescomplemented
564C4×C22⋊C4C22×C1112yescomplemented
565C4×C22⋊C4C22×C1112yescomplemented
566C4×C22⋊C4C22×C1112yescomplemented
567C4×C22⋊C4C22×C1112yescomplemented
568C4×C22⋊C4C22×C1112yescomplemented
569C4×C22⋊C4C22×C1112yescomplemented
570C2×#95C22×C1111yescharacteristic, complemented
571C2×#95C22×C1111yescharacteristic, complemented
572C22×C11—22no—
573C22×C11—22no—
574C22×C11—22no—
575C22×C11—22no—
576C22×C11—22no—
577C22×C11—22no—
578C22×C11—24no—
579C22×C11—24no—
580C22×C11—24no—
581C22×C11—24no—
582C22×C11—24no—
583C22×C11—24no—
584C22×C11—24no—
585C22×C11—24no—
586C22×C11—24no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11—42no—
594C22×C11—42no—
595C22×C11—42no—
596C22×C11—42no—
597C22×C11—42no—
598C22×C11—42no—
599C22×C11—88no—
600C22×C11—816no—
601C22×C11#51814yes—
602C22×C11C24×C411yescharacteristic
603C22×C11C2×H(5,𝔽2)11yescharacteristic
604C22×C11C2×H(5,𝔽2)11yescharacteristic
605C22×C11C2×H(5,𝔽2)11yescharacteristic
606C22×C11C2×H(5,𝔽2)11yescharacteristic
607C22×C11#58511yescharacteristic
608C22×C11#58511yescharacteristic
609C4×C11—24no—
610C4×C11—24no—
611C4×C11—22no—
612C4×C11—22no—
613C4×C11—24no—
614C4×C11—22no—
615C4×C11—22no—
616C4×C11—41no—
617C4×C11—42no—
618C4×C11—41no—
619C4×C11—42no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—42no—
623C4×C11—42no—
624C25C23×C1111yescharacteristic
625C25C23×C1112yes—
626C22×D4—44no—
627C22×D4—44no—
628C22×D4C2×C4×C11116yescomplemented
629C22×D4C23×C1112yes—
630C22×D4C23×C1112yes—
631C22×D4C23×C1111yescharacteristic
632C22×D4C23×C1112yes—
633C22×D4C23×C1111yescharacteristic
634C22×D4C23×C1112yes—
635C22×D4C23×C1112yes—
636C23×C4C23×C1111yescharacteristic
637C23×C4C23×C1111yescharacteristic
638C23×C4C23×C1111yescharacteristic
639C23×C4C23×C1111yescharacteristic
640C23×C4C23×C1112yes—
641C23×C4C23×C1112yes—
642C23×C4C23×C1112yes—
643C23×C4C23×C1112yes—
644C23×C4C23×C1111yescharacteristic
645C23×C4C23×C1111yescharacteristic
646C23×C4C23×C1112yes—
647#123C2×C4×C11116yescomplemented
648#123C2×C4×C11116yescomplemented
649#121C2×C4×C1118yescomplemented
650#121C2×C4×C1118yescomplemented
651#121C2×C4×C11116yescomplemented
652#120C2×C4×C11116yescomplemented
653#120C2×C4×C11116yescomplemented
654C4×D4—42no—
655C4×D4—42no—
656C4×D4—44no—
657C4×D4—44no—
658C4×D4—44no—
659C4×D4—44no—
660C4×D4—44no—
661C2×C4⋊C4—42no—
662C2×C4⋊C4C23×C1112yes—
663C2×C4⋊C4C23×C1112yes—
664C2×C4⋊C4C23×C1112yes—
665C2×C4⋊C4C23×C1111yescharacteristic
666C2×C4⋊C4C23×C1112yes—
667C2×C4⋊C4C23×C1112yes—
668C2×C4⋊C4C23×C1112yes—
669C2×C4⋊C4C23×C1111yescharacteristic
670C2×C4⋊C4C23×C1111yescharacteristic
671C2×C4⋊C4C23×C1111yescharacteristic
672C2×C4⋊C4C23×C1111yescharacteristic
673C2×C4⋊C4C23×C1111yescharacteristic
674C2×C4⋊C4C23×C1112yes—
675C2×C22⋊C4—42no—
676C2×C22⋊C4—42no—
677C2×C22⋊C4—44no—
678C2×C22⋊C4—44no—
679C2×C22⋊C4C2×C4×C1118yescomplemented
680C2×C22⋊C4C23×C1112yes—
681C2×C22⋊C4C23×C1112yes—
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×C1112yes—
692C2×C22⋊C4C23×C1112yes—
693C2×C22⋊C4C23×C1112yes—
694C2×C22⋊C4C23×C1112yes—
695C2×C22⋊C4C23×C1112yes—
696C2×C22⋊C4C23×C1112yes—
697C2×C22⋊C4C23×C1112yes—
698C2×C22⋊C4C23×C1112yes—
699C2×C22⋊C4C23×C1112yes—
700C2×C22⋊C4C23×C1112yes—
701C2×C22⋊C4C23×C1112yes—
702C2×C22⋊C4C23×C1112yes—
703C2×C22⋊C4C23×C1112yes—
704C2×C22⋊C4C23×C1112yes—
705C2×C22⋊C4C23×C1112yes—
706C2×C22⋊C4C23×C1112yes—
707C2×C22⋊C4C23×C1112yes—
708C2×C42—42no—
709C2×C42C23×C1111yescharacteristic
710C2×C42C23×C1111yescharacteristic
711C2×C42C23×C1112yes—
712C2×C42C23×C1112yes—
713C2×C42C23×C1112yes—
714C2×C42C23×C1112yes—
715C2×C42C23×C1112yes—
716C2×C42C23×C1112yes—
717C2×C42C23×C1111yescharacteristic
718C2×C42C23×C1111yescharacteristic
719#95C23×C1112yes—
720#95C23×C1112yes—
721#95C23×C1112yes—
722#95C23×C1112yes—
723#95C23×C1112yes—
724#95C23×C1112yes—
725#95C23×C1112yes—
726#95C23×C1112yes—
727#95C23×C1112yes—
728#95C23×C1112yes—
729#95C23×C1112yes—
730#95C23×C1112yes—
731#95C23×C1112yes—
732#95C23×C1112yes—
733#95C23×C1112yes—
734#95C23×C1112yes—
735C2×C11—24no—
736C2×C11—44no—
737C2×C11—44no—
738C2×C11—44no—
739C2×C11C2×#51811yescharacteristic
740C2×C11C4×H(5,𝔽2)11yescharacteristic
741C2×C11C4×H(5,𝔽2)11yescharacteristic
742C2×C11#353411yescharacteristic
743C2×C11#353711yescharacteristic
744C2×C11#355811yescharacteristic
745C2×C11#356011yescharacteristic
746C24—22no—
747C24—22no—
748C24—41no—
749C24—41no—
750C24—42no—
751C24—42no—
752C24—42no—
753C24—42no—
754C24—41no—
755C24—41no—
756C24—42no—
757C24—42no—
758C24C22×C4×C1114yes—
759C24C22×C4×C1118yes—
760C24C24×C1112yes—
761C24C24×C1112yes—
762C24C24×C1112yes—
763C24C24×C1111yescharacteristic
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—41no—
769C2×D4—41no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—432no—
779C2×D4C22×C4×C1118yes—
780C2×D4C22×C4×C1118yes—
781C2×D4C22×C4×C1114yes—
782C2×D4C22×C4×C1118yes—
783C2×D4C22×C4×C1114yes—
784C2×D4C22×C4×C1118yes—
785C2×D4C22×C4×C1118yes—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—41no—
795C22×C4—41no—
796C22×C4—41no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—42no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—42no—
806C22×C4—41no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—41no—
816C22×C4C22×C4×C1114yes—
817C22×C4C22×C4×C1114yes—
818C22×C4C22×C4×C1118yes—
819C22×C4C24×C1112yes—
820C22×C4C24×C1112yes—
821C22×C4C24×C1111yescharacteristic
822C22×C4C24×C1112yes—
823C22×C4C24×C1112yes—
824C22×C4C24×C1112yes—
825C22×C4C24×C1112yes—
826C22×C4C24×C1111yescharacteristic
827C22×C4C24×C1111yescharacteristic
828C22×C4C24×C1111yescharacteristic
829C22×C4C24×C1112yes—
830C22×C4C24×C1112yes—
831C22×C4C24×C1112yes—
832C22×C4C24×C1111yescharacteristic
833C22×C4C24×C1111yescharacteristic
834C4⋊C4—24no—
835C4⋊C4—42no—
836C4⋊C4—41no—
837C4⋊C4—41no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4C22×C4×C1114yes—
845C4⋊C4C22×C4×C1114yes—
846C4⋊C4C22×C4×C1118yes—
847C22⋊C4—24no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—42no—
854C22⋊C4—42no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—42no—
859C22⋊C4—42no—
860C22⋊C4—42no—
861C22⋊C4—42no—
862C22⋊C4—42no—
863C22⋊C4—42no—
864C22⋊C4—42no—
865C22⋊C4—42no—
866C22⋊C4—42no—
867C22⋊C4—42no—
868C22⋊C4—42no—
869C22⋊C4C22×C4×C1118yes—
870C22⋊C4C22×C4×C1118yes—
871C22⋊C4C22×C4×C1118yes—
872C22⋊C4C22×C4×C1118yes—
873C22⋊C4C22×C4×C1118yes—
874C22⋊C4C22×C4×C1118yes—
875C42—22no—
876C42—22no—
877C42—41no—
878C42—41no—
879C42—42no—
880C42—42no—
881C42—42no—
882C42—42no—
883C42—42no—
884C42—42no—
885C11#3443711yescharacteristic, direct product factor, Sylow
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—28no—
909C23—48no—
910C23—44no—
911C23—44no—
912C23—48no—
913C23—48no—
914C23—82no—
915C23—82no—
916C23—82no—
917C23—82no—
918C23—84no—
919C23—84no—
920C23—84no—
921C23—84no—
922C23C23×C4×C1114yes—
923C23C23×C4×C1114yes—
924C23C23×C4×C1114yes—
925C23C23×C4×C1112yes—
926C23C11×H(5,𝔽2)12yes—
927C23C11×H(5,𝔽2)12yes—
928C23C25×C1111yescharacteristic
929D4—216no—
930D4—216no—
931D4—48no—
932D4—48no—
933D4—44no—
934D4—44no—
935D4—48no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—44no—
975C2×C4—44no—
976C2×C4—48no—
977C2×C4—44no—
978C2×C4—44no—
979C2×C4—84no—
980C2×C4—84no—
981C2×C4—82no—
982C2×C4—82no—
983C2×C4—84no—
984C2×C4—84no—
985C2×C4C23×C4×C1112yes—
986C2×C4C23×C4×C1112yes—
987C2×C4C23×C4×C1114yes—
988C2×C4C23×C4×C1114yes—
989C2×C4C23×C4×C1114yes—
990C2×C4C11×H(5,𝔽2)12yes—
991C2×C4C11×H(5,𝔽2)12yes—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—22no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—88no—
1020C22—816no—
1021C22C11×#51814yes—
1022C22C24×C4×C1111yescharacteristic
1023C22C2×C11×H(5,𝔽2)11yescharacteristic
1024C22C2×C11×H(5,𝔽2)11yescharacteristic
1025C22C2×C11×H(5,𝔽2)11yescharacteristic
1026C22C2×C11×H(5,𝔽2)11yescharacteristic
1027C22C11×#58511yescharacteristic
1028C22C11×#58511yescharacteristic
1029C4—24no—
1030C4—24no—
1031C4—22no—
1032C4—22no—
1033C4—24no—
1034C4—22no—
1035C4—22no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C2—24no—
1045C2—44no—
1046C2—44no—
1047C2—44no—
1048C2C2×C11×#51811yescharacteristic
1049C2C4×C11×H(5,𝔽2)11yescharacteristic
1050C2C4×C11×H(5,𝔽2)11yescharacteristic
1051C2C11×#353411yescharacteristic
1052C2C11×#353711yescharacteristic
1053C2C11×#355811yescharacteristic
1054C2C11×#356011yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#534C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2376C2semidirect
3. C11×#2375C2semidirect
4. C11×#2374C2semidirect
5. C11×#2364C2semidirect
6. C11×#2361C2semidirect
7. C11×#2358C2semidirect
8. D4×C11×C22⋊C4C2semidirect
9. D4×C11×C22⋊C4C2semidirect
10. C11×#2335C2semidirect
11. C11×#2335C2semidirect
12. C11×#2325C2semidirect
13. C11×#2325C2semidirect
14. C11×#2321C2semidirect
15. C11×#2321C2semidirect
16. C11×#2312C2semidirect
17. C4×C11×#121C2semidirect
18. C4×C11×#121C2semidirect
19. C2×C11×#388C2semidirect
21. C11×#534C4semidirect
29. C2×C4×D4×C11C22semidirect
30. C2×C4×D4×C11C22semidirect
31. C2×C4×D4×C11C22semidirect
32. C2×C4×D4×C11C22semidirect
33. C2×C4×D4×C11C22semidirect
34. C2×C4×D4×C11C22semidirect
35. C2×C4×D4×C11C22semidirect
36. C22×C11×C4⋊C4C22semidirect
40. C22×C11×C22⋊C4C22semidirect
41. C22×C11×C22⋊C4C22semidirect
42. C22×C42×C11C22semidirect
47. C11×#390C22semidirect
48. C11×#390C22semidirect
49. C11×#390C22semidirect
50. C11×#389C22semidirect
51. C11×#389C22semidirect
52. C11×#389C22semidirect
53. C11×#388C22semidirect
54. C11×#388C22semidirect
55. C11×#388C22semidirect
56. C11×#388C22semidirect
57. C11×#388C22semidirect
58. C11×#388C22semidirect
59. C11×#388C22semidirect
60. C11×#388C22semidirect
61. C11×#388C22semidirect
62. C11×#388C22semidirect
63. C11×#388C22semidirect
64. C11×#388C22semidirect
65. C11×#388C22semidirect
66. C11×#388C22semidirect
67. C11×#388C22semidirect
68. C11×#388C22semidirect
69. C11×#387C22semidirect
70. C11×#387C22semidirect
71. C11×#387C22semidirect
72. C11×#387C22semidirect
77. C11×#386C22semidirect
78. C11×#386C22semidirect
79. C11×#386C22semidirect
80. C11×#386C22semidirect
81. C11×#386C22semidirect
82. C11×#386C22semidirect
83. C11×#386C22semidirect
84. C11×#386C22semidirect
85. C11×#385C22semidirect
86. C11×#385C22semidirect
87. C11×#385C22semidirect
88. C11×#385C22semidirect
89. C11×#380C22semidirect
90. C11×#380C22semidirect
91. C11×#380C22semidirect
92. C11×#380C22semidirect
94. C11×#379C22semidirect
95. C11×#379C22semidirect
96. C4×C11×C4⋊C4C22semidirect
97. C4×C11×C4⋊C4C22semidirect
98. C4×C11×C4⋊C4C22semidirect
99. C4×C11×C22⋊C4C22semidirect
100. C4×C11×C22⋊C4C22semidirect
101. C4×C11×C22⋊C4C22semidirect
102. C4×C11×C22⋊C4C22semidirect
103. C4×C11×C22⋊C4C22semidirect
104. C4×C11×C22⋊C4C22semidirect
105. C4×C11×C22⋊C4C22semidirect
106. C2×C11×#95C22semidirect
107. C2×C11×#95C22semidirect
112. C22×D4×C11C2×C4semidirect
131. C11×#123C2×C4semidirect
132. C11×#123C2×C4semidirect
133. C11×#121C2×C4semidirect
134. C11×#121C2×C4semidirect
135. C11×#121C2×C4semidirect
136. C11×#120C2×C4semidirect
137. C11×#120C2×C4semidirect
163. C2×C11×C22⋊C4C2×C4semidirect
219. #34437C11direct (N × H)
360. #2376C2×C11semidirect
361. #2375C2×C11semidirect
362. #2374C2×C11semidirect
363. #2364C2×C11semidirect
364. #2361C2×C11semidirect
365. #2358C2×C11semidirect
366. D4×C22⋊C4C2×C11semidirect
367. D4×C22⋊C4C2×C11semidirect
368. #2335C2×C11semidirect
369. #2335C2×C11semidirect
370. #2325C2×C11semidirect
371. #2325C2×C11semidirect
372. #2321C2×C11semidirect
373. #2321C2×C11semidirect
374. #2312C2×C11semidirect
375. C4×#121C2×C11semidirect
376. C4×#121C2×C11semidirect
377. C2×#388C2×C11semidirect
485. #534C4×C11semidirect
493. C2×C4×D4C22×C11semidirect
494. C2×C4×D4C22×C11semidirect
495. C2×C4×D4C22×C11semidirect
496. C2×C4×D4C22×C11semidirect
497. C2×C4×D4C22×C11semidirect
498. C2×C4×D4C22×C11semidirect
499. C2×C4×D4C22×C11semidirect
500. C22×C4⋊C4C22×C11semidirect
504. C22×C22⋊C4C22×C11semidirect
505. C22×C22⋊C4C22×C11semidirect
506. C22×C42C22×C11semidirect
511. #390C22×C11semidirect
512. #390C22×C11semidirect
513. #390C22×C11semidirect
514. #389C22×C11semidirect
515. #389C22×C11semidirect
516. #389C22×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. #388C22×C11semidirect
527. #388C22×C11semidirect
528. #388C22×C11semidirect
529. #388C22×C11semidirect
530. #388C22×C11semidirect
531. #388C22×C11semidirect
532. #388C22×C11semidirect
533. #387C22×C11semidirect
534. #387C22×C11semidirect
535. #387C22×C11semidirect
536. #387C22×C11semidirect
541. #386C22×C11semidirect
542. #386C22×C11semidirect
543. #386C22×C11semidirect
544. #386C22×C11semidirect
545. #386C22×C11semidirect
546. #386C22×C11semidirect
547. #386C22×C11semidirect
548. #386C22×C11semidirect
549. #385C22×C11semidirect
550. #385C22×C11semidirect
551. #385C22×C11semidirect
552. #385C22×C11semidirect
553. #380C22×C11semidirect
554. #380C22×C11semidirect
555. #380C22×C11semidirect
556. #380C22×C11semidirect
558. #379C22×C11semidirect
559. #379C22×C11semidirect
560. C4×C4⋊C4C22×C11semidirect
561. C4×C4⋊C4C22×C11semidirect
562. C4×C4⋊C4C22×C11semidirect
563. C4×C22⋊C4C22×C11semidirect
564. C4×C22⋊C4C22×C11semidirect
565. C4×C22⋊C4C22×C11semidirect
566. C4×C22⋊C4C22×C11semidirect
567. C4×C22⋊C4C22×C11semidirect
568. C4×C22⋊C4C22×C11semidirect
569. C4×C22⋊C4C22×C11semidirect
570. C2×#95C22×C11semidirect
571. C2×#95C22×C11semidirect
628. C22×D4C2×C4×C11semidirect
647. #123C2×C4×C11semidirect
648. #123C2×C4×C11semidirect
649. #121C2×C4×C11semidirect
650. #121C2×C4×C11semidirect
651. #121C2×C4×C11semidirect
652. #120C2×C4×C11semidirect
653. #120C2×C4×C11semidirect
679. C2×C22⋊C4C2×C4×C11semidirect
885. C11#34437direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5342
C11×#23762
C11×#23752
C11×#23742
C11×#23642
C11×#23612
C11×#23582
D4×C11×C22⋊C42
C11×#23352
C11×#23252
C11×#23212
C11×#23122
C4×C11×#1212
C2×C11×#3882
#3443711