Finite Group Databasebeta

← C11×#24276 #14601469

Subgroups — C11×#24276 #14601469

Order 2816.

1412 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic, complemented
2C2×C11×#470C211yesmaximal, characteristic, complemented
3C2×C11×#468C211yesmaximal, characteristic, complemented
4C2×C11×#436C211yesmaximal, characteristic, complemented
5C11×#2409C211yesmaximal, characteristic, complemented
6C11×#2407C211yesmaximal, characteristic
7C11×#2056C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#2001C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1969C211yesmaximal, characteristic, complemented
12C11×#1968C211yesmaximal, characteristic, complemented
13C11×#1809C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C2×C11×#137—24no—
19C2×C11×#137—24no—
20C2×C11×#137—24no—
21C22×C11×Q16C2211yescharacteristic
22C22×C11×Q16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×M16C2211yescharacteristic
26C22×C11×M16C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C11×#470—24no—
33C11×#468—24no—
34C11×#436—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C4×C8×C11C2211yescharacteristic
49C11×#395—21no—
50C11×#394—21no—
51C11×#393—21no—
52C11×#392—21no—
53C11×#391C2211yescharacteristic
54C11×#391C2211yescharacteristic
55C11×#391C2211yescharacteristic
56C11×#390C2211yescharacteristic
57C11×#386—21no—
58C11×#386—21no—
59C11×#385—21no—
60C11×#385—21no—
61C11×#380C2211yescharacteristic
62C11×#380C2211yescharacteristic
63C11×#340C2211yescharacteristic
64C11×#340C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C22×Q8×C11—21no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—22no—
75C22×Q8×C11—22no—
76C22×Q8×C11—41no—
77C22×Q8×C11—41no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C11×#137—232no—
90C2×C11×Q16—22no—
91C2×C11×Q16—22no—
92C2×C11×Q16—22no—
93C2×C11×Q16—22no—
94C2×C11×Q16—22no—
95C2×C11×Q16D414yescomplemented
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—22no—
100C2×C11×SD16—22no—
101C2×C11×SD16D414yescomplemented
102C2×C11×M16—22no—
103C2×C11×M16—22no—
104C2×C11×M16—22no—
105C2×C11×M16—22no—
106C2×C11×M16—22no—
107C2×C11×M16D414yescomplemented
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—41no—
116C11×C22⋊Q8—41no—
117C11×C22⋊Q8—41no—
118C11×#121—22no—
119C11×#121—41no—
120C4×D4×C11—22no—
121C4×D4×C11—22no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4D411yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4D411yescharacteristic
139C2×C11×C22⋊C4D411yescharacteristic
140C2×C42×C11C2311yescharacteristic
141C11×#107—22no—
142C11×#106—22no—
143C11×C4⋊C8—22no—
144C11×#103—22no—
145C11×#103—22no—
146C11×#103—22no—
147C11×#103—41no—
148C11×#103—41no—
149C11×#103—41no—
150C11×#102—22no—
151C11×#102—41no—
152C11×C22⋊C8—22no—
153C11×C22⋊C8—22no—
154C4×C8×C11—22no—
155C11×#95—21no—
156C11×#95—21no—
157C11×#95—21no—
158C11×#95—21no—
159C11×#95—21no—
160C11×#95—21no—
161C11×#95—21no—
162C11×#95—21no—
163#24276C1111yesmaximal, characteristic, direct product factor, Sylow
164C24×C11—21no—
165C24×C11C2×D411yescharacteristic
166C24×C11C2×D411yescharacteristic
167C11×#41—28no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—44no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—28no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—42no—
188C2×Q8×C11—42no—
189C2×Q8×C11—44no—
190C2×Q8×C11—44no—
191C2×Q8×C11—44no—
192C2×Q8×C11—42no—
193C2×Q8×C11C2×D412yes—
194C2×Q8×C11C2×D412yes—
195C2×Q8×C11C2×D412yes—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—41no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11—42no—
209C2×D4×C11—81no—
210C2×D4×C11C2×D412yes—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—42no—
229C22×C4×C11—42no—
230C22×C4×C11—42no—
231C22×C4×C11—42no—
232C22×C4×C11—42no—
233C22×C4×C11—42no—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11#4112yes—
240C22×C4×C11C2411yescharacteristic
241C11×Q16—28no—
242C11×Q16—28no—
243C11×SD16—28no—
244C11×SD16—28no—
245C11×M16—28no—
246C11×M16—44no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11C2×D412yes—
256C2×C8×C11C2×D412yes—
257C2×C8×C11C2×D412yes—
258C2×C8×C11C2×D412yes—
259C11×C4⋊C4—22no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—42no—
269C11×C4⋊C4—42no—
270C11×C4⋊C4—42no—
271C11×C22⋊C4—22no—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—42no—
274C11×C22⋊C4—42no—
275C11×C22⋊C4—42no—
276C11×C22⋊C4—42no—
277C11×C22⋊C4—42no—
278C11×C22⋊C4—42no—
279C11×C22⋊C4—81no—
280C11×C22⋊C4—81no—
281C42×C11—21no—
282C42×C11—21no—
283C22×#137C2×C1111yescharacteristic, complemented
284C2×#470C2×C1111yescharacteristic, complemented
285C2×#468C2×C1111yescharacteristic, complemented
286C2×#436C2×C1111yescharacteristic, complemented
287#2409C2×C1111yescharacteristic, complemented
288#2407C2×C1111yescharacteristic
289#2056C2×C1111yescharacteristic, complemented
290#2055C2×C1111yescharacteristic, complemented
291#2001C2×C1111yescharacteristic, complemented
292#2000C2×C1111yescharacteristic, complemented
293#1969C2×C1111yescharacteristic, complemented
294#1968C2×C1111yescharacteristic, complemented
295#1809C2×C1111yescharacteristic, complemented
296#1788C2×C1111yescharacteristic, complemented
297#1787C2×C1111yescharacteristic, complemented
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—22no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11#12112yes—
319C23×C11C22×D411yescharacteristic
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—22no—
324Q8×C11—22no—
325Q8×C11—22no—
326Q8×C11—48no—
327Q8×C11—41no—
328Q8×C11—41no—
329Q8×C11—41no—
330Q8×C11—41no—
331Q8×C11—41no—
332Q8×C11—41no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—44no—
336D4×C11—48no—
337D4×C11—41no—
338D4×C11—41no—
339D4×C11—84no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—48no—
358C2×C4×C11—48no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11#12112yes—
382C2×C4×C11#13712yescomplemented
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C2×#4111yescharacteristic
387C2×C4×C11H(5,𝔽2)11yescharacteristic
388C2×C4×C11H(5,𝔽2)11yescharacteristic
389C8×C11—22no—
390C8×C11—41no—
391C8×C11—41no—
392C8×C11#12014yes—
393C22×#41C22×C1111yescharacteristic
394C23×Q8C22×C1111yescharacteristic
395C2×#137—24no—
396C2×#137—24no—
397C2×#137—24no—
398C22×Q16C22×C1111yescharacteristic
399C22×Q16C22×C1111yescharacteristic
400C22×SD16C22×C1111yescharacteristic
401C22×SD16C22×C1111yescharacteristic
402C22×M16C22×C1111yescharacteristic
403C22×M16C22×C1111yescharacteristic
404C2×C22⋊Q8C22×C1111yescharacteristic
405C2×C22⋊Q8C22×C1111yescharacteristic
406C2×C22⋊Q8C22×C1111yescharacteristic
407C2×#121C22×C1111yescharacteristic
408C2×C4×D4C22×C1111yescharacteristic
409#470—24no—
410#468—24no—
411#436—24no—
412C2×#107C22×C1111yescharacteristic
413C2×#106C22×C1111yescharacteristic
414C2×C4⋊C8C22×C1111yescharacteristic
415C2×#103C22×C1111yescharacteristic
416C2×#103C22×C1111yescharacteristic
417C2×#103C22×C1111yescharacteristic
418C2×#103C22×C1111yescharacteristic
419C2×#103C22×C1111yescharacteristic
420C2×#103C22×C1111yescharacteristic
421C2×#102C22×C1111yescharacteristic
422C2×#102C22×C1111yescharacteristic
423C2×C22⋊C8C22×C1111yescharacteristic
424C2×C22⋊C8C22×C1111yescharacteristic
425C2×C4×C8C22×C1111yescharacteristic
426#395—21no—
427#394—21no—
428#393—21no—
429#392—21no—
430#391C22×C1111yescharacteristic
431#391C22×C1111yescharacteristic
432#391C22×C1111yescharacteristic
433#390C22×C1111yescharacteristic
434#386—21no—
435#386—21no—
436#385—21no—
437#385—21no—
438#380C22×C1111yescharacteristic
439#380C22×C1111yescharacteristic
440#340C22×C1111yescharacteristic
441#340C22×C1111yescharacteristic
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—42no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—42no—
453C22×C11—41no—
454C22×C11—42no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11C2×#12111yescharacteristic
464C22×C11D4211yescharacteristic
465C22×C11D4211yescharacteristic
466C22×C11C2×#13711yescharacteristic
467C22×C11#57511yescharacteristic
468C22×C11#57711yescharacteristic
469C22×C11#57811yescharacteristic
470C4×C11—22no—
471C4×C11—22no—
472C4×C11—41no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—42no—
476C4×C11—41no—
477C4×C11—81no—
478C4×C11—81no—
479C4×C11—81no—
480C4×C11—81no—
481C4×C11C2×#12011yescharacteristic
482C4×C11#53511yescharacteristic
483C4×C11#54611yescharacteristic
484C4×C11#54611yescharacteristic
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8—21no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—22no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8C23×C1111yescharacteristic
499C22×Q8C23×C1111yescharacteristic
500C22×Q8C23×C1111yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C1111yescharacteristic
504C22×D4C23×C1111yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C1111yescharacteristic
508C23×C4C23×C1111yescharacteristic
509#137—232no—
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—22no—
513C2×Q16—22no—
514C2×Q16—22no—
515C2×Q16D4×C1114yescomplemented
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16D4×C1114yescomplemented
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—22no—
527C2×M16D4×C1114yescomplemented
528C22×C8C23×C1111yescharacteristic
529C22×C8C23×C1111yescharacteristic
530C22×C8C23×C1111yescharacteristic
531C22×C8C23×C1111yescharacteristic
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537C22⋊Q8—41no—
538#121—22no—
539#121—41no—
540C4×D4—22no—
541C4×D4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4D4×C1111yescharacteristic
546C2×C4⋊C4C23×C1111yescharacteristic
547C2×C4⋊C4C23×C1111yescharacteristic
548C2×C4⋊C4C23×C1111yescharacteristic
549C2×C4⋊C4C23×C1111yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4D4×C1111yescharacteristic
559C2×C22⋊C4D4×C1111yescharacteristic
560C2×C42C23×C1111yescharacteristic
561#107—22no—
562#106—22no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#103—22no—
567#103—41no—
568#103—41no—
569#103—41no—
570#102—22no—
571#102—41no—
572C22⋊C8—22no—
573C22⋊C8—22no—
574C4×C8—22no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581#95—21no—
582#95—21no—
583C2×C11—42no—
584C2×C11—81no—
585C2×C11—82no—
586C2×C11#240811yescharacteristic
587C2×C11#305611yescharacteristic
588C2×C11#306311yescharacteristic
589C2×C11#327511yescharacteristic
590C2×C11#327611yescharacteristic
591C2×C11#327711yescharacteristic
592C2×C11#327811yescharacteristic
593C24—21no—
594C24C2×D4×C1111yescharacteristic
595C24C2×D4×C1111yescharacteristic
596#41—28no—
597#41—44no—
598#41—44no—
599#41—44no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—28no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—42no—
617C2×Q8—42no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—42no—
622C2×Q8C2×D4×C1112yes—
623C2×Q8C2×D4×C1112yes—
624C2×Q8C2×D4×C1112yes—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—41no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—81no—
639C2×D4C2×D4×C1112yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4C2×D4×C1111yescharacteristic
664C22×C4C2×D4×C1111yescharacteristic
665C22×C4C2×D4×C1111yescharacteristic
666C22×C4C2×D4×C1112yes—
667C22×C4C2×D4×C1111yescharacteristic
668C22×C4C11×#4112yes—
669C22×C4C24×C1111yescharacteristic
670Q16—28no—
671Q16—28no—
672SD16—28no—
673SD16—28no—
674M16—28no—
675M16—44no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×D4×C1112yes—
685C2×C8C2×D4×C1112yes—
686C2×C8C2×D4×C1112yes—
687C2×C8C2×D4×C1112yes—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C42—21no—
711C42—21no—
712C11#2427611yescharacteristic, direct product factor, Sylow
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23C11×#12112yes—
734C23C22×D4×C1111yescharacteristic
735Q8—22no—
736Q8—22no—
737Q8—22no—
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—48no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—41no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—48no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4C11×#12112yes—
797C2×C4C11×#13712yescomplemented
798C2×C4C22×D4×C1111yescharacteristic
799C2×C4C22×D4×C1111yescharacteristic
800C2×C4C22×D4×C1111yescharacteristic
801C2×C4C2×C11×#4111yescharacteristic
802C2×C4C11×H(5,𝔽2)11yescharacteristic
803C2×C4C11×H(5,𝔽2)11yescharacteristic
804C8—22no—
805C8—41no—
806C8—41no—
807C8C11×#12014yes—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22C2×C11×#12111yescharacteristic
830C22D42×C1111yescharacteristic
831C22D42×C1111yescharacteristic
832C22C2×C11×#13711yescharacteristic
833C22C11×#57511yescharacteristic
834C22C11×#57711yescharacteristic
835C22C11×#57811yescharacteristic
836C4—22no—
837C4—22no—
838C4—41no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—41no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4C2×C11×#12011yescharacteristic
848C4C11×#53511yescharacteristic
849C4C11×#54611yescharacteristic
850C4C11×#54611yescharacteristic
851C2—42no—
852C2—81no—
853C2—82no—
854C2C11×#240811yescharacteristic
855C2C11×#305611yescharacteristic
856C2C11×#306311yescharacteristic
857C2C11×#327511yescharacteristic
858C2C11×#327611yescharacteristic
859C2C11×#327711yescharacteristic
860C2C11×#327811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2407C2
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
1. C22×C11×#137C2semidirect
2. C2×C11×#470C2semidirect
3. C2×C11×#468C2semidirect
4. C2×C11×#436C2semidirect
5. C11×#2409C2semidirect
7. C11×#2056C2semidirect
8. C11×#2055C2semidirect
9. C11×#2001C2semidirect
10. C11×#2000C2semidirect
11. C11×#1969C2semidirect
12. C11×#1968C2semidirect
13. C11×#1809C2semidirect
14. C11×#1788C2semidirect
15. C11×#1787C2semidirect
95. C2×C11×Q16D4semidirect
101. C2×C11×SD16D4semidirect
107. C2×C11×M16D4semidirect
163. #24276C11direct (N × H)
283. C22×#137C2×C11semidirect
284. C2×#470C2×C11semidirect
285. C2×#468C2×C11semidirect
286. C2×#436C2×C11semidirect
287. #2409C2×C11semidirect
289. #2056C2×C11semidirect
290. #2055C2×C11semidirect
291. #2001C2×C11semidirect
292. #2000C2×C11semidirect
293. #1969C2×C11semidirect
294. #1968C2×C11semidirect
295. #1809C2×C11semidirect
296. #1788C2×C11semidirect
297. #1787C2×C11semidirect
382. C2×C4×C11#137semidirect
515. C2×Q16D4×C11semidirect
521. C2×SD16D4×C11semidirect
527. C2×M16D4×C11semidirect
712. C11#24276direct (N × H)
797. C2×C4C11×#137semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C2×C11×#4702
C2×C11×#4682
C2×C11×#4362
C11×#24092
C11×#24072
C11×#20562
C11×#20552
C11×#20012
C11×#20002
C11×#19692
C11×#19682
C11×#18092
C11×#17882
C11×#17872
#2427611