Finite Group Databasebeta

← C11×#14518 #14591711

Subgroups — C11×#14518 #14591711

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#394C211yesmaximal, characteristic
2C2×C11×#390C211yesmaximal, characteristic
3C2×C11×#389C211yesmaximal, characteristic, complemented
4C2×C11×#388C211yesmaximal, characteristic, complemented
5C2×C11×#386C211yesmaximal, characteristic
6C2×C11×#385C211yesmaximal, characteristic, complemented
7C2×C11×#385C211yesmaximal, characteristic, complemented
8C11×#1444C211yesmaximal, characteristic, complemented
9C11×#1440C211yesmaximal, characteristic, complemented
10C11×#1439C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C11×#1439C211yesmaximal, characteristic, complemented
13C11×#1437C211yesmaximal, characteristic, complemented
14C11×#1436C211yesmaximal, characteristic, complemented
15C11×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊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×C11×C22⋊C4C2211yescharacteristic
35C22×C42×C11C2211yescharacteristic
36C22×C42×C11C2211yescharacteristic
37C11×#394C418yescomplemented
38C11×#390—24no—
39C11×#389—24no—
40C11×#388—24no—
41C11×#386—24no—
42C11×#385—24no—
43C11×#385—24no—
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×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—41no—
65C22×D4×C11—41no—
66C22×D4×C11C2×C414yes—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—41no—
71C23×C4×C11—41no—
72C23×C4×C11—41no—
73C23×C4×C11—41no—
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
86C23×C4×C11C2311yescharacteristic
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4—41no—
101C2×C11×C4⋊C4—41no—
102C2×C11×C4⋊C4—41no—
103C2×C11×C4⋊C4—41no—
104C2×C11×C4⋊C4C2×C414yescomplemented
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⋊C4C2×C414yes—
134C2×C11×C22⋊C4C2×C414yes—
135C2×C11×C22⋊C4C2×C414yescomplemented
136C2×C11×C22⋊C4C2×C414yescomplemented
137C2×C11×C22⋊C4D414yes—
138C2×C42×C11—22no—
139C2×C42×C11—22no—
140C2×C42×C11—22no—
141C2×C42×C11—22no—
142C2×C42×C11—41no—
143C2×C42×C11—41no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95—22no—
148C11×#95—22no—
149C11×#95—22no—
150C11×#95—22no—
151C11×#95—41no—
152C11×#95—41no—
153C11×#95—41no—
154C11×#95—41no—
155C11×#95C2×C414yescomplemented
156C11×#95D414yes—
157C11×#95D414yescomplemented
158#14518C1111yesmaximal, characteristic, direct product factor, Sylow
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×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11C22×C412yes—
186C24×C11C22×C412yes—
187C24×C11C2×D412yes—
188C24×C11#4112yes—
189C24×C11C2411yescharacteristic
190C2×D4×C11—28no—
191C2×D4×C11—28no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
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—21no—
272C22×C4×C11—21no—
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×C11C22×C412yes—
281C22×C4×C11C22×C412yes—
282C22×C4×C11C22×C412yes—
283C22×C4×C11C22×C412yes—
284C22×C4×C11C22×C412yes—
285C22×C4×C11C2×D412yes—
286C22×C4×C11C2×D412yes—
287C22×C4×C11C2×D412yes—
288C22×C4×C11C2×D412yes—
289C22×C4×C11C2×D412yes—
290C22×C4×C11C2×D412yes—
291C22×C4×C11C2×D412yes—
292C22×C4×C11C2×D412yes—
293C22×C4×C11#4112yes—
294C22×C4×C11#4112yes—
295C11×C4⋊C4—28no—
296C11×C4⋊C4—44no—
297C11×C4⋊C4—44no—
298C11×C4⋊C4—44no—
299C11×C4⋊C4—44no—
300C11×C4⋊C4—44no—
301C11×C22⋊C4—28no—
302C11×C22⋊C4—28no—
303C11×C22⋊C4—28no—
304C11×C22⋊C4—44no—
305C11×C22⋊C4—44no—
306C11×C22⋊C4—44no—
307C11×C22⋊C4—44no—
308C11×C22⋊C4—44no—
309C11×C22⋊C4—44no—
310C11×C22⋊C4—44no—
311C11×C22⋊C4—44no—
312C42×C11—44no—
313C42×C11—44no—
314C2×#394C2×C1111yescharacteristic
315C2×#390C2×C1111yescharacteristic
316C2×#389C2×C1111yescharacteristic, complemented
317C2×#388C2×C1111yescharacteristic, complemented
318C2×#386C2×C1111yescharacteristic
319C2×#385C2×C1111yescharacteristic, complemented
320C2×#385C2×C1111yescharacteristic, complemented
321#1444C2×C1111yescharacteristic, complemented
322#1440C2×C1111yescharacteristic, complemented
323#1439C2×C1111yescharacteristic, complemented
324#1439C2×C1111yescharacteristic, complemented
325#1439C2×C1111yescharacteristic, complemented
326#1437C2×C1111yescharacteristic, complemented
327#1436C2×C1111yescharacteristic, complemented
328#1434C2×C1111yescharacteristic, complemented
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—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×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11C4×D414yes—
399C23×C11C23×C411yescharacteristic
400C23×C11C22×D411yescharacteristic
401C23×C11C22×D411yescharacteristic
402C23×C11C22×D411yescharacteristic
403C23×C11C2×#4111yescharacteristic
404C23×C11C2×#4111yescharacteristic
405C23×C11C2×#4111yescharacteristic
406C23×C11H(5,𝔽2)11yescharacteristic
407C23×C11H(5,𝔽2)11yescharacteristic
408C23×C11H(5,𝔽2)11yescharacteristic
409C23×C11H(5,𝔽2)11yescharacteristic
410C23×C11H(5,𝔽2)11yescharacteristic
411C23×C112−1+411yescharacteristic
412C23×C112−1+411yescharacteristic
413C23×C112−1+411yescharacteristic
414D4×C11—416no—
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—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—416no—
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—
504C2×C4×C11—41no—
505C2×C4×C11C4×D414yes—
506C2×C4×C11C4×D414yes—
507C23×D4C22×C1111yescharacteristic
508C24×C4C22×C1111yescharacteristic
509C22×C4⋊C4C22×C1111yescharacteristic
510C22×C4⋊C4C22×C1111yescharacteristic
511C22×C4⋊C4C22×C1111yescharacteristic
512C22×C4⋊C4C22×C1111yescharacteristic
513C22×C4⋊C4C22×C1111yescharacteristic
514C22×C4⋊C4C22×C1111yescharacteristic
515C22×C22⋊C4C22×C1111yescharacteristic
516C22×C22⋊C4C22×C1111yescharacteristic
517C22×C22⋊C4C22×C1111yescharacteristic
518C22×C22⋊C4C22×C1111yescharacteristic
519C22×C22⋊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×C42C22×C1111yescharacteristic
527C22×C42C22×C1111yescharacteristic
528#394C4×C1118yescomplemented
529#390—24no—
530#389—24no—
531#388—24no—
532#386—24no—
533#385—24no—
534#385—24no—
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
544C2×#95C22×C1111yescharacteristic
545C2×#95C22×C1111yescharacteristic
546C2×#95C22×C1111yescharacteristic
547C2×#95C22×C1111yescharacteristic
548C2×#95C22×C1111yescharacteristic
549C22×C11—24no—
550C22×C11—24no—
551C22×C11—24no—
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—81no—
572C22×C11—81no—
573C22×C11—81no—
574C22×C11—81no—
575C22×C11—81no—
576C22×C11—81no—
577C22×C11—81no—
578C22×C11—81no—
579C22×C11C2×C4×D411yescharacteristic
580C22×C11C2×C4×D411yescharacteristic
581C22×C11C2×C4×D411yescharacteristic
582C22×C11#51811yescharacteristic
583C22×C11#52011yescharacteristic
584C22×C11#52011yescharacteristic
585C22×C11#52011yescharacteristic
586C22×C11#53411yescharacteristic
587C22×C11#53511yescharacteristic
588C22×C11#53511yescharacteristic
589C22×C11#53611yescharacteristic
590C22×C11#53611yescharacteristic
591C22×C11#53711yescharacteristic
592C22×C11#53911yescharacteristic
593C22×C11#53911yescharacteristic
594C22×C11#54011yescharacteristic
595C22×C11#54211yescharacteristic
596C22×C11#54211yescharacteristic
597C22×C11#54211yescharacteristic
598C22×C11D4211yescharacteristic
599C22×C11D4211yescharacteristic
600C22×C11D4211yescharacteristic
601C22×C11#54611yescharacteristic
602C22×C11#54611yescharacteristic
603C22×C11#54711yescharacteristic
604C22×C11#54711yescharacteristic
605C22×C11#54811yescharacteristic
606C22×C11#54811yescharacteristic
607C22×C11#55111yescharacteristic
608C22×C11#55311yescharacteristic
609C22×C11#55311yescharacteristic
610C22×C11#56011yescharacteristic
611C22×C11#56211yescharacteristic
612C22×C11#56211yescharacteristic
613C22×C11#56311yescharacteristic
614C4×C11—24no—
615C4×C11—24no—
616C4×C11—42no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—42no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—42no—
623C4×C11—42no—
624C4×C11—42no—
625C4×C11—81no—
626C4×C11—81no—
627C25C23×C1111yescharacteristic
628C25C23×C1111yescharacteristic
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—41no—
634C22×D4—41no—
635C22×D4C2×C4×C1114yes—
636C23×C4—22no—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—41no—
640C23×C4—41no—
641C23×C4—41no—
642C23×C4—41no—
643C23×C4C23×C1111yescharacteristic
644C23×C4C23×C1111yescharacteristic
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
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4C2×C4×C1114yescomplemented
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—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
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⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4C2×C4×C1114yes—
703C2×C22⋊C4C2×C4×C1114yes—
704C2×C22⋊C4C2×C4×C1114yescomplemented
705C2×C22⋊C4C2×C4×C1114yescomplemented
706C2×C22⋊C4D4×C1114yes—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712C2×C42—41no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95—41no—
724#95C2×C4×C1114yescomplemented
725#95D4×C1114yes—
726#95D4×C1114yescomplemented
727C2×C11—44no—
728C2×C11—82no—
729C2×C11#232211yescharacteristic
730C2×C11#232411yescharacteristic
731C2×C11#232611yescharacteristic
732C2×C11#235811yescharacteristic
733C2×C11#236111yescharacteristic
734C2×C11#236111yescharacteristic
735C2×C11#237611yescharacteristic
736C2×C11#266911yescharacteristic
737C2×C11#267211yescharacteristic
738C2×C11#267411yescharacteristic
739C2×C11#268111yescharacteristic
740C2×C11#270111yescharacteristic
741C2×C11#271111yescharacteristic
742C2×C11#272311yescharacteristic
743C2×C11#275711yescharacteristic
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—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24C22×C4×C1112yes—
771C24C22×C4×C1112yes—
772C24C2×D4×C1112yes—
773C24C11×#4112yes—
774C24C24×C1111yescharacteristic
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
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×C4—21no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4C22×C4×C1112yes—
866C22×C4C22×C4×C1112yes—
867C22×C4C22×C4×C1112yes—
868C22×C4C22×C4×C1112yes—
869C22×C4C22×C4×C1112yes—
870C22×C4C2×D4×C1112yes—
871C22×C4C2×D4×C1112yes—
872C22×C4C2×D4×C1112yes—
873C22×C4C2×D4×C1112yes—
874C22×C4C2×D4×C1112yes—
875C22×C4C2×D4×C1112yes—
876C22×C4C2×D4×C1112yes—
877C22×C4C2×D4×C1112yes—
878C22×C4C11×#4112yes—
879C22×C4C11×#4112yes—
880C4⋊C4—28no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C42—44no—
898C42—44no—
899C11#1451811yescharacteristic, direct product factor, Sylow
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—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—
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—
969C23C4×D4×C1114yes—
970C23C23×C4×C1111yescharacteristic
971C23C22×D4×C1111yescharacteristic
972C23C22×D4×C1111yescharacteristic
973C23C22×D4×C1111yescharacteristic
974C23C2×C11×#4111yescharacteristic
975C23C2×C11×#4111yescharacteristic
976C23C2×C11×#4111yescharacteristic
977C23C11×H(5,𝔽2)11yescharacteristic
978C23C11×H(5,𝔽2)11yescharacteristic
979C23C11×H(5,𝔽2)11yescharacteristic
980C23C11×H(5,𝔽2)11yescharacteristic
981C23C11×H(5,𝔽2)11yescharacteristic
982C23C11×2−1+411yescharacteristic
983C23C11×2−1+411yescharacteristic
984C23C11×2−1+411yescharacteristic
985D4—416no—
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—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—416no—
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—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4C4×D4×C1114yes—
1077C2×C4C4×D4×C1114yes—
1078C22—24no—
1079C22—24no—
1080C22—24no—
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—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22C2×C4×D4×C1111yescharacteristic
1109C22C2×C4×D4×C1111yescharacteristic
1110C22C2×C4×D4×C1111yescharacteristic
1111C22C11×#51811yescharacteristic
1112C22C11×#52011yescharacteristic
1113C22C11×#52011yescharacteristic
1114C22C11×#52011yescharacteristic
1115C22C11×#53411yescharacteristic
1116C22C11×#53511yescharacteristic
1117C22C11×#53511yescharacteristic
1118C22C11×#53611yescharacteristic
1119C22C11×#53611yescharacteristic
1120C22C11×#53711yescharacteristic
1121C22C11×#53911yescharacteristic
1122C22C11×#53911yescharacteristic
1123C22C11×#54011yescharacteristic
1124C22C11×#54211yescharacteristic
1125C22C11×#54211yescharacteristic
1126C22C11×#54211yescharacteristic
1127C22D42×C1111yescharacteristic
1128C22D42×C1111yescharacteristic
1129C22D42×C1111yescharacteristic
1130C22C11×#54611yescharacteristic
1131C22C11×#54611yescharacteristic
1132C22C11×#54711yescharacteristic
1133C22C11×#54711yescharacteristic
1134C22C11×#54811yescharacteristic
1135C22C11×#54811yescharacteristic
1136C22C11×#55111yescharacteristic
1137C22C11×#55311yescharacteristic
1138C22C11×#55311yescharacteristic
1139C22C11×#56011yescharacteristic
1140C22C11×#56211yescharacteristic
1141C22C11×#56211yescharacteristic
1142C22C11×#56311yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—81no—
1156C2—44no—
1157C2—82no—
1158C2C11×#232211yescharacteristic
1159C2C11×#232411yescharacteristic
1160C2C11×#232611yescharacteristic
1161C2C11×#235811yescharacteristic
1162C2C11×#236111yescharacteristic
1163C2C11×#236111yescharacteristic
1164C2C11×#237611yescharacteristic
1165C2C11×#266911yescharacteristic
1166C2C11×#267211yescharacteristic
1167C2C11×#267411yescharacteristic
1168C2C11×#268111yescharacteristic
1169C2C11×#270111yescharacteristic
1170C2C11×#271111yescharacteristic
1171C2C11×#272311yescharacteristic
1172C2C11×#275711yescharacteristic
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
3. C2×C11×#389C2semidirect
4. C2×C11×#388C2semidirect
6. C2×C11×#385C2semidirect
7. C2×C11×#385C2semidirect
8. C11×#1444C2semidirect
9. C11×#1440C2semidirect
10. C11×#1439C2semidirect
11. C11×#1439C2semidirect
12. C11×#1439C2semidirect
13. C11×#1437C2semidirect
14. C11×#1436C2semidirect
15. C11×#1434C2semidirect
37. C11×#394C4semidirect
104. C2×C11×C4⋊C4C2×C4semidirect
135. C2×C11×C22⋊C4C2×C4semidirect
136. C2×C11×C22⋊C4C2×C4semidirect
155. C11×#95C2×C4semidirect
157. C11×#95D4semidirect
158. #14518C11direct (N × H)
316. C2×#389C2×C11semidirect
317. C2×#388C2×C11semidirect
319. C2×#385C2×C11semidirect
320. C2×#385C2×C11semidirect
321. #1444C2×C11semidirect
322. #1440C2×C11semidirect
323. #1439C2×C11semidirect
324. #1439C2×C11semidirect
325. #1439C2×C11semidirect
326. #1437C2×C11semidirect
327. #1436C2×C11semidirect
328. #1434C2×C11semidirect
528. #394C4×C11semidirect
673. C2×C4⋊C4C2×C4×C11semidirect
704. C2×C22⋊C4C2×C4×C11semidirect
705. C2×C22⋊C4C2×C4×C11semidirect
724. #95C2×C4×C11semidirect
726. #95D4×C11semidirect
899. C11#14518direct (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×#3902
C2×C11×#3892
C2×C11×#3882
C2×C11×#3862
C2×C11×#3852
C11×#14442
C11×#14402
C11×#14392
C11×#14372
C11×#14362
C11×#14342
#1451811