Finite Group Databasebeta

← C11×#22405 #14599598

Subgroups — C11×#22405 #14599598

Order 2816.

1668 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic
2C2×C11×#410C211yesmaximal, characteristic, complemented
3C22×C11×#99C211yesmaximal, characteristic, complemented
4C11×#2342C212yesmaximal, complemented
5C11×#1964C212yesmaximal, complemented
6C11×#1899C212yesmaximal, complemented
7C11×#1898C212yesmaximal, complemented
8C11×#1799C211yesmaximal, characteristic, complemented
9C11×#1782C211yesmaximal, characteristic, complemented
10C11×#1781C211yesmaximal, characteristic, complemented
11C4×C11×#99C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C11×#546—22no—
15C11×#546—22no—
16C11×#546—22no—
17C11×#546—22no—
18C2×C11×#124C411yescharacteristic, complemented
19C2×C11×#123C411yescharacteristic, complemented
20C2×C11×#123C2211yescharacteristic
21C2×C11×C22⋊Q8C411yescharacteristic, complemented
22C2×C11×#121C411yescharacteristic, complemented
23C2×C11×#121C411yescharacteristic, complemented
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120C411yescharacteristic, complemented
26C2×C11×#120C2211yescharacteristic
27C2×C4×D4×C11C411yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2212yescomplemented
30C22×C11×C22⋊C4C411yescharacteristic, complemented
31C22×C11×C22⋊C4C2212yes—
32C22×C11×C22⋊C4C2211yescharacteristic
33C11×#410—24no—
34C2×C11×#99—24no—
35C2×C11×#99C2212yes—
36C2×C11×#99C2211yescharacteristic
37C2×C11×#99C2211yescharacteristic
38C2×C11×#99C2211yescharacteristic
39C2×C11×#99C2212yes—
40C2×C11×#99C2211yescharacteristic
41C2×C11×#99C2212yescomplemented
42C2×C11×#99C2212yescomplemented
43C11×#388—22no—
44C11×#388—22no—
45C11×#385—22no—
46C11×#381C2212yescomplemented
47C11×#380C2212yescomplemented
48C11×#379C2212yes—
49C4×C11×C22⋊C4—22no—
50C4×C11×C22⋊C4C2212yescomplemented
51C11×#342C2212yescomplemented
52C11×#342C2212yescomplemented
53C25×C11C2×C411yescharacteristic
54C25×C11C2311yescharacteristic
55C2×C11×#41—22no—
56C2×C11×#41—22no—
57C2×C11×#41—22no—
58C2×C11×#41—22no—
59C2×C11×#41—42no—
60C22×Q8×C11C2×C411yescharacteristic, complemented
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—42no—
66C22×D4×C11C2×C411yescharacteristic
67C22×D4×C11C2×C411yescharacteristic
68C22×D4×C11C2×C411yescharacteristic
69C22×D4×C11C2×C411yescharacteristic
70C22×D4×C11C2×C411yescharacteristic, complemented
71C22×D4×C11C2×C411yescharacteristic, complemented
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11—22no—
76C23×C4×C11C2×C411yescharacteristic
77C23×C4×C11C2×C411yescharacteristic, complemented
78C23×C4×C11C2×C411yescharacteristic, complemented
79C23×C4×C11C2×C411yescharacteristic, complemented
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C11×#124—22no—
83C11×#124—22no—
84C11×#123—22no—
85C11×#123—22no—
86C11×#123—22no—
87C11×#123—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—22no—
93C11×#121—22no—
94C11×#121—22no—
95C11×#121—22no—
96C11×#120—22no—
97C11×#120—22no—
98C11×#120—22no—
99C11×#120—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C11×#117—24no—
107C11×#117—42no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
111C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
112C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
113C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—42no—
123C2×C11×C22⋊C4C2×C411yescharacteristic
124C2×C11×C22⋊C4C2×C411yescharacteristic
125C2×C11×C22⋊C4C2×C411yescharacteristic
126C2×C11×C22⋊C4C2×C411yescharacteristic
127C2×C11×C22⋊C4C2×C411yescharacteristic
128C2×C11×C22⋊C4C2×C411yescharacteristic
129C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
130C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
131C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
132C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
133C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
134C2×C11×C22⋊C4D412yes—
135C2×C11×C22⋊C4D412yes—
136C2×C11×C22⋊C4D412yes—
137C2×C11×C22⋊C4D412yes—
138C2×C11×C22⋊C4C2312yes—
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4C2312yes—
143C2×C42×C11—22no—
144C2×C42×C11—22no—
145C2×C42×C11C2×C411yescharacteristic, complemented
146C11×#99—22no—
147C11×#99—22no—
148C11×#99—22no—
149C11×#99—24no—
150C11×#99—24no—
151C11×#99—42no—
152C11×#99—42no—
153C11×#99D414yescomplemented
154C11×#95—22no—
155C11×#95—22no—
156C11×#95—22no—
157C11×#95—22no—
158#22405C1111yesmaximal, characteristic, direct product factor, Sylow
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—22no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—22no—
165C24×C11—41no—
166C24×C11—42no—
167C24×C11—42no—
168C24×C11—81no—
169C24×C11—81no—
170C24×C11C22×C411yescharacteristic
171C24×C11C22×C411yescharacteristic
172C24×C11C22×C411yescharacteristic
173C24×C11C22×C411yescharacteristic
174C24×C11C22×C411yescharacteristic
175C24×C11C2×D412yes—
176C24×C11C2×D412yes—
177C24×C11C2411yescharacteristic
178C11×#41—44no—
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
182C2×Q8×C11—22no—
183C2×Q8×C11—22no—
184C2×Q8×C11—41no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—41no—
206C2×D4×C11—41no—
207C2×D4×C11—41no—
208C2×D4×C11—44no—
209C2×D4×C11—44no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
212C2×D4×C11—42no—
213C2×D4×C11—81no—
214C2×D4×C11—81no—
215C2×D4×C11C2×D412yes—
216C2×D4×C11#4112yes—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—22no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—41no—
236C22×C4×C11—41no—
237C22×C4×C11—41no—
238C22×C4×C11—44no—
239C22×C4×C11—44no—
240C22×C4×C11—81no—
241C22×C4×C11—82no—
242C22×C4×C11—81no—
243C22×C4×C11C22×C411yescharacteristic
244C22×C4×C11C22×C411yescharacteristic
245C22×C4×C11C22×C411yescharacteristic
246C22×C4×C11C22×C411yescharacteristic
247C22×C4×C11C22×C411yescharacteristic
248C22×C4×C11C22×C411yescharacteristic
249C22×C4×C11C22×C411yescharacteristic
250C22×C4×C11C22×C411yescharacteristic
251C22×C4×C11C22×C411yescharacteristic
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C11×C4⋊C4—22no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—22no—
260C11×C4⋊C4—22no—
261C11×C4⋊C4—44no—
262C11×C4⋊C4—82no—
263C11×C22⋊C4—21no—
264C11×C22⋊C4—21no—
265C11×C22⋊C4—22no—
266C11×C22⋊C4—22no—
267C11×C22⋊C4—22no—
268C11×C22⋊C4—21no—
269C11×C22⋊C4—21no—
270C11×C22⋊C4—21no—
271C11×C22⋊C4—21no—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—21no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—22no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—22no—
279C11×C22⋊C4—22no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—44no—
283C11×C22⋊C4—44no—
284C11×C22⋊C4—82no—
285C11×C22⋊C4C22⋊C411yescharacteristic
286C11×C22⋊C4C22⋊C411yescharacteristic
287C11×C22⋊C4C22⋊C411yescharacteristic
288C11×C22⋊C4C22⋊C411yescharacteristic
289C11×C22⋊C4C22⋊C412yes—
290C11×C22⋊C4C22⋊C412yes—
291C11×C22⋊C4C22⋊C412yes—
292C11×C22⋊C4C22⋊C412yes—
293C11×C22⋊C4C22⋊C412yes—
294C11×C22⋊C4C22⋊C412yes—
295C11×C22⋊C4C2×D414yes—
296C42×C11—21no—
297C42×C11—21no—
298C42×C11—44no—
299C42×C11—82no—
300C2×#546C2×C1111yescharacteristic
301C2×#410C2×C1111yescharacteristic, complemented
302C22×#99C2×C1111yescharacteristic, complemented
303#2342C2×C1112yescomplemented
304#1964C2×C1112yescomplemented
305#1899C2×C1112yescomplemented
306#1898C2×C1112yescomplemented
307#1799C2×C1111yescharacteristic, complemented
308#1782C2×C1111yescharacteristic, complemented
309#1781C2×C1111yescharacteristic, complemented
310C4×#99C2×C1111yescharacteristic, complemented
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—24no—
318C23×C11—22no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—42no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—42no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—42no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—42no—
347C23×C11—81no—
348C23×C11—81no—
349C23×C11—82no—
350C23×C11—82no—
351C23×C11—84no—
352C23×C11—84no—
353C23×C11—84no—
354C23×C11C2×C22⋊C411yescharacteristic
355C23×C11C2×C22⋊C412yes—
356C23×C11C2×C22⋊C411yescharacteristic
357C23×C11C4×D412yes—
358C23×C11C23×C411yescharacteristic
359C23×C11C22×D412yes—
360C23×C11C22×D411yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11H(5,𝔽2)12yes—
363Q8×C11—44no—
364D4×C11—24no—
365D4×C11—24no—
366D4×C11—44no—
367D4×C11—44no—
368D4×C11—44no—
369D4×C11—42no—
370D4×C11—42no—
371D4×C11—42no—
372D4×C11—42no—
373D4×C11—42no—
374D4×C11—42no—
375D4×C11—82no—
376D4×C11—82no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—24no—
396C2×C4×C11—42no—
397C2×C4×C11—42no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—42no—
401C2×C4×C11—42no—
402C2×C4×C11—42no—
403C2×C4×C11—42no—
404C2×C4×C11—42no—
405C2×C4×C11—42no—
406C2×C4×C11—42no—
407C2×C4×C11—42no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—42no—
411C2×C4×C11—42no—
412C2×C4×C11—42no—
413C2×C4×C11—42no—
414C2×C4×C11—42no—
415C2×C4×C11—42no—
416C2×C4×C11—42no—
417C2×C4×C11—42no—
418C2×C4×C11—42no—
419C2×C4×C11—81no—
420C2×C4×C11—81no—
421C2×C4×C11—88no—
422C2×C4×C11C2×C22⋊C411yescharacteristic
423C2×C4×C11C2×C22⋊C411yescharacteristic
424C2×C4×C11C2×C22⋊C412yes—
425C2×C4×C11C2×C22⋊C411yescharacteristic
426C2×C4×C11C2×C22⋊C411yescharacteristic
427C2×C4×C11C2×C22⋊C412yes—
428C2×C4×C11C4×D412yes—
429C22×#41C22×C1111yescharacteristic
430C23×D4C22×C1111yescharacteristic
431#546—22no—
432#546—22no—
433#546—22no—
434#546—22no—
435C2×#124C4×C1111yescharacteristic, complemented
436C2×#123C4×C1111yescharacteristic, complemented
437C2×#123C22×C1111yescharacteristic
438C2×C22⋊Q8C4×C1111yescharacteristic, complemented
439C2×#121C4×C1111yescharacteristic, complemented
440C2×#121C4×C1111yescharacteristic, complemented
441C2×#121C22×C1111yescharacteristic
442C2×#120C4×C1111yescharacteristic, complemented
443C2×#120C22×C1111yescharacteristic
444C2×C4×D4C4×C1111yescharacteristic, complemented
445C2×C4×D4C22×C1111yescharacteristic
446C2×#117C22×C1112yescomplemented
447C22×C22⋊C4C4×C1111yescharacteristic, complemented
448C22×C22⋊C4C22×C1112yes—
449C22×C22⋊C4C22×C1111yescharacteristic
450#410—24no—
451C2×#99—24no—
452C2×#99C22×C1111yescharacteristic
453C2×#99C22×C1111yescharacteristic
454C2×#99C22×C1112yes—
455C2×#99C22×C1111yescharacteristic
456C2×#99C22×C1112yes—
457C2×#99C22×C1111yescharacteristic
458C2×#99C22×C1112yescomplemented
459C2×#99C22×C1112yescomplemented
460#388—22no—
461#388—22no—
462#385—22no—
463#381C22×C1112yescomplemented
464#380C22×C1112yescomplemented
465#379C22×C1112yes—
466C4×C22⋊C4—22no—
467C4×C22⋊C4C22×C1112yescomplemented
468#342C22×C1112yescomplemented
469#342C22×C1112yescomplemented
470C22×C11—21no—
471C22×C11—22no—
472C22×C11—21no—
473C22×C11—22no—
474C22×C11—21no—
475C22×C11—21no—
476C22×C11—22no—
477C22×C11—21no—
478C22×C11—22no—
479C22×C11—21no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—21no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11—44no—
487C22×C11—44no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—41no—
493C22×C11—41no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—41no—
499C22×C11—41no—
500C22×C11—82no—
501C22×C11—82no—
502C22×C11—81no—
503C22×C11—81no—
504C22×C11—84no—
505C22×C11—81no—
506C22×C11—81no—
507C22×C11—81no—
508C22×C11—81no—
509C22×C11—84no—
510C22×C11#41012yescomplemented
511C22×C11C22×C22⋊C411yescharacteristic
512C22×C11C2×C4×D411yescharacteristic
513C22×C11#51811yescharacteristic
514C22×C11D4212yes—
515C22×C11#54612yes—
516C4×C11—21no—
517C4×C11—21no—
518C4×C11—22no—
519C4×C11—22no—
520C4×C11—21no—
521C4×C11—21no—
522C4×C11—22no—
523C4×C11—44no—
524C4×C11—41no—
525C4×C11—41no—
526C4×C11—41no—
527C4×C11—41no—
528C4×C11—82no—
529C4×C11—82no—
530C4×C11—82no—
531C25C2×C4×C1111yescharacteristic
532C25C23×C1111yescharacteristic
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—42no—
538C22×Q8C2×C4×C1111yescharacteristic, complemented
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—42no—
544C22×D4C2×C4×C1111yescharacteristic
545C22×D4C2×C4×C1111yescharacteristic
546C22×D4C2×C4×C1111yescharacteristic
547C22×D4C2×C4×C1111yescharacteristic
548C22×D4C2×C4×C1111yescharacteristic, complemented
549C22×D4C2×C4×C1111yescharacteristic, complemented
550C22×D4C23×C1111yescharacteristic
551C22×D4C23×C1111yescharacteristic
552C22×D4C23×C1111yescharacteristic
553C23×C4—22no—
554C23×C4C2×C4×C1111yescharacteristic
555C23×C4C2×C4×C1111yescharacteristic, complemented
556C23×C4C2×C4×C1111yescharacteristic, complemented
557C23×C4C2×C4×C1111yescharacteristic, complemented
558C23×C4C23×C1111yescharacteristic
559C23×C4C23×C1111yescharacteristic
560#124—22no—
561#124—22no—
562#123—22no—
563#123—22no—
564#123—22no—
565#123—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584#117—24no—
585#117—42no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
589C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
590C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
591C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4C2×C4×C1111yescharacteristic
602C2×C22⋊C4C2×C4×C1111yescharacteristic
603C2×C22⋊C4C2×C4×C1111yescharacteristic
604C2×C22⋊C4C2×C4×C1111yescharacteristic
605C2×C22⋊C4C2×C4×C1111yescharacteristic
606C2×C22⋊C4C2×C4×C1111yescharacteristic
607C2×C22⋊C4C2×C4×C1111yescharacteristic, complemented
608C2×C22⋊C4C2×C4×C1111yescharacteristic, complemented
609C2×C22⋊C4C2×C4×C1111yescharacteristic, complemented
610C2×C22⋊C4C2×C4×C1111yescharacteristic, complemented
611C2×C22⋊C4C2×C4×C1111yescharacteristic, complemented
612C2×C22⋊C4D4×C1112yes—
613C2×C22⋊C4D4×C1112yes—
614C2×C22⋊C4D4×C1112yes—
615C2×C22⋊C4D4×C1112yes—
616C2×C22⋊C4C23×C1112yes—
617C2×C22⋊C4C23×C1112yes—
618C2×C22⋊C4C23×C1112yes—
619C2×C22⋊C4C23×C1111yescharacteristic
620C2×C22⋊C4C23×C1112yes—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42C2×C4×C1111yescharacteristic, complemented
624#99—22no—
625#99—22no—
626#99—22no—
627#99—24no—
628#99—24no—
629#99—42no—
630#99—42no—
631#99D4×C1114yescomplemented
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636C2×C11—22no—
637C2×C11—22no—
638C2×C11—21no—
639C2×C11—21no—
640C2×C11—22no—
641C2×C11—42no—
642C2×C11—41no—
643C2×C11—42no—
644C2×C11—81no—
645C2×C11—81no—
646C2×C11D4×C22⋊C411yescharacteristic
647C2×C11C2×#41011yescharacteristic
648C2×C11#288311yescharacteristic
649C24—21no—
650C24—21no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—22no—
655C24—41no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C22×C4×C1111yescharacteristic
661C24C22×C4×C1111yescharacteristic
662C24C22×C4×C1111yescharacteristic
663C24C22×C4×C1111yescharacteristic
664C24C22×C4×C1111yescharacteristic
665C24C2×D4×C1112yes—
666C24C2×D4×C1112yes—
667C24C24×C1111yescharacteristic
668#41—44no—
669#41—44no—
670#41—44no—
671#41—44no—
672C2×Q8—22no—
673C2×Q8—22no—
674C2×Q8—41no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4C2×D4×C1112yes—
706C2×D4C11×#4112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—22no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—81no—
731C22×C4—82no—
732C22×C4—81no—
733C22×C4C22×C4×C1111yescharacteristic
734C22×C4C22×C4×C1111yescharacteristic
735C22×C4C22×C4×C1111yescharacteristic
736C22×C4C22×C4×C1111yescharacteristic
737C22×C4C22×C4×C1111yescharacteristic
738C22×C4C22×C4×C1111yescharacteristic
739C22×C4C22×C4×C1111yescharacteristic
740C22×C4C22×C4×C1111yescharacteristic
741C22×C4C22×C4×C1111yescharacteristic
742C22×C4C2×D4×C1112yes—
743C22×C4C2×D4×C1112yes—
744C22×C4C2×D4×C1112yes—
745C22×C4C2×D4×C1112yes—
746C4⋊C4—22no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—22no—
750C4⋊C4—22no—
751C4⋊C4—44no—
752C4⋊C4—82no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—22no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—82no—
775C22⋊C4C11×C22⋊C411yescharacteristic
776C22⋊C4C11×C22⋊C411yescharacteristic
777C22⋊C4C11×C22⋊C411yescharacteristic
778C22⋊C4C11×C22⋊C411yescharacteristic
779C22⋊C4C11×C22⋊C412yes—
780C22⋊C4C11×C22⋊C412yes—
781C22⋊C4C11×C22⋊C412yes—
782C22⋊C4C11×C22⋊C412yes—
783C22⋊C4C11×C22⋊C412yes—
784C22⋊C4C11×C22⋊C412yes—
785C22⋊C4C2×D4×C1114yes—
786C42—21no—
787C42—21no—
788C42—44no—
789C42—82no—
790C11#2240511yescharacteristic, direct product factor, Sylow
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—22no—
796C23—22no—
797C23—24no—
798C23—22no—
799C23—21no—
800C23—21no—
801C23—22no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—42no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—41no—
815C23—41no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—41no—
820C23—41no—
821C23—42no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—42no—
827C23—81no—
828C23—81no—
829C23—82no—
830C23—82no—
831C23—84no—
832C23—84no—
833C23—84no—
834C23C2×C11×C22⋊C411yescharacteristic
835C23C2×C11×C22⋊C412yes—
836C23C2×C11×C22⋊C411yescharacteristic
837C23C4×D4×C1112yes—
838C23C23×C4×C1111yescharacteristic
839C23C22×D4×C1112yes—
840C23C22×D4×C1111yescharacteristic
841C23C2×C11×#4111yescharacteristic
842C23C11×H(5,𝔽2)12yes—
843Q8—44no—
844D4—24no—
845D4—24no—
846D4—44no—
847D4—44no—
848D4—44no—
849D4—42no—
850D4—42no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—82no—
856D4—82no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—24no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—88no—
902C2×C4C2×C11×C22⋊C411yescharacteristic
903C2×C4C2×C11×C22⋊C411yescharacteristic
904C2×C4C2×C11×C22⋊C412yes—
905C2×C4C2×C11×C22⋊C411yescharacteristic
906C2×C4C2×C11×C22⋊C411yescharacteristic
907C2×C4C2×C11×C22⋊C412yes—
908C2×C4C4×D4×C1112yes—
909C22—21no—
910C22—22no—
911C22—21no—
912C22—22no—
913C22—21no—
914C22—21no—
915C22—22no—
916C22—21no—
917C22—22no—
918C22—21no—
919C22—22no—
920C22—22no—
921C22—21no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—44no—
926C22—42no—
927C22—42no—
928C22—44no—
929C22—42no—
930C22—42no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—82no—
940C22—82no—
941C22—81no—
942C22—81no—
943C22—84no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—84no—
949C22C11×#41012yescomplemented
950C22C22×C11×C22⋊C411yescharacteristic
951C22C2×C4×D4×C1111yescharacteristic
952C22C11×#51811yescharacteristic
953C22D42×C1112yes—
954C22C11×#54612yes—
955C4—21no—
956C4—21no—
957C4—22no—
958C4—22no—
959C4—21no—
960C4—21no—
961C4—22no—
962C4—44no—
963C4—41no—
964C4—41no—
965C4—41no—
966C4—41no—
967C4—82no—
968C4—82no—
969C4—82no—
970C2—22no—
971C2—22no—
972C2—21no—
973C2—21no—
974C2—22no—
975C2—41no—
976C2—42no—
977C2—42no—
978C2—81no—
979C2—81no—
980C2D4×C11×C22⋊C411yescharacteristic
981C2C2×C11×#41011yescharacteristic
982C2C11×#288311yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#546C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#410C2semidirect
3. C22×C11×#99C2semidirect
4. C11×#2342C2semidirect
5. C11×#1964C2semidirect
6. C11×#1899C2semidirect
7. C11×#1898C2semidirect
8. C11×#1799C2semidirect
9. C11×#1782C2semidirect
10. C11×#1781C2semidirect
11. C4×C11×#99C2semidirect
18. C2×C11×#124C4semidirect
19. C2×C11×#123C4semidirect
21. C2×C11×C22⋊Q8C4semidirect
22. C2×C11×#121C4semidirect
23. C2×C11×#121C4semidirect
25. C2×C11×#120C4semidirect
27. C2×C4×D4×C11C4semidirect
29. C2×C11×#117C22semidirect
30. C22×C11×C22⋊C4C4semidirect
41. C2×C11×#99C22semidirect
42. C2×C11×#99C22semidirect
46. C11×#381C22semidirect
47. C11×#380C22semidirect
50. C4×C11×C22⋊C4C22semidirect
51. C11×#342C22semidirect
52. C11×#342C22semidirect
60. C22×Q8×C11C2×C4semidirect
70. C22×D4×C11C2×C4semidirect
71. C22×D4×C11C2×C4semidirect
77. C23×C4×C11C2×C4semidirect
78. C23×C4×C11C2×C4semidirect
79. C23×C4×C11C2×C4semidirect
110. C2×C11×C4⋊C4C2×C4semidirect
111. C2×C11×C4⋊C4C2×C4semidirect
112. C2×C11×C4⋊C4C2×C4semidirect
113. C2×C11×C4⋊C4C2×C4semidirect
129. C2×C11×C22⋊C4C2×C4semidirect
130. C2×C11×C22⋊C4C2×C4semidirect
131. C2×C11×C22⋊C4C2×C4semidirect
132. C2×C11×C22⋊C4C2×C4semidirect
133. C2×C11×C22⋊C4C2×C4semidirect
145. C2×C42×C11C2×C4semidirect
153. C11×#99D4semidirect
158. #22405C11direct (N × H)
301. C2×#410C2×C11semidirect
302. C22×#99C2×C11semidirect
303. #2342C2×C11semidirect
304. #1964C2×C11semidirect
305. #1899C2×C11semidirect
306. #1898C2×C11semidirect
307. #1799C2×C11semidirect
308. #1782C2×C11semidirect
309. #1781C2×C11semidirect
310. C4×#99C2×C11semidirect
435. C2×#124C4×C11semidirect
436. C2×#123C4×C11semidirect
438. C2×C22⋊Q8C4×C11semidirect
439. C2×#121C4×C11semidirect
440. C2×#121C4×C11semidirect
442. C2×#120C4×C11semidirect
444. C2×C4×D4C4×C11semidirect
446. C2×#117C22×C11semidirect
447. C22×C22⋊C4C4×C11semidirect
458. C2×#99C22×C11semidirect
459. C2×#99C22×C11semidirect
463. #381C22×C11semidirect
464. #380C22×C11semidirect
467. C4×C22⋊C4C22×C11semidirect
468. #342C22×C11semidirect
469. #342C22×C11semidirect
510. C22×C11#410semidirect
538. C22×Q8C2×C4×C11semidirect
548. C22×D4C2×C4×C11semidirect
549. C22×D4C2×C4×C11semidirect
555. C23×C4C2×C4×C11semidirect
556. C23×C4C2×C4×C11semidirect
557. C23×C4C2×C4×C11semidirect
588. C2×C4⋊C4C2×C4×C11semidirect
589. C2×C4⋊C4C2×C4×C11semidirect
590. C2×C4⋊C4C2×C4×C11semidirect
591. C2×C4⋊C4C2×C4×C11semidirect
607. C2×C22⋊C4C2×C4×C11semidirect
608. C2×C22⋊C4C2×C4×C11semidirect
609. C2×C22⋊C4C2×C4×C11semidirect
610. C2×C22⋊C4C2×C4×C11semidirect
611. C2×C22⋊C4C2×C4×C11semidirect
623. C2×C42C2×C4×C11semidirect
631. #99D4×C11semidirect
790. C11#22405direct (N × H)
949. C22C11×#410semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5462
C2×C11×#4102
C22×C11×#992
C11×#23422
C11×#19642
C11×#18992
C11×#18982
C11×#17992
C11×#17822
C11×#17812
C4×C11×#992
#2240511