Finite Group Databasebeta

← C11×#22389 #14599582

Subgroups — C11×#22389 #14599582

Order 2816.

788 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#124C211yesmaximal, characteristic
2C11×#1985C211yesmaximal, characteristic, complemented
3C11×#1984C211yesmaximal, characteristic, complemented
4C11×#1924C211yesmaximal, characteristic, complemented
5C11×#1923C211yesmaximal, characteristic, complemented
6C11×#1923C211yesmaximal, characteristic, complemented
7C11×#1923C211yesmaximal, characteristic, complemented
8C11×#1870C211yesmaximal, characteristic
9C11×#1869C211yesmaximal, characteristic
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1850C211yesmaximal, characteristic, complemented
12C11×#1839C211yesmaximal, characteristic, complemented
13C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
14C11×#1753C211yesmaximal, characteristic, complemented
15C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#124C411yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C2×C4×C8×C11C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#391C411yescharacteristic
36C11×#390C411yescharacteristic
37C11×#388C411yescharacteristic
38C11×#388C411yescharacteristic
39C11×#388C411yescharacteristic
40C11×#388C411yescharacteristic
41C11×#382C411yescharacteristic
42C4×C11×C22⋊C4C2211yescharacteristic
43C4×C11×C22⋊C4C2211yescharacteristic
44C4×C11×C22⋊C4C2211yescharacteristic
45C4×C11×C22⋊C4C2211yescharacteristic
46C43×C11C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×Q8×C11C2×C411yescharacteristic
60C22×D4×C11C2×C411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—41no—
65C2×C11×M16—41no—
66C22×C8×C11—22no—
67C22×C8×C11—41no—
68C22×C8×C11—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#124—24no—
78C4×Q8×C11—41no—
79C4×Q8×C11—41no—
80C4×D4×C11—41no—
81C4×D4×C11—41no—
82C2×C11×C4⋊C4C2×C411yescharacteristic
83C2×C11×C4⋊C4C2×C411yescharacteristic
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C11×C22⋊C4C2×C411yescharacteristic
92C2×C11×C22⋊C4C2×C411yescharacteristic
93C2×C11×C22⋊C4C2×C411yescharacteristic
94C2×C11×C22⋊C4C2×C411yescharacteristic
95C2×C11×C22⋊C4C2×C411yescharacteristic
96C2×C42×C11C2×C411yescharacteristic
97C2×C42×C11C2×C411yescharacteristic
98C2×C42×C11C2×C411yescharacteristic
99C2×C42×C11C2×C411yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C11×C4⋊C8—22no—
106C11×C4⋊C8—22no—
107C11×C4⋊C8—41no—
108C11×C4⋊C8—41no—
109C11×C22⋊C8—22no—
110C11×C22⋊C8—22no—
111C11×C22⋊C8—41no—
112C11×C22⋊C8—41no—
113C11×C22⋊C8—41no—
114C11×C22⋊C8—41no—
115C11×#97—41no—
116C4×C8×C11—41no—
117C4×C8×C11—41no—
118C4×C8×C11—41no—
119C11×#95C2×C411yescharacteristic
120C11×#95C2×C411yescharacteristic
121C11×#95C2×C411yescharacteristic
122C11×#95C2×C411yescharacteristic
123C11×#95C2×C411yescharacteristic
124C11×#95C2×C411yescharacteristic
125C11×#95C2×C411yescharacteristic
126C11×#95C2×C411yescharacteristic
127#22389C1111yesmaximal, characteristic, direct product factor, Sylow
128C24×C11C22×C411yescharacteristic
129C24×C11C22×C411yescharacteristic
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—41no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—41no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C11×M16—44no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—44no—
185C2×C8×C11#4112yes—
186C2×C8×C11#4112yes—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4M1614yescomplemented
201C42×C11—22no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11—22no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C4×#124C2×C1111yescharacteristic
216#1985C2×C1111yescharacteristic, complemented
217#1984C2×C1111yescharacteristic, complemented
218#1924C2×C1111yescharacteristic, complemented
219#1923C2×C1111yescharacteristic, complemented
220#1923C2×C1111yescharacteristic, complemented
221#1923C2×C1111yescharacteristic, complemented
222#1870C2×C1111yescharacteristic
223#1869C2×C1111yescharacteristic
224#1851C2×C1111yescharacteristic, complemented
225#1850C2×C1111yescharacteristic, complemented
226#1839C2×C1111yescharacteristic, complemented
227C4×C4⋊C8C2×C1111yescharacteristic, complemented
228#1753C2×C1111yescharacteristic, complemented
229C8×C22⋊C4C2×C1111yescharacteristic, complemented
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11C2×M1612yes—
244C23×C11C23×C411yescharacteristic
245Q8×C11—44no—
246D4×C11—44no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11C2×M1612yes—
287C2×C4×C11C2×M1612yes—
288C2×C4×C11#13112yes—
289C2×C4×C11#13112yes—
290C2×C4×C11#13112yes—
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×C4×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C112−1+411yescharacteristic
297C8×C11—22no—
298C8×C11—22no—
299C8×C11—41no—
300C8×C11—41no—
301C8×C11—41no—
302C8×C11—41no—
303C8×C11—41no—
304C8×C11—41no—
305C22×M16C22×C1111yescharacteristic
306C23×C8C22×C1111yescharacteristic
307C2×#124C4×C1111yescharacteristic
308C2×C4×Q8C22×C1111yescharacteristic
309C2×C4×D4C22×C1111yescharacteristic
310C2×C4⋊C8C22×C1111yescharacteristic
311C2×C4⋊C8C22×C1111yescharacteristic
312C2×C4⋊C8C22×C1111yescharacteristic
313C2×C4⋊C8C22×C1111yescharacteristic
314C2×C22⋊C8C22×C1111yescharacteristic
315C2×C22⋊C8C22×C1111yescharacteristic
316C2×C22⋊C8C22×C1111yescharacteristic
317C2×C22⋊C8C22×C1111yescharacteristic
318C2×C22⋊C8C22×C1111yescharacteristic
319C2×C22⋊C8C22×C1111yescharacteristic
320C2×#97C22×C1111yescharacteristic
321C2×C4×C8C22×C1111yescharacteristic
322C2×C4×C8C22×C1111yescharacteristic
323C2×C4×C8C22×C1111yescharacteristic
324#391C4×C1111yescharacteristic
325#390C4×C1111yescharacteristic
326#388C4×C1111yescharacteristic
327#388C4×C1111yescharacteristic
328#388C4×C1111yescharacteristic
329#388C4×C1111yescharacteristic
330#382C4×C1111yescharacteristic
331C4×C22⋊C4C22×C1111yescharacteristic
332C4×C22⋊C4C22×C1111yescharacteristic
333C4×C22⋊C4C22×C1111yescharacteristic
334C4×C22⋊C4C22×C1111yescharacteristic
335C43C22×C1111yescharacteristic
336#336C22×C1111yescharacteristic
337#336C22×C1111yescharacteristic
338#336C22×C1111yescharacteristic
339#336C22×C1111yescharacteristic
340#336C22×C1111yescharacteristic
341#336C22×C1111yescharacteristic
342#336C22×C1111yescharacteristic
343#336C22×C1111yescharacteristic
344#336C22×C1111yescharacteristic
345#336C22×C1111yescharacteristic
346#336C22×C1111yescharacteristic
347#336C22×C1111yescharacteristic
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11C4×#4111yescharacteristic
363C22×C11#51811yescharacteristic
364C22×C11#52011yescharacteristic
365C22×C11C22×M1611yescharacteristic
366C22×C11C2×#13111yescharacteristic
367C22×C11C2×#13111yescharacteristic
368C22×C11C2×#13111yescharacteristic
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11#53811yescharacteristic
382C4×C11#53811yescharacteristic
383C4×C11#54211yescharacteristic
384C4×C11#54211yescharacteristic
385C22×Q8C2×C4×C1111yescharacteristic
386C22×D4C2×C4×C1111yescharacteristic
387C23×C4C23×C1111yescharacteristic
388C23×C4C23×C1111yescharacteristic
389C2×M16—22no—
390C2×M16—41no—
391C2×M16—41no—
392C22×C8—22no—
393C22×C8—41no—
394C22×C8—41no—
395C22×C8C23×C1111yescharacteristic
396C22×C8C23×C1111yescharacteristic
397C22×C8C23×C1111yescharacteristic
398C22×C8C23×C1111yescharacteristic
399C22×C8C23×C1111yescharacteristic
400C22×C8C23×C1111yescharacteristic
401C22×C8C23×C1111yescharacteristic
402C22×C8C23×C1111yescharacteristic
403#124—24no—
404C4×Q8—41no—
405C4×Q8—41no—
406C4×D4—41no—
407C4×D4—41no—
408C2×C4⋊C4C2×C4×C1111yescharacteristic
409C2×C4⋊C4C2×C4×C1111yescharacteristic
410C2×C4⋊C4C2×C4×C1111yescharacteristic
411C2×C4⋊C4C2×C4×C1111yescharacteristic
412C2×C22⋊C4C2×C4×C1111yescharacteristic
413C2×C22⋊C4C2×C4×C1111yescharacteristic
414C2×C22⋊C4C2×C4×C1111yescharacteristic
415C2×C22⋊C4C2×C4×C1111yescharacteristic
416C2×C22⋊C4C2×C4×C1111yescharacteristic
417C2×C22⋊C4C2×C4×C1111yescharacteristic
418C2×C22⋊C4C2×C4×C1111yescharacteristic
419C2×C22⋊C4C2×C4×C1111yescharacteristic
420C2×C22⋊C4C2×C4×C1111yescharacteristic
421C2×C22⋊C4C2×C4×C1111yescharacteristic
422C2×C42C2×C4×C1111yescharacteristic
423C2×C42C2×C4×C1111yescharacteristic
424C2×C42C2×C4×C1111yescharacteristic
425C2×C42C2×C4×C1111yescharacteristic
426C2×C42C23×C1111yescharacteristic
427C2×C42C23×C1111yescharacteristic
428C2×C42C23×C1111yescharacteristic
429C2×C42C23×C1111yescharacteristic
430C2×C42C23×C1111yescharacteristic
431C4⋊C8—22no—
432C4⋊C8—22no—
433C4⋊C8—41no—
434C4⋊C8—41no—
435C22⋊C8—22no—
436C22⋊C8—22no—
437C22⋊C8—41no—
438C22⋊C8—41no—
439C22⋊C8—41no—
440C22⋊C8—41no—
441#97—41no—
442C4×C8—41no—
443C4×C8—41no—
444C4×C8—41no—
445#95C2×C4×C1111yescharacteristic
446#95C2×C4×C1111yescharacteristic
447#95C2×C4×C1111yescharacteristic
448#95C2×C4×C1111yescharacteristic
449#95C2×C4×C1111yescharacteristic
450#95C2×C4×C1111yescharacteristic
451#95C2×C4×C1111yescharacteristic
452#95C2×C4×C1111yescharacteristic
453C2×C11—42no—
454C2×C11—81no—
455C2×C11#233711yescharacteristic
456C2×C11#296511yescharacteristic
457C2×C11#296611yescharacteristic
458C2×C11#297411yescharacteristic
459C2×C11#297911yescharacteristic
460C2×C11#299011yescharacteristic
461C2×C11#299411yescharacteristic
462C24C22×C4×C1111yescharacteristic
463C24C22×C4×C1111yescharacteristic
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—41no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—41no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4C22×C4×C1111yescharacteristic
483C22×C4C22×C4×C1111yescharacteristic
484C22×C4C22×C4×C1111yescharacteristic
485C22×C4C22×C4×C1111yescharacteristic
486C22×C4C22×C4×C1111yescharacteristic
487C22×C4C22×C4×C1111yescharacteristic
488C22×C4C22×C4×C1111yescharacteristic
489C22×C4C22×C4×C1111yescharacteristic
490C22×C4C22×C4×C1111yescharacteristic
491C22×C4C22×C4×C1111yescharacteristic
492C22×C4C22×C4×C1111yescharacteristic
493C22×C4C22×C4×C1111yescharacteristic
494C22×C4C24×C1111yescharacteristic
495M16—44no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—44no—
519C2×C8C11×#4112yes—
520C2×C8C11×#4112yes—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4C11×M1614yescomplemented
535C42—22no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C11#2238911yescharacteristic, direct product factor, Sylow
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23C2×C11×M1612yes—
564C23C23×C4×C1111yescharacteristic
565Q8—44no—
566D4—44no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4C2×C11×M1612yes—
607C2×C4C2×C11×M1612yes—
608C2×C4C11×#13112yes—
609C2×C4C11×#13112yes—
610C2×C4C11×#13112yes—
611C2×C4C2×C11×#4111yescharacteristic
612C2×C4C2×C11×#4111yescharacteristic
613C2×C4C11×H(5,𝔽2)11yescharacteristic
614C2×C4C11×H(5,𝔽2)11yescharacteristic
615C2×C4C11×H(5,𝔽2)11yescharacteristic
616C2×C4C11×2−1+411yescharacteristic
617C8—22no—
618C8—22no—
619C8—41no—
620C8—41no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C4×C11×#4111yescharacteristic
640C22C11×#51811yescharacteristic
641C22C11×#52011yescharacteristic
642C22C22×C11×M1611yescharacteristic
643C22C2×C11×#13111yescharacteristic
644C22C2×C11×#13111yescharacteristic
645C22C2×C11×#13111yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4C11×#53811yescharacteristic
659C4C11×#53811yescharacteristic
660C4C11×#54211yescharacteristic
661C4C11×#54211yescharacteristic
662C2—42no—
663C2—81no—
664C2C11×#233711yescharacteristic
665C2C11×#296511yescharacteristic
666C2C11×#296611yescharacteristic
667C2C11×#297411yescharacteristic
668C2C11×#297911yescharacteristic
669C2C11×#299011yescharacteristic
670C2C11×#299411yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1985C2semidirect
3. C11×#1984C2semidirect
4. C11×#1924C2semidirect
5. C11×#1923C2semidirect
6. C11×#1923C2semidirect
7. C11×#1923C2semidirect
10. C11×#1851C2semidirect
11. C11×#1850C2semidirect
12. C11×#1839C2semidirect
13. C4×C11×C4⋊C8C2semidirect
14. C11×#1753C2semidirect
15. C8×C11×C22⋊C4C2semidirect
127. #22389C11direct (N × H)
200. C11×C22⋊C4M16semidirect
216. #1985C2×C11semidirect
217. #1984C2×C11semidirect
218. #1924C2×C11semidirect
219. #1923C2×C11semidirect
220. #1923C2×C11semidirect
221. #1923C2×C11semidirect
224. #1851C2×C11semidirect
225. #1850C2×C11semidirect
226. #1839C2×C11semidirect
227. C4×C4⋊C8C2×C11semidirect
228. #1753C2×C11semidirect
229. C8×C22⋊C4C2×C11semidirect
534. C22⋊C4C11×M16semidirect
549. C11#22389direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1242
C11×#19852
C11×#19842
C11×#19242
C11×#19232
C11×#18702
C11×#18692
C11×#18512
C11×#18502
C11×#18392
C4×C11×C4⋊C82
C11×#17532
C8×C11×C22⋊C42
#2238911