Finite Group Databasebeta

← C11×#22988 #14600181

Subgroups — C11×#22988 #14600181

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#436C211yesmaximal, characteristic, complemented
2C2×C11×#435C211yesmaximal, characteristic, complemented
3C2×C11×#435C211yesmaximal, characteristic, complemented
4C2×C11×#423C211yesmaximal, characteristic, complemented
5C4×C11×#121C211yesmaximal, characteristic
6C11×#1955C211yesmaximal, characteristic, complemented
7C11×#1940C211yesmaximal, characteristic, complemented
8C11×#1924C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1870C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1771C211yesmaximal, characteristic, complemented
15C11×#1749C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#121C411yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C11×#436—24no—
26C11×#435—24no—
27C11×#435—24no—
28C11×#423—24no—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43C2×C11×#97C2211yescharacteristic
44C2×C11×#97C2211yescharacteristic
45C2×C11×#97C2211yescharacteristic
46C2×C4×C8×C11C2211yescharacteristic
47C11×#390C411yescharacteristic
48C11×#389C411yescharacteristic
49C11×#388C411yescharacteristic
50C11×#388C411yescharacteristic
51C11×#386C411yescharacteristic
52C11×#386C411yescharacteristic
53C11×#380C411yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C23×C4×C11C2×C411yescharacteristic
67C23×C4×C11C2×C411yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C2×C11×M16—41no—
78C2×C11×M16—41no—
79C2×C11×M16—41no—
80C22×C8×C11—22no—
81C22×C8×C11—22no—
82C22×C8×C11—41no—
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×#121—24no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C2×C11×C4⋊C4C2×C411yescharacteristic
99C2×C11×C4⋊C4C2×C411yescharacteristic
100C2×C11×C4⋊C4C2×C411yescharacteristic
101C2×C11×C4⋊C4C2×C411yescharacteristic
102C2×C11×C4⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C11×C22⋊C4C2×C411yescharacteristic
107C2×C11×C22⋊C4C2×C411yescharacteristic
108C2×C11×C22⋊C4C2×C411yescharacteristic
109C2×C11×C22⋊C4C2×C411yescharacteristic
110C2×C11×C22⋊C4C2×C411yescharacteristic
111C2×C11×C22⋊C4C2×C411yescharacteristic
112C2×C11×C22⋊C4C2×C411yescharacteristic
113C2×C42×C11—22no—
114C2×C42×C11—22no—
115C2×C42×C11C2×C411yescharacteristic
116C2×C42×C11C2×C411yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C4⋊C8—22no—
125C11×C4⋊C8—22no—
126C11×C4⋊C8D414yescomplemented
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8—22no—
132C11×C22⋊C8—41no—
133C11×C22⋊C8—41no—
134C11×C22⋊C8D414yescomplemented
135C11×#97—22no—
136C11×#97—22no—
137C11×#97—22no—
138C4×C8×C11—22no—
139C11×#95C2×C411yescharacteristic
140C11×#95C2×C411yescharacteristic
141C11×#95C2×C411yescharacteristic
142C11×#95C2×C411yescharacteristic
143C11×#95C2×C411yescharacteristic
144C11×#95C2×C411yescharacteristic
145#22988C1111yesmaximal, characteristic, direct product factor, Sylow
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C24×C11C22×C411yescharacteristic
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11—41no—
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C2×D412yes—
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
194C11×M16—44no—
195C11×M16—44no—
196C11×M16—44no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—44no—
218C2×C8×C11C2×D412yes—
219C2×C8×C11C2×D412yes—
220C2×C8×C11C2×D412yes—
221C2×C8×C11C2×D412yes—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—22no—
226C11×C4⋊C4—41no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—41no—
235C11×C22⋊C4—41no—
236C11×C22⋊C4M1614yescomplemented
237C42×C11—22no—
238C42×C11—22no—
239C42×C11—21no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—21no—
245C42×C11C2×D412yes—
246C42×C11#4112yes—
247C2×#436C2×C1111yescharacteristic, complemented
248C2×#435C2×C1111yescharacteristic, complemented
249C2×#435C2×C1111yescharacteristic, complemented
250C2×#423C2×C1111yescharacteristic, complemented
251C4×#121C2×C1111yescharacteristic
252#1955C2×C1111yescharacteristic, complemented
253#1940C2×C1111yescharacteristic, complemented
254#1924C2×C1111yescharacteristic, complemented
255#1923C2×C1111yescharacteristic, complemented
256#1870C2×C1111yescharacteristic, complemented
257#1870C2×C1111yescharacteristic, complemented
258#1851C2×C1111yescharacteristic, complemented
259#1850C2×C1111yescharacteristic, complemented
260#1771C2×C1111yescharacteristic, complemented
261#1749C2×C1111yescharacteristic, complemented
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11C4×D412yes—
282C23×C11C2×M1612yes—
283C23×C11C23×C411yescharacteristic
284D4×C11—44no—
285D4×C11—44no—
286D4×C11—44no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—44no—
320C2×C4×C11—44no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11C4×D412yes—
330C2×C4×C11C4×D412yes—
331C2×C4×C11C4×D412yes—
332C2×C4×C11C2×M1612yes—
333C2×C4×C11C2×M1612yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C112−1+411yescharacteristic
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—22no—
343C8×C11—22no—
344C8×C11—41no—
345C8×C11—41no—
346C8×C11—41no—
347C8×C11—41no—
348C22×M16C22×C1111yescharacteristic
349C22×M16C22×C1111yescharacteristic
350C22×M16C22×C1111yescharacteristic
351C23×C8C22×C1111yescharacteristic
352C2×#121C4×C1111yescharacteristic
353C2×C4×D4C22×C1111yescharacteristic
354C2×C4×D4C22×C1111yescharacteristic
355C2×C4×D4C22×C1111yescharacteristic
356C22×C42C22×C1111yescharacteristic
357#436—24no—
358#435—24no—
359#435—24no—
360#423—24no—
361C2×C4⋊C8C22×C1111yescharacteristic
362C2×C4⋊C8C22×C1111yescharacteristic
363C2×C4⋊C8C22×C1111yescharacteristic
364C2×C4⋊C8C22×C1111yescharacteristic
365C2×C4⋊C8C22×C1111yescharacteristic
366C2×C4⋊C8C22×C1111yescharacteristic
367C2×C22⋊C8C22×C1111yescharacteristic
368C2×C22⋊C8C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×C22⋊C8C22×C1111yescharacteristic
371C2×C22⋊C8C22×C1111yescharacteristic
372C2×C22⋊C8C22×C1111yescharacteristic
373C2×C22⋊C8C22×C1111yescharacteristic
374C2×C22⋊C8C22×C1111yescharacteristic
375C2×#97C22×C1111yescharacteristic
376C2×#97C22×C1111yescharacteristic
377C2×#97C22×C1111yescharacteristic
378C2×C4×C8C22×C1111yescharacteristic
379#390C4×C1111yescharacteristic
380#389C4×C1111yescharacteristic
381#388C4×C1111yescharacteristic
382#388C4×C1111yescharacteristic
383#386C4×C1111yescharacteristic
384#386C4×C1111yescharacteristic
385#380C4×C1111yescharacteristic
386C4×C4⋊C4C22×C1111yescharacteristic
387C4×C22⋊C4C22×C1111yescharacteristic
388C4×C22⋊C4C22×C1111yescharacteristic
389#336C22×C1111yescharacteristic
390#336C22×C1111yescharacteristic
391#336C22×C1111yescharacteristic
392#336C22×C1111yescharacteristic
393#336C22×C1111yescharacteristic
394#336C22×C1111yescharacteristic
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11C2×C4×D411yescharacteristic
417C22×C11C2×C4×D411yescharacteristic
418C22×C11#52011yescharacteristic
419C22×C11C22×M1611yescharacteristic
420C22×C11#56811yescharacteristic
421C22×C11#56811yescharacteristic
422C22×C11#56811yescharacteristic
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—22no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—41no—
433C4×C11—41no—
434C4×C11D4211yescharacteristic
435C4×C11#54711yescharacteristic
436C4×C11#54811yescharacteristic
437C4×C11#55311yescharacteristic
438C22×D4C2×C4×C1111yescharacteristic
439C22×D4C2×C4×C1111yescharacteristic
440C22×D4C2×C4×C1111yescharacteristic
441C23×C4C2×C4×C1111yescharacteristic
442C23×C4C2×C4×C1111yescharacteristic
443C23×C4C23×C1111yescharacteristic
444C23×C4C23×C1111yescharacteristic
445C23×C4C23×C1111yescharacteristic
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—41no—
453C2×M16—41no—
454C2×M16—41no—
455C22×C8—22no—
456C22×C8—22no—
457C22×C8—41no—
458C22×C8C23×C1111yescharacteristic
459C22×C8C23×C1111yescharacteristic
460C22×C8C23×C1111yescharacteristic
461C22×C8C23×C1111yescharacteristic
462C22×C8C23×C1111yescharacteristic
463C22×C8C23×C1111yescharacteristic
464C22×C8C23×C1111yescharacteristic
465C22×C8C23×C1111yescharacteristic
466#121—24no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C2×C4⋊C4C2×C4×C1111yescharacteristic
474C2×C4⋊C4C2×C4×C1111yescharacteristic
475C2×C4⋊C4C2×C4×C1111yescharacteristic
476C2×C4⋊C4C2×C4×C1111yescharacteristic
477C2×C4⋊C4C2×C4×C1111yescharacteristic
478C2×C22⋊C4C2×C4×C1111yescharacteristic
479C2×C22⋊C4C2×C4×C1111yescharacteristic
480C2×C22⋊C4C2×C4×C1111yescharacteristic
481C2×C22⋊C4C2×C4×C1111yescharacteristic
482C2×C22⋊C4C2×C4×C1111yescharacteristic
483C2×C22⋊C4C2×C4×C1111yescharacteristic
484C2×C22⋊C4C2×C4×C1111yescharacteristic
485C2×C22⋊C4C2×C4×C1111yescharacteristic
486C2×C22⋊C4C2×C4×C1111yescharacteristic
487C2×C22⋊C4C2×C4×C1111yescharacteristic
488C2×C42—22no—
489C2×C42—22no—
490C2×C42C2×C4×C1111yescharacteristic
491C2×C42C2×C4×C1111yescharacteristic
492C2×C42C23×C1111yescharacteristic
493C2×C42C23×C1111yescharacteristic
494C2×C42C23×C1111yescharacteristic
495C2×C42C23×C1111yescharacteristic
496C4⋊C8—22no—
497C4⋊C8—22no—
498C4⋊C8—22no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8D4×C1114yescomplemented
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—41no—
508C22⋊C8—41no—
509C22⋊C8D4×C1114yescomplemented
510#97—22no—
511#97—22no—
512#97—22no—
513C4×C8—22no—
514#95C2×C4×C1111yescharacteristic
515#95C2×C4×C1111yescharacteristic
516#95C2×C4×C1111yescharacteristic
517#95C2×C4×C1111yescharacteristic
518#95C2×C4×C1111yescharacteristic
519#95C2×C4×C1111yescharacteristic
520C2×C11—42no—
521C2×C11—42no—
522C2×C11—81no—
523C2×C11#236111yescharacteristic
524C2×C11#293011yescharacteristic
525C2×C11#293211yescharacteristic
526C2×C11D4×M1611yescharacteristic
527C2×C11D4×M1611yescharacteristic
528C2×C11#298911yescharacteristic
529C2×C11#299511yescharacteristic
530C24C22×C4×C1111yescharacteristic
531C24C22×C4×C1111yescharacteristic
532C24C22×C4×C1111yescharacteristic
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—41no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4C22×C4×C1111yescharacteristic
565C22×C4C22×C4×C1111yescharacteristic
566C22×C4C22×C4×C1111yescharacteristic
567C22×C4C22×C4×C1111yescharacteristic
568C22×C4C22×C4×C1111yescharacteristic
569C22×C4C22×C4×C1111yescharacteristic
570C22×C4C22×C4×C1111yescharacteristic
571C22×C4C22×C4×C1111yescharacteristic
572C22×C4C22×C4×C1111yescharacteristic
573C22×C4C22×C4×C1111yescharacteristic
574C22×C4C22×C4×C1111yescharacteristic
575C22×C4C2×D4×C1112yes—
576C22×C4C11×#4112yes—
577C22×C4C24×C1111yescharacteristic
578M16—44no—
579M16—44no—
580M16—44no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—44no—
602C2×C8C2×D4×C1112yes—
603C2×C8C2×D4×C1112yes—
604C2×C8C2×D4×C1112yes—
605C2×C8C2×D4×C1112yes—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—41no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4C11×M1614yescomplemented
621C42—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42C2×D4×C1112yes—
630C42C11×#4112yes—
631C11#2298811yescharacteristic, direct product factor, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23C4×D4×C1112yes—
652C23C2×C11×M1612yes—
653C23C23×C4×C1111yescharacteristic
654D4—44no—
655D4—44no—
656D4—44no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4C4×D4×C1112yes—
700C2×C4C4×D4×C1112yes—
701C2×C4C4×D4×C1112yes—
702C2×C4C2×C11×M1612yes—
703C2×C4C2×C11×M1612yes—
704C2×C4C22×D4×C1111yescharacteristic
705C2×C4C22×D4×C1111yescharacteristic
706C2×C4C2×C11×#4111yescharacteristic
707C2×C4C2×C11×#4111yescharacteristic
708C2×C4C11×H(5,𝔽2)11yescharacteristic
709C2×C4C11×2−1+411yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—22no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22C2×C4×D4×C1111yescharacteristic
740C22C2×C4×D4×C1111yescharacteristic
741C22C11×#52011yescharacteristic
742C22C22×C11×M1611yescharacteristic
743C22C11×#56811yescharacteristic
744C22C11×#56811yescharacteristic
745C22C11×#56811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4D42×C1111yescharacteristic
758C4C11×#54711yescharacteristic
759C4C11×#54811yescharacteristic
760C4C11×#55311yescharacteristic
761C2—42no—
762C2—42no—
763C2—81no—
764C2C11×#236111yescharacteristic
765C2C11×#293011yescharacteristic
766C2C11×#293211yescharacteristic
767C2D4×C11×M1611yescharacteristic
768C2D4×C11×M1611yescharacteristic
769C2C11×#298911yescharacteristic
770C2C11×#299511yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#121C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#436C2semidirect
2. C2×C11×#435C2semidirect
3. C2×C11×#435C2semidirect
4. C2×C11×#423C2semidirect
6. C11×#1955C2semidirect
7. C11×#1940C2semidirect
8. C11×#1924C2semidirect
9. C11×#1923C2semidirect
10. C11×#1870C2semidirect
11. C11×#1870C2semidirect
12. C11×#1851C2semidirect
13. C11×#1850C2semidirect
14. C11×#1771C2semidirect
15. C11×#1749C2semidirect
126. C11×C4⋊C8D4semidirect
134. C11×C22⋊C8D4semidirect
145. #22988C11direct (N × H)
236. C11×C22⋊C4M16semidirect
247. C2×#436C2×C11semidirect
248. C2×#435C2×C11semidirect
249. C2×#435C2×C11semidirect
250. C2×#423C2×C11semidirect
252. #1955C2×C11semidirect
253. #1940C2×C11semidirect
254. #1924C2×C11semidirect
255. #1923C2×C11semidirect
256. #1870C2×C11semidirect
257. #1870C2×C11semidirect
258. #1851C2×C11semidirect
259. #1850C2×C11semidirect
260. #1771C2×C11semidirect
261. #1749C2×C11semidirect
501. C4⋊C8D4×C11semidirect
509. C22⋊C8D4×C11semidirect
620. C22⋊C4C11×M16semidirect
631. C11#22988direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4362
C2×C11×#4352
C2×C11×#4232
C4×C11×#1212
C11×#19552
C11×#19402
C11×#19242
C11×#19232
C11×#18702
C11×#18512
C11×#18502
C11×#17712
C11×#17492
#2298811