Finite Group Databasebeta

← C11×#22493 #14599686

Subgroups — C11×#22493 #14599686

Order 2816.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C2×C11×#435C211yesmaximal, characteristic, complemented
3D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4C11×#1992C211yesmaximal, characteristic, complemented
5C11×#1989C211yesmaximal, characteristic, complemented
6C11×#1895C211yesmaximal, characteristic, complemented
7C11×#1893C211yesmaximal, characteristic, complemented
8C11×#1874C211yesmaximal, characteristic, complemented
9C11×#1874C211yesmaximal, characteristic, complemented
10C11×#1825C211yesmaximal, characteristic, complemented
11C11×#1824C211yesmaximal, characteristic, complemented
12C11×#1802C211yesmaximal, characteristic, complemented
13C11×#1762C211yesmaximal, characteristic, complemented
14C11×#1736C211yesmaximal, characteristic, complemented
15C2×C11×#340C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C11×#553—24no—
19C11×#553C418yescomplemented
20C2×C11×#126—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C22×C11×C4⋊C4C2211yescharacteristic
34C11×#435—24no—
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C11×#97C2211yescharacteristic
43C11×#389—21no—
44C11×#385—21no—
45C11×#385—21no—
46C11×#384C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—41no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#126—28no—
83C11×#125—22no—
84C11×#125C2×C414yescomplemented
85C11×#123—28no—
86C11×#121—28no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121C2×C414yescomplemented
90C11×#121C2×C414yescomplemented
91C4×D4×C11—28no—
92C4×D4×C11—22no—
93C4×D4×C11—44no—
94C4×D4×C11C2×C414yes—
95C4×D4×C11C2×C414yescomplemented
96C4×D4×C11D414yes—
97C11×#117—22no—
98C11×#117C2×C414yescomplemented
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—41no—
110C2×C11×C4⋊C4—41no—
111C2×C11×C4⋊C4C2×C414yescomplemented
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4D411yescharacteristic
127C2×C11×C22⋊C4D411yescharacteristic
128C2×C42×C11—21no—
129C2×C42×C11—21no—
130C2×C42×C11C2311yescharacteristic
131C11×C4⋊C8—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—41no—
135C11×#102—41no—
136C11×C22⋊C8—22no—
137C11×C22⋊C8—22no—
138C11×#97—22no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142#22493C1111yesmaximal, characteristic, direct product factor, Sylow
143C24×C11—21no—
144C24×C11C2×D411yescharacteristic
145C24×C11C2×D411yescharacteristic
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11—81no—
158C2×D4×C11—81no—
159C2×D4×C11C22⋊C414yes—
160C2×D4×C11C22×C412yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
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—24no—
174C22×C4×C11—24no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—81no—
183C22×C4×C11—81no—
184C22×C4×C11—81no—
185C22×C4×C11—81no—
186C22×C4×C11—81no—
187C22×C4×C11—81no—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C22×C412yes—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2411yescharacteristic
197C11×M16—44no—
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—44no—
210C2×C8×C11#4112yes—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—42no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—81no—
228C11×C4⋊C4C22⋊C414yes—
229C11×C4⋊C4C22×C412yes—
230C11×C4⋊C4C22×C412yes—
231C11×C4⋊C4C22×C412yes—
232C11×C4⋊C4#4112yes—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4C22⋊C414yes—
240C11×C22⋊C4C22⋊C414yes—
241C42×C11—24no—
242C42×C11—42no—
243C42×C11C22×C412yes—
244C42×C11C2×D412yes—
245C2×#553C2×C1111yescharacteristic
246C2×#435C2×C1111yescharacteristic, complemented
247D4×C4⋊C4C2×C1111yescharacteristic, complemented
248#1992C2×C1111yescharacteristic, complemented
249#1989C2×C1111yescharacteristic, complemented
250#1895C2×C1111yescharacteristic, complemented
251#1893C2×C1111yescharacteristic, complemented
252#1874C2×C1111yescharacteristic, complemented
253#1874C2×C1111yescharacteristic, complemented
254#1825C2×C1111yescharacteristic, complemented
255#1824C2×C1111yescharacteristic, complemented
256#1802C2×C1111yescharacteristic, complemented
257#1762C2×C1111yescharacteristic, complemented
258#1736C2×C1111yescharacteristic, complemented
259C2×#340C2×C1111yescharacteristic, complemented
260C23×C11—21no—
261C23×C11—21no—
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—22no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11C2×C22⋊C412yes—
278C23×C11C2×C22⋊C412yes—
279C23×C11AGL(1,ℤ/8)12yes—
280C23×C11#13712yes—
281C23×C11C22×D411yescharacteristic
282D4×C11—28no—
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—48no—
286D4×C11—41no—
287D4×C11—41no—
288D4×C11—84no—
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—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—84no—
327C2×C4×C11—84no—
328C2×C4×C11—84no—
329C2×C4×C11—84no—
330C2×C4×C11C2×C22⋊C412yes—
331C2×C4×C11C2×C22⋊C412yes—
332C2×C4×C11C2×C22⋊C412yes—
333C2×C4×C11C2×C22⋊C412yes—
334C2×C4×C11C23×C411yescharacteristic
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—41no—
342C8×C11—41no—
343C8×C11—41no—
344C22×M16C22×C1111yescharacteristic
345C23×C8C22×C1111yescharacteristic
346#553—24no—
347#553C4×C1118yescomplemented
348C2×#126—21no—
349C2×#125C22×C1111yescharacteristic
350C2×#123—21no—
351C2×#121—21no—
352C2×#121C22×C1111yescharacteristic
353C2×#121C22×C1111yescharacteristic
354C2×C4×D4—21no—
355C2×C4×D4—21no—
356C2×C4×D4C22×C1111yescharacteristic
357C2×C4×D4C22×C1111yescharacteristic
358C2×#117C22×C1111yescharacteristic
359C22×C4⋊C4C22×C1111yescharacteristic
360C22×C4⋊C4C22×C1111yescharacteristic
361C22×C4⋊C4C22×C1111yescharacteristic
362#435—24no—
363C2×C4⋊C8C22×C1111yescharacteristic
364C2×#102C22×C1111yescharacteristic
365C2×#102C22×C1111yescharacteristic
366C2×#102C22×C1111yescharacteristic
367C2×#102C22×C1111yescharacteristic
368C2×C22⋊C8C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×#97C22×C1111yescharacteristic
371#389—21no—
372#385—21no—
373#385—21no—
374#384C22×C1111yescharacteristic
375#380C22×C1111yescharacteristic
376#380C22×C1111yescharacteristic
377C4×C4⋊C4C22×C1111yescharacteristic
378#340C22×C1111yescharacteristic
379#340C22×C1111yescharacteristic
380#340C22×C1111yescharacteristic
381#340C22×C1111yescharacteristic
382#340C22×C1111yescharacteristic
383#340C22×C1111yescharacteristic
384#340C22×C1111yescharacteristic
385#340C22×C1111yescharacteristic
386#340C22×C1111yescharacteristic
387#340C22×C1111yescharacteristic
388#340C22×C1111yescharacteristic
389#340C22×C1111yescharacteristic
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11#41714yes—
411C22×C11C22×C22⋊C411yescharacteristic
412C22×C11#54611yescharacteristic
413C22×C11#54711yescharacteristic
414C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C11C2×#13711yescharacteristic
416C22×C11#57611yescharacteristic
417C22×C11#57711yescharacteristic
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11C4×#4111yescharacteristic
430C4×C11#52011yescharacteristic
431C4×C11#54611yescharacteristic
432C4×C11#54711yescharacteristic
433C22×D4—21no—
434C22×D4—21no—
435C22×D4D4×C1111yescharacteristic
436C22×D4C23×C1111yescharacteristic
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—21no—
441C23×C4C23×C1111yescharacteristic
442C23×C4C23×C1111yescharacteristic
443C2×M16—22no—
444C2×M16—22no—
445C2×M16—41no—
446C22×C8—22no—
447C22×C8—22no—
448C22×C8—41no—
449C22×C8C23×C1111yescharacteristic
450C22×C8C23×C1111yescharacteristic
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453#126—28no—
454#125—22no—
455#125C2×C4×C1114yescomplemented
456#123—28no—
457#121—28no—
458#121—22no—
459#121—22no—
460#121C2×C4×C1114yescomplemented
461#121C2×C4×C1114yescomplemented
462C4×D4—28no—
463C4×D4—22no—
464C4×D4—44no—
465C4×D4C2×C4×C1114yes—
466C4×D4C2×C4×C1114yescomplemented
467C4×D4D4×C1114yes—
468#117—22no—
469#117C2×C4×C1114yescomplemented
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4C2×C4×C1114yescomplemented
483C2×C4⋊C4D4×C1111yescharacteristic
484C2×C4⋊C4C23×C1111yescharacteristic
485C2×C4⋊C4C23×C1111yescharacteristic
486C2×C4⋊C4C23×C1111yescharacteristic
487C2×C4⋊C4C23×C1111yescharacteristic
488C2×C4⋊C4C23×C1111yescharacteristic
489C2×C4⋊C4C23×C1111yescharacteristic
490C2×C4⋊C4C23×C1111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4D4×C1111yescharacteristic
498C2×C22⋊C4D4×C1111yescharacteristic
499C2×C42—21no—
500C2×C42—21no—
501C2×C42C23×C1111yescharacteristic
502C4⋊C8—22no—
503#102—22no—
504#102—22no—
505#102—41no—
506#102—41no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509#97—22no—
510#95—21no—
511#95—21no—
512#95—21no—
513C2×C11—24no—
514C2×C11—42no—
515C2×C11—82no—
516C2×C11#233911yescharacteristic
517C2×C11C2×#41711yescharacteristic
518C2×C11#289711yescharacteristic
519C2×C11#331811yescharacteristic
520C2×C11#332011yescharacteristic
521C2×C11#334511yescharacteristic
522C2×C11#334611yescharacteristic
523C24—21no—
524C24C2×D4×C1111yescharacteristic
525C24C2×D4×C1111yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—81no—
538C2×D4—81no—
539C2×D4C11×C22⋊C414yes—
540C2×D4C22×C4×C1112yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4C22×C4×C1112yes—
569C22×C4C22×C4×C1112yes—
570C22×C4C2×D4×C1111yescharacteristic
571C22×C4C2×D4×C1111yescharacteristic
572C22×C4C2×D4×C1111yescharacteristic
573C22×C4C2×D4×C1111yescharacteristic
574C22×C4C2×D4×C1112yes—
575C22×C4C2×D4×C1112yes—
576C22×C4C24×C1111yescharacteristic
577M16—44no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
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—44no—
590C2×C8C11×#4112yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—81no—
608C4⋊C4C11×C22⋊C414yes—
609C4⋊C4C22×C4×C1112yes—
610C4⋊C4C22×C4×C1112yes—
611C4⋊C4C22×C4×C1112yes—
612C4⋊C4C11×#4112yes—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4C11×C22⋊C414yes—
620C22⋊C4C11×C22⋊C414yes—
621C42—24no—
622C42—42no—
623C42C22×C4×C1112yes—
624C42C2×D4×C1112yes—
625C11#2249311yescharacteristic, direct product factor, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23C2×C11×C22⋊C412yes—
644C23C2×C11×C22⋊C412yes—
645C23C11×AGL(1,ℤ/8)12yes—
646C23C11×#13712yes—
647C23C22×D4×C1111yescharacteristic
648D4—28no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4C2×C11×C22⋊C412yes—
697C2×C4C2×C11×C22⋊C412yes—
698C2×C4C2×C11×C22⋊C412yes—
699C2×C4C2×C11×C22⋊C412yes—
700C2×C4C23×C4×C1111yescharacteristic
701C2×C4C22×D4×C1111yescharacteristic
702C2×C4C2×C11×#4111yescharacteristic
703C2×C4C2×C11×#4111yescharacteristic
704C2×C4C11×H(5,𝔽2)11yescharacteristic
705C2×C4C11×2−1+411yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C11×#41714yes—
731C22C22×C11×C22⋊C411yescharacteristic
732C22C11×#54611yescharacteristic
733C22C11×#54711yescharacteristic
734C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
735C22C2×C11×#13711yescharacteristic
736C22C11×#57611yescharacteristic
737C22C11×#57711yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C4×C11×#4111yescharacteristic
750C4C11×#52011yescharacteristic
751C4C11×#54611yescharacteristic
752C4C11×#54711yescharacteristic
753C2—24no—
754C2—42no—
755C2—82no—
756C2C11×#233911yescharacteristic
757C2C2×C11×#41711yescharacteristic
758C2C11×#289711yescharacteristic
759C2C11×#331811yescharacteristic
760C2C11×#332011yescharacteristic
761C2C11×#334511yescharacteristic
762C2C11×#334611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#553C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#435C2semidirect
3. D4×C11×C4⋊C4C2semidirect
4. C11×#1992C2semidirect
5. C11×#1989C2semidirect
6. C11×#1895C2semidirect
7. C11×#1893C2semidirect
8. C11×#1874C2semidirect
9. C11×#1874C2semidirect
10. C11×#1825C2semidirect
11. C11×#1824C2semidirect
12. C11×#1802C2semidirect
13. C11×#1762C2semidirect
14. C11×#1736C2semidirect
15. C2×C11×#340C2semidirect
19. C11×#553C4semidirect
84. C11×#125C2×C4semidirect
89. C11×#121C2×C4semidirect
90. C11×#121C2×C4semidirect
95. C4×D4×C11C2×C4semidirect
98. C11×#117C2×C4semidirect
111. C2×C11×C4⋊C4C2×C4semidirect
142. #22493C11direct (N × H)
246. C2×#435C2×C11semidirect
247. D4×C4⋊C4C2×C11semidirect
248. #1992C2×C11semidirect
249. #1989C2×C11semidirect
250. #1895C2×C11semidirect
251. #1893C2×C11semidirect
252. #1874C2×C11semidirect
253. #1874C2×C11semidirect
254. #1825C2×C11semidirect
255. #1824C2×C11semidirect
256. #1802C2×C11semidirect
257. #1762C2×C11semidirect
258. #1736C2×C11semidirect
259. C2×#340C2×C11semidirect
347. #553C4×C11semidirect
455. #125C2×C4×C11semidirect
460. #121C2×C4×C11semidirect
461. #121C2×C4×C11semidirect
466. C4×D4C2×C4×C11semidirect
469. #117C2×C4×C11semidirect
482. C2×C4⋊C4C2×C4×C11semidirect
625. C11#22493direct (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
C2×C11×#4352
D4×C11×C4⋊C42
C11×#19922
C11×#19892
C11×#18952
C11×#18932
C11×#18742
C11×#18252
C11×#18242
C11×#18022
C11×#17622
C11×#17362
C2×C11×#3402
#2249311