Finite Group Databasebeta

← C11×#14517 #14591710

Subgroups — C11×#14517 #14591710

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#394C211yesmaximal, characteristic
2C2×C11×#388C211yesmaximal, characteristic, complemented
3C2×C11×#386C211yesmaximal, characteristic
4C2×C11×#386C211yesmaximal, characteristic
5C2×C11×#385C211yesmaximal, characteristic, complemented
6C11×#1445C211yesmaximal, characteristic, complemented
7C11×#1443C211yesmaximal, characteristic, complemented
8C11×#1441C211yesmaximal, characteristic, complemented
9C11×#1440C211yesmaximal, characteristic, complemented
10C11×#1439C211yesmaximal, characteristic, complemented
11C11×#1437C211yesmaximal, characteristic, complemented
12C11×#1436C211yesmaximal, characteristic, complemented
13C11×C22⋊#95C211yesmaximal, characteristic, complemented
14C11×C22⋊#95C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
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×C42×C11C2211yescharacteristic
33C11×#394C418yescomplemented
34C11×#388—24no—
35C11×#386—24no—
36C11×#386—24no—
37C11×#385—24no—
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
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
56C25×C11C2311yescharacteristic
57C25×C11C2311yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—41no—
63C22×D4×C11—41no—
64C22×D4×C11C2×C414yes—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—41no—
72C23×C4×C11—41no—
73C23×C4×C11—41no—
74C23×C4×C11—41no—
75C23×C4×C11—41no—
76C23×C4×C11—41no—
77C23×C4×C11—41no—
78C23×C4×C11—41no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
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
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4—41no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4C2×C414yescomplemented
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—41no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4—41no—
116C2×C11×C22⋊C4—41no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4—41no—
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×C414yescomplemented
126C2×C11×C22⋊C4C2×C414yescomplemented
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—41no—
133C2×C42×C11—41no—
134C11×#95—22no—
135C11×#95—22no—
136C11×#95—22no—
137C11×#95—22no—
138C11×#95—22no—
139C11×#95—22no—
140C11×#95—22no—
141C11×#95—22no—
142C11×#95—22no—
143C11×#95—41no—
144C11×#95—41no—
145C11×#95—41no—
146C11×#95—41no—
147C11×#95—41no—
148C11×#95—41no—
149C11×#95—41no—
150C11×#95—41no—
151C11×#95C2×C414yescomplemented
152#14517C1111yesmaximal, characteristic, direct product factor, Sylow
153C24×C11—21no—
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×C11C22×C412yes—
178C24×C11C22×C412yes—
179C24×C11C2×D412yes—
180C24×C11C2×D412yes—
181C24×C11#4112yes—
182C24×C11#4112yes—
183C24×C11C2411yescharacteristic
184C2×D4×C11—28no—
185C2×D4×C11—28no—
186C2×D4×C11—44no—
187C2×D4×C11—44no—
188C2×D4×C11—44no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
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—44no—
272C22×C4×C11—44no—
273C22×C4×C11—44no—
274C22×C4×C11—44no—
275C22×C4×C11—44no—
276C22×C4×C11—44no—
277C22×C4×C11—44no—
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×C11—44no—
285C22×C4×C11C22×C412yes—
286C22×C4×C11C22×C412yes—
287C22×C4×C11C22×C412yes—
288C22×C4×C11C22×C412yes—
289C22×C4×C11C22×C412yes—
290C22×C4×C11C2×D412yes—
291C22×C4×C11C2×D412yes—
292C22×C4×C11C2×D412yes—
293C22×C4×C11C2×D412yes—
294C22×C4×C11#4112yes—
295C22×C4×C11#4112yes—
296C11×C4⋊C4—44no—
297C11×C4⋊C4—44no—
298C11×C4⋊C4—44no—
299C11×C22⋊C4—28no—
300C11×C22⋊C4—28no—
301C11×C22⋊C4—44no—
302C11×C22⋊C4—44no—
303C11×C22⋊C4—44no—
304C11×C22⋊C4—44no—
305C11×C22⋊C4—44no—
306C11×C22⋊C4—44no—
307C11×C22⋊C4—44no—
308C11×C22⋊C4—44no—
309C42×C11—44no—
310C2×#394C2×C1111yescharacteristic
311C2×#388C2×C1111yescharacteristic, complemented
312C2×#386C2×C1111yescharacteristic
313C2×#386C2×C1111yescharacteristic
314C2×#385C2×C1111yescharacteristic, complemented
315#1445C2×C1111yescharacteristic, complemented
316#1443C2×C1111yescharacteristic, complemented
317#1441C2×C1111yescharacteristic, complemented
318#1440C2×C1111yescharacteristic, complemented
319#1439C2×C1111yescharacteristic, complemented
320#1437C2×C1111yescharacteristic, complemented
321#1436C2×C1111yescharacteristic, complemented
322C22⋊#95C2×C1111yescharacteristic, complemented
323C22⋊#95C2×C1111yescharacteristic, complemented
324C22⋊#95C2×C1111yescharacteristic, complemented
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—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—22no—
360C23×C11—22no—
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×C11C4×D414yes—
394C23×C11C4×D414yes—
395C23×C11C23×C411yescharacteristic
396C23×C11C22×D411yescharacteristic
397C23×C11C22×D411yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11C2×#4111yescharacteristic
401C23×C11C2×#4111yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C11H(5,𝔽2)11yescharacteristic
405C23×C11H(5,𝔽2)11yescharacteristic
406C23×C11H(5,𝔽2)11yescharacteristic
407C23×C11H(5,𝔽2)11yescharacteristic
408C23×C112−1+411yescharacteristic
409C23×C112−1+411yescharacteristic
410D4×C11—416no—
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—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—416no—
445C2×C4×C11—416no—
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—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C23×D4C22×C1111yescharacteristic
505C24×C4C22×C1111yescharacteristic
506C24×C4C22×C1111yescharacteristic
507C22×C4⋊C4C22×C1111yescharacteristic
508C22×C4⋊C4C22×C1111yescharacteristic
509C22×C4⋊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×C22⋊C4C22×C1111yescharacteristic
519C22×C22⋊C4C22×C1111yescharacteristic
520C22×C42C22×C1111yescharacteristic
521#394C4×C1118yescomplemented
522#388—24no—
523#386—24no—
524#386—24no—
525#385—24no—
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
541C2×#95C22×C1111yescharacteristic
542C2×#95C22×C1111yescharacteristic
543C2×#95C22×C1111yescharacteristic
544C22×C11—24no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—24no—
548C22×C11—24no—
549C22×C11—24no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
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×C11C2×C4×D411yescharacteristic
575C22×C11C2×C4×D411yescharacteristic
576C22×C11C4×#4111yescharacteristic
577C22×C11#51811yescharacteristic
578C22×C11#51811yescharacteristic
579C22×C11#52011yescharacteristic
580C22×C11#52011yescharacteristic
581C22×C11#53411yescharacteristic
582C22×C11#53411yescharacteristic
583C22×C11#53611yescharacteristic
584C22×C11#53711yescharacteristic
585C22×C11#53811yescharacteristic
586C22×C11#53811yescharacteristic
587C22×C11#53811yescharacteristic
588C22×C11#53911yescharacteristic
589C22×C11#53911yescharacteristic
590C22×C11#53911yescharacteristic
591C22×C11#54211yescharacteristic
592C22×C11#54211yescharacteristic
593C22×C11D4211yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54611yescharacteristic
598C22×C11#54611yescharacteristic
599C22×C11#54711yescharacteristic
600C22×C11#55111yescharacteristic
601C22×C11#55111yescharacteristic
602C22×C11#55211yescharacteristic
603C22×C11#55311yescharacteristic
604C22×C11#55311yescharacteristic
605C22×C11#56011yescharacteristic
606C22×C11#56011yescharacteristic
607C22×C11#56211yescharacteristic
608C22×C11#56211yescharacteristic
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—42no—
612C4×C11—42no—
613C4×C11—42no—
614C4×C11—42no—
615C4×C11—42no—
616C4×C11—42no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—42no—
620C4×C11—81no—
621C4×C11—81no—
622C25C23×C1111yescharacteristic
623C25C23×C1111yescharacteristic
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—41no—
629C22×D4—41no—
630C22×D4C2×C4×C1114yes—
631C23×C4—22no—
632C23×C4—22no—
633C23×C4—22no—
634C23×C4—22no—
635C23×C4—22no—
636C23×C4—22no—
637C23×C4—41no—
638C23×C4—41no—
639C23×C4—41no—
640C23×C4—41no—
641C23×C4—41no—
642C23×C4—41no—
643C23×C4—41no—
644C23×C4—41no—
645C23×C4C23×C1111yescharacteristic
646C23×C4C23×C1111yescharacteristic
647C23×C4C23×C1111yescharacteristic
648C23×C4C23×C1111yescharacteristic
649C23×C4C23×C1111yescharacteristic
650C23×C4C23×C1111yescharacteristic
651C23×C4C23×C1111yescharacteristic
652C23×C4C23×C1111yescharacteristic
653C23×C4C23×C1111yescharacteristic
654C23×C4C23×C1111yescharacteristic
655C23×C4C23×C1111yescharacteristic
656C23×C4C23×C1111yescharacteristic
657C23×C4C23×C1111yescharacteristic
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4C2×C4×C1114yescomplemented
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—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
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⋊C4C2×C4×C1114yescomplemented
692C2×C22⋊C4C2×C4×C1114yescomplemented
693C2×C22⋊C4C2×C4×C1114yescomplemented
694C2×C22⋊C4C2×C4×C1114yescomplemented
695C2×C22⋊C4D4×C1114yes—
696C2×C22⋊C4D4×C1114yes—
697C2×C42—22no—
698C2×C42—41no—
699C2×C42—41no—
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#95—41no—
714#95—41no—
715#95—41no—
716#95—41no—
717#95C2×C4×C1114yescomplemented
718C2×C11—44no—
719C2×C11—44no—
720C2×C11#232211yescharacteristic
721C2×C11#232511yescharacteristic
722C2×C11#233711yescharacteristic
723C2×C11#235811yescharacteristic
724C2×C11#235911yescharacteristic
725C2×C11#236411yescharacteristic
726C2×C11#237711yescharacteristic
727C2×C11#266811yescharacteristic
728C2×C11#267211yescharacteristic
729C2×C11#268711yescharacteristic
730C2×C11#269111yescharacteristic
731C2×C11#269711yescharacteristic
732C2×C11#270811yescharacteristic
733C2×C11#274611yescharacteristic
734C2×C11#275011yescharacteristic
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—
759C24C22×C4×C1112yes—
760C24C22×C4×C1112yes—
761C24C2×D4×C1112yes—
762C24C2×D4×C1112yes—
763C24C11×#4112yes—
764C24C11×#4112yes—
765C24C24×C1111yescharacteristic
766C2×D4—28no—
767C2×D4—28no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
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—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4C22×C4×C1112yes—
868C22×C4C22×C4×C1112yes—
869C22×C4C22×C4×C1112yes—
870C22×C4C22×C4×C1112yes—
871C22×C4C22×C4×C1112yes—
872C22×C4C2×D4×C1112yes—
873C22×C4C2×D4×C1112yes—
874C22×C4C2×D4×C1112yes—
875C22×C4C2×D4×C1112yes—
876C22×C4C11×#4112yes—
877C22×C4C11×#4112yes—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C42—44no—
892C11#1451711yescharacteristic, direct product factor, Sylow
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
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—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—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23C4×D4×C1114yes—
962C23C4×D4×C1114yes—
963C23C23×C4×C1111yescharacteristic
964C23C22×D4×C1111yescharacteristic
965C23C22×D4×C1111yescharacteristic
966C23C2×C11×#4111yescharacteristic
967C23C2×C11×#4111yescharacteristic
968C23C2×C11×#4111yescharacteristic
969C23C2×C11×#4111yescharacteristic
970C23C11×H(5,𝔽2)11yescharacteristic
971C23C11×H(5,𝔽2)11yescharacteristic
972C23C11×H(5,𝔽2)11yescharacteristic
973C23C11×H(5,𝔽2)11yescharacteristic
974C23C11×H(5,𝔽2)11yescharacteristic
975C23C11×H(5,𝔽2)11yescharacteristic
976C23C11×2−1+411yescharacteristic
977C23C11×2−1+411yescharacteristic
978D4—416no—
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—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—416no—
1013C2×C4—416no—
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×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—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22C2×C4×D4×C1111yescharacteristic
1103C22C2×C4×D4×C1111yescharacteristic
1104C22C4×C11×#4111yescharacteristic
1105C22C11×#51811yescharacteristic
1106C22C11×#51811yescharacteristic
1107C22C11×#52011yescharacteristic
1108C22C11×#52011yescharacteristic
1109C22C11×#53411yescharacteristic
1110C22C11×#53411yescharacteristic
1111C22C11×#53611yescharacteristic
1112C22C11×#53711yescharacteristic
1113C22C11×#53811yescharacteristic
1114C22C11×#53811yescharacteristic
1115C22C11×#53811yescharacteristic
1116C22C11×#53911yescharacteristic
1117C22C11×#53911yescharacteristic
1118C22C11×#53911yescharacteristic
1119C22C11×#54211yescharacteristic
1120C22C11×#54211yescharacteristic
1121C22D42×C1111yescharacteristic
1122C22C11×#54611yescharacteristic
1123C22C11×#54611yescharacteristic
1124C22C11×#54611yescharacteristic
1125C22C11×#54611yescharacteristic
1126C22C11×#54611yescharacteristic
1127C22C11×#54711yescharacteristic
1128C22C11×#55111yescharacteristic
1129C22C11×#55111yescharacteristic
1130C22C11×#55211yescharacteristic
1131C22C11×#55311yescharacteristic
1132C22C11×#55311yescharacteristic
1133C22C11×#56011yescharacteristic
1134C22C11×#56011yescharacteristic
1135C22C11×#56211yescharacteristic
1136C22C11×#56211yescharacteristic
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C2—44no—
1151C2—44no—
1152C2C11×#232211yescharacteristic
1153C2C11×#232511yescharacteristic
1154C2C11×#233711yescharacteristic
1155C2C11×#235811yescharacteristic
1156C2C11×#235911yescharacteristic
1157C2C11×#236411yescharacteristic
1158C2C11×#237711yescharacteristic
1159C2C11×#266811yescharacteristic
1160C2C11×#267211yescharacteristic
1161C2C11×#268711yescharacteristic
1162C2C11×#269111yescharacteristic
1163C2C11×#269711yescharacteristic
1164C2C11×#270811yescharacteristic
1165C2C11×#274611yescharacteristic
1166C2C11×#275011yescharacteristic
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×#388C2semidirect
5. C2×C11×#385C2semidirect
6. C11×#1445C2semidirect
7. C11×#1443C2semidirect
8. C11×#1441C2semidirect
9. C11×#1440C2semidirect
10. C11×#1439C2semidirect
11. C11×#1437C2semidirect
12. C11×#1436C2semidirect
13. C11×C22⋊#95C2semidirect
14. C11×C22⋊#95C2semidirect
15. C11×C22⋊#95C2semidirect
33. C11×#394C4semidirect
100. C2×C11×C4⋊C4C2×C4semidirect
125. C2×C11×C22⋊C4C2×C4semidirect
126. C2×C11×C22⋊C4C2×C4semidirect
127. C2×C11×C22⋊C4C2×C4semidirect
128. C2×C11×C22⋊C4C2×C4semidirect
151. C11×#95C2×C4semidirect
152. #14517C11direct (N × H)
311. C2×#388C2×C11semidirect
314. C2×#385C2×C11semidirect
315. #1445C2×C11semidirect
316. #1443C2×C11semidirect
317. #1441C2×C11semidirect
318. #1440C2×C11semidirect
319. #1439C2×C11semidirect
320. #1437C2×C11semidirect
321. #1436C2×C11semidirect
322. C22⋊#95C2×C11semidirect
323. C22⋊#95C2×C11semidirect
324. C22⋊#95C2×C11semidirect
521. #394C4×C11semidirect
666. C2×C4⋊C4C2×C4×C11semidirect
691. C2×C22⋊C4C2×C4×C11semidirect
692. C2×C22⋊C4C2×C4×C11semidirect
693. C2×C22⋊C4C2×C4×C11semidirect
694. C2×C22⋊C4C2×C4×C11semidirect
717. #95C2×C4×C11semidirect
892. C11#14517direct (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×#3882
C2×C11×#3862
C2×C11×#3852
C11×#14452
C11×#14432
C11×#14412
C11×#14402
C11×#14392
C11×#14372
C11×#14362
C11×C22⋊#952
#1451711