Finite Group Databasebeta

← C11×#16294 #14593487

Subgroups — C11×#16294 #14593487

Order 2816.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#394C211yesmaximal, characteristic
2C2×C11×#394C211yesmaximal, characteristic
3C2×C11×#393C211yesmaximal, characteristic, complemented
4C2×C11×#393C211yesmaximal, characteristic, complemented
5C2×C11×#391C211yesmaximal, characteristic, complemented
6C2×C11×#388C211yesmaximal, characteristic, complemented
7C11×#1444C211yesmaximal, characteristic, complemented
8C11×#1443C211yesmaximal, characteristic, complemented
9C11×#1441C211yesmaximal, characteristic, complemented
10C11×#1440C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C11×#1439C211yesmaximal, characteristic, complemented
13C11×#1439C211yesmaximal, characteristic, complemented
14C11×#1438C211yesmaximal, characteristic
15C11×#1437C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C42×C11C2211yescharacteristic
35C11×#394—24no—
36C11×#394—24no—
37C11×#393—24no—
38C11×#393—24no—
39C11×#391—24no—
40C11×#388—24no—
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C25×C11C2311yescharacteristic
58C25×C11C2311yescharacteristic
59C22×Q8×C11—22no—
60C22×Q8×C11—22no—
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—41no—
65C22×Q8×C11—41no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11—41no—
72C22×D4×C11—41no—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4—41no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—41no—
122C2×C11×C22⋊C4—41no—
123C2×C11×C22⋊C4—41no—
124C2×C11×C22⋊C4—41no—
125C2×C11×C22⋊C4—41no—
126C2×C11×C22⋊C4—41no—
127C2×C11×C22⋊C4—41no—
128C2×C11×C22⋊C4—41no—
129C2×C11×C22⋊C4—41no—
130C2×C11×C22⋊C4—41no—
131C2×C11×C22⋊C4—41no—
132C2×C11×C22⋊C4—41no—
133C2×C11×C22⋊C4D414yes—
134C2×C42×C11—22no—
135C2×C42×C11—22no—
136C2×C42×C11—41no—
137C11×#95—22no—
138C11×#95—22no—
139C11×#95—22no—
140C11×#95—22no—
141C11×#95—22no—
142C11×#95—22no—
143C11×#95—22no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95—41no—
148C11×#95—41no—
149C11×#95—41no—
150C11×#95—41no—
151C11×#95D414yes—
152C11×#95D414yescomplemented
153#16294C1111yesmaximal, characteristic, direct product factor, Sylow
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11C2×D412yes—
183C24×C11#4112yes—
184C24×C11C2411yescharacteristic
185C2×Q8×C11—28no—
186C2×Q8×C11—44no—
187C2×Q8×C11—44no—
188C2×Q8×C11—44no—
189C2×Q8×C11—44no—
190C2×Q8×C11—44no—
191C2×Q8×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C2×D4×C11—44no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
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—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
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—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×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—21no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—21no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11C2×D412yes—
280C22×C4×C11C2×D412yes—
281C22×C4×C11C2×D412yes—
282C22×C4×C11C2×D412yes—
283C22×C4×C11C2×D412yes—
284C22×C4×C11C2×D412yes—
285C22×C4×C11C2×D412yes—
286C22×C4×C11C2×D412yes—
287C22×C4×C11#4112yes—
288C22×C4×C11#4112yes—
289C22×C4×C11#4112yes—
290C11×C4⋊C4—44no—
291C11×C4⋊C4—44no—
292C11×C4⋊C4—44no—
293C11×C4⋊C4—44no—
294C11×C22⋊C4—28no—
295C11×C22⋊C4—44no—
296C11×C22⋊C4—44no—
297C11×C22⋊C4—44no—
298C11×C22⋊C4—44no—
299C11×C22⋊C4—44no—
300C11×C22⋊C4—44no—
301C11×C22⋊C4—44no—
302C11×C22⋊C4—44no—
303C11×C22⋊C4—44no—
304C11×C22⋊C4—44no—
305C11×C22⋊C4—44no—
306C42×C11—44no—
307C2×#394C2×C1111yescharacteristic
308C2×#394C2×C1111yescharacteristic
309C2×#393C2×C1111yescharacteristic, complemented
310C2×#393C2×C1111yescharacteristic, complemented
311C2×#391C2×C1111yescharacteristic, complemented
312C2×#388C2×C1111yescharacteristic, complemented
313#1444C2×C1111yescharacteristic, complemented
314#1443C2×C1111yescharacteristic, complemented
315#1441C2×C1111yescharacteristic, complemented
316#1440C2×C1111yescharacteristic, complemented
317#1439C2×C1111yescharacteristic, complemented
318#1439C2×C1111yescharacteristic, complemented
319#1439C2×C1111yescharacteristic, complemented
320#1438C2×C1111yescharacteristic
321#1437C2×C1111yescharacteristic, complemented
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—41no—
337C23×C11—41no—
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—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394C23×C11C22×D411yescharacteristic
395C23×C11C2×#4111yescharacteristic
396C23×C11C2×#4111yescharacteristic
397C23×C11C2×#4111yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11H(5,𝔽2)11yescharacteristic
400C23×C11H(5,𝔽2)11yescharacteristic
401C23×C11H(5,𝔽2)11yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C112−1+411yescharacteristic
405C23×C112−1+411yescharacteristic
406C23×C112−1+411yescharacteristic
407Q8×C11—416no—
408D4×C11—416no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11#12114yes—
500C23×Q8C22×C1111yescharacteristic
501C23×D4C22×C1111yescharacteristic
502C22×C4⋊C4C22×C1111yescharacteristic
503C22×C4⋊C4C22×C1111yescharacteristic
504C22×C4⋊C4C22×C1111yescharacteristic
505C22×C4⋊C4C22×C1111yescharacteristic
506C22×C22⋊C4C22×C1111yescharacteristic
507C22×C22⋊C4C22×C1111yescharacteristic
508C22×C22⋊C4C22×C1111yescharacteristic
509C22×C22⋊C4C22×C1111yescharacteristic
510C22×C22⋊C4C22×C1111yescharacteristic
511C22×C22⋊C4C22×C1111yescharacteristic
512C22×C22⋊C4C22×C1111yescharacteristic
513C22×C22⋊C4C22×C1111yescharacteristic
514C22×C22⋊C4C22×C1111yescharacteristic
515C22×C22⋊C4C22×C1111yescharacteristic
516C22×C22⋊C4C22×C1111yescharacteristic
517C22×C22⋊C4C22×C1111yescharacteristic
518C22×C42C22×C1111yescharacteristic
519#394—24no—
520#394—24no—
521#393—24no—
522#393—24no—
523#391—24no—
524#388—24no—
525C2×#95C22×C1111yescharacteristic
526C2×#95C22×C1111yescharacteristic
527C2×#95C22×C1111yescharacteristic
528C2×#95C22×C1111yescharacteristic
529C2×#95C22×C1111yescharacteristic
530C2×#95C22×C1111yescharacteristic
531C2×#95C22×C1111yescharacteristic
532C2×#95C22×C1111yescharacteristic
533C2×#95C22×C1111yescharacteristic
534C2×#95C22×C1111yescharacteristic
535C2×#95C22×C1111yescharacteristic
536C2×#95C22×C1111yescharacteristic
537C2×#95C22×C1111yescharacteristic
538C2×#95C22×C1111yescharacteristic
539C2×#95C22×C1111yescharacteristic
540C2×#95C22×C1111yescharacteristic
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—81no—
556C22×C11—81no—
557C22×C11—81no—
558C22×C11—81no—
559C22×C11—81no—
560C22×C11—81no—
561C22×C11—81no—
562C22×C11—81no—
563C22×C11—81no—
564C22×C11—81no—
565C22×C11—81no—
566C22×C11—81no—
567C22×C11—81no—
568C22×C11—81no—
569C22×C11—81no—
570C22×C11—81no—
571C22×C11C2×#12111yescharacteristic
572C22×C11#52511yescharacteristic
573C22×C11#52911yescharacteristic
574C22×C11#53511yescharacteristic
575C22×C11#53511yescharacteristic
576C22×C11#53611yescharacteristic
577C22×C11#53611yescharacteristic
578C22×C11#53711yescharacteristic
579C22×C11#53711yescharacteristic
580C22×C11#53811yescharacteristic
581C22×C11#53811yescharacteristic
582C22×C11#53811yescharacteristic
583C22×C11#53911yescharacteristic
584C22×C11#54211yescharacteristic
585C22×C11#54211yescharacteristic
586C22×C11#54211yescharacteristic
587C22×C11#54211yescharacteristic
588C22×C11#54211yescharacteristic
589C22×C11#54211yescharacteristic
590C22×C11D4211yescharacteristic
591C22×C11D4211yescharacteristic
592C22×C11#54611yescharacteristic
593C22×C11#54611yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54711yescharacteristic
598C22×C11#54811yescharacteristic
599C22×C11#54811yescharacteristic
600C22×C11#55211yescharacteristic
601C22×C11#55911yescharacteristic
602C22×C11H(3,𝔽4)11yescharacteristic
603C22×C11#56211yescharacteristic
604C22×C11#56211yescharacteristic
605C22×C11#56311yescharacteristic
606C4×C11—24no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—42no—
612C4×C11—42no—
613C4×C11—42no—
614C4×C11—42no—
615C4×C11—81no—
616C4×C11—81no—
617C4×C11—81no—
618C4×C11—81no—
619C25C23×C1111yescharacteristic
620C25C23×C1111yescharacteristic
621C22×Q8—22no—
622C22×Q8—22no—
623C22×Q8—22no—
624C22×Q8—22no—
625C22×Q8—22no—
626C22×Q8—41no—
627C22×Q8—41no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—41no—
632C22×D4—41no—
633C22×D4—41no—
634C22×D4—41no—
635C23×C4C23×C1111yescharacteristic
636C23×C4C23×C1111yescharacteristic
637C23×C4C23×C1111yescharacteristic
638C23×C4C23×C1111yescharacteristic
639C23×C4C23×C1111yescharacteristic
640C23×C4C23×C1111yescharacteristic
641C23×C4C23×C1111yescharacteristic
642C23×C4C23×C1111yescharacteristic
643C23×C4C23×C1111yescharacteristic
644C23×C4C23×C1111yescharacteristic
645C23×C4C23×C1111yescharacteristic
646C23×C4C23×C1111yescharacteristic
647C23×C4C23×C1111yescharacteristic
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4D4×C1114yes—
696C2×C42—22no—
697C2×C42—22no—
698C2×C42—41no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95D4×C1114yes—
714#95D4×C1114yescomplemented
715C2×C11—82no—
716C2×C11—82no—
717C2×C11#242411yescharacteristic
718C2×C11#242711yescharacteristic
719C2×C11#245811yescharacteristic
720C2×C11#262011yescharacteristic
721C2×C11#263211yescharacteristic
722C2×C11#265311yescharacteristic
723C2×C11#267011yescharacteristic
724C2×C11#267411yescharacteristic
725C2×C11#267611yescharacteristic
726C2×C11#268111yescharacteristic
727C2×C11#268711yescharacteristic
728C2×C11#270211yescharacteristic
729C2×C11#271011yescharacteristic
730C2×C11#271211yescharacteristic
731C2×C11#283211yescharacteristic
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24C2×D4×C1112yes—
761C24C11×#4112yes—
762C24C24×C1111yescharacteristic
763C2×Q8—28no—
764C2×Q8—44no—
765C2×Q8—44no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4C2×D4×C1112yes—
858C22×C4C2×D4×C1112yes—
859C22×C4C2×D4×C1112yes—
860C22×C4C2×D4×C1112yes—
861C22×C4C2×D4×C1112yes—
862C22×C4C2×D4×C1112yes—
863C22×C4C2×D4×C1112yes—
864C22×C4C2×D4×C1112yes—
865C22×C4C11×#4112yes—
866C22×C4C11×#4112yes—
867C22×C4C11×#4112yes—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C22⋊C4—28no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C42—44no—
885C11#1629411yescharacteristic, direct product factor, Sylow
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23C22×D4×C1111yescharacteristic
957C23C22×D4×C1111yescharacteristic
958C23C22×D4×C1111yescharacteristic
959C23C2×C11×#4111yescharacteristic
960C23C2×C11×#4111yescharacteristic
961C23C2×C11×#4111yescharacteristic
962C23C2×C11×#4111yescharacteristic
963C23C11×H(5,𝔽2)11yescharacteristic
964C23C11×H(5,𝔽2)11yescharacteristic
965C23C11×H(5,𝔽2)11yescharacteristic
966C23C11×H(5,𝔽2)11yescharacteristic
967C23C11×H(5,𝔽2)11yescharacteristic
968C23C11×2−1+411yescharacteristic
969C23C11×2−1+411yescharacteristic
970C23C11×2−1+411yescharacteristic
971Q8—416no—
972D4—416no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4C11×#12114yes—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22C2×C11×#12111yescharacteristic
1095C22C11×#52511yescharacteristic
1096C22C11×#52911yescharacteristic
1097C22C11×#53511yescharacteristic
1098C22C11×#53511yescharacteristic
1099C22C11×#53611yescharacteristic
1100C22C11×#53611yescharacteristic
1101C22C11×#53711yescharacteristic
1102C22C11×#53711yescharacteristic
1103C22C11×#53811yescharacteristic
1104C22C11×#53811yescharacteristic
1105C22C11×#53811yescharacteristic
1106C22C11×#53911yescharacteristic
1107C22C11×#54211yescharacteristic
1108C22C11×#54211yescharacteristic
1109C22C11×#54211yescharacteristic
1110C22C11×#54211yescharacteristic
1111C22C11×#54211yescharacteristic
1112C22C11×#54211yescharacteristic
1113C22D42×C1111yescharacteristic
1114C22D42×C1111yescharacteristic
1115C22C11×#54611yescharacteristic
1116C22C11×#54611yescharacteristic
1117C22C11×#54611yescharacteristic
1118C22C11×#54611yescharacteristic
1119C22C11×#54611yescharacteristic
1120C22C11×#54711yescharacteristic
1121C22C11×#54811yescharacteristic
1122C22C11×#54811yescharacteristic
1123C22C11×#55211yescharacteristic
1124C22C11×#55911yescharacteristic
1125C22C11×H(3,𝔽4)11yescharacteristic
1126C22C11×#56211yescharacteristic
1127C22C11×#56211yescharacteristic
1128C22C11×#56311yescharacteristic
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C2—82no—
1143C2—82no—
1144C2C11×#242411yescharacteristic
1145C2C11×#242711yescharacteristic
1146C2C11×#245811yescharacteristic
1147C2C11×#262011yescharacteristic
1148C2C11×#263211yescharacteristic
1149C2C11×#265311yescharacteristic
1150C2C11×#267011yescharacteristic
1151C2C11×#267411yescharacteristic
1152C2C11×#267611yescharacteristic
1153C2C11×#268111yescharacteristic
1154C2C11×#268711yescharacteristic
1155C2C11×#270211yescharacteristic
1156C2C11×#271011yescharacteristic
1157C2C11×#271211yescharacteristic
1158C2C11×#283211yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#393C2semidirect
4. C2×C11×#393C2semidirect
5. C2×C11×#391C2semidirect
6. C2×C11×#388C2semidirect
7. C11×#1444C2semidirect
8. C11×#1443C2semidirect
9. C11×#1441C2semidirect
10. C11×#1440C2semidirect
11. C11×#1439C2semidirect
12. C11×#1439C2semidirect
13. C11×#1439C2semidirect
15. C11×#1437C2semidirect
152. C11×#95D4semidirect
153. #16294C11direct (N × H)
309. C2×#393C2×C11semidirect
310. C2×#393C2×C11semidirect
311. C2×#391C2×C11semidirect
312. C2×#388C2×C11semidirect
313. #1444C2×C11semidirect
314. #1443C2×C11semidirect
315. #1441C2×C11semidirect
316. #1440C2×C11semidirect
317. #1439C2×C11semidirect
318. #1439C2×C11semidirect
319. #1439C2×C11semidirect
321. #1437C2×C11semidirect
714. #95D4×C11semidirect
885. C11#16294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3942
C2×C11×#3932
C2×C11×#3912
C2×C11×#3882
C11×#14442
C11×#14432
C11×#14412
C11×#14402
C11×#14392
C11×#14382
C11×#14372
#1629411