Finite Group Databasebeta

← C11×#24394 #14601587

Subgroups — C11×#24394 #14601587

Order 2816.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#468C211yesmaximal, characteristic, complemented
3C2×C11×#465C211yesmaximal, characteristic, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C2×C11×#408C211yesmaximal, characteristic, complemented
6C11×#2616C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1895C211yesmaximal, characteristic, complemented
12C11×#1893C211yesmaximal, characteristic, complemented
13C11×#1873C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C23×C8×C11C2211yescharacteristic, complemented
22C11×#535—24no—
23C11×#535—24no—
24C2×C11×#127—21no—
25C2×C11×#124—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic, complemented
28C2×C11×C22⋊Q8C2211yescharacteristic, complemented
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C11×#121C2211yescharacteristic
33C2×C11×#120—21no—
34C2×C11×#120—21no—
35C2×C11×#117C2211yescharacteristic
36C11×#468—24no—
37C11×#465—24no—
38C11×#450—24no—
39C2×C11×#107C2211yescharacteristic, complemented
40C2×C11×#106C2211yescharacteristic, complemented
41C2×C11×#103C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C11×#408—24no—
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C11×#395—21no—
55C11×#394—21no—
56C11×#394—21no—
57C11×#394—21no—
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic, complemented
60C11×#380C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#340C2211yescharacteristic, complemented
64C11×#340C2211yescharacteristic, complemented
65C25×C11—21no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C22×Q8×C11D411yescharacteristic
73C22×Q8×C11C2311yescharacteristic
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—22no—
79C22×D4×C11—22no—
80C22×D4×C11—21no—
81C22×D4×C11—22no—
82C22×D4×C11—22no—
83C22×D4×C11—41no—
84C22×D4×C11—41no—
85C22×D4×C11D411yescharacteristic
86C22×D4×C11D411yescharacteristic
87C22×D4×C11D411yescharacteristic
88C22×D4×C11C2311yescharacteristic
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—41no—
98C2×C11×SD16—41no—
99C2×C11×M16—22no—
100C2×C11×M16—22no—
101C2×C11×M16—41no—
102C22×C8×C11—22no—
103C22×C8×C11—22no—
104C22×C8×C11—41no—
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×#127—28no—
110C11×#124—28no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—41no—
116C11×C22⋊Q8—41no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121D414yes—
124C11×#121D414yes—
125C11×#120—28no—
126C11×#120—28no—
127C11×#117—22no—
128C11×#117—22no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C42×C11—21no—
149C11×#107—22no—
150C11×#106—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—41no—
158C11×#102—41no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—22no—
162C11×C22⋊C8D414yescomplemented
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24394C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—24no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—81no—
173C24×C11—81no—
174C24×C11—81no—
175C24×C11—81no—
176C24×C11C2×D411yescharacteristic
177C24×C11C2×D411yescharacteristic
178C24×C11C2×D411yescharacteristic
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
182C11×#41—44no—
183C2×Q8×C11—22no—
184C2×Q8×C11—22no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—41no—
192C2×D4×C11—24no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—24no—
198C2×D4×C11—24no—
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—44no—
217C2×D4×C11—41no—
218C2×D4×C11—41no—
219C2×D4×C11—41no—
220C2×D4×C11—42no—
221C2×D4×C11—42no—
222C2×D4×C11—81no—
223C2×D4×C11—81no—
224C2×D4×C11—81no—
225C2×D4×C11—81no—
226C2×D4×C11—81no—
227C2×D4×C11—81no—
228C2×D4×C11—81no—
229C2×D4×C11—81no—
230C2×D4×C11C2×D412yes—
231C2×D4×C11C2×D412yes—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11#4112yes—
259C22×C4×C11C2411yescharacteristic
260C11×SD16—44no—
261C11×SD16—44no—
262C11×M16—44no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—44no—
274C2×C8×C11C2×D412yes—
275C2×C8×C11C2×D412yes—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—42no—
285C11×C4⋊C4—42no—
286C11×C4⋊C4—42no—
287C11×C4⋊C4C2×D412yes—
288C11×C4⋊C4C2×D412yes—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—42no—
295C11×C22⋊C4—42no—
296C11×C22⋊C4—42no—
297C11×C22⋊C4—81no—
298C11×C22⋊C4—81no—
299C11×C22⋊C4—81no—
300C42×C11—24no—
301C2×#535C2×C1111yescharacteristic
302C2×#468C2×C1111yescharacteristic, complemented
303C2×#465C2×C1111yescharacteristic, complemented
304C2×#450C2×C1111yescharacteristic, complemented
305C2×#408C2×C1111yescharacteristic, complemented
306#2616C2×C1111yescharacteristic, complemented
307#2034C2×C1111yescharacteristic, complemented
308#2033C2×C1111yescharacteristic, complemented
309#2000C2×C1111yescharacteristic, complemented
310#2000C2×C1111yescharacteristic, complemented
311#1895C2×C1111yescharacteristic, complemented
312#1893C2×C1111yescharacteristic, complemented
313#1873C2×C1111yescharacteristic, complemented
314#1854C2×C1111yescharacteristic, complemented
315#1786C2×C1111yescharacteristic, complemented
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—21no—
336C23×C11—21no—
337C23×C11—48no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—84no—
351C23×C11—84no—
352C23×C11—84no—
353C23×C11—84no—
354C23×C11—84no—
355C23×C11—84no—
356C23×C11#12012yes—
357C23×C11#12112yes—
358C23×C11C22×D411yescharacteristic
359Q8×C11—44no—
360Q8×C11—41no—
361Q8×C11—41no—
362Q8×C11—41no—
363Q8×C11—41no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—44no—
369D4×C11—44no—
370D4×C11—48no—
371D4×C11—44no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—84no—
377D4×C11—84no—
378D4×C11—84no—
379D4×C11—84no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11#12012yes—
418C2×C4×C11#12112yes—
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C2×#4111yescharacteristic
423C2×C4×C11H(5,𝔽2)11yescharacteristic
424C2×C4×C11H(5,𝔽2)11yescharacteristic
425C8×C11—22no—
426C8×C11—22no—
427C8×C11—41no—
428C8×C11—41no—
429C22×#41C22×C1111yescharacteristic
430C23×D4C22×C1111yescharacteristic
431C22×SD16C22×C1111yescharacteristic
432C22×SD16C22×C1111yescharacteristic
433C22×M16C22×C1111yescharacteristic, complemented
434C23×C8C22×C1111yescharacteristic, complemented
435#535—24no—
436#535—24no—
437C2×#127—21no—
438C2×#124—21no—
439C2×C22⋊Q8C22×C1111yescharacteristic
440C2×C22⋊Q8C22×C1111yescharacteristic, complemented
441C2×C22⋊Q8C22×C1111yescharacteristic, complemented
442C2×#121C22×C1111yescharacteristic
443C2×#121C22×C1111yescharacteristic
444C2×#121C22×C1111yescharacteristic
445C2×#121C22×C1111yescharacteristic
446C2×#120—21no—
447C2×#120—21no—
448C2×#117C22×C1111yescharacteristic
449#468—24no—
450#465—24no—
451#450—24no—
452C2×#107C22×C1111yescharacteristic, complemented
453C2×#106C22×C1111yescharacteristic, complemented
454C2×#103C22×C1111yescharacteristic, complemented
455C2×#103C22×C1111yescharacteristic, complemented
456C2×#102C22×C1111yescharacteristic
457C2×#102C22×C1111yescharacteristic
458C2×#102C22×C1111yescharacteristic
459C2×#102C22×C1111yescharacteristic
460C2×#102C22×C1111yescharacteristic
461C2×#102C22×C1111yescharacteristic
462#408—24no—
463C2×C22⋊C8C22×C1111yescharacteristic
464C2×C22⋊C8C22×C1111yescharacteristic
465C2×C22⋊C8C22×C1111yescharacteristic, complemented
466C2×C22⋊C8C22×C1111yescharacteristic, complemented
467#395—21no—
468#394—21no—
469#394—21no—
470#394—21no—
471#380C22×C1111yescharacteristic
472#380C22×C1111yescharacteristic, complemented
473#380C22×C1111yescharacteristic, complemented
474#340C22×C1111yescharacteristic, complemented
475#340C22×C1111yescharacteristic, complemented
476#340C22×C1111yescharacteristic, complemented
477#340C22×C1111yescharacteristic, complemented
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—41no—
490C22×C11—41no—
491C22×C11—41no—
492C22×C11—41no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—41no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—41no—
504C22×C11—41no—
505C22×C11—816no—
506C22×C11—81no—
507C22×C11—81no—
508C22×C11—81no—
509C22×C11—81no—
510C22×C11—81no—
511C22×C11—81no—
512C22×C11—81no—
513C22×C11—81no—
514C22×C11C2×#12011yescharacteristic
515C22×C11C2×#12111yescharacteristic
516C22×C11#53411yescharacteristic
517C22×C11#57611yescharacteristic
518C22×C11#57711yescharacteristic
519C22×C11#57711yescharacteristic
520C22×C11#57711yescharacteristic
521C4×C11—22no—
522C4×C11—22no—
523C4×C11—41no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—81no—
527C4×C11—81no—
528C4×C11—81no—
529C4×C11—81no—
530C4×C11D4211yescharacteristic
531C4×C11D4211yescharacteristic
532C4×C11#54611yescharacteristic
533C4×C11#54611yescharacteristic
534C25—21no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—22no—
538C2×#41—22no—
539C2×#41—41no—
540C2×#41—41no—
541C22×Q8D4×C1111yescharacteristic
542C22×Q8C23×C1111yescharacteristic
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—22no—
551C22×D4—22no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4D4×C1111yescharacteristic
555C22×D4D4×C1111yescharacteristic
556C22×D4D4×C1111yescharacteristic
557C22×D4C23×C1111yescharacteristic
558C22×D4C23×C1111yescharacteristic
559C23×C4C23×C1111yescharacteristic
560C23×C4C23×C1111yescharacteristic
561C23×C4C23×C1111yescharacteristic
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×M16—22no—
569C2×M16—22no—
570C2×M16—41no—
571C22×C8—22no—
572C22×C8—22no—
573C22×C8—41no—
574C22×C8C23×C1111yescharacteristic
575C22×C8C23×C1111yescharacteristic
576C22×C8C23×C1111yescharacteristic
577C22×C8C23×C1111yescharacteristic
578#127—28no—
579#124—28no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121D4×C1114yes—
593#121D4×C1114yes—
594#120—28no—
595#120—28no—
596#117—22no—
597#117—22no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4C23×C1111yescharacteristic
602C2×C4⋊C4C23×C1111yescharacteristic
603C2×C4⋊C4C23×C1111yescharacteristic
604C2×C4⋊C4C23×C1111yescharacteristic
605C2×C4⋊C4C23×C1111yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C42—21no—
618#107—22no—
619#106—22no—
620#103—22no—
621#103—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—41no—
627#102—41no—
628C22⋊C8—22no—
629C22⋊C8—22no—
630C22⋊C8—22no—
631C22⋊C8D4×C1114yescomplemented
632#95—21no—
633#95—21no—
634#95—21no—
635C2×C11—42no—
636C2×C11—42no—
637C2×C11—81no—
638C2×C11—82no—
639C2×C11—82no—
640C2×C11#241011yescharacteristic
641C2×C11#300911yescharacteristic
642C2×C11#301211yescharacteristic
643C2×C11#305711yescharacteristic
644C2×C11#306211yescharacteristic
645C2×C11#319811yescharacteristic
646C2×C11#320011yescharacteristic
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—81no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24C2×D4×C1111yescharacteristic
657C24C2×D4×C1111yescharacteristic
658C24C2×D4×C1111yescharacteristic
659#41—44no—
660#41—44no—
661#41—44no—
662#41—44no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—41no—
672C2×D4—24no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4C2×D4×C1112yes—
711C2×D4C2×D4×C1112yes—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4C2×D4×C1111yescharacteristic
733C22×C4C2×D4×C1111yescharacteristic
734C22×C4C2×D4×C1112yes—
735C22×C4C2×D4×C1112yes—
736C22×C4C2×D4×C1111yescharacteristic
737C22×C4C2×D4×C1112yes—
738C22×C4C11×#4112yes—
739C22×C4C24×C1111yescharacteristic
740SD16—44no—
741SD16—44no—
742M16—44no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—44no—
754C2×C8C2×D4×C1112yes—
755C2×C8C2×D4×C1112yes—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—42no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4C2×D4×C1112yes—
768C4⋊C4C2×D4×C1112yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—81no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C42—24no—
781C11#2439411yescharacteristic, direct product factor, Sylow
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23C11×#12012yes—
823C23C11×#12112yes—
824C23C22×D4×C1111yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4C11×#12012yes—
884C2×C4C11×#12112yes—
885C2×C4C22×D4×C1111yescharacteristic
886C2×C4C22×D4×C1111yescharacteristic
887C2×C4C22×D4×C1111yescharacteristic
888C2×C4C2×C11×#4111yescharacteristic
889C2×C4C11×H(5,𝔽2)11yescharacteristic
890C2×C4C11×H(5,𝔽2)11yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×C11×#12011yescharacteristic
932C22C2×C11×#12111yescharacteristic
933C22C11×#53411yescharacteristic
934C22C11×#57611yescharacteristic
935C22C11×#57711yescharacteristic
936C22C11×#57711yescharacteristic
937C22C11×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C1111yescharacteristic
948C4D42×C1111yescharacteristic
949C4C11×#54611yescharacteristic
950C4C11×#54611yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C11×#241011yescharacteristic
957C2C11×#300911yescharacteristic
958C2C11×#301211yescharacteristic
959C2C11×#305711yescharacteristic
960C2C11×#306211yescharacteristic
961C2C11×#319811yescharacteristic
962C2C11×#320011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#468C2semidirect
3. C2×C11×#465C2semidirect
4. C2×C11×#450C2semidirect
5. C2×C11×#408C2semidirect
6. C11×#2616C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#2000C2semidirect
10. C11×#2000C2semidirect
11. C11×#1895C2semidirect
12. C11×#1893C2semidirect
13. C11×#1873C2semidirect
14. C11×#1854C2semidirect
15. C11×#1786C2semidirect
20. C22×C11×M16C22semidirect
21. C23×C8×C11C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
39. C2×C11×#107C22semidirect
40. C2×C11×#106C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#103C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. C2×C11×C22⋊C8C22semidirect
59. C11×#380C22semidirect
60. C11×#380C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
162. C11×C22⋊C8D4semidirect
166. #24394C11direct (N × H)
302. C2×#468C2×C11semidirect
303. C2×#465C2×C11semidirect
304. C2×#450C2×C11semidirect
305. C2×#408C2×C11semidirect
306. #2616C2×C11semidirect
307. #2034C2×C11semidirect
308. #2033C2×C11semidirect
309. #2000C2×C11semidirect
310. #2000C2×C11semidirect
311. #1895C2×C11semidirect
312. #1893C2×C11semidirect
313. #1873C2×C11semidirect
314. #1854C2×C11semidirect
315. #1786C2×C11semidirect
433. C22×M16C22×C11semidirect
434. C23×C8C22×C11semidirect
440. C2×C22⋊Q8C22×C11semidirect
441. C2×C22⋊Q8C22×C11semidirect
452. C2×#107C22×C11semidirect
453. C2×#106C22×C11semidirect
454. C2×#103C22×C11semidirect
455. C2×#103C22×C11semidirect
465. C2×C22⋊C8C22×C11semidirect
466. C2×C22⋊C8C22×C11semidirect
472. #380C22×C11semidirect
473. #380C22×C11semidirect
474. #340C22×C11semidirect
475. #340C22×C11semidirect
476. #340C22×C11semidirect
477. #340C22×C11semidirect
631. C22⋊C8D4×C11semidirect
781. C11#24394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4682
C2×C11×#4652
C2×C11×#4502
C2×C11×#4082
C11×#26162
C11×#20342
C11×#20332
C11×#20002
C11×#18952
C11×#18932
C11×#18732
C11×#18542
C11×#17862
#2439411