Finite Group Databasebeta

← C11×#21489 #14598682

Subgroups — C11×#21489 #14598682

Order 2816.

1116 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×#435C211yesmaximal, characteristic, complemented
2C2×C11×#435C211yesmaximal, characteristic, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic, complemented
4C22×C11×#97C211yesmaximal, characteristic, complemented
5C4×C11×#121C211yesmaximal, characteristic
6C11×#1955C211yesmaximal, characteristic, complemented
7C11×#1940C211yesmaximal, characteristic, complemented
8C11×#1924C211yesmaximal, characteristic, complemented
9C11×#1924C211yesmaximal, characteristic, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1797C211yesmaximal, characteristic, complemented
13C11×#1771C211yesmaximal, characteristic, complemented
14C11×#1753C211yesmaximal, characteristic, complemented
15C11×#1752C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#121C411yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C11×#435—24no—
26C11×#435—24no—
27C8×D4×C11—24no—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×#97—24no—
41C2×C11×#97C2211yescharacteristic
42C2×C11×#97C2211yescharacteristic
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—
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—22no—
79C22×C8×C11—22no—
80C22×C8×C11—22no—
81C22×C8×C11—22no—
82C22×C8×C11D414yescomplemented
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×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8—22no—
132C11×C22⋊C8—22no—
133C11×#97—22no—
134C11×#97—22no—
135C11×#97—22no—
136C11×#97—22no—
137C11×#97D414yescomplemented
138C4×C8×C11—22no—
139C11×#95C2×C411yescharacteristic
140C11×#95C2×C411yescharacteristic
141C11×#95C2×C411yescharacteristic
142C11×#95C2×C411yescharacteristic
143C11×#95C2×C411yescharacteristic
144C11×#95C2×C411yescharacteristic
145#21489C1111yesmaximal, 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—22no—
156C2×D4×C11—41no—
157C2×D4×C11M1614yescomplemented
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—22no—
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—21no—
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—
195C2×C8×C11—28no—
196C2×C8×C11—28no—
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—44no—
216C2×C8×C11C2×D412yes—
217C2×C8×C11C2×D412yes—
218C2×C8×C11C2×D412yes—
219C2×C8×C11C2×D412yes—
220C2×C8×C11#4112yes—
221C2×C8×C11#4112yes—
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—22no—
235C11×C22⋊C4—41no—
236C11×C22⋊C4—41no—
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×#435C2×C1111yescharacteristic, complemented
248C2×#435C2×C1111yescharacteristic, complemented
249C2×C8×D4C2×C1111yescharacteristic, complemented
250C22×#97C2×C1111yescharacteristic, complemented
251C4×#121C2×C1111yescharacteristic
252#1955C2×C1111yescharacteristic, complemented
253#1940C2×C1111yescharacteristic, complemented
254#1924C2×C1111yescharacteristic, complemented
255#1924C2×C1111yescharacteristic, complemented
256#1869C2×C1111yescharacteristic, complemented
257#1869C2×C1111yescharacteristic, complemented
258#1797C2×C1111yescharacteristic, complemented
259#1771C2×C1111yescharacteristic, complemented
260#1753C2×C1111yescharacteristic, complemented
261#1752C2×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×C11C4×D412yes—
280C23×C11C2×M1612yes—
281C23×C11C2×M1612yes—
282C23×C11#13112yes—
283C23×C11C23×C411yescharacteristic
284D4×C11—28no—
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—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
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—21no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
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×C11—41no—
330C2×C4×C11C4×D412yes—
331C2×C4×C11C4×D412yes—
332C2×C4×C11C4×D412yes—
333C2×C4×C11C2×M1612yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—22no—
343C8×C11—41no—
344C8×C11—41no—
345C8×C11—41no—
346C8×C11—41no—
347C8×C11#12114yescomplemented
348C22×M16C22×C1111yescharacteristic
349C23×C8C22×C1111yescharacteristic
350C23×C8C22×C1111yescharacteristic
351C23×C8C22×C1111yescharacteristic
352C2×#121C4×C1111yescharacteristic
353C2×C4×D4C22×C1111yescharacteristic
354C2×C4×D4C22×C1111yescharacteristic
355C2×C4×D4C22×C1111yescharacteristic
356C22×C42C22×C1111yescharacteristic
357#435—24no—
358#435—24no—
359C8×D4—24no—
360C2×C4⋊C8C22×C1111yescharacteristic
361C2×C4⋊C8C22×C1111yescharacteristic
362C2×C4⋊C8C22×C1111yescharacteristic
363C2×C4⋊C8C22×C1111yescharacteristic
364C2×C22⋊C8C22×C1111yescharacteristic
365C2×C22⋊C8C22×C1111yescharacteristic
366C2×C22⋊C8C22×C1111yescharacteristic
367C2×C22⋊C8C22×C1111yescharacteristic
368C2×C22⋊C8C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×C22⋊C8C22×C1111yescharacteristic
371C2×C22⋊C8C22×C1111yescharacteristic
372C2×#97—24no—
373C2×#97C22×C1111yescharacteristic
374C2×#97C22×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—22no—
402C22×C11—22no—
403C22×C11—22no—
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#43514yescomplemented
416C22×C11C2×C4×D411yescharacteristic
417C22×C11C2×C4×D411yescharacteristic
418C22×C11C4×#4111yescharacteristic
419C22×C11C22×M1611yescharacteristic
420C22×C11C2×#13111yescharacteristic
421C22×C11#56811yescharacteristic
422C22×C11#56811yescharacteristic
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—41no—
433C4×C11—41no—
434C4×C11C2×#12111yescharacteristic
435C4×C11#52511yescharacteristic
436C4×C11#52911yescharacteristic
437C4×C11#53211yescharacteristic
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—
449C22×C8—22no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—22no—
453C22×C8—22no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—22no—
457C22×C8D4×C1114yescomplemented
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—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508#97—22no—
509#97—22no—
510#97—22no—
511#97—22no—
512#97D4×C1114yescomplemented
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—24no—
521C2×C11—42no—
522C2×C11—81no—
523C2×C11C4×#12111yescharacteristic
524C2×C11C2×#43511yescharacteristic
525C2×C11#293211yescharacteristic
526C2×C11#293311yescharacteristic
527C2×C11D4×M1611yescharacteristic
528C2×C11#296811yescharacteristic
529C2×C11#297011yescharacteristic
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—22no—
540C2×D4—41no—
541C2×D4C11×M1614yescomplemented
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
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—21no—
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—
579C2×C8—28no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—28no—
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—44no—
600C2×C8C2×D4×C1112yes—
601C2×C8C2×D4×C1112yes—
602C2×C8C2×D4×C1112yes—
603C2×C8C2×D4×C1112yes—
604C2×C8C11×#4112yes—
605C2×C8C11×#4112yes—
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—22no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C42—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42C2×D4×C1112yes—
630C42C11×#4112yes—
631C11#2148911yescharacteristic, 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—
649C23C4×D4×C1112yes—
650C23C2×C11×M1612yes—
651C23C2×C11×M1612yes—
652C23C11×#13112yes—
653C23C23×C4×C1111yescharacteristic
654D4—28no—
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—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
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—21no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4C4×D4×C1112yes—
701C2×C4C4×D4×C1112yes—
702C2×C4C4×D4×C1112yes—
703C2×C4C2×C11×M1612yes—
704C2×C4C22×D4×C1111yescharacteristic
705C2×C4C22×D4×C1111yescharacteristic
706C2×C4C2×C11×#4111yescharacteristic
707C2×C4C2×C11×#4111yescharacteristic
708C2×C4C2×C11×#4111yescharacteristic
709C2×C4C2×C11×#4111yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8C11×#12114yescomplemented
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22C11×#43514yescomplemented
739C22C2×C4×D4×C1111yescharacteristic
740C22C2×C4×D4×C1111yescharacteristic
741C22C4×C11×#4111yescharacteristic
742C22C22×C11×M1611yescharacteristic
743C22C2×C11×#13111yescharacteristic
744C22C11×#56811yescharacteristic
745C22C11×#56811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4C2×C11×#12111yescharacteristic
758C4C11×#52511yescharacteristic
759C4C11×#52911yescharacteristic
760C4C11×#53211yescharacteristic
761C2—24no—
762C2—42no—
763C2—81no—
764C2C4×C11×#12111yescharacteristic
765C2C2×C11×#43511yescharacteristic
766C2C11×#293211yescharacteristic
767C2C11×#293311yescharacteristic
768C2D4×C11×M1611yescharacteristic
769C2C11×#296811yescharacteristic
770C2C11×#297011yescharacteristic
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×#435C2semidirect
2. C2×C11×#435C2semidirect
3. C2×C8×D4×C11C2semidirect
4. C22×C11×#97C2semidirect
6. C11×#1955C2semidirect
7. C11×#1940C2semidirect
8. C11×#1924C2semidirect
9. C11×#1924C2semidirect
10. C11×#1869C2semidirect
11. C11×#1869C2semidirect
12. C11×#1797C2semidirect
13. C11×#1771C2semidirect
14. C11×#1753C2semidirect
15. C11×#1752C2semidirect
82. C22×C8×C11D4semidirect
137. C11×#97D4semidirect
145. #21489C11direct (N × H)
157. C2×D4×C11M16semidirect
247. C2×#435C2×C11semidirect
248. C2×#435C2×C11semidirect
249. C2×C8×D4C2×C11semidirect
250. C22×#97C2×C11semidirect
252. #1955C2×C11semidirect
253. #1940C2×C11semidirect
254. #1924C2×C11semidirect
255. #1924C2×C11semidirect
256. #1869C2×C11semidirect
257. #1869C2×C11semidirect
258. #1797C2×C11semidirect
259. #1771C2×C11semidirect
260. #1753C2×C11semidirect
261. #1752C2×C11semidirect
347. C8×C11#121semidirect
415. C22×C11#435semidirect
457. C22×C8D4×C11semidirect
512. #97D4×C11semidirect
541. C2×D4C11×M16semidirect
631. C11#21489direct (N × H)
717. C8C11×#121semidirect
738. C22C11×#435semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C2×C8×D4×C112
C22×C11×#972
C4×C11×#1212
C11×#19552
C11×#19402
C11×#19242
C11×#18692
C11×#17972
C11×#17712
C11×#17532
C11×#17522
#2148911