Finite Group Databasebeta

← C11×#34323 #14611516

Subgroups — C11×#34323 #14611516

Order 2816.

2472 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C11×#2373C212yesmaximal, complemented
3C11×#2370C211yesmaximal, characteristic, complemented
4C11×#2363C211yesmaximal, characteristic, complemented
5C11×#2361C211yesmaximal, characteristic, complemented
6C11×#2361C212yesmaximal, complemented
7C11×#2359C212yesmaximal, complemented
8C11×#2352C212yesmaximal, complemented
9C11×#2352C211yesmaximal, characteristic, complemented
10C11×#2349C211yesmaximal, characteristic, complemented
11C11×#2346C211yesmaximal, characteristic, complemented
12C11×#2345C211yesmaximal, characteristic, complemented
13C11×#2335C212yesmaximal, complemented
14C11×#2334C212yesmaximal, complemented
15C11×#2325C212yesmaximal, complemented
16C4×C11×#125C211yesmaximal, characteristic, complemented
17C4×C11×#121C211yesmaximal, characteristic, complemented
18C4×C11×#121C211yesmaximal, characteristic, complemented
19C11×#2296C211yesmaximal, characteristic, complemented
20C11×#2293C211yesmaximal, characteristic, complemented
21C2×C11×#389C211yesmaximal, characteristic, complemented
22C11×#2275C212yesmaximal, 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×C11C2212yes—
35C2×C4×D4×C11C2211yescharacteristic
36C2×C4×D4×C11C2211yescharacteristic
37C2×C4×D4×C11C2212yes—
38C2×C4×D4×C11C2211yescharacteristic
39C2×C4×D4×C11C2212yes—
40C2×C4×D4×C11C2211yescharacteristic
41C2×C11×#117C2212yes—
42C2×C11×#117C2211yescharacteristic
43C2×C11×#117C2211yescharacteristic
44C22×C11×C4⋊C4C2212yes—
45C22×C11×C4⋊C4C2211yescharacteristic
46C22×C11×C4⋊C4C2211yescharacteristic
47C22×C42×C11C2211yescharacteristic
48C22×C42×C11C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#390C2212yes—
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#389C2212yes—
55C11×#389C2211yescharacteristic
56C11×#389C2212yes—
57C11×#389C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#389C2211yescharacteristic
60C11×#389C2211yescharacteristic
61C11×#389C2211yescharacteristic
62C11×#389C2212yes—
63C11×#388C2212yes—
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×#385C2212yes—
88C11×#385C2212yes—
89C11×#382C2211yescharacteristic
90C11×#382C2212yes—
91C11×#380C2211yescharacteristic
92C11×#380C2211yescharacteristic
93C11×#380C2212yes—
94C11×#380C2212yes—
95C4×C11×C4⋊C4C2211yescharacteristic
96C4×C11×C4⋊C4C2211yescharacteristic
97C4×C11×C4⋊C4C2211yescharacteristic
98C4×C11×C4⋊C4C2212yes—
99C4×C11×C4⋊C4C2212yes—
100C4×C11×C4⋊C4C2212yes—
101C4×C11×C4⋊C4C2211yescharacteristic
102C4×C11×C4⋊C4C2212yes—
103C4×C11×C4⋊C4C2211yescharacteristic
104C4×C11×C4⋊C4C2211yescharacteristic
105C4×C11×C4⋊C4C2211yescharacteristic
106C4×C11×C4⋊C4C2211yescharacteristic
107C4×C11×C4⋊C4C2212yes—
108C4×C11×C22⋊C4C2211yescharacteristic
109C4×C11×C22⋊C4C2211yescharacteristic
110C4×C11×C22⋊C4C2211yescharacteristic
111C4×C11×C22⋊C4C2211yescharacteristic
112C4×C11×C22⋊C4C2211yescharacteristic
113C4×C11×C22⋊C4C2211yescharacteristic
114C4×C11×C22⋊C4C2212yes—
115C4×C11×C22⋊C4C2212yes—
116C4×C11×C22⋊C4C2212yes—
117C4×C11×C22⋊C4C2212yes—
118C4×C11×C22⋊C4C2212yes—
119C4×C11×C22⋊C4C2212yes—
120C11×#376C2212yes—
121C2×C11×#95C2212yes—
122C2×C11×#95C2212yes—
123C43×C11C2211yescharacteristic
124C22×D4×C11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2312yes—
134C23×C4×C11C2312yes—
135C23×C4×C11C2312yes—
136C23×C4×C11C2312yes—
137C23×C4×C11C2312yes—
138C23×C4×C11C2311yescharacteristic
139C11×#126C2×C4116yescomplemented
140C11×#125C2×C418yescomplemented
141C11×#123C2×C4116yescomplemented
142C11×#121C2×C4116yescomplemented
143C11×#121C2×C418yescomplemented
144C11×#121C2×C418yescomplemented
145C4×D4×C11—24no—
146C4×D4×C11—28no—
147C4×D4×C11—24no—
148C4×D4×C11—28no—
149C4×D4×C11—42no—
150C4×D4×C11—42no—
151C4×D4×C11—44no—
152C4×D4×C11C2×C4116yescomplemented
153C4×D4×C11C2×C418yescomplemented
154C4×D4×C11C2×C418yescomplemented
155C11×#117—44no—
156C11×#117—42no—
157C11×#117C2×C418yescomplemented
158C2×C11×C4⋊C4—42no—
159C2×C11×C4⋊C4—44no—
160C2×C11×C4⋊C4C2×C418yescomplemented
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2312yes—
174C2×C11×C4⋊C4C2312yes—
175C2×C11×C4⋊C4C2312yes—
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2311yescharacteristic
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C4⋊C4C2311yescharacteristic
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2311yescharacteristic
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2311yescharacteristic
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2311yescharacteristic
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C11×C22⋊C4C2312yes—
193C2×C11×C22⋊C4C2312yes—
194C2×C11×C22⋊C4C2312yes—
195C2×C11×C22⋊C4C2312yes—
196C2×C11×C22⋊C4C2311yescharacteristic
197C2×C11×C22⋊C4C2312yes—
198C2×C11×C22⋊C4C2311yescharacteristic
199C2×C11×C22⋊C4C2312yes—
200C2×C11×C22⋊C4C2312yes—
201C2×C11×C22⋊C4C2311yescharacteristic
202C2×C42×C11—42no—
203C2×C42×C11—42no—
204C2×C42×C11C2311yescharacteristic
205C2×C42×C11C2311yescharacteristic
206C2×C42×C11C2311yescharacteristic
207C2×C42×C11C2311yescharacteristic
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2312yes—
212C2×C42×C11C2312yes—
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2311yescharacteristic
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2311yescharacteristic
218C2×C42×C11C2312yes—
219C2×C42×C11C2312yes—
220C2×C42×C11C2312yes—
221C2×C42×C11C2312yes—
222C2×C42×C11C2311yescharacteristic
223C2×C42×C11C2312yes—
224C11×#95C2312yes—
225C11×#95C2311yescharacteristic
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2311yescharacteristic
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2311yescharacteristic
235C11×#95C2311yescharacteristic
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247#34323C1111yesmaximal, characteristic, direct product factor, Sylow
248C24×C11C2412yes—
249C24×C11C2411yescharacteristic
250C24×C11C2411yescharacteristic
251C2×D4×C11—22no—
252C2×D4×C11—24no—
253C2×D4×C11—22no—
254C2×D4×C11—24no—
255C2×D4×C11—22no—
256C2×D4×C11—22no—
257C2×D4×C11—42no—
258C2×D4×C11—42no—
259C2×D4×C11C22×C418yes—
260C2×D4×C11C22×C414yes—
261C2×D4×C11C22×C414yes—
262C2×D4×C11C22×C418yes—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—22no—
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11—24no—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—24no—
274C22×C4×C11—24no—
275C22×C4×C11—41no—
276C22×C4×C11—41no—
277C22×C4×C11—41no—
278C22×C4×C11—41no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11—41no—
283C22×C4×C11—41no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11C22×C414yes—
292C22×C4×C11C22×C414yes—
293C22×C4×C11C22×C418yes—
294C22×C4×C11C22×C418yes—
295C22×C4×C11#4114yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2412yes—
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2412yes—
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C22×C4×C11C2412yes—
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2411yescharacteristic
315C22×C4×C11C2411yescharacteristic
316C11×C4⋊C4—22no—
317C11×C4⋊C4—24no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—24no—
320C11×C4⋊C4—24no—
321C11×C4⋊C4—22no—
322C11×C4⋊C4—24no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—42no—
327C11×C4⋊C4—42no—
328C11×C4⋊C4—42no—
329C11×C4⋊C4—42no—
330C11×C4⋊C4—42no—
331C11×C4⋊C4C22×C414yes—
332C11×C4⋊C4C22×C414yes—
333C11×C4⋊C4C22×C418yes—
334C11×C4⋊C4C22×C414yes—
335C11×C4⋊C4C22×C418yes—
336C11×C4⋊C4C22×C414yes—
337C11×C4⋊C4C22×C418yes—
338C11×C22⋊C4—22no—
339C11×C22⋊C4—24no—
340C11×C22⋊C4—22no—
341C11×C22⋊C4—24no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—24no—
344C11×C22⋊C4—24no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—42no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4—42no—
349C11×C22⋊C4—42no—
350C11×C22⋊C4C22×C418yes—
351C11×C22⋊C4C22×C414yes—
352C11×C22⋊C4C22×C418yes—
353C11×C22⋊C4C22×C418yes—
354C11×C22⋊C4C22×C414yes—
355C11×C22⋊C4C22×C418yes—
356C11×C22⋊C4#4114yes—
357C42×C11—22no—
358C42×C11—24no—
359C42×C11—22no—
360C42×C11—24no—
361C42×C11—22no—
362C42×C11—22no—
363C42×C11—22no—
364C42×C11—22no—
365C42×C11—22no—
366C42×C11—41no—
367C42×C11—41no—
368C42×C11—41no—
369C42×C11—41no—
370C42×C11—41no—
371C42×C11—42no—
372C42×C11—42no—
373C42×C11—42no—
374C42×C11—42no—
375C42×C11C22×C418yes—
376C42×C11C22×C414yes—
377C2×#553C2×C1111yescharacteristic
378#2373C2×C1112yescomplemented
379#2370C2×C1111yescharacteristic, complemented
380#2363C2×C1111yescharacteristic, complemented
381#2361C2×C1112yescomplemented
382#2361C2×C1111yescharacteristic, complemented
383#2359C2×C1112yescomplemented
384#2352C2×C1112yescomplemented
385#2352C2×C1111yescharacteristic, complemented
386#2349C2×C1111yescharacteristic, complemented
387#2346C2×C1111yescharacteristic, complemented
388#2345C2×C1111yescharacteristic, complemented
389#2335C2×C1112yescomplemented
390#2334C2×C1112yescomplemented
391#2325C2×C1112yescomplemented
392C4×#125C2×C1111yescharacteristic, complemented
393C4×#121C2×C1111yescharacteristic, complemented
394C4×#121C2×C1111yescharacteristic, complemented
395#2296C2×C1111yescharacteristic, complemented
396#2293C2×C1111yescharacteristic, complemented
397C2×#389C2×C1111yescharacteristic, complemented
398#2275C2×C1112yescomplemented
399C42×D4C2×C1111yescharacteristic, complemented
400C23×C11—21no—
401C23×C11—21no—
402C23×C11—21no—
403C23×C11—21no—
404C23×C11—21no—
405C23×C11—22no—
406C23×C11—21no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—22no—
412C23×C11—21no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—21no—
416C23×C11C23×C412yes—
417C23×C11C23×C414yes—
418C23×C11C23×C412yes—
419C23×C11C2×#4112yes—
420C23×C11C2×#4112yes—
421C23×C11C2511yescharacteristic
422D4×C11—216no—
423D4×C11—28no—
424D4×C11—28no—
425D4×C11—48no—
426C2×C4×C11—22no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—22no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—21no—
450C2×C4×C11—28no—
451C2×C4×C11—28no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—22no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—48no—
474C2×C4×C11—48no—
475C2×C4×C11—44no—
476C2×C4×C11—44no—
477C2×C4×C11—44no—
478C2×C4×C11—44no—
479C2×C4×C11—84no—
480C2×C4×C11—84no—
481C2×C4×C11—84no—
482C2×C4×C11C23×C412yes—
483C2×C4×C11C23×C414yes—
484C2×C4×C11C23×C412yes—
485C2×C4×C11C23×C414yes—
486C2×C4×C11C23×C412yes—
487C2×C4×C11C23×C412yes—
488C2×C4×C11C23×C414yes—
489C2×C4×C11C23×C412yes—
490C2×C4×C11C2×#4112yes—
491C2×C4×C11C2×#4112yes—
492C2×C4×C11C2×#4112yes—
493C2×C4×C11C2×#4112yes—
494C2×C4×C11H(5,𝔽2)12yes—
495C2×C4×C11H(5,𝔽2)12yes—
496C2×C4×C112−1+412yes—
497#553C4×C11116yescomplemented
498C2×#126C22×C1112yes—
499C2×#125C22×C1111yescharacteristic
500C2×#123C22×C1112yes—
501C2×#121C22×C1112yes—
502C2×#121C22×C1111yescharacteristic
503C2×#121C22×C1111yescharacteristic
504C2×C4×D4C22×C1111yescharacteristic
505C2×C4×D4C22×C1112yes—
506C2×C4×D4C22×C1111yescharacteristic
507C2×C4×D4C22×C1112yes—
508C2×C4×D4C22×C1111yescharacteristic
509C2×C4×D4C22×C1111yescharacteristic
510C2×C4×D4C22×C1112yes—
511C2×C4×D4C22×C1111yescharacteristic
512C2×C4×D4C22×C1111yescharacteristic
513C2×C4×D4C22×C1112yes—
514C2×#117C22×C1112yes—
515C2×#117C22×C1111yescharacteristic
516C2×#117C22×C1111yescharacteristic
517C22×C4⋊C4C22×C1112yes—
518C22×C4⋊C4C22×C1111yescharacteristic
519C22×C4⋊C4C22×C1111yescharacteristic
520C22×C42C22×C1111yescharacteristic
521C22×C42C22×C1111yescharacteristic
522#390C22×C1112yes—
523#390C22×C1111yescharacteristic
524#390C22×C1111yescharacteristic
525#389C22×C1111yescharacteristic
526#389C22×C1111yescharacteristic
527#389C22×C1112yes—
528#389C22×C1112yes—
529#389C22×C1111yescharacteristic
530#389C22×C1111yescharacteristic
531#389C22×C1111yescharacteristic
532#389C22×C1112yes—
533#389C22×C1111yescharacteristic
534#389C22×C1111yescharacteristic
535#389C22×C1111yescharacteristic
536#388C22×C1112yes—
537#388C22×C1112yes—
538#388C22×C1112yes—
539#388C22×C1112yes—
540#388C22×C1112yes—
541#388C22×C1112yes—
542#388C22×C1112yes—
543#388C22×C1112yes—
544#388C22×C1112yes—
545#387C22×C1112yes—
546#387C22×C1112yes—
547#387C22×C1112yes—
548#387C22×C1112yes—
549#387C22×C1112yes—
550#387C22×C1112yes—
551#387C22×C1112yes—
552#386C22×C1112yes—
553#386C22×C1112yes—
554#386C22×C1112yes—
555#386C22×C1112yes—
556#386C22×C1112yes—
557#385C22×C1112yes—
558#385C22×C1112yes—
559#385C22×C1112yes—
560#385C22×C1112yes—
561#385C22×C1112yes—
562#382C22×C1111yescharacteristic
563#382C22×C1112yes—
564#380C22×C1112yes—
565#380C22×C1112yes—
566#380C22×C1111yescharacteristic
567#380C22×C1111yescharacteristic
568C4×C4⋊C4C22×C1112yes—
569C4×C4⋊C4C22×C1111yescharacteristic
570C4×C4⋊C4C22×C1111yescharacteristic
571C4×C4⋊C4C22×C1112yes—
572C4×C4⋊C4C22×C1111yescharacteristic
573C4×C4⋊C4C22×C1112yes—
574C4×C4⋊C4C22×C1111yescharacteristic
575C4×C4⋊C4C22×C1111yescharacteristic
576C4×C4⋊C4C22×C1111yescharacteristic
577C4×C4⋊C4C22×C1111yescharacteristic
578C4×C4⋊C4C22×C1112yes—
579C4×C4⋊C4C22×C1112yes—
580C4×C4⋊C4C22×C1111yescharacteristic
581C4×C22⋊C4C22×C1112yes—
582C4×C22⋊C4C22×C1111yescharacteristic
583C4×C22⋊C4C22×C1112yes—
584C4×C22⋊C4C22×C1111yescharacteristic
585C4×C22⋊C4C22×C1112yes—
586C4×C22⋊C4C22×C1111yescharacteristic
587C4×C22⋊C4C22×C1111yescharacteristic
588C4×C22⋊C4C22×C1112yes—
589C4×C22⋊C4C22×C1111yescharacteristic
590C4×C22⋊C4C22×C1112yes—
591C4×C22⋊C4C22×C1112yes—
592C4×C22⋊C4C22×C1111yescharacteristic
593#376C22×C1112yes—
594C2×#95C22×C1112yes—
595C2×#95C22×C1112yes—
596C43C22×C1111yescharacteristic
597C22×C11—22no—
598C22×C11—22no—
599C22×C11—22no—
600C22×C11—22no—
601C22×C11—22no—
602C22×C11—22no—
603C22×C11—22no—
604C22×C11—24no—
605C22×C11—22no—
606C22×C11—24no—
607C22×C11—24no—
608C22×C11—22no—
609C22×C11—41no—
610C22×C11—42no—
611C22×C11—42no—
612C22×C11—41no—
613C22×C11—41no—
614C22×C11—42no—
615C22×C11—41no—
616C22×C11—42no—
617C22×C11C4×#4114yes—
618C22×C11C24×C411yescharacteristic
619C22×C11C22×#4111yescharacteristic
620C22×C11C22×#4111yescharacteristic
621C22×C11C2×H(5,𝔽2)11yescharacteristic
622C22×C11C2×H(5,𝔽2)11yescharacteristic
623C22×C11C2×2−1+411yescharacteristic
624C22×C11#58511yescharacteristic
625C4×C11—24no—
626C4×C11—22no—
627C4×C11—22no—
628C4×C11—22no—
629C4×C11—22no—
630C4×C11—24no—
631C4×C11—24no—
632C4×C11—22no—
633C4×C11—22no—
634C4×C11—22no—
635C4×C11—22no—
636C4×C11—22no—
637C4×C11—41no—
638C4×C11—42no—
639C4×C11—41no—
640C4×C11—42no—
641C4×C11—41no—
642C4×C11—42no—
643C4×C11—42no—
644C4×C11#52014yes—
645C22×D4C23×C1111yescharacteristic
646C22×D4C23×C1112yes—
647C22×D4C23×C1111yescharacteristic
648C22×D4C23×C1112yes—
649C23×C4C23×C1111yescharacteristic
650C23×C4C23×C1111yescharacteristic
651C23×C4C23×C1111yescharacteristic
652C23×C4C23×C1111yescharacteristic
653C23×C4C23×C1112yes—
654C23×C4C23×C1112yes—
655C23×C4C23×C1112yes—
656C23×C4C23×C1111yescharacteristic
657C23×C4C23×C1112yes—
658C23×C4C23×C1112yes—
659C23×C4C23×C1111yescharacteristic
660#126C2×C4×C11116yescomplemented
661#125C2×C4×C1118yescomplemented
662#123C2×C4×C11116yescomplemented
663#121C2×C4×C11116yescomplemented
664#121C2×C4×C1118yescomplemented
665#121C2×C4×C1118yescomplemented
666C4×D4—24no—
667C4×D4—28no—
668C4×D4—24no—
669C4×D4—28no—
670C4×D4—42no—
671C4×D4—42no—
672C4×D4—44no—
673C4×D4C2×C4×C11116yescomplemented
674C4×D4C2×C4×C1118yescomplemented
675C4×D4C2×C4×C1118yescomplemented
676#117—44no—
677#117—42no—
678#117C2×C4×C1118yescomplemented
679C2×C4⋊C4—42no—
680C2×C4⋊C4—44no—
681C2×C4⋊C4C2×C4×C1118yescomplemented
682C2×C4⋊C4C23×C1112yes—
683C2×C4⋊C4C23×C1111yescharacteristic
684C2×C4⋊C4C23×C1111yescharacteristic
685C2×C4⋊C4C23×C1112yes—
686C2×C4⋊C4C23×C1111yescharacteristic
687C2×C4⋊C4C23×C1111yescharacteristic
688C2×C4⋊C4C23×C1111yescharacteristic
689C2×C4⋊C4C23×C1112yes—
690C2×C4⋊C4C23×C1112yes—
691C2×C4⋊C4C23×C1111yescharacteristic
692C2×C4⋊C4C23×C1112yes—
693C2×C4⋊C4C23×C1112yes—
694C2×C4⋊C4C23×C1112yes—
695C2×C4⋊C4C23×C1112yes—
696C2×C4⋊C4C23×C1112yes—
697C2×C4⋊C4C23×C1111yescharacteristic
698C2×C4⋊C4C23×C1111yescharacteristic
699C2×C4⋊C4C23×C1112yes—
700C2×C4⋊C4C23×C1111yescharacteristic
701C2×C4⋊C4C23×C1112yes—
702C2×C4⋊C4C23×C1111yescharacteristic
703C2×C4⋊C4C23×C1112yes—
704C2×C22⋊C4C23×C1112yes—
705C2×C22⋊C4C23×C1111yescharacteristic
706C2×C22⋊C4C23×C1112yes—
707C2×C22⋊C4C23×C1111yescharacteristic
708C2×C22⋊C4C23×C1112yes—
709C2×C22⋊C4C23×C1111yescharacteristic
710C2×C22⋊C4C23×C1112yes—
711C2×C22⋊C4C23×C1112yes—
712C2×C22⋊C4C23×C1112yes—
713C2×C22⋊C4C23×C1112yes—
714C2×C22⋊C4C23×C1112yes—
715C2×C22⋊C4C23×C1112yes—
716C2×C22⋊C4C23×C1112yes—
717C2×C22⋊C4C23×C1111yescharacteristic
718C2×C22⋊C4C23×C1112yes—
719C2×C22⋊C4C23×C1112yes—
720C2×C22⋊C4C23×C1111yescharacteristic
721C2×C22⋊C4C23×C1112yes—
722C2×C22⋊C4C23×C1111yescharacteristic
723C2×C42—42no—
724C2×C42—42no—
725C2×C42C23×C1111yescharacteristic
726C2×C42C23×C1111yescharacteristic
727C2×C42C23×C1111yescharacteristic
728C2×C42C23×C1112yes—
729C2×C42C23×C1112yes—
730C2×C42C23×C1111yescharacteristic
731C2×C42C23×C1111yescharacteristic
732C2×C42C23×C1111yescharacteristic
733C2×C42C23×C1111yescharacteristic
734C2×C42C23×C1112yes—
735C2×C42C23×C1112yes—
736C2×C42C23×C1112yes—
737C2×C42C23×C1111yescharacteristic
738C2×C42C23×C1111yescharacteristic
739C2×C42C23×C1111yescharacteristic
740C2×C42C23×C1112yes—
741C2×C42C23×C1111yescharacteristic
742C2×C42C23×C1111yescharacteristic
743C2×C42C23×C1112yes—
744C2×C42C23×C1111yescharacteristic
745#95C23×C1112yes—
746#95C23×C1111yescharacteristic
747#95C23×C1112yes—
748#95C23×C1112yes—
749#95C23×C1112yes—
750#95C23×C1112yes—
751#95C23×C1112yes—
752#95C23×C1111yescharacteristic
753#95C23×C1112yes—
754#95C23×C1112yes—
755#95C23×C1111yescharacteristic
756#95C23×C1111yescharacteristic
757#95C23×C1111yescharacteristic
758#95C23×C1111yescharacteristic
759#95C23×C1112yes—
760#95C23×C1112yes—
761#95C23×C1112yes—
762#95C23×C1112yes—
763#95C23×C1112yes—
764#95C23×C1112yes—
765#95C23×C1112yes—
766#95C23×C1112yes—
767#95C23×C1112yes—
768C2×C11—24no—
769C2×C11—42no—
770C2×C11—44no—
771C2×C11C2×C4×#4111yescharacteristic
772C2×C11C2×#52011yescharacteristic
773C2×C11C4×H(5,𝔽2)11yescharacteristic
774C2×C11#350511yescharacteristic
775C2×C11#351111yescharacteristic
776C2×C11#351511yescharacteristic
777C2×C11#351911yescharacteristic
778C24C24×C1112yes—
779C24C24×C1111yescharacteristic
780C24C24×C1111yescharacteristic
781C2×D4—22no—
782C2×D4—24no—
783C2×D4—22no—
784C2×D4—24no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4C22×C4×C1118yes—
790C2×D4C22×C4×C1114yes—
791C2×D4C22×C4×C1114yes—
792C2×D4C22×C4×C1118yes—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4C22×C4×C1114yes—
822C22×C4C22×C4×C1114yes—
823C22×C4C22×C4×C1118yes—
824C22×C4C22×C4×C1118yes—
825C22×C4C11×#4114yes—
826C22×C4C24×C1111yescharacteristic
827C22×C4C24×C1112yes—
828C22×C4C24×C1111yescharacteristic
829C22×C4C24×C1112yes—
830C22×C4C24×C1112yes—
831C22×C4C24×C1111yescharacteristic
832C22×C4C24×C1112yes—
833C22×C4C24×C1111yescharacteristic
834C22×C4C24×C1111yescharacteristic
835C22×C4C24×C1112yes—
836C22×C4C24×C1111yescharacteristic
837C22×C4C24×C1111yescharacteristic
838C22×C4C24×C1112yes—
839C22×C4C24×C1112yes—
840C22×C4C24×C1111yescharacteristic
841C22×C4C24×C1111yescharacteristic
842C22×C4C24×C1111yescharacteristic
843C22×C4C24×C1111yescharacteristic
844C22×C4C24×C1111yescharacteristic
845C22×C4C24×C1111yescharacteristic
846C4⋊C4—22no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4C22×C4×C1114yes—
862C4⋊C4C22×C4×C1114yes—
863C4⋊C4C22×C4×C1118yes—
864C4⋊C4C22×C4×C1114yes—
865C4⋊C4C22×C4×C1118yes—
866C4⋊C4C22×C4×C1114yes—
867C4⋊C4C22×C4×C1118yes—
868C22⋊C4—22no—
869C22⋊C4—24no—
870C22⋊C4—22no—
871C22⋊C4—24no—
872C22⋊C4—22no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—42no—
878C22⋊C4—42no—
879C22⋊C4—42no—
880C22⋊C4C22×C4×C1118yes—
881C22⋊C4C22×C4×C1114yes—
882C22⋊C4C22×C4×C1118yes—
883C22⋊C4C22×C4×C1118yes—
884C22⋊C4C22×C4×C1114yes—
885C22⋊C4C22×C4×C1118yes—
886C22⋊C4C11×#4114yes—
887C42—22no—
888C42—24no—
889C42—22no—
890C42—24no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—22no—
895C42—22no—
896C42—41no—
897C42—41no—
898C42—41no—
899C42—41no—
900C42—42no—
901C42—42no—
902C42—42no—
903C42—41no—
904C42—42no—
905C42C22×C4×C1118yes—
906C42C22×C4×C1114yes—
907C11#3432311yescharacteristic, direct product factor, Sylow
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—22no—
914C23—21no—
915C23—22no—
916C23—22no—
917C23—21no—
918C23—21no—
919C23—22no—
920C23—21no—
921C23—22no—
922C23—22no—
923C23—21no—
924C23C23×C4×C1112yes—
925C23C23×C4×C1114yes—
926C23C23×C4×C1112yes—
927C23C2×C11×#4112yes—
928C23C2×C11×#4112yes—
929C23C25×C1111yescharacteristic
930D4—216no—
931D4—28no—
932D4—28no—
933D4—48no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—28no—
959C2×C4—28no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—48no—
982C2×C4—48no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—44no—
987C2×C4—84no—
988C2×C4—84no—
989C2×C4—84no—
990C2×C4C23×C4×C1112yes—
991C2×C4C23×C4×C1114yes—
992C2×C4C23×C4×C1112yes—
993C2×C4C23×C4×C1114yes—
994C2×C4C23×C4×C1112yes—
995C2×C4C23×C4×C1112yes—
996C2×C4C23×C4×C1114yes—
997C2×C4C23×C4×C1112yes—
998C2×C4C2×C11×#4112yes—
999C2×C4C2×C11×#4112yes—
1000C2×C4C2×C11×#4112yes—
1001C2×C4C2×C11×#4112yes—
1002C2×C4C11×H(5,𝔽2)12yes—
1003C2×C4C11×H(5,𝔽2)12yes—
1004C2×C4C11×2−1+412yes—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—24no—
1013C22—22no—
1014C22—24no—
1015C22—24no—
1016C22—22no—
1017C22—41no—
1018C22—42no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—42no—
1025C22C4×C11×#4114yes—
1026C22C24×C4×C1111yescharacteristic
1027C22C22×C11×#4111yescharacteristic
1028C22C22×C11×#4111yescharacteristic
1029C22C2×C11×H(5,𝔽2)11yescharacteristic
1030C22C2×C11×H(5,𝔽2)11yescharacteristic
1031C22C2×C11×2−1+411yescharacteristic
1032C22C11×#58511yescharacteristic
1033C4—24no—
1034C4—22no—
1035C4—22no—
1036C4—22no—
1037C4—22no—
1038C4—24no—
1039C4—24no—
1040C4—22no—
1041C4—22no—
1042C4—22no—
1043C4—22no—
1044C4—22no—
1045C4—41no—
1046C4—42no—
1047C4—41no—
1048C4—42no—
1049C4—41no—
1050C4—42no—
1051C4—42no—
1052C4C11×#52014yes—
1053C2—24no—
1054C2—42no—
1055C2—44no—
1056C2C2×C4×C11×#4111yescharacteristic
1057C2C2×C11×#52011yescharacteristic
1058C2C4×C11×H(5,𝔽2)11yescharacteristic
1059C2C11×#350511yescharacteristic
1060C2C11×#351111yescharacteristic
1061C2C11×#351511yescharacteristic
1062C2C11×#351911yescharacteristic
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×#2373C2semidirect
3. C11×#2370C2semidirect
4. C11×#2363C2semidirect
5. C11×#2361C2semidirect
6. C11×#2361C2semidirect
7. C11×#2359C2semidirect
8. C11×#2352C2semidirect
9. C11×#2352C2semidirect
10. C11×#2349C2semidirect
11. C11×#2346C2semidirect
12. C11×#2345C2semidirect
13. C11×#2335C2semidirect
14. C11×#2334C2semidirect
15. C11×#2325C2semidirect
16. C4×C11×#125C2semidirect
17. C4×C11×#121C2semidirect
18. C4×C11×#121C2semidirect
19. C11×#2296C2semidirect
20. C11×#2293C2semidirect
21. C2×C11×#389C2semidirect
22. C11×#2275C2semidirect
23. C42×D4×C11C2semidirect
24. C11×#553C4semidirect
139. C11×#126C2×C4semidirect
140. C11×#125C2×C4semidirect
141. C11×#123C2×C4semidirect
142. C11×#121C2×C4semidirect
143. C11×#121C2×C4semidirect
144. C11×#121C2×C4semidirect
152. C4×D4×C11C2×C4semidirect
153. C4×D4×C11C2×C4semidirect
154. C4×D4×C11C2×C4semidirect
157. C11×#117C2×C4semidirect
160. C2×C11×C4⋊C4C2×C4semidirect
247. #34323C11direct (N × H)
378. #2373C2×C11semidirect
379. #2370C2×C11semidirect
380. #2363C2×C11semidirect
381. #2361C2×C11semidirect
382. #2361C2×C11semidirect
383. #2359C2×C11semidirect
384. #2352C2×C11semidirect
385. #2352C2×C11semidirect
386. #2349C2×C11semidirect
387. #2346C2×C11semidirect
388. #2345C2×C11semidirect
389. #2335C2×C11semidirect
390. #2334C2×C11semidirect
391. #2325C2×C11semidirect
392. C4×#125C2×C11semidirect
393. C4×#121C2×C11semidirect
394. C4×#121C2×C11semidirect
395. #2296C2×C11semidirect
396. #2293C2×C11semidirect
397. C2×#389C2×C11semidirect
398. #2275C2×C11semidirect
399. C42×D4C2×C11semidirect
497. #553C4×C11semidirect
660. #126C2×C4×C11semidirect
661. #125C2×C4×C11semidirect
662. #123C2×C4×C11semidirect
663. #121C2×C4×C11semidirect
664. #121C2×C4×C11semidirect
665. #121C2×C4×C11semidirect
673. C4×D4C2×C4×C11semidirect
674. C4×D4C2×C4×C11semidirect
675. C4×D4C2×C4×C11semidirect
678. #117C2×C4×C11semidirect
681. C2×C4⋊C4C2×C4×C11semidirect
907. C11#34323direct (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×#23732
C11×#23702
C11×#23632
C11×#23612
C11×#23592
C11×#23522
C11×#23492
C11×#23462
C11×#23452
C11×#23352
C11×#23342
C11×#23252
C4×C11×#1252
C4×C11×#1212
C11×#22962
C11×#22932
C2×C11×#3892
C11×#22752
C42×D4×C112
#3432311