Finite Group Databasebeta

← C11×#24453 #14601646

Subgroups — C11×#24453 #14601646

Order 2816.

1404 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#470C211yesmaximal, characteristic, complemented
3C2×C11×#451C211yesmaximal, characteristic, complemented
4C2×C11×#451C211yesmaximal, characteristic, complemented
5C2×C11×#419C211yesmaximal, characteristic, complemented
6C11×#2415C211yesmaximal, characteristic
7C11×#2043C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#2016C211yesmaximal, characteristic, complemented
10C11×#2001C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1873C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic
14C11×#1865C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22D4×Q8×C11—24no—
23D4×Q8×C11—24no—
24C2×C11×C4⋊Q8—21no—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8—21no—
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic
33C2×C4×D4×C11—21no—
34C2×C4×D4×C11C2211yescharacteristic
35C2×C11×#117C2211yescharacteristic
36C11×#470—24no—
37C11×#451—24no—
38C11×#451—24no—
39C2×C11×#106C2211yescharacteristic
40C11×#419—24no—
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#397—21no—
55C11×#394—21no—
56C11×#391C2211yescharacteristic
57C11×#389—21no—
58C11×#389C2211yescharacteristic
59C11×#388—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—21no—
68C22×Q8×C11—21no—
69C22×Q8×C11—22no—
70C22×Q8×C11—22no—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—41no—
75C22×Q8×C11—41no—
76C22×Q8×C11—41no—
77C22×Q8×C11—41no—
78C22×Q8×C11D414yes—
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11D411yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C2×C11×Q16—22no—
89C2×C11×Q16—22no—
90C2×C11×Q16—22no—
91C2×C11×Q16—22no—
92C2×C11×Q16—22no—
93C2×C11×Q16—22no—
94C2×C11×Q16—41no—
95C2×C11×Q16—41no—
96C2×C11×Q16—41no—
97C2×C11×M16—22no—
98C2×C11×M16—22no—
99C2×C11×M16—41no—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C11×C4⋊Q8—28no—
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8—22no—
107C11×C22⋊Q8—28no—
108C11×C22⋊Q8—28no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—41no—
116C11×C22⋊Q8D414yes—
117C4×Q8×C11—22no—
118C4×Q8×C11—22no—
119C4×D4×C11—28no—
120C4×D4×C11—22no—
121C4×D4×C11—22no—
122C11×#117—22no—
123C11×#117—41no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4D411yescharacteristic
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⋊C4D411yescharacteristic
144C2×C11×C22⋊C4D411yescharacteristic
145C2×C42×C11—21no—
146C2×C42×C11—21no—
147C2×C42×C11C2311yescharacteristic
148C11×#106—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—22no—
155C11×#103—22no—
156C11×#103—22no—
157C11×#103—41no—
158C11×#103D414yescomplemented
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#24453C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11C2×D411yescharacteristic
168C24×C11C2×D411yescharacteristic
169C2×Q8×C11—24no—
170C2×Q8×C11—24no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—28no—
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—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—42no—
192C2×Q8×C11—42no—
193C2×Q8×C11—42no—
194C2×Q8×C11—42no—
195C2×Q8×C11—44no—
196C2×Q8×C11—44no—
197C2×Q8×C11—44no—
198C2×Q8×C11—44no—
199C2×Q8×C11—44no—
200C2×Q8×C11—44no—
201C2×Q8×C11—44no—
202C2×Q8×C11C2×D412yes—
203C2×Q8×C11C2×D412yes—
204C2×Q8×C11C2×D412yes—
205C2×Q8×C11C2×D412yes—
206C2×Q8×C11#4112yes—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—24no—
216C22×C4×C11—24no—
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—21no—
229C22×C4×C11—21no—
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×D412yes—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C11×Q16—44no—
242C11×Q16—44no—
243C11×Q16—44no—
244C11×M16—44no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
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×C11—21no—
256C2×C8×C11C2×D412yes—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—24no—
261C11×C4⋊C4—24no—
262C11×C4⋊C4—22no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—42no—
270C11×C4⋊C4—42no—
271C11×C4⋊C4—42no—
272C11×C4⋊C4C2×D412yes—
273C11×C4⋊C4C2×D412yes—
274C11×C22⋊C4—24no—
275C11×C22⋊C4—24no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—42no—
279C11×C22⋊C4—42no—
280C11×C22⋊C4—42no—
281C11×C22⋊C4—42no—
282C42×C11—24no—
283C42×C11—21no—
284C42×C11—21no—
285C42×C11—42no—
286C2×D4×Q8C2×C1111yescharacteristic
287C2×#470C2×C1111yescharacteristic, complemented
288C2×#451C2×C1111yescharacteristic, complemented
289C2×#451C2×C1111yescharacteristic, complemented
290C2×#419C2×C1111yescharacteristic, complemented
291#2415C2×C1111yescharacteristic
292#2043C2×C1111yescharacteristic, complemented
293#2035C2×C1111yescharacteristic, complemented
294#2016C2×C1111yescharacteristic, complemented
295#2001C2×C1111yescharacteristic, complemented
296#1878C2×C1111yescharacteristic, complemented
297#1873C2×C1111yescharacteristic, complemented
298#1870C2×C1111yescharacteristic
299#1865C2×C1111yescharacteristic, complemented
300#1787C2×C1111yescharacteristic, complemented
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11#12012yes—
314C23×C11#13712yes—
315C23×C11C22×D411yescharacteristic
316Q8×C11—22no—
317Q8×C11—22no—
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—48no—
324Q8×C11—48no—
325Q8×C11—41no—
326Q8×C11—41no—
327Q8×C11—41no—
328Q8×C11—41no—
329Q8×C11—41no—
330Q8×C11—41no—
331Q8×C11—41no—
332Q8×C11—41no—
333Q8×C11#12114yes—
334D4×C11—28no—
335C2×C4×C11—21no—
336C2×C4×C11—22no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—21no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—21no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—48no—
357C2×C4×C11—48no—
358C2×C4×C11—41no—
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#12012yes—
380C2×C4×C11#13712yes—
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C2×#4111yescharacteristic
385C2×C4×C11H(5,𝔽2)11yescharacteristic
386C2×C4×C11H(5,𝔽2)11yescharacteristic
387C8×C11—22no—
388C8×C11—41no—
389C8×C11—41no—
390C8×C11—41no—
391C23×Q8C22×C1111yescharacteristic
392C23×Q8C22×C1111yescharacteristic
393C22×Q16C22×C1111yescharacteristic
394C22×Q16C22×C1111yescharacteristic
395C22×Q16C22×C1111yescharacteristic
396C22×M16C22×C1111yescharacteristic
397D4×Q8—24no—
398D4×Q8—24no—
399C2×C4⋊Q8—21no—
400C2×C4⋊Q8C22×C1111yescharacteristic
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8C22×C1111yescharacteristic
404C2×C22⋊Q8C22×C1111yescharacteristic
405C2×C22⋊Q8C22×C1111yescharacteristic
406C2×C22⋊Q8C22×C1111yescharacteristic
407C2×C4×Q8C22×C1111yescharacteristic
408C2×C4×D4—21no—
409C2×C4×D4C22×C1111yescharacteristic
410C2×#117C22×C1111yescharacteristic
411#470—24no—
412#451—24no—
413#451—24no—
414C2×#106C22×C1111yescharacteristic
415#419—24no—
416C2×#103C22×C1111yescharacteristic
417C2×#103C22×C1111yescharacteristic
418C2×#103C22×C1111yescharacteristic
419C2×#103C22×C1111yescharacteristic
420C2×#103C22×C1111yescharacteristic
421C2×#103C22×C1111yescharacteristic
422C2×#103C22×C1111yescharacteristic
423C2×#103C22×C1111yescharacteristic
424C2×#103C22×C1111yescharacteristic
425C2×#103C22×C1111yescharacteristic
426C2×C22⋊C8C22×C1111yescharacteristic
427C2×C22⋊C8C22×C1111yescharacteristic
428C2×C22⋊C8C22×C1111yescharacteristic
429#397—21no—
430#394—21no—
431#391C22×C1111yescharacteristic
432#389—21no—
433#389C22×C1111yescharacteristic
434#388—21no—
435#380C22×C1111yescharacteristic
436#340C22×C1111yescharacteristic
437#340C22×C1111yescharacteristic
438#336C22×C1111yescharacteristic
439#336C22×C1111yescharacteristic
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11C2×#12011yescharacteristic
455C22×C11D4211yescharacteristic
456C22×C11#54611yescharacteristic
457C22×C11C2×#13711yescharacteristic
458C22×C11C2×#13711yescharacteristic
459C22×C11#57811yescharacteristic
460C22×C11#57811yescharacteristic
461C4×C11—22no—
462C4×C11—24no—
463C4×C11—22no—
464C4×C11—41no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—41no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—81no—
471C4×C11—81no—
472C4×C11—81no—
473C4×C11C2×#12111yescharacteristic
474C4×C11#53411yescharacteristic
475C4×C11D4211yescharacteristic
476C4×C11#54611yescharacteristic
477C22×Q8—22no—
478C22×Q8—22no—
479C22×Q8—21no—
480C22×Q8—21no—
481C22×Q8—22no—
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—22no—
485C22×Q8—22no—
486C22×Q8—41no—
487C22×Q8—41no—
488C22×Q8—41no—
489C22×Q8—41no—
490C22×Q8D4×C1114yes—
491C22×Q8C23×C1111yescharacteristic
492C22×Q8C23×C1111yescharacteristic
493C22×Q8C23×C1111yescharacteristic
494C22×Q8C23×C1111yescharacteristic
495C22×D4D4×C1111yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4C23×C1111yescharacteristic
499C23×C4C23×C1111yescharacteristic
500C2×Q16—22no—
501C2×Q16—22no—
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16—22no—
506C2×Q16—41no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—41no—
512C22×C8C23×C1111yescharacteristic
513C22×C8C23×C1111yescharacteristic
514C22×C8C23×C1111yescharacteristic
515C22×C8C23×C1111yescharacteristic
516C4⋊Q8—28no—
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C22⋊Q8—28no—
520C22⋊Q8—28no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—22no—
526C22⋊Q8—22no—
527C22⋊Q8—41no—
528C22⋊Q8D4×C1114yes—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×D4—28no—
532C4×D4—22no—
533C4×D4—22no—
534#117—22no—
535#117—41no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4D4×C1111yescharacteristic
545C2×C4⋊C4C23×C1111yescharacteristic
546C2×C4⋊C4C23×C1111yescharacteristic
547C2×C4⋊C4C23×C1111yescharacteristic
548C2×C4⋊C4C23×C1111yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C1111yescharacteristic
556C2×C22⋊C4D4×C1111yescharacteristic
557C2×C42—21no—
558C2×C42—21no—
559C2×C42C23×C1111yescharacteristic
560#106—22no—
561#103—22no—
562#103—22no—
563#103—22no—
564#103—22no—
565#103—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—41no—
570#103D4×C1114yescomplemented
571C22⋊C8—22no—
572C22⋊C8—22no—
573C22⋊C8—41no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C2×C11—42no—
579C2×C11—42no—
580C2×C11#241011yescharacteristic
581C2×C11#300411yescharacteristic
582C2×C11#301111yescharacteristic
583C2×C11#327011yescharacteristic
584C2×C11#327611yescharacteristic
585C2×C11#331211yescharacteristic
586C2×C11#332811yescharacteristic
587C24C2×D4×C1111yescharacteristic
588C24C2×D4×C1111yescharacteristic
589C2×Q8—24no—
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—28no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—42no—
612C2×Q8—42no—
613C2×Q8—42no—
614C2×Q8—42no—
615C2×Q8—44no—
616C2×Q8—44no—
617C2×Q8—44no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8C2×D4×C1112yes—
623C2×Q8C2×D4×C1112yes—
624C2×Q8C2×D4×C1112yes—
625C2×Q8C2×D4×C1112yes—
626C2×Q8C11×#4112yes—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
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—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4C2×D4×C1111yescharacteristic
655C22×C4C2×D4×C1111yescharacteristic
656C22×C4C2×D4×C1111yescharacteristic
657C22×C4C2×D4×C1112yes—
658C22×C4C2×D4×C1112yes—
659C22×C4C2×D4×C1111yescharacteristic
660C22×C4C24×C1111yescharacteristic
661Q16—44no—
662Q16—44no—
663Q16—44no—
664M16—44no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8C2×D4×C1112yes—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4C2×D4×C1112yes—
693C4⋊C4C2×D4×C1112yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C42—24no—
703C42—21no—
704C42—21no—
705C42—42no—
706C11#2445311yescharacteristic, direct product factor, Sylow
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23C11×#12012yes—
720C23C11×#13712yes—
721C23C22×D4×C1111yescharacteristic
722Q8—22no—
723Q8—22no—
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—48no—
730Q8—48no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8C11×#12114yes—
740D4—28no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—48no—
763C2×C4—48no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
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×C4C11×#12012yes—
786C2×C4C11×#13712yes—
787C2×C4C22×D4×C1111yescharacteristic
788C2×C4C22×D4×C1111yescharacteristic
789C2×C4C22×D4×C1111yescharacteristic
790C2×C4C2×C11×#4111yescharacteristic
791C2×C4C11×H(5,𝔽2)11yescharacteristic
792C2×C4C11×H(5,𝔽2)11yescharacteristic
793C8—22no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22C2×C11×#12011yescharacteristic
812C22D42×C1111yescharacteristic
813C22C11×#54611yescharacteristic
814C22C2×C11×#13711yescharacteristic
815C22C2×C11×#13711yescharacteristic
816C22C11×#57811yescharacteristic
817C22C11×#57811yescharacteristic
818C4—22no—
819C4—24no—
820C4—22no—
821C4—41no—
822C4—42no—
823C4—42no—
824C4—41no—
825C4—42no—
826C4—42no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×C11×#12111yescharacteristic
831C4C11×#53411yescharacteristic
832C4D42×C1111yescharacteristic
833C4C11×#54611yescharacteristic
834C2—42no—
835C2—42no—
836C2C11×#241011yescharacteristic
837C2C11×#300411yescharacteristic
838C2C11×#301111yescharacteristic
839C2C11×#327011yescharacteristic
840C2C11×#327611yescharacteristic
841C2C11×#331211yescharacteristic
842C2C11×#332811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
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×#451C2semidirect
4. C2×C11×#451C2semidirect
5. C2×C11×#419C2semidirect
7. C11×#2043C2semidirect
8. C11×#2035C2semidirect
9. C11×#2016C2semidirect
10. C11×#2001C2semidirect
11. C11×#1878C2semidirect
12. C11×#1873C2semidirect
14. C11×#1865C2semidirect
15. C11×#1787C2semidirect
158. C11×#103D4semidirect
166. #24453C11direct (N × H)
287. C2×#470C2×C11semidirect
288. C2×#451C2×C11semidirect
289. C2×#451C2×C11semidirect
290. C2×#419C2×C11semidirect
292. #2043C2×C11semidirect
293. #2035C2×C11semidirect
294. #2016C2×C11semidirect
295. #2001C2×C11semidirect
296. #1878C2×C11semidirect
297. #1873C2×C11semidirect
299. #1865C2×C11semidirect
300. #1787C2×C11semidirect
570. #103D4×C11semidirect
706. C11#24453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C11×#4702
C2×C11×#4512
C2×C11×#4192
C11×#24152
C11×#20432
C11×#20352
C11×#20162
C11×#20012
C11×#18782
C11×#18732
C11×#18702
C11×#18652
C11×#17872
#2445311