Finite Group Databasebeta

← C11×#14098 #14591291

Subgroups — C11×#14098 #14591291

Order 2816.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#124C211yesmaximal, characteristic
2C2×C11×#391C211yesmaximal, characteristic, complemented
3C2×C11×#388C211yesmaximal, characteristic, complemented
4C2×C11×#386C211yesmaximal, characteristic
5C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6C11×#1446C211yesmaximal, characteristic, complemented
7C11×#1440C211yesmaximal, characteristic, complemented
8C11×#1439C211yesmaximal, characteristic, complemented
9C11×#1438C211yesmaximal, characteristic
10C11×#1437C211yesmaximal, characteristic, complemented
11C11×#1437C211yesmaximal, characteristic, complemented
12C11×#1437C211yesmaximal, characteristic, complemented
13C11×#1434C211yesmaximal, characteristic, complemented
14C11×C22⋊#95C211yesmaximal, characteristic, complemented
15C4×C11×#95C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C2×C11×#124—24no—
20C2×C11×#124—24no—
21C2×C11×#124C418yescomplemented
22C22×C11×C4⋊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
35C22×C42×C11C2211yescharacteristic
36C22×C42×C11C2211yescharacteristic
37C22×C42×C11C2211yescharacteristic
38C11×#391—24no—
39C11×#388—24no—
40C11×#386—24no—
41C4×C11×C22⋊C4—24no—
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
57C2×C11×#95C2211yescharacteristic
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
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×Q8×C11C2×C414yescomplemented
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—22no—
70C22×D4×C11—22no—
71C22×D4×C11—41no—
72C22×D4×C11—41no—
73C22×D4×C11C2×C414yes—
74C23×C4×C11—22no—
75C23×C4×C11—22no—
76C23×C4×C11—22no—
77C23×C4×C11—22no—
78C23×C4×C11—22no—
79C23×C4×C11—41no—
80C23×C4×C11—41no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C11×#124—232no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
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—41no—
120C2×C11×C22⋊C4—41no—
121C2×C11×C22⋊C4—41no—
122C2×C11×C22⋊C4—41no—
123C2×C11×C22⋊C4—41no—
124C2×C11×C22⋊C4—41no—
125C2×C11×C22⋊C4C2×C414yes—
126C2×C11×C22⋊C4C2×C414yes—
127C2×C11×C22⋊C4C2×C414yescomplemented
128C2×C11×C22⋊C4C2×C414yescomplemented
129C2×C11×C22⋊C4D414yes—
130C2×C11×C22⋊C4D414yes—
131C2×C42×C11—22no—
132C2×C42×C11—22no—
133C2×C42×C11—22no—
134C2×C42×C11—22no—
135C2×C42×C11—22no—
136C2×C42×C11—22no—
137C2×C42×C11—22no—
138C2×C42×C11—22no—
139C2×C42×C11—41no—
140C2×C42×C11—41no—
141C2×C42×C11—41no—
142C2×C42×C11C2×C414yescomplemented
143C11×#95—22no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95—22no—
148C11×#95—22no—
149C11×#95—22no—
150C11×#95—22no—
151C11×#95—22no—
152C11×#95—22no—
153C11×#95—22no—
154C11×#95—22no—
155C11×#95—22no—
156C11×#95—41no—
157C11×#95—41no—
158C11×#95D414yes—
159#14098C1111yesmaximal, characteristic, direct product factor, Sylow
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×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11C22×C412yes—
187C24×C11C22×C412yes—
188C24×C11C2×D412yes—
189C24×C11C2×D412yes—
190C24×C11C2411yescharacteristic
191C2×Q8×C11—28no—
192C2×Q8×C11—28no—
193C2×Q8×C11—44no—
194C2×Q8×C11—44no—
195C2×Q8×C11—44no—
196C2×Q8×C11—44no—
197C2×Q8×C11—44no—
198C2×D4×C11—28no—
199C2×D4×C11—28no—
200C2×D4×C11—44no—
201C2×D4×C11—44no—
202C2×D4×C11—44no—
203C2×D4×C11—44no—
204C2×D4×C11—44no—
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—28no—
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—44no—
279C22×C4×C11—44no—
280C22×C4×C11—44no—
281C22×C4×C11—44no—
282C22×C4×C11—44no—
283C22×C4×C11—44no—
284C22×C4×C11C22×C412yes—
285C22×C4×C11C22×C412yes—
286C22×C4×C11C22×C412yes—
287C22×C4×C11C22×C412yes—
288C22×C4×C11C22×C412yes—
289C22×C4×C11C2×D412yes—
290C22×C4×C11C2×D412yes—
291C22×C4×C11C2×D412yes—
292C22×C4×C11C2×D412yes—
293C22×C4×C11C2×D412yes—
294C22×C4×C11C2×D412yes—
295C22×C4×C11C2×D412yes—
296C22×C4×C11#4112yes—
297C22×C4×C11#4112yes—
298C22×C4×C11#4112yes—
299C22×C4×C11#4112yes—
300C22×C4×C11#4112yes—
301C22×C4×C11#4112yes—
302C22×C4×C11#4112yes—
303C11×C4⋊C4—44no—
304C11×C22⋊C4—28no—
305C11×C22⋊C4—28no—
306C11×C22⋊C4—28no—
307C11×C22⋊C4—28no—
308C11×C22⋊C4—44no—
309C11×C22⋊C4—44no—
310C11×C22⋊C4—44no—
311C11×C22⋊C4—44no—
312C11×C22⋊C4—44no—
313C11×C22⋊C4—44no—
314C11×C22⋊C4C22⋊C4116yescomplemented
315C42×C11—28no—
316C42×C11—44no—
317C42×C11—44no—
318C42×C11—44no—
319C22×#124C2×C1111yescharacteristic
320C2×#391C2×C1111yescharacteristic, complemented
321C2×#388C2×C1111yescharacteristic, complemented
322C2×#386C2×C1111yescharacteristic
323C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
324#1446C2×C1111yescharacteristic, complemented
325#1440C2×C1111yescharacteristic, complemented
326#1439C2×C1111yescharacteristic, complemented
327#1438C2×C1111yescharacteristic
328#1437C2×C1111yescharacteristic, complemented
329#1437C2×C1111yescharacteristic, complemented
330#1437C2×C1111yescharacteristic, complemented
331#1434C2×C1111yescharacteristic, complemented
332C22⋊#95C2×C1111yescharacteristic, complemented
333C4×#95C2×C1111yescharacteristic, complemented
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
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×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11C2×C22⋊C414yes—
404C23×C11C23×C411yescharacteristic
405C23×C11C22×D411yescharacteristic
406C23×C11C22×D411yescharacteristic
407C23×C11C22×D411yescharacteristic
408C23×C11C2×#4111yescharacteristic
409C23×C11C2×#4111yescharacteristic
410C23×C11C2×#4111yescharacteristic
411C23×C11C2×#4111yescharacteristic
412C23×C11C2×#4111yescharacteristic
413C23×C11C2×#4111yescharacteristic
414C23×C11C2×#4111yescharacteristic
415C23×C11H(5,𝔽2)11yescharacteristic
416C23×C11H(5,𝔽2)11yescharacteristic
417C23×C11H(5,𝔽2)11yescharacteristic
418C23×C112−1+411yescharacteristic
419Q8×C11—416no—
420D4×C11—416no—
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—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—416no—
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—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11C2×C22⋊C414yes—
510C2×C4×C11C2×C22⋊C414yes—
511C2×C4×C11C4×D414yes—
512C2×C4×C11#12414yescomplemented
513C23×Q8C22×C1111yescharacteristic
514C23×D4C22×C1111yescharacteristic
515C24×C4C22×C1111yescharacteristic
516C2×#124—24no—
517C2×#124—24no—
518C2×#124C4×C1118yescomplemented
519C22×C4⋊C4C22×C1111yescharacteristic
520C22×C22⋊C4C22×C1111yescharacteristic
521C22×C22⋊C4C22×C1111yescharacteristic
522C22×C22⋊C4C22×C1111yescharacteristic
523C22×C22⋊C4C22×C1111yescharacteristic
524C22×C22⋊C4C22×C1111yescharacteristic
525C22×C22⋊C4C22×C1111yescharacteristic
526C22×C22⋊C4C22×C1111yescharacteristic
527C22×C22⋊C4C22×C1111yescharacteristic
528C22×C22⋊C4C22×C1111yescharacteristic
529C22×C22⋊C4C22×C1111yescharacteristic
530C22×C22⋊C4C22×C1111yescharacteristic
531C22×C42C22×C1111yescharacteristic
532C22×C42C22×C1111yescharacteristic
533C22×C42C22×C1111yescharacteristic
534C22×C42C22×C1111yescharacteristic
535#391—24no—
536#388—24no—
537#386—24no—
538C4×C22⋊C4—24no—
539C2×#95C22×C1111yescharacteristic
540C2×#95C22×C1111yescharacteristic
541C2×#95C22×C1111yescharacteristic
542C2×#95C22×C1111yescharacteristic
543C2×#95C22×C1111yescharacteristic
544C2×#95C22×C1111yescharacteristic
545C2×#95C22×C1111yescharacteristic
546C2×#95C22×C1111yescharacteristic
547C2×#95C22×C1111yescharacteristic
548C2×#95C22×C1111yescharacteristic
549C2×#95C22×C1111yescharacteristic
550C2×#95C22×C1111yescharacteristic
551C2×#95C22×C1111yescharacteristic
552C2×#95C22×C1111yescharacteristic
553C2×#95C22×C1111yescharacteristic
554C2×#95C22×C1111yescharacteristic
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—24no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—81no—
578C22×C11—81no—
579C22×C11—81no—
580C22×C11—81no—
581C22×C11—81no—
582C22×C11—81no—
583C22×C11—81no—
584C22×C11—81no—
585C22×C11C22×C22⋊C411yescharacteristic
586C22×C11C2×C4×D411yescharacteristic
587C22×C11C4×#4111yescharacteristic
588C22×C11C4×#4111yescharacteristic
589C22×C11C4×#4111yescharacteristic
590C22×C11#51811yescharacteristic
591C22×C11#52011yescharacteristic
592C22×C11#52511yescharacteristic
593C22×C11#52511yescharacteristic
594C22×C11C2×#12411yescharacteristic
595C22×C11#52911yescharacteristic
596C22×C11#52911yescharacteristic
597C22×C11#53211yescharacteristic
598C22×C11#53211yescharacteristic
599C22×C11#53211yescharacteristic
600C22×C11#53811yescharacteristic
601C22×C11#53811yescharacteristic
602C22×C11#54211yescharacteristic
603C22×C11#54211yescharacteristic
604C22×C11D4211yescharacteristic
605C22×C11D4211yescharacteristic
606C22×C11#54611yescharacteristic
607C22×C11#54611yescharacteristic
608C22×C11#54611yescharacteristic
609C22×C11#54611yescharacteristic
610C22×C11#54611yescharacteristic
611C22×C11#54711yescharacteristic
612C22×C11#54711yescharacteristic
613C22×C11#54811yescharacteristic
614C22×C11#55111yescharacteristic
615C22×C11#55111yescharacteristic
616C22×C11#55511yescharacteristic
617C22×C11#55511yescharacteristic
618C22×C11#55611yescharacteristic
619C22×C11#55911yescharacteristic
620C4×C11—24no—
621C4×C11—24no—
622C4×C11—24no—
623C4×C11—24no—
624C4×C11—42no—
625C4×C11—42no—
626C4×C11—42no—
627C4×C11—42no—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—42no—
631C4×C11—81no—
632C4×C11—81no—
633C25C23×C1111yescharacteristic
634C25C23×C1111yescharacteristic
635C22×Q8—22no—
636C22×Q8—22no—
637C22×Q8—22no—
638C22×Q8—22no—
639C22×Q8—41no—
640C22×Q8—41no—
641C22×Q8C2×C4×C1114yescomplemented
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—22no—
645C22×D4—22no—
646C22×D4—41no—
647C22×D4—41no—
648C22×D4C2×C4×C1114yes—
649C23×C4—22no—
650C23×C4—22no—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—41no—
655C23×C4—41no—
656C23×C4C23×C1111yescharacteristic
657C23×C4C23×C1111yescharacteristic
658C23×C4C23×C1111yescharacteristic
659C23×C4C23×C1111yescharacteristic
660C23×C4C23×C1111yescharacteristic
661C23×C4C23×C1111yescharacteristic
662C23×C4C23×C1111yescharacteristic
663C23×C4C23×C1111yescharacteristic
664C23×C4C23×C1111yescharacteristic
665C23×C4C23×C1111yescharacteristic
666C23×C4C23×C1111yescharacteristic
667C23×C4C23×C1111yescharacteristic
668C23×C4C23×C1111yescharacteristic
669#124—232no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—41no—
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—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4C2×C4×C1114yes—
701C2×C22⋊C4C2×C4×C1114yes—
702C2×C22⋊C4C2×C4×C1114yescomplemented
703C2×C22⋊C4C2×C4×C1114yescomplemented
704C2×C22⋊C4D4×C1114yes—
705C2×C22⋊C4D4×C1114yes—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—41no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×C4×C1114yescomplemented
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—41no—
732#95—41no—
733#95D4×C1114yes—
734C2×C11—44no—
735C2×C11—82no—
736C2×C11#229711yescharacteristic
737C2×C11C4×#12411yescharacteristic
738C2×C11#233711yescharacteristic
739C2×C11D4×C22⋊C411yescharacteristic
740C2×C11#233911yescharacteristic
741C2×C11#236711yescharacteristic
742C2×C11#237211yescharacteristic
743C2×C11#245911yescharacteristic
744C2×C11#246111yescharacteristic
745C2×C11#247211yescharacteristic
746C2×C11#247411yescharacteristic
747C2×C11#249111yescharacteristic
748C2×C11#252111yescharacteristic
749C2×C11#255511yescharacteristic
750C2×C11#255711yescharacteristic
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24C22×C4×C1112yes—
778C24C22×C4×C1112yes—
779C24C2×D4×C1112yes—
780C24C2×D4×C1112yes—
781C24C24×C1111yescharacteristic
782C2×Q8—28no—
783C2×Q8—28no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
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—28no—
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×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4C22×C4×C1112yes—
876C22×C4C22×C4×C1112yes—
877C22×C4C22×C4×C1112yes—
878C22×C4C22×C4×C1112yes—
879C22×C4C22×C4×C1112yes—
880C22×C4C2×D4×C1112yes—
881C22×C4C2×D4×C1112yes—
882C22×C4C2×D4×C1112yes—
883C22×C4C2×D4×C1112yes—
884C22×C4C2×D4×C1112yes—
885C22×C4C2×D4×C1112yes—
886C22×C4C2×D4×C1112yes—
887C22×C4C11×#4112yes—
888C22×C4C11×#4112yes—
889C22×C4C11×#4112yes—
890C22×C4C11×#4112yes—
891C22×C4C11×#4112yes—
892C22×C4C11×#4112yes—
893C22×C4C11×#4112yes—
894C4⋊C4—44no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4C11×C22⋊C4116yescomplemented
906C42—28no—
907C42—44no—
908C42—44no—
909C42—44no—
910C11#1409811yescharacteristic, direct product factor, Sylow
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
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—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C11×C22⋊C414yes—
981C23C23×C4×C1111yescharacteristic
982C23C22×D4×C1111yescharacteristic
983C23C22×D4×C1111yescharacteristic
984C23C22×D4×C1111yescharacteristic
985C23C2×C11×#4111yescharacteristic
986C23C2×C11×#4111yescharacteristic
987C23C2×C11×#4111yescharacteristic
988C23C2×C11×#4111yescharacteristic
989C23C2×C11×#4111yescharacteristic
990C23C2×C11×#4111yescharacteristic
991C23C2×C11×#4111yescharacteristic
992C23C11×H(5,𝔽2)11yescharacteristic
993C23C11×H(5,𝔽2)11yescharacteristic
994C23C11×H(5,𝔽2)11yescharacteristic
995C23C11×2−1+411yescharacteristic
996Q8—416no—
997D4—416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—416no—
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×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4C2×C11×C22⋊C414yes—
1087C2×C4C2×C11×C22⋊C414yes—
1088C2×C4C4×D4×C1114yes—
1089C2×C4C11×#12414yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C11×C22⋊C411yescharacteristic
1121C22C2×C4×D4×C1111yescharacteristic
1122C22C4×C11×#4111yescharacteristic
1123C22C4×C11×#4111yescharacteristic
1124C22C4×C11×#4111yescharacteristic
1125C22C11×#51811yescharacteristic
1126C22C11×#52011yescharacteristic
1127C22C11×#52511yescharacteristic
1128C22C11×#52511yescharacteristic
1129C22C2×C11×#12411yescharacteristic
1130C22C11×#52911yescharacteristic
1131C22C11×#52911yescharacteristic
1132C22C11×#53211yescharacteristic
1133C22C11×#53211yescharacteristic
1134C22C11×#53211yescharacteristic
1135C22C11×#53811yescharacteristic
1136C22C11×#53811yescharacteristic
1137C22C11×#54211yescharacteristic
1138C22C11×#54211yescharacteristic
1139C22D42×C1111yescharacteristic
1140C22D42×C1111yescharacteristic
1141C22C11×#54611yescharacteristic
1142C22C11×#54611yescharacteristic
1143C22C11×#54611yescharacteristic
1144C22C11×#54611yescharacteristic
1145C22C11×#54611yescharacteristic
1146C22C11×#54711yescharacteristic
1147C22C11×#54711yescharacteristic
1148C22C11×#54811yescharacteristic
1149C22C11×#55111yescharacteristic
1150C22C11×#55111yescharacteristic
1151C22C11×#55511yescharacteristic
1152C22C11×#55511yescharacteristic
1153C22C11×#55611yescharacteristic
1154C22C11×#55911yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—24no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—82no—
1170C2C11×#229711yescharacteristic
1171C2C4×C11×#12411yescharacteristic
1172C2C11×#233711yescharacteristic
1173C2D4×C11×C22⋊C411yescharacteristic
1174C2C11×#233911yescharacteristic
1175C2C11×#236711yescharacteristic
1176C2C11×#237211yescharacteristic
1177C2C11×#245911yescharacteristic
1178C2C11×#246111yescharacteristic
1179C2C11×#247211yescharacteristic
1180C2C11×#247411yescharacteristic
1181C2C11×#249111yescharacteristic
1182C2C11×#252111yescharacteristic
1183C2C11×#255511yescharacteristic
1184C2C11×#255711yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#391C2semidirect
3. C2×C11×#388C2semidirect
5. C2×C4×C11×C22⋊C4C2semidirect
6. C11×#1446C2semidirect
7. C11×#1440C2semidirect
8. C11×#1439C2semidirect
10. C11×#1437C2semidirect
11. C11×#1437C2semidirect
12. C11×#1437C2semidirect
13. C11×#1434C2semidirect
14. C11×C22⋊#95C2semidirect
15. C4×C11×#95C2semidirect
21. C2×C11×#124C4semidirect
66. C22×Q8×C11C2×C4semidirect
127. C2×C11×C22⋊C4C2×C4semidirect
128. C2×C11×C22⋊C4C2×C4semidirect
142. C2×C42×C11C2×C4semidirect
159. #14098C11direct (N × H)
314. C11×C22⋊C4C22⋊C4semidirect
320. C2×#391C2×C11semidirect
321. C2×#388C2×C11semidirect
323. C2×C4×C22⋊C4C2×C11semidirect
324. #1446C2×C11semidirect
325. #1440C2×C11semidirect
326. #1439C2×C11semidirect
328. #1437C2×C11semidirect
329. #1437C2×C11semidirect
330. #1437C2×C11semidirect
331. #1434C2×C11semidirect
332. C22⋊#95C2×C11semidirect
333. C4×#95C2×C11semidirect
512. C2×C4×C11#124semidirect
518. C2×#124C4×C11semidirect
641. C22×Q8C2×C4×C11semidirect
702. C2×C22⋊C4C2×C4×C11semidirect
703. C2×C22⋊C4C2×C4×C11semidirect
717. C2×C42C2×C4×C11semidirect
905. C22⋊C4C11×C22⋊C4semidirect
910. C11#14098direct (N × H)
1089. C2×C4C11×#124semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1242
C2×C11×#3912
C2×C11×#3882
C2×C11×#3862
C2×C4×C11×C22⋊C42
C11×#14462
C11×#14402
C11×#14392
C11×#14382
C11×#14372
C11×#14342
C11×C22⋊#952
C4×C11×#952
#1409811