Finite Group Databasebeta

← C11×#24442 #14601635

Subgroups — C11×#24442 #14601635

Order 2816.

1570 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic
2C2×C11×#470C211yesmaximal, characteristic, complemented
3C2×C11×#452C211yesmaximal, characteristic, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C2×C11×#418C211yesmaximal, characteristic, complemented
6C11×#2415C211yesmaximal, characteristic, complemented
7C11×#2042C211yesmaximal, characteristic, complemented
8C11×#2034C211yesmaximal, characteristic, complemented
9C11×#2015C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1873C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1864C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic, complemented
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#546—24no—
23C11×#546—24no—
24C2×C11×#124C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic, complemented
29C2×C11×#121—21no—
30C2×C11×#121C2211yescharacteristic
31C2×C11×#120—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic
35C22×C11×C22⋊C4—21no—
36C11×#470—24no—
37C11×#452—24no—
38C11×#450—24no—
39C2×C11×#106C2211yescharacteristic, complemented
40C11×#418—24no—
41C2×C11×#103C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#103C2211yescharacteristic, complemented
44C2×C11×#103C2211yescharacteristic, complemented
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C11×#397—21no—
55C11×#394—21no—
56C11×#391C2211yescharacteristic, complemented
57C11×#389—21no—
58C11×#389C2211yescharacteristic, complemented
59C11×#388—21no—
60C11×#380C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#336C2211yescharacteristic, complemented
64C11×#336C2211yescharacteristic, 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×C11C2311yescharacteristic
73C22×Q8×C11C2311yescharacteristic
74C22×D4×C11—22no—
75C22×D4×C11—22no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—22no—
80C22×D4×C11—41no—
81C22×D4×C11—41no—
82C22×D4×C11D414yes—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C2×C11×Q16—22no—
91C2×C11×Q16—22no—
92C2×C11×Q16—41no—
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×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#124—22no—
107C11×#124—22no—
108C11×#123—28no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—41no—
114C11×C22⋊Q8D414yes—
115C11×#121—28no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#120—28no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C11×#117—22no—
124C11×#117—41no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4D411yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C22⋊C4—28no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
145C2×C11×C22⋊C4D411yescharacteristic
146C2×C42×C11—21no—
147C2×C42×C11C2311yescharacteristic
148C11×#106—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—41no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102D414yescomplemented
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—41no—
162C11×#95—21no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24442C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—24no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—81no—
175C24×C11—81no—
176C24×C11C2×D411yescharacteristic
177C24×C11C2×D411yescharacteristic
178C11×#41—44no—
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
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—21no—
192C2×Q8×C11—21no—
193C2×Q8×C11C2×D412yes—
194C2×D4×C11—28no—
195C2×D4×C11—24no—
196C2×D4×C11—22no—
197C2×D4×C11—24no—
198C2×D4×C11—24no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—44no—
208C2×D4×C11—44no—
209C2×D4×C11—44no—
210C2×D4×C11—41no—
211C2×D4×C11—41no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—81no—
217C2×D4×C11—81no—
218C2×D4×C11C2×D412yes—
219C2×D4×C11C2×D412yes—
220C2×D4×C11C2×D412yes—
221C2×D4×C11#4112yes—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—24no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—24no—
231C22×C4×C11—21no—
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—42no—
241C22×C4×C11—42no—
242C22×C4×C11—81no—
243C22×C4×C11—81no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2411yescharacteristic
251C11×Q16—44no—
252C11×SD16—44no—
253C11×SD16—44no—
254C11×M16—44no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11C2×D412yes—
267C11×C4⋊C4—24no—
268C11×C4⋊C4—22no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—42no—
276C11×C4⋊C4—42no—
277C11×C4⋊C4—42no—
278C11×C4⋊C4C2×D412yes—
279C11×C4⋊C4C2×D412yes—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—22no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—22no—
287C11×C22⋊C4—42no—
288C11×C22⋊C4—42no—
289C11×C22⋊C4—42no—
290C11×C22⋊C4—42no—
291C42×C11—21no—
292C42×C11—21no—
293C42×C11—42no—
294C2×#546C2×C1111yescharacteristic
295C2×#470C2×C1111yescharacteristic, complemented
296C2×#452C2×C1111yescharacteristic, complemented
297C2×#450C2×C1111yescharacteristic, complemented
298C2×#418C2×C1111yescharacteristic, complemented
299#2415C2×C1111yescharacteristic, complemented
300#2042C2×C1111yescharacteristic, complemented
301#2034C2×C1111yescharacteristic, complemented
302#2015C2×C1111yescharacteristic, complemented
303#2000C2×C1111yescharacteristic, complemented
304#1877C2×C1111yescharacteristic, complemented
305#1873C2×C1111yescharacteristic, complemented
306#1870C2×C1111yescharacteristic, complemented
307#1864C2×C1111yescharacteristic, complemented
308#1788C2×C1111yescharacteristic, complemented
309C23×C11—22no—
310C23×C11—21no—
311C23×C11—22no—
312C23×C11—21no—
313C23×C11—22no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—22no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—48no—
327C23×C11—48no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—84no—
339C23×C11—84no—
340C23×C11—84no—
341C23×C11—84no—
342C23×C11—84no—
343C23×C11#12012yes—
344C23×C11C22×D411yescharacteristic
345Q8×C11—22no—
346Q8×C11—22no—
347Q8×C11—41no—
348Q8×C11—41no—
349Q8×C11—41no—
350Q8×C11—41no—
351Q8×C11—41no—
352Q8×C11—41no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—48no—
359D4×C11—44no—
360D4×C11—48no—
361D4×C11—41no—
362D4×C11—41no—
363D4×C11—84no—
364D4×C11#12114yes—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—22no—
374C2×C4×C11—21no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
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—48no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
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—84no—
404C2×C4×C11#12012yes—
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C2×#4111yescharacteristic
409C2×C4×C11H(5,𝔽2)11yescharacteristic
410C2×C4×C11H(5,𝔽2)11yescharacteristic
411C8×C11—22no—
412C8×C11—41no—
413C8×C11—41no—
414C8×C11—41no—
415C22×#41C22×C1111yescharacteristic
416C23×D4C22×C1111yescharacteristic
417C22×Q16C22×C1111yescharacteristic, complemented
418C22×SD16C22×C1111yescharacteristic
419C22×SD16C22×C1111yescharacteristic
420C22×M16C22×C1111yescharacteristic
421#546—24no—
422#546—24no—
423C2×#124C22×C1111yescharacteristic
424C2×#123—21no—
425C2×C22⋊Q8C22×C1111yescharacteristic
426C2×C22⋊Q8C22×C1111yescharacteristic
427C2×C22⋊Q8C22×C1111yescharacteristic, complemented
428C2×#121—21no—
429C2×#121C22×C1111yescharacteristic
430C2×#120—21no—
431C2×C4×D4C22×C1111yescharacteristic
432C2×C4×D4C22×C1111yescharacteristic
433C2×#117C22×C1111yescharacteristic
434C22×C22⋊C4—21no—
435#470—24no—
436#452—24no—
437#450—24no—
438C2×#106C22×C1111yescharacteristic, complemented
439#418—24no—
440C2×#103C22×C1111yescharacteristic, complemented
441C2×#103C22×C1111yescharacteristic, complemented
442C2×#103C22×C1111yescharacteristic, complemented
443C2×#103C22×C1111yescharacteristic, complemented
444C2×#102C22×C1111yescharacteristic
445C2×#102C22×C1111yescharacteristic
446C2×#102C22×C1111yescharacteristic
447C2×#102C22×C1111yescharacteristic
448C2×#102C22×C1111yescharacteristic
449C2×#102C22×C1111yescharacteristic
450C2×C22⋊C8C22×C1111yescharacteristic
451C2×C22⋊C8C22×C1111yescharacteristic, complemented
452C2×C22⋊C8C22×C1111yescharacteristic, complemented
453#397—21no—
454#394—21no—
455#391C22×C1111yescharacteristic, complemented
456#389—21no—
457#389C22×C1111yescharacteristic, complemented
458#388—21no—
459#380C22×C1111yescharacteristic, complemented
460#340C22×C1111yescharacteristic, complemented
461#340C22×C1111yescharacteristic, complemented
462#336C22×C1111yescharacteristic, complemented
463#336C22×C1111yescharacteristic, complemented
464C22×C11—22no—
465C22×C11—24no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—41no—
471C22×C11—42no—
472C22×C11—41no—
473C22×C11—42no—
474C22×C11—41no—
475C22×C11—42no—
476C22×C11—41no—
477C22×C11—42no—
478C22×C11—41no—
479C22×C11—42no—
480C22×C11—41no—
481C22×C11—42no—
482C22×C11—41no—
483C22×C11—42no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—816no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11C2×#12011yescharacteristic
494C22×C11D4211yescharacteristic
495C22×C11#54611yescharacteristic
496C22×C11#57511yescharacteristic
497C22×C11#57511yescharacteristic
498C22×C11#57711yescharacteristic
499C22×C11#57711yescharacteristic
500C4×C11—22no—
501C4×C11—41no—
502C4×C11—42no—
503C4×C11—41no—
504C4×C11—41no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—81no—
508C4×C11—81no—
509C4×C11—81no—
510C4×C11C2×#12111yescharacteristic
511C4×C11#53411yescharacteristic
512C4×C11D4211yescharacteristic
513C4×C11#54611yescharacteristic
514C25—21no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—41no—
520C2×#41—41no—
521C22×Q8C23×C1111yescharacteristic
522C22×Q8C23×C1111yescharacteristic
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4D4×C1114yes—
532C22×D4D4×C1111yescharacteristic
533C22×D4C23×C1111yescharacteristic
534C22×D4C23×C1111yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C23×C1111yescharacteristic
538C23×C4C23×C1111yescharacteristic
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—41no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—41no—
551C22×C8C23×C1111yescharacteristic
552C22×C8C23×C1111yescharacteristic
553C22×C8C23×C1111yescharacteristic
554C22×C8C23×C1111yescharacteristic
555#124—22no—
556#124—22no—
557#123—28no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—41no—
563C22⋊Q8D4×C1114yes—
564#121—28no—
565#121—22no—
566#121—22no—
567#120—28no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572#117—22no—
573#117—41no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4D4×C1111yescharacteristic
579C2×C4⋊C4C23×C1111yescharacteristic
580C2×C4⋊C4C23×C1111yescharacteristic
581C2×C4⋊C4C23×C1111yescharacteristic
582C2×C4⋊C4C23×C1111yescharacteristic
583C2×C22⋊C4—28no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4D4×C1111yescharacteristic
594C2×C22⋊C4D4×C1111yescharacteristic
595C2×C42—21no—
596C2×C42C23×C1111yescharacteristic
597#106—22no—
598#103—22no—
599#103—22no—
600#103—22no—
601#103—41no—
602#102—22no—
603#102—22no—
604#102—22no—
605#102—22no—
606#102—22no—
607#102D4×C1114yescomplemented
608C22⋊C8—22no—
609C22⋊C8—22no—
610C22⋊C8—41no—
611#95—21no—
612#95—21no—
613#95—21no—
614#95—21no—
615C2×C11—42no—
616C2×C11—44no—
617C2×C11—81no—
618C2×C11—82no—
619C2×C11#241011yescharacteristic
620C2×C11#300511yescharacteristic
621C2×C11#300911yescharacteristic
622C2×C11#326711yescharacteristic
623C2×C11#327511yescharacteristic
624C2×C11#331111yescharacteristic
625C2×C11#332311yescharacteristic
626C24—21no—
627C24—21no—
628C24—24no—
629C24—42no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—81no—
634C24—81no—
635C24C2×D4×C1111yescharacteristic
636C24C2×D4×C1111yescharacteristic
637#41—44no—
638#41—44no—
639#41—44no—
640#41—44no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8C2×D4×C1112yes—
653C2×D4—28no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—41no—
670C2×D4—41no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C1112yes—
678C2×D4C2×D4×C1112yes—
679C2×D4C2×D4×C1112yes—
680C2×D4C11×#4112yes—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—81no—
702C22×C4—81no—
703C22×C4C2×D4×C1111yescharacteristic
704C22×C4C2×D4×C1111yescharacteristic
705C22×C4C2×D4×C1111yescharacteristic
706C22×C4C2×D4×C1111yescharacteristic
707C22×C4C2×D4×C1112yes—
708C22×C4C2×D4×C1112yes—
709C22×C4C24×C1111yescharacteristic
710Q16—44no—
711SD16—44no—
712SD16—44no—
713M16—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8C2×D4×C1112yes—
726C4⋊C4—24no—
727C4⋊C4—22no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4C2×D4×C1112yes—
738C4⋊C4C2×D4×C1112yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—22no—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C42—21no—
751C42—21no—
752C42—42no—
753C11#2444211yescharacteristic, direct product factor, Sylow
754C23—22no—
755C23—21no—
756C23—22no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—48no—
772C23—48no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23C11×#12012yes—
789C23C22×D4×C1111yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—44no—
805D4—48no—
806D4—41no—
807D4—41no—
808D4—84no—
809D4C11×#12114yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—84no—
849C2×C4C11×#12012yes—
850C2×C4C22×D4×C1111yescharacteristic
851C2×C4C22×D4×C1111yescharacteristic
852C2×C4C22×D4×C1111yescharacteristic
853C2×C4C2×C11×#4111yescharacteristic
854C2×C4C11×H(5,𝔽2)11yescharacteristic
855C2×C4C11×H(5,𝔽2)11yescharacteristic
856C8—22no—
857C8—41no—
858C8—41no—
859C8—41no—
860C22—22no—
861C22—24no—
862C22—22no—
863C22—22no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—42no—
868C22—41no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—816no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22C2×C11×#12011yescharacteristic
890C22D42×C1111yescharacteristic
891C22C11×#54611yescharacteristic
892C22C11×#57511yescharacteristic
893C22C11×#57511yescharacteristic
894C22C11×#57711yescharacteristic
895C22C11×#57711yescharacteristic
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—42no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4C2×C11×#12111yescharacteristic
907C4C11×#53411yescharacteristic
908C4D42×C1111yescharacteristic
909C4C11×#54611yescharacteristic
910C2—42no—
911C2—44no—
912C2—81no—
913C2—82no—
914C2C11×#241011yescharacteristic
915C2C11×#300511yescharacteristic
916C2C11×#300911yescharacteristic
917C2C11×#326711yescharacteristic
918C2C11×#327511yescharacteristic
919C2C11×#331111yescharacteristic
920C2C11×#332311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#546C2
LCSG ▷ C22×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×#470C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C11×#450C2semidirect
5. C2×C11×#418C2semidirect
6. C11×#2415C2semidirect
7. C11×#2042C2semidirect
8. C11×#2034C2semidirect
9. C11×#2015C2semidirect
10. C11×#2000C2semidirect
11. C11×#1877C2semidirect
12. C11×#1873C2semidirect
13. C11×#1870C2semidirect
14. C11×#1864C2semidirect
15. C11×#1788C2semidirect
18. C22×C11×Q16C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
39. C2×C11×#106C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
44. C2×C11×#103C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. C2×C11×C22⋊C8C22semidirect
56. C11×#391C22semidirect
58. C11×#389C22semidirect
60. C11×#380C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
158. C11×#102D4semidirect
166. #24442C11direct (N × H)
295. C2×#470C2×C11semidirect
296. C2×#452C2×C11semidirect
297. C2×#450C2×C11semidirect
298. C2×#418C2×C11semidirect
299. #2415C2×C11semidirect
300. #2042C2×C11semidirect
301. #2034C2×C11semidirect
302. #2015C2×C11semidirect
303. #2000C2×C11semidirect
304. #1877C2×C11semidirect
305. #1873C2×C11semidirect
306. #1870C2×C11semidirect
307. #1864C2×C11semidirect
308. #1788C2×C11semidirect
417. C22×Q16C22×C11semidirect
427. C2×C22⋊Q8C22×C11semidirect
438. C2×#106C22×C11semidirect
440. C2×#103C22×C11semidirect
441. C2×#103C22×C11semidirect
442. C2×#103C22×C11semidirect
443. C2×#103C22×C11semidirect
451. C2×C22⋊C8C22×C11semidirect
452. C2×C22⋊C8C22×C11semidirect
455. #391C22×C11semidirect
457. #389C22×C11semidirect
459. #380C22×C11semidirect
460. #340C22×C11semidirect
461. #340C22×C11semidirect
462. #336C22×C11semidirect
463. #336C22×C11semidirect
607. #102D4×C11semidirect
753. C11#24442direct (N × H)

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×#4702
C2×C11×#4522
C2×C11×#4502
C2×C11×#4182
C11×#24152
C11×#20422
C11×#20342
C11×#20152
C11×#20002
C11×#18772
C11×#18732
C11×#18702
C11×#18642
C11×#17882
#2444211