Finite Group Databasebeta

← C11×#16292 #14593485

Subgroups — C11×#16292 #14593485

Order 2816.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#398C211yesmaximal, characteristic, complemented
2C2×C11×#396C211yesmaximal, characteristic, complemented
3C2×C11×#394C211yesmaximal, characteristic
4C2×C11×#394C211yesmaximal, characteristic
5C2×C11×#390C211yesmaximal, characteristic
6C2×C11×#387C211yesmaximal, characteristic, complemented
7C11×#1444C211yesmaximal, characteristic, complemented
8C11×#1440C211yesmaximal, characteristic, complemented
9C11×#1440C211yesmaximal, characteristic, complemented
10C11×#1439C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C11×#1439C211yesmaximal, characteristic, complemented
13C11×#1439C211yesmaximal, characteristic, complemented
14C11×#1439C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
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×C11×C22⋊C4C2211yescharacteristic
36C22×C42×C11C2211yescharacteristic
37C11×#398—24no—
38C11×#396—24no—
39C11×#394—24no—
40C11×#394—24no—
41C11×#390—24no—
42C11×#387—24no—
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×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—41no—
65C22×D4×C11—41no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
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×C4⋊C4—41no—
99C2×C11×C4⋊C4D414yes—
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⋊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⋊C4—41no—
134C2×C11×C22⋊C4—41no—
135C2×C11×C22⋊C4D414yes—
136C2×C42×C11—22no—
137C2×C42×C11—22no—
138C2×C42×C11—41no—
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—22no—
148C11×#95—22no—
149C11×#95—41no—
150C11×#95—41no—
151C11×#95—41no—
152C11×#95D414yes—
153#16292C1111yesmaximal, 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×D4×C11—28no—
186C2×D4×C11—44no—
187C2×D4×C11—44no—
188C2×D4×C11—44no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
191C2×D4×C11—44no—
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—21no—
272C22×C4×C11C2×D412yes—
273C22×C4×C11C2×D412yes—
274C22×C4×C11C2×D412yes—
275C22×C4×C11C2×D412yes—
276C22×C4×C11C2×D412yes—
277C22×C4×C11C2×D412yes—
278C22×C4×C11C2×D412yes—
279C22×C4×C11C2×D412yes—
280C22×C4×C11#4112yes—
281C22×C4×C11#4112yes—
282C22×C4×C11#4112yes—
283C11×C4⋊C4—28no—
284C11×C4⋊C4—44no—
285C11×C4⋊C4—44no—
286C11×C4⋊C4—44no—
287C11×C4⋊C4—44no—
288C11×C4⋊C4—44no—
289C11×C4⋊C4—44no—
290C11×C22⋊C4—44no—
291C11×C22⋊C4—44no—
292C11×C22⋊C4—44no—
293C11×C22⋊C4—44no—
294C11×C22⋊C4—44no—
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—
302C42×C11—44no—
303C2×#398C2×C1111yescharacteristic, complemented
304C2×#396C2×C1111yescharacteristic, complemented
305C2×#394C2×C1111yescharacteristic
306C2×#394C2×C1111yescharacteristic
307C2×#390C2×C1111yescharacteristic
308C2×#387C2×C1111yescharacteristic, complemented
309#1444C2×C1111yescharacteristic, complemented
310#1440C2×C1111yescharacteristic, complemented
311#1440C2×C1111yescharacteristic, complemented
312#1439C2×C1111yescharacteristic, complemented
313#1439C2×C1111yescharacteristic, complemented
314#1439C2×C1111yescharacteristic, complemented
315#1439C2×C1111yescharacteristic, complemented
316#1439C2×C1111yescharacteristic, complemented
317#1436C2×C1111yescharacteristic, complemented
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
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—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
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×C11C22×D411yescharacteristic
389C23×C11C22×D411yescharacteristic
390C23×C11C22×D411yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C23×C11C2×#4111yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11C2×#4111yescharacteristic
395C23×C11H(5,𝔽2)11yescharacteristic
396C23×C11H(5,𝔽2)11yescharacteristic
397C23×C11H(5,𝔽2)11yescharacteristic
398C23×C11H(5,𝔽2)11yescharacteristic
399C23×C11H(5,𝔽2)11yescharacteristic
400C23×C112−1+411yescharacteristic
401C23×C112−1+411yescharacteristic
402C23×C112−1+411yescharacteristic
403D4×C11—416no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
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—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
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#12114yes—
495C23×D4C22×C1111yescharacteristic
496C22×C4⋊C4C22×C1111yescharacteristic
497C22×C4⋊C4C22×C1111yescharacteristic
498C22×C4⋊C4C22×C1111yescharacteristic
499C22×C4⋊C4C22×C1111yescharacteristic
500C22×C4⋊C4C22×C1111yescharacteristic
501C22×C4⋊C4C22×C1111yescharacteristic
502C22×C4⋊C4C22×C1111yescharacteristic
503C22×C22⋊C4C22×C1111yescharacteristic
504C22×C22⋊C4C22×C1111yescharacteristic
505C22×C22⋊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×C42C22×C1111yescharacteristic
516#398—24no—
517#396—24no—
518#394—24no—
519#394—24no—
520#390—24no—
521#387—24no—
522C2×#95C22×C1111yescharacteristic
523C2×#95C22×C1111yescharacteristic
524C2×#95C22×C1111yescharacteristic
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
536C22×C11—42no—
537C22×C11—42no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
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—81no—
551C22×C11—81no—
552C22×C11—81no—
553C22×C11—81no—
554C22×C11—81no—
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×C11C2×#12111yescharacteristic
567C22×C11#52511yescharacteristic
568C22×C11#52911yescharacteristic
569C22×C11#53411yescharacteristic
570C22×C11#53511yescharacteristic
571C22×C11#53611yescharacteristic
572C22×C11#53611yescharacteristic
573C22×C11#53711yescharacteristic
574C22×C11#53711yescharacteristic
575C22×C11#53811yescharacteristic
576C22×C11#53911yescharacteristic
577C22×C11#53911yescharacteristic
578C22×C11#53911yescharacteristic
579C22×C11#54011yescharacteristic
580C22×C11#54011yescharacteristic
581C22×C11#54211yescharacteristic
582C22×C11#54211yescharacteristic
583C22×C11#54211yescharacteristic
584C22×C11#54211yescharacteristic
585C22×C11D4211yescharacteristic
586C22×C11D4211yescharacteristic
587C22×C11#54611yescharacteristic
588C22×C11#54611yescharacteristic
589C22×C11#54611yescharacteristic
590C22×C11#54611yescharacteristic
591C22×C11#54711yescharacteristic
592C22×C11#54811yescharacteristic
593C22×C11#54811yescharacteristic
594C22×C11#55011yescharacteristic
595C22×C11#55211yescharacteristic
596C22×C11#55311yescharacteristic
597C22×C11#56011yescharacteristic
598C22×C11#56211yescharacteristic
599C22×C11#56211yescharacteristic
600C22×C11#56311yescharacteristic
601C4×C11—24no—
602C4×C11—42no—
603C4×C11—42no—
604C4×C11—42no—
605C4×C11—42no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—81no—
611C4×C11—81no—
612C4×C11—81no—
613C4×C11—81no—
614C25C23×C1111yescharacteristic
615C25C23×C1111yescharacteristic
616C22×D4—22no—
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—41no—
622C22×D4—41no—
623C23×C4C23×C1111yescharacteristic
624C23×C4C23×C1111yescharacteristic
625C23×C4C23×C1111yescharacteristic
626C23×C4C23×C1111yescharacteristic
627C23×C4C23×C1111yescharacteristic
628C23×C4C23×C1111yescharacteristic
629C23×C4C23×C1111yescharacteristic
630C23×C4C23×C1111yescharacteristic
631C23×C4C23×C1111yescharacteristic
632C23×C4C23×C1111yescharacteristic
633C23×C4C23×C1111yescharacteristic
634C23×C4C23×C1111yescharacteristic
635C23×C4C23×C1111yescharacteristic
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4D4×C1114yes—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
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—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
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⋊C4—41no—
692C2×C22⋊C4D4×C1114yes—
693C2×C42—22no—
694C2×C42—22no—
695C2×C42—41no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95D4×C1114yes—
710C2×C11—82no—
711C2×C11—82no—
712C2×C11#242411yescharacteristic
713C2×C11#242611yescharacteristic
714C2×C11#246811yescharacteristic
715C2×C11#262011yescharacteristic
716C2×C11#263811yescharacteristic
717C2×C11#265111yescharacteristic
718C2×C11#267111yescharacteristic
719C2×C11#267311yescharacteristic
720C2×C11#267411yescharacteristic
721C2×C11#268111yescharacteristic
722C2×C11#269111yescharacteristic
723C2×C11#269411yescharacteristic
724C2×C11#270711yescharacteristic
725C2×C11#271111yescharacteristic
726C2×C11#283011yescharacteristic
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
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—
755C24C2×D4×C1112yes—
756C24C11×#4112yes—
757C24C24×C1111yescharacteristic
758C2×D4—28no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
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×C4C2×D4×C1112yes—
846C22×C4C2×D4×C1112yes—
847C22×C4C2×D4×C1112yes—
848C22×C4C2×D4×C1112yes—
849C22×C4C2×D4×C1112yes—
850C22×C4C2×D4×C1112yes—
851C22×C4C2×D4×C1112yes—
852C22×C4C2×D4×C1112yes—
853C22×C4C11×#4112yes—
854C22×C4C11×#4112yes—
855C22×C4C11×#4112yes—
856C4⋊C4—28no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C42—44no—
876C11#1629211yescharacteristic, direct product factor, Sylow
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
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—
947C23C22×D4×C1111yescharacteristic
948C23C22×D4×C1111yescharacteristic
949C23C22×D4×C1111yescharacteristic
950C23C2×C11×#4111yescharacteristic
951C23C2×C11×#4111yescharacteristic
952C23C2×C11×#4111yescharacteristic
953C23C2×C11×#4111yescharacteristic
954C23C11×H(5,𝔽2)11yescharacteristic
955C23C11×H(5,𝔽2)11yescharacteristic
956C23C11×H(5,𝔽2)11yescharacteristic
957C23C11×H(5,𝔽2)11yescharacteristic
958C23C11×H(5,𝔽2)11yescharacteristic
959C23C11×2−1+411yescharacteristic
960C23C11×2−1+411yescharacteristic
961C23C11×2−1+411yescharacteristic
962D4—416no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
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—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
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×C4C11×#12114yes—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22C2×C11×#12111yescharacteristic
1085C22C11×#52511yescharacteristic
1086C22C11×#52911yescharacteristic
1087C22C11×#53411yescharacteristic
1088C22C11×#53511yescharacteristic
1089C22C11×#53611yescharacteristic
1090C22C11×#53611yescharacteristic
1091C22C11×#53711yescharacteristic
1092C22C11×#53711yescharacteristic
1093C22C11×#53811yescharacteristic
1094C22C11×#53911yescharacteristic
1095C22C11×#53911yescharacteristic
1096C22C11×#53911yescharacteristic
1097C22C11×#54011yescharacteristic
1098C22C11×#54011yescharacteristic
1099C22C11×#54211yescharacteristic
1100C22C11×#54211yescharacteristic
1101C22C11×#54211yescharacteristic
1102C22C11×#54211yescharacteristic
1103C22D42×C1111yescharacteristic
1104C22D42×C1111yescharacteristic
1105C22C11×#54611yescharacteristic
1106C22C11×#54611yescharacteristic
1107C22C11×#54611yescharacteristic
1108C22C11×#54611yescharacteristic
1109C22C11×#54711yescharacteristic
1110C22C11×#54811yescharacteristic
1111C22C11×#54811yescharacteristic
1112C22C11×#55011yescharacteristic
1113C22C11×#55211yescharacteristic
1114C22C11×#55311yescharacteristic
1115C22C11×#56011yescharacteristic
1116C22C11×#56211yescharacteristic
1117C22C11×#56211yescharacteristic
1118C22C11×#56311yescharacteristic
1119C4—24no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C2—82no—
1133C2—82no—
1134C2C11×#242411yescharacteristic
1135C2C11×#242611yescharacteristic
1136C2C11×#246811yescharacteristic
1137C2C11×#262011yescharacteristic
1138C2C11×#263811yescharacteristic
1139C2C11×#265111yescharacteristic
1140C2C11×#267111yescharacteristic
1141C2C11×#267311yescharacteristic
1142C2C11×#267411yescharacteristic
1143C2C11×#268111yescharacteristic
1144C2C11×#269111yescharacteristic
1145C2C11×#269411yescharacteristic
1146C2C11×#270711yescharacteristic
1147C2C11×#271111yescharacteristic
1148C2C11×#283011yescharacteristic
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
1. C2×C11×#398C2semidirect
2. C2×C11×#396C2semidirect
6. C2×C11×#387C2semidirect
7. C11×#1444C2semidirect
8. C11×#1440C2semidirect
9. C11×#1440C2semidirect
10. C11×#1439C2semidirect
11. C11×#1439C2semidirect
12. C11×#1439C2semidirect
13. C11×#1439C2semidirect
14. C11×#1439C2semidirect
15. C11×#1436C2semidirect
153. #16292C11direct (N × H)
303. C2×#398C2×C11semidirect
304. C2×#396C2×C11semidirect
308. C2×#387C2×C11semidirect
309. #1444C2×C11semidirect
310. #1440C2×C11semidirect
311. #1440C2×C11semidirect
312. #1439C2×C11semidirect
313. #1439C2×C11semidirect
314. #1439C2×C11semidirect
315. #1439C2×C11semidirect
316. #1439C2×C11semidirect
317. #1436C2×C11semidirect
876. C11#16292direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3982
C2×C11×#3962
C2×C11×#3942
C2×C11×#3902
C2×C11×#3872
C11×#14442
C11×#14402
C11×#14392
C11×#14362
#1629211